Metrology and Characterization

Introduction and Context

Nanoelectronics depends on the ability to measure structures and phenomena whose dimensions may be only a few nanometres. At this scale, measurement is not a passive activity: the probe can perturb the sample, the instrument response may be comparable to the feature being measured, and surface contamination or environmental noise can dominate the result. Consequently, nanometrology is concerned not only with obtaining an image or numerical value, but also with establishing traceability, uncertainty, reproducibility, and the physical meaning of the measurement.

Metrology is the science of measurement, including measurement units, procedures, calibration, uncertainty evaluation, and comparison of results. Characterization is the broader process of determining the structural, chemical, electrical, optical, magnetic, and thermal properties of a material or device. In nanoelectronics, characterization normally combines several complementary methods because no single instrument provides complete information.

A practical measurement workflow is:

1. Define the measurand precisely, such as line width, film thickness, surface roughness, dopant concentration, contact resistance, or thermal boundary conductance.

2. Select a technique whose spatial resolution, sensitivity, and measurement environment are appropriate.

3. Calibrate the instrument and verify its performance using reference materials or standards.

4. Prepare and document the sample without introducing artefacts.

5. Acquire data using a controlled and reproducible protocol.

6. Separate instrument response and artefacts from the sample signal.

7. Estimate uncertainty and report the result with suitable significant figures.

8. Confirm important conclusions using an independent technique.

Learning Objectives

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

• distinguish imaging, spectroscopy, diffraction, surface analysis, electrical probing, and thermal measurements;
• select suitable characterization methods for nanoscale materials and devices;
• interpret the principal signals and limitations of electron, scanning-probe, optical, X-ray, and ion-based techniques;
• design electrical measurements that separate contact, access, and intrinsic device effects;
• explain nanoscale thermal measurement methods and their principal error sources;
• evaluate resolution, sensitivity, calibration, uncertainty, reproducibility, and traceability;
• develop a defensible multi-technique characterization plan.

Measurement Concepts in the Nanoscale Regime

The measurand and the measurement model

A measurand is the quantity intended to be measured. “Nanowire diameter” is incomplete unless the measurement plane, edge definition, environment, and analysis method are specified. A measurement model expresses the reported quantity in terms of measured inputs. For example, for a four-point-probe sheet-resistance measurement on a uniform large-area film,

R_s = (π/ln 2)(V/I),

where R_s is sheet resistance in ohms per square, V is the measured voltage, and I is the applied current. The expression assumes collinear equally spaced probes, a uniform film, negligible probe contact resistance in the voltage path, and sufficiently large sample dimensions. Finite geometry requires a correction factor.

Resolution, sensitivity, accuracy, and precision

Spatial resolution is the smallest separation at which two features can be distinguished under specified conditions. It is not identical to pixel size, which is merely the sampling interval. Sensitivity is the change in signal per change in measurand. Accuracy describes closeness to a reference value, whereas precision describes the scatter of repeated measurements. A method may be precise but inaccurate if calibration is biased.

The interaction volume is the region of the sample contributing to a signal. In scanning electron microscopy it depends on beam energy and material; in secondary-ion mass spectrometry it depends on sputtering and collision processes; in optical microscopy it is determined by diffraction and the optical system. The apparent feature size is therefore a convolution of the true feature, probe function, instrument response, and data-processing procedure.

Uncertainty and reproducibility

For a result y = f(x1, x2, ..., xn), the standard uncertainty under a first-order model is commonly estimated as

u²(y) = Σ[i=1 to n] (∂f/∂xi)²u²(xi) + 2Σ[i<j](∂f/∂xi)(∂f/∂xj)u(xi,xj),

where u(xi) is the standard uncertainty of input xi and u(xi,xj) is their covariance. If inputs are independent, the covariance terms vanish. This approximation is appropriate when the model is sufficiently linear over the uncertainty range.

For independent repeated observations with standard deviation s and n measurements, the standard uncertainty of the mean is s/√n. Repetition reduces random uncertainty but does not remove systematic bias. Reproducibility concerns agreement under changed conditions, such as different operators, instruments, laboratories, or days; repeatability concerns agreement under substantially unchanged conditions.

An expanded uncertainty is often reported as U = ku_c, where u_c is the combined standard uncertainty and k is a coverage factor. For approximately normal errors and a sufficiently large effective number of degrees of freedom, k ≈ 2 corresponds roughly to a 95% coverage interval. The coverage statement and confidence assumptions must be reported.

