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A battery of emf 2V is connected across ...

A battery of emf `2V` is connected across a block of length `0.1m` and area of cros-section `1xx10^(-4)m^(2)`. If the block is of intrinsic silocon at `300K`, find the electron and hole currents. What will be the magnitude of the total current? What will be the magnitude of the total current if germanium is used instead of silicon?
Given that for `Si` at `300K`: `mu_(e)=0.135m^(2)V^(-1)s^(-1),mu_(h)=0.048m^(2)V^(-1)s^(-1)` and intristic carrier concentration `n_(i)=1.5xx10^(16)m^(-3)`. For `Ge` at `300K: mu_(e)=0.39m^(2)V^(-1)s^(-1),mu_(h)=0.19m^(2)V^(-1)s^(-1)` and `n_(i)=2.4xx10^(19)m^(-3)`

Text Solution

Verified by Experts

For silicon
Total current, `I=eA(n_(e)v_(e)+n_(h)v_(h))`
or `I_(s)=eA(n_(e)E mu_(e)+n_(h)Emu_(h))`
`=eA(n_(e)mu_(e)+n_(h)mu_(h))E`
`=eA (e_(e)mu_(e)+n_(h)mu_(h))V/I`
`=(1.6xx10^(19))xx(1xx10^(4))[(1.5xx10^(16))xx(0.135)+(1.5xx10^(16))xx0.048]xx2/0.1`
`=8.7xx10^(-7)A`
For Germanium `I_(G)=(1.6xx10^(-19))xx(1xx10^(-4))[(2.4xx10^(19))xx0.39+(2.4xx10^(19))xx0.19]xx2/0.1`
`=4.46xx10^(-3)A`
`I_(G)/I_(s)=(4.46xx10^(-3))/(8.7xx10^(-7))~~0.512xx10^(4)~~10^(4)`
Therefore, the total current in germanium is about four orders of the total current in silicon.
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