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Find the minimum energy of electron-hole pair formation in an impurity-free semiconductor whose electric conductor increase eta=5.0 times when the temperature increases from T_(1)= 300K t o T_(2)= 400K |
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Answer» Solution :In a pure(intrinsic) SEMICONDUCTOR the conductivity is related to the temperature by the FOLLOWING formula very closely: `sigma= sigma_(0)e^(-Delta epsilon//2kt)` where `Delta epsilon` is the ENERGY gap between the top of valence BAND and the bottom of conduction band, it is also the minimum enrgy required for the FORMATION of electron-hole pair. The conductivity increases with temperature and we have `eta=2^(+(DeltaE)/(2k)((1)/(T_(1))-(1)/(T_(2)))` or In `eta=(Deltaepsilon)/(2k)(T_(2)-T_(1))/(T_(1)-T_(2))` Hence `Delta epsilon=(2kT_(1)T_(2))/(T_(2)-T_(1)) In eta` Substitution gives delta epsilon= 0.333eV`=E_(mi n)` |
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