1. 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

2.  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.

3.  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.

4.  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. BLOCK
Block method will solve some equations fully-coupled while
others are decoupled.

5.  A coupled system is formed by two differential
equations with two dependent variables and one
independent variable.
 For example:
𝑑𝑦(𝑡)
𝑑𝑥(𝑡)
= 𝑎𝑥(𝑡) + 𝑏𝑦(𝑡)
𝑑𝑥(𝑡)
𝑑𝑡
= 𝑐𝑥(𝑡) + 𝑑𝑦(𝑡)
a, b, c and d are constants while x and y are functions of t

6.  In decoupled system one variable is solved while other
are kept constant.
 For example
𝜕𝑦(𝑡)
𝜕𝑡
= 𝑎𝑦 𝑡 + 𝑏𝑥(𝑡)
𝜕𝑥(𝑡)
𝜕𝑡
= 𝑐𝑦 𝑡 + 𝑑𝑥(𝑡)
a, b, c and d are constants while x and y are functions of t

7.  Gummel Method
 Weakly coupled system of equations
 Linear convergence
 Provide better initial guess
 Newton Method
 Strongly coupled system of equations
 Quadratic convergence
 May spend extra time
 Requires more accurate initial guess

8.  Block Method
 Provide faster simulation time
 Useful to start with few Gummel iterations
 Then switch to Newton to complete the solution
 Generates better guess
 We compare the performance of algorithm by their
rate of convergence.

9.  This model requires the solution of three equations for
 Potential
 Electron Concentration
 Hole 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)

10.  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

11.  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.

12.  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.

13.  Old Syntax New Syntax
 Symbolic newton Method newton
 Symbolic gummel Method gummel

14.  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.

15.  Atlas can solve both electron and hole continuity
equation.
 We can make this choice by using CARRIER
parameters.
 METHOD CARRIER = 2
 Specifies, when a solution for both carriers is required.
 This method is default.
 METHOD CARRIER = 1 HOLE
 For one carrier either electron or hole.
 METHOD CARRIER = 0
 For potential only.

16.  The following cases require ‘METHOD NEWTON
CARRIER = 2’ to be set for isothermal drift diffusion
simulations
 Current boundary conditions
 Distributed or Lumped external elements
 AC analysis
 Impact ionization
 Both Block or Newton are permitted for lattice heat
and energy balance.