Aufgabe 2

clear all;
u = 1.6605e-27
u = 1.6605e-27
c = 299792458
c = 299792458
e = 1.602e-19
e = 1.6020e-19
h = 6.626e-34;
hQuer = h / (2*pi);
me = 9.11e-31;
k = 1.38064852e-23
k = 1.3806e-23

Fermienergie

ne = 1.7e21 / (1e-2)^3
ne = 1.7000e+27
Ef = hQuer^2 / (2 * me) *(3 * pi^2 * ne)^(2/3)
Ef = 8.3210e-20
Ef_eV = Ef / e
Ef_eV = 0.5194

Wahrscheinlichkeit

T = 293

T = 293

f = @(E) (exp((E - Ef) ./ (k*T)) + 1).^(-1);

E2eV = Ef_eV + 0.01

E2eV = 0.5294

p = f(E2eV*e)

p = 0.4023

EeV = linspace(0,2*Ef_eV,100);

fAll = f(EeV * e);

plot(EeV,fAll); hold on;

plot([Ef_eV Ef_eV],[0 1])

plot([0 E2eV E2eV], [p p 0],'k--')

xlabel('E [eV]');

ylabel('f(E)');

title('Fermi Dirac Statistik')

legend('f(E)', 'E_F', 'f(E_F + 0.01 eV)')