1. Semiconductor Physics and Device Fundamentals

Introduction and Context

Semiconductor devices are the physical foundation of modern electronics. Diodes, bipolar junction transistors, field-effect transistors, light-emitting diodes, solar cells, sensors, integrated circuits, and power switches all depend on the controlled movement of charge in semiconductor materials. Although device structures differ greatly, their operation can be understood through a common set of physical ideas: energy bands, carrier statistics, doping, carrier transport, generation and recombination, mobility, and charge continuity.

A semiconductor is neither a perfect conductor nor an ideal insulator. Its electrical behavior is strongly influenced by temperature, impurities, crystal structure, electric fields, illumination, and applied voltage. This controllability distinguishes semiconductors from metals and insulators and makes them suitable for engineered electronic functions.

At postgraduate level, semiconductor physics should not be treated as a collection of isolated equations. The equations describe linked physical processes. An applied electric field produces drift; a concentration gradient produces diffusion; recombination changes carrier concentration; and the continuity equation connects these mechanisms to charge conservation. Device models are useful only when their assumptions and limits are understood.

Learning Objectives

After completing this chapter, the reader should be able to:

1. Explain the origin and significance of energy bands in crystalline solids.

2. Distinguish intrinsic and extrinsic semiconductor behavior.

3. Use Fermi–Dirac statistics and appropriate approximations to estimate carrier concentrations.

4. Explain donor and acceptor doping and the movement of the Fermi level.

5. Derive and interpret drift and diffusion current densities.

6. Relate mobility, conductivity, scattering, and temperature.

7. Explain carrier generation, recombination, and carrier lifetime.

8. Formulate and apply electron and hole continuity equations.

9. Identify the assumptions behind common semiconductor device models.

10. Apply these concepts to practical device and engineering situations.

From Atomic Orbitals to Energy Bands

An isolated atom has discrete electron energy levels. When many atoms form a crystal, neighboring atomic orbitals interact. Each atomic level splits into a very large number of closely spaced levels, which collectively form an energy band. The allowed energies are separated by forbidden energy regions called band gaps.

The two bands most important for electronic devices are the valence band and the conduction band. The valence band is generally associated with bonding electrons, whereas electrons in the conduction band can move through the crystal and contribute substantially to electrical conduction. The energy difference between the conduction-band edge, denoted by E_C, and the valence-band edge, denoted by E_V, is the band-gap energy:

E_g = E_C − E_V.

In a metal, an allowed band is partially filled or bands overlap, so mobile electrons are available even at very low temperature. In an insulator, the band gap is large and thermal excitation produces very few carriers. A semiconductor has a moderate band gap, allowing its carrier concentration to be controlled by temperature, impurities, optical excitation, and electrical fields.

The band diagram is an energy representation, not a literal spatial picture of electron trajectories. A horizontal energy level may represent a region of constant potential, while bending of the bands indicates a spatially varying electrostatic potential. This distinction becomes essential when analyzing junctions and field-effect structures.

For an electron, the conduction-band effective density of states is commonly represented as

N_C = 2(2πm_n* kT/h²)^(3/2),

and for holes in the valence band,

N_V = 2(2πm_p* kT/h²)^(3/2),

where m_n and m_p are effective masses, k is Boltzmann’s constant, T is absolute temperature, and h is Planck’s constant. Effective mass incorporates the influence of the crystal lattice on carrier motion. It is not necessarily equal to the free-electron mass.

Carrier Statistics and the Fermi Level

The probability that an available state of energy E is occupied by an electron is given by the Fermi–Dirac function:

f(E) = 1/[1 + exp((E − E_F)/kT)],

where E_F is the Fermi level. At E = E_F, the occupation probability is one-half. The Fermi level is therefore a statistical reference energy, not necessarily an energy level occupied by a physical electron.

For a nondegenerate semiconductor, in which the Fermi level is not too close to a band edge, the Fermi–Dirac function can be approximated by Maxwell–Boltzmann statistics. The equilibrium electron and hole concentrations then become

n_0 = N_C exp[−(E_C − E_F)/kT],

p_0 = N_V exp[−(E_F − E_V)/kT].

Multiplication gives the mass-action law:

n_0p_0 = N_CN_V exp(−E_g/kT) = n_i²,

where n_i is the intrinsic carrier concentration. Thus,

n_0p_0 = n_i².

