december2004 swissfederalinstituteoftechnologyzurich ...schenk/apmc04_slides.pdf · apmc’04...

APMC’04

Integrated Systems Laboratory

Simulation of Physical Semiconductor Devices under

Large and Small Signal Conditions

Bernhard Schmithusen, Andreas Schenk, Ivan Ruiz, Wolfgang Fichtner

Swiss Federal Institute of Technology ZurichDecember 2004

APMC’04


Outline

(A) Physics-Based Analysis of a RF-Bipolar Transistor

• Simulation Frame• DC, AC, Noise, Large Signal Transient Analysis

(B) Harmonic Balance for Mixed-Mode Simulations

• HB Equation Solving Strategies• Examples

PN Diode, Varactor Frequency Doubler,MOSFET, Simple Bipolar

Conclusions

APMC’04


RF-Bipolar

Physics-Based Characterizationof the Intrinsic RF-Bipolar Transistorand of Mixed-Mode Power Amplifier

Figures of Merit:

• DC: Early and Gummel Plots• Small Signal: S-Parameters, Power Gain,Current Gain

• Noise: Voltage and Current Noise Spectra• Large Signal: Distortion,Compression Point CP1dB, IP3

RF-Bipolar Structure (Segment)with Doping

APMC’04


Simulation Frame

Transport:DD, TD, HD, QDD, MC, ...

Physical Description:Thermionic Emission, Tunneling,Gate Currents, Schrodinger,Optics, Physical Model Interface (PMI), ...

Computational Features:1D - 3D, Hetero Structures,DC Grid Adaptation,Mixed-Mode (HSPICE),Compact Model Interface (CMI)

Analysis:DC, Transient, AC, Noise

Drift-Diffusion Model

−∇ · (ε∇ψ) = q (p− n + C)

q∂n

∂t−∇ · jn = −q R

q∂p

∂t+∇ · jp = −q R

jn = q (Dn∇n− µnn∇ψ)

jp = −q (Dp∇p + µpp∇ψ)

and boundary conditions

d

dtq(r, u(t)) + f(r, u(t), w(t)) = 0

APMC’04


RF-Bipolar: DC

0 1 2 3 4 5 6 7 8Collector voltage (V)

0e+00

1e-04

2e-04

3e-04

4e-04

Col

lect

or c

urre

nt (

A)

Ib=2.5µAIb=2.0µAIb=1.5µAIb=1.0µAIb=0.5µA

Early characteristics

0.2 0.4 0.6 0.8 1.0 1.2Base voltage (V)

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

Cur

rent

(A

)IbIc

Forward Gummel characteristics

Physical Effects:Bandgap Narrowing,Minority Diffusion Length,Saturation Velocity, Doping of Collector,Pre-Breakdown, ...

Grid Size NV = 6654

APMC’04


AC Analysis

Linearization around DC Solution u0

[jωq′(u0) + f ′(u0)]U1 = −WU1 Phasors of Solution Variables

Results:• Y-Parameters• Locally Distributed Responseof Potential, Densities, and Current Densities

Computational Aspects

• Solve Linear System in C

• Requires Direct Linear Solver !

108

1010

−40

−30

−20

−10

0

10

20

30

|Sij|

[dB

]

S−parameters Vbe=0.9V Vce=2V

Frequency [Hz]

|s22||s12||s21||s11|

S-Parameters

APMC’04


RF-Bipolar: Small Signal

Electron Current Hole Current

Local AC Current Densities (∣∣Re(J1)∣∣ )

APMC’04


RF-Bipolar: Small Signal

10 20 300

5

10

15

20

25

30

35

Collector current [mA]

Gai

n [d

B]

VCE

=3V

f=1GHz

f=1.52GHzf=2.31GHz

f=3.51GHz

f=5.34GHzf=8.11GHz

108

109

1010

100

101

|h21| Vbe=0.9V Vce=2V

Frequency [Hz]

|h21

| [dB

]

108

109

1010

1011

−10

0

10

20

30

40

Frequency [Hz]

Gai

n [d

B]

Vce=2V Ic=1.45mA

MAG

|s21|2

MSG

APMC’04


Noise Analysis

Shockley’s Impedance Field Method

Langevin Equation

L(D,u0)δu = s

Noise Voltage Spectral Density

SV,V (r, r′;ω) =

=∑α,β

∫

Ω

Γα(r, r1;ω)Kα,β(r1;ω)Γ∗β(r

′, r1;ω)d r1 +

+∑α,β

∫

X

Γα(r, r1;ω)Kjα,jβ(r1;ω) Γ

∗β(r

′, r1;ω)d r1

Diffusion Noise Source

Kjn,jn

(r) = 4q2n(r)µn(r)

