AIIMS AIIMS Solved Paper-2015

  • question_answer
    A semiconductor having electron and hole mobilities \[2A\] and \[\frac{12}{7}A\] respectively if its intrinsic carrier density is\[{{n}_{i}},\]then what will be the value of hole concentration P for which the conductivity will be minimum at a given temperature?

    A) \[\omega =\sqrt{rg\,\sin \theta }\]         

    B) \[\omega =\sqrt{g/r\,\,\cos \theta }\]

    C) \[\omega =\sqrt{\frac{gr}{\cos \theta }\,\,}\]                    

    D) \[\omega =\sqrt{\frac{gr}{\tan \theta }\,\,}\]

    Correct Answer: A

    Solution :

    The overall conductivity of a semiconductor is                 \[{{C}_{2}}{{H}_{5}}CHBr-C{{H}_{3}}\,\,and\,\,{{C}_{2}}{{H}_{5}}-C{{H}_{2}}-C{{H}_{2}}Br\]                 \[PC{{l}_{5}}\] Also \[PC{{l}_{5}}(g)PC{{l}_{3}}(g)+C{{l}_{2}}(g)\] (For an intrinsic semiconductor) \[PC{{l}_{5}}\] Now.       \[\frac{X}{a}={{\left( \frac{{{K}_{p}}}{P} \right)}^{1/2}}\] On differentiating, \[\frac{X}{a}=\frac{{{K}_{p}}}{{{K}_{p}}+p}\] \[\frac{X}{a}={{\left( \frac{{{K}_{p}}}{{{K}_{p}}+p} \right)}^{1/2}}\]          \[\frac{X}{a}={{\left( \frac{{{K}_{p}}+p}{{{K}_{p}}} \right)}^{1/2}}\]


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