1In the classical free electron theory, the electrons in a metal are assumed to behave like:
A.A solid crystal lattice
B.A perfect gas molecules
C.Liquid molecules
D.Bound atomic electrons
Correct Answer: A perfect gas molecules
Explanation:Classical free electron theory (Drude-Lorentz theory) assumes that free electrons in a metal move randomly like molecules of a perfect gas within the container of the metal.
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2Which of the following is a drawback of the Classical Free Electron Theory?
A.It cannot explain Ohm's Law
B.It fails to explain the electrical conductivity
C.It fails to explain the specific heat capacity and paramagnetic susceptibility
D.It implies that electrons are stationary
Correct Answer: It fails to explain the specific heat capacity and paramagnetic susceptibility
Explanation:While the classical theory explains Ohm's law and conductivity, it predicts incorrect values for specific heat and magnetic susceptibility because it uses Maxwell-Boltzmann statistics instead of Fermi-Dirac statistics.
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3The drift velocity is related to the applied electric field and mobility by the relation:
A.
B.
C.
D.
Correct Answer:
Explanation:Drift velocity is directly proportional to the applied electric field. The constant of proportionality is the mobility .
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4Diffusion current in a semiconductor is caused by:
A.Applied electric field
B.Applied magnetic field
C.Concentration gradient of charge carriers
D.Temperature difference only
Correct Answer: Concentration gradient of charge carriers
Explanation:Diffusion current arises due to the random thermal motion of carriers from a region of higher concentration to a region of lower concentration (concentration gradient).
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5The Einstein relation relating the diffusion coefficient and mobility is given by:
A.
B.
C.
D.
Correct Answer:
Explanation:Einstein's relation states that the ratio of the diffusion coefficient to mobility is proportional to the thermal voltage ().
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6The Fermi energy () of a metal at 0 K is defined as:
A.The average energy of electrons
B.The energy of the lowest occupied state
C.The maximum energy possessed by an electron at 0 K
D.The minimum energy required to remove an electron
Correct Answer: The maximum energy possessed by an electron at 0 K
Explanation:At absolute zero temperature, electrons fill energy states starting from the lowest. is the energy of the highest filled state.
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7The Fermi-Dirac distribution function represents:
A.The density of energy states
B.The probability of occupancy of an energy state
C.The energy gap between bands
D.The number of electrons per unit volume
Correct Answer: The probability of occupancy of an energy state
Explanation:The Fermi-Dirac function gives the probability that an available energy state at energy will be occupied by an electron at temperature .
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8Mathematically, the Fermi-Dirac distribution function is given by:
A.
B.
C.
D.
Correct Answer:
Explanation:This is the standard formula for Fermi-Dirac statistics, where is Boltzmann's constant and is temperature.
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9At temperature K, what is the probability of occupancy of the Fermi energy level ()?
A.
B.1
C.0.5
D.Undefined
Correct Answer: 0.5
Explanation:Substituting into the Fermi function, .
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10The density of states for free electrons in a three-dimensional metal is proportional to:
A.
B.
C.
D.
Correct Answer:
Explanation:The density of states function usually derived from quantum mechanics for a 3D potential box is proportional to the square root of energy ().
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11According to the Band Theory of Solids, the energy gap () in an insulator is approximately:
A.Zero
B.Less than 1 eV
C.Greater than 3 eV
D.Exactly 0.7 eV
Correct Answer: Greater than 3 eV
Explanation:Insulators have a large forbidden energy gap (typically > 3 eV up to 6 eV or more), preventing electrons from jumping from the valence to the conduction band at room temperature.
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12In a conductor (metal), the valence band and conduction band:
A.Are separated by a large gap
B.Are separated by a small gap
C.Overlap with each other
D.Are both empty
Correct Answer: Overlap with each other
Explanation:In conductors, the valence band overlaps with the conduction band (or the conduction band is partially filled), allowing electrons to move freely.