This relation applies at thermal equilibrium under nondegenerate conditions. It does not imply that electron and hole concentrations are always equal. In an intrinsic semiconductor, n_0 = p_0 = n_i. In an n-type semiconductor, electrons are the majority carriers and holes are minority carriers; in a p-type semiconductor, the reverse is true.

The intrinsic concentration is highly temperature dependent because of the exponential factor involving E_g. This dependence explains why semiconductor leakage currents and switching behavior can change significantly with temperature.

In strongly doped or degenerate semiconductors, the Maxwell–Boltzmann approximation fails. The Fermi level may lie inside a band, and Fermi–Dirac statistics must be retained. This is important in heavily doped contacts, nanoscale devices, and some modern optoelectronic structures.

Doping and Charge Neutrality

Pure semiconductor material is called intrinsic semiconductor. Its carrier concentration is determined primarily by thermal generation. Controlled addition of impurity atoms produces an extrinsic semiconductor.

A donor impurity has one more valence electron than the host atom. In silicon, a pentavalent impurity such as phosphorus can contribute an electron to the conduction band. The donor energy level is usually close to the conduction band, so donor ionization is relatively easy at ordinary temperatures. After donating an electron, the donor becomes positively charged.

An acceptor impurity has one fewer valence electron than the host atom. A trivalent impurity such as boron can accept an electron from the valence band, leaving behind a mobile hole. The ionized acceptor is negatively charged.

For a compensated semiconductor containing donors and acceptors, charge neutrality is expressed as

p_0 + N_D^+ = n_0 + N_A^-.

Here, N_D^+ and N_A^- are the concentrations of ionized donors and acceptors. Under complete ionization and strong n-type doping, n_0 is approximately N_D − N_A. Under strong p-type doping, p_0 is approximately N_A − N_D. Minority concentrations follow from the mass-action law.

Doping shifts the Fermi level. Donor doping moves E_F toward E_C, while acceptor doping moves E_F toward E_V. This shift is not merely a graphical convenience; it changes equilibrium carrier populations and determines contact and junction behavior.

At low temperature, dopants may not be completely ionized. At very high doping levels, impurity interactions, band-gap narrowing, and degeneracy may become important. Therefore, the simple relations n ≈ N_D or p ≈ N_A should be used only after checking their assumptions.

Equilibrium, Nonequilibrium, and Quasi-Fermi Levels

At thermal equilibrium, a semiconductor has no net current, and the Fermi level is spatially constant. Local carrier movements still occur, but opposing processes balance statistically.

External bias, illumination, injection, or time-dependent excitation can disturb equilibrium. In nonequilibrium conditions, electrons and holes may no longer be described by a single Fermi level. Instead, electron and hole populations are represented by separate quasi-Fermi levels, F_n and F_p. Their separation is related to the departure from equilibrium and, in optoelectronic devices, to the attainable voltage or emitted photon energy.

This distinction is important in solar cells, LEDs, photodiodes, and transistor operation. A device may have nearly equilibrium carrier concentrations in one region and strongly nonequilibrium concentrations in another. Applying equilibrium formulas indiscriminately can produce incorrect conclusions.

Carrier Transport: Drift and Diffusion

Carrier transport describes the current produced by carrier motion. Two mechanisms dominate ordinary semiconductor devices: drift caused by an electric field and diffusion caused by a carrier concentration gradient.

Drift Transport

An electric field exerts a force on charged particles. Electrons accelerate opposite to the electric field, while holes move in the direction of the electric field. Frequent scattering prevents unlimited acceleration and produces an average drift velocity:

v_n,drift = −μ_n E,

v_p,drift = μ_p E,

where μ_n and μ_p are electron and hole mobilities. The corresponding drift current densities are

J_n,drift = q n μ_n E,

J_p,drift = q p μ_p E.

Both expressions are positive in the conventional direction of current associated with the electric field. Electron velocity is opposite to conventional electron current because electrons carry negative charge.

The conductivity of a semiconductor is

σ = q(nμ_n + pμ_p),

and resistivity is ρ = 1/σ. In an n-type semiconductor, conductivity is often dominated by qnμ_n; in a p-type semiconductor, it is often dominated by qpμ_p. However, minority carriers and compensation may become important in precision devices.

Mobility depends on scattering. Lattice vibrations, ionized impurities, neutral defects, interface roughness, alloy disorder, and carrier–carrier interactions can all limit mobility. At low impurity concentration, phonon scattering often dominates and mobility tends to decrease as temperature rises. At low temperature or high impurity concentration, ionized-impurity scattering can dominate. The total mobility is frequently approximated using Matthiessen’s rule:

1/μ_total ≈ 1/μ_lattice + 1/μ_impurity + 1/μ_other.