Microscopy and Surface Topography

Optical and near-field methods

Optical microscopy is rapid, non-destructive, and valuable for locating devices and assessing large-area uniformity. Conventional far-field resolution is limited approximately by diffraction; a commonly used estimate is d ≈ 0.61λ/NA, where d is the lateral resolution, λ is wavelength, and NA is numerical aperture. This estimate assumes a conventional imaging system and does not represent a universal hard limit for all optical methods.

Confocal microscopy improves optical sectioning by rejecting out-of-focus light and can produce three-dimensional topographic information. Raman microscopy adds chemical and structural information through vibrational spectra, although fluorescence, weak scattering, laser heating, and diffraction-limited spot size can limit nanoscale interpretation. Tip-enhanced Raman spectroscopy can provide much finer spatial localization but requires careful control of tip enhancement and sample-tip geometry.

Scanning electron microscopy

Scanning electron microscopy (SEM) scans a focused electron beam over a surface and detects secondary electrons, backscattered electrons, or characteristic X-rays. Secondary-electron images are strongly sensitive to surface topography; backscattered-electron contrast is related to composition and atomic number. Energy-dispersive X-ray spectroscopy (EDS) identifies elemental composition, but its interaction volume can be much larger than the nanoscale feature of interest. Light-element detection, peak overlaps, matrix effects, and limited sensitivity must be considered.

SEM resolution depends on electron-optical performance, beam energy, working distance, sample conductivity, vibration, and charging. Charging can distort images or deflect the beam. Conductive coatings may reduce charging but can obscure small features and alter surface chemistry. Low-voltage operation, grounding, environmental SEM, or charge compensation may be preferable.

Transmission electron microscopy

Transmission electron microscopy (TEM) transmits electrons through an electron-transparent specimen. Bright-field, dark-field, and high-resolution TEM can reveal morphology, crystal lattice fringes, interfaces, and defects. Scanning TEM (STEM) forms an image by scanning a focused transmitted beam; high-angle annular dark-field STEM often gives strong atomic-number-dependent contrast.

Electron diffraction, including selected-area diffraction and convergent-beam diffraction, provides crystallographic information. The interpretation depends on sample thickness, orientation, dynamical scattering, strain, and preparation damage. Focused-ion-beam thinning is powerful for site-specific cross sections but may introduce implantation, amorphization, redeposition, or curtaining. Low-energy cleaning and protective layers can mitigate some artefacts.

Scanning probe microscopy

Atomic force microscopy (AFM) measures the interaction between a sharp tip and a surface. In tapping or intermittent-contact mode, the cantilever oscillates and feedback maintains a selected amplitude or phase condition. AFM can measure height, roughness, adhesion, stiffness, friction, capacitance, potential, and magnetic response, depending on the mode.

A measured AFM image is affected by tip geometry, convolution, feedback bandwidth, scan speed, drift, vibration, thermal fluctuations, and contamination. Lateral dimensions are often overestimated because the tip has finite radius; vertical dimensions are usually more reliable when the surface is stable and the calibration is valid. Tip-shape artefacts can be diagnosed by imaging calibration standards or by recognizing repeated shapes in nominally different features.

Scanning tunnelling microscopy (STM) measures a tunnelling current between a conductive tip and sample. In the idealized regime, current depends approximately exponentially on tip-sample separation. STM provides atomic-scale information on suitable conductive or semiconducting surfaces, but requires a stable tunnel junction, vibration isolation, and controlled bias and current. It measures electronic structure as well as topography, so apparent height need not equal geometric height.

Spectroscopy and Diffraction

Raman and photoluminescence spectroscopy

Raman spectroscopy measures inelastic photon scattering and is useful for identifying bonding, crystal phase, strain, defects, temperature, and carrier-related changes. Peak position, width, intensity, and polarization can all carry information. Strain may shift a Raman mode, but temperature, doping, crystal orientation, and local heating can produce similar shifts; interpretation should therefore use multiple peaks or independent measurements.

Photoluminescence (PL) probes radiative recombination. Peak energies can indicate band gaps, quantum confinement, excitons, defects, or interface states. PL intensity is not a direct measure of material quality without controlling excitation density, collection efficiency, surface recombination, and optical absorption.

X-ray photoelectron spectroscopy

X-ray photoelectron spectroscopy (XPS) measures the kinetic energy of photoelectrons. Their binding energy is calculated from

E_B = hν − E_K − φ,

where E_B is binding energy, hν is photon energy, E_K is measured kinetic energy, and φ is the spectrometer work function. The equation assumes a consistent energy reference and appropriate correction for charging. XPS is surface sensitive because electrons lose energy while travelling through matter; typical information depth is on the order of several nanometres, depending on material and electron energy.

