Chapter 23: Band Theory, Semiconductors and Superconductivity (Set-2)
In a crystal, allowed energy ranges are mainly called
A Forbidden gaps
B Lattice nodes
C Energy bands
D Photon shells
Because of the periodic lattice potential, electron energies do not take all values. Instead, they group into continuous allowed ranges called bands, separated by forbidden gaps where solutions are not allowed.
In band diagrams, a forbidden gap means electron energies are
A Not permitted there
B Always negative
C Always continuous
D Equal for all k
A forbidden gap is an energy interval where electron wave solutions cannot exist in the periodic lattice. It forms due to strong Bragg reflection and state mixing near zone boundaries.
In a periodic solid, the wavevector k is best represented in
A Real-space map
B k-space diagram
C Time-only graph
D Temperature scale
Electron states in crystals are conveniently described using wavevector k in reciprocal space. Band structure E(k) and zone boundaries are naturally expressed in k-space using reciprocal lattice vectors.
The first Brillouin zone is essentially the region
A Around one atom
B With maximum energy
C Closest to k=0
D Outside reciprocal space
The first Brillouin zone is the Wigner–Seitz cell in reciprocal space centered at k=0. It contains all k-points closer to the origin than to any other reciprocal lattice point.
The main physical cause of a gap at zone boundary is
A State mixing
B Electron decay
C Lattice melting
D Photon pressure
At zone boundaries, electron waves with k and k−G have the same energy and strongly mix due to the periodic potential. This splits energies into two levels, creating a band gap.
In the extended zone scheme, k-values are shown
A Only inside first zone
B Only at k=0
C Without any energy
D Across multiple zones
The extended zone scheme keeps k increasing beyond the first Brillouin zone. It displays the band dispersion continuously while gaps appear at each zone boundary where Bragg reflection occurs.
Band folding mainly happens because k and k+G are
A Equivalent in crystal
B Always unequal states
C Different temperatures
D Different charge signs
In a periodic lattice, adding a reciprocal vector G gives an equivalent wave description. So E(k) repeats in reciprocal space, and bands can be “folded” back into the first zone.
A flat E–k curve near band edge implies
A Small effective mass
B No carriers exist
C Large effective mass
D Infinite conductivity
Effective mass depends inversely on band curvature. If E(k) is nearly flat, curvature is small, so effective mass becomes large, meaning the carrier accelerates less for the same applied field.
The density of states in 3D generally increases with energy because
A Fewer k-states exist
B More k-states available
C Energy gaps disappear
D Temperature becomes zero
As energy rises, the radius of the allowed k-space sphere increases, creating more available states. Thus the number of states per energy interval grows, affecting carrier concentration and conductivity.
A “hole” is best described as the absence of
A Electron in valence
B Proton in lattice
C Neutron in nucleus
D Phonon in crystal
When an electron is missing from an otherwise filled valence band, the vacancy behaves like a positive charge carrier called a hole. Hole motion represents electron motion in the opposite direction.
Hole effective mass is linked to curvature near
A Conduction band bottom
B Vacuum level only
C Valence band top
D Impurity band center
Holes are described near the top of the valence band. The curvature of E(k) there determines the hole effective mass, which influences mobility, diffusion, and how strongly holes respond to fields.
Conductivity effective mass is used mainly when relating
A Heat to pressure
B Spin to gravity
C Light to sound
D Current to electric field
Conductivity depends on how carriers accelerate and scatter under an electric field. Conductivity effective mass accounts for band structure effects, especially when masses differ along directions in anisotropic crystals.
Anisotropic effective mass means effective mass depends on
A Carrier color
B Crystal direction
C Earth rotation
D Atomic symbol
In some crystals, band curvature differs along different k-directions. This makes effective mass direction-dependent, affecting mobility and transport differently along various crystal axes.
A key band-theory reason for high metal conductivity is high
A Band gap value
B Crystal brittleness
C Carrier availability
D Ionic radius only
Metals have many available states near the Fermi level due to partially filled bands or band overlap. Electrons can easily move to nearby states when an electric field is applied, giving high conductivity.
In insulators, the Fermi level typically lies
A Inside large gap
B Inside conduction band
C Inside metal band
D Above vacuum level
Insulators have a large band gap and the Fermi level usually lies within it. With no nearby available states at room temperature, very few carriers exist, so conductivity remains extremely low.
In an intrinsic semiconductor, electron concentration equals
A Donor concentration
B Ion concentration
C Hole concentration
D Photon concentration
In a pure semiconductor, electrons and holes are created in pairs by thermal excitation. Therefore, their concentrations are equal at equilibrium, and the Fermi level lies roughly near mid-gap.
Donor impurities in Si are typically elements from group
A Group V
B Group III
C Group I
D Group VII
Group V atoms (like P, As) have five valence electrons, one more than silicon. The extra electron is weakly bound and easily contributes to conduction, producing n-type behavior.
