Added matlab listings and fixed matlab colouring

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David Lenfesty 2021-02-08 21:03:25 -07:00
parent 15b3adfb1d
commit ca5b0a6de1

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@ -16,29 +16,35 @@
\definecolor{gray}{rgb}{0.5,0.5,0.5}
\definecolor{mauve}{rgb}{0.58,0,0.82}
%\lstset{language=Matlab,%
% %basicstyle=\color{red},
% breaklines=true,%
% morekeywords={matlab2tikz},
% keywordstyle=\color{blue},%
% morekeywords=[2]{1}, keywordstyle=[2]{\color{black}},
% identifierstyle=\color{black},%
% stringstyle=\color{mylilas},
% commentstyle=\color{mygreen},%
% showstringspaces=false,%without this there will be a symbol in the places where there is a space
% numbers=left,%
% numbersty_sumle={\tiny \color{black}},% size of th_sume numbers
% numbersep=9pt, % this defines how far the numbers are from the text
% emph=[1]{for,end,break},emphstyle=[1]\color{red}, %some words to emphasise
% %emph=[2]{word1,word2}, emphstyle=[2]{style},
%}
\lstset{basicstyle=\small,
keywordstyle=\color{mauve},
identifierstyle=\color{dkgreen},
stringstyle=\color{gray},
numbers=left,
xleftmargin=5em
}
\definecolor{mygreen}{RGB}{28,172,0} % color values Red, Green, Blue
\definecolor{mylilas}{RGB}{170,55,241}
\lstset{language=Matlab,%
%basicstyle=\color{red},
breaklines=true,%
morekeywords={matlab2tikz},
keywordstyle=\color{blue},%
morekeywords=[2]{1}, keywordstyle=[2]{\color{black}},
identifierstyle=\color{black},%
stringstyle=\color{mylilas},
commentstyle=\color{mygreen},%
showstringspaces=false,%without this there will be a symbol in the places where there is a space
numbers=left,%
numberstyle={\tiny \color{black}},% size of th_sume numbers
numbersep=9pt, % this defines how far the numbers are from the text
emph=[1]{for,end,break},emphstyle=[1]\color{red}, %some words to emphasise
%emph=[2]{word1,word2}, emphstyle=[2]{style},
xleftmargin=5em
}
%\lstset{basicstyle=\small,
% keywordstyle=\color{mauve},
% identifierstyle=\color{dkgreen},
% stringstyle=\color{gray},
% numbers=left,
% xleftmargin=5em
% }
\title{ECE 456 - Problem Set 1}
\date{2021-02-06}
@ -230,6 +236,8 @@ ylabel('Current [A]');
\subsection*{(c)}
Code for this section can be found in appendix A.
\subsubsection*{(i)}
\begin{figure}[H]
\centering
@ -443,6 +451,77 @@ ylabel('Current [A]');
Below is our code. Note that some variable names are different from those in the example code.
\begin{lstlisting}[language=Matlab]
% Thermo-electric current
% Physical constants
hbar = 1.054e-34;
q = 1.602e-19;
% Parameters (eV)
kBT_1 = 0.025;
kBT_2 = 0.026;
mu = 0;
gamma_1 = 0.005;
gamma_2 = gamma_1;
gamma_sum = gamma_1 + gamma_2;
% Channel energy levels, varying between -0.25eV and 0.25eV
epsilon = linspace(-0.25, 0.25, 101);
depsilon = epsilon(2) - epsilon(1);
% Energy grid
E = linspace(-1, 1, 501);
dE = E(2) - E(1);
% Contact fermi functions
f_1 = 1 ./ (1 + exp((E - mu)./kBT_1));
f_2 = 1 ./ (1 + exp((E - mu)./kBT_2));
% Iterate through channel energy levels
for n = 1:length(epsilon)
% Compute energy level density functions - integral normalized to unity
D = (gamma_sum./(2*pi))./((E-epsilon(n)).^2+((gamma_sum./2).^2));
D = D./(dE*sum(D));
% Compute number of channel electrons
N(n) = dE*sum( ((gamma_1./gamma_sum).*f_1 + (gamma_2./gamma_sum).*f_2).*D );
% Compute the current in Amps; factor of q to resolve units
I(n) = q*(q/hbar)*dE*sum((f_1 - f_2).*D.*gamma_1.*gamma_2./gamma_sum);
%plot f_1 - f_2 and D/2
if (abs(epsilon(n) + 0.05) <= depsilon / 2) & (epsilon(n) <= 0)
figure(3);
h = plot(f_1-f_2, E, 'x', D/2500, E, 'k-');
set(gca, 'Fontsize', [18]);
axis([-0.01 0.02 -1 1]);
xlabel('f1(E) - f2(E), D(E)/2500');
ylabel('ENERGY [eV]');
legend('f1-f2', 'D(E)/2500');
title('CHANNEL LEVEL = -0.05 eV');
elseif (abs(epsilon(n)) <= depsilon / 2) & (epsilon(n) <= 0)
figure(4);
h = plot(f_1-f_2, E, 'x', D/2500, E, 'k-');
set(gca, 'Fontsize', [18]);
axis([-0.01 0.02 -1 1]);
xlabel('f1(E) - f2(E), D(E)/2500');
ylabel('ENERGY [eV]');
legend('f1-f2', 'D(E)/2500');
title('CHANNEL LEVEL = 0 eV');
end
end
% Final plots
figure(1);
\end{lstlisting}
\subsection*{(b)}
\begin{figure}[H]
@ -700,9 +779,178 @@ ylabel('Current [A]');
\end{equation*}
%
We conclude there are 3 levels.
