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Global Modeling of High Frequency Circuits and Devices PhD defense by Julien Branlard Committee chairman: Dr. M. Saraniti, (ECE, IIT) Committee members:Dr.

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Presentation on theme: "Global Modeling of High Frequency Circuits and Devices PhD defense by Julien Branlard Committee chairman: Dr. M. Saraniti, (ECE, IIT) Committee members:Dr."— Presentation transcript:

1 Global Modeling of High Frequency Circuits and Devices PhD defense by Julien Branlard Committee chairman: Dr. M. Saraniti, (ECE, IIT) Committee members:Dr. T.Y. Wong, (ECE, IIT) Dr. A.Z. Wang, (ECE, IIT)Dr. C.U. Segre, (BCPS, IIT) Dr. D.K. Ferry, (EE, ASU) Chicago, November 19 th 2004

2 1 Chicago, November 19 th, 2004 The simulation tool GaAs devices Small-signal analysis Noise analysis Memory management Conclusions I NTRODUCTION 1- Presentation outline

3 1 Chicago, November 19 th, 2004 Full-band model Cellular Monte Carlo (CMC) I NTRODUCTION 2- Full-band particle-based simulations GaAs

4 1 Chicago, November 19 th, 2004 Full-band model Cellular Monte Carlo (CMC) Scattering phonon, impurity, impact ionization I NTRODUCTION 2- Full-band particle-based simulations

5 1 Chicago, November 19 th, 2004 Full-band model Cellular Monte Carlo (CMC) Scattering phonon, impurity, impact ionization Bulk simulations very good agreement with published data I NTRODUCTION 2- Full-band particle-based simulations

6 1 Chicago, November 19 th, 2004 I NTRODUCTION 3- Ensemble* and Cellular ◊ Monte Carlo carrier (   k) (  ’  k’) scattering EMC CMC Pre-compute all possible final energies and momenta Associate a probability Store these rates in look up tables * M.V. Fischetti and S.E. Laux, “MC analysis of electron transport in small semiconductor devices” ◊ M. Saraniti and S.M. Goodnick, “Hybrid Fullband Cellular Automaton/ Monte Carlo Approach for Fast Simulation of Charge Transport in Semiconductor” Compute the new energy and momentum during run-time

7 2 Chicago, November 19 th, 2004 GaAs D EVICES 1- GaAs MESFETs: geometry Structural simplicity “High speed”, low noise applications S G D SGD ND+ND+ N

8 2 Chicago, November 19 th, 2004 GaAs D EVICES 2- GaAs MESFETs: DC characteristics Gate length and width:L G, W G Doping profile:N D +, N Operating point: V DS, V GS

9 2 Chicago, November 19 th, 2004 GaAs D EVICES 3- GaAs MESFETs: 3D devices Various geometry: L G, W G 2D / 3D characterization S D n+n+ n WGWG LGLG n+n+ n LGLG S D WGWG WGWG WGWG G G

10 2 Chicago, November 19 th, 2004 GaAs D EVICES 4- GaAs MESFETs: Gunn oscillations Gunn domain d =1300 nm N D =10 17 cm -3 f osc = 50 GHz d =650 nm N D =2x10 17 cm -3 f osc = 100 GHz substrate G NDND d SD

11 2 Chicago, November 19 th, 2004 GaAs D EVICES 5- AlGaAs/GaAs HEMTs: geometry SOURCE GATE DRAIN AlGaAs n + GaAs n spacer V GS < 0 V DS > 0 2DEG

12 2 Chicago, November 19 th, 2004 GaAs D EVICES 6- AlGaAs/GaAs HEMTs: DC characteristics

13 2 Chicago, November 19 th, 2004 GaAs D EVICES 6- AlGaAs/GaAs HEMTs: DC characteristics

14 3 Chicago, November 19 th, 2004 Frequency Analysis 1- Problem definition: impedance 0T i (t) 0T ΔVΔV v (t) i(t) VGVG S GD maximum reactive frequency

15 3 Chicago, November 19 th, 2004 Frequency Analysis 1- Problem definition: 0T i (t) 0T ΔVΔV v (t) i(t) VGVG S GD STEP 1: Apply a voltage perturbation on one electrode STEP 2: Compute the Fourier transform STEP 3: Compute the complex impedance and gains

