I have attached the code but i don't know how to initialize

phit1=0.026;

Nd1=1e19;

phim1=5.2

ni=1.5e10;

chi=4.1;

Eg=1.1

Vfb1=phim1-(chi+(Eg/2)-phit1*(log(Nd1/ni)))

ni=1.5e10;

q=1.6e-19;

eox=3.9*8.8*1e-14

tf1=6*10^-7

tox=0.7*10^-7

Cox=eox/tox

esi=8.8*11.7*1e-14

Qss1=3*10^-6

Qc1=2*10^-5

Ec1=1.4*10^6;

Tsc1=1*10^-6;

p1=q*Nd1*Tsc1

alpha_1=-((3*sqrt(3))/4)*(Ec1/Qss1)

beeta_1=((3*sqrt(3))/8)*(Ec1/(Qss1^3))

damma_1=0

alpha1=2*tf1*alpha_1

beeta1=4*tf1*beeta_1

damma1=6*tf1*damma_1

Vgd1=1;

N=30;

Vds=linspace(0,1,N);

Qd1=zeros(1,N);

for i=1:N

syms x

assume(x,'real')

eqnLeft = (Vgd1-Vfb1-Vds(i)+((Tsc1/(8*esi))*(x+p1)))-0.026*(log(2*sqrt(((x+p1)*Tsc1)/(8*3.14*0.026*esi))*(1-((x+p1)/(p1)))));

eqnRight =((alpha1+(1/Cox))*((x+p1)/2))+(beeta1*(((x+p1)/2).^3))+(damma1*(((x+p1)/2).^5));

Qd1(1,i)=vpasolve(eqnLeft == eqnRight,x);

end

%Qd1(1,i)=vpasolve(eqnLeft == eqnRight,x,"What should be here?");

Answer 1

[BhaTTa]

Hey @mohd ayaz, i can see that you have initilized all the variable correctly, Here's a refined version of your code with comments to help you understand each step, please refer to it which is intended to solve a set of equations for a range of values of Vds and store the results in Qd1:

% Constants and Parameters
phit1 = 0.026;
Nd1 = 1e19;
phim1 = 5.2;
ni = 1.5e10;
chi = 4.1;
Eg = 1.1;
Vfb1 = phim1 - (chi + (Eg / 2) - phit1 * (log(Nd1 / ni)));
q = 1.6e-19;
eox = 3.9 * 8.8 * 1e-14;
tf1 = 6 * 10^-7;
tox = 0.7 * 10^-7;
Cox = eox / tox;
esi = 8.8 * 11.7 * 1e-14;
Qss1 = 3 * 10^-6;
Qc1 = 2 * 10^-5;
Ec1 = 1.4 * 10^6;
Tsc1 = 1 * 10^-6;
p1 = q * Nd1 * Tsc1;
alpha_1 = -((3 * sqrt(3)) / 4) * (Ec1 / Qss1);
beeta_1 = ((3 * sqrt(3)) / 8) * (Ec1 / (Qss1^3));
damma_1 = 0;
alpha1 = 2 * tf1 * alpha_1;
beeta1 = 4 * tf1 * beeta_1;
damma1 = 6 * tf1 * damma_1;
Vgd1 = 1;
N = 30;
Vds = linspace(0, 1, N);
Qd1 = zeros(1, N);

% Loop to solve the equation for each value of Vds
for i = 1:N
    syms x
    assume(x, 'real')
    
    % Define the left and right sides of the equation
    eqnLeft = (Vgd1 - Vfb1 - Vds(i) + ((Tsc1 / (8 * esi)) * (x + p1))) - ...
              0.026 * (log(2 * sqrt(((x + p1) * Tsc1) / (8 * pi * 0.026 * esi)) * ...
              (1 - ((x + p1) / p1))));
    eqnRight = ((alpha1 + (1 / Cox)) * ((x + p1) / 2)) + ...
               (beeta1 * (((x + p1) / 2).^3)) + ...
               (damma1 * (((x + p1) / 2).^5));
    
    % Solve the equation
    sol = vpasolve(eqnLeft == eqnRight, x);
    
    % Select the first solution (or handle as needed)
    if ~isempty(sol)
        Qd1(i) = sol(1); % Assuming you want the first solution
    else
        Qd1(i) = NaN; % Assign NaN if no solution is found
    end
end

% Plotting the results
figure;
plot(Vds, Qd1, 'b-o');
xlabel('Vds (V)');
ylabel('Qd1');
title('Charge Density vs. Vds');
grid on;