UNIVERSITY of CALIFORNIA Santa Barbara Noise of AlGaN/GaN HEMTs and Oscillators A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Electrical and Computer Engineering by Christopher Sanabria Committee in charge: Professor Robert A. York, Chair Professor Umesh K. Mishra Professor Mark J. Rodwell Dr. Yifeng Wu June 2006
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UNIVERSITY of CALIFORNIASanta Barbara
Noise of AlGaN/GaN HEMTs and Oscillators
A dissertation submitted in partial satisfaction of the
requirements for the degree of
Doctor of Philosophy
in
Electrical and Computer Engineering
by
Christopher Sanabria
Committee in charge:
Professor Robert A. York, ChairProfessor Umesh K. MishraProfessor Mark J. RodwellDr. Yifeng Wu
June 2006
The dissertation of Christopher Sanabria is approved:
Bachelor of Science in Electrical Engineering, Magna Cum Laude, University ofNotre Dame, May 2001.
Master of Science in Electrical and Computer Engineering, University of California,Santa Barbara, December 2002.
Doctor of Philosophy in Electrical Engineering, University of California, Santa Bar-bara, June 2006.
PROFESSIONAL EMPLOYMENT
May 1998 - August 1998, Intern, Delphi-Delco Electronics, Kokomo, IN.
May 1999 - August 1999, Intern, Delphi-Delco Electronics, Kokomo, IN.
May 2000 - August 2000, Intern, Texas Instruments, Houston, TX.
September 2001 - March 2002, Teaching Assistant, Department of Electrical andComputer Engineering, University of California, Santa Barbara.
June 2003 - September 2003, Intern, Agilent Labs, Agilent Technologies, Palo Alto,CA.
March 2002 - May 2006, Research assistant, Department of Electrical and ComputerEngineering, University of California, Santa Barbara.
iv
PUBLICATIONS
S. Gao,C. Sanabria, H. Xu, S. Heikman, U. K. Mishra and R. A. York,MMIC Class-F Power Amplifiers using Field-Plated GaN HEMTs, accepted IEEE Proceedings onMicrowave, Antennas and Propagation, 2006.
C. Sanabria, A. Chakraborty, H. Xu, M. J. Rodwell, U. K. Mishra, and R. A. York,The Effect of Gate Leakage on the Noise Figure of AlGaN/GaN HEMTs, IEEE Elec-tron Device Letters, January 2006, pp. 19-21.
C. Sanabria, H. Xu, A. Chakraborty, M. J. Rodwell, U. K. Mishra, and R. A. York,Noise Figure Measurements and Modeling of Field-Plated AlGaN/GaN HEMTs, In-ternational Conference on Nitride Semiconductors, Bremen, Germany, August 2005.
C. Sanabria, H. Xu, S. Heikman, U. K. Mishra, R. A. York,A GaN Differential Os-cillator with Improved Harmonic Performance, IEEE Microwave and Wireless Com-ponents Letters, July 2005, pp. 463-465.
H. Xu, C. Sanabria, S. Heikman, S. Keller, U. K. Mishra, and R. A. York,HighPower GaN Oscillators using Field-Plated HEMT Structure, IEEE Microwave The-ory and Technique International Microwave Symposium, June 2005.
C. Sanabria, H. Xu, T. Palacios, A. Chakraborty, S. Heikman, U. K. Mishra, R. A.York, Influence of Epitaxial Structure in the Noise Figure of AlGaN/GaN HEMTs,IEEE Microwave Theory and Technique Transactions, Vol. 53, February 2005, pp.762-769.
H. Xu, C. Sanabria, Y. Wei, S. Heikman, S. Keller, U. K. Mishra, and R. A. York,Characterization of two field-plated GaN HEMT structures, IEEE Topical Workshopon Power Amplifiers for Wireless Communications, September 2004.
H. Xu, C. Sanabria, A. Chini, Y. Wei, S. Heikman, S. Keller, U. K. Mishra and R. A.York, A new field-plated GaN HEMT structure with improved power and noise per-formance, IEEE Lester Eastman Conference on High Performance Devices, August2004.
H. Xu, C. Sanabria, A. Chini, S. Keller, U. K. Mishra, and R. A. York,A C-bandhigh-dynamic range GaN HEMT low-noise amplifier, IEEE Microwave and WirelessComponents Letters, Vol. 14, June 2004, pp. 262 264.
v
C. Sanabria, H. Xu, T. Palacios, A. Chakraborty, S. Heikman, U. K. Mishra, R. A.York, Influence of the Heterostructure Design on Noise Figure of AlGaN/GaN HEMTs,Device Research Conference, June 2004.
H. Xu, C. Sanabria, A. Chini, S. Keller, U. K. Mishra, and R. A. York,Robust C-band MMIC Low Noise Amplifier using AlGaN/GaN HEMT Power Devices, 8th Wide-Bandgap III-Nitride Workshop, September 2003.
vi
Abstract
Noise of AlGaN/GaN HEMTs and Oscillators
by
Christopher Sanabria
GaN HEMTs will likely become the solid-state device of choice for power in mi-
crowave and millimeter-wave circuits. These products, such as base stations and other
communication systems, tend to be space-constrained. Hence solutions continuously
move from a hybrid (circuit board plus components) approach to a microwave mono-
lithic integrated circuit (MMIC). To be successful in a MMIC design, GaN will have
to perform well in other areas besides power. One of the most crucial metrics of a
system is its noise. The noise of GaN devices and circuits has only been critically
examined in the last five years.
This work will investigate several aspects of the noise performance of GaN HEMTs.
Measurements of noise figure (NF) and low-frequency noise (LFN) are used to char-
acterize devices. Modeling useful for calculations and circuit simulation are applied,
with some introduced. Several studies of NF and LFN are presented. Some confirm
or challenge previous publications while others are new observations. Two differen-
tial oscillators were built to characterize the phase noise. As it is believed that GaN
vii
HEMTs will replace GaAs HEMTs in various applications, the NF, LFN, and phase
3.6 Change in noise parameters with drain-source voltage. . . . . . . . . 693.7 Typical plots of the noise parameters versus drain source current with
Correlated Noise and Pospieszalski models. . . . . . . . . . . . . . . 713.8 Noise variables for the Pospieszalski and a CN noise model versus
drain-source current. . . . . . . . . . . . . . . . . . . . . . . . . . . 733.9 Minimum noise figure, small signal associated and maximum gain for
devices on sapphire and SiC substrates. . . . . . . . . . . . . . . . . 753.10 Noise parameters versus frequency for devices of different aluminum
composition in the barrier. . . . . . . . . . . . . . . . . . . . . . . . 773.11 Minimum noise figure of samples with different aluminum composi-
tion in the barrier at varying drain-source current. . . . . . . . . . . . 783.12 Minimum noise figure, fτ , andfmax versus drain-source current for a
sample with and without an AlN interlayer. . . . . . . . . . . . . . . 793.13 (a) Associated and maximum gain and (b) source resistance for de-
vices with and without an AlN interlayer at different applied currents. 803.14 (a) Minimum noise figure, (b) device associated gain, and maximum
gain versus frequency for devices with different gate leakage currents 823.15 Simulated (line) and measured (crosses) noise parameters for devices
with different gate leakage currents. . . . . . . . . . . . . . . . . . . 833.16 fτ and fmax of devices with different field-plate lengths. . . . . . . . . 843.17 Noise parameters versus frequency for devices with field plates of dif-
length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873.19 Electric field profile for a device with and without a field plate. . . . . 873.20 Small-signal parameters that change with a field plate. . . . . . . . . 893.21 Minimum noise figure versus gate width for devices with and without
a long field plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903.22 Minimum noise figure of the field-plated devices at different measure-
ment frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903.23 Noise parameters versus drain-source current of a thick cap device
(triangles) and a standard HEMT (squares). . . . . . . . . . . . . . . 923.24 Minimum noise figure of two 0.15µm gate length transistors provided
4.1 Sketch of the key features of low-frequency noise. . . . . . . . . . . . 1034.2 Variation ofα with (a) drain-source voltage bias and (b) frequency of
extraction for two devices on the same sample. . . . . . . . . . . . . 106
xiii
4.3 Measured noise floor of the HP 3561A DSA only and with the SRSSR560 LNA (short-circuited input). . . . . . . . . . . . . . . . . . . 109
A.1 First page oftemplatesmall signal parameterextraction.dds. . . . . 156
xiv
A.2 Schematic used for simulating S-parameters of the small-signal circuitand for optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . 158
A.3 Schematic used for simulating noise parameters. . . . . . . . . . . . . 159A.4 Schematic used for extracting correlated noise model noise variables. 162A.5 Data display used for extracting correlated noise model noise variables. 162
2.2 Comparison of Pospieszalski and Correlated Noise models to mea-sured data. Devices have a gate geometry of 0.7× 150 µm . . . . . . 33
2.3 Comparison of the various noise models’ input and output noise currents. 56
3.1 Minimum noise figure for devices in many technologies. . . . . . . . 94
5.1 Comparison of GaN oscillators from this and other works to oscilla-tors in other materials (FET, MMICs, only). . . . . . . . . . . . . . . 144
xvi
Acknowledgements
BEHIND the candy Santa Barbara exterior of sun, perfect weather, surfing, andtourists is a university that is a powerhouse of research that I didn’t have the
foggiest idea existed until I decided to come to graduate school. I’ve been impressedwith the faculty, facilities, labs, peers, and the graduate sciences and engineering pro-grams at UCSB. It has made for a great research experience and I want to thank andacknowledge all those who have helped me along the way toward getting my Ph.D.
I would first like to thank my advisor Professor Robert York. Not only did hetake me in, he has provided (along with my co-advisor) five years of constant, un-interrupted, financial support. Watching peers struggle with funding shortfalls andchanging projects has made me realize what a blessing funding is. I would also liketo thank him for giving me a great deal of freedom. This was frightening for me atfirst as I thought I would become lost, but later I realized what research I wanted to doand was able to do it without restraint. Professor York has always steered me in theright direction on important matters of publications, research, and things in general.We had many good, frank, talks that I enjoyed.
I thank my co-advisor Professor Umesh Mishra for many things. The first is theamusement of watching someone juggle the work of five men like some god with 10arms. Yet, when I needed to discuss work, we always got a few minutes in and I neverfelt pushed away. I also salute the GaN program he has put together at UCSB. Umeshis one of the smartest, and slyest, individuals I have met and it was fun to be aroundfor the show. I also really appreciate the happy hours he would host.
My other committee members, Professor Mark Rodwell and Dr. Yifeng Wu, havebeen a great help to me not only in preparing the thesis but in important researchdiscussions over the years. Professor Rodwell’s class notes on noise and exchangeshave steered me through to the basic truths about noise figure. With Dr. Wu I’ve hadmany conversations: load-pull, noise, circuits, and even high-end audio equipment. Ihave enjoyed it all. I also thank Professor Long for the conversations that we havehad.
My peers in the trenches have been of tremendous help toward this work. HongtaoXu taught me his fabrication techniques for MMICs and offered very useful sugges-tions for my microwave circuits. We worked collectively on several projects and be-came friends. Tom´as Palacios, the wonder Spaniard, has been of tremendous help. Hisenormous curiosity, knowledge, and keen eye helped me out several times by pointingme in the right direction or giving me inspiration that lead to useful research. Mygroup mates (past and present), Nadia, Val, Raj, Jaehoon, Jiwei, Justin, Paolo (e-lo?),Vicki, Conradin, Jim, and Pengcheng have helped me out many a time (or helped pro-vide a refreshing work break). The small army known as Professor Mishra’s grouphave also helped a great deal: Rob, Siddarth, Likun (Mona), Mike, Dario, Arpan, Ale,Naiqian, Sten, Lee M., Ilan, Yuvaraj, Felix, Pei Yi, Eric, Chang, Chris, Jeff, Karl, and
xvii
Man Hoi. I would especially like to thank those who grew my material for devices andcircuits, Arpan, Sten, Stacia, and Nick, without whom I would have had no project.
I also had useful discussions with students in the groups of both Professors Rodwelland Long. I had many conversations, interactions, and chats with Vikas and Joe,whose projects focused heavily on phase noise. Vikas also provided the GaAs devicesthat were measured in this work and both of them helped with equipment and setups.Navin, Zack, and Paidi all gave me some useful information at one point or another.Also, I had discussions with Adam about low-frequency noise and Professor ElliotBrown let me borrow some equipment from his personal collection for a measurement.
I thank Agilent and Maury for their technical support on various pieces of equip-ment (I calleda lot). I am greatful to the cleanroom staff (Jack, Bob, Neil, Tom,Brian T., Bill, Don, Mike, Luis and Ning) who kept our excellent facilities going 24x7and for being available for the occasional evening crisis. The assistants over the year(Masika, Pam, Emeka, Lee B., and Laura) have been a big help with red tape. I thankVal de Veyra and the other assistants in the ECE graduate student office, with whom Ihad a good laugh because of a non-unique nickname in my email address book.
I very much thank Dr. Harry Dietrich and the Office of Naval Research (ONR) whofunded and oversaw the Center for Advance Nitride Electronics (CANE) program thatI was on.
I would also like to thank Dr. Joy Vann-Hamilton. Joy, who was director of theMinority Engineering Program (MEP) while I was an undergraduate at the Universityof Notre Dame, listened to all my unhappy college complaints, pointed me towardresources that got me through undergraduate, and is solely responsible for my goingto graduate school. Grad school wasn’t even on my radar and I didn’t think I had thetalent. I can’t thank her enough.
As if I hadn’t thanked enough people and entities, I would also like to thank all myfriends who made my time here enjoyable (even if it was jokes at my expense, Perkand Dave). Also, I don’t know what my parents did that I turned out the way I did,but I want to give them applause for all that they have done. Don’t worry, I won’t doanything to embarrass you like I did at high school graduation.
Finally, no stay in Santa Barbara is complete without picking up a wife. Sarah, whowould have guessed we would meet here instead of at Notre Dame? I thank you forhandling all my rants with grace, giving me hope when I had none, distracting me so Iwould realize there are a whole lot of interesting things to do in the world, and beingsome one worth living for.
“Thanks y’all”...
xviii
For those who never quit.
xix
1Introduction
1.1 Motivation
GALLIUM nitride (GaN) and its related compound materials, indium nitride
(InN) and aluminum nitride (AlN), have already been commercialized for
several applications. This is an impressive feat for an immature technology where each
year research continues to bring improvements. The reason for this rush to market is
the needs the nitrides are addressing. For optical applications, GaN-based solutions
include LEDs, lasers, and detectors in the UV and blue wavelengths. For electronic
applications, GaN high electron mobility transistors (HEMTs) provide some of the
highest microwave power performance to be found from solid state devices.
GaN-based electronics have two major setbacks. The first is the cost. This re-
sults largely from the expensive substrates needed, with the better substrates currently
costing nearly an order of magnitude more than lower-performance options. The other
hurdle is growth immaturity, which causes reliability to be mediocre. Because of these
disadvantages, if another material system (Si, GaAs, InP, etc.) can meet the needs of an
1
CHAPTER 1. INTRODUCTION
application, industry will choose it over GaN. This means GaN HEMTs are being con-
sidered mainly for power amplifiers in microwave products such as base stations [1,2].
Industry has a great need for these products to be compact. Designers continuously
move from hybrid (a circuit board with discrete components) to integrated (a single,
small chip) solutions. Instead of a chip with just a power amplifier, it is preferred to
have the amplifier, and complete transmit and receive paths, in a single chip called a
front-end module (FEM). Figure 1.1 shows an example of a simple transmitter, and the
preferred integration boundary of power amplifier plus other components. It may be
possible that GaN monolithic microwave integrated circuits (MMICs) provide better
performance in terms of power, radiation hardness, and operation temperature, leading
to future products.
ModulatorFrom
DSP
Oscillator
Mixer Filter Power
Amp.
Antenna
Ideally implemented as a single transmitter MMIC
Figure 1.1: Cartoon of a very simple transmitter.
2
CHAPTER 1. INTRODUCTION
Frequency
Power
Channel
Width
Channel
SpaceNoise
Side
Band
Noise
Floor
Figure 1.2: Cartoon of a CDMA-like spectrum with four channels.
Basic GaN MMIC building blocks are now appearing in the literature [3–7], and
it is only a matter of time before GaN transmit and receive MMICs are made. An
important metric of such circuits will be their noise performance. In particular, phase
noise and noise figure (NF) are common figures of merit for characterizing noise. A
main focus of this work is examining these aspects of GaN HEMTs and oscillators.
Communication channel spacing is set based on specifications of the maximum
noise a channel will produce out-of-band. This is shown in figure 1.2. Setting the
space between channels as small as possible isextremelyimportant due to regulated
bandwidth restrictions.1 Typically the component that sets the minimum on this noise
1In fact, whenever the Federal Communications Commission (FCC) auctions bandwidth the sellingprice is in the hundreds of millions [8].
3
CHAPTER 1. INTRODUCTION
performance is an oscillator in the circuit, as in figure 1.1. An oscillator provides
a signal source at a (usually variable) reference frequency. In addition, oscillators
produce a large amount of noise at frequencies close to the reference frequency. This
is called phase noise.
It is understood that various device noise sources contribute to the phase noise.
These include thermal, shot, and low-frequency (also called flicker, or 1/f) sources.
The quantitative analysis of how these sources contribute to the phase noise is difficult
even for the simplest of cases. A qualitative description that embodies many important
points was presented by Leeson [9], and is described as
L (∆ω) = 10 log
2FkT
Psig
1 +
(ω0
2Q∆ω
)2
(1 +
∆ω1/f3
|∆ω|
) (1.1.1)
where the script L is the phase noise in a 1 Hz bandwidth at an offset angular fre-
quency,∆w, from the carrier angular frequency,ω0, Q is the quality of the resonator,
Psig the signal power, and F the effective noise figure.2 Shot and thermal noise sources
contribute to F, a measure of the background noise of the device and circuit. The low-
frequency noise (LFN) contributes through∆ω1/f3, a corner frequency for the phase
noise that presumably relates to the corner frequency of the LFN. From equation 1.1.1,
we can discern that knowledge of the noise sources in the device and circuit will help
in understanding the phase noise, and if we can reduce them the phase noise will be
2The parameter F here is not the device noise figure or factor but an “Effective noise figure” whichsome see as just a fitting parameter. F in this chapter should not be confused with noise factor in theother chapters.
4
CHAPTER 1. INTRODUCTION
improved. Leeson’s equation also tells us that ifPsig can be increased, we should
see an improvement in phase noise. Because GaN devices are capable of providing
an order of magnitude more power than gallium arsenide (GaAs) devices, the next
best commercial material, it is of great interest to know if the phase noise of GaN
circuits can be better than GaAs circuits. One of the goals of this work is to answer
this question.
This dissertation will look at several aspects of the noise performance of GaN
HEMTs. NF and LFN measurements are used to evaluate the noise performance of
the GaN HEMTs. Comparisons are made to measurements of GaAs HEMTs, the most
similar commercial device, which GaN is trying to displace. Models for NF and LFN
noise, some old and some new, are presented. To study the phase noise, differen-
tial oscillators were constructed and measured. Their performance is explained in the
context of LFN.
A quick review of previous noise measurements and studies of GaN HEMTs and
oscillators is now presented, followed by a sketch of this work.
1.2 Literature Review of Noise in GaN HEMTs
This section gives a short background of the GaN HEMT literature for NF, LFN,
and phase noise prior to this work (late 2002). Most publications after this point in
time are already referenced throughout the work. More background information on
5
CHAPTER 1. INTRODUCTION
each noise subject can also be found at the beginning of its respective chapter.
Of the three types of noise measurements performed on GaN HEMTs, LFN has
the longest history. Reports of measurements first started to appear in 1998 [10, 11].
Because LFN measurements can be used as a way of monitoring crystal quality, some
reports came from materials scientists [12]. Physicists have measured GaN LFN and
are using some of the following arguments to explain it: tail states near the band gap
edge [11], mobility fluctuations [13], and tunneling of electrons from the channel to
traps in surrounding layers [12]. No theory is yet accepted as the best explanation.
Various other LFN papers have appeared [12,14–16]. Most measurements are at very
low biasings such that the device is in the linear region. The only publication that stud-
ies gate and drain LFN for the full biasing range of a GaN HEMT is Hsu et al. [17].
This paper will be returned to in chapter 4. Due to the use of the Hooge parame-
ter, the devices not being optimized HEMTs (some are doped channel HFETs), and
measurements only in the linear region, many of the above results are not of use to a
circuit designer or device engineer who is trying to characterize and optimize LFN.
Accurate measurements of LFN can also be difficult. Therefore, this work presents
measurements and modeling of LFN that will be of use to the engineering community.
The first published NF report for a GaN HEMT was performed by Ping in 2000 [18].