16 3 Chicago, November 19 th, 2004 Frequency Analysis 1- Problem definition: figures-of-merit  V DS  V GS for constant V GS for constant V DS

17 3 Chicago, November 19 th, 2004 Frequency Analysis 1- Problem definition: Y-parameters

18 3 Chicago, November 19 th, 2004 Frequency Analysis 1- Problem definition: gain 0T i (t) 0T ΔVΔV v (t) i(t) VGVG S GD * * S. S. Pennathur, S.M. Goodnick, “ MC investigation of 3D effects in sub-micron GaAs MESFETs ”

19 3 Chicago, November 19 th, 2004 Frequency Analysis 2- Sinusoidal excitation: Apply a sinusoidal voltage on one electrode Simulation time: T Frequency of interest I SS

20 3 Chicago, November 19 th, 2004 Frequency Analysis 2- Sinusoidal excitation: STEP 2 Take the Fourier transform of the current variation

21 3 Chicago, November 19 th, 2004 Frequency Analysis 2- Sinusoidal excitation: Compute the complex output impedance f Xm  50 GHz L G = 100 nm

22 3 Frequency Analysis 2- Sinusoidal excitation How many periods to apply ? Chicago, November 19 th, 2004

23 3 Frequency Analysis 3- Fourier decomposition* Apply a voltage perturbation on one electrode Take the Fourier transform of the current variation Compute the complex output impedance * R.W. Hockney, and J.W. Eastwood: Computer Simulation Using Particles, 1988 0T ΔVΔV 0T ΔVΔV

24 3 Chicago, November 19 th, 2004 Frequency Analysis 3- Fourier decomposition: current response Sampling time step: DT Maximum reachable frequency: Simulation time: T Frequency resolution: 0T ΔVΔV 0T ΔVΔV

25 3 Chicago, November 19 th, 2004 Frequency Analysis 3- Fourier decomposition* Sampling time step: DT Maximum reachable frequency: Simulation time: T Frequency resolution: 0T ΔVΔV * R.W. Hockney, and J.W. Eastwood: Computer Simulation Using Particles, 1988

26 3 Chicago, November 19 th, 2004 Frequency Analysis 3- Fourier decomposition f T  60 GHz L G = 98 nm Compute the complex output impedance f Xm 60 GHz ~ ~

27 3 Chicago, November 19 th, 2004 Frequency Analysis 4- Polychromatic sinusoids Apply a sum of sinusoids voltage on one electrode Simulation time: TFrequency of interest Harmonics: for

28 3 Frequency Analysis 4- Polychromatic sinusoids Importance of the operating point V GS, V DS Chicago, November 19 th, 2004

29 3 Frequency Analysis 4- Polychromatic sinusoids Take the Fourier transform of the current variations N S = 3 /0/0  v ds  x V  /  0 ] ^ N S = 10 /0/0  v ds  x V  /  0 ] ^ Chicago, November 19 th, 2004

30 3 Frequency Analysis 4- Polychromatic sinusoids Compute the complex output impedance for L G = 100 nm Chicago, November 19 th, 2004

31 3 Frequency Analysis 5- Approach comparison Fourier Decomposition frequency spectrum long simulation time Sinusoidal Excitation more flexible more precise Chicago, November 19 th, 2004 f Xm = 50 GHz

32 3 Frequency Analysis 6- Perturbation on the gate: derive gains Chicago, November 19 th, 2004 Output voltage gain: L G = 100 nm MESFET

33 3 Frequency Analysis 6- Perturbation on the gate: derive gains Chicago, November 19 th, 2004 Short circuit current gain: L G = 100 nm MESFETHEMT f T = 70 GHz f T = 125 GHz

34 3 Frequency Analysis 6- Perturbation on the gate: derive gains Chicago, November 19 th, 2004 Comparison with published data * F. Schwierz, J.J. Liou, “ Modern Microwave transistors”, 2003 *

35 3 Frequency Analysis 6- Perturbation on the gate: derive gains Chicago, November 19 th, 2004 Unilateral Power Gain (UPG) L G =100 nm MESFET

36 3 Frequency Analysis 6- Perturbation on the gate: derive gains Chicago, November 19 th, 2004 Maximum Stable Gain (MSG) MESFET L G =100 nm

37 4 Chicago, November 19 th, 2004 Noise Analysis 1- Basic principles Device maintained in steady state: I ss V ss simulation time T time step DT Current fluctuations drain, gate electrodes Voltage fluctuations potential snapshots time AND space

