EXAM IN COURSE TFY4220 Solid State Physics

Concentration n of electrons in the conduction band:∞∞321N 1 −( E−µ)/ kT V ⎛2m⎞Bn = f ( E) D( E)dE e ( E E ) 22 2CdEV∫ ⋅ =V∫ ⋅ ⎜ ⎟ −2πECE⎝ ⎠C3 µ2 ∞11 ⎛2m⎞ kT B −EkT/ Bn = e e ( E E ) 22 ⎜ 2 ⎟⋅ −CdE2π⎝ ∫⎠ ECThis was done in the lectures and in Kittel on page 206.We have to use the integral∞ 12 −uu e du =20π∫ (This is the Gammafunction of 3/2)(http://no.wikipedia.org/wiki/Gammafunksjonen) and can be found in Rottmann.The answer becomes:n3 ( µ −E)2C⎛mkBT⎞ kT B= 2 ⎜ e 22 ⎟⎝π⎠8