12th Class Physics Semiconducting Devices Question Bank Semiconducting Devices Conceptual Problems

  • question_answer
    Why do semiconductors obey Ohm's law for only low fields?

    Answer:

                        The drift velocity of a charge carrier is proportional to electric field E. \[\upsilon =\frac{eE}{m}\tau \] i.e., \[\upsilon \propto E\] But \[\upsilon \] 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 \[({{\upsilon }_{th}}=10m{{s}^{-1}})\] and becomes independent of electric field at higher values of E. At \[\text{3}00\text{K},\] \[{{\upsilon }_{th}}={{\left( \frac{3{{k}_{B}}T}{m} \right)}^{1/2}}={{10}^{5}}m{{s}^{-1}}\] \[\tau ={{10}^{-12}}s.\] An electric filed of \[\text{1}{{0}^{\text{6}}}\text{V}{{\text{m}}^{-}}^{\text{1}}\] causes saturation of drift velocity. Hence semiconductors obey Ohm's law for low electric fields \[(E<{{10}^{6}}V{{m}^{-1}})\] and above this field \[I\] becomes independent of \[V\].


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