UNIVERSIDAD DE CHILEFACULTAD DE CIENCIAS FSICAS Y
MATEMTICASDEPARTAMENTO DE INGENIERA ELCTRICA
Propuesta de Proyecto de Tesis Programa de Doctorado en
Ingeniera Elctrica
Simulaciones fsicas de la radiacin de la potencia de salida de
radiacin de terahercios desde un fotomezclador verticalmente
iluminado UTC y un estudio de la usabilidad de campos magnticos
para una mejorada caracterizacin de sus propiedades de transporte
de portadores
Thesis ProposalDoctoral Program in Electrical Engineering
Physical simulations on the terahertz radiation output power
from a vertically illuminated travelling wave UTC photomixer, and a
study of the usability of magnetic fields for improved
characterization of its carrier transport properties
Victor Hugo Calle GilThesis Advisor: Ernest Michael
SANTIAGO DE CHILE CHILE 2010
Contents1.Introduction131.1.Introduction and General
Context131.2.Thesis Project and State-of-the-Art141.3.Radio
astronomy Applications152.Fundamental Theory192.1.Photomixing
Theory192.2.PIN Photodiode202.3.Theory of UTC-PD
Photodetectors222.3.1.Structure232.3.2.How does it
work232.3.3.Performance features242.3.4.Modeling252.3.5.Boundary
Conditions292.4.Theory of vertically illuminated Traveling-wave
Photomixers312.5.Vertically illuminated
UTC-TW-Photodiode332.6.Numerical Analysis of a Vertically
Illuminated UTC-TW-Photodiode342.6.1.Finite Difference
Methods352.6.2.Finite Element
Method362.6.3.Transmission-Line-Matrix Method362.7.Models and
Devices372.7.1.CPW-Bowtie Aperture Antenna372.7.2.310 GHz
Uni-Traveling-Carrier Photodiode382.7.3.1.5 THz
Uni-Traveling-Carrier Photomixer392.7.4.Theoretical 340 GHz
Uni-Traveling Carrier Photomixer392.7.5.Theoretical 110 GHz UTC-TW
Photodetector402.7.6.Experimental UTC-TW Photomixer402.8.Influence
of a magnetic field412.8.1.Magnetotransport423.Proposed Research
work453.1.Hypothesis453.2.Goals453.2.1.Main Goal453.2.2.Specific
Goals453.3.Methodology453.3.1.Literature Review463.3.2.Carrier
Transport Modeling473.3.3.Electromagnetic
Modeling483.3.4.Combination of Electromagnetic and Carrier
Modeling494.Working Plan514.1.Phases and activities to be
performed514.2.Gantt chart525.Expected Results555.1.Physical
parameters555.2.Simulations and experiments to be
performed555.2.1.Proposed simulations555.2.2.Proposed
Publications576.Conclusions597.References61
List of FiguresFigure 1:16Figure 2:20Figure 3:20Figure
4:20Figure 5:21Figure 6:22Figure 7:23Figure 8:24Figure 9:32Figure
10.33Figure 11:34Figure 12:35Figure 13:36Figure 14:37Figure
15:38Figure 16.41Figure 17.43Figure 18:46Figure 19:47Figure
20:48Figure 21:49Figure 22:50Figure 23:50Figure 24:56
List of TablesTable 1: State of the art [23]
[36][37][41][42].15Table 2: Layer Composition of the 310 GHz
Uni-Traveling-Carrier Photodiode [64].38Table 3: Layer Composition
of the 310 GHz Uni-Traveling-Carrier Photomixer [15].39Table 4:
Layer Composition of the Theoretical 340 GHz Uni-Traveling-Carrier
Photomixer [41].39Table 5: Layer Composition of the Theoretical 110
GHz Uni-Traveling-Carrier Photodetector [37].40Table 6. Layer
Composition of the Experimental UTC-TW photomixer [31].40
List of AbbreviationsCPS: Coplanar striplineCPW:Coplanar-wave
guideCTA:Carrier Transport AlgorithmCW: Continuous-waveDD:
Drift-Diffusion equationsDDM:Drift-Diffusion
ModelEA:Electromagnetic Algorithm.EC: Equivalent circuitFEM:Finite
Element MethodFDM:Finite Difference MethodGaAs: Gallium ArsenideGHz
GigahertzHD: Hydrodynamic-Diffusion
equationsHDM:Hydrodynamic-Diffusion ModelHEB: Hot-electron
bolometerHECA:Hybrid Electromagnetic-Carrier AlgorithmHEDDA:Hybrid
Electromagnetic-Drift-Diffusion AlgorithmHEHDA:Hybrid
Electromagnetic-Drift-Diffusion AlgorithmLO: Local
OscillatorLT-GaAS: Low Temperature-Grown Gallium
ArsenideMSM:Metal-Semiconductor-MetalNIR: Near-infraredPD:
PhotodiodeRLT: Receiver Lab TelescopeSIS:
Superconductor-Insulator-SuperconductorTEM: Transversal
electromagneticTHz: TerahertzTLM:Transmission Line Matrix
MethodTLMM:Transmission Line Matrix MethodTW: Traveling-waveTWPD:
Traveling-wave photodetectorUTC-PD: Uni-traveling-carrier
PhotodiodeUTC-TW-PD:Uni-traveling-carrier Traveling-wave
photodetectorYIG: Yttrium-Iron-Garnet
