Question

Calculate the Fermi energy and the conductivity at room temperature for germanium containing 5×10^16 arsenic atoms per cubic centimeter. (Hint: Use the mobility of the electrons in the host material.)Use the mobility of the electrons in the host material.

Answer 1

Answer:

The Fermi energy is 0.568 eV and the conductivity at room temperature is 31.24 (Ωcm)⁻¹

Explanation:

Data given:

Nd = doping concentration = 5x10⁶/cm³

According the mass action law, the hole concentration is:

$P_{0} =\frac{n_{i}^{2} }{n_{0} } ,n_{i}=2x10^{13} /cm^{3}$

$E_{f} =E_{i} +KTln(\frac{n_{D} }{n_{i} } ),K=8.61x10^{-19} ,KT=0.026eV$

$E_{i} =\frac{E_{0} }{2} =\frac{0.63}{2} =0.315eV\\E_{f}=0.315+0.203=0.568eV$

The conductivity of n-type of semi-conductor is equal to:

The mobility of Germanium is 3900 cm²/Vs

σ = 1.6x10⁻¹⁹ * 5x10¹⁶ * 3900 = 31.24 (Ωcm)⁻¹