XPS provides elemental composition and chemical-state information. Quantification requires sensitivity factors, background treatment, peak-shape assumptions, and correction for overlapping lines. Ar-ion sputtering can produce depth profiles but may cause preferential sputtering, atomic mixing, reduction, or implantation. Angle-resolved XPS changes sampling depth without sputtering, although interpretation requires a model.

Diffraction and reciprocal-space interpretation

X-ray diffraction (XRD) identifies crystal structure, phase, texture, lattice parameter, and strain. Bragg’s law is

nλ = 2d sinθ,

where n is diffraction order, λ is wavelength, d is interplanar spacing, and θ is the Bragg angle. It applies to constructive interference from lattice planes under the stated geometry. Peak broadening may arise from finite crystallite size, microstrain, instrument broadening, defects, and overlap; it should not automatically be attributed to size alone.

For nanoscale films, grazing-incidence XRD increases surface sensitivity. Reciprocal-space mapping can separate in-plane and out-of-plane lattice information and distinguish relaxed from strained layers. Electron diffraction provides higher spatial localization than conventional XRD but is more affected by dynamical scattering and specimen thickness.

Surface and Chemical Analysis

Secondary-ion mass spectrometry (SIMS) sputters a surface with a primary ion beam and analyzes ejected secondary ions by mass-to-charge ratio. It offers excellent trace sensitivity and depth profiling, but quantitative results require matrix-matched standards. Sputter rate, crater geometry, atomic mixing, charging, and transient signals at interfaces affect depth accuracy. Three-dimensional SIMS can map dopants and impurities, but spatial resolution and quantification must be validated.

Auger electron spectroscopy uses an electron beam to excite Auger electrons and is highly surface sensitive. It can provide elemental maps with good lateral localization, but peak overlaps, charging, beam damage, and sensitivity to surface cleanliness must be managed. Helium ion microscopy provides high-resolution surface imaging and can generate secondary-electron contrast with relatively shallow interaction, although ion-induced damage and charging remain concerns.

The choice between XPS, SIMS, Auger spectroscopy, EDS, and electron-energy-loss spectroscopy should be based on the measurand. For example, XPS is strong for chemical states, SIMS for trace dopants and depth profiles, EDS for relatively higher-concentration elemental mapping, and EELS for local bonding, composition, and electronic excitations in thin specimens.

Electrical Probing at the Nanoscale

Electrical characterization must distinguish the intrinsic device property from contacts, access resistance, leakage, parasitic capacitance, probe resistance, and instrumentation limits.

Two-terminal and four-terminal measurements

In a two-terminal measurement, the measured resistance includes the device and contact contributions:

R_2T = R_C1 + R_device + R_C2,

where R_C1 and R_C2 are contact and access contributions. A four-terminal measurement drives current through outer terminals and senses voltage with inner terminals. If voltage-sense current is negligible, voltage-probe contact resistance is largely excluded, allowing a more intrinsic resistance measurement.

For a uniform nanowire of length L, cross-sectional area A, and resistivity ρ,

R = ρL/A.

This relation assumes uniform material, ohmic transport, a well-defined cross section, and negligible contact and size-dependent corrections. At nanoscale dimensions, surface scattering, grain boundaries, quantum confinement, ballistic or quasi-ballistic transport, and contact barriers may invalidate a bulk-resistivity interpretation.

Contact resistance and transfer-length methods

In a contact test structure, total resistance can be expressed as the sum of channel and contact terms. Transfer-length methods use devices with different channel lengths to separate the intercept associated with contacts from the length-dependent channel resistance. The method assumes comparable contacts, uniform channel properties, and a valid linear model. Nonlinear contacts, current crowding, and short-channel effects require more advanced analysis.

Scanning electrical probes

Conductive AFM maps local current while a bias is applied between a conductive tip and an electrode. Scanning Kelvin probe microscopy measures contact-potential differences and can reveal work-function variation, trapped charge, and illumination effects. Scanning capacitance and scanning microwave methods provide local carrier or dielectric information. These techniques are powerful but strongly dependent on tip condition, contact force, parasitic capacitance, humidity, grounding, and calibration.