106

107

108

109

1010

1011

1012

1013

frequency (Hz)

10−20

10−19

10−18

10−17

10−16

10−15

10−14

10−13

10−12

10−11

10−10

10−9

nois

e vo

ltage

spe

ctra

l den

sity

(V

2 /Hz) Sv(base)

Sv(collector)|Re Sv(base,collector)||Im Sv(base,collector)|

Noise Voltage Spectral Densities

of the Bipolar

APMC’04


RF-Bipolar: Noise

Bias: VBE = 0.84 V, VCE = 2V, f = 10 GHz

+6.161e-36

+2.247e-31

+8.199e-27

+2.991e-22

+1.091e-17C2/(s*cm)eeDiffLNS

+5.973e-20

+6.426e-13

+6.866e-06

+7.335e+01

+7.837e+08V2s2/(C2*cm2)g2_GradPoEC

+0.000e+00

+9.555e-19

+1.826e-16

+3.490e-14

+6.670e-12V2s/cm3LNVSD

Diffusion Noise Source Square of Green’s Function Total Noise Spectral Densityfor Collector Node (Electrons) for Potential (Electrons) for Voltage at Collector Node

APMC’04


RF-Bipolar: Large Signal Transient

−35 −30 −25 −20 −15 −10

−100

−80

−60

−40

−20

0

Psav

[dBm]

Plo

ad(f

k) [d

Bm

]

Fundamental2nd harmonic3rd harmonic

−18 −16 −14 −12 −10 −8

0

2

4

6

8

Psav

[dBm]

Plo

ad(f

0) [d

Bm

] 1dB

Simulation: RL = 22.5 kOhm, f = 1 GHz, Compression Point Reached

APMC’04


Harmonic Balance (HB)

Periodic/Almost-Periodic Excitated Systems

Standard Method for RF Circuits

Optimization of RF Devices

Device Level HB

• Geometry and Materials• Physics-Based• No Quasistatic Assumption• Benefits: Faster in case of Widespread Time Constants, View Inside

• Bottlenecks: Memory Consumption, Time Consumption, Convergence, Aliasing

Time Domain:

d

dtq (r, x(t)) + f (r, x(t), w(t)) = 0

Fourier Ansatz (One-Tone):

x(t) =

H∑k=−H

Xk exp(jωkt)

HB Equation:

H(X) = ΩNΓq(·)Γ−1X + Γf(·)Γ−1X = 0

APMC’04


DESSIS HB: Status of Implementation

(Under Development)

One-Tone HB for Mixed-Mode Simulations

Nonlinear Solving Strategies:

•Continuation of Amplitude, Frequency, Parameters, and Bias•Newton Algorithm– Direct Solver PARDISO

– Iterative Solver ILS: e.g. BiCGStab with Standard ILU Preconditioners

– BBP-GMRES(m,b): Block-Band-Preconditioned GMRES(m) withMemory-Free Jacobian

•H-Decoupled: Decoupling of Harmonics

Use of Densities or Quasi-Fermi Potentials

Problems: Memory, Time, Nonlinear Convergence, Linear Systems.

APMC’04


HB: Iterative Linear Solvers

Krylow Subspace MethodsMatrix-Vector Products → Memory-Less Matrix

HB Equation

• BiCGStab with ILUT Preconditioner:Fails with Reasonable Thresholds

• Block-Band Preconditioned GMRES(m):– Fine for Small Amplitudes

– FFT per Matrix

– Preconditioning with Direct Solver

– Surprisingly Robust

– Local Solutions

Newton:[ΩΓqΓ−1 + ΓfΓ−1

]δU = −H(U)

Preconditioner:

P ≈ A

P−1Ax = P−1b

Block-Band Preconditioner:

ΓfΓ−1 ≈

A0,0 A1,1

A1,0 A1,1. . .

. . . . . . AH−1,H

AH,H−1 AH,H

APMC’04


PN Diode: Harmonic Balance

0 0.2 0.4 0.6 0.8 1

x 10−3

0

0.5

1

1.5

2

Time [s]

Diode voltage f=1kHz

Vol

tage

[V]

0 0.2 0.4 0.6 0.8 1

x 10−3

−2

0

2

4

6

8

10x 10

−3

Time [s]

Cur

rent

[A]

Diode current f=1kHz

0 0.2 0.4 0.6 0.8 1

x 10−9

−1

0

1

2

3

Time [s]

Vol

tage

[V]

Diode voltage f=1GHz

0 0.2 0.4 0.6 0.8 1

x 10−9

−4

−2

0

2

4

6x 10

−3

Time [s]

Cur

rent

[A]

Diode current f=1GHz

APMC’04


Varactor frequency doubler

HB Simulation:Voltage Source f = 1 GHz, H = 4, Grid Size NV = 478, Direct Solver.