For a 0.25 x 100µm gate device, a minimum noise figure (NFmin) of 1.06 dB and a
gain of 12 dB at a frequency of 10 GHz was demonstrated. This was followed shortly
6
CHAPTER 1. INTRODUCTION
by Nguyen [19], presenting a NFmin of 0.6 dB at 10 GHz and 13.5 dB gain with a
0.15 x 100 µm gate. Other results [20, 21], with improved performance, followed
the next year. After optimizing the device geometry, Moon showed in 2002 that a
GaN HEMT could present similar NF at a similar biasing to a GaAs HEMT [22]. The
next notable result in the field was when Lu showed that GaN HEMTs on a sapphire
substrate can have similar NFmin performance to HEMTs on a SiC substrate [23]. All
previously published results had been on SiC substrates. This work seeks to extend
on the noise figure literature and to confirm or deny some of the previously published
results, in addition to adding new studies. Table 3.1 lists many GaN (as well as GaAs,
SiGe, and InP) HEMT NF results.
Prior to this work, GaN oscillator references were scarce. The first GaN oscillator
was reported by Shealy in 2001 [24]. The phase noise was respectable: -92 dBc at
100 kHz for a 6 GHz carrier frequency. While Shealy’s work was a hybrid design, the
first MMIC oscillator was presented by Kaper in 2002 [25]. He estimated (but did not
show measurements) the phase noise to be -87 dBc at 100 kHz. These works left room
for further investigation. A summary of all published GaN oscillators appears in table
5.1.
The existing literature was thin at the beginning of this project. The noise research
of GaN has since approximately doubled to tripled. Because noise is difficult to mea-
sure, second and third opinions are valuable. This work will do this, in addition to its
7
CHAPTER 1. INTRODUCTION
own unique studies and modeling.
1.3 Thesis Outline
Chapter 2 builds up to a NF model. This model is an extension of previous mod-
els and fills the need of understanding how various noise sources and small-signal
parameters influence NF and other noise parameters without the need for prior NF
measurements. The chapter starts with reviews of noise sources, the equivalent circuit
model, NF and parameters, and previous models. The proposed model is then derived
and discussed in detail.
With the modeling in place, several NF studies are presented in chapter 3. Effects
of bias and gate leakage are studied. Different epitaxial structures are compared, as
is the addition of a field plate. High-frequency GaN HEMT devices were borrowed,
measured, and compared to HEMTs in other technologies (in particular, GaAs).
A LFN setup was constructed and measurements performed to help understand the
phase noise performance. Chapter 4 covers these results. It first shows through mea-
surements why the Hooge parameter should not be used for comparing devices (only
materials). LFN versus bias shows the need for an improved model for the drain noise,
which was then added. LFN studies are then presented and comparisons to measured
GaAs HEMTs are made.
Differential oscillators are constructed in chapter 5 and phase noise is measured
8
CHAPTER 1. INTRODUCTION
and evaluated. The first version had excellent linearity but poor phase noise. A second
version had good phase noise. The oscillators are compared to other published GaN
oscillators and to differential oscillators in Si and GaAs technologies.
References
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[8] R. Rast, “The Dawn of Digital TV,”Spectrum, IEEE, vol. 42, no. 10, pp. 26–31,2005.
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9
CHAPTER 1. INTRODUCTION
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[12] A. Balandin, Ed.,Noise and Fluctuations Control in Electronic Devices. Steven-son Ranch, CA: American Scientific Publishers, 2002.
[13] J. A. Garrido, B. E. Foutz, J. A. Smart, J. R. Shealy, M. J. Murphy, W. J. Schaff,L. F. Eastman, and E. Munoz, “Low-Frequency Noise and Mobility Fluctuationsin AlGaN/GaN Heterostructure Field-Effect Transistors.”Applied Physics Letters,vol. 76, no. 23, pp. 3442–4, June 2000.
[14] M. Levinshtein, S. Rumyantsev, M. Shur, R. Gaska, and M. Khan, “Low Frequencyand 1/f Noise in Wide-Gap Semiconductors: Silicon Carbide and Gallium Nitride,”Circuits, Devices and Systems, IEE Proceedings [see also IEE Proceedings G-Circuits, Devices and Systems], vol. 149, no. 1, pp. 32–39, 2002.
[15] A. Balandin, S. Morozov, S. Cai, R. Li, K. Wang, G. Wijeratne, andC. Viswanathan, “Low Flicker-Noise GaN/AlGaN Heterostructure Field-EffectTransistors for Microwave Communications,”Microwave Theory and Techniques,IEEE Transactions on, vol. 47, no. 8, pp. 1413–1417, 1999.
[16] S. Rumyantsev, N. Pala, M. Shur, M. Levinshtein, R. Gaska, X. Hu, J. Yang,G. Simin, and M. Khan, “Low Frequency Noise in GaN-Based Transistors,” inHigh Performance Devices, 2000. Proceedings. 2000 IEEE/Cornell Conferenceon, 2000, pp. 257–264.
[17] S. Hsu, P. Valizadeh, D. Pavlidis, J. Moon, M. Micovic, D. Wong, and T. Hus-sain, “Characterization and Analysis of Gate and Drain Low-Frequency Noise inAlGaN/GaN HEMTs,” inHigh Performance Devices, 2002. Proceedings. IEEELester Eastman Conference on, 2002, pp. 453–460.
[18] A. Ping, E. Piner, J. Redwing, M. Khan, and I. Adesida, “Microwave Noise Perfor-mance of AlGaN/GaN HEMTs,”Electron. Lett., vol. 36, no. 2, pp. 175–176, Jan.2000.
[19] N. Nguyen, M. Micovic, W.-S. Wong, P. Hashimoto, P. Janke, D. Harvey, andC. Nguyen, “Robust Low Microwave Noise GaN MODFETs with 0.6 dB NoiseFigure at 10 GHz,”IEEE Electron. Lett., vol. 36, pp. 469–471, March 2000.
[20] S. Hsu and D. Pavlidis, “Low Noise AlGaN/GaN MODFETs with High Break-down and Power Characteristics,”Gallium Arsenide Integrated Circuit (GaAs IC)Symposium, 2001. 23rd Annual Technical Digest, pp. 229–232, Oct. 2001.
10
CHAPTER 1. INTRODUCTION
[21] W. Lu, J. Yang, M. Khan, and I. Adesida, “AlGaN/GaN HEMTs on SiC with over100 GHzfT and Low Microwave Noise,”IEEE Trans. Electron Devices, vol. 48,no. 3, pp. 581–585, Mar. 2001.
[22] J. Moon, M. Micovic, A. Kurdoghlian, P. Janke, P. Hashimoto, W.-S. Wong, L. Mc-Cray, and C. Nguyen, “Microwave Noise Performance of AlGaNGaN HEMTsWith Small DC Power Dissipation,”IEEE Electron Devices Lett., vol. 23, no. 11,pp. 637–639, Nov. 2002.
[23] W. Lu, V. Kumar, R. Schwindt, E. Piner, and I. Adesida, “DC, RF, and MicrowaveNoise Performance of AlGaN/GaN HEMTs on Sapphire Substrates,”IEEE Trans.Microwave Theory Tech., vol. 50, pp. 2499–2503, Nov. 2002.
[24] J. B. Shealy, J. A. Smart, and J. R. Shealy, “Low-Phase Noise AlGaN/GaN FET-Based Voltage Controlled Oscillators (VCOs),”IEEE Microwave ComponentsLett., vol. 11, no. 6, pp. 244–245, Jun. 2001.
[25] V. Kaper, V. Tilak, H. Kim, R. Thompson, T. Prunty, J. Smart, L. F. Eastman, andJ. Shealy, “High Power Monolithic AlGaN/GaN HEMT Oscillator,”IEEE GaAsDigest, pp. 251–254, 2002.
11
2Noise Figure Modeling of AlGaN/GaN
HEMTs
2.1 Introduction
TO characterize, compare, and improve the noise performance of devices, a
theoretical framework is needed that identifies the noise sources, how these
sources contribute to the overall noise, and how the noise changes with other param-
eters, such as bias and matching conditions. A common approach is to add discrete
noise sources to a small-signal model [1–3]. Depending on the model, the sources may
be correlated, adding complexity to the derivation and interpretation of the particular
model.
This chapter first fills in background for the model. Noise sources of interest to
noise figure (NF) are reviewed, as is a full small-signal model. NF is then defined
in § 2.4, along with the noise parameters NFmin , Γopt andrn. Those familiar with
noise sources, NF, and small-signal modeling could skip these sections and continue
on to § 2.5. The more widely-used models are presented along with their strengths
12
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
and weaknesses in§ 2.5. Noise modeling derived from these previous models is then
introduced. Its strengths and weaknesses are also discussed. Finally, the NF model
is used for simulation of device noise figure performance of AlGaN/GaN HEMTs,
compared to other models, and discussed in depth.
2.2 Noise Sources
The two most common types of noise are shot and thermal noise. Both are referred
to as “flat” or “white,” meaning the noise power versus frequency is constant. Each
will be reviewed in this section. The relevance of other noise sources to NF is also
discussed.
2.2.1 Thermal Noise
Thermal noise was first studied in detail by Johnson in 1927 [4], and explained
mathematically by Nyquist [5]. Its physical origin is the agitation of electrons in a
conductor. The random scattering of electrons by atoms followed by their relaxation
back to a ground state leads to fluctuations that can be measured as a voltage or current.
The use of statistical analysis and thermal physics [6] leads to the following expression
that represents the available noise power from a resistance into a matched load
PThermal =
hf
2+
hf
exp(hfkT
)− 1
∆f (2.2.1)
13
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
whereh is Planck’s constant,k is Boltzmann’s constant, T is temperature, andf is the
frequency.
The term∆f is the bandwidth in which the noise is being measured. To determine
the total noise coming from, for example, an amplifier, this expression would be inte-
grated over the bandwidth of the amplifier. A noise measurement might be performed
over a small bandwidth, less than one Hertz for some low-frequency noise measure-
ments, showing the need to keep this fact in mind. When values are quoted and a
bandwidth is not specified, it is assumed to be a 1 Hz bandwidth. This convention is
followed in this work.
Equation 2.2.1 is a general expression, and is needed if operating at cryogenic tem-
peratures or extreme frequencies (such as the THz range). For most engineering pur-
poses, the simpler expression
PThermal ≈ kT∆f (2.2.2)
can be used. A handy value from this expression is that the available noise at room
temperature in a 1 Hz bandwidth is -174 dBm (4× 10−21 W).
When the load is not matched, or the noise needs to be expressed as a voltage or
current (described by a variance), the following forms are useful:
⟨v2n
⟩= 4kTR∆f (2.2.3)
⟨i2n⟩
=4kT
R∆f (2.2.4)
14
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
R is the resistance of the noise generating material or medium. A 1kΩ resistor gener-
ates 4 nV/√
Hz of noise. Not every resistor represented in a circuit schematic generates
noise. For example,rπ in a bipolar transistor is a manifestation of the transistor’s I-V
characteristics, and is not a real resistance.
Ideal reactive components do not generate noise. However, because real inductors
and capacitors are lossy, the circuit-modeled parasitic resistances of these components
will generate thermal noise. Also, these components shape the bandwidth of the noise
in ways similar to shaping a signal.
Finally, the above equations only apply at thermal equilibrium. A biased transistor
is notat thermal equilibrium. However, a small-signal model of a HEMT, which does
not include bias, can have its parasitic resistances considered at thermal equilibrium.
Later, in§ 2.6.3, the channel noise, which is a form of non-equilibrium thermal noise,
are derived. Further information on thermal noise can be found in [6–9].
2.2.2 Shot Noise
Shot noise was reported and explained by W. Schottky in 1918. The analogy of this
noise to buck shot being dropped into a bucket is the basis for its name [8]. Shot noise
exists when two conditions are met: (1) a DC current is flowing and (2) the charge
carriers composing the DC current cross a potential barrier. This second condition
is why resistors and the channel of a HEMT do not generate shot noise. The noise
15
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
exists because charge is discrete and will cross the potential barrier atrandomtimes.
If the charge crossed at the same time or equal time intervals, the spectrum of the shot
noise would not be white and could be better dealt with in circuit design (possibly by
filtering).
As with thermal noise, shot noise is not constant at all frequencies. The noise de-
creases at frequencies above which the transit time across the barrier is short compared
to the inverse of this frequency [7]. Because devices are operated at frequencies well
below this, the noise can be considered flat [7].
Using math from random processes [9], shot noise is describe by the following
equation for current fluctuations:
⟨i2n⟩
= 2qIDC∆f (2.2.5)
with q being electronic charge (1.6 × 10−19 C), IDC the DC current (Amps), and∆f
again the bandwidth of interest.
2.2.3 Other Sources of Noise
Shot and thermal are the important noise sources for NF modeling. Others exist, and
at frequencies lower than RF should be considered. They will be briefly mentioned
here. Flicker and generation-recombination noise (covered in detail in chapter 4) are
important for oscillator phase noise, but are not of concern for NF measurements in
the RF frequency range. Burst noise is interpreted as a type of low-frequency noise
16
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
with a 1/f2 spectrum. It also would not affect NF measurements in the GHz range, nor
has it been reported in GaN-based HEMTs. Avalanche noise is a form of shot noise,
and usually applies to a semiconductor junction. With a high enough field across a
junction, avalanche multiplication can occur [10]. This increase in carriers leads to
an increase in the shot noise proportional to the cube of the multiplication factor [9].
While the fields can be very high, no evidence has been shown that this type of noise
appears in GaN-based HEMTs. As will be seen in modeling later, shot and thermal
types of noise are sufficient to predict the noise figure of GaN HEMTs.
2.3 Equivalent Circuit Model
A small-signal model will be used in determining the device noise figure. Device
small-signal modeling has been covered extensively in the literature [11–17]. Here
a short summary will be given. The model used in this work is superimposed on
the cross section of a HEMT in figure 2.1. The parameters are bias-dependent but
frequency independent. In this chapter and chapter 3, the parameters are extracted at
the bias of best device minimum noise figure performance.
At the heart of the model is the gate-source capacitance,Cgs, and the transconduc-
tance,gm. The phase associated withgm, ωτ , is a necessary delay that accounts for
channel charge to redistribute after a change in gate voltage. The drain-source resis-
tance,Rds, is a measure of how effectively a signal can be extracted from the device.
17
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
Rg
Ri
Rds
DrainSource Gate
gmejwτvc
Cgs
Vc+
-Rs
Rgd
Cgd
Cpgd
Rd
Ld
Cpds
Lg
Cds
Cpgs
Ls
Figure 2.1: Cartoon showing the device small-signal model on a cross section of aHEMT.
This is because it will reduce the effective load of the device. There are two primary
causes for its degradation: conduction in the buffer due to poor growth (traps) and
spread of electrons from the 2DEG when the device is under extreme biasing (very
high electric fields).
The channel and gate-drain resistances,Ri andRgd, have vague physical interpre-
tations.Ri is regarded as either a physical channel resistance or charging resistance
for Cgs. Because it is hard to extract separately from the gate resistance,Rg, the two
are sometimes lumped together. The gate-drain capacitance,Cgd, is setup by the space
charge region between the gate and drain, similar toCgs, but typically an order of mag-
nitude smaller. It introduces a bothersome feedback which reduces the high-frequency
18
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
performance of the device. The gate-drain resistance,Rgd, is also argued as a charging
resistance forCgd. Any capacitance between the drain and source, which will be very
small, is accounted for withCds.
The parametersCgs, gm, τ ,Ri,Rds,Rgd,Cgd, andCds taken together are referred to
as theintrinsic device. The other elements of the model are unfortunate side-effects of
having to provide physical connections to the device and the parasitic and distributed
effects that occur when operating at frequencies in the GHz range. These parasitic
elements are called theextrinsicelements of the device.
The drain and source resistances,Rd andRs, come from two physical processes.
The first is the finite resistance of the 2DEG, and so the access regions between gate
source and gate drain contribute to these parasitics. The second source is the non-
ideal ohmic contact behavior between the metal pads and the semiconductor. These
resistances scale directly with the device width as used in§ 2.6.5. Because the gate
length is short (0.7µm here), the resistances of the gate metals contribute toRg.
From an AC viewpoint, the signal decays as it propagates along the length of the gate
resistance. A distributed model argument shows this resistance to be approximately
1/3 of its DC value [14]. All of these resistances generate thermal noise.Rs and
Rg will be important for modeling of noise figure as seen later. BecauseRd is at
the output, and its magnitude of noise is far smaller than the channel noise, it can be
ignored.
19
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
The drain, gate, and source inductances,Ld Lg, andLs, respectively, account for
signal delay along the various contact pads.Lg is usually largest, and will affect
any input match (noise or power) to the device. Finally there are the various pad
capacitances between their respective device terminals:Cpgs, Cpgd, andCpds. Cpgs
andCpgd are small, whileCpds for devices used in this work is of the same order as
Cgd.
S-parameter measurements of devices along with open and shorted test structures
were used to find the small-signal parameters. In addition, DC measurements of TLM
structures and some basic hand calculations [14] were used to determineRg, Rs, and
Rd. For a better fit, optimization was performed using Advanced Design System
(ADS). It is important to have accurate small-signal parameters; any discrepancies
directly translate into incorrect noise figure parameter prediction. Some ADS files
useful for extracting and optimizing the small-signal parameters can be found in ap-
pendix A.
Extracted small-signal parameters of devices from various samples are displayed in
table 2.1. The top half of the table is the intrinsic parameters, while the bottom half is
the extrinsic parameters. Many of the extrinsic parasitics come from the geometry of
the device or the pad parasitics and will be the same for the different samples. These
parameters will be used in this chapter and in chapter 3.
20
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
Table 2.1: Extracted small-signal parameters for various samples. Devices have a gategeometry of 0.7× 150µm.
2.4 Noise Figure and Noise Parameters
An amplifier provides gain to both the input signal and the noise. The amplifier will
also add noise from its intrinsic noise sources. This makes the signal to noise ratio at
the output worse than at the input. Expressing a ratio of these two ratios at a reference
temperature leads to the definition of noise figure.
F ≡ (S/N)in(S/N)out
∣∣∣∣∣T=Treference=290K
(2.4.1)
It can be applied to any two port [3] (by extension even to mixers [7]). Here, it will
21
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
be applied to a single HEMT. Sometimes NF is called noise factor, F. Traditionally,
the names were interchangeable, but now it is common that noise figure is the noise
factor expressed in decibels (NF = 10 log10(F)). This is the convention followed in
this work. Sometimes it is expressed as a temperature (Tnoise = (F − 1)Treference).
Noise figure by itself gives no details of the noise sources of the device or amplifier.
However, noise sources can be added as in Figure 2.2.Inoise is the equivalent short-
circuited noise current source andEnoise the equivalent open-circuited noise voltage
source. Together, they account for all noise sources of the device which can now be
modeled as a noiseless two port. These two sources will likely be correlated because
of the various physical noise sources of the device that contribute to them [8]. Models
that describe these sources of noise are discussed in the next section. An input is
connected to the device, represented as a source impedance in figure 2.2. This input
will generate its own noise, represented asEsource. This could be thermal noise from
Zsource
Noiseless
2-port
network
+-
Enoise
+-
InoiseEsource
Figure 2.2: Equivalent model of a transistor driven by a noisy source of impedanceZsource.
22
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
a passive network and/or active device noise. From this, F (and hence, NF) can be
written as [8]
F = 1 +
⟨|Enoise + InoiseZsource|2
⟩
〈Esource〉2(2.4.2)
As can be seen, the value of the source impedance actually affects the noise figure.
OnceEnoise andInoise have been determined through whichever model is applied, the
noise figure can be predicted for changing source impedance. F can also be expressed
as [18,19]:
F = Fmin +4Rn
Zo
|Γsource − Γopt|2
(1 − |Γsource|2) |1 + Γopt|2(2.4.3)
Γsource is the reflection coefficient of the source impedance. Equation 2.4.3 contains
four parameters that taken together are called thenoise parameters. They are:
Fmin The best achievable noise figure. It occurs only when the source impedance isset toZopt (converselyΓopt).
|Γopt| The magnitude of the source reflection coefficient that provides the minimumnoise figure,Fmin.
6 Γopt The angle of the source reflection coefficient that providesFmin.
Rn An effective “slope.” The larger its value, the quicker the noise figure increasesasΓsource is changed from its optimum value.1
These parameters are usually measured as described in§ 3.3. As can be reasoned
from equation 2.4.3, there are circles of constant noise on an impedance or Smith
1Rn has units of ohms. It can also be normalized to the reference impedance,Zo. Then the variableis usually written asrn instead.
23
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
NFmin
NFmin+1dB
NFmin+2dB
NFmin+3dB
Gmax
Gmax-1dB
Gmax-2dB
Figure 2.3: Smith Chart showing minimum noise figure and circles of constant noisefigure (solid circles) along with maximum gain and circles of constant gain (dashedcircles).
Chart plane. This is shown in Figure 2.3. It should not be surprising to find the small-
signal gain circles and noise circles do not overlap becauseΓopt is an intentional gain
mismatch to minimize noise [20].
That the noise performance changes with the source match is extremely important
for LNA design. In the next section, noise models for HEMTs that are more in depth
than in figure 2.2 will be reviewed. Once these noise sources are determined, they can
be used elsewhere, such as assisting in oscillator phase noise prediction.
