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In a p-type semiconductor, if the hole mobility is reduced to one-third of its value, keeping the hole concentration constant, the conductivity will:
Increase by 3 times
Decrease to one-third
Remain unchanged
Increase by 9 times
Decrease to one-third
In a p-type semiconductor, the electrical conductivity is directly proportional to the carrier concentration and carrier mobility. Since conductivity is given by ╧Г=pe╬╝hтАЛ, reducing the hole mobility ╬╝hтАЛ to one-third while keeping the hole concentration p constant results in a proportional reduction in conductivity.
In a p-type semiconductor, the electrical conductivity is directly proportional to the carrier concentration and carrier mobility. Since conductivity is given by ╧Г=pe╬╝hтАЛ, reducing the hole mobility ╬╝hтАЛ to one-third while keeping the hole concentration p constant results in a proportional reduction in conductivity.
╧Г=pтЛЕeтЛЕ╬╝hтАЛ тАФ Expression for conductivity in p-type semiconductors
╬╝hтАЛ=EvdтАЛтАЛ тАФ Definition of hole mobility
Conductivity in semiconductors arises from the drift of charge carriers under an applied electric field. The drift velocity is defined as vdтАЛ=╬╝E, where ╬╝ is mobility and E is the electric field. Since the total current density J=pe╬╝hтАЛE and ╧Г=EJтАЛ, it follows that ╧Г scales linearly with ╬╝hтАЛ.
Conductivity is the product of charge carrier concentration, electronic charge, and mobility.
For p-type semiconductors, holes are the majority charge carriers.
A decrease in mobility implies that holes travel more slowly under the same electric field, decreasing the net current density.
Predictable linear relationship between mobility and conductivity
Facilitates precise control of material electrical properties via doping and temperature
High sensitivity to temperature fluctuations which impact mobility
Mobility degradation at high impurity concentrations due to ionized impurity scattering
Designing p-channel MOSFETs
Calibration of Hall effect sensors
Here, p represents hole concentration, e is the elementary charge (1.6├Ч10тИТ19┬аC), and ╬╝hтАЛ is the hole mobility.
Option A is incorrect because conductivity is not inversely proportional to mobility.
Option C is incorrect because conductivity is fundamentally dependent on carrier mobility.
Option D is incorrect because it confuses the relationship with an inverse-square law.
B is correct тАФ Conductivity in a semiconductor is linearly proportional to carrier mobility; therefore, reducing mobility to one-third results in one-third the conductivity.
Remember that in semiconductors, mobility ╬╝ is affected by temperature (usually decreasing with T due to phonon scattering), which is a common follow-up question in GATE and IES exams.