3. Metal–Semiconductor and Semiconductor Heterojunctions

Introduction and context

A semiconductor device is useful only when carriers can be injected, confined, collected, or controlled. These functions are determined not only by the properties of the semiconductor bulk but also by the interfaces through which carriers enter and leave it. Two interface classes are especially important: the metal–semiconductor contact and the semiconductor heterojunction.

A metal–semiconductor interface may behave as a rectifying Schottky contact or as a low-resistance ohmic contact. Its behavior depends on work functions, electron affinity, doping, interface charge, barrier height, and transport mechanisms. A heterojunction is formed when two different semiconductors are joined. Their band gaps, electron affinities, dielectric constants, and lattice parameters may differ, producing band offsets that control carrier transfer and confinement.

These ideas underlie Schottky diodes, metal–semiconductor field-effect transistors, heterojunction bipolar transistors, high-electron-mobility transistors, quantum-well lasers, photodetectors, solar cells, and modern compound-semiconductor integrated circuits. At postgraduate level, the central task is not merely to draw band diagrams, but to relate band alignment and interface physics to measurable current, capacitance, switching speed, noise, reliability, and contact resistance.

Learning objectives

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

1. Explain the formation of energy bands at metal–semiconductor and semiconductor–semiconductor interfaces.

2. Derive and interpret Schottky barrier height, depletion width, built-in potential, and contact current relations.

3. Distinguish thermionic emission, thermionic-field emission, field emission, diffusion, and recombination transport.

4. Explain interface states, Fermi-level pinning, image-force lowering, and nonideal diode behavior.

5. Design and evaluate ohmic contacts using doping, barrier reduction, tunnelling, and specific contact resistivity.

6. Construct band diagrams for straddling, staggered, and broken-gap heterojunctions.

7. Analyze carrier transport, accumulation, depletion, and quantum confinement in heterostructures.

8. Relate contact and heterojunction properties to practical device performance and fabrication decisions.

1. Energy alignment at a metal–semiconductor interface

The work function of a material is the energy required to move an electron from the Fermi level to the vacuum level. For a metal,

φm = Evac − EF.

For a semiconductor, the work function is

φs = χ + (Ec − EF),

where χ is the electron affinity and Ec − EF depends on doping. In an n-type semiconductor, increasing donor concentration moves EF toward Ec and reduces φs. In a p-type semiconductor, EF lies closer to Ev and φs is generally larger.

Before contact, the metal and semiconductor have separate Fermi levels. After intimate contact and thermal equilibrium, the Fermi level must be constant throughout the structure. Charge therefore transfers across the interface. For an ideal n-type semiconductor with φm > φs, electrons leave the semiconductor and enter the metal. The semiconductor side becomes positively charged, producing upward band bending and a depletion region. The resulting energy barrier for electrons moving from the semiconductor into the metal is the Schottky barrier.

Under the ideal electron-affinity model, the electron barrier height for an n-type semiconductor is

φBn = φm − χ.

The built-in potential across the semiconductor depletion region is not equal to φBn in volts because the semiconductor Fermi level is not located at the conduction-band edge. In energy units,

qVbi = qφBn − (Ec − EF).

For a uniformly doped n-type semiconductor, the depletion width at zero applied bias is approximately

W = [2εsVbi/(qND)]1/2,

where εs is semiconductor permittivity and ND is donor concentration. Under an applied voltage V, with forward bias defined as reducing the barrier, the depletion width is approximately

W(V) = [2εs(Vbi − V)/(qND)]1/2.

The electric field is largest at the interface and decreases toward the neutral semiconductor. The depletion approximation is useful for device design, although it becomes less accurate for graded doping, degenerate semiconductors, interface charge, and very thin barriers.

For a p-type semiconductor, the relevant barrier is often described as a hole barrier. The polarity of band bending and the dominant carriers change, but the same requirements remain: equilibrium Fermi-level alignment and charge neutrality.