24
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
2.5 HEMT Noise Figure Models
The major noise figure models used for HEMTs are now presented. The work by
van der Ziel, Pucel, Fukui, and Pospieszalski is the basis for most other investigations
and modeling of noise figure. The key ideas, equations, strengths and weaknesses of
each will be reviewed. Shortcomings found in each will show the need for further
work and provide motivation for the next section.
2.5.1 van der Ziel and Pucel Models
The theoretical work for noise sources in FETs at microwave frequencies was in-
troduced by van der Ziel in the early 1960s [3, 21, 22]. He derived noise sources for
the channel and “induced gate noise.” This gate noise is explained as fluctuating noise
in the channel capacitively coupling to the gate throughCgs andCgd, causing an ef-
fective, and correlated, noise source at the gate. The gate noise, channel (drain) noise,
correlation (C), and cross-term〈igi∗d〉 can be written as [3]
⟨i2g⟩
= 4kTaδω2C2
gs
5gd0∆f (2.5.1)
⟨i2d⟩
= 4kTaΓgd0∆f (2.5.2)
C =〈igi∗d〉√⟨i2g⟩〈i2d〉
(2.5.3)
〈igi∗d〉 =2
3jωCgskTa∆f (2.5.4)
25
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
ω is the angular frequency,Ta is the ambient temperature,gd0 is the drain-source con-
ductance whenVds is zero,δ is a parameter van der Ziel gives as 4/3, andΓ will be
derived in§ 2.6.2 (for now, it can be considered a constant of 2/3). Van der Ziel orig-
inally found a correlation of 0.395j for JFETs [3]. For aggressively-scaled HEMTs,
the correlation is experimentally found to be∼0.7j [23,24]. Van der Ziel does give ex-
pressions for noise figure, but they are often in terms of more complicated parameters,
under specific conditions, or for different devices, making them of limited use [3].
While the gate and drain noise expressions above allow for noise prediction, for accu-
rate results the correlation must be measured. This is because small changes in cor-
relation can have a large effect in predicted noise parameters. Also, the noise sources
are bias-and frequency-dependent.
In 1975, Pucel and his co-workers took what was learned from van der Ziel and
extended it in a very detailed publication [2]. Their work was explicitly for a GaAs
MESFET (and thus more applicable to a HEMT), whereas van der Ziel’s work was
mainly for JFETs. The Pucel modeling takes into account velocity saturation and how
the noise changes with bias based on changes in the small-signal parameters and their
noise variables P, R, and C. The model also uses a gate and drain noise source that
are correlated, shown in a small-signal model in figure 2.4. In this figure, the gate
and drain noise sources account for all noise generated by the intrinsic device (inside
the dashed “Noiseless” box). The parasitic resistances,Rg, Rs, andRd, still generate
26
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
Rg
Ri
Cgs
Rds
Drain
Source
Gate
gmejwτvc
Vc
+
-
Ls
Rs
Rgd Cgd
Cpgd
Rd Ld
CpdsCpgs
Lg Noiseless
Ig IdCds
Figure 2.4: Pucel noise model in a small-signal circuit.
thermal noise. The gate and drain noise sources are related to the noise variables by
P =〈i2d〉
4kTa |Y21|2 ∆f=
〈i2d〉4kTagm∆f
(2.5.5)
R =|Y21|2
4kTa |Y11|2 ∆f
⟨i2g⟩
=gm
4kTaω2C2gs∆f
⟨i2g⟩
(2.5.6)
and the same correlation as in equation 2.5.3. Although Pucel determined very de-
tailed expressions for these noise variables, for accurate results the modeling had to
be fitted to data. Today, if this model is used, the parameters are determined empiri-
cally [7], fitting to noise figure measurements. An excellent paper using this model on
GaN HEMTs that shows directly how to extract these parameters from measurements
is found in [25]. This method also treats both parts of the correlation, magnitude and
phase, as variables to be determined instead of restricting the phase to 90 (strictly
imaginary). This formulation is used in this work. Information about an ADS project
27
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
that helps in determining these parameters, contains a small-signal circuit with this
type of noise modeling, and calculates noise figure can be found in appendix A. Be-
cause it uses the same correlation as van der Ziel’s modeling, the Pucel model suffers
the same drawbacks. As mentioned, the parameters usually must be determined from
measurements, limiting its predictive power. Because the noise sources are similar for
both models, they will be referred to ascorrelated noise (CN) models in this work.
2.5.2 Fukui Model
Fukui garnered much attention in the late 1970s with the introduction of his empir-
ical model [26]. Although it involved empirical parameters, it was far simpler than
the previously reported noise models, was expressed directly in terms of the noise
parameters, and made clear how key small-signal parameters contributed to the noise
performance. The model is also convenient because the noise at different frequencies
and device scaling can be easily determined. His expressions for the noise parameters
are:
Fmin = 1 + k1fCgs
√Rg +Rs
gm(2.5.7)
Ropt = k3
[1
4gm+Rg +Rs
](2.5.8)
Xopt =k4
fCgs(2.5.9)
Rn =k2
g2m
(2.5.10)
28
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
The variablesk1−4, are the fitting parameters, and will change with the device tech-
nology and bias. While this model can be useful for hand calculations, the Pucel and
Pospieszalski models are more complete and directly usable in a simulator such as
ADS.
2.5.3 Pospieszalski Model
In the late 1980’s, Pospieszalski introduced a new noise figure model that took a
different approach than the previous methods by removing correlation between the
noise sources [1]. There are only two noise sources for the entire transistor: thermal
noise ofRi andRds. Instead of these resistors being at ambient temperature,Ta, they
are at higher effective temperaturesTg andTd, shown in figure 2.5.Tg is usually
(but not always) close to room temperature, whileTd can be several thousand degrees
Kelvin. These elevated temperatures are not linked to a physical temperature. There
Rg
Ri
Cgs
Rds
Drain
Source
Gate
gmejwτvc
Vc
+
-
Ls
Rs
Rgd Cgd
Cpgd
Rd Ld
CpdsCpgs
Lg
T = Tg
T = Td
Cds
4kTg/Ri∆f
4kTd/Rds∆f
Figure 2.5: Pospieszalski noise model in a small-signal circuit. Resistances (and theirthermal noise sources)Ri andRds are at elevated temperaturesTg andTd respectively.
29
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
have been attempts to link these noise temperatures to the device physics, but none
were viewed as successful. The noise can be described by the noise temperaturesTg
andTd as:
Fmin = 1 + 2
(f
fT
)2RiTdRdsTa
+2f
fTTa
√√√√RiTgTdRds
+
(f
fT
)2R2i T
2d
R2ds
(2.5.11)
Ropt =
√√√√(fTf
)2TgRiRds
Td+R2
i (2.5.12)
Xopt =1
ωCgs(2.5.13)
Rn =TgRi
Ta+
TdTaRdsg2
m
(1 + ω2C2gsR
2i ) (2.5.14)
After measuring S-parameters and noise parameters, the noise temperatures can be
extracted by solving the above equations. A Matlab script using equations 2.5.11
and 2.5.12 to perform this calculation can be found in appendix C. A criteria that
Pospieszalski mentions for the model to work is
1 ≤ 4Ropt
Rn(F − 1)< 2 (2.5.15)
The lower limit is fundamental and is because the noise of a 2-port modeled by a pair
of noise sources must be Hermitian and non-negative definite as shown by Pospieszal-
ski [27]. The upper limit comes from the model itself [1]. As with the other models, it
can be used to determine the match for noise and expected noise at other frequencies.
The model is criticized for its dependence onRi as a thermal noise source, which is
30
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
hard to determine precisely, and for the noise temperatures not having a physical basis.
As with the other models, the noise parameters must be measured prior to modeling.
Thus the model does not “predict” noise. In addition, the noise temperatures change
with device bias [28]. How they change with bias is reported in the literature, but not
modeled or predicted. Information for an ADS project that contains a small-signal
circuit with this type of noise modeling and that calculates noise figure can be found
in appendix A.
2.5.4 Pospieszalski and Correlated Noise Models Applied to Al-GaN/GaN HEMTs
Based on the above discussion, the Pospieszalski and CN models are useful for:
1. Modeling device noise figure in a circuit simulator versus frequency and inputmatch
2. Devices that are stable and well-characterized, such that the noise variables ofthe model (Tg, Td, R, P, C) do not change
3. Predicting noise at frequencies outside the range of available measurement equip-ment.
4. When the bias in a design will not be much different from what gives the bestNF performance
Thus, they are useful for basic LNA designs as shown in [17, 29]. The application of
these models to GaN-based HEMTs is relatively new, with very few publications [25,
28,30].
In table 2.2, the Pospieszalski and CN model have been applied to devices from six
samples. The fτ and fmax of the different devices at the biasing for best NFmin are
31
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
listed along with the bias at the top of the table. The next section contains the mea-
sured noise parameters, obtained as described in§ 3.3, along with the gain that could
be expected from the device having an input match ofΓopt and an output match for
small-signal gain. These noise measurements, along with the small-signal parameters
from table 2.1, were used to calculate the noise variables for both the Pospieszalski
and a CN model. These models’ variables are listed in table 2.2 with the predicted
noise parameters using each model at 5 GHz. The fit is generally very good. Both
models predict NFmin and|Γopt| well. The Pospieszalski model does not predict6 Γopt
as well as the other parameters, and the CN model has trouble with predictingrn.
From equation 2.5.13, it is seen that the Pospieszalski model’s prediction ofXopt only
depends onCgs. A better prediction agreement would be expected. An explanation for
this discrepancy will be offered in§ 3.5.4. Both these models fit the noise parameters
versus frequency, shown in figure 2.6 for one of the sets of measurements in table 2.2.
Variations in the predictedTg of Pospieszalski’s model is large, a factor of 4. This
is likely because of the differences inRi in the measurements of table 2.1, but they
change by only a factor of 2. This high sensitivity toRi might make the model difficult
to use in predicting noise. However, it should be stressed that the model works well
without the need for correlation.
32
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
The factor of 1 is the input noise contribution to the noise figure. If the device does
not generate noise, noise figure would be 1. There would then be no degradation in
the signal to noise ratio going into and coming out of the device. Equation 2.6.16
describes the noise figure in terms of the match provided to the device, the device
small-signal parameters, and the measured gate-leakage. There are no fitting param-
42
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
eters. This is not the minimum noise figure. To determine it, we find the source
impedance that minimizes equation 2.6.16. This is found by taking partial derivatives
and solving equal to zero.
F = Fmin∣∣∣
∂F∂Rgen
=0, ∂F∂Xgen
=0(2.6.19)
This leads to the following expressions for the optimal source impedance that provides
the minimum noise figure:
Xopt =1
ωCgs
a
a+ b(2.6.20)
Ropt =
√√√√1 + aRin
a+ bRin +
ab
(a+ b)2
1
(ωCgs)2(2.6.21)
The last parameter, the noise resistance, can be obtained by using equation 2.4.3
and the equation for noise figure, 2.6.16, at two different source impedances. The
most convenient to choose are the minimum noise figure and when the source is at
its reference impedance,Γgen = 0. We shall call the laterFZ0. Entering this into
equation 2.4.3 and rearranging,
Rn =Z0
4(FZ0 − Fmin)
∣∣∣∣∣1 +1
Γopt
∣∣∣∣∣
2
(2.6.22)
An explicit expression is complicated. A Matlab script that implements all four of
the noise parameters can be found in appendix B. These equations will be discussed
43
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
more in§ 2.6.5, and used in chapter 3. For the moment, let us turn our attention to the
factorΓ, and the derivation of the channel noise source.
2.6.3 Derivation of Drain Noise Source
We will quickly go through the derivation ofΓ (and, therefore, the channel noise
source) to show that it is not a fitting parameter. Van der Ziel has shown the formula-
tion for a MOSFET [3]. Here, it will be explicitly done for a HEMT. The formulation
involves the DC drain current,Id, so it is needed as well. Assume for the moment that
the device is biased in the linear region (no velocity saturation). Following arguments
as found in [11,33], the drain current can be written in general as
Id = g(Vx)dVxdx
= qµWns(x)dVxdx
(2.6.23)
W is the device width (cm), ns(x) is the sheet charge of the 2DEG (cm−2), andµ
is the mobility(cm2
V s
). Vx is the potential difference at a distancex from the source,
relative to the source.g(Vx) is the channel conductivity per unit length at some point
along the channel, which depends onVx.
An expression is needed forns(x) in terms ofVx. First, an effective capacitance can
be defined [11,33]
C =Q
V=
εBd + ∆d
(2.6.24)
with εB andd being the dielectric permittivity and thickness of the AlGaN layer re-
spectively and∆d the centroid of the electron wave functions in the quantum well
44
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
(that is, the 2DEG). The charge of this capacitance isqns(x), with a voltage along the
channel ofVg − Vt − Vx. Vt is the threshold voltage. Combining all this together and
rearranging
ns(x) =εB
q(d+ ∆d)(Vg − Vt − Vx) (2.6.25)
and substituting into equation 2.6.23
Id =µεBW
d+ ∆d(Vg − Vt − Vx)
dVxdx
(2.6.26)
We can now define
g(Vx) =µεBW
d + ∆d(Vg − Vt − Vx) (2.6.27)
Its usefulness will soon be apparent.Id can now be found. Because of continuity, the
DC current entering and leaving the device must be the same. Integrating over the
length of the device,L,
∫ L
0Iddx = IdL =
∫ Vd
0g(Vx)dVx (2.6.28)
which gives
Id =µεBW
L(d + ∆d)
[(Vg − Vt)Vd −
V 2d
2
](2.6.29)
From this, the transconductance (gm)
gm =∂Id∂Vg
=µεBW
L(d + ∆d)Vd (2.6.30)
45
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
and the saturation current,Id,sat, can be found. The saturation current is found by
differentiating equation 2.6.29 with respect toVd and setting it equal to zero. This
returns the voltage ofVd that maximizesId, which we will callVd,sat. However, if the
device has a short channel, the velocity may saturate before the above condition. Then
the voltage that the current saturates is the lesser of the following two quantities:
Vd,sat = Vg − Vt (2.6.31)
or
Vd,sat = EcritLg (2.6.32)
Ecrit is the critical field strength andLg is the device gate length. Putting equa-
tion 2.6.31 back into equation 2.6.29, we find the saturation current resulting from
channel pinch off.
Id,sat =1
2
µεBW
L(d+ ∆d)(Vg − Vt)2 (2.6.33)
equation 2.6.29 only works for a device in the linear region until the device saturates,
Id = Id,sat. Beyond this, the current can be approximated to be the same asId,sat (if
short-channel effects are ignored).
We will follow the work of van der Ziel to derive the channel noise [3]. Assume
that a thermal voltage noise source,vn, creates a drain noise current fluctuation,∆Id,
along the distributed channel. This is shown in figure 2.10. The thermal noise source
can be written as
〈vnv∗n〉 =4kT
g(V )(2.6.34)
46
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
Similar to equation 2.6.23, we can write an expression for the drain current fluctua-
tions:
∆Id = g(V )dV
dx+ vng(V ) (2.6.35)
with V = Vx + ∆V (x, t). Separating the derivative and integrating gives
∫ L
0∆Iddx =
∫ L
0g(V )dV +
∫ L
0vng(V )dx (2.6.36)
An expression for the noise only is desired. If we consider the drain AC shorted, the
first term on the right of the equality in equation 2.6.36 will be zero. Continuing we
have
∆IdL =∫ L
0vng(V )dx (2.6.37)
Taking the spectral density we have
〈∆Id∆I∗d〉 =1
L2
∫ L
0〈vnv∗n〉 g2(V )dx =
4kT
L2
∫ L
0g(V )dx (2.6.38)
with the use of equation 2.6.35. The variable being integrated over,x, can be changed
to V through the use of equation 2.6.23. It is rearranged here as
dx =g(V )
IddV (2.6.39)
g(V)
Vx(x) + ∆Vx(x,t)
+_
Vx(x+∆x) + ∆Vx(x+∆x,t)
Id + ∆Id(t)Vn
+_ +_... ...
Figure 2.10: Cartoon used for deriving the channel noise.
47
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
Substituting and changing the limits of integration we arrive at the following key equa-
tion:
〈∆Id∆I∗d〉 =⟨i2d⟩
=4kT
L2Id
∫ Vd
0g2(Vx)dVx (2.6.40)
It is now clear the usefulness of knowingId andg(Vx) explicitly. Combining equa-
tions 2.6.27, 2.6.29, and 2.6.40 leads to an expression for the noise
⟨i2d⟩
= 4kTgmΓ (2.6.41)
with
Γ =1 − Vd
Vg−Vt+
V 2d
3(Vg−Vt)2
1− 12
Vd
Vg−Vt
(2.6.42)
When the device saturates, the value ofVd that saturates the current is used in
equation 2.6.42 instead of the value past saturation. Equation 2.6.42 then becomes
Γ = 2/3. A plot of Γ for different gate and drain biasings is in figure 2.11. A thresh-
old voltage of -6 V has been assumed. It can be inferred from this graph that a device
operating in the linear region has a largerΓ.
One final note: while there was no evidence of hot electron effects in devices pre-
sented in this chapter, van der Ziel mentions that they will change the expected noise.
Instead of equation 2.6.40, the following equation would have to be used [3]
⟨i2d⟩
=4kT
L2Id
∫ Vd
0Te(x)g(Vx)
2dVx (2.6.43)
Te is the effective electron temperature. He gives an empirical relationship for it in
48
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
0 1 2 3 4 5 6 7 80.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Vds (V)
Γ Decreasing Vg
Vg=0
Vg=-6
Figure 2.11: Variation inΓ for different drain and gate voltages. The gate voltage isvaried from -6 to 0 V by steps of 1 V. The threshold voltage is -6 V.
terms of the electric field relative to the critical field value:
Te(x) =(1 +
E
Ecrit
)n(2.6.44)
n is either 0, 1, or 2. If it is zero, then we have equation 2.6.40. This leads to values of
Γ a few times 1 (as opposed to less than 1 when n = 0).
2.6.4 Noise Parameter Scaling
To the above model, scaling can be added for varying gate width and number of gate
fingers. Simple linear scaling based on a starting device width of 150µm and 1 gate
finger was performed. This allows prediction for a comfortable range of usable gate
49
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
fingers and widths, but will not be accurate for large devices (1 mm or greater). Based
on [34], the following equations can be used to scale the small-signal parameters:
The parameters labeled asnew, are the values to be determined based on the un-
scaled extracted values, theold parameters.n is the number of gate fingers. The
simulated noise parameters versus gate width for a single fingered device are in fig-
ure 2.12. With increasing unity-gate width, the noise increases. However, the mag-
nitude of the optimal match decreases, which may make matching simpler. Also, the
noise resistance drops, making a design more robust in terms of the expected noise.
These predicted results agree with measurements in [17]. At small gate widths,Rs
andRi will be large and keep a lower bound on NFmin (not shown in figure 2.12).
The noise increases with a wider gate finger because of increasing gate resistance and
gate leakage current (Fα Igs, R2g in equation 2.6.16). So as the width increases, NFmin
goes from being limited byRs andRi to Rg andIgs. The noise parameters are also
simulated against number of gate fingers in figure 2.13. Due to layout constraints and
considerations for symmetric designs (particularly CPW implementations), the gate
50
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
0 200 400 6000.8
1
1.2
1.4
1.6
Gate Width (µm)
NF
min
(dB
)
0 200 400 6000.4
0.6
0.8
1
Gate Width (µm)
|Γo
pt|
0 200 400 6000
10
20
30
40
Gate Width (µm)
Ph
as
eΓ o
pt
[deg
.]
0 200 400 6000
2
4
6
Gate Width (µm)
r n
(a) (b)
(c) (d)
Figure 2.12: (a) Minimum noise figure, (b) magnitude and (d) phase of optimumsource reflection, and noise resistance (c) all versus total gate width. Simulation fre-quency is 5 GHz.
finger number was kept to even values or a single gate. The total gate width is kept
constant at 150µm. A change in this parameter for small devices does little to affect
the match or the noise resistance. In going from one to two gate fingers, there is a
slight improvement in noise figure. This can be explained solely by an improvement
in gate resistance. Beyond two fingers, there is little additional benefit. These scaling
51
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
results will be used in§ 3.5.4 and§ 3.5.5.
Therefore, the best geometry is a smaller total gate width, to keepRg andIgs from
becoming to large, and two or four gate fingers. Too small a device, andRs andRi
will be too large. Many papers published for best NFmin performance typically have
device widths of∼100µm .
0 2 4 6 8 100.85
0.9
0.95
1
Gate Fingers
NF
min
(dB
)
0 2 4 6 8 100.76
0.77
0.78
0.79
0.8
Gate Fingers
|Γo
pt|
0 2 4 6 8 1014
15
16
17
18
Gate Fingers
Ph
as
eΓ o
pt
(de
gre
es)
0 2 4 6 8 100.7
0.72
0.74
0.76
0.78
0.8
Gate Fingers
r n
(a) (b)
(c) (d)
Figure 2.13: (a) Minimum noise figure, (b) magnitude and (d) phase of optimumsource reflection, and noise resistance (c) all versus number of gate fingers for a con-stant total gate width.
