Atomistic Simulation

Atomistic S

imulati

on

First Principles DFT

Tight Binding

Next Generation EM Solver

Circuit Simulator

Hopping integrals

Quantum-classicalcircuit mapping

Electric signals

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)

1.Steady state• ω=0 & ω≠02. Time dependent

)(2

EdEGi

)(4)(2 rrV

Non-equilibrium Green’s function (NEGF) method

])Im()Im(Tr[)(

)()]()([2

Rar

L

RL

GGET

ETEfEfdEh

eI

Landauer Formula:

DFT & TB for Quantum Transport (Guo, Wang)

TDDFT for transient currents TDDFT for transient currents (Chen)(Chen)

Left electrode right electrode

system to solve

boundary condition

Poisson Equation with boundary condition via potentials at SL and SR

L R

Dissipation functional Q

(energy and particle exchange with the

electrodes)

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

• Advanced simulator must allow simultaneous simulation of on-silicon components (passives) and in-silicon components (actives)

EM simulations Device simulations

Metal: Ohm’s law

0

J E

Jt

, 0

,

D B

B DE H J

t t

Basics: MaxwellBasics: Maxwell

( )

( ) 0

, { , }

D A

x

x x x

q p n N N

xJ q q R G

tJ q xE kT x x n p

Semiconductor: Drift-DiffusionSemiconductor: Drift-Diffusion

0

0J

InsulatorInsulator

: scalar potential

: vector potential ( )

, : electron & hole density

V

A B A

n p

Basic variables:Basic variables:

Interface Condition• Metal/semiconductor interface (ohmic contact)

V is double-valued,

Basic equation: 0metal semiV V V

J

• Metal/insulator interfaceV is continuous

Basic equation: 0J • Semiconductor/insulator interface

V is continuous

Basic equation: D= , 0J • Metal/semiconductor/insulator interface

1V is triple-valued, ,

2Basic equation: 0

semi metal insul metalV V V V V V

J

Quantum Mechanics / Molecular Mechanics (QM/MM) Method

QMMM

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

QMEM

EM solver

QM region

QM region

QM regionAtomistic

details

PEEC/ DPEC

Quantum mechanics

Molecular mechanics

~100 atoms1Ǻ~1nmAtomic scale

1,000 ~100,000 atoms1nm~10nm

>>1,000,00010um~100um

1023

100~1000umContinuum scale

~ 1,000,00010~10um

Coarse grain

Finite element

Continuum model

Astronomy

Multi-scale simulation methodsMulti-scale simulation methods(Engineering & Science)(Engineering & Science)