108 lines
2.4 KiB
Matlab
108 lines
2.4 KiB
Matlab
clear all;
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%% Constants
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% Physical constants
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%hbar = 1.052e-34;
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%q = 1.602e-19;
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%epsilon_0 = 8.854e-12;
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%epsilon_r = 4;
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%mstar = 0.25 * 9.11e-31;
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% Single-charge coupling energy (eV)
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U_0 = 0.25;
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% (eV)
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kBT = 0.025;
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% Contact coupling coefficients (eV)
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gamma_1 = 0.005;
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gamma_2 = gamma_1;
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gamma_sum = gamma_1 + gamma_2;
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% Capacitive gate coefficient
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a_G = 0.5;
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% Capacitive drain coefficient
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a_D = 0.5;
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a_S = 1 - a_G - a_D;
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% Central energy level
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mu = 0;
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% Energy grid, from -1eV to 1eV
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NE = 501;
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E = linspace(-1, 1, NE);
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dE = E(2) - E(1);
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% TODO name this better
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cal_E = 0.2;
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% Lorentzian density of states, normalized so the integral is 1
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D = (gamma_sum / (2*pi)) ./ ( (E-cal_E).^2 + (gamma_sum/2).^2);
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D = D ./ (dE*sum(D));
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% Reference no. of electrons in channel
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N_0 = 0;
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voltages = linspace(0, 1, 101);
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% Terminal Voltages
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V_G = 0;
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V_S = 0;
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for n = 1:length(voltages)
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% Set varying drain voltage
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V_D = voltages(n);
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% Shifted energy levels of the contacts
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mu_1 = mu - V_S;
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mu_2 = mu - V_D;
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% Laplace potential, does not change as solution is found (eV)
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U_L = - (a_G*V_G - a_D*V_D - a_S*V_S);
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% Poisson potential must change, assume 0 initially (eV)
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U_P = 0;
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% Assume large rate of change
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dU_P = 1;
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% Run until we get close enough to the answer
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while dU_P > 1e-6
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% source Fermi function
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f_1 = 1 ./ (1 + exp((E + U_L + U_P - mu_1) ./ kBT));
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% drain Fermi function
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f_2 = 1 ./ (1 + exp((E + U_L + U_P - mu_2) ./ kBT));
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% Update channel electrons against potential
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N(n) = dE * sum( ((gamma_1/gamma_sum) .* f_1 + (gamma_2/gamma_sum) .* f_2) .* D);
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% Re-update Poisson portion of potential
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tmpU_P = U_0 * ( N(n) - N_0);
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dU_P = abs(U_P - tmpU_P);
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% Unsure why U_P is updated incrementally, perhaps to avoid oscillations?
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U_P = tmpU_P;
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% U_P = U_P + 0.1 * (tmpU_P - U_P)
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end
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% Calculate current based on solved potential.
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% Note: f1 is dependent on changes in U but has been updated prior in the loop
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I(n) = q * (q/hbar) * (gamma_1 * gamma_1 / gamma_sum) * dE * sum((f_1-f_2).*D);
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end
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%%Plotting commands
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figure(1);
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h = plot(voltages, N,'k');
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grid on;
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set(h,'linewidth',[2.0]);
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set(gca,'Fontsize',[18]);
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xlabel('Drain voltage [V]');
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ylabel('Number of electrons');
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figure(2);
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h = plot(voltages, I,'k');
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grid on;
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set(h,'linewidth',[2.0]);
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set(gca,'Fontsize',[18]);
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xlabel('Drain voltage [V]');
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ylabel('Current [A]'); |