52
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
2.6.5 Discussion of the Model
The model is now checked against measurements, compared to the other noise mod-
els, and its limitations are discussed. Figure 2.14 shows noise parameter data for the
35% device of table 2.1 and prediction using the model in Matlab and a circuit simula-
tion. The fit forall four parametersis very good for both the small-signal simulation
and the equations entered into Matlab. The small-signal simulation using ADS is for a
4 6 8 10 120.5
1
1.5
2
2.5
Frequency (GHz)
NF
min
(d
B)
4 6 8 10 120.55
0.6
0.65
0.7
0.75
0.8
Frequency (GHz)
|Γo
pt|
4 6 8 10 1210
20
30
40
50
60
Frequency (GHz)
An
gle
Γo
pt (
Deg
ress
)
4 6 8 10 120.5
0.6
0.7
0.8
0.9
1
Frequency (GHz)
r n
Figure 2.14: Noise parameters predicted using the model (solid line) and in a fullsmall-signal circuit simulation (dotted line) compared to measurements (crosses). Thesmall-signal parameters are from table 2.1.
53
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
full small-signal model (includingCgd) and noise sources as in figure 2.7. The phase
match ofΓopt with the Matlab script could be further improved by including the gate
inductance. Only the small-signal parameters and gate leakage were needed for the
Matlab script. The measured noise parameters were not needed beforehand as with
the Pospieszalski and CN models. This predictive power can help in better designs of
noise performance for devices, accurate estimations of the noise and the match to the
device, and understanding differences in noise performance for devices as performed
in chapter 3.
Of interest is how much different noise sources contribute to the overall noise figure.
This is presented in figure 2.15 using the model at an optimal bias for noise perfor-
mance. The channel thermal noise accounts for half the contribution to noise figure.
The resistances contribute roughly in proportion to their values relative to one another
as one might expect; they are all lumped together at the input. However,Rs effectively
degrades thegm andCgs through source degeneration and should be minimized. The
gate leakage contributes about 10% for a device with a reasonably low amount of gate
leakage. This can be a much larger contributer, and will be discussed in§ 3.5.4.
Some insightful parallels can be drawn between this modeling (equations 2.6.16,
2.6.20, 2.6.21 and 2.6.22), and Pospieszalski’s model (equations 2.5.11, 2.5.12, 2.5.13,
and 2.5.14). The simplest to see is thatXopt is the same for both models if the gate
leakage tends to zero. If the gate leakage is negligible, then the reactance of the match
54
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
53%
11%
Ri 18%
Rg 7%
Rs 11%
DrainNoise
GateShotNoise
Figure 2.15: Relative contributions of different noise sources to the overall noisefigure.
reduces to that predicted by both Pospieszalski and Fukui. Not as easy to see is that
Ropt is of similar form for both models ifb→ 0. The other two parameters cannot be
compared so easily. However, the modeledRn for both show that it increases slightly
with increasing frequency and both predict thatFmin depends on the square of the
frequency (which will be linear in plots of NFmin vs. frequency).
All the noise models discussed so far have a noise source at the gate and drain.
Table 2.3 shows typical input and output noise currents for the models. All the models
predict relatively the same magnitude of output noise. The models with correlation
show an input noise similar to one another, but two orders of magnitude smaller than
what Pospieszalski or this work predicts. This means that the cross-correlation terms
55
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
(see, for example, equation 2.6.14) generate more noise than the gate noise. That
the model introduced here generates noise similar to that of Pospieszalski helps to
reinforce its validity.
Model: van der Ziel Pucel Pospieszalski This Work
〈iinput〉2(10−24 A2
Hz
)5.0 7.2 3100 1370
〈ioutput〉2(10−24 A2
Hz
)490 480 300 490
Table 2.3: Comparison of the various noise models’ input and output noise currents.
The model can help in predicting NF, but it has its limitations. The most important
is the modeling fails when the gain drops because it does not take into accountCgd
or self-heating effects. This means it fails at frequencies close tofτ (f > fτ/2) and
at high DC biasings (Ids > 40 mA). A derivation withCgd was undertaken, but no
closed form solutions could be found for the noise parameters and the equations were
too complicated to yield insight. It is possible that the gain could be corrected using
the Miller effect [31].
Also, the small-signal parameters must be accurately known. The parasitics re-
sistances need to be correctly modeled and the measured S-parameters must be as
accurate as possible. For example, the modeling was found to be poor when superior
network analyzer was substituted with a less accurate network analyzer.
56
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
2.7 Summary
This chapter lead up to the presentation of a noise figure model that does not need
prior noise parameter measurements for accurate prediction. It will be used in other
parts of this work. All necessary background leading up to it was introduced, its
derivation presented in full, the model’s strengths and weakness explained, and how it
compares to the other popular noise models discussed.
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[32] F. Danneville, H. Happy, G. Dambrine, J.-M. Belquin, and A. Cappy, “Microscop-ice Noise Modeling and Macroscopic Noise Models: How Good a Connection?”IEEE Trans. Electron Devices, vol. 41, no. 5, pp. 779–786, May 1994.
[33] M. Shur,Physics of Semiconductor Devices. Prentice Hall, 1990.
[34] J. M. Golio, Ed.,Microwave MESFETs and HEMTs. Norwood, MA: ArtechHouse, Inc., 1991.
59
3Noise Figure Measurements and Studies
3.1 Introduction
WITH the frame work for noise figure laid in the previous section, we now
concentrate on noise figure measurements of AlGaN/GaN HEMTs. The
technology used to fabricated the devices is presented first. The setup used for the
measurements will be discussed, and the methodology used for comparisons explained.
The bulk of this chapter is devoted to several noise figure studies of AlGaN HEMTs.
These studies look at how different epitaxial material and device structures affect the
noise figure performance. The effect of a field plate (FP) and gate leakage on noise
figure are profound, and will be covered in§ 3.5.4 and§ 3.5.5. The modeling devel-
oped in the previous chapter is used to understand how a FP and gate leakage affect
the noise performance. Another interesting type of GaN HEMT, known as a thick cap
HEMT, was measured and will be briefly covered. It is of great interest to know about
the state-of-the-art of GaN HEMT noise performance and how it compares to HEMTs
in GaAs and Si material systems. This is done in§ 3.6
60
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
3.2 Device Details
Devices from several samples with different epitaxial structures will be discussed,
but they are similar from growth and processing points of view. The devices were
all grown by metal-organic chemical vapor deposition (MOCVD) on both c-plane
sapphire and c-plane 4H-SiC substrates. The epitaxial structures that will most com-
monly appear in this work are in figure 3.1, which will be referenced throughout the
chapter. The key differences in the samples are choice of substrate (sapphire or SiC)
and inclusion of an AlN interlayer between the AlGaN barrier and the GaN channel.
29 nm 27% AlGaN: Si
1700 nm UID GaN
65 nm AlN
750 nm GaN: Fe
Sapphire Substrate
(a)
29 nm 35% AlGaN: Si
0.6 nm AlN
1700 nm UID GaN
65 nm AlN
750 nm GaN: Fe
Sapphire Substrate
(b)
29 nm 27% AlGaN: Si
1300 nm UID GaN
300 nm GaN: Fe
160 nm AlN
SiC Substrate
(c)
Figure 3.1: Typical epitaxial structure for the devices in this work: (a) standard HEMTon a sapphire substrate (b) HEMT with AlN interlayer (c) standard HEMT on silicon-carbide substrate
After choice of substrate, growth consists of a nucleation layer. This layer may in-
clude iron (Fe, an accepter) in it, as in figure 3.1 (a), to reduce the buffer conductive
(caused by unintentional doping). The decrease in conductivity improves the break-
down of the device for power applications. An unintentionally doped GaN layer grown
61
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
next will be the channel, and a 29 nm AlGaN Si-doped layer finishes the structure. The
Al composition varies with the sample, but is 27 % if not stated explicity.
Device processing began with Ti/Al/Ni/Au electron beam evaporated source and
drain contacts. These were annealed at 870C for 30 s in a rapid thermal annealer
(RTA). Device isolation was achieved by reactive ion etching (RIE) in Cl2. Stepper
photolithography Ni/Au/Ni gates were electron beam evaporated with a gate length of
0.7µm. SiN passivation was achieved with plasma-enhanced chemical vapor deposi-
tion (PECVD). If a field plate is used, it would now be added as a repeated and slightly
shifted gate metal layer. All devices in this chapter have a gate width of 1x150µm,
a gate-source spacing of 0.7µm, and a gate-drain spacing of 2µm. The pads are a
coplanar waveguide (CPW) layout.
Typical measurements of fτ and fmax are 23 and 47 GHz respectively. Contact
resistance is from 0.3 to 0.6Ω–mm. Charge and mobility vary with the Al composition
of the barrier. For compositions ranging from 15 % to 35 %, the mobility was found
to be 1100-1565 cm2/Vs and the charge 0.4-1.3x1013 cm−2 by Hall measurements.
More details about the device details and processing can be found in [1–4].
3.3 Noise Figure Measurement Setup and Method
Noise figure measurements were performed with a PC–controlled source–pull noise
figure setup. A schematic is in figure 3.2. At the heart of the system is the noise figure
62
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
NoiseSource
SourceTuner
LoadTuner
RF ProbeStation
Computer
TunerController
BiasController
NetworkAnalyzer
NoiseFigureMeter
BNCCable
Bias-TBias-T
RFSwitch
RFSwitch
GPIBCable
Figure 3.2: Schematic of the source-pull noise figure setup.
meter, noise source, and source tuner. The HP 8970S noise-figure meter system con-
sists of the HP 8970B noise figure meter, HP 8970C test set, and a signal generator
that acts as a local oscillator for the 8970C. Typical error is±0.15 dB. To find the de-
vice minimum noise figure, a variable source impedance is generated by a Maury Mi-
crowave MT982A02 mechanical motorized tuner. The load tuner was set to 50Ω. The
device gain during measurement could have been improved by moving the load tuner
63
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
to a small-signal match, but due to a combination of hardware and software problems
better measurements were obtained with it at the reference impedance. However, the
software automatically calculates the gain for a noise input match and power output
match.
The device S-parameters at each bias are needed. A Maury Microwave MT998C
RF switch box and an HP 8722D vector network analyzer (VNA) made it possible to
seamlessly switch between noise and S-parameter measurements of devices. All mea-
surements were performed on-wafer with Cascade-Microtech ACP40 ground-signal-
ground CPW probes. The bias was set automatically by an HP 6625A DC–power
supply system. All components were controlled over a general-purpose interface bus
(GPIB) by a Maury Microwave proprietary software program which calculates the
noise parameters.
The accuracy of the system was checked in two ways. The first was by measur-
ing devices that were characterized elsewhere. The second was fabrication of CPW
on-wafer 10 dB attenuators alongside devices and circuits. The schematic and a pho-
tograph of the attenuator are in figure 3.3. Figure 3.3 (c) shows the measured loss and
minimum noise figure (NFmin). A passive device’s loss and NFmin will be the same in
decimals. As can be seen, the agreement is good.
To make NF comparisons, several factors need to be taken into consideration. First,
devices across a GaN wafer are not uniform due to the quality of research-grade mate-
64
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
In
Out
GroundGround
R1
R1
2R22R2
4 5 6 7 8 9 10 11 12 13 14 159
9.2
9.4
9.6
9.8
10
10.2
10.4
10.6
10.8
11
dB
Frequency (GHz)
NFmin
Loss
R1R1
R2
In Out
(a)
(b) (c)
Figure 3.3: Coplanar waveguide attenuator (a) schematic, (b) photograph, and (c)measured loss and minimum noise figure against frequency.
0 20 40 60 80 100 120 140
1.3
1.4
1.5
1.6
1.7
1.8
1.9
F
(un
itle
ss)
Current (mA)
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
(1/G
Hz)
F
1/fτ1/fmax
0 20 40 60 80 100 120 140
1.2
1.4
1.6
1.8
2.0
2.2
F
(un
itle
ss)
Current (mA)
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
(1/G
Hz)
F
1/fτ1/fmax
Figure 3.4: Noisefactor, fτ and fmax for devices from different samples versuscurrent.
65
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
rial and growth reactors. These variations across a sample cause changes in the device
small-signal parameters and therefore in the fτ and fmax . Noise has a relationship to
fτ and fmax such that improvements in one of the quantities usually means an improve-
ment in the others. Figure 3.4 helps this argument. Here the inverse of fτ , inverse of
fmax, and noise factor, F (NF = 10 log10(F)), are plotted for devices from two samples
as the drain-source current is changed. As the current increases, all three parameters
increase. There appears to be a close relationship between F and 1/fmax. This relation-
ship can be seen from the modeling in the previous chapter. fτ and fmax are usually
defined as
fτ =gm
Cgs + Cgd(3.3.1)
fmax = fτ
√Rds
4(Ri +Rg)(3.3.2)
Examining the last term in equation 2.6.16, we see a factor 1/ω2tau that is very similar
to equation 3.3.1. An exact instance of fmax is not seen in equation 2.6.16 (there is no
Rds), but there is some similarity. The use of source degeneration, as demonstrated in
§ 2.6.1, modifiesCgs andgm. This would affect fτ , fmax, and thus NFmin. That NFmin
would depend on fmax instead of fτ also makes sense from a power argument: noise
figure and fmax are based on power quantities while fτ is a current gain quantity. The
conclusion of this aside is that devices with similar fτ and fmax should have similar
noise.
Device geometry is also important when making comparisons. As seen in§ 2.6.4,
66
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
a wider device has a larger NFmin. Also, a device of smaller gate length usually has
better fτ and fmax. For a fair comparison then, only devices of the same geometry
should be compared.
Finally, there is the matter of device bias. As the DC bias to the transistor is changed
the noise parameters also change. The optimum bias for NFmin may change with
devices from different samples. In all measurements in this work, the bias is swept
twice, firstVds thenIds, to find the best NFmin performance possible for the device.
It is better to sweepIds thanVgs as the threshold voltage changes across a sample.
The transistor’s noise parameters were then measured versus frequency at this bias. It
should be noted that the best bias for noise may not be the same as that of fmax, but it
is a good starting value.
To show the importance of having similar devices to NF, Rs, Ri, and Cgs variations
were simulated over the range of extracted values and entered into the model of chap-
ter 2. The results of this are in figure 3.5. Each parameter spans a change of NFmin of
0.2 to 0.3 dB. All measurements in this work are at a bias and source-impedance for the
best NFmin attainable from the device. For measurements versus bias, a frequency was
used that gave the most stable and repeatable measurement (usually 5 GHz, sometimes
10 GHz). As the bias was changed, S-parameters were re-measured and the optimum
source-impedance re-evaluated. When comparing devices from different samples, fτ
and fmax measurements were first performed to find devices with similar performance.
67
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
3 4 5 6 7 8 9 10 11 12
1.7
1.8
1.9
2.0
2.1
2.2
NF
min
(dB
)
Ri
Rs
Resistance (Ω)
0.20 0.21 0.22 0.23 0.24 0.25
Capacitance (pF)
Cgs
Figure 3.5: Variation in expected minimum noise figure with changes in three small-signal parameters.
3.4 Bias Dependence
Transistors in Low Noise Amplifiers (LNA) are biased at low currents and voltages
for maximum NF performance and to reduce power consumption. A GaN HEMT
biased at a “low” bias is likely beyond the breakdown of other material technologies.
Therefore, it is of interest to know how the noise parameters change with device bias,
which leads to some interesting results in this work. Also, knowing how the noise
changes with bias is necessary for noise sources extracted from NF measurements
that are included in device circuit simulations for oscillator phase noise.
Figure 3.6 displays all four noise parameters, the associated gain, and maximum
gain at a frequency of 10 GHz for drain-source voltages,Vds, 2 to 20 V. The drain-
68
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
Figure 3.6: Change in noise parameters with drain-source voltage at 10 GHz: (a)Minimum noise figure (b) magnitude and phase of optimum reflection coefficient (c)noise resistance (d) device associated and maximum gains.
69
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
source current,Ids, is kept constant at the best bias for NFmin. The small-signal asso-
ciated power gain is that available when the input is matched for noise and the output
for power. The maximum gain is of a small-signal input and output conjugate match.
NFmin flattens out aboveVds ∼3 V. The other noise parameters are nearly flat, except
for the phase which decreases slightly. This is probably from a slight change inCgd
with Vgd. From these measurements, it can be concluded that once the device saturates
the noise parameters can be considered constant.
What is more interesting is how the noise parameters change with the drain-source
current. The measured noise parameters of this are the solid circles in figure 3.7
for a sample with a sapphire substrate and 35 % Al in the barrier at a measurement
frequency of 5 GHz. Now we find that NFmin andrn increase with current. NFmin does
not increase because of a large increase in device noise. The reason is that the gain
drops with the increasing current. The gain is lower because the channel is opened
(loss of transconductance) and self-heating (from the high currents involved). That
the gain affects the noise figure directly is seen in equation 2.6.9. The magnitude
of the optimum source reflection coefficient,Γopt, decreases with increasing current
while its phase decreases. This is a result of the match changing with loss of gain and
increasingCgs.
To further investigate the usefulness of the Pospieszalski and CN models, they
were applied to these noise measurements. Measurements of fτ and fmax (needed
70
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
(a) (b)
(c) (d)
Figure 3.7: Typical plots of the noise parameters versus drain source current as mea-sured (circles) and using the Pospieszalski (dash-dot line) and CN (solid line) models:(a) Minimum noise figure (b) magnitude of optimum reflection coefficient (c) noiseresistance (d) and phase of optimum reflection coefficient. Measurement frequency is5 GHz.
71
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
for Pospieszalski’s formulation) and extracted small-signal parameters were collected
at each bias the noise parameters were measured at in figure 3.7. Then, using meth-
ods in§ 2.5, a small-signal model with noise sources from either Pospieszalski’s or
the CN formulation were created in ADS. ADS was then used to simulate the noise
parameters. The results were added to figure 3.7. The solid lines are simulations us-
ing the CN model and the dash-dot lines using the Pospieszalski model. Both models
predict the noise parameters for the GaN HEMT versus bias well and can be used for
bias-dependent noise parameter modeling of GaN HEMTs.
The modeling in§ 2.6 does not work to predict the noise parameters versus bias.
It only works at low biasings (Ids < ∼40 mA in this work) because it does not take
into account reduction in gain from self-heating. Because the Pospieszalski and CN
models are fitting to the data at these high biases, they predict the noise parameters
correctly. However, the model can still be used to explain trends seen in the noise
parameters versus bias. Equation 2.6.22 shows that as NFmin increases and|Γopt|
decreases with increasing current, thenRn should increase as well.
Figure 3.8 shows how the noise variables used for the simulations in figure 3.7
change with bias. These variables are the quantitative values of noise sources entered
in a circuit simulator, such as ADS. For example: shot noise changes with DC cur-
rent, thermal noise changes with resistance, and a Pospieszalski thermal noise source
changes with the noise temperature. We see in figure 3.8 (a) that the correlation coef-
72
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
(a)
(c)
(b)
Figure 3.8: Noise variables for the Pospieszalski and a CN noise model versus drainsource current: (a) magnitude and phase of the correlation coefficient and (b) gate anddrain noise for a CN model. The devicegm, multiplied by a factor of 10 to better fitthe scale, is also in (b). (c) Drain and gate noise temperatures of the Pospieszalskimodel for varying current.
ficient magnitude and phase are relatively flat versus current. This supports the work
of S. Lee on GaN HEMTs [5,6]. After detailed analysis using the CN model, Lee con-
cluded that the correlation coefficient could be considered constant with a magnitude
73
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
of 0.7 and phase of 90 after de-embedding extrinsic thermal and shot noise. Here,
we see the same magnitude but a slightly higher phase. The increase in phase is likely
from the shot noise of the gate leakage. While Lee’s results were only versus fre-
quency, we see here that it holds versus bias as well. To the author’s knowledge, there
is no reference in the GaN literature that has the noise variables using the CN model
versus bias. We might expect the input and output noise currents in figure 3.8 (b) to
behave as van der Ziel predicts in equations 2.5.1 and 2.5.2. Then the drain noise,
〈i2d〉, should follow changes ingm versus bias. Ten times the value ofgm (for the con-
venience of plotting) is also in figure 3.8 (b).〈i2d〉 appears to follow the same trend.
The gate noise,⟨i2g⟩, also seems to follow what van der Ziel would predict (aC2
gs/gm
dependence).
Turning to the Pospieszalski model in figure 3.8 (c), the two noise temperatures are
plotted againstIds. The gate noise temperature is relatively flat. This agrees with the
one GaN reference in the literature [7], and what is seen in GaAs HEMTs. Here, the
drain noise temperature drops. This is the opposite of what would be expected but is
easily explained. The sapphire sample the device was on did not have a good buffer,
makingRds low (less than 1 kΩ instead of∼1.5 kΩ). As the current increased,Rds
dropped off dramatically (900Ω to 100Ω). The termTd/Rds is prevalent through
Pospieszalski’s equations. In fitting to the data,Td decreased along withRds to keep
the correct proportion. In other samples with a good buffer (only a slight drop inRds),
74
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
Td will increase.
