Calculate the current product in a germanium sample of area of cross section 1 $cm^2$and thickness of 0.01 m, when a potential difference of 2V is applied cross it. Given :- the concentration of free electron in germanium is $2×10^{19}/m^3$ and mobilities of electrons and holes are $0.36 m^2/volts sec$ and $0.17 m^2/volts sec$ respectively.

DRIFT CURRENT :-

Drift current is the electric current caused by particles getting pulled by an electric field. Direction of the drift current is always in the direction of the electric field.

The amount of drift current depends on the concentration of charge carriers and their mobility in the material or medium.

MOBILITY OF CHARGE CARRIERS :-

This is a property of conductor, defined as the ratio of drift velocity to applied electric field in a conductor. Drift velocity of charge carriers in a conductor depend upon two factors, one is the intensity of applied electric field across the conductor and other is one property of the conductor called Mobility of Charge Carrier.

The SI unit of mobility is m^2/V sec

NUMERICAL:

Given data :- A = $1cm^2=10^{(-4)} m^2$, t = 0.01m, V = 2 volts. $ n_i=2×10^{19}/m^3, \hspace{1cm} μ_e=0.36 m^2/V-sec, \hspace{1cm} μ_h= 0.17 m^2/V-sec$

Formula :- $σ=n_i (μ_e+ μ_h )e, \hspace{1cm} R=r t/A ,\hspace{1cm} V = IR$.

Solution :- $σ=n_i (μ_e+ μ_h )e$

$ =2× 10^19 (0.36+0.17)×1.6×10^{(-19)} $

$ =1.696 mho/m$

$ R=r t/A = 1/σ t/A$

$ =1/1.696×0.01/10^{(-4)} = 58.96 Ω$

$ I = V/R = 2/58.96=0.0339 Amp$

Current :- 0.0339 Amp.