The resistivity of a extrinsic semiconductor (i.e. Si) with single dopant (acceptor/donor) level is proportional to P=P0 exp(Ei/2kT) at low temperature. So, what should be the temperature dependence of resistivity (P) at high temperature (
The resistivity of a doped semiconductor (e.g n-Si) follows a non-monotonic trend vs Temperature. At low temperature (< 100-120 °C in the case of Si) the resistivity is quite high and increases more or less slightly with T, as it were a metal. This is due to the parallel decrease of mobility resulting from a more and more effective carrier-carrier scattering in conduction band. At hogh temperature the so-called "intrinsic" regimedominates, where the resistivity falls quite rapidly with increasing T, simply due to the exponential increase of (intrinsic) electrons concentration in CB (due to more and more effective jumping from the valence band across the Gap). Only in this regime the behaviour is dominated by the exponential one you wrote - exp(-Eg/2kT) - being the mobility contribution ( T^1.5) much slower than the exp one of course.
You can find details in whatever book on Semiconductor physics.
Some illustrations might be found here:
http://www.ioffe.ru/SVA/NSM/Semicond/Si/electric.html
Sabyasachi Sen Viktor Brus Nikolay Pavlov Giuseppe Curro
Dear all,
Great discussion!!
Doping is the last resort. The temperature dependence of resistivity of a extrinsic semiconductor at high temperature is still a big challenge and the mechanistic details are yet to understood.
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