List of Symbols: Absorption coefficient: Angular frequency:
Antenna resistance: Bias Voltage, :Constants >0: Carrier transit
distance: Carrier drift velocity, , : Constants >0: Electrical
Photocurrent: Electric DC current: Effective response time
(semiconductor): Electron recombination time: Electron trap time:
Electrical photo current at : Electrons photocurrent at : Electron
photocurrent saturation: Electron photocurrent of electrons or
holes (or): Electron mobility: Admittance matrix of coupled
waveguides: Frequency of operation: Frequency difference : 3dB down
frequency (cut-off frequency): Hole recombination time: Intrinsic
impedance of the medium: Intrinsic mobility: Optical electric
field: Optical intensity: Optical electric field from two lasers, :
Optical input power: Planck's constant: Photocurrent density in the
intrinsic region: Photogeneration rate: Power in terahertz range:
Recharge-time capacitance of the lumped elementRCbandwidth limit
(in frequency): Recombination time of the intrinsic region:
Saturation velocity of electrons: Saturation velocity of holes:
Transit time cut-off frequencyTransit time:
IntroductionIntroduction and General ContextThe generation of
powerful tunable continuous wave (CW) radiation in the
so-calledterahertz gap" has been intensively studied and there is
rapid progress in thelast couple of decades[1]-[15]. CW systems
based on photoconductive mixers (photomixers) have several
attractivefeatures: high spectral resolution, easily tunable in a
widefrequency range, and based on the relative cheap semiconductor
lasers.Nevertheless, THz photomixers have a substantial
disadvantage; so far their output power (efficiency) is very
low[16]. The generation of THz power with photonictechnology is
promising for new developments in several marked applications, such
as high-speed measurements [17], spectroscopy[18],wireless
communications[19], security and medicine[17][20][21], as photonic
Local Oscillators (LO) in astronomy applications [22] (for a more
detailed discussion about the astronomical applications see section
1.3),due to synergies with low-cost photonic techniquesalready
available for communication technologies.The development of
photonic local LO supplied for heterodyne receivers in radio
telescopes, could be regarded as a challenging research because of
the difficulty for obtaining high power and ultra wide bandwidth.
In order to get such powerful devices, the present research
proposal is part of the development of photomixers. The main
advantages of this technique over the conventional electronic
devices are the extremely wide bandwidth (e.g. 700 GHz for
LT-GaAs). In the last years, several research groups have developed
new high-speed photodiodes in order to obtain higher conversion
efficiency (responsivity) and ultra wide bandwidth. Among them are
the Uni-Traveling Carrier (UTC) photodiodes which have been
demonstrated as the most efficient for the generation of CW THz
signal[23][24][25][16]. On the other hand, the concept of
Traveling-Wave (TW) in photomixers [26] has been applied for
developing edge-coupled photodetectors with larger
bandwidth-efficiency products [9][27][28][29]. However, while
edge-coupled devices inherently suffer from velocity mismatch
between optical and submm-wave and power limitations due to the
small optical cross section [30], vertically illuminated
TW-MSM-mixer structures were demonstrated to be in full TW mode due
to the in-situ adjustability of the optical fringe velocity and to
have high power capabilities if large optical absorption areas are
realized.Actually, the Radio Astronomical Instrumentation Group
(RAIG) is developing a novel device, which it is a merger of two
ideas, the concept of vertically illuminated TW photomixers and the
concept of UTC layer systems: vertically pumped TW-UTC structures
[31]. It is interesting to take into account the thicknesses used
in the manufacture of an UTC-photodiode. For example, the
UTC-photodiode developed by Ishibashi et al[32], its device
thickness of the most important layer, the absorption layer, is
about 220 nm [33]. Therefore, the reduced feature sizes require
more complicated and time-consuming manufacturing processes [34].
