GATE EC 2020 Set 1 — Question 16
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Electronic Devices → Semiconductor Physics → Fermi Level & Doping
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Question
A single crystal intrinsic semiconductor is at a temperature of 300 K with effective density of states for holes twice that of electrons. The thermal voltage is 26 mV.
The intrinsic Fermi level is shifted from mid-bandgap energy level by
The intrinsic Fermi level is shifted from mid-bandgap energy level by
Correct answer
(B) 9.01 meV.
Solution
For an intrinsic semiconductor, the intrinsic Fermi level is given by:Where:
is the conduction band edge.
is the valence band edge.
is the thermal energy.
is the effective density of states in the valence band.
is the effective density of states in the conduction band.The mid-bandgap energy level is .The shift of the intrinsic Fermi level from the mid-bandgap energy level is:Given:
Temperature K.
Thermal voltage mV V.
So, eV.
Effective density of states for holes () is twice that of electrons (), so .Substitute these values into the equation for :Using eV: (since )Converting to meV:Therefore, the intrinsic Fermi level is shifted from the mid-bandgap energy level by approximately 9.01 meV.The correct answer is (B).
is the conduction band edge.
is the valence band edge.
is the thermal energy.
is the effective density of states in the valence band.
is the effective density of states in the conduction band.The mid-bandgap energy level is .The shift of the intrinsic Fermi level from the mid-bandgap energy level is:Given:
Temperature K.
Thermal voltage mV V.
So, eV.
Effective density of states for holes () is twice that of electrons (), so .Substitute these values into the equation for :Using eV: (since )Converting to meV:Therefore, the intrinsic Fermi level is shifted from the mid-bandgap energy level by approximately 9.01 meV.The correct answer is (B).
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