added phase calc, writing part b, phase diagrams

2D-Conductivity/conductivity_phase_calculations.m

@@ -0,0 +1,130 @@
+%% conductivity_phase_calculations.m
+%%
+%% calculate and present 2D sheet conductivty phase for graphene
+
+close all; clear all; clc;
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%    FLAGS & OPTIONS
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+DISPLAY_HZ = true; % convert rads back to Hz for presenting
+
+MIN_F = 9;
+MAX_F = 15;
+F_TOTAL = 1e2; % number of points to generate
+
+% EXCITATION_TYPE = 'intra';
+% EXCITATION_TYPE = 'inter';
+EXCITATION_TYPE = 'all';
+
+MULTIPLE_SERIES = true; % for comparing two dopants
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%     CALCULATE
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+x_vals = logspace(MIN_F, MAX_F, F_TOTAL); % hz
+x_vals = x_vals .* (2*pi); % rads-1
+
+% CALCULATE SHEET CONDUCTIVITY
+cond = zeros(length(x_vals), 2);
+for x=1:length(x_vals)
+    cond(x, :) = sheet_conductivity(x_vals(x),... % omega (rads-1)
+                                    fermi_from_carrier_density(1.3e17, ev_to_j(3)),... % fermi_level (J)
+                                    300,... % temp (K)
+                                    5e-12); % scatter_lifetime (s)
+end
+
+if MULTIPLE_SERIES
+    cond2 = zeros(length(x_vals), 2);
+    for x=1:length(x_vals)
+        cond2(x, :) = sheet_conductivity(x_vals(x),... % omega (rads-1)
+                                        fermi_from_carrier_density(1.3e17, ev_to_j(3)),... % fermi_level (J)
+                                        300,... % temp (K)
+                                        1e-12); % scatter_lifetime (s)
+    end
+    
+    cond3 = zeros(length(x_vals), 2);
+    for x=1:length(x_vals)
+        cond3(x, :) = sheet_conductivity(x_vals(x),... % omega (rads-1)
+                                        fermi_from_carrier_density(1.3e17, ev_to_j(3)),... % fermi_level (J)
+                                        300,... % temp (K)
+                                        1e-13); % scatter_lifetime (s)
+    end
+end
+
+if DISPLAY_HZ % divide radians back to hertz
+    x_vals = x_vals ./ (2*pi);
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%       RENDER
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+RE_COLOUR = 'r-';
+IM_COLOUR = 'r--';
+MAG_COLOUR = 'r:';
+RE_COLOUR2 = 'g-';
+IM_COLOUR2 = 'g--';
+MAG_COLOUR2 = 'g:';
+RE_COLOUR3 = 'b';
+IM_COLOUR3 = 'b--';
+MAG_COLOUR3 = 'b:';
+LW = 2;
+
+figure(1);
+hold on;
+% INTRA
+if strcmp(EXCITATION_TYPE, 'intra')
+    plot(x_vals, angle(cond(:, 1)) .* (180/pi), RE_COLOUR, 'LineWidth', LW);
+    
+    if MULTIPLE_SERIES
+        plot(x_vals, angle(cond2(:, 1)) .* (180/pi), RE_COLOUR2, 'LineWidth', LW);
+        
+        plot(x_vals, angle(cond3(:, 1)) .* (180/pi), RE_COLOUR3, 'LineWidth', LW);
+    end
+    title('2D Intraband Sheet Conductivity Phase');
+
+% INTER
+elseif strcmp(EXCITATION_TYPE, 'inter')
+    plot(x_vals, angle(cond(:, 2)) .* (180/pi), RE_COLOUR, 'LineWidth', LW);
+    
+    if MULTIPLE_SERIES
+        plot(x_vals, angle(cond2(:, 2)) .* (180/pi), RE_COLOUR2, 'LineWidth', LW);
+        
+        plot(x_vals, angle(cond3(:, 2)) .* (180/pi), RE_COLOUR3, 'LineWidth', LW);
+    end
+    title('2D Interband Sheet Conductivity Phase');
+    
+% COMPLEX
+else
+    plot(x_vals, angle(sum(cond, 2)) .* (180/pi), RE_COLOUR, 'LineWidth', LW);
+    
+    if MULTIPLE_SERIES
+        plot(x_vals, angle(sum(cond2, 2)) .* (180/pi), RE_COLOUR2, 'LineWidth', LW);
+        
+        plot(x_vals, angle(sum(cond3, 2)) .* (180/pi), RE_COLOUR3, 'LineWidth', LW);
+    end
+    title('2D Sheet Conductivity Phase');
+end
+
+set(gca,'Xscale','log')
+% set(gca,'Yscale','log')
+axis tight
+
+if MULTIPLE_SERIES
+%     legend('\phi(TTF)', '\phi(CoCp_2)');
+%     legend('\phi(1x10^8m^{-2})', '\phi(1x10^{15}m^{-2})', '\phi(1.3x10^{17}m^{-2})');
+%     legend('\phi(10K)', '\phi(300K)', '\phi(2230K)');
+    legend('\phi(5x10^{-12} s)', '\phi(1x10^{-12} s)', '\phi(1x10^{-13} s)');
+else
+    legend('\phi');
+end
+grid;
+ylabel('Conductivity Phase (Degrees)');
+if DISPLAY_HZ
+    xlabel('Frequency (Hz)');
+else
+    xlabel('Frequency (rads-1)');
+end

Report/references.bib

@@ -56,3 +56,12 @@
 	year = {2014}
 }
 
+@misc{fermi-dirac-dist,
+	author = {Zeghbroeck, Bart Van},
+	organization = {University of Colorado, Boulder},
+	title = {Carrier distribution functions},
+	url = {https://ecee.colorado.edu/~bart/book/book/chapter2/ch2_5.htm#fig2_5_2},
+	urldate = {2021-04-24},
+	year = {2011}
+}
+