Quantum, Single-Electron and Tunneling Devices

Introduction and Context

Nanoelectronics exploits physical effects that become dominant when device dimensions approach characteristic quantum, electrostatic, and material length scales. In conventional transistors, charge is treated approximately as a continuous quantity and current is controlled mainly by drift and diffusion. At nanometre dimensions, however, electron wave nature, discrete energy levels, barrier penetration, Coulomb charging, and phase coherence can determine circuit behaviour.

This chapter examines four important device families: resonant-tunneling devices, single-electron transistors, quantum-dot devices, negative-capacitance structures, and quantum-interference devices. They do not all rely on the same physical mechanism. Resonant-tunneling devices use energy-selective transmission; single-electron devices control individual charge states; quantum dots confine carriers in three dimensions; negative-capacitance devices use polarization physics to amplify internal voltage; and interference devices control current through phase relationships between quantum paths.

These devices offer opportunities for ultralow-power logic, high-frequency operation, sensing, memory, radiation detection, and quantum information processing. They also face serious limitations, including temperature sensitivity, fabrication variability, leakage, decoherence, compatibility with conventional CMOS, and difficult circuit-level biasing.

Learning Objectives

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

1. Explain tunneling, resonant transmission, Coulomb blockade, quantum confinement, negative capacitance, and quantum interference.

2. Compare resonant-tunneling devices, single-electron transistors, quantum-dot devices, and interference devices.

3. Apply the principal energy, capacitance, and current relations governing these devices.

4. Determine operating limits imposed by temperature, charging energy, coherence, and fabrication variation.

5. Evaluate circuit opportunities and implementation challenges at postgraduate engineering level.

6. Analyse an applied nanoscale device scenario and select an appropriate architecture.

1. Quantum Transport Foundations

1.1 Tunneling through a potential barrier

In classical mechanics, an electron with energy below a barrier cannot cross it. Quantum mechanics gives the electron a finite wavefunction inside and beyond the barrier, producing a nonzero transmission probability. For a one-dimensional rectangular barrier of height V0, width a, and electron energy E less than V0, the approximate transmission dependence for a sufficiently thick barrier is

T ≈ exp[-2κa], κ = √[2m*(V0 − E)]/ℏ,

where m* is the effective mass and ℏ is the reduced Planck constant. This expression emphasizes exponential dependence on barrier width and height. It is an approximation: it neglects detailed interface matching and assumes a simple parabolic band and a one-dimensional barrier. Exact transmission requires solving the Schrödinger equation with boundary conditions.

The tunneling current depends additionally on the density of states, occupation probabilities, and applied bias. A general transition-current expression is obtained from Fermi’s golden rule and has the form

I ∝ ∫ D1(E)D2(E)|M(E)|²[f1(E) − f2(E)]dE,

where D1 and D2 are densities of states, M is a coupling matrix element, and f1 and f2 are Fermi–Dirac occupation functions. The proportionality constant depends on device geometry and normalization.

1.2 Quantum confinement

When a dimension becomes comparable with the carrier de Broglie wavelength or confinement length, allowed energies become discrete. For an ideal one-dimensional infinite well of width L,

En = n²π²ℏ²/(2m*L²), n = 1, 2, 3, … .

This model is useful for illustrating size dependence but overestimates confinement in real finite wells. In a quantum dot, confinement occurs in three dimensions, producing atom-like discrete states. Surface disorder, strain, dielectric environment, and many-body interactions modify the ideal spectrum.

1.3 Coherent and incoherent transport

Coherent transport preserves the phase relation of an electron wave over the relevant device length. Incoherent transport involves phase-randomizing events such as phonon scattering, charge noise, and interaction with defects. Interference devices require the device dimensions to be shorter than, or comparable to, the phase-coherence length. Thermal broadening can obscure narrow quantum features even when geometric dimensions are small.

2. Resonant-Tunneling Devices

2.1 Resonant-tunneling diode

A resonant-tunneling diode (RTD) consists, ideally, of a quantum well between two thin potential barriers. Under bias, electrons can tunnel from an emitter through the first barrier, occupy a quasi-bound state in the well, and tunnel through the second barrier to the collector. Transmission becomes large when the electron energy aligns with a quasi-bound energy level.

A simplified transmission resonance can be represented by a Breit–Wigner form,

T(E) = Tpeak Γ²/[4(E − E0)² + Γ²],

where E0 is the resonant energy, Γ is the energy linewidth, and Tpeak is the maximum transmission. This representation assumes a single isolated resonance and approximately energy-independent coupling near the resonance.