Low-noise measurements require shielding, guarding, filtering, stable bias sources, appropriate compliance limits, and awareness of thermoelectric voltages. Current-voltage sweeps should include both sweep directions and controlled dwell times to identify hysteresis, charging, electromigration, and self-heating.

Nanoscale Thermal Measurements

Thermal properties affect reliability, switching speed, energy efficiency, and the performance of two-dimensional and nanostructured materials. Important measurands include thermal conductivity, thermal conductance, interface or boundary conductance, temperature rise, and thermal time constant.

In a suspended microbridge method, a heated platform and a sensor platform are connected by the test specimen. Under steady state, an idealized relation is

G = P/ΔT,

where G is thermal conductance, P is net heat flow through the specimen, and ΔT is the temperature difference. The actual model must include parasitic heat loss through radiation, residual gas, electrical leads, and supports. If the specimen length L and cross-sectional area A are known and diffusive one-dimensional conduction is valid, thermal conductivity is estimated by

κ = GL/A.

At nanoscale dimensions, ballistic transport, temperature-dependent properties, contact thermal resistance, non-uniform temperature, and uncertain cross-sectional area can dominate.

Time-domain thermoreflectance (TDTR) uses a modulated pump laser to heat a surface and a delayed probe laser to monitor reflectance changes. Model fitting can estimate film thermal conductivity and interface conductance. The result is model dependent: optical penetration, spot size, modulation frequency, multilayer thickness, heat capacity, and correlation between fitted parameters must be considered.

Scanning thermal microscopy uses a thermally sensitive probe to map temperature or local thermal conductance. It offers spatial localization but requires calibration against standards and careful treatment of tip-sample thermal resistance. Laser thermometry, Raman thermometry, and electrical self-heating thermometry can complement one another. Raman thermometry requires a calibrated relation between Raman shift and temperature and must account for laser-induced heating.

A Multi-Technique Characterization Strategy

A robust strategy begins with the decision that must be made. If the question is whether a two-dimensional channel is contaminated, XPS may establish surface chemistry, AFM may reveal residue and roughness, and electrical measurements may quantify its effect. If the question is whether a thin film is epitaxial, XRD or electron diffraction establishes crystallographic relation, while cross-sectional TEM verifies interfaces and defects.

Measurements should be ordered from least destructive to most destructive where practical. Optical microscopy, AFM, Raman, and electrical tests may precede sputtering or ion milling. The same coordinate system and sample identifiers should be used so that measurements can be correlated. Raw data, calibration files, instrument settings, environmental conditions, processing scripts, and excluded observations should be archived.

Agreement between methods does not guarantee correctness if both share a systematic error. Conversely, disagreement is diagnostically valuable. For instance, an AFM thickness value and an XPS-derived overlayer thickness may differ because of roughness, density assumptions, contamination, or lateral non-uniformity. The appropriate response is to examine models and measurands, not simply average the values.

Worked Example: Uncertainty in a Four-Point-Probe Measurement

A uniform film is measured with current I = 1.00 mA and voltage V = 25.0 mV. The current standard uncertainty is 0.01 mA and the voltage standard uncertainty is 0.2 mV. Assuming independent uncertainties and ideal probe geometry,

R_s = (π/ln 2)(V/I).

The voltage-to-current ratio is 0.0250 V / 0.00100 A = 25.0 Ω. Since π/ln 2 ≈ 4.5324,

R_s ≈ 4.5324 × 25.0 = 113.3 Ω/square.

For independent V and I, the relative standard uncertainty is

u(R_s)/R_s = [(u(V)/V)² + (u(I)/I)²]^(1/2).

Here u(V)/V = 0.2/25.0 = 0.008 and u(I)/I = 0.01/1.00 = 0.010. Thus the relative uncertainty is approximately √(0.008² + 0.010²) = 0.0128. The standard uncertainty is therefore about 113.3 × 0.0128 = 1.45 Ω/square. A suitable result, excluding additional geometry and calibration uncertainty, is R_s = (113.3 ± 1.5) Ω/square, with the coverage convention stated separately.

The numerical result is only valid if the film is uniform and the geometry correction is negligible. In a nanoscale patterned device, these assumptions may fail; a four-terminal nanodevice measurement or a geometrically appropriate model would be required.

Illustrative Case Study: Diagnosing Performance Variation in a MoS₂ Nanoelectronic Device

Background

A research group fabricates field-effect transistors using mechanically transferred MoS₂ flakes on an oxide substrate. Devices fabricated in the same batch show a factor-of-five variation in field-effect mobility and substantial threshold-voltage scatter.