2. Schottky diode transport

The dominant current mechanism in a moderately doped Schottky diode is often thermionic emission. Carriers with sufficient energy cross the barrier, and the current density is modeled by

J = J0 [exp(qV/nkT) − 1],

where

J0 = A**T2 exp(−qφB/kT).

Here A** is the effective Richardson constant, T is absolute temperature, φB is the effective barrier height, and n is the ideality factor. For an ideal thermionic-emission diode, n is close to unity. In practice, n may exceed one because of interface states, barrier inhomogeneity, recombination, series resistance, or tunnelling.

The strong exponential dependence on φB means that a small change in barrier height can produce a large change in saturation current. This is why interface cleaning, metal selection, annealing, and surface preparation are central to Schottky-device engineering.

Several transport regimes should be distinguished:

• Thermionic emission: carriers pass over the barrier; it dominates at moderate doping and sufficiently high temperature.
• Field emission: carriers tunnel through a thin barrier; it dominates in heavily doped, degenerate semiconductors.
• Thermionic-field emission: carriers possess some thermal energy and then tunnel through the remaining barrier.
• Diffusion or drift-diffusion transport: bulk transport limits current, particularly when the interface barrier is not the sole controlling resistance.
• Recombination-generation transport: interface or depletion-region recombination contributes significantly, often giving an ideality factor near two.

Image-force lowering reduces the electrostatic barrier because an electron approaching the metal induces an image charge. The reduction is approximately

ΔφIF = [qEm/(4πεs)]1/2,

where Em is the maximum electric field. Consequently, the effective barrier depends on applied bias and electric field. At high reverse bias, image-force lowering increases leakage current and contributes to breakdown-related limitations.

A Schottky diode has no minority-carrier storage comparable to a conventional p–n diode. It can therefore switch rapidly. This advantage is accompanied by higher reverse leakage, temperature sensitivity, and a lower forward voltage than many p–n junctions. The choice is consequently application-dependent rather than universally favorable.

3. Interface states and nonideal contacts

The ideal relation φBn = φm − χ frequently fails. Surface atoms have unsatisfied bonds, defects, impurities, reconstruction, and chemical reactions. These produce interface states whose occupancy changes with the local Fermi level. Interface charge modifies the electrostatic potential and may pin the Fermi level near a charge-neutrality level. Under strong pinning, changing the metal work function produces only a small change in measured barrier height.

A useful empirical description is

φB ≈ Sφm + (1 − S)φ0,

where S is the pinning factor. S near unity indicates weak pinning and strong dependence on metal work function; S near zero indicates strong pinning. The relation is not a universal law, but it is a valuable engineering measure of interface sensitivity.

Interface states also create capacitance and frequency-dependent conductance. At low frequency, carriers may follow the applied signal and contribute to measured capacitance. At high frequency, they may not respond rapidly enough. This behavior is used in capacitance–voltage and conductance methods to estimate interface-state density and response time.

Nonidealities commonly produce:

• an ideality factor greater than one;
• excess reverse leakage;
• barrier-height inhomogeneity over the contact area;
• hysteresis caused by trapping and detrapping;
• bias- and temperature-dependent barrier height;
• enhanced noise and long-term drift.

A practical model may represent the interface as a distribution of microscopic patches with different barrier heights. Current then preferentially flows through low-barrier patches, so the extracted barrier depends on temperature and measurement method. This explains why a contact can show a high apparent barrier in capacitance measurements but a lower effective barrier in current–voltage measurements.

Surface preparation is therefore a device variable. Cleaning, passivation, controlled oxidation, insertion of an interfacial dielectric, and optimized deposition can reduce defect density. However, passivation may also increase tunnelling distance or introduce additional fixed charge. Interface engineering always involves a trade-off.

4. From rectifying to ohmic behavior

An ohmic contact permits current to flow in either direction with a small voltage drop compared with the voltage across the active device. It need not have zero barrier; rather, its total resistance must be sufficiently low and its current–voltage characteristic sufficiently linear over the operating range.

