%NANO 705 - Spring 2014
%Homework 1 - Problem 2

clear all

%Constant
q=1.602e-19;%electron charge in C

%Parameters
kT=0.025;%thermal energy
eps0_m_mu0=-0.20;%chemical potential of isolated channel
mu0_m_mus=0.50;%source chemical potential
Up=0.128;%single-electron charging energy
Cfac=0.9;%laplace factor Cfac=1/(1+Cs/Cg)
Neps=10.0;% Number of degenerate states in level eps
r=5.0e12;%transport rate in s^-1
Vg=-0.5;%gate bias

%pre-calculation
eps0_m_mus=mu0_m_mus+eps0_m_mu0;
f0=1./(1+exp(eps0_m_mu0/kT));%initial fermi function for level
fs0=1./(1+exp((eps0_m_mus)/kT));

'------------------------------'
I0=q*r*Neps*(fs0-f0)%display initial current
N0=Neps*f0%display initially filled states

UL=Cfac*Vg;
U=-UL;%Self-consistent field
dU=1;%to ensure at least one pass
alpha=0.1;%convergence factor

%iterate
iter=0;
while dU>1e-10 && iter<10000
    eps_m_mus=eps0_m_mus+U;
    f=1./(1+exp((eps_m_mus)/kT));
    N=Neps*f;
    dN=N-N0;
    Unew=Up*dN-UL;
    dU=abs(U-Unew);
    U=(1-alpha)*U+alpha*Unew;
    iter=iter+1;
end%while
 
N%filled states in channel
U%channel potential
eps_m_mus%position of the level