12th Class Physics Sample Paper Physics Sample Paper-3

  • question_answer Semiconductors obey Ohm's law at only low fields. Why?


    The drift velocity of a charge carrier is proportional to electric field E. i.e.,       \[v=eE\tau /m\] or \[v\propto E\] But v cannot be increased indefinitely by increasing E. At high speeds, relaxation time t begins to decrease due to the increase in collision frequency So, drift velocity saturates at the thermal velocity \[({{v}_{th}})\] and becomes independent of electric field at highest values of E. At 300 K,           \[{{v}_{th}}={{\left( \frac{3{{k}_{B}}T}{m} \right)}^{1/2}}={{10}^{5}}m{{s}^{-1}}\] and       \[\tau ={{10}^{1/2}}s\] An electric field of 106 VnrT1 causes saturation of drift velocity. Hence, semiconductor obeys Ohm's law for low electric field \[(E<{{10}^{6}}V{{m}^{-1}})\] and above this field, I becomes independent of V.

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