3.5 GaN HEMT Noise Figure Studies
3.5.1 Substrate
The effect of substrate on the noise parameters was carried out on samples with
SiC and sapphire substrates having 25% Al in the barrier and structures similar to
figure 3.1 (a) and (c). Versus frequency, devices from both samples had very similar
Figure 3.9: Minimum noise figure, small signal associated and maximum gain fordevices on sapphire and SiC substrates.
75
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
noise parameters. As the current was varied, a difference in performance of NFmin
emerged. Figure 3.9 shows that the sapphire sample had worse noise figure perfor-
mance at higher biasings. At 100 mA, the difference is more than 0.5 dB. Also plotted
are the associated and max gains for both devices shown. The sapphire sample gains
fall much quicker as the bias increases. As stated earlier, if the gain drops then the
noise figure will too. Devices on sapphire have degraded power performance at high
biasings because of self-heating. Here, we see it affects noise figure performance as
well. A previous study confirms the noise degradation is caused by self-heating with
temperature dependent measurements [8].
3.5.2 Al Composition in the Barrier
To investigate if changing the Al composition in the AlGaN barrier had an effect
on noise, four samples were grown with 15%, 25%, 27%, and 35% Al on a sapphire
substrate. The rest of the structure for all four samples was the same as in figure 3.1 (a).
Lu previously published this study for GaN HEMTs [9]. He found that devices of high
Al composition (35 %) had better noise performance than low Al composition (15 %).
However, the reported fτ and fmax for the samples were not similar. fτ increased with
higher Al composition from 25 GHz to 50 GHz and fmax increased from 55 GHz to
101 GHz. The four samples in this study had reasonably similar fτ and fmax. Noise
parameters of the four samples for changing frequency are plotted in figure 3.10. Also,
76
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
3 4 5 6 7 8 9 10 11 12 13
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
3 4 5 6 7 8 9 10 11 12 130.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
3 4 5 6 7 8 9 10 11 12 136
8
10
12
14
16
(b)(a)
35% 27% 25% 15%
NF
min
Frequency (GHz)
(d)
r n
Frequency (GHz)
4 6 8 10 120.0
0.2
0.4
0.6
0.8
1.0
Frequency (GHz)
|Γ|
0
20
40
60
80
100
120
140
160
180
35% 27% 25% 15%
Ph
as
e
Γ
(De
gre
es)
(c)
Ga
in
(dB
)
Frequency (GHz)
Figure 3.10: Noise parameters versus frequency for devices of different aluminumcomposition in the barrier: (a) Minimum noise figure (b) magnitude and phase ofoptimum reflection coefficient (c) noise resistance (d) device associated gain.
77
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
0 20 40 60 80 100 120 140
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
NF
min
(dB
)
Current (mA)
35% 27% 25% 15%
Figure 3.11: Minimum noise figure of samples with different aluminum compositionin the barrier at varying drain-source current.
NFmin for the samples versusIds are in figure 3.11. The data are astonishingly similar
for noise measurements, and challenge the previous report. The application of the CN
and Pospieszalski models to these devices, presented earlier in table 2.2, also agrees
that the noise parameters should be very similar. It is interesting that the drain-source
current bias for best NFmin was similar for the different samples (15±5mA). For the
15 % Al sample this was nearly halfIds,sat while only 8 % Ids,sat for the 35 % Al
sample.
3.5.3 AlN Interlayer
The addition of an extremely thin (one or two monolayers) AlN layer between the
GaN channel and the AlGaN barrier has been found to increase the conduction-band
78
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
0 20 40 60 80 100 120 140
1.0
1.5
2.0
2.5
3.0
3.5
4.0
NF
min
(d
B)
Current (mA)
NFmin
AlN NF
min no AlN
fτ AlN
fτ no AlN
fmax
AlN f
max no AlN
0
5
10
15
20
25
30
35
40
45
F
req
ue
nc
y
(GH
z)
Figure 3.12: Minimum noise figure, fτ , andfmax versus drain-source current for asample with (squares) and without (circles) an AlN interlayer.
offset, better confining the 2-DEG and improving mobility [10]. This should improve
the device fτ and fmax. It is therefore worth determining if it improves the noise
performance as well. Samples with structures as in figure 3.1 (a) and (b) with 35%
Al in the barrier on sapphire substrates were measured for noise. Overall, devices on
the sample with the AlN-interlayer had fτ and fmax values marginally higher than the
sample without. However, for the noise measurements devices with as similar of fτ
and fmax as could be found were used.
There were no differences in the noise parameters versus frequency, but as the drain
current increased a large difference in NFmin was apparent. This is in figure 3.12 as
the solid symbols. At a current of 100 mA, there is a 0.4 dB difference and at the
79
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
0 10 20 30 40 50 60 70 80 90
6
8
10
12
14
16
18
20
22
24
26
with AlN interlayer without AlN
Rs
(Ω)
Current (mA)0 20 40 60 80 100 120 140
2
4
6
8
10
12
14
16
Gain AlN layer Gain no AlN Gmax AlN layer Gmax no AlN
(dB
)
Current (mA)
(a) (b)
Figure 3.13: (a) Associated and maximum gain and (b) source resistance for deviceswith and without an AlN interlayer at different applied currents.
max current a 0.8 dB difference. While the gain (figure 3.13 (a)), fτ , and fmax (also
in figure 3.12) do drop off slightly faster for the sample without the AlN, it is not as
dramatic as the sapphire/SiC substrate comparison and not enough to explain such a
large NFmin difference.
Rs appears to be the cause of the difference. Palacios has shown thatRs increases
drastically with drain-source current [11]. Figure 3.13 (b) shows the measured source
resistance (using the method in [11]) for devices from both samples. The devices with
the AlN-interlayer see anRs increase of about two times, while the devices without
the interlayer see an increase of three times. TheseRs measurements are only out to
80 mA (equipment limitations), instead of 135 mA as in figure 3.12. The difference
in Rs would be even larger at higher biases. As seen with the modeling using source-
degeneration in chapter 2,Rs can be thought of as directly adding noise at the input,
80
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
which increases the noise.
As mentioned, devices on the sample with the AlN-interlayer overall tend to have
higher fτ and fmax. These devices will have a slightly better NFmin. However, the
improvement is at best 0.1 dB in the X-band.
3.5.4 Gate Leakage
While trying to do a comparative study, devices from a sample (27% Al content
barrier with SiC substrate) that had similar fτ and fmax did not have similar NFmin.
In fact, NFmin differed by almost 1 dB despite the gains being identical as seen in
figure 3.14. It was realized that the gate leakage was very different for the three devices
in figure 3.14. The three terminal gate leakage, Igs, at a bias of Ids = 10 mA, Vds = 5 V
for the devices was found to be: 22µA (or 140 µA/mm); 73 µA (or 486 µA/mm);
141µA (or 940µA/mm). The devices are labeled as such in figure 3.14. We see that
as the gate leakage increases, so does the noise figure. To explore how gate leakage
affects the noise parameters, the modeling in§ 2.6 was used. Small-signal parameters
that approximately matched all three devices in figure 3.14 were entered into Matlab
using the script in appendix B. The gate leakage was swept from10−8 to 10−2 A and
the calculated noise parameters plotted (as lines) in figure 3.15 with data (crosses) for
the devices in figure 3.14. The circles are data from another sample that exhibits an
expected amount of gate leakage. The agreement of simulation and data for NFmin
81
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
Figure 3.14: (a) Minimum noise figure, (b) device associated gain, and maximum gainversus frequency for devices with different gate leakage currents. The gate leakagequoted is at the same bias as the noise measurements (Ids = 10 mA, Vds = 5 V).
is excellent. The other parameters do not agree perfectly, but it should be reiterated
that the small-signal parameters used were typical for all three devices (they were not
identical). No change inrn was predicted or measured.
Gate leakage has a large effect on the noise parameters. It must be monitored, along
with fτ andfmax, when measuring noise figure of GaN devices. While gate leakage
and NFmin have been studied previously [6, 12–14], these studies are all lacking in
at least one of the following ways: use of fitting, inadequate data, only predicting
NFmin, or not applied to GaN. The combination of analytical modeling (without fitting
parameters), data presented, and agreement of modeling and data here is unique and
82
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
10-8
10 -7
10 -6
10 -5
10 -4
10 -3
10 -2
1
2
3
4
5
Igs
(A)
NF
min
(d
B)
10 -8
10 -7
10 -6
10 -5
10 -4
10 -3
10 -2
0
0.2
0.4
0.6
0.8
1
Igs
(A)
|Γo
pt|
10 -8
10 -7
10 -6
10 -5
10 -4
10 -3
10 -2
20
40
60
80
100
120
140
Igs
(A)
Ph
as
e Γ
op
t (d
eg
res
s)
10 -8
10 -7
10 -6
10 -5
10 -4
10 -3
10 -2
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
Igs
(A)
r n
(a) (b)
(c) (d)
Figure 3.15: Simulated (line) and measured (crosses) noise parameters for deviceswith different gate leakage currents: (a) Minimum noise figure (b) magnitude of op-timum reflection coefficient (c) noise resistance (d) phase of optimum reflection co-efficient. Frequency is 10 GHz. The circles are data from another sample with thetypically expected amount of gate leakage.
clear.
A final note: GaN HEMTs on MBE were measured by the author. Their power and
small-signal performance are comparable to MOCVD-based HEMTs, but the devices
had higher gate leakage and thus∼0.15 dB more noise.
83
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
3.5.5 Field-Plated Devices
The addition of a FP has led to GaN HEMTs having impressive power handling
capability at microwave frequencies [15, 16]. There is a penalty, which is shown in
figure 3.16.1 A FP increasesCgd, and that reduces fτ and fmax. In fact, the longer
the FP, the higher the breakdown and lower the fτ , fmax , and gain of the device. The
author decided to investigate the noise performance. Based on the studies presented
thus far, one would predict that a FP device would have worse NF performance.
0.0 0.2 0.4 0.6 0.8 1.0 1.2
15
20
25
30
35
40
45
50
55
60
fτ fmax
Fre
qu
en
cy
(G
Hz)
Field-Plate Length (µm)
Figure 3.16: fτ and fmax of devices with different field-plate lengths.
This turned out not to be the case. Figure 3.17 (a) demonstrates that as the FP
length increases the NFmin improves despite decreasing gain (Figure 3.17 (d)). The
1For all measurements in this section, the devices with different FP lengths are on the same die of asample.
84
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
4 6 8 100.8
1.0
1.2
1.4
1.6
1.8
4 6 8 10
0.4
0.6
0.8
1.0
1.2
4 6 8 10
4
6
8
10
12
14
1.1 µm 0.9 µm 0.7 µm 0.5 µm None
1.1 µm 0.9 µm 0.7 µm 0.5 µm None
NF
min
(d
B)
Frequency (GHz)4 6 8 10
0.0
0.2
0.4
0.6
0.8
(a)
(c)
Frequency (GHz)
20
40
60
80
100
120
140
160
180
Ph
as
e
Γ
(de
gre
e)
(d)
(b)
r n
Frequency (GHz)
Ga
in
(dB
)
Frequency (GHz)
|Γ|
Figure 3.17: Noise parameters versus frequency for devices with field plates of differ-ent length: (a) Minimum noise figure (b) magnitude and phase of optimum reflectioncoefficient (c) noise resistance (d) device gain when matched at the input for best noiseperformance and the output for power performance.
85
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
improvement is almost 0.2 dB. There is little additional improvement for a FP longer
than 0.9µm. The match changes monotonically with the FP in Figure 3.17 (b). The
improvement in NF with a FP was first reported by the author in [17] and was later
confirmed in [18].
Several explanations to understand this result were explored. The first was to look
at the gate leakage. It was thought that maybe the FP was reducing the electric field
and possibly the gate-drain contribution to gate leakage. The three and two-terminal
gate leakage of 100µm wide devices with different FP lengths was measured. Some
of the three-terminal measurements are in figure 3.18. The bias was set toVds 5 V
(similar to noise measurements) andVds 20 V (a low bias for power) andVgs a volt
past the threshold voltage. It does not appear that the FP lowers gate leakage. In fact,
it appears to increase slightly with the FP.
Another thought was that perhaps there was a difference in electric field causing a
change elsewhere than gate leakage. The analysis ofΓ in § 2.6.3 was examined to see
if it might change because of a FP. This proved to not be true. A change inΓ would
mean a change in the DC I–V characteristics of a FP from a non-FP device. The only
real change is that the knee voltage is better defined for a FP device [19]. That would
only causeΓ to go to its final value of 2/3 quicker. More proof that it was not the
electric field-profile was found by two other means. One was to look at NFmin versus
drain source voltage. No difference was apparent. Another was to run an ATLAS
86
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
100
200
300
400
500
600
700
, Vds
20 V, V
ds 5 V
Gate
L
eakag
e
(µA
)
Field-Plate Length (µm)
Figure 3.18: Typical change in gate leakage for devices of increasing field-platelength. Biasings areVds 5 V, Ids 10 mA andVds 20 V,Vgs one volt past threshold.
0.0 0.5 1.0 1.5 2.0 2.5
0.0
2.0M
4.0M
6.0M
Ele
ctr
ic
Fie
ld
(V/c
m)
Distance (µm)
no FP, Vds 5 V no FP, Vds 20 V FP, Vds 5 V FP, Vds 20 V
Figure 3.19: Electric field profile for a device with and without a FP at a bias ofVds 5and 20 V with the gate biased close toVt. The gray bars are the “physical lengths” ofthe gate and field plate. Atlas simulation provided by Yuvaraj Dora.
87
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
simulation and look at the difference in the electric field profile. This was done, and
the results are in figure 3.19.2 The simulations atVds 5 and 20 V show the total electric
field versus distance. The gate is biased close to the threshold voltage, as is the case
for best NFmin results. The bars sitting atop the x-axis represent the gate length (short)
and FP (long) lengths. While the peak electric field at the drain edge of the gate will
be significantly reduced when a HEMT is biased to 80 V or more, here for 5 and 20 V,
there is no difference. In fact, atVds 5 V, there is practically no change in the field.
The small-signal parameters were also examined. Those that were found to change
with a FP are in figure 3.20.Cgd increases because of the extra capacitance the FP
provides. ThatRgd decreases hints that it is either easier to chargeCgd or that the
leakage has increased the conductance between gate and drain.Rd decreases because
the effective distance between gate and drain is reduced by the length of the FP.Ri
does not appear to change. Any change in it is probably due to error in the small-signal
extraction having difficulty differentiatingRg andRi. As the gate now has another set
of fingers in parallel, its resistance, and thusRg, decreases. The FP and gate fingers
can be connected at their ends, further reducing gate resistance and the noise [20].
When trying to explain FP device NF performance, it was first thought thatRg was
the cause. However, the modeling at the time argued that the improvement inRg was
not enough to cause the difference, particularly for the results in [18]. It was later
realized the devices and the modeling were not the same. Devices of different widths,
2ATLAS simulation graciously provided by Yuvaraj Dora to the author’s specifications
88
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
0.0 0.2 0.4 0.6 0.8 1.0
0
10
20
30
40
50
60
70
0
10
20
30
40
50
60
70
R
gd
(Ω)
Cg
d
(fF
)
Field-Plate Length (µm)0.0 0.2 0.4 0.6 0.8 1.0
1
2
3
4
5
6
7
8
15
16
17
18
19
Rd Ri Rg
Re
sis
tan
ce
(Ω)
Field-Plate Length (µm)
Figure 3.20: Small-signal parameters that change with a field plate.
and with/without the FP plus gate ends shorted, were being compared. The scaling
and modeling of chapter 2 were used yet again. How NFmin changes with gate width
for devices with and without a FP were simulated in Matlab and compared to the
author’s and Wu’s [18] measurements. Figure 3.21 makes this clear. The agreement
is very good, and it can now be concluded that the FP lowering the gate resistance
is what improves NFmin. That NFmin decreases despite the lower gain is because the
FP is acting as an external feedback capacitance between gate and drain (in parallel
with Cgd). Lossless feedback does not harm the noise figure, but it does lower the
gain [21]).
The reduction in NF does not justify the use of a FP as it reduces the gain consider-
ably (several decibels). Gain is in short supply at microwave frequencies and reducing
it so much may not justify NFmin improvement of just a few tenths of a decimal. In
89
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
0 50 100 150 200 250 3000
0.5
1
1.5
2
2.5
3
Gate Width (µm)
NF
min
(d
B)
No FP
Long FP
Difference
Figure 3.21: Minimum noise figure versus gate width for devices with and without along field plate at a simulation frequency of 10 GHz. The difference between them, indecimals, is plotted as the dotted line. The “x’s” are from this work (150µm ) and Y.Wu (243µm ) [18].
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
NF
min
Field-Plate Length (µm)
4 GHz 7 GHz 10 GHz
Figure 3.22: Minimum noise figure of the field-plated devices at different measure-ment frequencies of 4, 7, and 10 GHz. As the frequency increases, the improvementfrom a field plate decreases.
90
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
addition, the benefit is reduced the higher the operating frequency because of the skin
effect on the gate resistance. This is demonstrated in figure 3.22. At 4 GHz, the im-
provement can be as much as 0.3 dB, but at 10 GHz the improvement is 0.1 dB. This
agrees with the results in [18].
3.5.6 Thick-Epitaxial Cap Devices
Shen has proposed a HEMT with a thick GaN cap on top of the AlGaN [22]. The
advantage of this structure is that a SiN passivation is not needed. As passivation
leads to problems of reliability for standard HEMTs, this new HEMT holds great
promise. It has the record for power performance without passivation. Its small-signal
characteristics are similar to standard HEMTs. Dr. Shen allowed the devices to be
measured for noise. The performance was similar versus frequency (in particular,
the gains), although the drain-source current needed to be higher for optimum noise
performance. The reason for this is clear after viewing the noise parameters versus
bias in figure 3.23. The cap devices have a NFmin optimum bias at 45 mA instead of
10 mA as seen with normal HEMTs.Rn and NFmin follow remarkably similar trends,
further reinforcing arguments made earlier in the chapter. NFmin for the thick cap is
much lower at higher biasings than a standard HEMT, but is higher at low biasings.
The reason for this is likely the large gate leakage the device has at a low bias (68µA
atIds 10 mA for a 150µm wide device). If the leakage can be controlled, these devices
91
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
0 20 40 60 80 1002.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
0 20 40 60 80 1000.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0 20 40 60 80 1004
6
8
10
12
14
16
18
Standard HEMT
Thick Cap
NF
min
(d
B)
Current (mA)0 20 40 60 80 100
0.0
0.2
0.4
0.6
0.8
1.0
(a)
(c)
Current (mA)
|Γ
|
0
20
40
60
80
100
120
140
160
180
Ph
as
e
Γ
(deg
ree
s)
(d)
(b)
r n
Current (mA)
Ga
in
(dB
)
Current (mA)
Figure 3.23: Noise parameters versus drain-source current of a thick cap device anda standard HEMT: (a) Minimum noise figure (b) magnitude and phase of optimumreflection coefficient (c) noise resistance (d) and associated gain. Measurement fre-quency is 10 GHz.
92
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
show great promise for noise performance.
3.6 Comparison of High-Performance GaN HEMTs toOther Material Systems
By now, the reader might have asked the question, “How does GaN HEMT noise
figure performance compare to other material systems?” This will now be addressed.
Most all the devices in this work have a gate length of 0.7µm due to equipment lim-
itations. It is hard to find published noise results in the literature at such a relatively
“long” gate length. In addition, many published noise figure results have large varia-
tions in the accuracy of their measurements.
Bearing this disclaimer in mind, 0.15µm gate-length devices optimized for high-
frequency performance were obtained from Tom´as Palacios. These devices are sim-
ilar to those in a recent publication that had an fτ of 150 GHz and fmax of over
200 GHz [23]. The measured NFmin against frequency is in figure 3.24 for two de-
vices. Repeated measurements at 10 GHz gave a consistent NFmin of 0.4 dB.
Keeping in mind this very good value, let us turn our attention to table 3.1. Here
we have an abundance of data on HEMTs from different material systems: GaN,
SiGe, InAlGaAs systems on GaAs and on InP. The gate lengths, gate widths, NFmin,
measurement frequency for NFmin, relevant information, and the reference number
found at the end of the chapter are all listed. Most obvious is that SiGe has some work
to do before its noise performance can be competitive with the other materials. InP
93
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
Lg (µm) Wg ( µm ) NFmin (dB) Freq. (GHz) Note Ref.
