Mechanisms of 1/f noise and Gain Instabilities in metamorphic HEMTS

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Mechanisms of 1/f noise and Gain Instabilities in metamorphic HEMTS

D. Bruch; M. Seelmann-Eggebert; S. Guha

Fraunhofer Institute for Applied Solid State Physics IAFTullastrasse 7279108 Freiburg Germany

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IAF Departement for High Frequency Devices and Circuits

Status 35 nm mHEMT

fT > 500 GHz

fmax > 900 GHz

Target

20 nm mHEMT fmax > 1.3 THz

Transit Frequency

100 nm

50 nm

35 nm

20 nm

fT = 220 GHz

fT = 515 GHz

fT = 375 GHz

fT = 660 GHz 400 420 440 460 480 500-30

-20

-10

0

10

20

30

S-P

aram

eter

s [

dB]

Frequency [GHz]

S21

S11

S22

Good RF performance (e.g. Gain and Noise properties)

But Low frequency noise comes into play for frequency converting (non-linear)circuits (e.g. Mixers, oscillators) and (Low-Frequency) Amplifiers.

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Stochastic Processes and Noise

Measurement of entity u vs. time

u

P(u)

probability distribution- expectation value- variance

Autocorrelation function (ACF)

T

T dttuu0

1 )(222)( uuuu

T

TA dttutu0

1 )()()(

- Constant for static process- contains information on deterministic dynamics

Noise = power density spectrum= fourier transform of ACF

Dynamics underlying stochastic process

defS Afj )()( 2

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Noise - Frequency Dependency

: white noise: 1/f-Noise (Flicker Noise, pink noise): „Brownian“-Noise (red noise)

ffS

1)(

05.15.0 2

Noise Power Density Spectrum:

Autocorrelation function:

)()()( tAtAA

djffS a )2exp()(2)(

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Hooge‘s Parameter

Empirical Approach to define 1/f Noise, independent of noise origin:

NfI

fS HI

2

)(

:Hooge‘s Parameter initialy found to be ::Number of carriersH 3102

* „1/f Noise is no surface effect“, F.N. Hooge, Physics Letters A, 1969.** „1/f Noise in GaAs Filaments“ M. Tacano et. al., IEEE Transactions on Electonic Devices ,1991. *** „Bulk and Surface 1/f“, Lode Vandamme, IEEE Transactions on Electronic Devices,1989.

*

Device

GaAs MESFET**

GaAs filament**

N-type Silicon-Res.***

-

H4102 3102

7101 5101

N

If a 1/f Noise-Spectrum is observed it can bedescribed by:

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Low-frequency noise: Dynamic processes with long time constants

Generation-Recombination Processes

Typical for deep traps and lattice mismatch

The high electron mobility transistor (HEMT) is a “surface” component

Layer composition ofFraunhofer IAF‘s 35nm mHEMT

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Generation-Recombination Process with two states

),1()1(),1(),1(),()]()([),(

),()](1)][(1[),1(),1(),1()1(),(

jPjGjPjRjPjRjGjPd

d

djPjRjGdjPjRdjPjGdjP

Probability for j carriers at state b at time under the assumption that only one transition is possible during .

dt d

GR

1With this leads to: )exp()(

GR

R

The Autocorrelation is given by an Expectation (value)and hence depending on .

)()()( tAtAA

),( jP

Which is solved by:

exp),( jP

2)2(1

1)(

ffSGR

b

a

G R

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Generation-Recombination Process and the McWhorter-Model

*„Low-Frequency Noise Characterisitcs of Lattice-Matched (x = 0.53) And Strained (x > 0.53I InAlAs/InGaAs HEMT‘s“ G.I. Ng et. al., 1992, IEEE Transactions on Electron Devices.

This does not give a 1/f noisespectrum by itself!

But the superposition of plentyof GR-processes featuring differentTime constants leads to a spectrumwhich behaves LIKE 1/f noise.

„Non-fundamental“-1/f noise.With reported f up to ~700 MHz C

*

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Fundamental Quantum 1/f Noise

„Random“ change in carrier velocity/mobility caused by scattering mechanisms.

Voltage and current fluctuations not only due to carrier densitybut also due to carrier velocity

Scattering of carriers in HEMTs:

Confinement layers e.g.: , Spacer, Buffer, …

Scattering in the channel, the confinementlayers or the interface

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Fundamental Quantum 1/f noise

The Photons generated by the decelerated charge carriers influence the carriersthemself (feedback mechanism).*

After P.H. Handel this leads to a spectrum density of:

*„Fundamental Quantum 1/f Noise in Semiconductor Devices“ P. Handel, 1994, IEEE Transactions on Electron Devices.

fAfS j /2)(

: Sommerfield‘s fine structure constant

A: proportional constant

c

e

2

2

2

3

22

c

a

f ~ 100 kHzknee

Hooge‘s Parameter predicting quantum 1/f noise:

2

22

3

4

c

v

c

eH

v : average change in velocity

*

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Bremsstrahlung due to Scattering

Scattering at impurities, phonons, interface roughness, etc.

„Loss“ of energy (Larmor)

e: charge of electrona: acceleration (approximated by Δ function)c: speed of light

)3/(2 322 caeP

f

#Photo

n

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Fundamental 1/f Noise

fhE

3

22

3

)(4

cfh

vqNoP

: Number of Photons

Generation of „soft“-Photons with shifting a part of the DeBroglie waves to lower frequencies, resulting in a beat term.

Spectral density of the emitted Bremsstrahlung energy: .3

)(43

22

constc

vq

The resulting spectral density of the beat term is then given by:

Nfch

vqfS j

3

22

3

)(42)(

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Measurement Observations

„Well behaved“ 100nm TransistorSize: 4x30 µm

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Measurement Observations

„Bad behaved“ 50nm TransistorSize: 2x30 µm

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Model Extension: 1/f-Noisesource

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Thank You!

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