added q2 plots

PS1/q2.m

@@ -0,0 +1,183 @@
+clear all;
+
+% Physical constants in MKS units
+
+hbar = 1.054e-34;
+q = 1.602e-19;
+epsilon_0 = 8.854e-12;
+epsilon_r = 4;
+mstar = 0.25*9.11e-31;
+
+% MOSFET dimensions in meters
+
+W = 1.0e-6;
+L = 10.0e-9;
+tox = 1.5e-9;
+
+% Capacitances and capacitance parameters
+
+CG = epsilon_r*epsilon_0*W*L/tox;
+CS = 0.05*CG;
+CD = 0.05*CG;
+CE = CG + CS + CD;
+alpha_G = CG / CE;
+alpha_D = CD / CE;
+alpha_S = (1 - alpha_G - alpha_D);
+
+% Energy parameters in eV
+
+kBT = 0.025;
+U0 = q/CE;
+
+% Energy grid in eV, from -1 eV to 1 eV
+
+NE = 501;
+E = linspace(-1,1,NE);
+dE = E(2) - E(1);
+
+% Escape velocity [m/s] and gamma values [eV]
+
+vR = 1e5;
+gamma_1 = hbar*vR/(q*L);
+gamma_2 = gamma_1;
+gamma = gamma_1 + gamma_2;
+
+% Step-like density of states, stepping from 0 to a finite value
+% at an energy of 0 eV
+
+D0 = mstar*q*W*L/(pi*hbar*hbar);
+D = D0*[zeros(1,251) ones(1,250)];
+
+% Equilibrium Fermi level in eV
+
+mu = -0.2;
+
+% Reference number of channel electrons
+
+f0 = 1./(1+exp((E - mu)./kBT));
+N0 = dE*sum(D.*f0);
+
+% Voltage values to consider for the final plots
+
+NV = 61;
+VV = linspace(0,0.6,NV);
+
+% Loop over voltage values and compute number of electrons and current
+% for each voltage value in a self-consistent manner
+
+for VG = [0.25 0.5]
+
+   for count = 1:NV
+
+      % Set terminal voltages
+
+      VD = VV(count);
+      VS = 0;
+
+      % Values of mu1 and mu2; notice that the usual factor of q multiplying
+      % the voltages is omitted, because in this code, energy is in eV
+
+      mu1 = mu - VS;
+      mu2 = mu - VD;
+
+      % Value of Laplace potential in eV
+
+      UL = - (alpha_G*VG) - (alpha_D*VD) - (alpha_S*VS);
+
+      % Initial value of Poisson part in eV
+
+      UP = 0;
+
+      % Iterate until self-consistent potential is achieved by monitoring
+      % the Poisson part (the Laplace part does not change)
+
+      dUP = 1;
+      while dUP > 1e-6
+
+         % Compute source and drain Fermi functions
+
+         f1 = 1./(1+exp((E + UL + UP - mu1)./kBT));
+         f2 = 1./(1+exp((E + UL + UP - mu2)./kBT));
+
+         % Compute number of channel electrons
+
+         N(count) = dE*sum( ((gamma_1/gamma).*f1 + (gamma_2/gamma).*f2).*D );
+
+         % Update Poisson part of self-consistent potential
+
+         UPnew = U0*( N(count) - N0 );
+         dUP = abs(UP - UPnew);
+         UP = UP + 0.1*(UPnew - UP);
+
+      end
+
+      % Compute the current in A after the self-consistent potential
+      % has been achieved; notice the extra factor of q preceding the
+      % equation, which is needed since the gammas are in eV 
+
+      ID(count) = q*(q/hbar)*(gamma_1*gamma_2)/(gamma) ...
