Line in Matlab plot do not appear

I am self studying Matlab and I want to create a plot with electron concentration and inverse temperature as the picture shows:

% Constants
k = 1.38e-23;  % Boltzmann's constant (J/K)
Eg = 1.12;     % Energy band gap of silicon (eV)
A = 2.5e19;    % Constant for intrinsic carrier concentration calculation
Nc = 2.8e19;   % Effective density of states in conduction band (cm^-3)
Nd = 1e16;     % Doping concentration (cm^-3)

% Temperature range
T = linspace(100, 1000, 100);  % Temperature range from 100 K to 1000 K

% Electron concentration for n-type doping
n = (Nc * Nv)^0.5 * exp(-Eg./(2*k*T));

% Calculate ln(n)
ln_n = log(n);

% Calculate 1/T
inv_T = 1 ./ T;

% Plot
plot(inv_T, ln_n, 'r', 'LineWidth', 2);
xlabel('1/T');
ylabel('ln(N_D)');
title('ln(Electron Concentration) vs. 1/T for Silicon');
grid on;

Does anyone knows ?

[Star Strider]

The ‘Nv’ definition is missing.

Answer 1

[Walter Roberson]

Your exp() results in extremely small values, so you are getting NaN

Q = @(v) sym(v);

Nv = Q(1e23);    %guess to run the program

% Constants
k = Q(1.38e-23);  % Boltzmann's constant (J/K)
Eg = Q(1.12);     % Energy band gap of silicon (eV)
A = Q(2.5e19);    % Constant for intrinsic carrier concentration calculation
Nc = Q(2.8e19);   % Effective density of states in conduction band (cm^-3)
Nd = Q(1e16);     % Doping concentration (cm^-3)

% Temperature range
T = linspace(100, 1000, 100);  % Temperature range from 100 K to 1000 K

% Electron concentration for n-type doping
n = (Nc * Nv)^0.5 * exp(-Eg./(2*k*T));

% Calculate ln(n)
ln_n = log(n);

% Calculate 1/T
inv_T = 1 ./ T;

TTTT = ln_n(1:2).'

TTTT = 

[vpa(TTTT(1)),vpa(TTTT(2))]

ans = 

double(TTTT)

Error using mupadengine/feval2char
Singularity.

Error in sym/double (line 755)
Xstr = feval2char(symengine, "symobj::double", S);

% Plot
plot(inv_T, ln_n, 'r', 'LineWidth', 2);
xlabel('1/T');
ylabel('ln(N_D)');
title('ln(Electron Concentration) vs. 1/T for Silicon');
grid on;

[Walter Roberson]

Doing the log operation directly:

Q = @(v) sym(v);

Nv = Q(1e23);    %guess to run the program

% Constants
k = Q(1.38e-23);  % Boltzmann's constant (J/K)
Eg = Q(1.12);     % Energy band gap of silicon (eV)
A = Q(2.5e19);    % Constant for intrinsic carrier concentration calculation
Nc = Q(2.8e19);   % Effective density of states in conduction band (cm^-3)
Nd = Q(1e16);     % Doping concentration (cm^-3)

% Temperature range
T = linspace(100, 1000, 100);  % Temperature range from 100 K to 1000 K

% Electron concentration for n-type doping
ln_n = 0.5*log(Nc * Nv) + (-Eg./(2*k*T));

ln_n(1:5).'

ans = 

double(ans)

ans = 5x1

1.0e+20 * -4.0580 -3.7198 -3.4337 -3.1884 -2.9758

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% Calculate 1/T
inv_T = 1 ./ T;


% Plot
plot(inv_T, ln_n, 'r', 'LineWidth', 2);
xlabel('1/T');
ylabel('ln(N_D)');
title('ln(Electron Concentration) vs. 1/T for Silicon');
grid on;