Acceptor impurities in Si are typically elements from group
A Group V
B Group III
C Group VI
D Group VIII
Group III atoms (like B, Al) have three valence electrons, one less than silicon. They create acceptor levels that capture electrons, leaving holes as majority carriers, producing p-type behavior.
In n-type semiconductors, the Fermi level shifts
A Toward valence band
B Outside band gap
C Toward conduction band
D To mid-gap always
Donor doping increases electron concentration, so the equilibrium Fermi level moves closer to the conduction band. This higher Fermi level reflects increased probability of conduction band occupation.
In p-type semiconductors, the Fermi level shifts
A Toward valence band
B Toward conduction band
C Above vacuum level
D To mid-gap always
Acceptor doping increases holes, so the Fermi level moves closer to the valence band. This indicates a higher probability that valence states are unfilled, supporting hole conduction.
Minority carriers in n-type are mainly
A Electrons
B Ions
C Cooper pairs
D Holes
In n-type material, electrons are majority carriers due to donor doping. Holes still exist due to thermal generation but at much lower concentration, so they are called minority carriers.
Minority carriers in p-type are mainly
A Holes
B Phonons
C Electrons
D Vortices
In p-type material, holes dominate conduction. Electrons are still thermally generated but are fewer than holes, so they are minority carriers and strongly affect reverse-bias junction behavior.
Recombination in a semiconductor means
A Electron meets hole
B Two holes join
C Two donors collide
D Phonons disappear
Recombination occurs when a conduction electron drops into a hole in the valence band. This removes both carriers and releases energy as heat or sometimes light, affecting carrier lifetime.
Generation in a semiconductor typically means creating an electron–hole pair by
A Random scattering only
B Thermal or optical energy
C Magnetic shielding
D Zero resistance flow
Generation happens when sufficient energy excites an electron from valence to conduction band, leaving a hole behind. Heat or absorbed photons can supply this energy, increasing carrier concentration.
The p–n junction forms mainly because of
A Neutron diffusion
B Nuclear fusion
C Carrier diffusion
D Crystal cracking
When p-type and n-type materials contact, electrons diffuse into p-side and holes into n-side. This creates a depletion region and built-in electric field that strongly influences diode behavior.
The depletion region in a p–n junction is mostly depleted of
A Mobile carriers
B Ions only
C Lattice atoms
D Photons
Near the junction, electrons and holes recombine, leaving behind fixed ionized donors and acceptors. The region has few mobile carriers, so it acts like an insulating barrier.
Forward bias mainly does what to the junction barrier
A Increases barrier
B Reduces barrier
C Reverses lattice
D Stops diffusion
Forward bias lowers the built-in potential barrier, allowing majority carriers to cross the junction more easily. This produces a large current due to carrier injection and recombination.
Zener breakdown is most strongly associated with
A Very low fields
B High mechanical stress
C Strong electric fields
D Superconducting gap
In heavily doped junctions, the depletion region is very thin. A strong electric field can cause quantum tunneling of electrons across the gap, producing Zener breakdown at low reverse voltage.
A thermoelectric (Seebeck) effect occurs when a temperature difference creates
A Voltage difference
B Pressure gradient
C Magnetic vortex
D Band overlap
When two different conductors or semiconductors have a temperature difference between junctions, charge carriers diffuse differently, generating an EMF. This is used in thermocouples and sensors.
In superconductors, a persistent current means current flows
A With heating loss
B Only for seconds
C Only with high voltage
D Without decay
In an ideal superconducting loop below Tc and within limits, current can circulate indefinitely without resistance. This is a key evidence of zero DC resistance and coherent superconducting state.
The critical current is the maximum current above which
A Band gap increases
B Resistivity becomes zero
C Superconductivity breaks
D Hall sign reverses
If current exceeds the critical value, magnetic fields and energy in the material become too large and destroy superconductivity. The material then returns to a normal resistive state.
For many superconductors, Hc decreases as temperature
A Moves toward 0 K
B Moves toward Tc
C Becomes negative
D Equals vacuum level
As temperature approaches Tc, the superconducting state weakens. The critical field falls to zero at Tc because even a small external field can destroy superconductivity near the transition temperature.
Type II superconductors are preferred for high-field magnets mainly because they have
A Large Hc2 values
B No vortices
C Single Hc only
D Zero penetration depth
Type II materials remain superconducting up to very high upper critical fields. Their vortex mixed state allows them to operate in strong magnetic fields, making them suitable for MRI and research magnets.
The mixed state exists in type II superconductors between
A 0 and Tc
B Hc2 and infinity
C Tc and 0 K only
D Hc1 and Hc2
Below Hc1 the Meissner state dominates, but above Hc1 vortices enter. Between Hc1 and Hc2, superconductivity coexists with quantized flux vortices until it vanishes at Hc2.