This rule is an engineering approximation rather than a universal law.

At sufficiently high fields, drift velocity may cease to increase linearly with field. Velocity saturation, hot-carrier effects, and intervalley transfer can then become important. Low-field mobility models are inappropriate for short-channel transistors and high-field power devices unless the operating field is verified to be within the low-field regime.

Diffusion Transport

If carrier concentration varies spatially, random thermal motion produces a net flux from regions of high concentration toward regions of low concentration. For one-dimensional transport, the diffusion current densities are

J_n,diff = qD_n (dn/dx),

J_p,diff = −qD_p (dp/dx),

where D_n and D_p are electron and hole diffusion coefficients. The signs arise from the negative charge of electrons and positive charge of holes.

The total current densities are therefore

J_n = qnμ_nE + qD_n(dn/dx),

J_p = qpμ_pE − qD_p(dp/dx).

These equations are central to semiconductor device analysis. A concentration gradient can produce current even when the electric field is zero, while an electric field can produce current even in a spatially uniform material.

The Einstein relation connects diffusion coefficient and mobility under nondegenerate, near-equilibrium conditions:

D_n/μ_n = D_p/μ_p = kT/q.

At room temperature, kT/q is approximately 25.9 mV. The relation reflects the common statistical origin of thermal diffusion and field-driven drift. It may require modification in degenerate semiconductors or under conditions where generalized carrier statistics apply.

Generation, Recombination, and Carrier Lifetime

Generation creates electron–hole pairs, while recombination removes them. Thermal energy, photons, energetic particles, or high electric fields can generate carriers. Recombination may occur radiatively, through defects, or through Auger interactions.

Radiative recombination produces a photon and is particularly important in direct-band-gap optoelectronic materials. Shockley–Read–Hall recombination occurs through defect or trap states within the band gap. These states capture one type of carrier and subsequently facilitate recombination with the opposite type. Auger recombination transfers the recombination energy to a third carrier and becomes important at high carrier concentrations.

The excess minority-carrier lifetime, τ, characterizes the approximate time required for a nonequilibrium carrier population to decay. In a simple low-level injection model,

Δn(t) = Δn(0) exp(−t/τ),

and similarly for excess holes. The lifetime is not a universal material constant; it depends on defect density, injection level, temperature, surface recombination, and measurement method.

A useful diffusion length is

L_n = (D_nτ_n)^(1/2),

for electrons, and

L_p = (D_pτ_p)^(1/2),

for holes. Diffusion length estimates how far a carrier can travel before recombination. It is central to the design of bipolar transistor bases, photodiodes, solar cells, and minority-carrier detectors.

Surface recombination can dominate in thin structures. Passivation layers reduce the density of electrically active surface states and can substantially improve carrier lifetime. In practical devices, bulk lifetime alone is therefore insufficient to predict performance.

Continuity Equations and Charge Conservation

The continuity equation expresses conservation of carriers. For electrons, the one-dimensional continuity equation is commonly written as

∂n/∂t = (1/q)(∂J_n/∂x) + G_n − R_n,

and for holes,

∂p/∂t = −(1/q)(∂J_p/∂x) + G_p − R_p.

The signs reflect the definitions of conventional current and carrier charge. A divergence in electron current changes the local electron population, while generation and recombination act as source and sink terms.

Together with Poisson’s equation,

d²φ/dx² = −ρ/ε,

and the drift–diffusion current equations, the continuity equations form the basic semiconductor device equations. The charge density is

ρ = q(p − n + N_D^+ − N_A^-).

These coupled equations are nonlinear because carrier concentrations, electric fields, and recombination rates influence one another. Analytical solutions are possible only under simplifying assumptions such as one-dimensional geometry, steady state, low-level injection, constant mobility, negligible generation, or quasi-neutrality.

Under steady state, ∂n/∂t = ∂p/∂t = 0. Under uniform generation and recombination equilibrium, G = R. In a quasi-neutral region, the net charge density is approximately zero even though substantial carrier transport may occur. Quasi-neutrality does not mean that current is zero; it means that positive and negative charge densities nearly balance.

A Unified View of Semiconductor Device Operation

The preceding concepts become especially powerful when considered together. A pn junction illustrates the connection. When p-type and n-type materials are joined, electrons diffuse from the n side to the p side and holes diffuse in the opposite direction. Recombination near the interface leaves behind fixed ionized donors and acceptors, producing a depletion region and an internal electric field. Drift caused by this field balances diffusion at equilibrium, resulting in zero net current.