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13At 0 K, a pure intrinsic semiconductor behaves as:
A.A perfect conductor
B.A perfect insulator
C.A superconductor
D.A semiconductor with high conductivity
Correct Answer: A perfect insulator
Explanation:At 0 K, the valence band is completely full and the conduction band is completely empty in an intrinsic semiconductor, so no conduction can occur.
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14The position of the Fermi level in an intrinsic semiconductor at absolute zero is located:
A.Inside the conduction band
B.Inside the valence band
C.Exactly in the middle of the forbidden energy gap
D.Near the bottom of the conduction band
Correct Answer: Exactly in the middle of the forbidden energy gap
Explanation:For an intrinsic semiconductor, the concentration of electrons equals holes (). This symmetry places the Fermi level essentially at the midpoint of the band gap at 0 K.
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15In an N-type semiconductor, the Fermi level at 0 K lies:
A.In the middle of the energy gap
B.Near the bottom of the conduction band
C.Near the top of the valence band
D.Inside the valence band
Correct Answer: Near the bottom of the conduction band
Explanation:N-type doping adds donor energy levels just below the conduction band. At low temperatures, the Fermi level shifts up towards these donor levels.
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16In a P-type semiconductor, the impurity atoms added are called:
A.Donors
B.Acceptors
C.Intrinsic
D.Phonons
Correct Answer: Acceptors
Explanation:P-type doping uses trivalent impurities (like Boron) which create holes by accepting electrons. These are called acceptor atoms.
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17As temperature increases, the Fermi level in an N-type semiconductor:
A.Moves closer to the conduction band
B.Moves towards the middle of the energy gap
C.Moves into the valence band
D.Remains constant
Correct Answer: Moves towards the middle of the energy gap
Explanation:As T increases, intrinsic carrier generation dominates over the fixed number of donor electrons, causing the material to behave more intrinsically, moving toward the center.
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18Which of the following represents the Law of Mass Action for semiconductors?
A.
B.
C.
D.
Correct Answer:
Explanation:The product of electron concentration () and hole concentration () at equilibrium is constant at a given temperature and equals the square of the intrinsic carrier concentration ().
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19A Direct Band Gap semiconductor is one where:
A.The maximum of the valence band and minimum of the conduction band occur at different values of wave vector
B.The maximum of the valence band and minimum of the conduction band occur at the same value of wave vector
C.There is no energy gap
D.Conduction is only due to holes
Correct Answer: The maximum of the valence band and minimum of the conduction band occur at the same value of wave vector
Explanation:In direct band gap semiconductors, an electron can transition from the valence to conduction band without a change in crystal momentum ().
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20An example of an Indirect Band Gap semiconductor is:
A.Gallium Arsenide (GaAs)
B.Silicon (Si)
C.Indium Phosphide (InP)
D.Cadmium Sulfide (CdS)
Correct Answer: Silicon (Si)
Explanation:Silicon and Germanium are classic examples of indirect band gap semiconductors, where phonon interaction is required for interband transitions.
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21Recombination of an electron and hole in a Direct Band Gap semiconductor results primarily in:
A.Emission of heat (phonons)
B.Emission of light (photons)
C.Change in crystal structure
D.Zero energy release
Correct Answer: Emission of light (photons)
Explanation:Since momentum is conserved directly, the energy difference is released as a photon. This makes them suitable for LEDs and Lasers.
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22The concept of Effective Mass () accounts for:
A.The relativistic change in mass
B.The interaction of the electron with the periodic potential of the crystal lattice
C.The weight of the electron due to gravity
D.The mass of the nucleus
Correct Answer: The interaction of the electron with the periodic potential of the crystal lattice
Explanation:Electrons in a solid do not move in a vacuum; they interact with internal fields. Effective mass lumps these internal forces into a parameter so we can use semi-classical equations (like ) with external forces.
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23Mathematically, the effective mass is related to the energy-wave vector () curvature by:
A.
B.
C.
D.
Correct Answer:
Explanation:Effective mass is inversely proportional to the curvature of the band (second derivative of Energy with respect to ).