Resources: 500 MB Memory, CPU Time 20 min.Convergence: Error Oscillations between Idler and Diode.

APMC’04


Varactor frequency doubler

0 0.2 0.4 0.6 0.8 1

x 10−9

−0.03

−0.02

−0.01

0

0.01

0.02

0.03

Sou

rce

curr

ent [

A]

0 0.2 0.4 0.6 0.8 1

x 10−9

−6

−4

−2

0

2

4

6

x 10−4

Time [s]

Load

cur

rent

[A]

HBTransient

HBTransient

1 2 3 4−180

−160

−140

−120

−100

−80

−60

−40

−20

Frequency [GHz]

|Vlo

adk | [

dB]

DESSIS−HBADS−HB

Comparison HB-Transient Comparison DESSIS-HB vs. ADS-HB

APMC’04


Simplified Bipolar

0.4 0.6 0.8 1 1.210

−15

10−10

10−5

100

Vbe [V]

Cur

rent

[A]

Gummel plot Vce=3V

IbIc

0 2 4 60

2

4

6

x 10−5

Vce [V]

Ic [A

]

Early plot

Ib=5.5µm

Ib=4.5µm

Ib=3.5µm

Ib=2.5µm

Ib=1.5µm

Ib=0.5µm

0 0.2 0.4 0.6 0.8 1

x 10−3

0.5

1

1.5

2

2.5x 10

−5

Time [s]

Ib [A

]

Base current f=1kHz

0 0.2 0.4 0.6 0.8 1

x 10−3

4

5

6

7

8

9

10x 10

−5

Time [s]

Ic [A

]

Collector current f=1kHz

Simulation

NV = 1191

APMC’04


Simplified Bipolar: Harmonic Balance

0 2 4 6 8

x 10−6

2.6

2.7

2.8

2.9

3

Ib amplitude [A]

Fundamental current gain

|Ic1 |/|

Ib1 |

100MHz1kHz

−140 −130 −120 −110 −100−350

−300

−250

−200

−150

−100

−50

|Ib1| [dB]

|I ck | [dB

]

Compression characteristic

0 2 4 6 8−350

−300

−250

−200

−150

−100

−50

Harmonics

abs(

I ck ) [d

B]

Collector current f=1kHz

APMC’04


Simplified Bipolar: Harmonic Balance

0 0.5 1 1.5 20

2e−3

4e−3

6e−3

8e−3

1e−2

Distance [µm]

|Φ1|

Ib0=0.174µA

ACHB

0 0.5 1 1.5 20

0.05

0.1

0.15

Ib0=2.653µA

Distance [µm]

|Φ1|

ACHB

0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

Ib0=6.265µA

Distance [µm]

|Φ1|

ACHB

0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

Ib0=7.5µA

Distance [µm]

|Φ1|

ACHB

APMC’04


MOSFET

Simulation

0 1 2 3 4

0

2

4

6

8

10

x 10−4

Drain voltage [V]

Dra

in c

urre

nt [A

]

Output characteristics

0 0.2 0.4 0.6 0.8 1

x 10−3

0

2

4

6

8

10x 10

−4

Time [s]

Dra

in c

urre

nt [A

]

f=1kHz Vg=1.4V Vd=1.5V

−20 −15 −10 −5 0 5−180

−160

−140

−120

−100

−80

−60

|Idk | [

dB]


Gate voltage [dB]0 0.5 1 1.5

−200

−100

0

100

200

Gate voltage [V]ar

g(Id

k ) [d

egre

es]


APMC’04


RF-Bipolar: Harmonic Balance

Failed !HB Simulations:

• Voltage or Current Source•With/Without NetworkObservations:

• Very Ill-Conditioned Linear Systems• ILUT Precondioner works only ”Direct”• Convergence only Linear• Large Voltage Amplitudes within Device → Accuracy Problem ?

Possible Reasons:

• Difficult Convergence already for DC• Very High Doping ?• Solution Singularities (Corners) ?• DFT of Positive Variables n, p > 0 ?

APMC’04


Concluding Remarks

Simulation Platform DESSIS

• Suitable for Characterization of RF Devices

•Optimization of Central Devices in RF Building Blocks

Device/Mixed-Mode Harmonic Balance

•Requires Significant Improvement to Compete withTransient Simulations

•Main Bottleneck is Lack of Robustness in Convergence

december2004 swissfederalinstituteoftechnologyzurich ...schenk/apmc04_slides.pdf · apmc’04...

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