Under forward bias, the barrier is reduced and minority-carrier injection increases. Under reverse bias, the depletion region widens and only a small minority-carrier current flows until breakdown or other nonideal effects occur. The junction behavior is therefore not explained by diffusion or drift alone; both mechanisms and their balance are essential.

The same framework extends to bipolar transistors, in which minority-carrier injection and transport through the base determine current gain; MOSFETs, in which electrostatic control of surface carrier density determines channel conduction; photodiodes, in which optical generation and electric-field collection determine photocurrent; and solar cells, in which generation, diffusion, recombination, and junction separation determine conversion efficiency.

Applied Scenario: Diagnosing Temperature-Dependent Leakage in a Photodiode

Background

Consider an illustrative silicon photodiode used in an optical communication receiver. The device is reverse biased so that photogenerated carriers are collected efficiently and junction capacitance remains low.

Situation

During laboratory testing, the dark current increases substantially as the temperature rises. The optical response remains approximately proportional to incident light, but the signal-to-noise ratio degrades at elevated temperature.

Analysis

The dark current can contain diffusion, generation–recombination, surface leakage, and field-enhanced components. As temperature increases, the intrinsic carrier concentration rises strongly. This increases minority-carrier concentrations and can increase diffusion current. Thermal generation in the depletion region also increases. If surface passivation is poor, temperature-dependent surface states may contribute additional leakage.

A first diagnostic step is to measure dark current at several reverse biases and temperatures. A nearly bias-independent component may indicate depletion-region generation, whereas a component that rises strongly with reverse bias may suggest field-assisted mechanisms or surface leakage. Comparing measured temperature activation behavior with expected band-gap-related trends can help distinguish mechanisms, but fitting alone cannot replace structural and process investigation.

Approach and Solution

The engineering response would include verifying junction quality, examining surface passivation, reducing defect density through process control, and selecting an operating temperature consistent with the receiver noise budget. Circuit-level compensation may reduce the impact of leakage, but it cannot substitute for controlling the physical source. Device simulation using coupled Poisson, drift–diffusion, and recombination models can identify whether bulk or surface processes dominate.

Outcome

Suppose the analysis shows that depletion-region generation dominates. Improving material lifetime and reducing trap density should lower dark current. If surface leakage dominates, improved passivation and guard-ring design are more appropriate. The same measured symptom—higher dark current—can therefore require different solutions depending on the governing mechanism.

Learning Points

1. Temperature dependence is often a clue to carrier generation and intrinsic concentration.

2. Reverse bias does not eliminate generation–recombination current.

3. Mobility, lifetime, surface recombination, and doping must be considered together.

4. Device measurements should be interpreted through a physical model rather than through a single empirical formula.

Assumptions, Limitations, and Common Errors

Several mistakes recur in elementary and advanced semiconductor analysis. First, carrier concentration should not automatically be equated with dopant concentration. Compensation, incomplete ionization, intrinsic carriers, and degeneracy may invalidate that approximation.

Second, drift and diffusion currents should not be treated as mutually exclusive alternatives. They commonly occur simultaneously and may oppose one another, as in an equilibrium junction.

Third, the Einstein relation is not universally valid in its simple form. Degenerate statistics, high fields, and strong nonequilibrium conditions require more advanced transport models.

Fourth, mobility is not constant across all operating conditions. Temperature, doping, field, geometry, and scattering mechanisms matter. High-field devices require velocity-saturation or hydrodynamic corrections.

Fifth, lifetime values should be used with care. A measured effective lifetime may combine bulk, surface, and contact effects. It may also depend on injection level.

Finally, sign conventions in current and continuity equations must be maintained consistently. Many apparent contradictions arise from changing between particle flux, conventional current, and electrical current without tracking charge signs.

Professional and Ethical Considerations

Semiconductor engineering has consequences beyond circuit performance. Device reliability, radiation tolerance, power dissipation, and failure behavior affect safety-critical systems, medical instruments, transportation, and energy infrastructure. Engineers should report model assumptions, uncertainty, and test conditions honestly. A device model that works under nominal laboratory conditions may fail under temperature extremes, radiation exposure, aging, or manufacturing variation.

Responsible practice also requires attention to process safety and environmental controls. Semiconductor fabrication involves hazardous chemicals, high temperatures, vacuum systems, and fine particulate control. Design decisions should consider reliability, material sourcing, energy consumption, and end-of-life recovery where relevant.

