2021-02-23 10:30:12 +00:00
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function conductivity = sheet_conductivity(omega, fermi_level, temp, scatter_lifetime)
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%SHEET_CONDUCTIVITY Calculate 2D sheet conductivity
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%% CONSTANTS
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e = 1.602e-19; % coulombs
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2021-03-10 19:59:34 +00:00
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kb = 1.380e-23; % J/K
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2021-02-23 10:30:12 +00:00
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hbar = 6.626e-34 / (2*pi); % Js
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2021-03-22 17:51:55 +00:00
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%% TERM 1 - INTRABRAND
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2021-02-23 10:30:12 +00:00
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term1_coeff = (2i*(e^2)*kb*temp) ...
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/ ...
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(pi*hbar^2*(omega + (1i/scatter_lifetime)));
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term1 = log(2*cosh(fermi_level ...
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/ ...
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(2*kb*temp)));
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2021-03-22 17:51:55 +00:00
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intraband = term1_coeff*term1;
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%% TERM 2 - INTERBAND
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2021-02-23 10:30:12 +00:00
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term2_coeff = (e^2) ...
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/ ...
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(4*hbar);
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term_2_term_1 = 1/2;
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term_2_term_2 = (1/pi) * ...
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atan((hbar*omega - 2*fermi_level) ...
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/ ...
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(2*kb*temp));
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term_2_term_3 = (1i/2*pi) * ...
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log((hbar*omega + 2*fermi_level)^2 ...
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/ ...
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((hbar*omega - 2*fermi_level)^2 + 4*((kb*temp)^2)));
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2021-03-22 17:51:55 +00:00
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interband = term2_coeff*(term_2_term_1 + term_2_term_2 - term_2_term_3);
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2021-02-23 10:30:12 +00:00
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%% OUTPUT
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2021-03-22 17:51:55 +00:00
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conductivity = [intraband interband]; % return separately for display or summing
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2021-02-23 10:30:12 +00:00
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end
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