As voltage increases, the emitter energy distribution may first align with the resonant level, producing increasing current. Further voltage shifts the level out of alignment, so current decreases. The resulting current–voltage characteristic contains a peak followed by a valley: this is negative differential resistance (NDR), defined by dI/dV < 0 over a voltage interval. At still higher bias, other states and nonresonant paths may increase current again.

The peak-to-valley current ratio, peak voltage, valley voltage, and peak current density are important design metrics. Barrier thickness controls coupling: thinner barriers increase current and broaden the resonance, whereas thicker barriers sharpen the resonance but reduce current. Temperature broadens carrier distributions and usually weakens the NDR contrast.

2.2 RTD circuits

NDR permits compact oscillators, frequency multipliers, multistable circuits, memory elements, and high-speed logic. An RTD oscillator operates when the negative small-signal resistance of the device offsets the positive resistance of a load and parasitic network. Stable operation requires a complete bias and load-line analysis; the RTD alone is not an oscillator.

RTDs can also be integrated with transistors, forming resonant-tunneling transistor structures. The transistor supplies gain while the RTD provides a nonlinear load or switching characteristic. Such circuits can reduce transistor count in selected logic functions, but process integration, thermal stability, and voltage-margin issues have limited widespread adoption.

2.3 Resonant-tunneling hot-electron and quantum-cascade concepts

Resonant tunneling may also be used for energy-selective injection into layered structures. In quantum-cascade lasers, repeated quantum wells and barriers enable engineered intersubband transitions. Although a quantum-cascade laser is not an RTD in the narrow circuit sense, both rely on designed tunneling between quantized states. The distinction between transport resonance and optical transition must be maintained.

3. Single-Electron Devices

3.1 Coulomb blockade

A small conducting island connected to source and drain through tunnel junctions can store an integer number N of excess electrons. Adding one electron costs charging energy. For a total island capacitance CΣ,

EC = e²/(2CΣ),

where e is the elementary charge. The electrostatic energy of the island is approximately

U(N) = [−Ne + Q0]²/(2CΣ),

where Q0 represents induced charge from gates, nearby conductors, and background charges. This constant-interaction model neglects detailed electron–electron interactions and level-dependent capacitances.

At low bias, current is suppressed when adding an electron requires energy not available from the applied voltage. This is Coulomb blockade. A gate changes the induced charge and periodically moves the island between energetically favourable charge states. Current peaks occur when two adjacent charge states have equal free energy.

A practical condition for observing strong Coulomb blockade is

EC >> kBT,

where kB is Boltzmann’s constant and T is absolute temperature. Since EC = e²/(2CΣ), small islands are essential for room-temperature operation. A second requirement is sufficiently high tunnel resistance. For each junction, resistance should generally be much larger than the quantum resistance h/e², approximately 25.8 kΩ, so that charge remains well defined and quantum fluctuations do not destroy blockade. The exact acceptable value depends on the circuit and measurement bandwidth.

3.2 Single-electron transistor

A single-electron transistor (SET) contains a source, drain, island, two tunnel junctions, and a capacitively coupled gate. The island potential is controlled by the source, drain, and gate capacitances. If CS, CD, and CG are the corresponding capacitances, then

CΣ = CS + CD + CG + Cpar,

where Cpar includes stray and parasitic capacitance.

The gate-induced charge is Qg = CGVG, ignoring offset charges. The gate-voltage period of Coulomb oscillations is approximately

ΔVG = e/CG.

This relation assumes fixed capacitances and negligible gate leakage. Changing the gate voltage by one period changes the induced charge by one electron charge. The resulting current oscillations provide a highly sensitive charge-detection mechanism.

The orthodox SET model treats tunneling as sequential, incoherent events and assumes metallic or sufficiently equilibrated islands. It is useful for many engineering calculations but does not fully describe coherent tunneling, cotunneling, quantum-dot excited states, or strong level quantization.

3.3 SET operating regimes and limitations

In the sequential-tunneling regime, one electron tunnels onto the island and later leaves. At higher-order cotunneling, an electron can traverse the device through a virtual intermediate state, causing leakage even inside the nominal blockade region. Direct source–drain leakage, background charge, charge traps, and random telegraph noise are major practical concerns.