It means that a pure trial-and-error approach to device
optimization will become impossible since it is both time consuming
and expensive [34]. Since computers are considerably cheaper
resources, simulation is becoming an indispensable tool for device
engineering[34]. Besides offering the possibility to test
hypothetical devices which have not yet been manufactured,
simulation offers unique insight into device behavior by allowing
the observation of phenomena that cannot be measured on real
devices[34].As it was mentioned above, the RAIG group is developing
TW-UTC photodiodes. In order to perform the present proposal
research, it is important to understand that it is necessary to
perform carrier transport and RF simulations [35][36][37]. Thesis
Project and State-of-the-ArtFor the first time in modeling of UTC
photodiodes, Ishibashi et al [38] used a Drift-Diffusion model for
analyzing carrier dynamics in the absorption layer. They treated
carefully the boundary conditions by taking into account the
thermionic emission velocity of electron in order to accurately
calculate the response in scaled UTC-PD structures. They found that
the velocity overshoot effect plays an essential role in broadening
the UTP-PD bandwidth.They also concluded that the response of a
UTC-PD is dominated by the electron transport in the absorption
layer. Moreover, calculations predicted that an UTC-PD with a
quasi-field in the absorption layer could generate a much broader
bandwidth than a conventional PD with similar internal quantum
efficiency.Pasalic et al [39] presented a hybrid method for
numerical analysis oftraveling-wave photodetectors (TWPDs). The
method is a combination of two-dimensional semiconductor and
three-dimensional full-wave electromagnetic (EM) simulators. The
time-domain drift-diffusion method is used to determine the
photogenerated currents at the cross section of the device to
calculate the microwave bandwidth and output current of the device.
In the analysis, the effects of the carrier velocity and lifetime,
optical power, bias voltage, velocity mismatch, and microwave loss
are taken into account. The method is tested in case of GaAs and
low-temperature-grown GaAs-based TWPDs. Again, Pasalic et al [37]
used their previous work to extend the hybrid drift-diffusion
(DD)TLM method to include the analysis ofuni-traveling-carrier
(UTC) photodetectors. The extended method considers the overshoot
velocityat which electrons in the collector of an UTC photodiode
drift. The method is used for large and smallsignal analysis of the
UTC traveling-wave photodetector (TWPD) and near-ballistic (NB) UTC
TWPD. They showed that there is a trade-off between the UTC TWPDs
bandwidth and saturation current that has to be considered in the
design. A higher bias voltage reduces the bandwidth, but also
increases the saturationcurrent of the photodetector. They
presented a UTC TWPD with bandwidths of 110 and 83 GHz
andsaturation currents of 15 and 30 mA under 1 and 5 V biases,
respectively. Mahmudur et al [40] presented results of a UTC
photodiode using the hydrodynamic carrier transport model. A
maximum responsivity of 0.25 A/W and a small signal 3-dB Bandwidth
of 52 GHz were obtained for a 220-nm-thick InGaAs absorption layer.
They investigated the physical properties of the UTC-PD under
different optical injection levels. Moreover, they observed a
modulation of the energy-band profile due to the space charge
effect at high injection level, and a velocity overshoot of 3107
cm/s has been found to effectively delay the onset of the space
charge effects. Also, they found that the speed of the photo
response of the UTC-PD could be improved by incorporating a graded
doping profile in the absorption layer.Banik et al [41]presented a
method to optimize the epitaxial layer structure of an InGaAs/InP
uni-traveling-carrier photo-diode (UTC-PD) for continuous THz-wave
generation. The design approach used is general in that it can be
applied for any target frequency while this study focuses on 340
GHz. The photodiode epitaxy is modeled and optimized using a
TCAD-software implementing the hydrodynamic semiconductor
equations. Their results showed that the UTC-PD can generate ~1 mW
at 340 GHz by choosing the optimum absorption layer and collection
layer thicknesses.All the above works rely in the modeling and
simulation of both electromagnetic and carrier transport phenomena.