GaN HEMTs0.12 100 0.72 12 SiC substrate [24]0.15 150 0.4 10 T. Palacios, UCSB —0.15 200 0.6 10 SiC substrate [25]0.15 100 0.75 10 SiC substrate [26]0.17 100 1.1 10 Si substrate [27]0.18 100 0.7 12 Sapphire substrate [8]0.25 100 0.8 10 SiC sub., from graph [28]0.25 100 1.05 18 Sap., from graph [9]0.25 100 1.04 10 Sapphire substrate [29]0.25 200 1.9 10 SiC substrate [30]
Table 3.1: Minimum noise figure for HEMT devices in many technologies. Also listedare the gate length and width, measurement frequency, some necessary information,and the reference.
94
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
6 8 10 12 14 16
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
NF
min
(dB
)
Frequency (GHz)
Figure 3.24: Minimum noise figure of two 0.15µm gate length transistors providedby Tomas Palacios.
provides the best performance, but GaAs and GaN are close competition in the X-
band. GaAs might have slightly better performance than GaN, but a 0.1 dB advantage
can be lost once the device is put in a circuit.
3.7 Summary
This chapter looked at a plethora of noise figure measurements of GaN HEMTs.
The methodology for procedures was explained and its importance made clear. Fac-
tors that changed NFmin (such as an AlN-interlayer and choice of substrate) were in-
vestigated. The importance of monitoring gate leakage was found and analyzed with
the modeling in§ 2.6. The unexpected result of a FP improving NFmin was discovered
95
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
and fully investigated, also with the use of the modeling from§ 2.6.
Together with modeling from the previous chapter, this chapter helps point out ways
of obtaining the best NFmin possible. Most important is reducing the gate leakage and
parasitic resistances at the input.Rg andRs also need to be minimized. The small-
signal power gain needs to be kept as high as possible. Self-heating causes an increase
in NFmin because of loss of device gain.
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[39] M.-Y. Kao, K. Duh, P. Ho, and P.-C. Chao, “An Extremely Low-Noise InP-BasedHEMT with Silicon Nitride Passivation,”Electron Devices Meeting Technical Di-gest., International, pp. 907–910, Dec. 1994.
[40] M. Murti, J. Laskar, S. Nuttinck, S. Yoo, A. Raghavan, J. Bergman, J. Bautista,R. Lai, R. Grundbacher, M. Barsky, P. Chin, and P. Liu, “Temperature-DependentSmall-Signal and Noise Parameter Measurements and Modeling on InP HEMTs,”IEEE Trans. Microwave Theory Tech., vol. 48, no. 12, pp. 2579–2587, Dec. 2000.
[41] Y. Ando, A. Cappy, K. Marubashi, K. Onda, H. Miyamoto, and M. Kuzuhara,“Noise Parameter Modeling for InP-Based Pseudomorphic HEMTs,”IEEE Trans.Electron Devices, vol. 44, no. 9, pp. 1367–1374, Sept. 1997.
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[42] H. C. Duran, B.-U. H. Klepser, and W. Bachtold, “Low-Noise Properties of DryGate Recess Etched InP HEMT’s,”IEEE Electron Devices Lett., vol. 17, pp. 482–484, Oct. 1996.
100
4Low-Frequency Noise of GaN HEMTs
4.1 Introduction
IT is surprising that a subject that has been studied for almost 80 years would not be
well-understood. But such is the case of low-frequency noise (LFN), the largest
contributor to phase noise of oscillators [1]. The main motivation of this chapter is to
create a model for circuit simulation. Most of the LFN literature for GaN consists of
theoretical explorations of devices (in some studies, just films), or measurements at
very low device biasing not suitable for practical device modeling. GaN HEMT LFN
studies at biasings typical for circuits are presented in this chapter. A new empirical
model is also presented. It is difficult to make LFN comparisons, particularly to most
published works due to the many ways the data are presented, but measurements by
the author for both GaAs and GaN HEMTs will be examined. In addition to the above
topics, the LFN setup will be described in detail, as most LFN setups are either poorly
described in papers or cannot bias as high as is necessary for GaN HEMTs.
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
4.2 Review of Low-Frequency Noise
The terms LFN, flicker, 1/f, and generation-recombination (G-R) noise need clari-
fication. Flicker (also called 1/f) noise refers to phenomena that generate noise with a
slope inversely proportional to the frequency, hence “one on f.” A sample spectrum,
showing flicker noise and other contributions, is shown in figure 4.1. Resistors and
bulk material tend to be strictly 1/f, but devices, including HEMTs, deviate as 1/fγ
whereγ is usually in the range of 0.7 to 1.3. For GaN HEMTs, experiments showγ
to be between 1 and 1.3 [2–4]. Generation-recombination noise refers to trap-related
capture and emission of carriers creating a spectrum of the form
SX(f) =⟨4∆X2
⟩ τ
1 + ω2τ 2(4.2.1)
that is measured as noise at low frequencies. Here,τ is the trap life time,ω the angular
frequency, andX a quantity that fluctuates (usually charge or mobility). Sometimes
the G-R spectrum, which will have a Lorentzian power spectral density, manifests
itself as a “bulge” on a 1/f spectrum, shown in figure 4.1. There is also a theory, most
often credited to McWhorter [5],1 that a continuum of traps, with spectra of the form
in equation 4.2.1, of different life times is the source of the 1/f noise spectrum. This
model appears to work for CMOS [2], but it is not accepted for all device technologies.
Therefore, when referring to the noise at these low frequencies (less than∼10 MHz),
be it from g-r, 1/f, or other unknown sources, the expression LFN will be used.
1In truth, he did not create the concept but extended the theory.
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
1/f Reference Line
Frequency
Noise
Spectral
Density
(I2 or V2)G-R "Bulge"
1/fγ noise
Noise Floor
Corner Frequency
Noise spurs
(outside source/interference)
Figure 4.1: Sketch of the key features of low-frequency noise.
It has already been hinted that traps with energies in the material band-gap are
one source of LFN. There are other possible sources: surface effects (such as surface
states), the bulk material itself, dislocations, tunneling, non-uniform channel resis-
tance, quantum effects, and others. Evidence for trying to explain LFN from any one
of these possible sources can be found in the literature. It is likely due to a combination
of several sources and that there will never be a unifying 1/f model for all devices.
HEMTs show orders of magnitudes more LFN noise than bipolar junction-transistor
(BJT) types of devices. This suggests a surface area or high-field dependence. Early
GaN HEMTs and material showed much worse LFN noise than results reported later.
The excess in the LFN was attributed to traps and dislocations [3]. Leinshtein re-
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
ported [3] that GaN HEMTs had less LFN than observed in measurements of GaN
thin films, and suggested there was some suppression of LFN caused by the device.
Some types of LFN vary with the square of bias current, such as that of diodes. A
relationship that describes this, and that is used in circuit simulators is:
⟨i2g,1/f
⟩= Kf
IAf
DC
fFfe(4.2.2)
Kf , Af , andFfe are all fitting parameters,IDC is the DC current, andf is fre-
quency. For making theoretical comparisons of voltage, current, and resistance LFN
spectrums (SV (f), SI(f), andSR(f) respectively), the spectrum is often normalized
(SV (f)/V 2DC , SI(f)/I2
DC , andSR(f)/R2 respectively). These spectrums are related
through Ohm’s law, and lead to the question, “What’s really fluctuating and causing
1/f noise?” If it is the resistance (which for HEMTs, means the channel resistance),
it has been reasoned that it is because of changes in mobility or charge. Because the
resistance varies with the inverse of mobility and charge, fluctuations in one of these
two quantities generates 1/f noise (in theory at least). This has lead to the two ma-
jor principles on which most 1/f theories are based: carrier density fluctuation and
mobility fluctuation modeling. The former is used in the G-R model (equation 4.2.1)
discussed earlier. In fact, equation 4.2.1 can be used to describe both models. It is
debated whether charge or mobility fluctuations are the source of noise; data supports
both. These models have been applied to describe GaN HEMT LFN [2–4].
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
An interesting empirical relationship was proposed in 1969 by Hooge:
SI(f)
I2DC
=αHNf
(4.2.3)
where N is the number of carriers in the device andαH is a dimensionless quantity
known as the Hooge parameter. It has since been used to characterize many materials
and devices. It has also been used as a figure of merit and at times as a constant, such
as for characterizing 1/f noise of materials. However, according to Hooge himself, it
was not meant to be considered a constant [6].αH was extracted for measurements
that appear in this chapter. As seen in figure 4.2 (a) and (b),αH changes considerably,
even with frequency of extraction (not surprising as the noise is not strictly 1/f). That
αH is not constant can be seen from other published results as well [3]. Therefore,
the author believes it should not be used for device comparisons and only for material
comparisons.
It is the aim of this chapter to create a LFN model that can be used in the computer-
aided design (CAD) software program Advanced Design System (ADS) and to make
comparisons of LFN in HEMTs. The theory discussed so far is not applicable to
circuit modeling. There is not yet agreement in the theory, and data are generally
at low biasings or not even for HEMTs. At high biasings where the electric fields
are high, traps may no longer be the dominant source of LFN. There is little published
literature of LFN models of HEMTs for use in circuit simulators. Therefore, work was
started from scratch. A setup that could handle the biasings typical of GaN HEMTs
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
(a) (b)
Figure 4.2: Variation ofα with (a) drain-source voltage bias and (b) frequency ofextraction for two devices on the same sample.
was built. Measurements of bias-dependence and geometry were performed. Other
studies of LFN performance were performed as time permitted.
A final consideration is how to present the data. There is little consistency in units
and an astonishing number of different choices:A2/Hz, V 2/Hz, A/√Hz, V/
√Hz,
A2, V 2, nV/√Hz, input-referred versions of these and representations in dB or linear
formats. Sufficient information is not always presented in published articles to be
able to convert from one type of units to another. How the data is presented can also
give different results. For example, normalizingSI(f) by I2 gives a different trend
of noise versus gate width than not normalizing. The author decided that presenting
noise asA2/Hz would be most familiar and convenient for a circuit designer and for
comparison purposes.
More information about LFN can be found in [3, 7–9]. A very good and easy-to-
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
follow review can be found in [10]. The book edited by Balandin, [3], is a collection of
articles about noise in GaN including two that treat LFN of GaN HEMTs extensively.
4.3 Low-Frequency Noise Setup
It is hard to find a complete description for a LFN setup. Much time was spent
creating a satisfactory setup for GaN. Therefore, this section will explain what an ex-
perimentalist needs to know to create a setup. There are four main equipment concerns
for a LFN setup. The first is instrumentation to measure the power spectrum versus
frequency. The measurement range of interest is usually 10 Hz to 1 MHz (possibly
wider). Provided that a given spectrum analyzer can even measure such frequencies,
the LFN of the analyzer itself is usually larger than the device’s noise. Increased aver-
aging and reduction of the resolution bandwidth can help these problems; however, the
time for a single measurement becomes prohibitively long. Other instruments that can
be used include computer-controlled oscilloscopes (a long time sample is measured
and a FFT is then performed on a computer) and, the preferred tool, a dedicated FFT
instrument. An HP 3561A dynamic signal analyzer (DSA) is a dedicated instrument
for these types of measurements and was used in this work. It is part of the HP 3048
phase-noise system. The DSA noise floor was superior to other options available and
the HP 3048 software could automatically control it. However, the DSA could only
measure a maximum frequency of 100 kHz. Most measurements in this chapter were
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
preformed from 10 Hz to 100 kHz with∼300 points per decade.
Even with the DSA, the noise floor was not adequate for some measurements.
Therefore, the second equipment concern is the noise floor for which a low-noise
amplifier (LNA) is needed. A Stanford Research Systems SR560 LNA was used to
improve the noise floor. Its voltage gain was typically set to 40 dB (100 V/V, the
minimum to meet the instrument’s specified noise floor) and sometimes as high as
60 dB (for gate noise measurements). The HP3048 software could be adjusted for
the gain. The LNA was run off of internal lead-acid batteries while measuring. The
measured noise floor for the 3561A when its input was shorted is shown together with
the measured noise floor of the LNA (also shorted input) plus 3561A in figure 4.3. An
improvement of more than four orders of magnitude is seen. The measured noise floor
of the LNA in figure 4.3 is identical to its specifications.
The third equipment concern is biasing the device without interfering with the mea-
surement. Almost all DC power supplies, including older analog models, have active
circuitry to maintain the bias set point. This, combined with noise from the AC lines,
makes them impractical to use for LFN measurements. Hence, batteries are used.
9 V batteries are usually preferred as they are recognized to be low-noise. For GaN
HEMTs, even small devices can require high current (easily 100 mA or more). An
attempt to use several 9 V batteries for the drain lead to unexpected measurement
results once the device bias increased above the knee voltage. A rechargeable 12 V
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
HP3561A alone
with SR560
Figure 4.3: Measured noise floor of the HP 3561A DSA only and with the SRS SR560LNA (short-circuited input).
lead-acid battery, that could output 90 mA without disturbing the measurement, was
used for the drain bias. A 9 V battery was used for the gate biasing (two in series for
large threshold devices). These were used with a bias box (discussed more below).
Biases ofVds from 0.1 to 12 V,Ids from 5 to 90 mA, andVgs from -0.05 to -9 V could
be obtained. This is far superior to most other setups, which are limited to biasing
conditions in the linear region of a GaN HEMT.
The final equipment concern is to protect the setup from outside electrical and me-
chanical interference. The setup was located on a vibration-isolation table, which
helped with mechanical interference (although it could still be determined when con-
struction work took place in the building or when a peer would walk by the setup).
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
A metal box, that could be grounded to the rest of the setup, was made to fit over
the sample and probes of the RF probe station to shield against electrical interference.
This was required to get a good measurement and helped to reduce spurs by∼30 dB.
Figure 4.4 shows the full schematic of the setup. The multimeters were Fluke
8012As and various hand-held battery-operated units. Multimeters for voltage and
current could be connected while measuring LFN, but ohm-meters had to be discon-
nected. A covered bias box was built. 10 turn, 3 W, 2 kΩ potentiometers were used
to vary the bias. The value of 2 kΩ was carefully selected to allow the maximum
range of measurable biasings. Ground loops destroy a measurement, so care must be
+-
3W
2kΩPot.
3W
2kΩPot.
12V
220Ω9V
10Ω
Bias Box
Capacitors
50pF to1000µF
Shielded
DeviceRds
+-
Voltmeter
Voltmeter
Ammeter
RL 100MΩ
50Ω
25pF
SR560 LNA
Gain = 1000 V/V
(60 dB)
BW: 0.01 to 1MHz
1MΩ
HP3561A
FFT Box
Figure 4.4: Schematic of the setup used for device drain-side low-frequency noisemeasurements.
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
taken with the grounding. The bias-box chassis and device shield were grounded to
the negative terminal of the battery. While other setups may use a load resistance,RL,
to keep the source resistance seen by the LNA a constant (making it easy to convert
the measured voltage spectrum to a current spectrum), the author found this additional
parallel resistance to limit the measurable range of biases and the dynamic range of
the DSA. Instead, the effectiveRL is determined for each LFN measurement. This
resistance is the parallel combination of that seen on the drain side of the bias box and
Rds of the transistor. A bank of capacitors were connected at the gate to provide an
AC short while measuring the drain LFN.
Most aspects of the measurement must be done manually, as automation would only
add noise and ruin the data. The steps for a measurement are:
1. Determine the DCRds of the device near the bias of interest (∆Vds/∆Ids).
2. Unplug power to drain and gate, and ground both ends of the drain pot (usingswitches on bias-box).
3. Disconnect the device and LNA.
4. Measure the resistance of the bias box,Rbox. This is the parallel combination ofboth halves of the potentiometer and associated circuitry.
5. Disconnect the multimeter used to measureRbox (this would add a voltage thatdisturbs the measurement).
6. Reconnect the device, LNA, and bias. Wait 1 minute for the LNA to settle (a voltchange at its input, such as turning on the device or changing the bias, causes itto saturate).
7. Measure. Adjust the measured voltage spectrum by the parallel combination ofresistances (SI = SV /(Rbox||Rds)
2).
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
Figure 4.5: A typical low-frequency plot.
The setup was checked by measuring the noise spectrum of resistors. This is flat
with a voltage spectrum equal to its thermal noise.2 A typical HEMT’s LFN is shown
in figure 4.5. The dotted line is a 1/f reference line, showing the data is very nearly 1/f
in slope. There are several spurs, including one at 60 Hz (from lights and various AC
sources) and another large one at∼70 kHz (believed to be a radio signal). The spurs
were found to always be present, and are removed from all other measurements in this
chapter.
2Only when DC current flows through a resistor does it generate low-frequency noise.
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
4.4 GaN HEMT Low-Frequency Noise Modeling
For modeling, the drain and gate LFN bias-dependence need to be determined. The
setup in§ 4.3 was used to measure drain noise while an AC short was applied to the
gate. LFN was measured with the drain voltage held constant atVds 5 V and the gate
voltage swept (changingIds). Then noise for a constantIds of 30 mA and varyingVds
was measured. Both of these results are plotted in figure 4.6. In this figure only three
of the decade values are plotted from each full LFN measurement for convenience
of displaying the data. Once the device saturates, the LFN does not change further
with Ids (and henceVgs). However, LFN increases withVds. This change, shown in
figure 4.6 (b), is more than an order of magnitude for the twelve volt bias range.
The magnitude of these LFN measurements at low biasings is consistent with the
literature. The only other published work of LFN noise of GaN HEMTs at high bias-
ings is by Hsu [4]. The measurements presented here for a saturated device agree with
that work, including the key result that the noise changes withVds. In fact, Hsu claims
more bulging at higher biases (Vds > 12 V), and that the bulging broadens. This in-
crease of LFN withVds was also observed in the GaAs devices to be discussed in§ 4.6.
The slope,γ, was extracted and found to typically be about 1.15, varying from less
than 1.1 to nearly 1.3. Bias dependence was not clear, but usuallyγ would decrease
with increasingVds and very slightly decrease with increasingIds. The changing of
γ with bias is not well understood. It has been shown to vary with temperature as
113
CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
(a) (b)
Figure 4.6: Plots of the measured drain low-frequency noise with (a) change in drain-source current and (b) voltage.
well. Previous research points to trap effects, tunneling, and hot-carriers as directions
to explore [2,4].
Despite the measurements being of noise, devices biased the same had very similar
measurements. This means that devices at the same bias can be compared. This is
used as a basis for device comparison studies later in the chapter.
The gate LFN was measured with the drain AC shorted.Vds was set to 5 V and the
gate voltage was varied. As seen in figure 4.7, even at its noisiest the gate LFN is more
than three orders of magnitude smaller than the drain noise. Measurements above a
few kHz hit the noise floor of the setup. Hsu finds similar results [4], as does Riddle
for GaAs MESFETs [11]. It was discovered that devices that had a large change in
gate leakage with applied gate bias also had a large change in LFN. Conversely, if the
device gate leakage was relatively constant with gate bias, the LFN did not change
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
Vgs, Igs
30 µAV,
15 µAV,
8.5 µAV,
4.5 µAV,
2.9 µAV,
Figure 4.7: Measured gate low-frequency noise versus gate-source voltage (andcurrent).
much. The device in figure 4.7 did have a large change in leakage as evident from the
x-axis labeling.γ was also very close to unity. These observations mean the gate LFN
can be modeled by the standard diode equation, 4.2.2. This helps reinforce the noise
figure modeling in chapter 2 using a shot noise source at the gate of the transistor.
It is desirable to add scaling to circuit modeling of noise, so the effect of device
geometry on LFN was also measured. Figure 4.8 shows that as the gate is made wider
the drain LFN noise increases. This trend agrees with the low-bias GaN HEMT LFN
measurements of Kuksenkov [12] and the HEMT modeling of Angelov [13]. This
trend is opposite to what is exhibited by MOSFETs [14]. Given this result, it makes
the gate length dependence all the more interesting. Figure 4.9 (a) and (b) show that a
shorter gate length increases the drain LFN. This means that the LFN does not display
115
CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
Figure 4.8: Change in low-frequency noise with gate width at various decade frequen-cies for three devices.
(a) (b)
Figure 4.9: (a) Change in low-frequency noise as the gate length, Lg is changed. (b)The 1 kHz data from (a) with a best fit line.
116
CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
a direct area dependence. It can be speculated that the gate length dependence LFN is
related to theVds dependence.
TheVds LFN dependence will harm the phase noise performance of GaN HEMT-
based oscillators. Also, it is not typical of previous LFN modeling, which has a current
dependence instead. Based on the measurements presented thus far, the gate and drain
have different LFN processes and should not be modeled in the same manner. It
needs to be determined whether the gate and drain LFN are mathematically correlated.
Measurements were performed with the gate AC shorted and not AC shorted, showing
no change in the drain LFN. The same was done for gate LFN measurements and the
drain did not appear to have an effect. Hsu found similar results [4]. Lee shows
that the gate and drain LFN are uncorrelated [15]. Therefore, a two-current noise
source model with no correlation as illustrated in figure 4.10 can be used. Based on
the measurements in this work, the following model of the drain LFN for a circuit
simulator is proposed:
<ig1/f2><ig1/f2>
<id1/f2><id1/f2>
Figure 4.10: Proposed low-frequency noise modeling of the HEMT with a gate anddrain noise source.