Contemporary Directions

Current semiconductor research increasingly combines classical drift–diffusion theory with atomistic, quantum, and data-driven approaches. Nanoscale devices may require quantum confinement, ballistic transport, tunneling, or nonequilibrium Green’s-function methods. Wide-band-gap materials such as silicon carbide and gallium nitride support high-temperature, high-voltage, and high-frequency applications, but introduce distinctive defect, interface, and mobility challenges.

Technology computer-aided design tools solve coupled semiconductor equations numerically and are widely used for process and device development. Machine-learning methods are being applied to process optimization, defect classification, compact-model extraction, and yield prediction. Such tools are valuable only when supported by physically meaningful data and validated against measurements. An accurate-looking prediction outside its training or calibration range can be misleading.

Best Practices for Semiconductor Analysis

A sound analysis normally follows a disciplined sequence:

• Define geometry, materials, contacts, temperature, and operating regime.
• Identify whether the material is intrinsic, doped, compensated, degenerate, or nonequilibrium.
• Establish the relevant carrier concentrations and charge neutrality condition.
• Determine whether drift, diffusion, generation, recombination, or electrostatic effects dominate.
• State assumptions such as low-level injection, constant mobility, complete ionization, or quasi-neutrality.
• Check units, signs, limiting cases, and temperature dependence.
• Compare analytical predictions with measurement or numerical simulation.
• Evaluate whether the model remains valid when device dimensions, fields, or carrier concentrations change.

Chapter Summary

Semiconductor device behavior begins with the electronic structure of crystalline materials. Valence and conduction bands, separated by a band gap, determine the availability of mobile carriers. Fermi–Dirac statistics describe state occupancy, while the nondegenerate approximation leads to useful expressions for electron and hole concentrations and the mass-action law.

Doping introduces donors or acceptors, shifts the Fermi level, and controls majority and minority carrier populations. Carrier transport occurs through drift in an electric field and diffusion caused by concentration gradients. Their current densities are linked through mobility and diffusion coefficients, with the Einstein relation providing a useful equilibrium connection. Mobility depends on scattering and may vary with temperature, doping, and electric field.

Generation and recombination determine how carrier populations change. Carrier lifetime and diffusion length provide practical measures of nonequilibrium behavior, but surface and defect effects must be considered. The continuity equations express carrier conservation and, together with Poisson’s equation and drift–diffusion relations, form the foundation of semiconductor device modeling.

These ideas explain pn junctions, transistors, photodiodes, solar cells, and integrated devices. Reliable engineering analysis requires explicit assumptions, careful sign conventions, awareness of model limits, and validation against physical measurements.

Key Terms

Band gap: Energy interval between the conduction-band edge and valence-band edge in which idealized electronic states are unavailable.

Conduction band: Allowed energy band containing states that can contribute to electronic conduction.

Valence band: Energy band generally occupied by bonding electrons in a semiconductor.

Fermi level: Statistical energy at which the electron occupation probability is one-half.

Intrinsic semiconductor: Semiconductor in which carrier concentrations are determined primarily by the material and temperature rather than intentional doping.

Extrinsic semiconductor: Semiconductor whose electrical behavior is modified by intentional impurity doping.

Donor: Impurity that can provide an electron to the conduction band.

Acceptor: Impurity that can accept an electron from the valence band, creating a hole.

Majority carrier: Carrier type present at the greater concentration in a doped semiconductor.

Minority carrier: Carrier type present at the lower concentration in a doped semiconductor.

Mobility: Proportionality between low-field drift velocity and electric-field magnitude.

Drift: Carrier transport caused by an electric field.

Diffusion: Net carrier transport caused by a spatial concentration gradient.

Generation: Creation of electron–hole pairs or other mobile carriers.

Recombination: Process in which an electron and hole cease to exist as separate mobile carriers.

Carrier lifetime: Characteristic time associated with the decay of excess carriers.

Diffusion length: Approximate distance a carrier travels by diffusion during its lifetime.

Continuity equation: Conservation equation describing the time variation of carrier concentration.

Quasi-Fermi level: Nonequilibrium statistical potential used separately for electrons or holes.

Quasi-neutrality: Condition in which positive and negative charge densities nearly cancel in a region.

