JEE Main & Advanced Physics Semiconducting Devices Question Bank Critical Thinking

  • question_answer
    In semiconductor the concentrations of electrons and holes are 8 ´ 1018/m3 and 5 ´ 1018/m respectively. If the mobilities of electrons and hole are 2.3 m2/volt-sec and 0.01 m2/volt-sec respectively, then semiconductor is

    A)             N-type and its resistivity is 0.34 ohm-metre

    B)             P-type and its resistivity is 0.034 ohm-metre

    C)            N-type and its resistivity is 0.034 ohm-metre

    D)            P-type and its resistivity is 3.40 ohm-metre

    Correct Answer: A

    Solution :

                       \[{{n}_{e}}=8\times {{10}^{18}}/{{m}^{3}},\ \ {{n}_{h}}=5\times {{10}^{18}}/{{m}^{3}}\]                    \[{{\mu }_{e}}=2.3\frac{{{m}^{2}}}{volt-\sec },\ \ {{\mu }_{h}}=0.01\frac{{{m}^{2}}}{volt-\sec }\]                    \[\because {{n}_{e}}>{{n}_{h}}\] so semiconductor is N-type                    Also conductivity \[\sigma =\frac{1}{\text{Resistivity}\,(\rho )}=e({{n}_{e}}{{\mu }_{e}}+{{n}_{h}}{{\mu }_{h}})\]                    Þ\[\frac{1}{\rho }=1.6\times {{10}^{-19}}[8\times {{10}^{18}}\times 2.3+5\times {{10}^{18}}\times 0.01]\]                      Þ r = 0.34 W-m.


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