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24Near the top of the valence band, the effective mass of an electron is:
A.Positive
B.Negative
C.Zero
D.Infinite
Correct Answer: Negative
Explanation:The curvature () is negative at the top of the valence band (concave down), resulting in a negative effective mass for electrons (which physically manifests as the behavior of positive holes).
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25A 'hole' in solid state physics is best described as:
A.A proton moving in the lattice
B.A positron
C.An empty state in an otherwise filled valence band behaving like a positive charge
D.A neutron
Correct Answer: An empty state in an otherwise filled valence band behaving like a positive charge
Explanation:A hole is a quasiparticle representing the absence of an electron in the valence band, acting as a carrier with positive charge .
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26The Hall Effect is the production of a voltage difference across an electrical conductor, transverse to an electric current and to an applied:
A.Electric field parallel to current
B.Magnetic field perpendicular to the current
C.Thermal gradient
D.Gravitational field
Correct Answer: Magnetic field perpendicular to the current
Explanation:The Hall effect occurs when a current-carrying conductor is placed in a perpendicular magnetic field, generating a transverse voltage.
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27The Hall coefficient is given by the relation:
A.
B.
C.
D.
Correct Answer:
Explanation:In the standard derivation, or depending on the carrier sign. It relates the induced field to the current density and magnetic field.
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28If the Hall coefficient is negative, the majority charge carriers are:
A.Holes
B.Electrons
C.Neutrons
D.Ions
Correct Answer: Electrons
Explanation:Since electrons have a negative charge (), the Hall coefficient is negative for N-type materials or metals where electrons dominate.
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29The Hall voltage generated in a slab of thickness , carrying current in a magnetic field , is:
A.
B.
C.
D.
Correct Answer:
Explanation:This is the standard formula derived from equating the Lorentz force to the electric force created by charge accumulation.
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30Which of the following is NOT an application of the Hall Effect?
A.Determination of semiconductor type (N or P)
B.Measurement of magnetic field strength (Fluxmeter)
C.Measurement of carrier concentration
D.Measuring the refractive index of the material
Correct Answer: Measuring the refractive index of the material
Explanation:The Hall effect is electrical/magnetic in nature. It is used for carrier type, concentration, mobility, and B-field measurement, not optical properties like refractive index.
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31The Hall angle is the angle between:
A.The magnetic field and the current
B.The electric field and the magnetic field
C.The resultant electric field and the current density direction
D.The crystal axis and current
Correct Answer: The resultant electric field and the current density direction
Explanation:The Hall angle represents the deflection of the electric field vector from the current direction due to the Hall field.
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32The Fermi temperature is related to Fermi energy by:
A.
B.
C.
D.
Correct Answer:
Explanation:Fermi temperature is defined such that equals the Fermi energy.
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33In the derivation of Hall effect, at equilibrium, the magnetic Lorentz force () is balanced by:
A.Gravitational force
B.Electric force due to Hall field ()
C.Frictional force
D.Nuclear force
Correct Answer: Electric force due to Hall field ()
Explanation:Charge accumulation stops when the electric force exactly opposes the magnetic force .
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34The mobility of holes () is generally _____ than the mobility of electrons () in the same semiconductor.
A.Greater
B.Less
C.Equal
D.Unrelated
Correct Answer: Less
Explanation:Effective mass of holes is typically larger than that of electrons, and since mobility , holes generally have lower mobility.
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35For an intrinsic semiconductor, the Hall coefficient is:
A.Zero
B.Very large positive
C.Very large negative
D.Ideally small, decreasing with temperature
Correct Answer: Ideally small, decreasing with temperature
Explanation:In intrinsic semiconductors, electrons and holes both contribute but deflect in opposite directions. However, since , the net result is usually negative but smaller in magnitude compared to extrinsic semiconductors, and it changes rapidly with .
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36The Wiedemann-Franz law states that the ratio of thermal conductivity () to electrical conductivity () is proportional to:
A.Temperature ()
B.Inverse of Temperature ()
C.Temperature squared ()
D.Ideally constant
Correct Answer: Temperature ()
Explanation:The law states , where is the Lorentz number.