Review Questions

Short Answer Questions

1. What physical meaning is assigned to the semiconductor band gap?

2. State the mass-action law and identify the conditions under which it is used.

3. Distinguish donor doping from acceptor doping.

4. Why do both drift and diffusion contribute to semiconductor current?

5. What is meant by carrier lifetime?

Long Answer Questions

1. Explain the formation of energy bands in a crystalline solid and compare metals, semiconductors, and insulators using band concepts.

2. Derive the expressions for equilibrium electron and hole concentrations under nondegenerate conditions.

3. Explain the physical origin of mobility and discuss how temperature and impurity concentration affect it.

4. Develop the electron and hole continuity equations and interpret each term physically.

5. Explain generation and recombination mechanisms and discuss their importance in photodiodes and solar cells.

Analytical / Application Questions

1. A compensated n-type semiconductor contains more donors than acceptors. Determine the approximate majority-carrier concentration under complete ionization and explain how the minority concentration can be found.

2. A device exhibits increasing reverse leakage current with temperature. Using generation, recombination, intrinsic concentration, and surface effects, propose a structured diagnostic procedure.

3. A semiconductor region has both an electric field and a nonuniform carrier concentration. Explain how the signs and magnitudes of drift and diffusion currents determine whether the net current is large, small, or zero.

22. Multiple Choice Questions with Answers

Question 1

Which statement best describes the Fermi level in a semiconductor at thermal equilibrium?

A. It is the energy of every conduction-band electron.

B. It is the energy at which the probability of state occupancy is one-half.

C. It is always located exactly at the middle of the band gap.

D. It is the highest occupied energy at absolute zero for every semiconductor.

Correct Answer: B. It is the energy at which the probability of state occupancy is one-half.

Question 2

A compensated semiconductor has donor concentration greater than acceptor concentration, with complete ionization and negligible intrinsic carriers. Which approximation is appropriate?

A. p ≈ N_A − N_D

B. n ≈ N_A + N_D

C. n ≈ N_D − N_A

D. n = p = n_i

Correct Answer: C. n ≈ N_D − N_A

Question 3

Which expression gives the total electron current density in the one-dimensional drift–diffusion model?

A. J_n = qnμ_nE + qD_n(dn/dx)

B. J_n = qnμ_nE − qD_n(dn/dx)

C. J_n = qpμ_pE − qD_p(dp/dx)

D. J_n = qD_n(dn/dx) only

Correct Answer: A. J_n = qnμ_nE + qD_n(dn/dx)

Question 4

Why can an equilibrium pn junction have substantial carrier motion but zero net current?

A. All carriers are immobilized in the depletion region.

B. Diffusion and drift currents balance each other.

C. The band gap becomes zero at equilibrium.

D. Generation and recombination are both absent.

Correct Answer: B. Diffusion and drift currents balance each other.

Question 5

Under low-level, nondegenerate conditions, which relation connects electron diffusion coefficient and mobility?

A. D_nμ_n = q/kT

B. D_n/μ_n = kT/q

C. D_n/μ_n = qkT

D. D_n = μ_nT²

Correct Answer: B. D_n/μ_n = kT/q

Question 6

If the excess minority-carrier lifetime is increased while diffusion coefficient remains constant, the diffusion length will

A. decrease in proportion to lifetime

B. remain unchanged

C. increase as the square root of lifetime

D. increase linearly with lifetime squared

Correct Answer: C. increase as the square root of lifetime

Question 7

Which process is most directly associated with recombination through defect levels in the band gap?

A. Radiative band-to-band recombination only

B. Shockley–Read–Hall recombination

C. Elastic lattice scattering

D. Fermi-level pinning only

Correct Answer: B. Shockley–Read–Hall recombination

Question 8

In a nondegenerate n-type semiconductor, increasing donor concentration generally moves the Fermi level

A. toward the valence band

B. toward the conduction band

C. outside the crystal lattice

D. to an energy independent of doping

Correct Answer: B. toward the conduction band

Question 9

A semiconductor region has a spatially varying electron concentration but no electric field. Which current mechanism can still produce electron current?

A. Drift only

B. Diffusion only

C. Neither drift nor diffusion

D. Displacement current only

Correct Answer: B. Diffusion only

Question 10

Which set of equations forms the basic classical framework for self-consistent semiconductor device modeling?

A. Only Ohm’s law and Kirchhoff’s voltage law

B. Only the mass-action law and Einstein relation

C. Poisson’s equation, drift–diffusion current equations, and continuity equations

D. Only the ideal gas law and Fermi–Dirac function

Correct Answer: C. Poisson’s equation, drift–diffusion current equations, and continuity equations