SETs have exceptional charge sensitivity but usually poor voltage gain and limited output drive. A conventional logic family requires signal restoration, fan-out, and tolerance to offset charge. Hybrid CMOS–SET circuits therefore use CMOS transistors for gain and SETs for charge sensing or threshold detection.

4. Quantum Dots and Quantum-Dot Devices

4.1 Physical nature of a quantum dot

A quantum dot is a nanoscale region in which carriers are confined in all three dimensions. Dots may be formed by semiconductor heterostructures, electrostatic gates, self-assembly, nanowires, carbon nanotubes, two-dimensional materials, or colloidal synthesis. Their discrete energy levels produce size-dependent optical and electrical properties.

The energy spectrum contains orbital quantization and, often, spin and valley degrees of freedom. In a simplified parabolic confinement model, the orbital level spacing scales approximately as

ΔE ∼ ℏ²/(m*L²),

where L is a characteristic confinement dimension. This scaling is qualitative because the numerical factor depends on confinement geometry.

4.2 Electrical and optical devices

Quantum-dot transistors use a dot as an island and can display Coulomb oscillations, excited-state transport, and spin-dependent effects. Quantum-dot cellular automata encode information in the charge configuration of coupled dots rather than in a conventional current flow. Quantum-dot memories store charge in isolated dots, while quantum-dot photodetectors and emitters exploit discrete optical transitions.

Self-assembled quantum-dot lasers benefit from three-dimensional carrier confinement, which can reduce threshold current and improve temperature performance compared with some quantum-well lasers. Colloidal quantum dots are used in displays and photodetectors, but surface chemistry, environmental stability, and toxicity of certain compositions require careful materials engineering.

4.3 Spin and valley opportunities

In a quantum dot, an electron spin can serve as a state variable. Electrical gates can manipulate exchange interactions or tunnel coupling, while spin-selective readout can be performed through charge sensing. Silicon and other materials also offer valley degrees of freedom. These opportunities are relevant to quantum computing, but they require very low noise, precise control, and cryogenic operation in many implementations.

5. Negative Capacitance and Steep-Slope Devices

5.1 Meaning of negative capacitance

A conventional capacitor satisfies dQ/dV > 0. In a ferroelectric, however, the voltage–charge relation can contain a region with negative differential capacitance:

dV/dQ < 0.

This does not mean that a stable isolated capacitor can indefinitely supply energy while having negative total capacitance. The negative-slope region is associated with the nonconvex free-energy landscape of ferroelectric polarization and is normally stabilized by a series dielectric, semiconductor, or another positive-energy element.

A simplified Landau free-energy density can be written as

F(P) = αP²/2 + βP⁴/4 + γP⁶/6 − EP,

where P is polarization, E is electric field, and α, β, γ are material parameters. Equilibrium satisfies dF/dP = 0. The differential response depends on d²F/dP²; a negative curvature region corresponds to negative differential susceptibility. This phenomenological model is material- and temperature-dependent and should not be used without experimentally determined coefficients.

5.2 Negative-capacitance field-effect transistor

In a negative-capacitance FET, a ferroelectric layer is incorporated into the gate stack. Voltage amplification inside the gate stack can increase the semiconductor surface-potential response to an applied gate voltage. The ideal subthreshold swing limit at temperature T for a conventional thermionic MOSFET is approximately

SSideal = (ln 10)kBT/q,

which is about 60 mV per decade at 300 K. Negative-capacitance concepts seek an internal body-factor below unity and hence a smaller external subthreshold swing.

Reported steep slopes must be interpreted carefully. Hysteresis, transient switching, interface traps, contact resistance, measurement bandwidth, and nonuniform ferroelectric domains can produce apparently steep characteristics. A practical design must demonstrate stable operation, low hysteresis, endurance, retention where relevant, and reproducibility across devices.

5.3 Circuit opportunities

Negative-capacitance FETs may reduce supply voltage and static power in selected logic circuits. They may also improve electrostatic control in scaled transistors. However, the ferroelectric layer introduces variability, wake-up and fatigue phenomena, process-integration constraints, and a dynamic trade-off between stabilization and voltage amplification. Circuit-level benefits must therefore be evaluated using measured compact models rather than idealized subthreshold slopes alone.

6. Quantum-Interference Devices

6.1 Phase-dependent transmission

When two or more quantum paths connect an input to an output, the total amplitude is the coherent sum of path amplitudes. For two paths,

A = A1 + A2 exp(iφ),

and the transmission probability is

T = |A|² = |A1|² + |A2|² + 2|A1A2|cosφ.