+                  *dE*sum((f1-f2).*D);
+
+      if (VG == 0.5)
+
+         switch VD
+            case 0.0
+               figure(2); title('VD = 0.0 V');
+               subplot(2,3,1); plot(f1,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('f1(E+U)'); ylabel('ENERGY  [eV]'); title('VD = 0.0 V');
+               subplot(2,3,2); plot(D/1E4,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('D(E)/1E4'); ylabel('ENERGY  [eV]'); title('VD = 0.0 V');
+               subplot(2,3,3); plot(f2,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('f2(E+U)'); ylabel('ENERGY  [eV]'); title('VD = 0.0 V');
+               subplot(2,3,5); plot(f1-f2,E,'--',D/1E4,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('f1(E+U)-f2(E+U), D(E)/1E4'); ylabel('ENERGY  [eV]'); title('VD = 0.0 V');
+            case 0.05
+               figure(3); title('VD = 0.05 V');
+               subplot(2,3,1); plot(f1,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('f1(E+U)'); ylabel('ENERGY  [eV]'); title('VD = 0.05 V');
+               subplot(2,3,2); plot(D/1E4,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('D(E)/1E4'); ylabel('ENERGY  [eV]'); title('VD = 0.05 V');
+               subplot(2,3,3); plot(f2,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('f2(E+U)'); ylabel('ENERGY  [eV]'); title('VD = 0.05 V');
+               subplot(2,3,5); plot(f1-f2,E,'--',D/1E4,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('f1(E+U)-f2(E+U), D(E)/1E4'); ylabel('ENERGY  [eV]'); title('VD = 0.05 V');
+            case 0.1
+               figure(4); title('VD = 0.1 V');
+               subplot(2,3,1); plot(f1,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('f1(E+U)'); ylabel('ENERGY  [eV]'); title('VD = 0.1 V');
+               subplot(2,3,2); plot(D/1E4,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('D(E)/1E4'); ylabel('ENERGY  [eV]'); title('VD = 0.1 V');
+               subplot(2,3,3); plot(f2,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('f2(E+U)'); ylabel('ENERGY  [eV]'); title('VD = 0.1 V');
+               subplot(2,3,5); plot(f1-f2,E,'--',D/1E4,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('f1(E+U)-f2(E+U), D(E)/1E4'); ylabel('ENERGY  [eV]'); title('VD = 0.1 V');
+            case 0.2
+               figure(5); title('VD = 0.2 V');
+               subplot(2,3,1); plot(f1,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('f1(E+U)'); ylabel('ENERGY  [eV]'); title('VD = 0.2 V');
+               subplot(2,3,2); plot(D/1E4,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('D(E)/1E4'); ylabel('ENERGY  [eV]'); title('VD = 0.2 V');
+               subplot(2,3,3); plot(f2,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('f2(E+U)'); ylabel('ENERGY  [eV]'); title('VD = 0.2 V');
+               subplot(2,3,5); plot(f1-f2,E,'--',D/1E4,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('f1(E+U)-f2(E+U), D(E)/1E4'); ylabel('ENERGY  [eV]'); title('VD = 0.2 V');
+            case 0.3
+               figure(6); title('VD = 0.3 V');
+               subplot(2,3,1); plot(f1,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('f1(E+U)'); ylabel('ENERGY  [eV]'); title('VD = 0.3 V');
+               subplot(2,3,2); plot(D/1E4,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('D(E)/1E4'); ylabel('ENERGY  [eV]'); title('VD = 0.3 V');
+               subplot(2,3,3); plot(f2,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('f2(E+U)'); ylabel('ENERGY  [eV]'); title('VD = 0.3 V');
+               subplot(2,3,5); plot(f1-f2,E,'--',D/1E4,E,'k-'); axis([-0.1 1.1 -1 1]);
+               xlabel('f1(E+U)-f2(E+U), D(E)/1E4'); ylabel('ENERGY  [eV]'); title('VD = 0.3 V');
+         end
+
+      end
+
+   end
+
+   figure(1); plot(VV,ID,'k-'); grid on; 
+   xlabel('DRAIN VOLTAGE  [V]'); ylabel('CURRENT  [A]'); hold on;
+
+end