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pkirwin 2021-02-06 15:20:27 -07:00
parent d08ccce643
commit feca86b40b
1 changed files with 37 additions and 8 deletions
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43
PS1/q1b.m
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@ -12,12 +12,11 @@ mstar = 0.25 * 9.11e-31;
% Single-charge coupling energy (eV)
U_0 = 0.25;
% (eV)
kb_T = 0.025;
kBT = 0.025;
% Contact coupling coefficients (eV)
gamma_1 = 0.0005;
gamma_2 = gamma_1;
% Energy level
E = 0.2;
gamma_sum = gamma_1 + gamma_2;
% Capacitive gate coefficient
a_G = 0.5;
% Capacitive drain coefficient
@ -31,6 +30,11 @@ mu = 0;
NE = 501;
E = linspace(-1, 1, NE);
dE = E(2) - E(1);
% TODO name this better
cal_E = 0.2;
% Lorentzian density of states, normalized so the integral is 1
D = (gamma_sum / (2*pi)) ./ ( (E-cal_E).^2 + (gamma_sum/2).^2);
% Reference no. of electrons in channel
@ -60,16 +64,41 @@ for n = 1:length(voltages)
dU_P = 1;
while dU_P > 1e-6
% source Fermi function
f_1 = 1 / (1 + exp((E + U_L + U_P - mu_1) / kb_T));
f_1 = 1 / (1 + exp((E + U_L + U_P - mu_1) / kBT));
% drain Fermi function
f_2 = 1 / (1 + exp((E + U_L + U_P - mu_2) / kb_T));
f_2 = 1 / (1 + exp((E + U_L + U_P - mu_2) / kBT));
N(n) = dE * sum( )
% Update channel electrons against potential
N(n) = dE * sum( ((gamma_1/gamma_sum) .* f1 + (gamma_2/gamma_sum) .* f2) .* D);
tmpU_P = U_0 *
% Re-update Poisson portion of potential
tmpU_P = U_0 * ( N(n) - N_0);
dU_P = abs(U_P - tmpU_P);
% Unsure why U_P is updated incrementally, perhaps to avoid oscillations?
U_P = tmpU_P;
% U_P = U_P + 0.1 * (tmpU_P - U_P)
end
I(n) = q * (q/hbar) * (gamma_1 * gamma_1 / gamma_sum) * dE * sum((f1-f2).*D);
end
%%Plotting commands
figure(1);
h = plot(voltages, N,'k');
grid on;
set(h,'linewidth',[2.0]);
set(gca,'Fontsize',[18]);
xlabel('Drain voltage [V]');
ylabel('Number of electrons');
figure(2);
h = plot(voltages, I,'k');
grid on;
set(h,'linewidth',[2.0]);
set(gca,'Fontsize',[18]);
xlabel('Drain voltage [V]');
ylabel('Current [A]');