Here φ is the relative phase. The interference term may enhance or suppress transmission. This equation assumes coherent superposition and does not include dephasing. If phase is randomized, the average interference term tends toward zero.

6.2 Aharonov–Bohm and interferometer devices

In an Aharonov–Bohm interferometer, electrons travel around two paths enclosing magnetic flux. The phase difference includes a magnetic contribution proportional to the enclosed flux divided by the flux quantum h/e. Conductance oscillations can therefore reveal phase coherence and magnetic-field response.

Mach–Zehnder and Fabry–Pérot geometries use beam splitters or partially transmitting barriers to create and recombine paths. These devices are valuable for investigating edge-state transport, topological systems, and quantum information. Their circuit use is constrained by phase noise, magnetic-field requirements in some designs, and cryogenic environments.

6.3 Interference logic and sensing

Interference can implement switching by changing phase rather than simply changing carrier concentration. It can also provide highly sensitive detection of magnetic field, charge, or chemical adsorption. However, the same sensitivity produces vulnerability to disorder and environmental noise. A practical interferometer must control path symmetry, contact reflection, phase stability, and calibration drift.

7. Operating Limits and Design Trade-offs

The major operating limits of these devices are summarized below.

Temperature: Thermal energy kBT broadens energy distributions and suppresses Coulomb blockade and narrow resonances. Room-temperature SET operation requires extremely small total capacitance or unusually large charging energy.

Quantum coherence: Interference requires phase coherence over the active path. Phonons, impurities, electromagnetic noise, and electron–electron interactions reduce coherence.

Barrier and junction variation: A small change in tunnel-barrier thickness can produce a large current change because tunneling is exponential. Fabrication control is consequently more demanding than geometric scaling alone suggests.

Background charge: Trapped charge and fluctuating defects shift SET oscillations and quantum-dot operating points. Multiple gates, calibration, and charge-sensing feedback can mitigate the problem.

Leakage and cotunneling: Imperfect barriers cause off-state leakage. At sufficiently small dimensions or high conductance, higher-order processes invalidate simple blockade models.

Power and gain: Quantum devices may have low intrinsic energy dissipation but often require cryogenic cooling, sensitive amplifiers, or bias circuitry. Their system-level energy is not determined by device switching energy alone.

Integration: Heterostructures, ferroelectrics, nanowires, or molecular layers may be difficult to integrate with mature silicon processes. Yield, packaging, thermal budgets, and reliability are decisive engineering factors.

A useful device-selection principle is to match the physical effect to the application. RTDs are attractive for high-speed nonlinear functions; SETs for charge sensing; quantum dots for discrete-state electronics, photonics, and quantum information; negative-capacitance structures for low-voltage electrostatics; and interference devices for phase-sensitive sensing and specialized quantum processing.

8. Worked Example: Charging Energy and Temperature Limit

Consider an SET with total island capacitance CΣ = 1.0 aF, where 1 aF = 10⁻¹⁸ F. Its charging energy is

EC = e²/(2CΣ)

= (1.602 × 10⁻¹⁹ C)²/[2(1.0 × 10⁻¹⁸ F)]

= 1.28 × 10⁻²⁰ J.

Converting to electron-volts using 1 eV = 1.602 × 10⁻¹⁹ J gives

EC ≈ 0.080 eV = 80 meV.

The condition EC >> kBT suggests a characteristic temperature scale

T* = EC/kB

= 1.28 × 10⁻²⁰/(1.381 × 10⁻²³)

≈ 928 K.

This does not guarantee room-temperature operation because “much greater than” is required for strong blockade, and other broadening mechanisms exist. At 300 K, kBT ≈ 25.9 meV, so EC/kBT ≈ 3.1. Coulomb effects may be observable, but robust room-temperature single-electron switching would require additional energy margin, reduced parasitics, and carefully engineered tunnel junctions.

9. Applied Case: Selecting a Device for an Ultralow-Power Sensor

Background

This illustrative case considers a nanoscale gas sensor intended to detect adsorption events that change the local charge by a fraction of an electron. The sensor must operate with very low input charge, but it need not deliver large output current directly.

Problem

A conventional MOSFET offers gain and easy integration but may not resolve the smallest charge perturbations without a large sensing area or high power. An RTD provides a nonlinear current response but is primarily energy-selective rather than charge-counting. An SET offers periodic conductance peaks that shift when an external charge is coupled to the island.

