## Plotting the different solution via fzero solver against a range of one of the variable

### Anil Kumar (view profile)

on 7 Jun 2019
Latest activity Commented on by Anil Kumar

on 7 Jun 2019

### Stephan (view profile)

I am bit new to the matlab; I am having trouble with this, I got different values of phi0 at different Nt using fzero solver; called phi0value. I want to plot Nt v/s phi0value? I used plot (Nt, phi0) for this, it is not working. I dont know how to plot a range of output against a range of variable? Please guide me through this.This will be a great help!! Thank You.
N = 100;
% define the parameters
Nd = 1e23;
e = 12*1e-12;
%r = 0
R = 20*1e-9;
Et_Ef = -0.21*1.6*1e-19;
K = 1.3807e-23;
T = 600;
Nt = linspace(1e15,1e17,N);
q = 1.6e-19;
for i = 1:N
Ld = sqrt(e*K*T/(q^2*Nd))
funct= @(R,phi0) (4.*pi.*(Nd-Nd.*exp(-phi0)).*R.^2)
equation = @(phi0)integral(@(R)funct(R,phi0),0,R,'ArrayValued',true)-(4*pi.*R.^2.*Nt(i)./(1+2*exp((Et_Ef + K*T .*(phi0 + (1/6).*(R/Ld).^2))/(K.*T))));
%X= [0 10];
phi0value = fzero(equation,10)
end
plot (Nt,phi0val)

### Stephan (view profile)

on 7 Jun 2019

N = 100;
% define the parameters
Nd = 1e23;
e = 12*1e-12;
%r = 0
R = 20*1e-9;
Et_Ef = -0.21*1.6*1e-19;
K = 1.3807e-23;
T = 600;
Nt = linspace(1e15,1e17,N);
q = 1.6e-19;
phi0value = zeros(1,N);
for ii = 1:N
Ld = sqrt(e*K*T/(q^2*Nd))
funct= @(R,phi0) (4.*pi.*(Nd-Nd.*exp(-phi0)).*R.^2)
equation = @(phi0)integral(@(R)funct(R,phi0),0,R,'ArrayValued',true)-(4*pi.*R.^2.*Nt(ii)./(1+2*exp((Et_Ef + K*T .*(phi0 + (1/6).*(R/Ld).^2))/(K.*T))));
%X= [0 10];
phi0value(ii) = fzero(equation,10)
end
plot (Nt,phi0value)

Anil Kumar

### Anil Kumar (view profile)

on 7 Jun 2019
Thank you for your response! I had resolved this problem already! anyway thank you for your time. I have another issue. I want to integrate "funneff" and want to plot neff against Nt! Problem is that I am not able to integrate the function "funneff". Also how to plot neff v/s Nt ? below is my code. I am beginner in matlab. below is my code. Thanks in advance!
Nd = 1e24;
N = 100;
e = 12*1e-12;
% R = [10e-9,20e-9,30e-9,40e-9];
R = [1e-9,2e-9,3e-9,4e-9,5e-9,6e-9,7e-9,8e-9];
Et_Ef = -1.21*1.6*1e-19;
K = 1.3807e-23;
T = 600;
Nt = linspace(1e13,1e16,N);
q = 1.6e-19;
Ld = sqrt(e*K*T/(q^2*Nd));
for j = 1:numel(R)
for i= 1:N
funct = @(R,phi0) (4*pi*(Nd-Nd*exp(-phi0))*R.^2);
equation = @(phi0)integral(@(R)funct(R,phi0),0,R(j))-(4*pi*R(j)^2*Nt(i)/(1+2*exp((Et_Ef + K*T *(phi0 + (1/6)*(R(j)/Ld)^2))/(K*T))));
%equation = @(phi0)integral(@(r)funct(r,phi0),0,R)-(4*pi*R^2*Nt(i)/(1+2*exp((Et_Ef + K*T *(phi0 + (1/6)*(R/Ld)^2))/(K*T))));
phi0val(j,i) = fzero(equation,40);
%phi0val(i) = fzero(equation,40)
end
end
% plot(Nt,phi0val(1,:))
% hold on
% plot(Nt,phi0val(2,:))
% hold on
% plot(Nt,phi0val(3,:))
% hold on
% plot(Nt,phi0val(4,:))
% hold on
% plot(Nt,phi0val(5,:))
% hold on
% plot(Nt,phi0val(6,:))
% hold on
% plot(Nt,phi0val(7,:))
% hold on
% plot(Nt,phi0val(8,:))
for j = 1:numel(R)
for i=1:N
funneff= @(R)1./(4/3.*pi.*R(j).^3).*(Nd.*exp(-phi0val(j,i))).*R(j).^2
neff(j,i)= integral(funneff,0,R(j),'Arrayvalued',true)
end
end
plot(neff(1,:),phi0val(1,:))
hold on
plot(neff(2,:),phi0val(2,:))
hold on
plot(neff(3,:),phi0val(3,:))
hold on
plot(neff(4,:),phi0val(4,:))
hold on
plot(neff(5,:),phi0val(5,:))
hold on
plot(neff(6,:),phi0val(6,:))
hold on
plot(neff(7,:),phi0val(7,:))
hold on
plot(neff(8,:),phi0val(8,:))