RUBRIC: Complete the coding task outlined below.  You may use any materials 
available on the WWW before the examination begins, and any material in your 
CPlab home directory.  You may not communicate with any other person by any 
means whatsoever (including email, webmail etc.).
<P>
Duration: 3 hours
<P>

Explanation of your work should be written in the green examination
script.  At the end of the examination you should also email your code
and and electronic pictures to graeme@ph.ed.ac.uk

<P>
A 2D semiconductor comprises a plane of atoms 50 wide located on a square 
lattice in the xy plane.  Electrons  are emitted from the y=0 plane and 
diffuse at random from site to adjacent site through the lattice.  Holes 
are produced at the y=49 plane and similarly diffuse at random through 
the lattice.  Periodic boundary conditions exist in the x-direction. 
Electrons are forbidden from moving to a site already occupied by an 
electron, and a similar exclusion holds for holes.  If an electron 
moves onto a site occupied by a hole, both are destroyed, if either 
electron or hole reaches the y-boundary, it is absorbed.

Write a code to simulate the motion of electrons and holes in this system.  

Your code should include changeable parameters to describe:

<P> N the number of electrons added per timestep at y=0

<P> P the number of holes added per timestep at y=49,

<P>  D_n the rate of diffusion of the electrons (probability that the electron 
attempts to move to an adjacent site)

<P> D_p the rate of diffusion of the holes.  You should include a
graphical representation of the motion of holes and electrons, and
write a full description of how a user could use the code 

(you do not
need a line-by-line commentary of your code to show how it
works). Half of the marks will be awarded to the working and
usable code. Describe the design criteria which you have chosen
(updating method, graphics, analysis code etc.)

Investigate the conduction of charge in the following cases. 
1) N=P=1 D_n=1: how does conduction vary with  D_p ?
<P>
2) N=1 D_n=1 D_p=1: how does conduction vary with P ?
<P>
3) N=1 P=1 D_n=1 D_p=1: how do the concentrations of electrons and holes 
vary as a function of y?  (Make or sketch a graph) 

<P> 
4) How does the graph in part (3) vary
as N goes from 0 to 50, and P=N.  

<P> Half of the marks will be
awarded for the answers to these questions, you should describe what
you calculated to obtain your results.