The specific contact resistivity is defined locally by

ρc = dV/dJ

near zero bias, with units of Ω·cm². The contact resistance of a practical electrode includes the metal–semiconductor interface resistance and current spreading in the semiconductor. A commonly used transfer-length model defines

LT = (ρc/Rsh)1/2,

where Rsh is the semiconductor sheet resistance. The transfer length indicates the approximate distance over which current transfers from the semiconductor into the metal. Contact resistance can be extracted using structures such as the transmission-line method, provided that current crowding and geometry are handled correctly.

Three design routes are common. First, a metal with a favorable work function may reduce the majority-carrier barrier. Second, heavy doping beneath the contact narrows the depletion width. Since tunnelling probability increases rapidly as barrier width decreases, a contact can become effectively ohmic even when its thermionic barrier remains appreciable. Third, a multilayer metallization and thermal anneal can create a heavily doped interfacial compound or alloy.

The last method is technologically powerful but potentially risky. Excessive reaction can consume the semiconductor, create roughness, increase leakage, or degrade a nearby junction. Contact design must therefore consider thermal budget, electromigration, adhesion, chemical stability, and compatibility with subsequent processing.

For high-frequency and power devices, contact resistance directly reduces transconductance, increases power dissipation, lowers voltage swing, and limits cutoff frequency. It should be treated as part of the device architecture rather than as a final packaging correction.

5. Heterojunction band alignment

A semiconductor heterojunction joins materials with different band gaps. When the materials are brought into contact, their Fermi levels align, while the conduction- and valence-band edges generally experience discontinuities. The conduction-band offset is ΔEc and the valence-band offset is ΔEv. For a simple interface,

ΔEg = Eg2 − Eg1 = ΔEc + ΔEv,

with signs determined by the chosen band-diagram convention.

Three idealized alignments are important.

In a type-I, or straddling, heterojunction, the smaller-gap material lies inside the band-gap range of the larger-gap material. Both electrons and holes tend to be confined in the same material. This is useful for light emission because electrons and holes overlap spatially.

In a type-II, or staggered, heterojunction, the electron minimum and hole maximum occur in different materials. Electrons and holes are spatially separated. This can improve carrier extraction and suppress recombination, but it may reduce radiative recombination because wave-function overlap is smaller.

In a type-III, or broken-gap, heterojunction, the conduction-band edge of one material lies below the valence-band edge of the other. Such alignment supports unusual interband tunnelling and negative differential resistance, as well as specialized infrared and quantum devices.

Band offsets are not determined solely by bulk band gaps. Electron affinity, interface dipoles, strain, composition, defects, and growth orientation affect the actual alignment. In compound semiconductors, composition can tune the band gap and offsets, but it may also introduce alloy disorder and strain.

At equilibrium, charge transfer creates band bending until a common Fermi level is established. Under bias or illumination, quasi-Fermi levels split and the relevant alignment becomes operating-point dependent. A band diagram should therefore always state whether it represents equilibrium, forward bias, reverse bias, or photoexcitation.

6. Heterojunction transport and carrier confinement

For a conduction-band discontinuity ΔEc, an electron approaching the interface may be reflected, thermionically emitted over the offset, or transmitted by tunnelling. A valence-band discontinuity similarly controls hole transport. The transport regime depends on barrier height, barrier thickness, temperature, effective mass, scattering, and electric field.

In a modulation-doped heterostructure, donors are placed in a wider-gap barrier while electrons accumulate in a lower-energy channel. Spatial separation between ionized donors and mobile electrons reduces ionized-impurity scattering. The resulting two-dimensional electron gas can have high mobility, provided that interface roughness, alloy disorder, phonons, and remote impurities are controlled.

Carrier density in a two-dimensional channel is controlled by charge transfer, gate voltage, polarization charge, and band offsets. In polarization-based heterostructures, spontaneous and piezoelectric polarization can generate interface charge without conventional intentional doping. This is important in wide-band-gap devices, although surface traps and dynamic trapping can cause current collapse and threshold-voltage instability.

