show mathematically that diodes obey ohm's law at low fields

The drift velocity of a charge carrier is proportional to electric E. Therefore V = eET/m ie. V ??E But V cannot be increased indefinitely by increasing E . At high speed relaxation time (T) begins to decrease due to increase in collision frequency. S: so drift velocity saturates at thermal velocity (lOms-1). An electric field of 106 V/m causes saturation of drift velocity. Hence semi- conduction obey ohm’s law for low electrical field and above this field ( E < 106 V/m ) current becomes independent of potential