Table 1 summarizes the State of Art of numerical modeling. As shown
in Table 1, the simulation and modeling using drift-diffusion and
hydrodynamic carrier transport models were applied only on the
UTC-photodiode. Modeling and simulation on UTC-TW photodiodes were
realized using only a hybrid drift-diffusion-TLM model. Therefore,
the present research proposal suggests a novel hybrid model for the
UTC-TW using the hydrodynamic carrier transport model and TLM. The
use of hydrodynamic carrier transport model has the advantage that
it takes into account more information than the drift-diffusion
carrier transport model like carrier temperature dependent
parameters such as motilities and diffusion coefficients and
thereby it models more accurately the carrier transport [41].
Carrier transport ModelThree-dimensional Full-wave electromagnetic
analysis
UTC-PDTW-PDUTC-TW-PD
Drift-Diffusion Carrier Transport ModelIshibashi et al:
Drift-Diffusion algorithm.Pasalic et al: TLM Method.Pasalic et al:
TLM Method.
Hydrodynamic Carrier transport ModelBanik et al: Sentaurus
TCAD.Mahmudur et al: ISE-TCAD (Now is Sentaurus TCAD).Not yet
done.Not yet done.
Table 1: State of the art [23][36][37][41][42].Moreover, as an
optional development, we will include an additional variable
magnetic field in the drift-diffusion carrier transport and
hydrodynamic models, with the purpose of investigating the effect
of a magnetic field in carrier transport properties of a UTC-TW
photodiode. This experimental was not achieved yet. By the optional
term I mean if there is enough time, the Hydrodynamic Carrier
Transport Model will be extended in order to include the magnetic
field parameter.Radio astronomy ApplicationsTerahertz technology is
a fast-growing field with a variety of applications in biology,
medicine, spectroscopy, astronomical instrumentation, security and
communications. Among the different terahertz continuous-wave (CW)
devices, photomixers have the best possibilities of small and
economical, low power consumption, highly coherent and tunable
devices[1]-[13]. A photomixer is a device that employs a heterodyne
scheme, in which two laser beams with their frequency difference
falling in the terahertz range mix in a medium like aphotoconductor
or superconductor, and generate a signal, whose frequency is equal
to the frequency difference of the two lasers[11]. This device can
exhibit a nonlinear I-V bias curve, but not necessarily. A
photomixer can also have linear I-V-curve, an example is
illustrated later.The spectral regionfrom 0.3 to 3 THz, located
between the radio range, controlled by macroscopic flows of
electrons (amplifiers, frequency multipliers), and the infrared
range controlled by optical media (lasers), is often called the
terahertz gap due to the lack of strong tunable sources. In that
scheme, terahertz photonic sources can be considered as an
interesting hybrid approach: a direct ultra-high speed control of
an electron flow, confined in space as much as possible at the
foot-point of a microscopic antenna by means of laser light. One of
the most important motivations to develop efficient CWterahertz
photomixers is their use as efficient local oscillators. In radio
astronomy, they are employed in heterodyne receivers, in which the
frequency of detected radiation is down-converted to an
intermediate frequency (IF) by mixing with a monochromatic local
oscillator signal. The main motivation for terahertz receivers is
the study of the terahertz frequency range (1-3 THz, or wavelength:
100-300 m), which provides a vision of the Universe in the far
infrared. This window provides unique goals for both the
interstellar chemical and star formation studies. For example, the
cold interstellar clouds (10-15 K) emit their strongest radiation
in the frequency range of 1.0-1.5 THz. Moreover, in the hot cores
(50-200 K) where the stars are forming, the species CO, CN, HCN and
HCO emit their strongest rotational radiation in this range of
frequencies[43].Near both young and evolved stars, molecules exist
across a large range of excitation levels, with the more
highly-excited states often located closer to the exciting source
or protostar[43].An inspection of the objects in theses spectral
lines is likely to provide a good discriminator of the various
stages of the protostellar evolution[43]. A broad range of
atmospheric windows open up to 1500 GHz (see Figure 1), at the
uniquely dry Chajnantor altiplano in the Chilean Andes, where the
ALMA (Atacama large Millimeter Array) interferometer and many other
internationally operated single-dish radio-telescopes are taking
advantage of this worldwide unique site. While ALMA has a photonic
local oscillator (LO) system already developed and will have ten
receiver bands covering all atmospheric windows up to 950 GHz, some
of the single-dish telescopes will have instrumentation projects up
to the 1500 GHz window (e.g. Receiver-Lab-Telescope (RLT), Nanten
2, Cornell-Caltech-Atacama-Telescope (CCAT), APEX Telescope. While
many spectral lines of high scientific interest are falling into
these atmospheric windows, these ground-based observatories will
offer significant advantages in terms of costs and
logisticscompared to aircraft and balloon-based platforms, and
therefore open access to technology-pushing experiments.
