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Derive the expression of current density and Mobility of charge carriers for semiconductor

Asked by jeetendrarajpoot818 | 08 Jun, 2022, 22:10: PM

Expert Answer

Current density J = n e v_d

where n is number density of charge carriers , e is unit charge and v_d is drift velocity

In semiconductor, we have two types of charge carriers , electron in conduction band and hole in valance band

Let n_e be the number of electrons per unit volume in conduction band .

Let n_h be the number of holes per unit volume in valance band .

Current density J = ( n_e e v_de + n_h e v_dh )

where v_de is drift velocity of electron and v_dh is drift velocity of hole .

Drift velocity is related to mobility as follows

v_de = μ_e E and v_dh = μ_h E

where μ_e is mobility of electron , μ_h is mobility of hole and E is electric field .

Current density J = ( n_e e μ_e + n_h e μ_h ) E

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In intrinsic semiconductor , there are equal number of electrons and holes

n_e = n_h = n

In intrinsic semiconductor , Current density J = n e ( μ_e + μ_h ) E

In n-type semiconductor , n_e > > n_h

In n-type semiconductor , Current density J = n_e e μ_e E

In p-type semiconductor , n_h > > n_e

In p-type semiconductor , Current density J = n_h e μ_h E

Answered by Thiyagarajan K | 09 Jun, 2022, 09:08: AM

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