process simulation

EEE 533 - Semiconductor Device and Process Simulation

EEE 533: Semiconductor Device andProcess Simulation

Spring 2001

Lecture 2

Instructor: Dragica VasileskaDepartment of Electrical Engineering

Arizona State University


A. INTRODUCTIONModeling

Representation of the physical structure or behavior of a device by an abstract mathematical model which approximates this behavior:

• closed form expression (analytical model), or • a system of simultaneous equations that are solved numerically.

• Analysis - method by which a complex problem of characterizing the device is resolved into similar component parts which allow the required investigation to be achieved in a near exact manner.

• Device Simulation - more approximate in nature (although this need not always be the case) and frequently takes a phenomenological approach.

• Process Simulation - Numerical simulation of the physical formation of the semiconductor device structure through one or more steps of processing.

* Traditional device modeling has involved a trial and error approach, which is becoming too expensive for ultra-small devices.


Solid State Device Models

• Equivalent circuit models:- Based on the electrical performance of the device- Suitable for circuit design applications- Limited in their range of application, since it is difficult to relate the model elements to physical parameters- Not suitable for predicting performance of novel device structures

• Physical device models:- Based on the physics of carrier transport (dc, transient, large signal, and high-frequency operation)- Detailed physical device models require substantial amount of computer time and memory- Physical device models are solved using: bulk carrier transport models, Boltzmann transport models, or quantum transport concepts- Suitable for predicting the performance of complex device structures


Hierarchy of Physical Device Models

Quantum Approaches

Boltzmann Equation Monte Carlo ParticleBased Approaches

Moments of Boltzmann TransportEquation (Hydrodynamic and Energy

Balance Approaches)

Drift-Diffusion Approaches

Compact Approaches


Validity of the Semiclassical Transport Models

Drift-Diffusion Model: Good for devices with LG>0.5 m Can’t deal with hot carrier effects

Hydrodynamic Model: Hot carrier effects, such as

velocity overshoot, included into the model

Overestimates the velocity at high fields

Particle-Based Simulation: Accurate up to classical limits Allows proper treatment of the

discrete impurity effects and e-e and e-i interactions

Time consuming

LG > 0.5 m

LG < 0.1 m

LG 0.1 m

discrete impurity effects,electron-electron interactions


Review of Field Equations

In general, one needs to solve Maxwell’s equations inside and outside the device

t

t

DJH

BE

0

BD

Numerical techniques to solve these equations include:

• Finite Difference Time domain solutions (FDTD)• Frequency domain solutions (spectral techniques)

At present, nearly all device simulation tools assume the quasi-static approximation, such that the electric field is obtained from Poisson’s equation:

VV Err

)()(2


V

pqDpqnqDnq

grqt

p

grqt

n

ppp

nnn

ppp

nnn

2

EJEJ

J1

J1

Phenomenological Transport Simulation

Drift-Diffusion Model (zeroth and first-order moments of the BTE):

Continuity equations

Current density equations

Poisson’s equation

Variables n, p, and V solved simultaneously on a mesh. Transport is local, and described by the phenomenological mobility v =(E)E and diffusion coefficient D(E)=kT/q (E) (Einstein relation).


Physical Device Simulation

There are two main components in any physical device simulator:

- Characterization of charge motion due to driving forces and diffusion process (transport)

- Fields due to charge distribution and motion

Recessed MOSFET represented on 3D mesh over finite domain (courtesy of S. M. Goodnick)

Initialize Data

Field Solver

Transport Kernel

yes

no Criterionsatisfied?

START

STOP


Historical Development of Physical Device Modeling

Closed-form analytical modeling:• Gradual-channel approximation (Schockley, 1952)

Numerical modeling:• Gummel’s 1D numerical scheme for BJTs (1964)• De Mari (1968): 1D numerical model for pn - junctions• Sharfetter and Gummel (1969): 1D simulation for Silicon Read

(IMPATT) diodes• Kenedy and O’Brien (1970): 2D simulation of silicon JFETs• Slotboom (1973): 2D simulation of BJTs• Yoshii et al. (1982): 3D modeling for a range of semiconductor devices

Commercial device simulators:• 2D MOS: MINMOS, GEMINI, PISCES, CADDET, HFIELDS, CURRY• 3D MOS: WATMOS, FIELDAY• 1D BJT: SEDAN, BIPOLE, LUSTRE• 2D BJT: BAMBI, CURRY• MESFETs: CUPID• Particle-based simulators: DAMOCLES• Quantum transport simulators: NEMO

process simulation

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