172 lines
4.7 KiB
Matlab
172 lines
4.7 KiB
Matlab
%% conductivity_calc_surface.m
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%%
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%% calculate and present 2D sheet conductivty for graphene
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close all; clear all; clc;
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% FLAGS & OPTIONS
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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DISPLAY_HZ = true; % convert rads back to Hz for presenting
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MIN_F = 9;
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MAX_F = 15; % Hz
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F_TOTAL = 50; % number of points to generate
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MAX_Y = 18; % carriers (m-2)
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Y_TOTAL = 50; % number of points to generate
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% EXCITATION_TYPE = 'intra';
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% EXCITATION_TYPE = 'inter';
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EXCITATION_TYPE = 'all';
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t = 2.8; % eV, energy scale for Fermi velocity
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% CALCULATE
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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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% Carrier Density
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%%%%%%%
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% carrier_vals = logspace(0, MAX_Y, Y_TOTAL); % m-2
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%
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% % below turns turns carrier densities into Fermi energies
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% fermi_vals = zeros(1, length(carrier_vals));
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% for carr=1:length(carrier_vals)
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% fermi_vals(carr) = fermi_from_carrier_density(carrier_vals(carr), ev_to_j(t));
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% end
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%
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% % CALCULATE SHEET CONDUCTIVITY
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% cond = zeros(length(f_vals),... % frequency
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% length(fermi_vals),... % fermi
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% 2); % intra/inter
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% for freq=1:length(f_vals)
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% for y=1:length(fermi_vals)
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%
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% cond(freq, y, :) = sheet_conductivity(f_vals(freq),... % omega (rads-1)
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% fermi_vals(y),... % fermi_level (J)
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% 300,... % temp (K)
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% 1e-12); % scatter_lifetime (s)
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% end
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% end
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% Temperature
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%%%%%%%
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% temp_vals = linspace(0, 2230, Y_TOTAL); % K
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%
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% % CALCULATE SHEET CONDUCTIVITY
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% cond = zeros(length(f_vals),... % frequency
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% length(temp_vals),... % fermi
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% 2); % intra/inter
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% for freq=1:length(f_vals)
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% for y=1:length(temp_vals)
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%
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% cond(freq, y, :) = sheet_conductivity(f_vals(freq),... % omega (rads-1)
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% fermi_from_carrier_density(1.3e13*10000, ev_to_j(t)),... % fermi_level (J)
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% temp_vals(y),... % temp (K)
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% 5e-12); % scatter_lifetime (s)
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% end
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% end
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% Scatter Lifetime
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%%%%%%%
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scatt_vals = logspace(-11, -13, Y_TOTAL); % s-1
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% CALCULATE SHEET CONDUCTIVITY
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cond = zeros(length(f_vals),... % frequency
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length(scatt_vals),... % fermi
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2); % intra/inter
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for freq=1:length(f_vals)
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for y=1:length(scatt_vals)
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cond(freq, y, :) = sheet_conductivity(f_vals(freq),... % omega (rads-1)
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fermi_from_carrier_density(1.3e13*10000, ev_to_j(t)),... % fermi_level (J), ttf = 1.3e13*10000, cocp2 = 2.2e13*10000
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300,... % temp (K)
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scatt_vals(y)); % scatter_lifetime (s)
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end
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end
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% RENDER
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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if DISPLAY_HZ % divide radians back to hertz
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f_vals = f_vals ./ (2*pi);
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end
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y_vals = scatt_vals;
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cond = cond * 1e3;
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% cond = sign(cond).*log10(abs(cond));
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figure(1)
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if strcmp(EXCITATION_TYPE, 'intra')
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surf(f_vals, y_vals, transpose(real(cond(:, :, 1))));
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title('2D Real Intraband Sheet Conductivity');
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elseif strcmp(EXCITATION_TYPE, 'inter')
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surf(f_vals, y_vals, transpose(real(cond(:, :, 2))));
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title('2D Real Interband Sheet Conductivity');
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else
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surf(f_vals, y_vals, transpose(real(sum(cond, 3))));
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title('2D Real Sheet Conductivity');
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end
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rotate3d on
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grid;
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colorbar;
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axis tight;
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set(gca, 'xscale', 'log')
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set(gca, 'yscale', 'log')
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% set(gca, 'zscale', 'log')
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set(gca, 'ColorScale', 'log')
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% ylabel('Net Carrier Density (m^{-2})');
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% ylabel('Temperature (K)');carrier_vals
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ylabel('Scatter Lifetime (s)');
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zlabel('Conductivity (mS)');
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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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if strcmp(EXCITATION_TYPE, 'intra')
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surf(f_vals, y_vals, transpose(imag(cond(:, :, 1))));
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title('2D Imaginary Intraband Sheet Conductivity');
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elseif strcmp(EXCITATION_TYPE, 'inter')
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surf(f_vals, y_vals, transpose(imag(cond(:, :, 2))));
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title('2D Imaginary Interband Sheet Conductivity');
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else
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surf(f_vals, y_vals, transpose(imag(sum(cond, 3))));
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title('2D Imaginary Sheet Conductivity');
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end
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rotate3d on
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grid;
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colorbar;
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axis tight;
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set(gca, 'xscale', 'log')
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set(gca, 'yscale', 'log')
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% set(gca, 'zscale', 'log')
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set(gca, 'ColorScale', 'log')
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% ylabel('Net Carrier Density (m^{-2})');
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% ylabel('Temperature (K)');
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ylabel('Scatter Lifetime (s)');
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zlabel('Conductivity (mS)');
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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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