GATE EC 2023 Set 1 — Question 56
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Electronic Devices → Carrier Transport → Diffusion & Drift Current
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Question
In an extrinsic semiconductor, the hole concentration is given to be where is the intrinsic carrier concentration of . The ratio of electron to hole mobility for equal hole and electron drift current is given as __________ (rounded off to two decimal places).
Correct answer
2.2 to 2.3
Solution
Given:
Hole concentration,
Intrinsic carrier concentration, From the mass action law:
The drift current densities for electrons () and holes () are given by:
For equal hole and electron drift currents ():
The ratio of electron mobility to hole mobility is:
Substituting the expressions for and :
Rounding to two decimal places, the ratio is 2.25.
Hole concentration,
Intrinsic carrier concentration, From the mass action law:
The drift current densities for electrons () and holes () are given by:
For equal hole and electron drift currents ():
The ratio of electron mobility to hole mobility is:
Substituting the expressions for and :
Rounding to two decimal places, the ratio is 2.25.
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