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-clear all;
-
-% Physical constants in MKS units
-
-hbar = 1.054e-34;
-6 q = 1.602e-19;
-
-% Energy parameters in eV; included are the single-electron charging
-% energy U0; the kBT product; the equilibrium Fermi level mu; and the
- % energy level cal_E, which is short-form for "calligraphic E"
-
- % Please especially note that ALL ENERGY VARIABLES IN THIS CODE
- % ARE IN eV (NOT joules); the equations from class must be adjusted
- % accordingly, multiplying or dividing appropriate terms by a factor of q
-
- U0 = 0.25;
- kBT = 0.025;
- mu = 0;
- cal_E = 0.2;
-
- % Capacitance parameters
-
- alpha_G = 0.5;
- alpha_D = 0.5;
- alpha_S = 1 - alpha_G - alpha_D;
-
- % Energy grid in eV, from -1 eV to 1 eV
-
- NE = 501;
-E = linspace(-1,1,NE);
- dE = E(2) - E(1);
-
- % Gamma parameters, in eV
-
- gamma_1 = 0.005;
- gamma_2 = 0.005;
- gamma = gamma_1 + gamma_2;
-
- % Lorentzian density of states, normalized so that its integral is unity
-
- D = (gamma/(2*pi))./((E-cal_E).ˆ2+(gamma/2)ˆ2);
- D = D./(dE*sum(D));
-
- % Reference number of electrons in the channel, assumed to be zero in
- % this code
-
- N0 = 0;
-
- % Voltage values to consider for the final plots
- 
- NV = 101;
- VV = linspace(0,1,NV);
- dV = VV(2) - VV(1);
-
- % Loop over voltage values and compute number of electrons and current
- % for each voltage value in a self-consistent manner
-
- for count = 1:NV
-
- % Set terminal voltages
-
- VG = 0;
- 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 );
-
- % Newly calculated Poisson part of self-consistent potential
-
- UPnew = U0*( N(count) - N0 );
-
- % Change in Poisson part between iterations
-
- dUP = abs(UP - UPnew);
-
-% New guess for next iteration, found by adding a fraction of the
-% difference between iterations to the old guess
-105
-106 UP = UP + 0.1*(UPnew - UP);
-107
-108 end
-109
-110 % Compute the current in A after the self-consistent potential
-111 % has been achieved; notice the extra factor of q preceding the
-112 % equation, which is needed since the gammas are in eV
-113
-114 I(count) = q*(q/hbar)*(gamma_1*gamma_2)/(gamma) ...
-115 *dE*sum((f1-f2).*D);
-116
-117 end
-118
-119 % Plotting commands, including lines to modify the linewidth
-120 % and Fontsize, just to make the plots look nicer; you don’t
- % need to worry about how these work
-
- figure(1); h = plot(VV,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(VV,I,’k’); grid on;
- set(h,’linewidth’,[2.0]); set(gca,’Fontsize’,[18]);
- xlabel(’DRAIN VOLTAGE [V]’); ylabel(’CURRENT [A]’);
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