fig7_2_5.m

1D的薛定谔－泊松自洽求解 用于模拟半导体器件中的电势 电场等特性

% --------------------------------------------------------------------------------
%  MATLAB code used to generate the figures in the book:
%
%    "Quantum Transport: Atom to Transistor," by Supriyo Datta
%    published by Cambridge University Press, May 2005
%      (ISBN-10: 0521631459 | ISBN-13: 9780521631457)
%    http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=0521631459
%
% THIS FILE FOR: Chapter 7, Figure 7.2.5
%
% --------------------------------------------------------------------------------
% Copyright (c) 2005  Supriyo Datta
% --------------------------------------------------------------------------------

clear all

%Constants (all MKS, except energy which is in eV)
hbar=1.06e-34;q=1.6e-19;eps0=8.85E-12;epsr=4;m=.25*9.1e-31;
mu=0;kT=.025;n0=m*kT*q/(2*pi*(hbar^2));n0

%inputs
a=3e-10;t0=(hbar^2)/(2*m*(a^2)*q);e0=q*a/eps0;
Nox=7;Nc=10;%use Nc=10,30 for 3,9nm channel respectively
Np=Nox+Nc+Nox;XX=a*1e9*[1:1:Np];
Ec=[3*ones(Nox,1);0*ones(Nc,1);3*ones(Nox,1)];

%Hamiltonian matrix
T=(2*t0*diag(ones(1,Np)))-(t0*diag(ones(1,Np-1),1))-(t0*diag(ones(1,Np-1),-1));

%dielectric constant matrix
D2=epsr*((2*diag(ones(1,Np)))-(diag(ones(1,Np-1),1))-(diag(ones(1,Np-1),-1)));
iD2=inv(D2);

Vg=.25;Ubdy=-epsr*[Vg;zeros(Np-2,1);Vg];
%Ubdy=-epsr*[0;zeros(Np-2,1);Vg];;%for asymmetric bias
U0=iD2*Ubdy;

%self-consistent calculation
	U1=1e-6*ones(Np,1);UU=U1;change=1;
	while change>1e-3
		U1=U1+(0.1*(UU-U1));
		[P,D]=eig(T+diag(Ec)+diag(U1));D=diag(D);
		rho=log(1+exp((mu-D)./kT));rho=P*diag(rho)*P';
		n=2*n0*diag(rho);
			for kp=1:Np
				ncl(kp)=a*2*(n0^1.5)*Fhalf((mu-Ec(kp)-U1(kp))/kT);
			end%n=ncl';%use for semiclassical calculation
			UU=U0+(iD2*e0*n);
			change=max(max((abs(UU-U1))));
		U=Ec+U1;%self-consistent band profile
end

%electron density in channel per cm2	
	ns=1e-4*sum(sum(n.*[zeros(Nox,1);ones(Nc,1);zeros(Nox,1)]));Vg,ns
		nn=1e-6*n./a;%electron density per cm3
		Fn=mu*ones(Nc+Nox+Nox,1);

hold on
h=plot(XX,nn,'k');
%h=plot(XX,Ec,'g--');
%h=plot(XX,Ec+U1,'g');
%h=plot(XX,Fn,'g:');

xlabel(' z (nm) ---> ')
%ylabel(' E (eV) ---> ')
ylabel(' n (/cm3) --->')
%axis([0 8 -.5 3])
axis([0 8 0 15e18])
grid on