Group Members

Aakash Rajper 1381-FET/BSEE/F-10

Abdul Haseeb 1382-FET/BSEE/F-10

Badar Jahangee 1383-FET/BSEE/F-10

Danish Javed 1384-FET/BSEE/F-10

Hamza Arshad 1382-FET/BSEE/F-10

MICROELECTRONICS LABSolution Methods And Their

Selection

Used for modeling devices.Devices are modeled in ATLAS by a set of one to

six PDEs. These PDEs are converted to approx. non-linear

then linear algebraic equations. These equations are solved iteratively until a

solution nearest to real values are achieved.Values for unknowns are calculated at mesh

points.Different solution procedures exhibit different

behavior with respect to convergence, accuracy, efficiency, and robustness.

Introduction

The two main aspects of convergence are whether a solution is obtained and how rapidly it is approached.

Accuracy is how closely the computed solution approximates the true solution.

Efficiency is the time required to produce a solution.Robustness is the ability of a technique or method

to cope with errors during execution.Different methods can work better for different

problems. Atlas has captured practical experience in the form of default methods and parameters that work well in almost all circumstances.

Introduction (continued)

Numerical Methods are given in the METHOD statements of the input file.

Example “METHOD GUMMEL NEWTON” There are three types of solution techniques.

1. Decoupled (GUMMEL)Gummel method will solve for each unknown in turn keeping the other variables constant, repeating the process until a stable solution is achieved.

2. Fully coupled (NEWTON)Newton method solve the total system of unknowns together.

3. BLOCKBlock method will solve some equations fully-coupled while others are decoupled.

Types Of Default Methods

A coupled system is formed by two differential equations with two dependent variables and one independent variable.

For example:

a, b, c and d are constants while x and y are functions of t

Coupled System

In decoupled system one variable is solved while other are kept constant.

For example

a, b, c and d are constants while x and y are functions of t

Decoupled System

Gummel MethodWeakly coupled system of equationsLinear convergenceProvide better initial guess

Newton MethodStrongly coupled system of equationsQuadratic convergenceMay spend extra timeRequires more accurate initial guess

SELECTION OF SOLUTION METHOD

Block MethodProvide faster simulation timeUseful to start with few Gummel iterationsThen switch to Newton to complete the

solutionGenerates better guess

We compare the performance of algorithm by their rate of convergence.

SELECTION OF SOLUTION METHOD(continued)

This model requires the solution of three equations forPotentialElectron ConcentrationHole concentration

For almost all cases NEWTON method is preferred and it is the default.

Block method in this model is robust but more time consuming.

Block method is highly recommended for all simulations with floating regions (e.g., SOI transistors)

BASIC DRIFT DIFFUSION CALCULATIONS

Extra equation is added when Latice heating model is added to drift diffusion

If we apply Block Method in this level it’ll solve three eq. by Newton and fourth with Gummel.

Newton Method solves all four equations in a coupled manner.

Newton is preferred for high temp. while Block is used for low temp. gradients

DRIFT DIFFUSION CALCULATIONS WITH LATTICE HEATING

It requires solution of up to five coupled equations.

Newton and Gummel have same meaning for this model

Block performs coupled solutions for all five equations

We can switch from Block to Newton for robust performance.

The switching point is pre-determined.It can be changed in the METHOD statement.

Energy Balance Calculations

Requires six equations system.

Gummel and Newton solve the equations iteratively.

Block functions initially performs the same as energy balance and performs lattice heating equation in decoupled manner.

Energy Balance With Lattice Heating

Old Syntax New Syntax

Symbolic newton Method newtonSymbolic gummel Method

gummel

Parameter Syntax Replacements

All numeric settings chosen on METHOD statement All structure/parameter specification must be before this

statement. All solution specification must be after it.

Fully Coupled Method solves for potential and carriers coupled

(METHOD NEWTON) Recommended for all cases even including SOI simulations.

De-Coupled method solves potential and carriers sequentially

(METHOD GUMMEL) Faster for low current cases.

Combined method (METHOD GUMMEL NEWTON) Runs initial decoupled iterations and switches to coupled. GUM.INIT parameter controls the number of initial

decoupled iterations.

most robust (but slowest) method.

Choice of Solution Method

Atlas can solve both electron and hole continuity equation.

We can make this choice by using CARRIER parameters.

METHOD CARRIER = 2Specifies, when a solution for both carriers is

required.This method is default.

METHOD CARRIER = 1 HOLEFor one carrier either electron or hole.

METHOD CARRIER = 0For potential only.

Setting Number of Carrier

The following cases require ‘METHOD NEWTON CARRIER = 2’ to be set for isothermal drift diffusion simulationsCurrent boundary conditionsDistributed or Lumped external elementsAC analysisImpact ionization

Both Block or Newton are permitted for lattice heat and energy balance.

Restrictions on the choice of METHOD statement

Questions and Queries

THAN

KS