• # 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.