117
CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
⟨i2d,1/f
⟩=Ki
(Wg,new
Wg,old
) (Lg,old
Lg,new
)c(msVds + 1)
fγ(4.4.1)
whereKi,ms, andc are fitting parameters representing the magnitude of the noise,
the slope change withVds , and an exponent of the change with gate length respec-
tively. Wg andLg are defined the same as in§ 2.6.4. Values found to work for devices
presented areKi = 4e-14,γ = 1.1,c = 1.5, andm = 2.6. As already mentioned, the
gate noise can be modeled with equation 4.2.2. Due to the limitations of hitting the
noise floor, the gate LFN geometry dependence could not be measured. However, as
it depends on the Schottky contact reverse-bias gate leakage, it might be assumed that
the gate LFN scales with the gate leakage as in equation 2.6.45. Parameters found to
work for the gate LFN areAf = 1.15,Ffe = 1, andKf = 2e-11.
The model was used to estimate the drain LFN corner frequency of the devices,
as equipment limitations prevented the measurement of this important quantity. The
noise figure modeling work in chapter 2 was used to estimate the noise floor, and
its intersection with the LFN was calculated. This value varies with bias because of
changes in LFN and gain, but was estimated to be close be 1-10 MHz. This is a
typical value for GaAs HEMTs. It was also attempted to use this model in phase noise
circuit simulations in ADS. However, limitations in the device model and the lack
of a native voltage bias-dependent low-frequency noise source component in ADS
prevented accurate prediction of phase noise.
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
4.5 GaN HEMT Low-Frequency Noise Studies
4.5.1 Substrate
There has already been some work comparing the noise of GaN HEMTs on different
substrates [3]. The findings were that SiC was less noisy than sapphire, having Hooge
parameters one to two orders of magnitude smaller. But the measurements were at
a low bias and it has already been explained why the Hooge parameter should not
be used for device comparisons. There is no data published comparing devices that
are in the saturation region. This was undertaken, and is presented in figure 4.11.
The devices are both biased atVds 5 V andIds 10 mA. Across the spectrum, there
is no apparent difference. While there appears to be a slight amount of bulging, it is
not stronger for either device. This suggests that at typical device biasings the LFN
is suppressed or another noise mechanism is stronger. Also, identical GaN HEMT-
based oscillators on both substrates constructed by the author (§ 5.4.1) did not show a
difference in LFN.
4.5.2 Passivation
There are two previous publications on the effect passivation has on LFN in GaN.
The first [16] measured HEMTs at a very low bias and normalized the noise to the
drain current. They showed that the passivation does improve the LFN performance,
119
CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
Figure 4.11: Measurement of devices on a sapphire and SiC substrate at a bias ofVds5 V, Ids 30 mA
(a) (b)
Figure 4.12: (a) Low-frequency noise of a device before and after passivation. (b)Low-frequency noise at 10 Hz and 1 kHz of a device before and after passivation atdifferentVgs .
120
CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
but based on their measurements the improvement varied with gate bias from as large
as an order of magnitude to almost no improvement. The other study also found
an improvement with passivation but only measured TLM structures [17]. LFN was
measured for a sample before and after passivation. In figure 4.12 (a), the LFN is
plotted for a device with and without passivation atVds 5 V andIds 10 mA. Passivation
improves the LFN by an order of magnitude across the spectrum. Passivation causes
a slight change in threshold voltage, so measurements were taken at different gate
biasings withVds still at 5 V. The measured data at 10 Hz and 1 kHz is plotted in
figure 4.12 (b). The improvement stays relatively constant with gate voltage. It is
believed that suppression of surface state traps, along with the increase of channel
charge, cause the improvement.
4.5.3 Thick-Epitaxial Cap Devices
After considering the result of passivation on LFN, it is interesting to look now at a
device that does not require passivation. Devices of similar design to those in§ 3.5.6
(AlGaN was used to cap the device instead of GaN) were measured. Figure 4.13 shows
LFN measurements of a few thick-cap devices (that have no passivation) and standard
passivated HEMTs. The performance of the thick-cap devices is as good as, if not
slightly better than, a passivated standard HEMT device. It can be concluded that a
LFN mechanism on the channel surface can be suppressed with either passivation or
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
Figure 4.13: Comparison of standard passivated HEMTs to an unpassivated thick capHEMTs. Bias isVds = 5 V andIds = 30 mA.
with another epitaxial layer.
4.5.4 Field-Plated Devices
A field plate (FP) was shown to lower NF in this work (§ 3.5.5). It has also been
shown that a FP improves oscillator phase noise in [18]. In fact, the longer the FP, the
less the phase noise. As the 30 dB/decade slope of this data suggests that a 1/f type of
noise is dominating the phase noise, it might be reasoned that the LFN of FP and non-
FP devices is different. If there is a difference, it is not apparent in the measurements
shown in figure 4.14. In part (a) of the figure, all FP and non-FP transistors display
the same LFN at different frequencies when biased under the same conditions. The
second plot, (b), shows that asVds increases, all devices’ LFN increase at nearly equal
122
CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
(a) (b)
Figure 4.14: (a) Decade low-frequency noise data for devices with different FP lengthsat a bias ofVds 5 V andIds 30 mA. (b) 100 Hz low-frequency noise for different FPlengths atVds 3, 5, and 8 V.
rates. The answer to the origin of the phase noise improvement with a FP will need to
be answered elsewhere.
4.6 Comparison to GaAs HEMTs
In the previous chapter the NF of GaN was shown to be similar to GaAs. Let us now
examine the LFN of these two materials. A few GaN LFN reports have claimed that
the noise is comparable (such as [2]). These previous results are usually done with a
measured GaN device and information for a GaAs device from a data sheet or another
paper. In addition, the Hooge parameter is used as the figure of merit.
The author obtained GaAs HEMTs and measured the LFN of these devices. They
are from the TriQuint TQP13 pHEMT process, with anfτ of ∼95 GHz. The device
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
gate geometry is 0.13 x 93µm. This is not the same as the 0.7 x 100µm GaN HEMT
devices to which they are compared to. However, based on the model presented in this
chapter, approximating the magnitude of the GaAs devices to be 3 times smaller than
what is actually measured should make for a fair comparison. The question arises
of how to bias the different devices. The following bias was chosen: 1.5 times the
knee voltage of the fully open channel and 3/4 the total gate bias (positive turn-on to
negative cut-off).
Figure 4.15 shows the measurements of (a) the full spectrum of one GaN and one
GaAs device and (b) selected frequency points for a few GaN and GaAs devices.
The GaAs has not been corrected for its difference in geometry. Considering this
difference, the LFN from a few kHz to 1 MHz is similar for both types of devices.
The slope (γ) of the GaAs devices was found to typically be 0.8 (it is common in the
(a) (b)
Figure 4.15: Low-frequency noise comparison of (a) a GaN and GaAs HEMT (fullspectrum) and (b) multiple GaN and GaAs HEMTs (decade measurements). Bias forall devices isVgs = 3/4Vtotal, Vds = 1.5Vknee.
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
GaAs FET literature forγ to be between 0.7 and 1), which is much less than the 1.2 for
GaN. Therefore, at lower frequencies GaAs has less noise. In§ 5.5, it will be shown
that the close-to-carrier phase noise of GaN oscillators is worse than for GaAs-based
oscillators because of these different slopes.
4.7 Summary
This chapter has provided a useful collection of quality high-bias low-frequency
noise data. It was shown that the noise depends heavily onVds while remaining nearly
constant to a changing gate voltage. The geometry dependence has also been shown to
be different than what is seen in other devices. A scalable, bias-dependent, empirical
model was proposed that can be used in circuit simulators. It was demonstrated that
neither the choice of substrate nor the addition of a FP change the LFN. Suppression
of LFN from surface effects was demonstrated through measurements of unpassivated
and thick-cap devices. References to the literature were added to support all measure-
ments where previous work exists. The full details of a LFN setup were explained. A
final note is that bulging (g-r noise presumably from traps) would occasionally show
up. The bulge would be very broad with a spectrum from around 100 Hz to 1 kHz. It
was not always present, even across the same sample. With improvement of material
it can be expected that the LFN will improve.
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References[1] A. Hajimiri and T. Lee,The Design of Low Noise Oscillators. Boston: Kluwer
Academic Publishers, 1999.
[2] A. Balandin, S. Morozov, S. Cai, R. Li, K. Wang, G. Wijeratne, andC. Viswanathan, “Low Flicker-Noise GaN/AlGaN Heterostructure Field-EffectTransistors for Microwave Communications,”Microwave Theory and Techniques,IEEE Transactions on, vol. 47, no. 8, pp. 1413–1417, 1999.
[3] A. Balandin, Ed.,Noise and Fluctuations Control in Electronic Devices. Steven-son Ranch, CA: American Scientific Publishers, 2002.
[4] S. Hsu, P. Valizadeh, D. Pavlidis, J. Moon, M. Micovic, D. Wong, and T. Hus-sain, “Characterization and Analysis of Gate and Drain Low-Frequency Noise inAlGaN/GaN HEMTs,” inHigh Performance Devices, 2002. Proceedings. IEEELester Eastman Conference on, 2002, pp. 453–460.
[5] A. L. McWhorter, “Semiconductor Surface Physics,” R. H. Kinston, Ed. Philadel-phia: Univ. of Pennsylvania Press, 1956, pp. 207–228.
[6] F. N. Hooge, “1/f Noise Sources,”IEEE Trans. Electron Devices, vol. 41, no. 11,pp. 1926–35, Nov. 1994.
[7] A. van der Ziel, “Unified Presentation of 1/f Noise in Electron Devices: Funda-mental 1/f Noise Sources,”Proc. IEEE, vol. 76, no. 3, pp. 233–258, 1988.
[8] ——, Noise in Solid State Devices and Circuits. New York: Wiley-Interscience,1986.
[9] M. J. Buckingham,Noise in Electronic Devices and Systems. New York: JohnWiley & Sons, 1983.
[10] D. A. Bell, “A survey of 1/f noise in electrical conductors.”Journal of Physics C:Solid State Physics, vol. 13, no. 24, pp. 4425–37, Aug. 1980.
[11] A. N. Riddle, “Oscillator Noise: Theory and Characterization,” Ph.D. dissertation,North Carolina State University, 1986.
[12] D. V. Kuksenkov, H. Temkin, R. Gaska, and J. W. Yang, “Low-Frequency Noisein AlGaN/GaN Heterostructure Field Effect Transistors,”IEEE Electron DevicesLett., vol. 19, no. 7, pp. 222–224, July 1998.
[13] I. Angelov, R. Kozhuharov, and H. Zirath, “A Simple Bias Dependant LF FETNoise Model for CAD,” inMicrowave Symposium Digest, 2001 IEEE MTT-S In-ternational, vol. 1, 2001, pp. 407–410 vol.1.
126
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[14] T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits, 2nd ed.New York: Cambridge University Pess, 2004.
[15] S. Lee, “Intrinsic Noise Characteriestics of Gallium Nitride High Electron MobilityTransistors,” Ph.D. dissertation, Purdue University, Aug. 2004.
[16] A. V. Vertiatchikh and L. Eastman, “Effect of the Surface and Barrier Defectson the AlGaN/GaN HEMT Low-Frequency Noise Performance,”IEEE ElectronDevices Lett., vol. 24, no. 9, pp. 535–537, Sept. 2003.
[17] S. A. Vitusevich, M. V. Petrychuk, S. V. Danylyuk, A. M. Kurakin, N. Klein, andA. E. Belyaev, “Influence of Surface Passivation on Low-Frequency Noise Proper-ties of AlGaN/GaN High Electron Mobility Transistor Structures,”phys. stat. sol.(a), no. 5, pp. 816–819, Mar. 2005.
[18] H. Xu, C. Sanabria, S. Heikman, S. Keller, U. Mishra, and R. York, “High PowerGaN Oscillators Using Field-Plated HEMT Structure,” inMicrowave SymposiumDigest, 2005 IEEE MTT-S International, 2005, pp. 1345–1348.
127
5GaN HEMT Based Oscillators
5.1 Introduction
OSCILLATORS are a key component of many communication systems. They
set fundamental limits of channel spacing because of their phase noise. This
work has demonstrated that NF and LFN of GaN HEMTs are only slightly worse
than the far more technologically mature GaAs HEMTs. Here the phase noise will
be compared to similar integrated circuit designs in Si and GaAs. Some guidelines
for low-phase noise design are discussed. A recently-developed MMIC process at
UCSB [1] was ideal for making the designs, and it will be reviewed briefly. The focus
of the chapter is the design and measurement of two LC differential oscillators. The
first did not have impressive phase noise performance but its linearity was excellent.
It is also the first GaN differential oscillator to appear in the literature [2]. A second
similar oscillator was fabricated that had fairly good phase noise performance. These
oscillators are compared to other published results of differential oscillators in Si and
GaAs, as well as GaN HEMT oscillators of all designs.
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
5.2 Concerning Phase Noise
The study of phase noise is a difficult undertaking. Entire books and dissertations
are devoted to its study [3–5]. Even today there is still not a consensus of how best to
approach the problem [6]. The reason for the difficulty of understanding phase noise
stems from three challenges. The first is that an oscillator is a non-linear problem, and
simple analytical analysis cannot capture all key aspects. The rigorous work is usually
too complicated for clear insight or practical design. LFN is the largest contributor to
phase noise, and the lack of its full understanding undermines any complete study of
phase noise. It is not unheard of for a designer to simulate phase noise without LFN
modeling in the circuit because of this shortcoming. Finally, the circuit design impacts
the phase noise, possibly in profound ways [5].
Defining phase noise is much simpler than designing for it. Any signal source is
bound to have fluctuations in phase and amplitude. We can write these fluctuations as
v(t) = v0(1− a(t)) cos(ω0t+ ψ(t)) (5.2.1)
v0 andω0 are the amplitude and angular frequency of resonance of the oscillator.
The amplitude fluctuations, a(t), and phase fluctuations,ψ(t), are both stochastic pro-
cesses. The power spectral density close to the carrier frequency is found to be [7]
Sv(ω) =v2024π(1− 〈φψ(0)〉)δ(ω − ω0) + Sa(ω − ω0)
+Sψ(ω − ω0) + 2Im [Sψa(ω − ω0)] (5.2.2)
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
Here we see the signal amplitude (v20/2) at the resonant frequency, along with an
autocorrelation term,φψ, from the phase fluctuations that reduces it.Sa is noise added
to the spectrum from the amplitude fluctuations, and is commonly known as amplitude
modulation (AM) noise. The phase fluctuations contribute to the spectrum throughSψ,
and is known as phase modulation (PM) or phase noise. A correlation term between
the amplitude and phase fluctuations can also contribute to the spectrum through the
cross spectral density,Sψa, called AM-PM noise. AM-PM noise is an odd function
(the others are even), and can lead to asymmetry of the noise spectrum around the
carrier. Proper circuit design reduces AM-PM noise. The nonlinearities of the gain-
producing element in an oscillator (usually, but not always, a transistor) provides a
restoring force that not only keeps the amplitude stable but also greatly reduces AM
noise. This means the noise near an oscillator’s resonance frequency is dominated by
phase noise.
Bearing in mind that there is AM, PM, and AM-PM noise, but PM (phase noise)
dominates, the phase noise can be observed with a spectrum analyzer. In fact, an Ag-
ilent E4440 spectrum analyzer with a phase noise personality was used for measure-
ments that appear in this chapter. Phase noise appears as a broadening of the frequency
of oscillation, shown in figure 5.1 (a). Its fine detail of shape varies, and is typically
one of three cases as seen in figure 5.1 (b-d). The resonator acts as a filter. Above or
below the resonant frequency a voltage signal would drop proportionally to 1/f, but
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
Frequency
Power
Noise Floor
ω0
Frequency
Power
1/f3
Noise Floor
Frequency
Power
1/f3
1/f2
Noise Floor
Frequency
Power
1/f3
1/f
Noise Floor
(a)
(c)
(b)
(d)
Figure 5.1: (a) A typical spectrum of an oscillator. (b-d) are zoomed in plots of thecircled portion in (a). The power in the various plots arenot scaled to one another.
the power would drop 1/f2 (20 dB/decade). This is exactly what happens to both flat
(such as thermal) noise sources and up-converted LFN leading to 20 dB/decade and
30 dB/decade slopes respectively. An oscillator with a very high Q, and the best noise
performance (the plots in figure 5.1 are not to scale to each other), would have a shape
such as that in figure 5.1 (b). The 1/f3 region is the resonator filtering up-converted
LFN, while the 1/f regions are up-converted LFN that is outside the resonator band-
width. If there were no LFN (a blissful ideality), the slope of the entire range would be
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
just 20 dB/decade. Figure 5.1 (c) is the most typical spectrum observed. Here again
is filtering of LFN, but now we see thermal noise being filtered as well. The last case,
figure 5.1 (d), is for an oscillator with an enormous amount of LFN. We will return
to this qualitative analysis later. Phase noise is specified in decibels below the carrier
(dBc) in a 1 Hz bandwidth at a offset-frequency from the carrier. For example, a phase
noise of -132 dBc/Hz at 100 kHz means the noise at a frequency 100 kHz in addition
to the oscillation frequency is 132 dB below the power the oscillator has at its resonant
frequency (ω0).
A concise background of phase noise would require more than a chapter. Despite
the complexity of phase noise, there are some guidelines that tend to show up repeat-
edly [3,5–9]:
• Increase the tank Q: This is the most important factor for improving phasenoise. Higher Q means more suppression of off-carrier frequency components.
• Minimize the LFN: Probably the next most important parameter after Q. Choiceof device (bipolars in general have much less LFN than FETs) and device ge-ometry can help, as well as improvement in material quality. But usually littlecan be done to quell LFN.
• Increase the Signal Amplitude: If all other influences could be consideredconstant, a larger signal amplitude increases signal to noise ratio and reducesthe phase noise.
• Minimize Other Noise Sources: Flat noise sources determine the phase noisein the 20 dB/decade range.
• Properly Design the Loop Gain: Designing the phase shift of the loop to havea maximum derivative at the center of the resonance of the loop gain maximizesthe resonator’s ability to attenuate phase noise.
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
• Linearize Cgs: The non-linearity ofCgs with Vgs makes the oscillator less sym-metric and increases noise. Additional capacitance can smoothCgs and improvephase noise. [3,10]
• Optimize the Circuit: Some oscillator topologies, particularly the Colpitts,provide better phase noise than others. Design of the circuit influences thephase noise performance. Use of techniques, such as automatic gain controland tapped resonators, can help as well.
The last point is the largest topic to expound upon. However, the other points go
far toward the goal of improving phase noise. Because of the very large powers GaN
HEMTs can produce, the improvement of phase noise with signal amplitude is of great
interest to GaN circuits and provides the motivation for building the oscillators in this
chapter.
To simulate phase noise, very accurate device small-signal, large-signal, and noise
modeling must be available. In addition, simulators vary in their accuracy in predicting
phase noise. Modeling from the previous chapters was used to attempt simulations
of phase noise. However, the device model had some shortcomings (discussed in
§ 6.2) that prevented even accurate modeling of the 20 dB/decade phase noise from
filtered thermal noise. Some interesting results could be determined: the gate-leakage
shot noise was found to be negligible compared to contributions of the gate resistance
thermal noise, the channel noise, and the LFN. It was also noted that a field plate (FP)
did help the simulated phase noise results. A surprising simulated improvement of
10 dB of a very long FP HEMT oscillator over a non-FP oscillator agrees with the
work of Dr. Xu [11]. The practices outlined above were followed as well as possible.
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
5.3 MMIC Process Description
The MMIC process developed by Hongtao Xu was used for circuit fabrication [1].
It integrates capacitors, inductors, resistors, and transmission lines. This follows the
HEMT process described in§ 3.2, but with additional steps. There are now two addi-
tional metal layers (metal 1, 1µm of gold, and metal 2, 3µm of gold), a resistor layer
(NiCr), and a dielectric spacer layer (3µm of PMGI). Inductors are made with metal
1 as an under-pass metal, then the dielectric spacer, and metal 2 to finish the over-pass
and most of the metalization of the square inductors. Capacitors are made with the
gate metal as a bottom electrode and the same film used for passivation as the capac-
itor dielectric. Metal 1 becomes the top electrode, and metal 2 connects the capacitor
bottom and top to the rest of the circuit (metal 2 is used over the PMGI to contact the
top electrode without shorting the capacitor). Resistor composition is Ti/SiO2/NiCr
and is protected by the same SiN film used for the capacitors and passivation. Trans-
mission lines are made exclusively with the thick metal 2. The same material structure
in § 3.2 is used here. Full details of the process, along with a process flow chart, can
be found in Hongtao Xu’s dissertation [1].
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
5.4 Differential Oscillators
5.4.1 High Linearity Oscillator
Some familiarity with oscillators will be assumed in this and the next subsection.