Thermionic emission over a heterojunction barrier often follows an expression analogous to Schottky transport, but the effective barrier is a band offset modified by bias and charge distribution. If the interface is abrupt and highly doped, tunnelling can dominate. If the interface is graded, carriers encounter a smoother potential and reduced reflection, but the physical thickness of the transition region becomes an additional design parameter.

At a heterojunction, current continuity does not imply continuity of carrier concentration or electric field. The displacement field satisfies

ε1E1 − ε2E2 = Qinterface,

where Qinterface is sheet charge. Differences in dielectric constant therefore change the electric field on each side. Incorrectly imposing equal fields across a charged or dielectric-mismatched interface is a common band-diagram error.

7. Quantum wells and heterostructure devices

A quantum well is a thin, lower-potential semiconductor layer bounded by higher-potential barriers. When the layer thickness becomes comparable to the carrier de Broglie wavelength, motion normal to the layers is quantized. For an ideal infinite well, the subband energies are approximately

En = n²π²ℏ²/(2m*L²),

where m* is effective mass and L is well width. Real wells have finite barriers, so wave functions penetrate into the surrounding materials and energy levels are lower than in the infinite-well approximation.

Quantum confinement changes the density of states, transition energies, optical absorption, gain, and transport. In a type-I quantum well, electrons and holes occupy the same well and can recombine radiatively. In a type-II well, spatial separation alters recombination lifetime and optical transition strength.

Quantum wells are used in semiconductor lasers, light-emitting diodes, infrared detectors, resonant-tunnelling diodes, and high-electron-mobility transistors. Their performance depends on well width, barrier height, interface roughness, strain, carrier density, and nonradiative defect density. A narrow well enhances confinement but may increase interface-scattering effects and shift the emission wavelength substantially.

A resonant-tunnelling structure illustrates the connection between contacts and heterojunctions. Two barriers surrounding a quantum well form discrete resonant states. When the emitter energy aligns with a state, current increases; when bias moves the state out of alignment, current can decrease, producing negative differential resistance. The effect is observable only when contact resistance, series resistance, and interface broadening are sufficiently small.

8. Measurement and design methodology

Band diagrams should be supported by measurements rather than treated as artistic illustrations. Current–voltage measurements reveal forward transport, leakage, ideality factor, and series resistance. Temperature-dependent current–voltage data help distinguish thermionic emission from tunnelling and reveal barrier inhomogeneity.

Capacitance–voltage measurements provide depletion width, apparent doping, built-in potential, and, with suitable frequency analysis, interface-state information. However, parasitic capacitance, frequency dispersion, nonuniform doping, and leakage can distort the extraction.

For heterostructures, Hall measurements determine sheet carrier density and mobility. Transmission electron microscopy and compositional analysis examine interface abruptness and defects. Optical methods such as photoluminescence reveal transition energies, confinement, strain, and nonradiative recombination. No single technique uniquely determines band offsets; reliable design commonly combines electrical, optical, structural, and simulation evidence.

A practical design sequence is:

1. Specify the required forward drop, leakage, switching speed, current density, and temperature range.

2. Select materials and crystal orientation using band gaps, offsets, mobility, thermal conductivity, and lattice compatibility.

3. Estimate depletion widths, barrier heights, carrier densities, and tunnelling probabilities.

4. Include interface states, image-force lowering, series resistance, and contact spreading resistance.

5. Choose contact metals, doping profiles, passivation, and annealing conditions.

6. Validate the model using temperature, bias, frequency, and geometry-dependent measurements.

7. Assess reliability under electrical, thermal, chemical, and radiation stress.

Illustrative case study: contact resistance in a high-frequency heterostructure transistor

Background

Consider an illustrative AlGaN/GaN high-electron-mobility transistor intended for high-frequency power amplification. The channel is a high-mobility two-dimensional electron gas formed near the heterointerface. The transistor requires a low-resistance source and drain so that the external terminals do not obscure the channel performance.