% TODO appendix for Part C code
\appendix
\newpage
\section{Question 1b Code}
\begin{lstlisting}[language=Matlab]
clear all;
%% Constants
% Physical constants
hbar = 1.052e-34;
q = 1.602e-19;
%epsilon_0 = 8.854e-12;
%epsilon_r = 4;
%mstar = 0.25 * 9.11e-31;
% Single-charge coupling energy (eV)
U_0 = 0.25;
% (eV)
kBT = 0.025;
% Contact coupling coefficients (eV)
gamma_1 = 0.005;
gamma_2 = gamma_1;
gamma_sum = gamma_1 + gamma_2;
% Capacitive gate coefficient
a_G = 0.5;
% Capacitive drain coefficient
a_D = 0.5;
a_S = 1 - a_G - a_D;
% Central energy level
mu = 0;
% Energy grid, from -1eV to 1eV
NE = 501;
E = linspace(-1, 1, NE);
dE = E(2) - E(1);
% TODO name this better
cal_E = 0.2;
% Lorentzian density of states, normalized so the integral is 1
D = (gamma_sum / (2*pi)) ./ ( (E-cal_E).^2 + (gamma_sum/2).^2 );
D = D ./ (dE*sum(D));
% Reference no. of electrons in channel
N_0 = 0;
voltages = linspace(0, 1, 101);
dV = voltages(2) - voltages(1);
% Terminal Voltages
V_G = 0;
V_S = 0;
for n = 1:length(voltages)
% Set varying drain voltage
V_D = voltages(n);
% Shifted energy levels of the contacts
mu_1 = mu - V_S;
mu_2 = mu - V_D;
% Laplace potential, does not change as solution is found (eV)
% q is factored out here, we are working in eV
U_L = - (a_G*V_G) - (a_D*V_D) - (a_S*V_S);
% Poisson potential must change, assume 0 initially (eV)
U_P = 0;
% Assume large rate of change
dU_P = 1;
% Run until we get close enough to the answer
while dU_P > 1e-6
% source Fermi function
f_1 = 1 ./ (1 + exp((E + U_L + U_P - mu_1) ./ kBT));
% drain Fermi function
f_2 = 1 ./ (1 + exp((E + U_L + U_P - mu_2) ./ kBT));
% Update channel electrons against potential
N(n) = dE * sum( ((gamma_1/gamma_sum) .* f_1 + (gamma_2/gamma_sum) .* f_2) .* D);
% Re-update Poisson portion of potential
tmpU_P = U_0 * ( N(n) - N_0);
dU_P = abs(U_P - tmpU_P);
% Unsure why U_P is updated incrementally, perhaps to avoid oscillations?