Analysis and approach

An SET is selected as the sensing element, coupled capacitively to a functionalized surface. The design uses a gate or feedback electrode to compensate slow background-charge drift and maintain operation near the steepest point of a Coulomb oscillation. A CMOS amplifier provides voltage gain, bias generation, and signal restoration. The sensor is characterized over temperature because thermal broadening changes peak height and width.

The total capacitance must be minimized to increase charging energy, while tunnel resistances must remain high enough for charge quantization and low enough to permit measurable bandwidth. Shielding and careful dielectric processing reduce parasitic charge fluctuations. Differential reference devices help distinguish target adsorption from environmental drift.

Outcome

The hybrid SET–CMOS architecture offers high charge sensitivity and practical readout. It does not provide a universal replacement for CMOS: its calibration burden, background-charge sensitivity, and fabrication complexity are significant. For a high-volume digital processor, a conventional transistor is preferable; for a specialized low-power chemical sensor, the SET’s sensitivity can justify the additional complexity.

Learning points

1. Device choice must follow the sensing mechanism and required signal level.

2. A nanoscale device rarely operates as a complete system without bias, amplification, and calibration circuits.

3. Parasitic capacitance and environmental noise can dominate ideal quantum behaviour.

4. Application value depends on system-level performance, not only on a distinctive device characteristic.

10. Contemporary Developments and Best Practices

Current research combines quantum dots with two-dimensional materials, superconducting circuits, nanowires, and spin-based architectures. Ferroelectric hafnium-oxide systems are particularly important because they are more compatible with semiconductor processing than many earlier ferroelectrics. Hybrid quantum–classical systems use cryogenic control electronics near quantum devices to reduce interconnect burden.

Best practice in research and engineering includes: reporting complete measurement conditions; distinguishing differential from total capacitance; separating contact, interface, and intrinsic device effects; using temperature and frequency sweeps; modelling parasitics explicitly; testing device-to-device variation; and comparing energy, delay, noise, yield, and reliability at circuit level. Claims of room-temperature operation, sub-60-mV/decade switching, or single-electron control should be supported by reproducible data and clear definitions.

Ethically and commercially, quantum and nanoelectronic technologies require responsible handling of materials, especially toxic or scarce elements; transparent reporting of reliability; secure management of sensor data; and realistic communication of performance. AI can assist compact-model extraction, process optimization, and defect classification, but models must be validated against physical measurements and must not replace uncertainty analysis.

Chapter Summary

Quantum nanoelectronic devices exploit effects that are negligible in larger devices: barrier penetration, discrete energy levels, Coulomb charging, ferroelectric polarization, and phase-coherent interference. RTDs produce resonant transmission and negative differential resistance, enabling oscillators and nonlinear circuits. SETs control individual charge states through Coulomb blockade and provide exceptional charge sensitivity, although they suffer from background charge, cotunneling, temperature sensitivity, and limited gain. Quantum dots provide three-dimensional confinement for electronic, optical, spin, and quantum-information applications. Negative-capacitance devices seek internal voltage amplification and steep switching, but stability, hysteresis, and measurement interpretation are critical. Quantum-interference devices use phase-dependent transmission and are powerful for sensing and specialized quantum circuits.

Successful engineering requires more than observing a quantum effect. Thermal broadening, decoherence, leakage, parasitics, variability, integration, reliability, and system-level energy must be evaluated together. The most promising applications are those in which the unique quantum mechanism directly addresses a requirement that conventional electronics cannot meet efficiently.

Key Terms

Quantum tunneling: Transmission through a barrier forbidden by classical mechanics.

Resonant-tunneling diode: A device containing a quantum well and barriers that exhibits energy-selective tunneling.

Negative differential resistance: A region where increasing voltage decreases current.

Quantum well: A region that confines carriers in one dimension.

Quantum dot: A structure confining carriers in three dimensions.

Coulomb blockade: Suppression of electron transport because adding one electron requires charging energy.

Charging energy: Electrostatic energy required to add an electron to an island.

Single-electron transistor: A gated island device that controls transport one electron at a time.

Tunnel junction: A barrier through which carriers pass by tunneling.

Cotunneling: Higher-order tunneling through a virtual intermediate state.

Background charge: Uncontrolled charge that shifts a nanoscale device’s operating point.

Negative capacitance: A negative differential voltage–charge response associated with ferroelectric polarization.

Ferroelectric: A material with switchable spontaneous polarization.

