128 lines
3.2 KiB
Plaintext
128 lines
3.2 KiB
Plaintext
clear all;
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% Physical constants in MKS units
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hbar = 1.054e-34;
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6 q = 1.602e-19;
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% Energy parameters in eV; included are the single-electron charging
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% energy U0; the kBT product; the equilibrium Fermi level mu; and the
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% energy level cal_E, which is short-form for "calligraphic E"
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% Please especially note that ALL ENERGY VARIABLES IN THIS CODE
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% ARE IN eV (NOT joules); the equations from class must be adjusted
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% accordingly, multiplying or dividing appropriate terms by a factor of q
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U0 = 0.25;
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kBT = 0.025;
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mu = 0;
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cal_E = 0.2;
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% Capacitance parameters
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alpha_G = 0.5;
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alpha_D = 0.5;
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alpha_S = 1 - alpha_G - alpha_D;
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% Energy grid in eV, from -1 eV to 1 eV
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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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% Gamma parameters, in eV
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gamma_1 = 0.005;
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gamma_2 = 0.005;
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gamma = gamma_1 + gamma_2;
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% Lorentzian density of states, normalized so that its integral is unity
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D = (gamma/(2*pi))./((E-cal_E).ˆ2+(gamma/2)ˆ2);
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D = D./(dE*sum(D));
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% Reference number of electrons in the channel, assumed to be zero in
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% this code
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N0 = 0;
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% Voltage values to consider for the final plots
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NV = 101;
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VV = linspace(0,1,NV);
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dV = VV(2) - VV(1);
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% Loop over voltage values and compute number of electrons and current
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% for each voltage value in a self-consistent manner
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for count = 1:NV
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% Set terminal voltages
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VG = 0;
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VD = VV(count);
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VS = 0;
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% Values of mu1 and mu2; notice that the usual factor of q multiplying
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% the voltages is omitted, because in this code, energy is in eV
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mu1 = mu - VS;
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mu2 = mu - VD;
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% Value of Laplace potential in eV
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UL = - (alpha_G*VG) - (alpha_D*VD) - (alpha_S*VS);
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% Initial value of Poisson part in eV
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UP = 0;
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% Iterate until self-consistent potential is achieved by monitoring
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% the Poisson part (the Laplace part does not change)
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dUP = 1;
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while dUP > 1e-6
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% Compute source and drain Fermi functions
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f1 = 1./(1+exp((E + UL + UP - mu1)./kBT));
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f2 = 1./(1+exp((E + UL + UP - mu2)./kBT));
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% Compute number of channel electrons
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N(count) = dE*sum( ((gamma_1/gamma).*f1 + (gamma_2/gamma).*f2).*D );
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% Newly calculated Poisson part of self-consistent potential
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UPnew = U0*( N(count) - N0 );
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% Change in Poisson part between iterations
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dUP = abs(UP - UPnew);
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% New guess for next iteration, found by adding a fraction of the
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% difference between iterations to the old guess
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105
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106 UP = UP + 0.1*(UPnew - UP);
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107
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108 end
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109
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110 % Compute the current in A after the self-consistent potential
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111 % has been achieved; notice the extra factor of q preceding the
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112 % equation, which is needed since the gammas are in eV
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113
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114 I(count) = q*(q/hbar)*(gamma_1*gamma_2)/(gamma) ...
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115 *dE*sum((f1-f2).*D);
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116
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117 end
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118
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119 % Plotting commands, including lines to modify the linewidth
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120 % and Fontsize, just to make the plots look nicer; you don’t
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% need to worry about how these work
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figure(1); h = plot(VV,N,’k’); grid on;
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set(h,’linewidth’,[2.0]); set(gca,’Fontsize’,[18]);
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xlabel(’DRAIN VOLTAGE [V]’); ylabel(’NUMBER OF ELECTRONS’);
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figure(2); h = plot(VV,I,’k’); grid on;
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set(h,’linewidth’,[2.0]); set(gca,’Fontsize’,[18]);
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xlabel(’DRAIN VOLTAGE [V]’); ylabel(’CURRENT [A]’); |