GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 15 of 65

Marks: +1, -0

A single crystal intrinsic semiconductor is at temp of

300 {K}

with effective density of states for holes twice that of electrons.

{V}_{ {T}}=26 {mV}

. The intrinsic Fermi level is shifted from mid bond gap energy level by

Solution:

{E}_{ {f}_{ {i}}}=\;{ {E}_{ {C}}+ {E}_{ {V}}}/{2}-\;{ {kT}}/{2} \ln \;{ {N}_{ {C}}}/{ {N}_{ {V}}}

=\;{ {E}_{ {g}}}/{2}-\;{ {kT}}/{2} \ln \;{ {N}_{ {C}}}/{2 {N}_{ {C}}}( ∵ {N}_{ {v}}=2 {N}_{ {c}})

{E}_{ {F}_{1}}=\;{ {E}_{ {g}}}/{2}-\;{ {kT}}/{2} \ln (\;{1}/{2})

{E}_{ {f}}=\;{ {E}_{ {g}}}/{2}+9.01 {meV}

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