Situation and problem

Initial devices show good transconductance at low drain current, but the measured high-frequency gain is substantially lower than predicted. The drain current also compresses earlier than expected. Temperature-dependent measurements indicate that the source and drain resistances increase with temperature.

Analysis

The heterointerface provides a high-density channel, but the metal contacts are not automatically ohmic to that channel. A barrier exists between the metal and semiconductor, and the access region may have insufficient carrier density. The total on-resistance can be written schematically as

Ron = Rc,source + Raccess,source + Rchannel + Raccess,drain + Rc,drain.

Even if Rchannel is small because of high mobility, the contact and access terms can dominate. Current crowding beneath the electrode further increases the effective resistance. Interface contamination and nonuniform annealing may create a distribution of local barriers.

Approach and solution

The design team first uses transmission-line structures to separate contact resistance from sheet resistance. It then increases carrier concentration beneath the contacts, optimizes surface cleaning, and adjusts a multilayer metallization and anneal schedule. The process is constrained by the need to avoid excessive reaction and roughness. A field-plate and surface passivation are also introduced to control electric field and trapping, but their parasitic capacitance is included in the RF model.

Temperature-dependent measurements are fitted using thermionic-field-emission concepts rather than assuming purely thermionic transport. The final layout enlarges the effective contact width while reducing unnecessary access length.

Outcome

The revised structure exhibits a more linear output characteristic, lower power dissipation, and improved high-frequency gain. The improvement does not result from a single material substitution; it comes from coordinated control of barrier width, doping, interface cleanliness, current spreading, and parasitic capacitance.

Learning points

The case demonstrates that a high-mobility channel cannot compensate indefinitely for poor contacts. Contact resistance is coupled to band alignment, processing, geometry, thermal behavior, and RF parasitics. It must be measured independently and included from the earliest stage of device design.

Challenges, limitations, and common mistakes

The Schottky–Mott rule is a useful first estimate but often fails because real interfaces contain states and dipoles. A second mistake is confusing barrier height with built-in voltage; they differ because the semiconductor Fermi level is not generally at a band edge. A third is assuming that a low forward voltage proves a good contact. Low voltage may instead result from leakage, tunnelling, or a large ideality factor.

In heterojunction analysis, band offsets are frequently drawn without specifying material composition, strain, orientation, or equilibrium condition. Another error is assuming that a larger band offset is always beneficial. A large offset can improve confinement but impede injection and increase operating voltage. Likewise, a type-II alignment may improve carrier separation while weakening optical recombination.

Extraction methods also have limitations. Series resistance distorts diode parameters, parasitic capacitance affects high-frequency measurements, and spatially nonuniform interfaces make area-averaged parameters misleading. Device simulation is valuable, but its results are only as reliable as the material parameters, interface models, and boundary conditions supplied.

Professional and ethical considerations

Contact and heterojunction engineering has direct reliability and safety implications in power electronics, RF transmitters, optoelectronics, and sensing. Reported barrier heights, mobilities, and contact resistivities should include measurement conditions and uncertainty. Selective reporting of the best microscopic region can misrepresent wafer-level performance. Process documentation should identify thermal budgets, hazardous chemicals, waste handling, and traceability of material lots.

Engineers must also distinguish measured data from fitted parameters. A fitted ideality factor is not, by itself, proof of a particular microscopic mechanism. Transparent reporting of model assumptions is essential when results inform safety-critical or high-power designs.

Current developments and emerging directions

Current research emphasizes ultrawide-band-gap semiconductors, two-dimensional materials, van der Waals heterostructures, polarization-engineered interfaces, and epitaxial integration of dissimilar materials. Two-dimensional materials can reduce dangling-bond density at certain interfaces, but contact resistance remains a major limitation because of weak coupling, contamination, and transfer residues.

Advanced computational methods combine density-functional calculations, drift–diffusion simulation, quantum transport, and machine-learning-assisted process optimization. These tools can screen band alignments and predict sensitivity to defects, but experimental validation remains indispensable. In manufacturing, automated parameter extraction from large current–voltage and wafer-mapping datasets is increasingly useful for identifying spatially varying contact defects and process drift.

