log space for x generation, fermi_from_carrier_density

2D-Conductivity/carrier_density_from_fermi.m

@@ -0,0 +1,18 @@
+function carrier_density = carrier_density_from_fermi(fermi)
+
+if fermi > 0
+    sf = 1;
+else
+    sf = -1;
+end
+
+a = 0.246e-9; % lattice constant (m)
+t = 2.8; % eV
+hbar = 6.626e-34 / (2*pi); % Js
+
+root_3_over_2 = sqrt(3) / 2;
+
+carrier_density = fermi^2 / (pi * (root_3_over_2 * a * ev_to_j(t))^2);
+carrier_density = sf * carrier_density;
+end
+

2D-Conductivity/conductivity_calc_surface.m

@@ -5,22 +5,26 @@
 close all; clear all; clc;
 
 DISPLAY_HZ = true;
-MAX_F = 1e12; % Hz
-F_TOTAL = 1e3;
-MAX_Y = 10; % ev
-Y_TOTAL = 100;
 
-f_vals = 1:MAX_F/F_TOTAL:MAX_F; % hz
+MIN_F = 0;
+MAX_F = 15; % Hz
+F_TOTAL = 50;
+
+MAX_Y = 30; % carriers
+Y_TOTAL = 50;
+
+f_vals = logspace(MIN_F, MAX_F, F_TOTAL); % hz
 f_vals = f_vals .* (2*pi); % rads-1
 
-y_vals = 1:MAX_Y/Y_TOTAL:MAX_Y; % ev
+y_vals = logspace(0, MAX_Y, Y_TOTAL); % ev
+%y_vals = -MAX_Y:2*MAX_Y/Y_TOTAL:MAX_Y; % ev
 %y_vals = y_vals + 273.15;
 
 cond = zeros(length(f_vals), length(y_vals));
 for freq=1:length(f_vals)
     for y=1:length(y_vals)
         % omega (rads-1), fermi_level (J), temp (K), scatter_lifetime (s-1)
-        cond(freq, y) = sheet_conductivity(f_vals(freq), ev_to_j(y_vals(y)), 300, 5e-12);
+        cond(freq, y) = sheet_conductivity(f_vals(freq), fermi_from_carrier_density(y_vals(y)), 300, 5e-15);
     end
 end
 
@@ -28,17 +32,35 @@ if DISPLAY_HZ % divide radians back to hertz
     f_vals = f_vals ./ (2*pi);
 end
 
-surf(f_vals, y_vals, transpose(abs(cond)));
-
+figure(1)
+surf(f_vals, y_vals, transpose(real(cond)));
 h = gca;
 rotate3d on
 grid();
 set(h, 'xscale', 'log')
-title('2D Sheet Conductivity');
-ylabel('Fermi Level (ev)');
+set(h, 'yscale', 'log')
+title('2D Sheet Real Conductivity');
+ylabel('Net Carrier Density');
 zlabel('Conductivity (S/m)');
 if DISPLAY_HZ
     xlabel('Frequency (Hz)');
 else
     xlabel('Frequency (rads-1)');
 end
+
+figure(2)
+surf(f_vals, y_vals, transpose(imag(cond)));
+h = gca;
+rotate3d on
+grid();
+set(h, 'xscale', 'log')
+set(h, 'yscale', 'log')
+title('2D Sheet Imaginary Conductivity');
+ylabel('Net Carrier Density');
+zlabel('Conductivity (S/m)');
+if DISPLAY_HZ
+    xlabel('Frequency (Hz)');
+else
+    xlabel('Frequency (rads-1)');
+end
+

2D-Conductivity/conductivity_calculations.m

@@ -2,27 +2,45 @@
 %%
 %% calculate and present 2D sheet conductivty for graphene
 
-close all; clear all; clc;
+close all;clear all; clc;
 
 DISPLAY_HZ = true;
-MAX_F = 1e12;
-F_TOTAL = 1e4;
+MIN_F = 9;
+MAX_F = 15;
+F_TOTAL = 1e2;
 
-x_vals = 1:MAX_F/F_TOTAL:MAX_F; % hz
+x_vals = logspace(MIN_F, MAX_F, F_TOTAL); % hz
 x_vals = x_vals .* (2*pi); % rads-1
 
-% omega (rads-1), fermi_level (J), temp (K), scatter_lifetime (s-1)
-cond = arrayfun(@(x) sheet_conductivity(x, ev_to_j(3), 300, 5e-12), x_vals);
+cond = [];
+for x=x_vals
+    % omega (rads-1), fermi_level (J), temp (K), scatter_lifetime (s-1)
+    cond = [cond sheet_conductivity(x, ev_to_j(3), 300, 5e-12)];
+end
 
 if DISPLAY_HZ % divide radians back to hertz
     x_vals = x_vals ./ (2*pi);
 end
 
-%plot(x_vals, cond);
-semilogx(x_vals, cond);
+figure(1);
+%plot(x_vals, real(cond));
+semilogx(x_vals, real(cond));
 
 grid();
-title('2D Sheet Conductivity');
+title('2D Sheet Real Conductivity');
+ylabel('Conductivity (S/m)');
+if DISPLAY_HZ
+    xlabel('Frequency (Hz)');
+else
+    xlabel('Frequency (rads-1)');
+end
+
+figure(2);
+%plot(x_vals, imag(cond));
+semilogx(x_vals, imag(cond));
+
+grid();
+title('2D Sheet Imaginary Conductivity');
 ylabel('Conductivity (S/m)');
 if DISPLAY_HZ
     xlabel('Frequency (Hz)');

2D-Conductivity/fermi_from_carrier_density.m

@@ -0,0 +1,21 @@
+function fermi = fermi_from_carrier_density(carrier_density)
+
+if carrier_density > 0
+    sf = 1;
+else
+    sf = -1;
+end
+
+carrier_density = abs(carrier_density);
+
+a = 0.246e-9; % lattice constant (m)
+t = 2.8; % eV
+hbar = 6.626e-34 / (2*pi); % Js
+
+root_3_over_2 = sqrt(3) / 2;
+
+fermi_velocity_eq = (root_3_over_2 * a * ev_to_j(t))^2;
+fermi = sf * sqrt(carrier_density * pi * fermi_velocity_eq);
+
+end
+