breakout fermi velocity into separate function

2D-Conductivity/carrier_density_from_fermi.m

@@ -1,4 +1,4 @@
-function carrier_density = carrier_density_from_fermi(fermi)
+function carrier_density = carrier_density_from_fermi(fermi, energy_scale) % J, J
 
 if fermi > 0
     sf = 1;
@@ -6,13 +6,11 @@ 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 ... 
-
+                    / ...
-carrier_density = fermi^2 / (pi * (root_3_over_2 * a * ev_to_j(t))^2);
+             (pi * ( hbar * fermi_velocity(energy_scale) )^2);
 carrier_density = sf * carrier_density;
 end
 

2D-Conductivity/conductivity_calc_surface.m

@@ -13,18 +13,24 @@ F_TOTAL = 50;
 MAX_Y = 30; % carriers
 Y_TOTAL = 50;
 
+t = 2.8; % eV
+
 f_vals = logspace(MIN_F, MAX_F, F_TOTAL); % hz
 f_vals = f_vals .* (2*pi); % rads-1
 
-y_vals = logspace(0, MAX_Y, Y_TOTAL); % ev
+carrier_vals = logspace(0, MAX_Y, Y_TOTAL); % m-2
-%y_vals = -MAX_Y:2*MAX_Y/Y_TOTAL:MAX_Y; % ev
+%carrier_vals = carrier_vals + 273.15;
-%y_vals = y_vals + 273.15;
 
-cond = zeros(length(f_vals), length(y_vals));
+fermi_vals = zeros(1, length(carrier_vals));
+for carr=1:length(carrier_vals)
+    fermi_vals(carr) = fermi_from_carrier_density(carrier_vals(carr), ev_to_j(t));
+end
+
+cond = zeros(length(f_vals), length(fermi_vals));
 for freq=1:length(f_vals)
-    for y=1:length(y_vals)
+    for y=1:length(fermi_vals)
-        % omega (rads-1), fermi_level (J), temp (K), scatter_lifetime (s-1)
+        % omega (rads-1), fermi_level (eV), temp (K), scatter_lifetime (s-1)
-        cond(freq, y) = sheet_conductivity(f_vals(freq), fermi_from_carrier_density(y_vals(y)), 300, 5e-15);
+        cond(freq, y) = sheet_conductivity(f_vals(freq), fermi_vals(y), 300, 5e-12);
     end
 end
 
@@ -33,7 +39,7 @@ if DISPLAY_HZ % divide radians back to hertz
 end
 
 figure(1)
-surf(f_vals, y_vals, transpose(real(cond)));
+surf(f_vals, carrier_vals, transpose(real(cond)));
 h = gca;
 rotate3d on
 grid;
@@ -50,7 +56,7 @@ else
 end
 
 figure(2)
-surf(f_vals, y_vals, transpose(imag(cond)));
+surf(f_vals, carrier_vals, transpose(imag(cond)));
 h = gca;
 rotate3d on
 grid;

2D-Conductivity/conductivity_calculations.m

@@ -15,7 +15,7 @@ x_vals = x_vals .* (2*pi); % rads-1
 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)];
+    cond = [cond sheet_conductivity(x, fermi_from_carrier_density(7e7, ev_to_j(2.8)), 3000, 5e-12)];
 end
 
 if DISPLAY_HZ % divide radians back to hertz

2D-Conductivity/fermi_from_carrier_density.m

@@ -1,4 +1,4 @@
-function fermi = fermi_from_carrier_density(carrier_density)
+function fermi = fermi_from_carrier_density(carrier_density, energy_scale), % cm-2, J
 
 if carrier_density > 0
     sf = 1;
@@ -6,16 +6,12 @@ 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;
+carrier_density = abs(carrier_density);
 
-fermi_velocity_eq = (root_3_over_2 * a * ev_to_j(t))^2;
+fermi = sqrt(carrier_density * pi * ( hbar * fermi_velocity(energy_scale) )^2 );
-fermi = sf * sqrt(carrier_density * pi * fermi_velocity_eq);
+fermi = sf * fermi;
 
 end
 

2D-Conductivity/fermi_velocity.m

@@ -0,0 +1,9 @@
+function fermi = fermi_velocity (energy_scale) % J
+
+a = 0.246e-9; % lattice constant (m)
+hbar = 6.626e-34 / (2*pi); % Js
+
+fermi = (sqrt(3)/2) * a * energy_scale / hbar;
+
+end
+% m/s

2D-Conductivity/j_to_ev.m

@@ -0,0 +1,4 @@
+function eV = j_to_ev(j)
+eV = j / 1.602e-19;
+end
+