38 4 Chicago, November 19 th, 2004 Noise Analysis 1- Basic principles Device maintained in steady state: I ss V ss Current fluctuations drain, gate electrodes Voltage fluctuations potential snapshots time AND space

39 4 Chicago, November 19 th, 2004 Noise Analysis 1- Two modes of analysis Device maintained in steady state: Iss Vss Current noise mode current fluctuations Autocorrelation function Power spectral density Voltage noise mode voltage fluctuations Autocorrelation function Power spectral density

40 4 Chicago, November 19 th, 2004 Noise Analysis 2- Spectrum analysis Biased autocorrelation Correlogram

41 4 Chicago, November 19 th, 2004 Noise Analysis 3- Current Noise Autocorrelation function AlGaAs/GaAs HEMT exponential decay plasma relaxation time dielectric relaxation time

42 4 Chicago, November 19 th, 2004 Noise Analysis 3- Current Noise Density spectrum AlGaAs/GaAs HEMT plasma oscillation f p (n) f p (n + )

43 4 Chicago, November 19 th, 2004 Noise Analysis 3- Current Noise Spectral Densities: low frequency GaAs n + n diode shot noise linear behavior carriers in the depletion region thermal noise spatially distributed independent of applied voltage excess noise hot carriers close to the drain electrode shotthermalexcess applied bias [mV]

44 4 Chicago, November 19 th, 2004 Noise Analysis 4- Voltage Noise Autocorrelation function GaAs n + n diode oscillations plasma relaxation time dielectric relaxation time higher voltages

45 4 Chicago, November 19 th, 2004 Noise Analysis 4- Voltage Noise Spectral Density GaAs n + n diode

46 4 Chicago, November 19 th, 2004 Noise Analysis 4- Voltage Noise Spectral Density GaAs n + n diode

47 4 Chicago, November 19 th, 2004 Noise Analysis 4- Voltage Noise Spectral Density: HEMT SOURCE GATE AlGaAs n + 2DEG

48 4 Chicago, November 19 th, 2004 Noise Analysis 4- Voltage Noise Spectral Density Derivative GaAs n + n diode shot thermal excess shot noise dominant for low voltages thermal noise spatially distributed excess noise hot carriers near end of the device

49 5 Chicago, November 19 th, 2004 CMC Memory Usage 1- CMC Scattering: problem definition Scattering Tables address rate 4 Bytes Total size: 8 Bytes Significant digits: 7

50 5 Chicago, November 19 th, 2004 CMC Memory Usage 2- First approach: 25% savings Principle address rate 4 Bytes Total size: 6 Bytes Lesser precision excellent agreement on all materials Memory misalignment compiler dependent slower execution overcome by faster arithmetic rate Significant digits: 4

51 5 Chicago, November 19 th, 2004 CMC Memory Usage 2- First approach: 25% savings Bulk simulations Tested on GaAs, Si, Ge, GaN (wurtzite and zincblende) Excellent agreement 25% reduction achieved

52 address 5 Chicago, November 19 th, 2004 CMC Memory Usage 3- Second approach: 50% savings Principle address rate 4 Bytes Total size: 4 Bytes Addressing absolute relative Use of offsets phonon scattering < impact ionization Normalizing the rates r max Joining the rate and the address rate Significant digits: dynamic distance

53 5 Chicago, November 19 th, 2004 CMC Memory Usage 3- Second approach: 50% savings Bulk simulations Tested on GaAs, Si, Ge, GaN (wurtzite and zincblende) Excellent agreement 50% reduction achieved

54 5 Chicago, November 19 th, 2004 CMC Memory Usage 3- Second approach: 50% savings Error estimation

55 5 Chicago, November 19 th, 2004 CMC Memory Usage 3- Second approach: 50% savings Performance

56 6 Chicago, November 19 th, 2004 Summary 2D and 3D simulations of GaAs devices diodes, MESFETs, HEMTs Small-signal analysis Investigated several methods Implemented a hybrid approach Derived full small-signal parameters Noise analysis Investigated current and voltage noise approach Studied GaAs devices Identified frequency behavior Voltage dependence Spatial distribution Memory management Implemented two algorithmic optimizations Achieved the requested compression Gain in computational efficiency New horizons for the CMC

57 Chicago, November 19 th, 2004 Thank You !

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