Subthreshold swing: Gate-voltage change required for one decade of subthreshold current change.

Quantum interference: Dependence of transmission on phase relationships between quantum paths.

Phase coherence: Preservation of relative quantum phase during transport.

Breit–Wigner resonance: A model describing transmission through a broadened discrete state.

Orthodox SET model: A sequential-tunneling model based on classical capacitances and quantized charge.

Quantum confinement: Modification of energy states caused by nanoscale spatial restriction.

Coulomb oscillation: Periodic conductance variation with gate-induced charge.

Review Questions

Short Answer Questions

1. What physical condition produces resonant tunneling in an RTD?

2. Define charging energy and state its dependence on total island capacitance.

3. Why does an SET require tunnel-junction resistance substantially greater than h/e²?

4. What is meant by negative differential resistance?

5. Why does phase coherence matter in a quantum-interference device?

Long Answer Questions

1. Explain the structure, operation, current–voltage characteristic, and circuit applications of an RTD.

2. Derive the gate-voltage period of Coulomb oscillations and discuss the assumptions behind the result.

3. Compare quantum dots and SETs in terms of confinement, transport, applications, and limitations.

4. Explain the physical basis of negative capacitance and critically evaluate its use in steep-slope FETs.

5. Discuss the principal operating limits of quantum devices and their implications for CMOS integration.

Analytical / Application Questions

1. An SET has CΣ = 2 aF. Calculate its charging energy in joules and electron-volts, and estimate EC/kBT at 300 K. Interpret whether strong room-temperature blockade is assured.

2. A proposed RTD has a narrow resonance but very low peak current. Analyse the barrier-thickness and circuit-load trade-offs and recommend a suitable application.

3. Select between an RTD, SET, quantum dot, negative-capacitance FET, and interferometer for a low-power chemical sensor. Justify the selection using sensitivity, gain, temperature, fabrication, and system-integration criteria.

Multiple Choice Questions with Answers

Question 1

Which mechanism is primarily responsible for the peak and valley in an RTD current–voltage characteristic?

A. Alignment and misalignment of a quasi-bound quantum-well state

B. Avalanche multiplication in a reverse-biased junction

C. Thermal generation of minority carriers

D. Magnetic domain reversal

Correct Answer: A. Alignment and misalignment of a quasi-bound quantum-well state

Question 2

For an SET with total capacitance CΣ, the charging energy is

A. eCΣ/2

B. e²/(2CΣ)

C. 2e²CΣ

D. CΣ/(2e²)

Correct Answer: B. e²/(2CΣ)

Question 3

The approximate gate-voltage period of SET Coulomb oscillations is

A. eCG

B. CG/e

C. e/CG

D. eCΣ

Correct Answer: C. e/CG

Question 4

Strong Coulomb blockade requires which condition?

A. kBT much greater than EC

B. EC much greater than kBT

C. CΣ approaching infinity

D. Tunnel resistance equal to zero

Correct Answer: B. EC much greater than kBT

Question 5

A quantum dot differs from an ideal quantum well because it confines carriers

A. Only along the transport direction

B. Only in the vertical direction

C. In all three spatial dimensions

D. Only through magnetic fields

Correct Answer: C. In all three spatial dimensions

Question 6

Negative differential resistance means that, over a voltage interval,

A. dI/dV is positive and constant

B. dI/dV is zero everywhere

C. dI/dV is negative

D. current is independent of voltage and temperature

Correct Answer: C. dI/dV is negative

Question 7

In a two-path quantum interferometer, the interference contribution depends on

A. The relative phase between paths

B. Only the DC supply voltage

C. The transistor threshold voltage alone

D. The physical mass of the package

Correct Answer: A. The relative phase between paths

Question 8

At 300 K, the approximate thermal energy kBT is

A. 2.59 meV

B. 25.9 meV

C. 259 meV

D. 2.59 eV

Correct Answer: B. 25.9 meV

Question 9

Which process can produce leakage through a nominal SET blockade region?

A. Cotunneling

B. Perfect phase cancellation in every path

C. Infinite tunnel resistance

D. Removal of all capacitance

Correct Answer: A. Cotunneling

Question 10

A practical negative-capacitance FET must be evaluated especially for

A. Hysteresis, stability, traps, and reliability

B. Only optical absorption in the substrate

C. Elimination of all parasitic capacitances

D. Operation without any gate dielectric

Correct Answer: A. Hysteresis, stability, traps, and reliability