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37The unit of Hall coefficient is:
A.
B.
C.
D.
Correct Answer:
Explanation:Since , the unit is .
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38If the effective mass of an electron is small, the curvature of the energy band is:
A.Small (flat band)
B.Large (steep curve)
C.Zero
D.Undefined
Correct Answer: Large (steep curve)
Explanation:. A small mass implies a large second derivative, which means a high curvature.
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39Which statistics are applicable to electrons in a solid?
A.Maxwell-Boltzmann
B.Bose-Einstein
C.Fermi-Dirac
D.Plank's Radiation Law
Correct Answer: Fermi-Dirac
Explanation:Electrons are fermions (spin 1/2) and obey the Pauli exclusion principle, thus they follow Fermi-Dirac statistics.
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40The Fermi level in a P-type semiconductor at room temperature is:
A.Closer to the valence band
B.Closer to the conduction band
C.At the center of the gap
D.Above the conduction band
Correct Answer: Closer to the valence band
Explanation:Acceptor levels create holes near the valence band, pulling the Fermi level down towards the valence band.
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41The probability that an energy level is occupied by a hole is given by:
A.
B.
C.
D.
Correct Answer:
Explanation:Since a hole is the absence of an electron, the probability of finding a hole is 1 minus the probability of finding an electron.
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42In the free electron gas model, the potential energy of an electron inside the metal is assumed to be:
A.Infinite
B.Periodic
C.Constant
D.Zero everywhere including boundaries
Correct Answer: Constant
Explanation:The free electron model assumes a constant potential (often set to zero) inside the metal and infinite potential at the boundaries (particle in a box).
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43The mean free path of an electron is defined as:
A.The average distance traveled between two successive collisions
B.The total distance traveled in one second
C.The distance from the nucleus to the surface
D.The wavelength of the electron
Correct Answer: The average distance traveled between two successive collisions
Explanation:Standard definition of mean free path in kinetic theory.
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44Electrical conductivity () is given by:
A.
B.
C.
D.
Correct Answer:
Explanation:Conductivity depends on carrier concentration (), charge (), and mobility ().
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45Which material is typically used for making LEDs?
A.Silicon (Si)
B.Germanium (Ge)
C.Gallium Arsenide (GaAs)
D.Carbon (C)
Correct Answer: Gallium Arsenide (GaAs)
Explanation:GaAs is a direct band gap semiconductor, allowing efficient photon emission, unlike Si and Ge which are indirect band gap materials.
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46At absolute zero, the electrical conductivity of a pure metal is:
A.Zero
B.Infinite (or extremely high)
C.Same as at room temperature
D.Negative
Correct Answer: Infinite (or extremely high)
Explanation:In a perfect crystal at 0 K, lattice vibrations (phonons) cease. Without scattering centers (assuming no impurities), resistance drops to zero (conductivity becomes infinite).
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47The total current density in a semiconductor is the sum of:
A.Electron drift and Hole drift only
B.Electron diffusion and Hole diffusion only
C.Drift current densities and Diffusion current densities for both electrons and holes
D.Conduction current and displacement current
Correct Answer: Drift current densities and Diffusion current densities for both electrons and holes
Explanation:Semiconductor current consists of drift (due to E-field) and diffusion (due to concentration gradient) components for both types of carriers.
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48The value of Fermi function ranges from:
A.0 to
B.-1 to +1
C.0 to 1
D.1 to 100
Correct Answer: 0 to 1
Explanation:Since represents a probability, its value must lie between 0 and 1.
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49In a p-type semiconductor, the minority carriers are:
A.Holes
B.Electrons
C.Positive Ions
D.Acceptor atoms
Correct Answer: Electrons
Explanation:In P-type, holes are majority carriers (created by doping) and electrons are minority carriers (created by thermal generation).
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50The dependence of Fermi energy on electron density in a metal at 0 K is:
A.
B.
C.
D.
Correct Answer:
Explanation:Derived from the density of states integration: .
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