Download What is Coupled EM-Semiconductor Simulation?

Task 6: Development of multi-scale EDA components for
devices and integrated circuits
(Chen, Wang, Guo, Chew, P. Chan, Lo, Wu, Jiang, Wong, M. Chan)
Circuit Simulator
Next Generation
EM Solver
Electric signals
Tight Binding
Quantum-classical
circuit mapping
First Principles
DFT
Hopping integrals
DFT & TB for Quantum Transport
(Guo, Wang)
1.Steady state
• ω=0 & ω≠0
2. Time dependent
Non-equilibrium Green’s function (NEGF) method
i

 
dEG ( E )

2
 2V (r )  4(r )
Landauer Formula:
2e 
I   dE[ f ( E   L )  f ( E   R )]T ( E )
h 
T ( E )  Tr[ Im(  L )G r Im(  R )G a ]
TDDFT for transient currents (Chen)
boundary condition
,L
Left electrode
,R
right electrode
system to solve
Dissipation functional Q
(energy and particle exchange
with the electrodes)
Poisson Equation with boundary condition via potentials at SL and SR
Electromagnetics Solver
(Chew, Jiang)
Circuit Simulator
(Wu, Jiang, P. Chan, M. Chan)
PEEC, DPEC & etc.
Coupled EM-Semiconductor Simulation?
N. Wong and Q. Chen
• Combine full-wave EM simulation and device simulation
EM simulations
Device simulations
• Advanced simulator must allow simultaneous simulation of
on-silicon components (passives) and in-silicon components
(actives)
Semiconductor: Drift-Diffusion
  q( p  n  N D  N A )
x
 q( R  G )  0
t
J x  q x xE  kT  xx, x  {n, p}
J x  q
Basics: Maxwell
  D  ,   B  0
B
D
 E  
,  H  J 
t
t
Basic variables:
V : scalar potential
A : vector potential (B    A)
n, p : electron & hole density
Metal: Ohm’s law
J E

 J 
t
Insulator
 0
J 0
0
Interface Condition
• Metal/semiconductor interface (ohmic contact)
V is double-valued, Vmetal  Vsemi  V
Basic equation:   J  0
• Metal/insulator interface
V is continuous
Basic equation:   J  0
• Semiconductor/insulator interface
V is continuous
Basic equation:   D= ,   J  0
• Metal/semiconductor/insulator interface
V is triple-valued, Vsemi  Vmetal  V , Vinsul  Vmetal
Basic equation:   J  0
1
 V
2
Quantum Mechanics / Molecular Mechanics
(QM/MM) Method
QM
MM
QM/EM Simulation
• Replace devices of interests (drift-diffusion etc)
by models using quantum mechanism (QM)
• Since only a small portion of semiconductor
can be handled by QM model, the interface
between QM and classical model in solution
scheme will be crucial
QM
EM
PEEC/
DPEC
EM solver
QM region
QM region
QM region
Atomistic
details
Multi-scale simulation methods
(Engineering & Science)
1023
100~1000um
Continuum scale
Astronomy
>>1,000,000
10um~100um
Continuum model
~ 1,000,000
10~10um
1,000 ~100,000 atoms
1nm~10nm
Finite element
~100 atoms
1Ǻ~1nm
Atomic scale
Coarse grain
Molecular mechanics
Quantum mechanics