A background can be found in textbooks such as [8]. The oscillators were designed
primarily as test vehicles, making the circuit design more flexible and less conven-
tional than typical commercial configurations. Design goals were to minimize phase
noise and maximize power and linearity without regard to other constraints such as
device size or ease of implementation. Design started with a basic cross-coupled pair
of 2× 100µm-wide HEMTs, seen in figure 5.2. Typically the drain bias would be set
with a current mirror at the HEMT sources (marked with an S) but it was desired to
have the freedom to change the bias. This also eliminates the LFN from devices in the
current mirror.
The tank, represented by the capacitorCt and inductorsLt, primarily set the reso-
nance frequency. A fixed capacitor was used instead of a varactor to improve the Q of
the resonator and allow better insight of the phase noise performance of the HEMTs.
The passive components used for the tank were based on measurements of fabricated
capacitors and inductors at 5 GHz, with the best Q components picked for the desired
oscillation frequency. Typical unloaded Q values at 5 GHz are 25 and 65 for the square
spiral inductors and the SiN capacitors respectively.
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
C2C2
Ct
L1L1
C1C1
Lt Lt
L3C3
L3Load
L2L2
C3
Load
SS
Figure 5.2: Circuit schematic of the oscillator (biasing not shown).
C2
Ct
L1
C1Lt
L2
C3
L1
Lt
L2
C3
C1
C2
Figure 5.3: Photograph of the high linearity oscillator. Darker areas are the twoHEMTs. Passive components are labeled as in figure 5.2.
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
The output is taken on either side of the tank. To keep from loading the tank, and
to match to a 50Ω output, an L-match (L1 andC2) is used. Bias is provided at the
gate and through the L-matches with the output. This required the use of off-chip
bias-Ts for the RF/DC ports, but not for the gate bias port. The gate uses large square
inductors (L2) as RF chokes.C1 is a DC block that prevents the drain of the HEMTs
from shorting, andC3 isolates the DC of the gate and drain. The lengths of line used
to cross-connect the HEMTs are modeled by the inductorsL3. The photograph of the
oscillator in figure 5.3 labels most of the circuit elements found in figure 5.2. Circuit
size is 2 x 1.65 mm2.
The circuit was simulated using ADS. Transient and harmonic simulations were
performed. Monitoring these, along with the dynamic load-line at the drain port of the
HEMTs, the circuit was optimized to give as linear an output as possible.
Measurements were performed on-wafer with air-coplanar (Cascade Microtech ACP-
40 GSG) probes. Off-chip bias-Ts were used for both the drains and gates. One side
of the oscillator was terminated in a dummy 50Ω load. All measurements that follow
(power, linearity, phase noise) were performed using an Agilent E4440 spectrum ana-
lyzer with phase noise personality. Figure 5.4 (a) shows the measured spectrum from
one side providing 22.9 dBm of power at a 4.166 GHz oscillation frequency. The cir-
cuit is biased atVds 20 V, Ids 233 mA, andVgs -1 V. The analyzer had a 10 MHz span
and 33 kHz resolution bandwidth for the measurement. How the power and efficiency
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
(a) (b)
Figure 5.4: Measurements of the oscillator: (a) power spectrum (b) frequency pulling.
(a) (b)
Figure 5.5: Output power (single-sided), second harmonic power, and efficiency (fullcircuit) of the high-linearity oscillator for changes in device (a) drain-source voltageand (b) gate-source voltage.
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
compare to other oscillators will be discussed in§ 5.5.
Of interest is the oscillator pulling, which is the change in oscillation frequency
with DC bias. This was measured for both the gate and drain voltages and plotted in
figure 5.4 (b). It is typical to express the pulling as a ratio of change in frequency to
change in bias. Approximating the data as linear in figure 5.4 (b) gives a pulling of
4.3 MHz/V for the gate and 0.6 MHz/V for the drain. These changes are less than
0.4% of the frequency of oscillation.
The power, 2nd harmonic, and efficiency for changes in bias appear in figure 5.5 (a)
and (b). The third harmonic was so small as to be buried in the noise floor of the spec-
trum analyzer, making it∼70 dB below the carrier. The 2nd harmonic was typically
better than 30 dBc for all biasings measured. If the output were taken differentially,
even harmonics would cancel and the oscillator would make for an extremely linear
source.
This oscillator was the first GaN differential oscillator to be reported in the litera-
ture, and also the best reported linearity for a GaN oscillator [2]. However, the phase
noise was not impressive, being only -86.3 dBc and -115.7 dBc at best. A second,
similar, oscillator was constructed and is now presented.
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
5.4.2 Low-Phase Noise Oscillator
The previous design was modified to improve phase noise performance. The Q
of the various inductors was reasoned to be a limiting factor, and were replaced. Mi-
crostrip lines,Lt in figure 5.6, were used in place of the tank inductors. The L-matches
were changed to tapped capacitors to help preserve the loaded tank Q. This meant the
drain biasing needed to be applied through the tank microstrip inductors. To provide
an AC ground acrossLt, the large blocking capacitor 2C3 was added. The circuit,
shown in figure 5.7, was slightly smaller than the previous at 2 x 1.4 mm2.
C2C2
CtC1
2C3Lt Lt
L1C4
L1Load
C1
L2L2
C4
Load
SS
Figure 5.6: Circuit schematic of the low-phase noise oscillator (biasing not shown).
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
C2 Ct
C3
Lt
C1
L2
C4
L2
C4
C2
Lt
C1
C3
Figure 5.7: Photograph of the low-phase noise oscillator. Passive components arelabeled as in figure 5.6.
Figure 5.8 is a typical measured phase noise spectrum. Above 10 kHz the oscillator
drift obstructs the measurement. From 10 kHz to 1 MHz the spectrum decreases with
a 30 dB per decade slope, similar to figure 5.1 (d). This means the low-frequency
noise (LFN) of the oscillator dominates and hides the 20 dB per decade thermal noise
region. So far, no published GaN-oscillator phase-noise measurements have shown
a strict 20 dB per decade slope below a 1 MHz offset [2, 11–15]. A phase noise
measurement above a 1 MHz offset usually approaches a spectrum analyzer’s noise
floor, hence the lack of phase noise measurements in the literature at larger offsets.
Now to answer the key question: does an increase of oscillator power improve the
phase noise? After the optimal bias forVgs was determined and set,Vds was varied.
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
Figure 5.8: Measured phase noise of the oscillator.
Figure 5.9: Phase noise at 100 kHz and 1 MHz offsets versus drain-source bias for afew oscillators.
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
The power of the oscillators increases from 15 dBm to 18 dBm asVds increased from
6 V to 35 V. BelowVds 5 V the power drops quickly (it was typically 7 dBm atVds
4 V). Phase noise for devices with differentVds is plotted in figure 5.9. The phase
noise does not improve with an increase in signal power, but actually increases. This
agrees with measurements in [12]. Of interest is that the general shape of figure 5.9 is
similar to the measured LFN bias dependence in figure 4.6. While proper design can
help to lower the offset frequency where the 30 dB/decade and 20 dB/decade slopes
meet, only Hajimiri’s model [5] addresses how this can be accomplished and its ability
to do this is still debated. With these results in mind, we now compare GaN oscillators
to other material systems for phase noise and for other oscillator measurements.
5.5 Comparison to Other Oscillators
A summary of measurements of several oscillators is found in table 5.1. Listed are
the measured frequency of oscillation (or range if the oscillator is tunable), the total
device (or devices) width, the oscillator power at its resonance frequency in addition
to second and third harmonics, the best efficiency of which the oscillator was capable,
phase noise measurements at 100 kHz and 1 MHz offsets, and the reference for each
work.
The table is separated into four parts depending on oscillator type. All oscillators in
the table are either HEMT or MESFET-based (no BJTs or HBTs) and integrated (no
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
Desc. Carrier Device Fund. 2nd 3rd Best Phase Noise Ref.Freq. Width Power Harm. Harm. Eff. 100 kHz,1 MHzGHz mm dBm dBm dBm % dBc/Hz
Table 5.1: Comparison of GaN oscillators from this and other works to oscillators inother materials (FET, MMICs, only).
hybrid circuits with high Q tanks). In order from top to bottom, they are the current
published literature of GaN oscillators besides those in this work, a GaAs oscillator
that is not of a differential architecture, the differential oscillators presented in this
work, and finally differential tunable oscillators in Si and GaAs.
Comparing the phase noise with other GaN oscillators first, the low-noise oscillator
of this work compares well with the best phase noise values reported for GaN oscilla-
tors. The Colpitts oscillator of [12] used high-Q BST thin films as blocking capacitors
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
in its circuit and [11] used a FP on the devices in the oscillator, providing astonish-
ing improvements in phase noise (∼10 dB over the same circuit using devices with
no FP). The oscillators in Si and GaAs technologies all used varactors for frequency
tuning. This will degrade the tank Q and lead to poorer phase noise performance. As
a safe assumption, assume that the phase noise would be -10 dBc/Hz lower (better)
than what is stated in the table. With this adjustment, we see that GaN has better or
comparable phase noise at a 1 MHz offset, but by offsets≤ 100 kHz the phase noise
is worse. Work by Rice [15] agrees with these measurements. The reason for this
difference is because GaN oscillators are dominated by their LFN and never show the
20 dB/decade slope from thermal noise. This is better-explained by figure 5.10. Here
the phase noise is displayed comparatively for a GaN oscillator and a typical low-noise
oscillator in GaAs or Si. Note that the magnitudes of the phase noise are not the same,
as phase noise is expressed relative to the carrier. The measured absolute power of the
phase noise sidebands for the GaN oscillator will be much larger than in GaAs or Si.
GaN oscillators provide at least an order of magnitude more power than the other
technologies. For the total device width of the HEMTs, the oscillators in this work
provide an average amount of power compared to the other GaN oscillators. The
standout is the FP HEMT oscillator, with 2 W/mm. The linearity of the first oscillator
in this work is second to none. The efficiencies of the GaN oscillators appears to be
much higher than GaAs and Si.
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
Figure 5.10: Relative comparison of GaN oscillator to a typical oscillator with lowphase noise (figure courtesy of Dr. Robert York).
5.6 Summary
Two GaN HEMT-based differential oscillators were presented. The first displayed
very good harmonic suppression but poor phase noise. This oscillator was also the first
GaN differential oscillator to appear in the literature [2]. The second oscillator showed
excellent phase noise performance at a 1 MHz offset of -132 dBc/Hz. However, be-
cause GaN oscillator phase noise appears to be dominated by very large amounts of
LFN, the noise performance is worse at offsets closer to the carrier. The hoped-for
benefit of better phase noise with more oscillator power is shattered by measurements
that show that more power actually increases the phase noise. This could be expected
because of the HEMT drain LFN bias dependence withVds. Because of these two
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
problems, GaN does not appear to have an advantage over GaAs or Si oscillators for
phase noise.
References[1] H. Xu, “MMICs using GaN HEMTs and Thin-Film BST Capacitors,” Ph.D. dis-
sertation, University of California, Santa Barbara, 2005.
[2] C. Sanabria, H. Xu, S. Heikman, U. Mishra, and R. York, “A GaN DifferentialOscillator With Improved Harmonic Performance,”IEEE Microwave ComponentsLett., vol. 15, pp. 463–465, Jul. 2005.
[3] A. N. Riddle, “Oscillator Noise: Theory and Characterization,” Ph.D. dissertation,North Carolina State University, 1986.
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6Summary, Conclusions, and Future
Directions For Noise Studies
6.1 Summary and Conclusions
THIS dissertation has looked at several aspects of the noise performance of
GaN HEMTs: noise figure, low-frequency noise, and phase noise. The noise
figure of GaN HEMTs is comparable to GaAs HEMTs. However, the gate leakage
needs to be well-controlled. Source resistance might also be too large a contributor for
small devices. At high biasings, self-heating causes the gain to drop, and an increase
in source resistance quickly degrades the noise figure performance.
A simple model, that included device scaling, was put together that not only pre-
dicts the minimum noise figure well, but also the other noise parameters:|Γopt|,6 Γopt,
andrn. It is useful for hand and Matlab calculations to predict and understand noise
without the need for noise parameter measurements beforehand. It was successfully
used to understand how gate leakage and a field plate influence noise figure. The
model does not work when the gain of the transistor drops, such as at high biasings
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CHAPTER 6. SUMMARY, CONCLUSIONS, AND FUTURE DIRECTIONS
or frequencies close tofτ . It was shown that the Pospieszalski and correlated noise
models can be successfully applied to GaN HEMTs, even for noise versus bias.
Summarizing the other noise figure studies, devices on either SiC or sapphire sub-
strates can have the same minimum noise figure as long as the bias is low. Thick-cap
devices show low noise at high biasings. However, their noise at lower biasings is
sub-par because of a very large amount of gate leakage.
A low-frequency noise setup that works at biasings typically needed for GaN HEMTs
was constructed and thoroughly explained. Unlike many other setups, this allowed
bias dependent studies well into the device saturation region. From this, a strongVds
dependence for the drain was discovered and a scalable, bias dependent, model that
could be entered in a circuit simulator was introduced. The gate was found to follow
the low-frequency noise modeling for a diode, as could be expected for a Schottky
contact.
Low-frequency noise studies were performed. Passivation was found to improve the
low-frequency noise by an order of magnitude. An unpassivated thick-cap device has
the same low-frequency noise performance as a passivated standard HEMT. A field-
plate does not appear to help LFN, unlike noise figure. GaN HEMT low-frequency
noise is worse than that of GaAs HEMTs because the slope of the noise is much larger.
The phase noise of two GaN HEMT-based differential oscillators were explored.
The first had poor phase noise, but very good harmonic suppression, and was the
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CHAPTER 6. SUMMARY, CONCLUSIONS, AND FUTURE DIRECTIONS
first GaN HEMT differential oscillator in the literature. The second oscillator showed
excellent phase noise performance at large offsets, but poor performance at closer
offsets because of the phase noise being dominated by the low-frequency noise. The
GaN power advantage that was hoped would improve the oscillator signal-to-noise,
and thus phase noise, was more than offset by the increase of low-frequency noise
with power. Because of these problems with low-frequency noise, GaN oscillators do
not perform better - they do not even meet the performance typically seen by GaAs
and Si oscillators.
6.2 Future Paths
Trying to make progress in an entire field of study which is not completely under-
stood and making three difficult-to-use measurement systems work allows room for
improvement. To improve noise figure, gate leakage needs to be controlled, but first
it needs to be understood. This is no doubt the pursuit of many champions of GaN
research because of its implications for reliability and power performance. It would
also be of interest to look at bias dependence of ion-implanted GaN HEMTs to see
if it improves the curve typically seen for minimum noise figure versus drain-source
current. As thick-cap HEMTs do not need passivation, they are an interesting device
with possible industry applications. Their noise figure performance at large current
biasings was better than any other measured by the author. A better understanding
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CHAPTER 6. SUMMARY, CONCLUSIONS, AND FUTURE DIRECTIONS
could be pursued.
The work on low-frequency noise studies was only started and could be greatly
expanded upon. In particular, while few researchers have even reported the drain low-
frequency noiseVds dependence, none have attempted to explain it. As this seems to
be directly linked to the measured phase noise of oscillators, it is strongly suggested
it be studied in depth.
There are many ways to try to improve phase noise. The oscillators presented here
were relatively simple. More-sophisticated circuits should be undertaken and with
smaller devices than those presented here or in other works. The researchers whose
work has been discussed were designing with high power in mind. Before these cir-
cuits can be attempted, the circuit model needs to be improved. There are several
shortcomings. First, the ADS circuit model predicts that minimum noise figure ver-
sus drain source current is flat, which is a glaring problem (see figure 3.7). Dynamic
source and drain resistances must be included along with self-heating effects. Gate
leakage is not included in the model and should be added. The attempt at using
an ADS symbolically-defined device to generate a voltage-controlled low-frequency
noise current source was not successful, as the simulator appeared to use the DC bias
instead of the varying large-signal voltage of the oscillation. A custom ADS compo-
nent might be required, which could involve a few hundred lines of code. With these
deficiencies corrected, it might be possible to more closely simulate phase noise and
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CHAPTER 6. SUMMARY, CONCLUSIONS, AND FUTURE DIRECTIONS
possibly better understand why a field plate helps the phase noise performance.
153
AADS Files
An ADS project that contains files used in this work can be downloaded at
which contains a small-signal model of a HEMT and noise sources and noise vari-
ables for the Pospieszalski model. The Pospieszalski noise variables are obtained from
noise parameter measurements and small-signal parameters with the Matlab code in
Figure A.3: Schematic used for simulating noise parameters.
159
APPENDIX A. ADS FILES
appendix C.
Returning to the circuit schematic, simulating brings up the data display
templatenoisefigure viewer.dds
Page 3 of this data display (use the shortcutAlt, p, eto navigate through the pages)
contains noise and gain circles on Smith Charts, the noise parameters, stability factor,
and noise figure for a 50Ω termination compared to NFmin versus frequency. The
other pages of the display also contain useful information for design.
A.3 Correlated Noise Model Extraction
To extract the noise variables for this type of noise model, the small-signal param-
eters need to be determined and entered into a circuit as explained in the first section
of this appendix. In particular, have all the small-signal parameters entered into the
variable (VAR) block of the circuit network
templateHEMT smallsignaland PucelNoisemodel.dsn
Measured noise parameters are also needed to determine the noise variables. Once
setup, open the circuit schematic
templateparasitic matrix for correlation extraction.dsn
which is shown in figure A.4. Here, there are two networks simulated for S-parameters.
They correspond to the intrinsic and extrinsic parameters, respectively. If the small-
signal network listed above was used, itsVARblock can just be pasted into this design
160
APPENDIX A. ADS FILES
and the previous one deleted.
Simulating should bring up the data display
templatenoisecorrelation extraction.dds
A screen shot of it is shown in figure A.5. The noise parameters will need to be entered
into the equations inside theChange Thesebox. Once this is done, theCpd unnorm
box andCextwill be the desired results:Cpd unnorm(1,1)is the gate noise in units
of A2/Hz, Cpd unnorm(2,2)is the drain noise in units of A2/Hz, Cpd unnorm(1,2)
andCpd unnorm(2,1)are the cross-correlation terms (not used here), andCext is the
correlation between the gate and drain noise. Entering these back into the secondVAR
block in
templateHEMT smallsignaland PucelNoisemodel.dsn
will allow for simulation of the noise parameters.
161
APPENDIX A. ADS FILES
Figure A.4: Schematic used for extracting correlated noise model noise variables.
Figure A.5: Data display used for extracting correlated noise model noise variables.
162
BMatlab Code for Noise
Parameter Modeling
THIS Matlab script computes all four of the noise parameters as developed in§ 2.6,displays them in different formats, and plots minimum noise figure versus fre-
quency. This should facilitate the model’s use for other researchers. A copy of the filecan be obtained by contacting the author [email protected].
% NF.m% NF and other noise parameters including gate leakage, but not Cgd.% Chris Sanabria, 12/03/04
clear all;close all;
% Variables (change)
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APPENDIX B. MATLAB CODE FOR NOISE PARAMETER MODELING
Igs = 6e-6; % Gate leakagerge = 3.03; % Gate resistancers = 6;gmi = 0.033;ri = 8;cgsi = 0.21e-12;rds = 1000; % Drain-source resistance. Only used for a gain calculation
% and not for noise prediciton.
G = 2/3; % Gamma, use 2/3
f = [5e9 10e9]; % Operating frequency or frequenciesZo = 50; % Reference impedance for calculating reflection coefficientTa = 290; % Kelvin. This is the input temp., NOT the channel temp.!
disp([’r n = ’ num2str(Rn./Zo)])disp([’|Gammaopt| = ’ num2str(abs(Gamopt))])disp([’phase Gammaopt = ’ num2str(angle(Gamopt)/pi*180)])disp([’Gain av [dB] = ’ num2str(10.*log10(Gav))])
% Some plottingfigure;plot(f./1e9,NFmin,’r’)xlabel(’Frequency [GHz]’)ylabel(’NF min [dB]’)
165
CMatlab Code for Pospieszalski Noise
Parameter Modeling
THIS Matlab script calculates the two noise temperatures for the Pospieszalskinoise model as discussed in§ 2.5.3. Because this involves solving a pair of
quadratic equations, it returns two sets of noise temperatures. The temperatures thatare negative in value are non-physical and should not be used.
% noisetemps.m% Uses Pospieszalski’s model to get the two noise temperatures. You need to% have taken noise figure measurements and have extracted a small signal% model. Because the solving is for a pair of quadratic equations, there% are two sets of solutions. Ignore the negative temperature pair.% Chris Sanabria, March 2003
clc;format compact
%Input these:
freq = 10e9; % HzNFmin = 2.03; % dBrn = .755; % NOT ohms, the normalized valuegamopt= 0.609*exp(j*54.4/180*pi); % Complex Reflection Coefficientft = 22.1e9; % In Hz. Pospieszalski defines this as gm/(Cgs*2*pi), but the% author finds that the measured ft can work better.Cgs = .258e-12; % Faradsrgs = 7.46; % Same as Ri
166
APPENDIX C. MATLAB CODE FOR POSPIESZALSKI NOISE PARAMETER MODELING