In a Si sample at 300K the fermi level is located at 035 eV

In a Si sample, at 300K, the fermi level is located at 0.35 eV below the conduction band minima. Find the electron and hole concentrations at that temperature. Say, the temperature is doubled now. Approximately what is the position of the Fermi level?

Solution

Given that, T=300K, K= 8.617x10^-5 ev/k

For Si: Nc=2.8x10^19 cm^-3 and Nv=1.04x10^19 cm^-3

    The electron concentration, n=Nc*e^-(Ec-Ef)/KT

                                   n = (2.8x10^19)*e^-(0.35)/0.026

                                      = (2.8x10^19) (0.12191x10^-5)

                                   n = 0.36x10^14 cm^-3

The hole concentration, p= Nv*e^-(Ef-Ev)/KT

                              Ef-Ev = KT ln(Nv/Na) = -0.025eV

                              p = (1.04x10^19) e^-(-0.025/0.026)

                                 = 2.716 x 10^19 cm^-3

Ec-Ef = KT ln(Nv/n) = 0.026 ln[(2.8x10^19)/(0.36x10^14)]

                             = 0.352 eV

Ef-Ev = KT ln(Nv/p) = 0.026 ln[(1.04x10^19)/(2.71x10^19)]

                             = -0.0249 eV