clear
close
clc
format long
%% Variables
dp = 11.6;
taup = 3710e-6;
dn = 2;
taun = 371e-6;
Jl = 50e-3;
ni = 9.696e9;
q = 1.602176634e-19;
k = 1.3880649e-23;
T = 300;
ep = 1.035918e-12;
vint = @(na,nd) k.*T/q.*log((na.*nd)./ni^2);
xn = @(na,nd) sqrt((2.*ep.*vint(na,nd).*na)./(q.*nd.*(na+nd)));
xp = @(na,nd) sqrt((2.*ep.*vint(na,nd).*nd)./(q.*na.*(na+nd)));
dnxp = @(V,na) ni^2./na.*(exp(q*V./(k*T))-1);
dpxn = @(V,nd) ni^2./nd.*(exp(q*V./(k*T))-1);
%% Functions
C1 = @(V,na,nd,wn) dnxp(V,na)./(-exp((-2.*wn-xp(na,nd))./sqrt(dn*taun))+exp(xp(na,nd)./sqrt(dn*taun)));
C3 = @(V,na,nd,wp) dpxn(V,nd)./(exp(-xn(na,nd)./sqrt(taup*dp))-exp((2.*wp+xn(na,nd))./sqrt(taup*dp)));
Jn = @(x,V,na,nd,wn) q*sqrt(dn/taun).*C1(V,na,nd,wn).*(exp((-2.*wn-x)./sqrt(dn*taun))+exp(x./sqrt(dn*taun)));
Jp = @(x,V,na,nd,wp) -q*sqrt(dp/taup).*C3(V,na,nd,wp).*(exp(x./sqrt(taup*dp))+exp((2.*wp-x)./sqrt(taup*dp)));
Jd = @(V,na,nd,wn,wp) Jp(-xn(na,nd),V,na,nd,wn)+Jn(xp(na,nd),V,na,nd,wp);
J = @(V,na,nd,wn,wp) Jl-Jd(V,na,nd,wn,wp);
P = @(V,na,nd,wn,wp) J(V,na,nd,wn,wp).*V;
%% Boundaries
wn = [0.05e-4, 0.75e-4];
wp = [100e-4, 200e-4];
nd = [1e18, 5e20];
na = [1e14, 1e16];
V = [0, 0.52];
% Either use the order of variables like in the vector of initial
% values and lower and upper bounds in the call to PP or
% change the order of the variables in the initial value vector P0 and
% in the lower and upper bounds to (V,na,nd,wn,wp) instead of (V,wn,wp,nd,na).
% I did the first, but I recommend the last (commented out) for clarity reasons.
P0 = [(V(1)+V(2))/2; (wn(1)+wn(2))/2; (wp(1)+wp(2))/2; (nd(1)+nd(2))/2; (na(1)+na(2))/2];
PP = @(p)-P(p(1),p(4),p(5),p(3),p(2));
lb = [min(V),wn(1),wp(1),nd(1),na(1)];
ub = [max(V),wn(2),wp(2),nd(2),na(2)];
%P0 = [(V(1)+V(2))/2; (na(1)+na(2))/2;(nd(1)+nd(2))/2;(wn(1)+wn(2))/2; (wp(1)+wp(2))/2 ];
%PP = @(p)-P(p(1),p(2),p(3),p(4),p(5));
%lb = [V(1),na(1),nd(1),wn(1),wp(1)];
%ub = [V(2),na(2),nd(2),wn(2),wp(2)];
-PP(P0)
%% Optimization
mx = fmincon(PP,P0,[],[],[],[],lb,ub);
-PP(mx)
V = mx(1)
wn = mx(2)
wp = mx(3)
nd = mx(4)
na = mx(5)
%V = mx(1)
%na = mx(2)
%nd = mx(3)
%wn = mx(4)
%wp = mx(5)