%U_P = tmpU_P;
U_P = U_P + 0.1 * (tmpU_P - U_P);
end
% 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);
if (abs(V_D-0.0) <= dV/2)
figure(3); title('VD = 0.0 V');
subplot(2,3,1); plot(f_1,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/100,E,'k-'); axis([-0.1 1.1 -1 1]);
xlabel('D(E)/100'); ylabel('ENERGY [eV]'); title('VD = 0.0 V');
subplot(2,3,3); plot(f_2,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(f_1-f_2,E,'--',D/100,E,'k-'); axis([-0.1 1.1 -1 1]);
xlabel('f1(E+U)-f2(E+U), D(E)/100'); ylabel('ENERGY [eV]'); title('VD = 0.0 V');
elseif (abs(V_D-0.2) <= dV/2)
figure(4); title('VD = 0.2 V');
subplot(2,3,1); plot(f_1,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/100,E,'k-'); axis([-0.1 1.1 -1 1]);
xlabel('D(E)/100'); ylabel('ENERGY [eV]'); title('VD = 0.2 V');
subplot(2,3,3); plot(f_2,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(f_1-f_2,E,'--',D/100,E,'k-'); axis([-0.1 1.1 -1 1]);
xlabel('f1(E+U)-f2(E+U), D(E)/100'); ylabel('ENERGY [eV]'); title('VD = 0.2 V');
elseif (abs(V_D-0.5) <= dV/2)
figure(5); title('VD = 0.5 V');
subplot(2,3,1); plot(f_1,E,'k-'); axis([-0.1 1.1 -1 1]);
xlabel('f1(E+U)'); ylabel('ENERGY [eV]'); title('VD = 0.5 V');
subplot(2,3,2); plot(D/100,E,'k-'); axis([-0.1 1.1 -1 1]);
xlabel('D(E)/100'); ylabel('ENERGY [eV]'); title('VD = 0.5 V');
subplot(2,3,3); plot(f_2,E,'k-'); axis([-0.1 1.1 -1 1]);
xlabel('f2(E+U)'); ylabel('ENERGY [eV]'); title('VD = 0.5 V');
subplot(2,3,5); plot(f_1-f_2,E,'--',D/100,E,'k-'); axis([-0.1 1.1 -1 1]);
xlabel('f1(E+U)-f2(E+U), D(E)/100'); ylabel('ENERGY [eV]'); title('VD = 0.5 V');
elseif (abs(V_D-0.8) <= dV/2)
figure(6); title('VD = 0.8 V');
subplot(2,3,1); plot(f_1,E,'k-'); axis([-0.1 1.1 -1 1]);
xlabel('f1(E+U)'); ylabel('ENERGY [eV]'); title('VD = 0.8 V');
subplot(2,3,2); plot(D/100,E,'k-'); axis([-0.1 1.1 -1 1]);
xlabel('D(E)/100'); ylabel('ENERGY [eV]'); title('VD = 0.8 V');
subplot(2,3,3); plot(f_2,E,'k-'); axis([-0.1 1.1 -1 1]);
xlabel('f2(E+U)'); ylabel('ENERGY [eV]'); title('VD = 0.8 V');
subplot(2,3,5); plot(f_1-f_2,E,'--',D/100,E,'k-'); axis([-0.1 1.1 -1 1]);
xlabel('f1(E+U)-f2(E+U), D(E)/100'); ylabel('ENERGY [eV]'); title('VD = 0.8 V');
elseif (abs(V_D-1.0) <= dV/2)
figure(7); title('VD = 1.0 V');
subplot(2,3,1); plot(f_1,E,'k-'); axis([-0.1 1.1 -1 1]);
xlabel('f1(E+U)'); ylabel('ENERGY [eV]'); title('VD = 1.0 V');
subplot(2,3,2); plot(D/100,E,'k-'); axis([-0.1 1.1 -1 1]);
xlabel('D(E)/100'); ylabel('ENERGY [eV]'); title('VD = 1.0 V');
subplot(2,3,3); plot(f_2,E,'k-'); axis([-0.1 1.1 -1 1]);
xlabel('f2(E+U)'); ylabel('ENERGY [eV]'); title('VD = 1.0 V');
subplot(2,3,5); plot(f_1-f_2,E,'--',D/100,E,'k-'); axis([-0.1 1.1 -1 1]);
xlabel('f1(E+U)-f2(E+U), D(E)/100'); ylabel('ENERGY [eV]'); title('VD = 1.0 V');
end
end
%%Plotting commands
figure(1);
h = plot(voltages, 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(voltages, I,'k');
grid on;
set(h,'linewidth',[2.0]);
set(gca,'Fontsize',[18]);
xlabel('Drain voltage [V]');
ylabel('Current [A]');
\end{lstlisting}
\end{document}