Cooperation with the RLT and CCAT groups is currently being
developed.
Figure 1:The leftfigure shows the atmospheric transmission
between 200 GHz and 1.6 THz for different PWV values. (source:
www.apex-telescope.org). The right figure shows the annual
variation of the Precipitable Water Vapor (PWV) content at
Chajnantor, based on 10 years of site testing.
Heterodyne receivers provide the spectral high resolution
necessary to study these spectral lines. They down-convert the high
frequency to one in the gigahertz-range by mixing with a coherent
continuous-wave radiation source, called local oscillator. The type
of local oscillators most commonly used in radio-astronomical
receivers is based on Gunn- and YIG- oscillators, both of them with
frequency multiplier chains. Typical terahertz power values
provided by frequency multiplier sources based on waveguides are
300 - 1000 W in the range 400 - 500 GHz, 20 - 30 W in the range 900
- 1100 GHz and 2 - 4 W in the range 1300 - 1600 GHz (see company
Virginia Diodes). Themain drawbacks are theirsmall relative
bandwidth which decreases toward higher frequencies and the
possible variations of power within these bandwidths. Therefore,
the full coverage up to frequencies above 1 THz is complicated and
expensive because it has to be provided by a collection of
individual costly local oscillators. Especially for 1 THz or
higher, frequency multipliers of the local oscillator are very
expensive and often not available for certain frequency ranges.In
contrast to this situation, a terahertz photomixer will deliver all
the frequencies and the spectrum will be flat except for the
overall roll-off in power. The crucial point is that if only enough
power is provided to pump SIS junctions
(Superconductor-Insulator-Superconductor) or HEB Bolometers
(Hot-Electron Bolometer), photonic local oscillator will bring
great benefits to radio-astronomy, especially in the higher
frequency ranges. Besides their unmatched tuning range, photomixers
are also particularly attractive for their all-solid-state,
non-cryogenic, non-high-voltage, low power consumption, and
relative low-cost approach.The pumping of SIS receivers and
recently HEB receivers has been demonstrated up to 700 GHz, but
only from the highest levels of power available from the photonic
mixers and with the LO source coupled to the receiver with a
diplexer. However, the supply of power offered at frequencies above
1 THz is still a challenge, although it is within the scope of the
current development of the LT-GaAs photomixers. Power requirements
necessary to excite SIS or HEB receivers increase with frequency:
recent values for pumping of SIS junction of small areas are
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Start
1D-BC
1D-DDA
1D-SR ~ 1D-DDAR?
Tuning 1D-DDA
2D-BC
2D-DDA
2D-SR ~ 2D-DDAR?
Tuning 2D-DDA
End
No
Yes
No
Yes
Start
1D-BC
1D-HDA
1D-SR ~ 1D-HDAR?
Tuning 1D-HDA
2D-BC
2D-HDA
2D-SR ~ 2D-HDAR?
Tuning 2D-HDA
End
No
Yes
No
Yes
3D-BC
Start
1D-BC
1D-EA
1D-HR ~ 1D-EAR?
Tuning 1D-EA
2D-BC
2D-EA
2D-HR ~ 2D-EAR?
Tuning 2D-EA
End
3D-EA
No
Yes
No
Yes
3D-HR ~ 3D-EAR?
Tuning 3D-EA
No
Yes
Start
BC
HEDDA
HEDDAR ~ PTM?
Tuning HEDDA
End
No
Yes
Start
BC
HEHDA
HEHDAR ~ PTM?
Tuning HEHDA
End
No
Yes