december2004 swissfederalinstituteoftechnologyzurich ...schenk/apmc04_slides.pdf · apmc’04...
TRANSCRIPT
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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
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APMC’04
Integrated Systems Laboratory
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
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APMC’04
Integrated Systems Laboratory
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
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APMC’04
Integrated Systems Laboratory
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
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APMC’04
Integrated Systems Laboratory
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
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APMC’04
Integrated Systems Laboratory
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
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APMC’04
Integrated Systems Laboratory
RF-Bipolar: Small Signal
Electron Current Hole Current
Local AC Current Densities (∣∣Re(J1)∣∣ )
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APMC’04
Integrated Systems Laboratory
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
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APMC’04
Integrated Systems Laboratory
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
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APMC’04
Integrated Systems Laboratory
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
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APMC’04
Integrated Systems Laboratory
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
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APMC’04
Integrated Systems Laboratory
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
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APMC’04
Integrated Systems Laboratory
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.
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APMC’04
Integrated Systems Laboratory
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
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APMC’04
Integrated Systems Laboratory
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
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APMC’04
Integrated Systems Laboratory
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.
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APMC’04
Integrated Systems Laboratory
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
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APMC’04
Integrated Systems Laboratory
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
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APMC’04
Integrated Systems Laboratory
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
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APMC’04
Integrated Systems Laboratory
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
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APMC’04
Integrated Systems Laboratory
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]
f=1kHz Vg=1.4V Vd=1.5V
Gate voltage [dB]0 0.5 1 1.5
−200
−100
0
100
200
Gate voltage [V]ar
g(Id
k ) [d
egre
es]
f=1kHz Vg=1.4V Vd=1.5V
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APMC’04
Integrated Systems Laboratory
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 ?
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APMC’04
Integrated Systems Laboratory
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