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Derive the expression of current density and Mobility of charge carriers for semiconductor
Asked by jeetendrarajpoot818 | 08 Jun, 2022, 10:10: PM
answered-by-expert Expert Answer
Current density  J = n e v
 
where n is number density of charge carriers , e is unit charge and vd is drift velocity
 
In  semiconductor, we have two types of charge carriers , electron in conduction band and hole in valance band
 
Let ne be the number of electrons per unit volume in conduction band .
Let nh be the number of holes per unit volume in valance band .
 
Current density J = ( ne e vde + nh e vdh )
 
where vde is drift velocity of electron and vdh is drift velocity of hole .
 
Drift velocity is related to mobility as follows
 
vde = μe E      and     vdh = μh
 
where μe is mobility of electron , μh is mobility of hole and E is electric field .
 
Current density J = ( neμe + nhμh ) E
 
----------------------------
 
In intrinsic semiconductor , there are equal number of electrons and holes
 
ne = nh = n
 
In intrinsic semiconductor , Current density J = n e ( μe + μh ) E
 
In n-type semiconductor , ne > > nh
 
In n-type semiconductor , Current density J = ne e μe E
 
In p-type semiconductor , nh > > ne
 
In p-type semiconductor , Current density J = nh e μh E
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