A vortex in a type II superconductor carries
A Continuous flux
B No magnetic field
C Quantized flux
D Only electric charge
Each vortex contains a tiny normal core and carries one quantum of magnetic flux. This quantization arises from the coherence of the superconducting wavefunction and pairing of electrons.
The Meissner effect enables magnetic levitation mainly because the superconductor
A Repels magnetic field
B Becomes ferromagnetic
C Absorbs magnetic energy
D Produces strong heat
Flux expulsion makes the superconductor act as a strong diamagnet, creating repulsive forces with a magnet. With stable configurations (often helped by pinning), this can produce levitation demonstrations.
Penetration depth λ becomes larger when superconducting carrier density
A Increases strongly
B Decreases
C Stays infinite
D Becomes negative
Penetration depth depends on how effectively supercurrents screen magnetic fields. Fewer superconducting carriers mean weaker screening, so magnetic fields penetrate deeper and λ increases, especially near Tc.
The two-fluid model assumes carriers are divided into
A Ions and atoms
B Protons and neutrons
C Normal and super
D Light and sound
The two-fluid model treats electrons as a mixture of normal carriers and superconducting carriers. As temperature increases toward Tc, the superconducting fraction decreases, explaining changes in λ and other properties.
The isotope effect is commonly summarized as Tc varying approximately with
A M^−1/2
B M^+1/2
C M^0
D M^+2
In many conventional superconductors, Tc roughly decreases as isotopic mass increases, often close to Tc ∝ M^−1/2. This links Tc to phonon frequency and supports electron–phonon pairing.
A weak or absent isotope effect is often discussed for
A Many high-Tc cuprates
B Conventional low-Tc
C Pure lead only
D All type I metals
Several high-Tc materials show reduced or complex isotope dependence, suggesting that pairing mechanisms may not be purely conventional electron–phonon. This is one reason high-Tc superconductivity is still debated.
In BCS theory, phonons mainly provide
A Repulsive force only
B Effective attraction
C Nuclear binding
D Constant resistance
Phonon interaction can cause a net attraction between electrons near the Fermi surface, despite Coulomb repulsion. This effective attraction allows formation of Cooper pairs, leading to superconductivity below Tc.
The coherence length roughly describes the size of
A A unit cell only
B Depletion region
C Cooper pair spread
D Band gap width
Coherence length gives the characteristic distance over which the superconducting wavefunction remains correlated. It is often interpreted as the typical spatial extent of a Cooper pair in the material.
Josephson junctions are based on
A Hole diffusion only
B Photon reflection only
C Band folding only
D Electron tunneling
A Josephson junction has two superconductors separated by a thin barrier. Cooper pairs can tunnel through the barrier, producing supercurrent without voltage and enabling very sensitive measurements.
SQUID devices are mainly used to measure extremely small
A Magnetic fields
B Temperatures
C Band gaps
D Pressures
SQUIDs use Josephson junctions and flux quantization to detect tiny changes in magnetic flux. They are among the most sensitive magnetometers and are used in medical, geophysical, and lab applications.
The superconducting phase transition at Tc is commonly treated as
A Magnetic explosion
B Nuclear reaction
C Phase change
D Crystal fracture
At Tc, the material changes from normal to superconducting state, similar to a phase transition. Many properties change sharply, including resistance dropping to zero and a jump in specific heat.
The specific heat jump at Tc supports the idea of
A No energy gap
B Energy gap opening
C Infinite band overlap
D Purely classical motion
In BCS theory, an energy gap opens at the Fermi surface below Tc, changing how electrons store thermal energy. This produces a characteristic discontinuity (jump) in specific heat at Tc.
A practical cryogenic coolant commonly used for low-Tc superconductors is
A Liquid helium
B Liquid mercury
C Liquid sodium
D Liquid bromine
Many conventional superconductors have very low Tc, requiring cooling near 4 K. Liquid helium is widely used because it can reach these temperatures and maintains stable cryogenic conditions.
The work function is the minimum energy needed to
A Break Cooper pairs
B Create a hole
C Remove an electron
D Fold a band
The work function is the energy required to take an electron from inside a solid to just outside the surface (vacuum level). It is important in emission, contact potentials, and device physics.
A Fermi surface is mainly defined in
A Reciprocal space
B Real space
C Temperature space
D Pressure graph
The Fermi surface is the boundary in k-space separating occupied from unoccupied electron states at zero temperature. Its shape strongly affects conductivity, effective mass, and many metal properties.
Band overlap in a solid most commonly indicates the solid behaves as
A Insulator
B Perfect vacuum
C Superfluid
D Metal
When conduction and valence bands overlap, electrons can move into available states without needing thermal excitation across a gap. This provides abundant carriers and typically results in metallic conduction behavior