Best practices for device design

• Draw equilibrium and biased band diagrams separately.
• Define the sign convention for every band offset and voltage.
• Use work functions and electron affinities as initial estimates, not unquestionable facts.
• Include interface states, fixed charge, image-force lowering, and barrier inhomogeneity when interpreting data.
• Design ohmic contacts by reducing barrier width as well as barrier height.
• Extract contact resistance independently from channel resistance.
• Consider thermal, chemical, mechanical, and RF compatibility of metallization.
• Use temperature, frequency, geometry, and bias sweeps to distinguish competing transport mechanisms.
• Treat band offsets, strain, and interface quality as coupled variables.
• Validate analytical models with structural, electrical, and optical measurements.

Chapter Summary

Metal–semiconductor contacts and semiconductor heterojunctions determine how carriers enter, cross, are confined within, and leave semiconductor devices. A Schottky barrier results from Fermi-level alignment and charge transfer, but its practical height is modified by interface states, pinning, image-force lowering, and microscopic nonuniformity. Thermionic emission, tunnelling, diffusion, and recombination provide different limiting descriptions of contact current.

Ohmic behavior is achieved not necessarily by eliminating the barrier, but by making the barrier sufficiently thin or low that majority carriers cross with small resistance. Specific contact resistivity and transfer length connect interface physics to electrode geometry and circuit performance. In heterojunctions, conduction- and valence-band offsets produce type-I, type-II, or type-III alignment. These offsets control carrier injection, separation, tunnelling, and quantum confinement. Quantum wells and modulation-doped structures exploit these effects in high-speed and optoelectronic devices.

Reliable design requires combining band models with measurement, process control, contact-resistance extraction, interface characterization, and reliability analysis. The most effective engineer treats every interface as an active part of the device rather than an ideal boundary.

Key Terms

Schottky barrier: Energy barrier formed at a metal–semiconductor interface that limits majority-carrier transport.

Work function: Energy difference between a material’s vacuum level and Fermi level.

Electron affinity: Energy difference between the vacuum level and the semiconductor conduction-band edge.

Fermi-level pinning: Weak dependence of barrier height on metal work function because of interface states or dipoles.

Interface state: Electronic state localized near an interface and capable of storing charge.

Depletion region: Space-charge region depleted of mobile majority carriers.

Thermionic emission: Carrier transport over an energy barrier by thermal excitation.

Field emission: Quantum tunnelling through a barrier without requiring substantial thermal excitation.

Thermionic-field emission: Transport involving both thermal excitation and tunnelling.

Specific contact resistivity: Differential resistance of a contact per unit area, expressed in Ω·cm².

Transfer length: Characteristic distance over which current transfers between a metal and a semiconductor sheet.

Heterojunction: Interface between two different semiconductor materials.

Band offset: Discontinuity in conduction- or valence-band energy at a heterojunction.

Type-I alignment: Heterojunction alignment in which electrons and holes are confined in the same lower-gap material.

Type-II alignment: Staggered alignment in which electrons and holes preferentially occupy different materials.

Type-III alignment: Broken-gap alignment in which one material’s conduction band lies below the other’s valence band.

Quantum well: Thin potential well that quantizes carrier motion in one spatial direction.

Two-dimensional electron gas: High-mobility electron system confined near a heterointerface.

Image-force lowering: Reduction of an electrostatic barrier caused by induced image charge in a nearby conductor.

Barrier inhomogeneity: Spatial variation of local barrier height across a nominally uniform contact.

