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JEE Main & Advanced Physics Semiconducting Devices Question Bank Self Evaluation Test - Semiconductor Electronics: Materials, Devices and Simple Circuits

  • question_answer
    Pure \[Si\] at \[500K\] has equal number of electron \[({{n}_{e}})\] and hole \[({{n}_{h}})\] concentrations of \[1.5\times {{10}^{16}}{{m}^{-3}}.\] Doping by indium increases \[{{n}_{h}}\] to \[4.5\times {{10}^{22}}{{m}^{-3}}.\] The doped semiconductor is of

    A)  n-type with electron concentration \[{{n}_{e}}=5\times {{10}^{22}}{{m}^{-3}}\]

    B)  p-type with electron concentration \[{{n}_{e}}=2.5\times {{10}^{10}}{{m}^{-3}}\]

    C)  n-type with electron concentration \[{{n}_{e}}=2.5\times {{10}^{23}}{{m}^{-3}}\]

    D)  p-type having electron concentration \[{{n}_{e}}=5\times {{10}^{9}}{{m}^{-3}}\]

    Correct Answer: D

    Solution :

    [d] \[{{n}_{i}}^{2}={{n}_{e}}{{n}_{h}}\] \[{{(1.5\times {{10}^{16}})}^{2}}={{n}_{e}}(4.5\times {{10}^{22}})\] \[\Rightarrow \,\,\,\,\,{{n}_{e}}=0.5\times {{10}^{10}}\] or \[{{n}_{e}}=5\times {{10}^{9}}\] Given \[{{n}_{h}}=4.5\times {{10}^{22}}\Rightarrow {{n}_{h}}>>{{n}_{e}}\] \[\therefore \] Semiconductor is p-type and \[{{n}_{e}}=5\times {{10}^{9}}\,{{m}^{-3}}.\]


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