Problem

The team must determine whether the variation originates from flake thickness, contamination, contact resistance, interface charge, or measurement artefacts.

Analysis and approach

Optical microscopy locates flakes but cannot reliably determine residue or thickness. AFM is used to measure step height and surface roughness at multiple positions, with a calibrated tip and repeated scans. Raman and PL mapping examine thickness, strain, defects, and spatial non-uniformity. XPS on representative witness samples evaluates surface contamination and chemical states. Four-terminal test structures and contact-length series are introduced to separate channel resistance from contact resistance. Electrical sweeps are performed in vacuum and controlled ambient conditions to identify adsorbate effects and hysteresis.

The team finds that apparent mobility from two-terminal measurements is lowest for devices with longer or more resistive contacts. After contact correction, a substantial part of the variation remains correlated with AFM-observed residue and PL quenching near transfer wrinkles. Vacuum measurements reduce hysteresis, indicating that adsorbates contribute to threshold shifts. Raman mapping reveals local strain near wrinkles, while XPS confirms polymer-related surface contamination on selected samples.

Outcome

The group adopts a controlled transfer-cleaning process, introduces four-terminal devices, records device history, and reports mobility together with contact resistance, environment, channel geometry, and uncertainty. Device-to-device variation decreases, and the remaining variation is attributed to genuine local material differences rather than a single instrumental cause.

Learning points

No measurement alone identified the root cause. Morphology, optical spectroscopy, chemical analysis, and electrical probing addressed different hypotheses. The case also illustrates that an extracted parameter such as mobility is model dependent and can be misleading when contact resistance and environmental effects are ignored.

Challenges, Limits, and Best Practices

Important limitations include probe-induced damage, contamination, charging, drift, finite tip radius, diffraction, interaction volume, sample-preparation artefacts, model non-uniqueness, and correlation between fitted parameters. Nanoscale thermal and electrical measurements are especially vulnerable to parasitic pathways and contact effects.

Best practice requires calibrated instruments, traceable standards where available, blank and reference measurements, repeated measurements at multiple locations, randomized measurement order when drift is possible, environmental monitoring, and independent confirmation. Measurement data should include uncertainty rather than excessive digits. Images should retain scale bars, acquisition parameters, and processing history. Automated image analysis and AI-assisted spectral classification can improve throughput, but training-data bias, segmentation errors, and non-transparent preprocessing must be validated against expert-labelled and reference data.

Ethically and professionally, researchers must not select only favourable fields of view, hide failed measurements without justification, or report a fitted parameter without its model and uncertainty. Instrument access, calibration records, sample provenance, and analysis code should support reproducibility. Safety requirements include high voltage, vacuum, X-rays, lasers, ionizing beams, cryogens, and chemical preparation. Institutional rules and relevant radiation, laser, electrical, and chemical regulations must be followed.

Contemporary Developments

Current research trends include correlative microscopy, operando and in situ characterization, cryogenic and ultrafast measurements, four-dimensional STEM, atom-probe methods, quantum sensors, and machine-learning-assisted image and spectrum analysis. Correlative methods connect structure and function at the same location, while operando methods reveal changes during biasing, heating, illumination, or chemical exposure. These advances increase information content but also increase data volume, model complexity, and the need for rigorous metadata and uncertainty analysis.

Chapter Summary

Nanometrology combines measurement science with structural, chemical, electrical, optical, and thermal characterization. Technique selection must follow the measurand, required resolution, sensitivity, sample condition, and acceptable disturbance. SEM, TEM, AFM, STM, Raman, PL, XPS, XRD, SIMS, Auger spectroscopy, electrical probing, and thermal methods provide complementary information rather than interchangeable answers. Instrument response, interaction volume, sample preparation, contact effects, and model assumptions can dominate nanoscale results. Reliable conclusions require calibration, traceability, uncertainty evaluation, reproducibility studies, careful documentation, and independent confirmation. A multi-technique strategy is therefore central to credible nanoelectronics research and manufacturing.

Key Terms

Metrology: Science of measurement, including calibration and uncertainty.

Characterization: Determination of material or device properties.

Measurand: Quantity intended to be measured.

Traceability: Ability to relate a result to references through an unbroken calibration chain.

Resolution: Ability to distinguish closely spaced features.

Sensitivity: Change in measurement signal per change in measurand.

Accuracy: Closeness of a result to a reference value.

Precision: Closeness of repeated results to one another.

Repeatability: Agreement under substantially unchanged conditions.

