log space for x generation, fermi_from_carrier_density
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18
2D-Conductivity/carrier_density_from_fermi.m
Normal file
18
2D-Conductivity/carrier_density_from_fermi.m
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@ -0,0 +1,18 @@
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function carrier_density = carrier_density_from_fermi(fermi)
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if fermi > 0
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sf = 1;
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else
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sf = -1;
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end
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a = 0.246e-9; % lattice constant (m)
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t = 2.8; % eV
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hbar = 6.626e-34 / (2*pi); % Js
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root_3_over_2 = sqrt(3) / 2;
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carrier_density = fermi^2 / (pi * (root_3_over_2 * a * ev_to_j(t))^2);
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carrier_density = sf * carrier_density;
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end
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@ -5,22 +5,26 @@
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close all; clear all; clc;
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close all; clear all; clc;
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DISPLAY_HZ = true;
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DISPLAY_HZ = true;
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MAX_F = 1e12; % Hz
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F_TOTAL = 1e3;
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MAX_Y = 10; % ev
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Y_TOTAL = 100;
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f_vals = 1:MAX_F/F_TOTAL:MAX_F; % hz
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MIN_F = 0;
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MAX_F = 15; % Hz
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F_TOTAL = 50;
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MAX_Y = 30; % carriers
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Y_TOTAL = 50;
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f_vals = logspace(MIN_F, MAX_F, F_TOTAL); % hz
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f_vals = f_vals .* (2*pi); % rads-1
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f_vals = f_vals .* (2*pi); % rads-1
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y_vals = 1:MAX_Y/Y_TOTAL:MAX_Y; % ev
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y_vals = logspace(0, MAX_Y, Y_TOTAL); % ev
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%y_vals = -MAX_Y:2*MAX_Y/Y_TOTAL:MAX_Y; % ev
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%y_vals = y_vals + 273.15;
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%y_vals = y_vals + 273.15;
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cond = zeros(length(f_vals), length(y_vals));
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cond = zeros(length(f_vals), length(y_vals));
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for freq=1:length(f_vals)
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for freq=1:length(f_vals)
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for y=1:length(y_vals)
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for y=1:length(y_vals)
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% omega (rads-1), fermi_level (J), temp (K), scatter_lifetime (s-1)
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% omega (rads-1), fermi_level (J), temp (K), scatter_lifetime (s-1)
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cond(freq, y) = sheet_conductivity(f_vals(freq), ev_to_j(y_vals(y)), 300, 5e-12);
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cond(freq, y) = sheet_conductivity(f_vals(freq), fermi_from_carrier_density(y_vals(y)), 300, 5e-15);
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end
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end
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end
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end
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@ -28,17 +32,35 @@ if DISPLAY_HZ % divide radians back to hertz
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f_vals = f_vals ./ (2*pi);
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f_vals = f_vals ./ (2*pi);
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end
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end
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surf(f_vals, y_vals, transpose(abs(cond)));
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figure(1)
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surf(f_vals, y_vals, transpose(real(cond)));
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h = gca;
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h = gca;
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rotate3d on
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rotate3d on
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grid();
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grid();
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set(h, 'xscale', 'log')
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set(h, 'xscale', 'log')
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title('2D Sheet Conductivity');
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set(h, 'yscale', 'log')
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ylabel('Fermi Level (ev)');
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title('2D Sheet Real Conductivity');
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ylabel('Net Carrier Density');
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zlabel('Conductivity (S/m)');
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zlabel('Conductivity (S/m)');
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if DISPLAY_HZ
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if DISPLAY_HZ
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xlabel('Frequency (Hz)');
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xlabel('Frequency (Hz)');
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else
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else
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xlabel('Frequency (rads-1)');
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xlabel('Frequency (rads-1)');
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end
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end
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figure(2)
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surf(f_vals, y_vals, transpose(imag(cond)));
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h = gca;
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rotate3d on
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grid();
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set(h, 'xscale', 'log')
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set(h, 'yscale', 'log')
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title('2D Sheet Imaginary Conductivity');
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ylabel('Net Carrier Density');
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zlabel('Conductivity (S/m)');
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if DISPLAY_HZ
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xlabel('Frequency (Hz)');
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else
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xlabel('Frequency (rads-1)');
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end
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@ -5,24 +5,42 @@
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close all;clear all; clc;
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close all;clear all; clc;
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DISPLAY_HZ = true;
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DISPLAY_HZ = true;
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MAX_F = 1e12;
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MIN_F = 9;
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F_TOTAL = 1e4;
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MAX_F = 15;
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F_TOTAL = 1e2;
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x_vals = 1:MAX_F/F_TOTAL:MAX_F; % hz
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x_vals = logspace(MIN_F, MAX_F, F_TOTAL); % hz
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x_vals = x_vals .* (2*pi); % rads-1
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x_vals = x_vals .* (2*pi); % rads-1
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cond = [];
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for x=x_vals
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% omega (rads-1), fermi_level (J), temp (K), scatter_lifetime (s-1)
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% omega (rads-1), fermi_level (J), temp (K), scatter_lifetime (s-1)
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cond = arrayfun(@(x) sheet_conductivity(x, ev_to_j(3), 300, 5e-12), x_vals);
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cond = [cond sheet_conductivity(x, ev_to_j(3), 300, 5e-12)];
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end
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if DISPLAY_HZ % divide radians back to hertz
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if DISPLAY_HZ % divide radians back to hertz
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x_vals = x_vals ./ (2*pi);
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x_vals = x_vals ./ (2*pi);
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end
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end
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%plot(x_vals, cond);
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figure(1);
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semilogx(x_vals, cond);
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%plot(x_vals, real(cond));
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semilogx(x_vals, real(cond));
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grid();
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grid();
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title('2D Sheet Conductivity');
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title('2D Sheet Real Conductivity');
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ylabel('Conductivity (S/m)');
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if DISPLAY_HZ
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xlabel('Frequency (Hz)');
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else
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xlabel('Frequency (rads-1)');
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end
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figure(2);
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%plot(x_vals, imag(cond));
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semilogx(x_vals, imag(cond));
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grid();
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title('2D Sheet Imaginary Conductivity');
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ylabel('Conductivity (S/m)');
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ylabel('Conductivity (S/m)');
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if DISPLAY_HZ
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if DISPLAY_HZ
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xlabel('Frequency (Hz)');
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xlabel('Frequency (Hz)');
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21
2D-Conductivity/fermi_from_carrier_density.m
Normal file
21
2D-Conductivity/fermi_from_carrier_density.m
Normal file
@ -0,0 +1,21 @@
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function fermi = fermi_from_carrier_density(carrier_density)
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if carrier_density > 0
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sf = 1;
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else
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sf = -1;
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end
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carrier_density = abs(carrier_density);
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a = 0.246e-9; % lattice constant (m)
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t = 2.8; % eV
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hbar = 6.626e-34 / (2*pi); % Js
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root_3_over_2 = sqrt(3) / 2;
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fermi_velocity_eq = (root_3_over_2 * a * ev_to_j(t))^2;
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fermi = sf * sqrt(carrier_density * pi * fermi_velocity_eq);
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end
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