Review Questions

Short Answer Questions

1. Define the metal work function and semiconductor electron affinity.

2. Why does Fermi-level alignment cause band bending at a metal–semiconductor interface?

3. Distinguish thermionic emission from field emission.

4. What is meant by specific contact resistivity?

5. State the defining feature of a type-II heterojunction.

Long Answer Questions

1. Derive the depletion width of an n-type Schottky contact and explain its dependence on doping and applied voltage.

2. Explain interface states and Fermi-level pinning, including their effects on measured Schottky barrier height.

3. Discuss the methods used to convert a rectifying metal–semiconductor contact into an ohmic contact.

4. Compare type-I, type-II, and type-III heterojunctions and relate each to a device application.

5. Explain quantum-well formation, subband quantization, and the factors that influence optical and electronic performance.

Analytical / Application Questions

1. A Schottky diode shows a strong temperature dependence of saturation current and an ideality factor greater than one. Propose two physically distinct mechanisms that could explain the observations and describe measurements that would distinguish them.

2. A high-mobility heterostructure transistor has excellent channel mobility but poor measured on-resistance. Develop a resistance decomposition and identify process changes that could reduce the dominant terms.

3. An optoelectronic designer must choose between a type-I and a type-II quantum well. Analyze the choice for a light emitter and for a photodetector, considering carrier overlap, recombination, extraction, and leakage.

22. Multiple Choice Questions with Answers

Question 1

For an ideal n-type metal–semiconductor contact, the Schottky barrier height is primarily estimated by which relation?

A. φBn = χ − φm

B. φBn = φm − χ

C. φBn = Eg + χ

D. φBn = qNDW/εs

Correct Answer: B. φBn = φm − χ

Question 2

Which change most directly promotes ohmic behavior by increasing tunnelling through a semiconductor contact barrier?

A. Reducing semiconductor doping beneath the contact

B. Increasing the depletion width

C. Heavily doping the semiconductor beneath the contact

D. Increasing the band-gap of the semiconductor

Correct Answer: C. Heavily doping the semiconductor beneath the contact

Question 3

A measured Schottky-diode ideality factor substantially greater than unity may indicate

A. perfectly uniform thermionic emission only

B. interface recombination or barrier inhomogeneity

C. zero series resistance

D. absence of interface states

Correct Answer: B. interface recombination or barrier inhomogeneity

Question 4

In a type-I heterojunction, electrons and holes generally

A. are confined in the same lower-band-gap material

B. are forced into different materials

C. have no band discontinuity

D. occupy only interface defect states

Correct Answer: A. are confined in the same lower-band-gap material

Question 5

Which transport mechanism is most associated with a heavily doped semiconductor having a very narrow contact barrier?

A. Field emission by tunnelling

B. Minority-carrier storage

C. Neutral diffusion only

D. Radiative recombination

Correct Answer: A. Field emission by tunnelling

Question 6

Why can the measured barrier height depend on temperature in a nonuniform Schottky contact?

A. The metal work function becomes zero at low temperature

B. Current preferentially samples lower-barrier regions as transport conditions change

C. The semiconductor band gap is always independent of temperature

D. The depletion approximation forbids current flow

Correct Answer: B. Current preferentially samples lower-barrier regions as transport conditions change

Question 7

A type-II heterojunction is especially useful when the design objective is to

A. maximize spatial overlap of electrons and holes for emission

B. separate electrons and holes for extraction

C. eliminate all band offsets

D. make both materials metallic

Correct Answer: B. separate electrons and holes for extraction

Question 8

For an ideal infinite quantum well, the confinement energy of a subband varies with well width approximately as

A. L

B. 1/L

C. L²

D. 1/L²

Correct Answer: D. 1/L²

Question 9

Which measurement is particularly useful for separating contact resistance from sheet resistance?

A. Transmission-line method

B. Only a single optical absorption measurement

C. Open-circuit voltage measurement

D. Crystal-density measurement

Correct Answer: A. Transmission-line method

Question 10

In a modulation-doped heterostructure, separating dopant ions from the mobile channel is intended primarily to

A. increase ionized-impurity scattering

B. reduce mobility by adding defects

C. improve mobility by reducing remote impurity scattering

D. remove the conduction-band offset

Correct Answer: C. improve mobility by reducing remote impurity scattering