Reproducibility: Agreement under changed conditions.

AFM: Scanning-probe method measuring tip-sample interactions.

SEM: Electron-beam surface imaging technique.

TEM: Electron-transmission technique for nanoscale structure and diffraction.

XPS: Surface-sensitive chemical-state spectroscopy.

SIMS: Mass spectrometry of sputtered secondary ions.

Raman spectroscopy: Vibrational spectroscopy based on inelastic scattering.

Sheet resistance: Resistance of a thin uniform film expressed in ohms per square.

Contact resistance: Resistance associated with electrical interfaces and access regions.

Thermal boundary conductance: Heat conductance across an interface per unit area.

Interaction volume: Region of a sample contributing to a measurement signal.

Review Questions

Short Answer Questions

1. Distinguish accuracy from precision in nanoscale measurement.

2. Why can AFM overestimate the lateral width of a nanostructure?

3. State two major limitations of EDS for nanoscale elemental analysis.

4. Why is a four-terminal electrical measurement less sensitive to voltage-contact resistance?

5. What information does XPS provide that ordinary optical microscopy cannot?

Long Answer Questions

1. Compare SEM, TEM, and AFM in terms of signal origin, spatial information, sample requirements, and artefacts.

2. Explain the role of calibration, traceability, uncertainty, repeatability, and reproducibility in nanometrology.

3. Discuss the interpretation of Raman, XPS, and XRD data for a strained two-dimensional semiconductor.

4. Describe the design and limitations of a nanoscale thermal-conductance measurement.

5. Develop a complete characterization plan for a nanowire transistor, including structural, chemical, electrical, and thermal measurements.

Analytical / Application Questions

1. A nanowire shows high two-terminal resistance but low four-terminal resistance. Construct a physical explanation and propose measurements to test it.

2. AFM indicates a uniform film thickness, while XPS depth profiling indicates an apparently different thickness. Identify possible causes and design an experiment to resolve the discrepancy.

3. A device parameter varies strongly between laboratories despite similar mean values. Analyze possible sources of reproducibility loss and propose a measurement-comparison protocol.

Multiple Choice Questions with Answers

Question 1

Which quantity is the intended quantity specified for measurement?

A. Sensitivity

B. Measurand

C. Precision

D. Resolution

Correct Answer: B. Measurand

Question 2

For a uniform film measured with an ideal equally spaced four-point probe, which expression gives sheet resistance?

A. R_s = V/I

B. R_s = ρA/L

C. R_s = (π/ln 2)(V/I)

D. R_s = I/V

Correct Answer: C. R_s = (π/ln 2)(V/I)

Question 3

Which microscopy method is most directly affected by finite tip radius when measuring lateral feature width?

A. AFM

B. XRD

C. XPS

D. PL

Correct Answer: A. AFM

Question 4

In XPS, binding energy is related to photon energy and photoelectron kinetic energy by which equation?

A. E_B = hν + E_K + φ

B. E_B = hν − E_K − φ

C. E_B = E_K − hν + φ

D. E_B = hν/E_K

Correct Answer: B. E_B = hν − E_K − φ

Question 5

What is a major advantage of four-terminal probing?

A. It eliminates sample heating in all cases

B. It removes the need for calibration

C. It largely excludes voltage-contact resistance from the measured voltage

D. It measures only surface chemistry

Correct Answer: C. It largely excludes voltage-contact resistance from the measured voltage

Question 6

Which technique is generally most suited to trace dopant depth profiling?

A. SIMS

B. Optical microscopy

C. Confocal imaging

D. Conventional PL

Correct Answer: A. SIMS

Question 7

In the idealized relation G = P/ΔT for a thermal test structure, G denotes

A. Electrical conductance

B. Thermal conductance

C. Optical gain

D. Specific heat

Correct Answer: B. Thermal conductance

Question 8

Which factor can broaden an XRD peak besides crystallite size?

A. Microstrain

B. Probe contact resistance

C. Laser wavelength only

D. Voltage compliance only

Correct Answer: A. Microstrain

Question 9

What does repeatability primarily describe?

A. Agreement under substantially unchanged conditions

B. Agreement between unrelated measurands

C. Closeness to a reference value only

D. Instrument spatial resolution

Correct Answer: A. Agreement under substantially unchanged conditions

Question 10

If independent random uncertainties are reduced by averaging n repeated measurements, the standard uncertainty of the mean is proportional to

A. n

B. n²

C. 1/n

D. 1/√n

Correct Answer: D. 1/√n