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pkirwin 2021-02-06 15:36:40 -07:00
parent feca86b40b
commit 9c17fcd819
1 changed files with 18 additions and 14 deletions
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32
PS1/q1b.m
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@ -3,18 +3,18 @@ clear all;
%% Constants %% Constants
% Physical constants % Physical constants
hbar = 1.052e-34; %hbar = 1.052e-34;
q = 1.602e-19; %q = 1.602e-19;
epsilon_0 = 8.854e-12; %epsilon_0 = 8.854e-12;
epsilon_r = 4; %epsilon_r = 4;
mstar = 0.25 * 9.11e-31; %mstar = 0.25 * 9.11e-31;
% Single-charge coupling energy (eV) % Single-charge coupling energy (eV)
U_0 = 0.25; U_0 = 0.25;
% (eV) % (eV)
kBT = 0.025; kBT = 0.025;
% Contact coupling coefficients (eV) % Contact coupling coefficients (eV)
gamma_1 = 0.0005; gamma_1 = 0.005;
gamma_2 = gamma_1; gamma_2 = gamma_1;
gamma_sum = gamma_1 + gamma_2; gamma_sum = gamma_1 + gamma_2;
% Capacitive gate coefficient % Capacitive gate coefficient
@ -35,13 +35,11 @@ cal_E = 0.2;
% Lorentzian density of states, normalized so the integral is 1 % Lorentzian density of states, normalized so the integral is 1
D = (gamma_sum / (2*pi)) ./ ( (E-cal_E).^2 + (gamma_sum/2).^2); D = (gamma_sum / (2*pi)) ./ ( (E-cal_E).^2 + (gamma_sum/2).^2);
D = D ./ (dE*sum(D));
% Reference no. of electrons in channel % Reference no. of electrons in channel
N_0 = 0; N_0 = 0;
fermi(-0.25, -0.2, kb_T)
voltages = linspace(0, 1, 101); voltages = linspace(0, 1, 101);
% Terminal Voltages % Terminal Voltages
@ -52,24 +50,28 @@ for n = 1:length(voltages)
% Set varying drain voltage % Set varying drain voltage
V_D = voltages(n); V_D = voltages(n);
% Shifted energy levels of the contacts
mu_1 = mu - V_S; mu_1 = mu - V_S;
mu_2 = mu - V_D; mu_2 = mu - V_D;
% Laplace potential, does not change as solution is found (eV) % Laplace potential, does not change as solution is found (eV)
U_L = -q * ((C_S*V_S + C_G*V_G + C_D*V_D) / C_E); U_L = - (a_G*V_G - a_D*V_D - a_S*V_S);
% Poisson potential must change, assume 0 initially (eV) % Poisson potential must change, assume 0 initially (eV)
U_P = 0; U_P = 0;
% Assume large rate of change
dU_P = 1; dU_P = 1;
% Run until we get close enough to the answer
while dU_P > 1e-6 while dU_P > 1e-6
% source Fermi function % source Fermi function
f_1 = 1 / (1 + exp((E + U_L + U_P - mu_1) / kBT)); f_1 = 1 ./ (1 + exp((E + U_L + U_P - mu_1) ./ kBT));
% drain Fermi function % drain Fermi function
f_2 = 1 / (1 + exp((E + U_L + U_P - mu_2) / kBT)); f_2 = 1 ./ (1 + exp((E + U_L + U_P - mu_2) ./ kBT));
% Update channel electrons against potential % Update channel electrons against potential
N(n) = dE * sum( ((gamma_1/gamma_sum) .* f1 + (gamma_2/gamma_sum) .* f2) .* D); N(n) = dE * sum( ((gamma_1/gamma_sum) .* f_1 + (gamma_2/gamma_sum) .* f_2) .* D);
% Re-update Poisson portion of potential % Re-update Poisson portion of potential
tmpU_P = U_0 * ( N(n) - N_0); tmpU_P = U_0 * ( N(n) - N_0);
@ -80,7 +82,9 @@ for n = 1:length(voltages)
% U_P = U_P + 0.1 * (tmpU_P - U_P) % U_P = U_P + 0.1 * (tmpU_P - U_P)
end end
I(n) = q * (q/hbar) * (gamma_1 * gamma_1 / gamma_sum) * dE * sum((f1-f2).*D); % Calculate current based on solved potential.
% Note: f1 is dependent on changes in U but has been updated prior in the loop
I(n) = q * (q/hbar) * (gamma_1 * gamma_1 / gamma_sum) * dE * sum((f_1-f_2).*D);
end end