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Image contrast from changes in secondary-electron escape and collection as surface slope, edges and detector-facing geometry vary. Secondary electrons originate near the surface, but brightness also depends on material, charging and the beam conditions.

The Seebeck coefficient $S(T)$ quantifies the thermoelectric voltage response per small temperature difference at zero electric current. Use $S=-dV/dT$ along a homogeneous material, with voltage understood through electrochemical potential. Its units are volts per kelvin, commonly $\mu V/K$. The word thermopower is also used, despite this being a voltage response rather than power; some authors use that word for $|S|$, so check their convention. ^[ref].

For the A-minus-B terminal order in the Seebeck effect experiment,Thus a small temperature difference around $T_0$ gives $V_{AB}\approx [S_A(T_0)-S_B(T_0)]\Delta T$. The finite-interval ratio $V_{AB}/\Delta T$ is an average of the coefficient difference, not necessarily its value at either endpoint. Ordinary two-material measurements determine a relative Seebeck coefficient: to recover $S_A$ from the measured difference, add a separately known $S_B$. Neither the choice of a zero for voltage nor the use of a familiar reference material makes $S_B$ identically zero.

A concrete research example is Martin and colleagues' 2021 certification experiment. They measured small temperature differences and voltages on six silicon–germanium specimens at 13 base temperatures between $295$ and $900\mathrm{K}$. At each setting they acquired 40 voltage-and-temperature-difference pairs and used linear regression with a free intercept, so a constant voltage offset did not become part of the slope. Platinum voltage leads required a reference-material correction; their terminal order gave $S_{\mathrm{measured}}=S_{\mathrm{Pt}}-S_{\mathrm{specimen}}$, hence $S_{\mathrm{specimen}}=S_{\mathrm{Pt}}-S_{\mathrm{measured}}$. This is an actual measurement protocol, unlike the toy plot above. ^[ref].

Microscopically, a temperature gradient changes charge carrier transport until an opposing electrical response balances it at zero net electric current. In the usual simple semiconductor picture, electrons and electron holes give opposite Seebeck coefficient signs, and their contributions are weighted by their electrical conductivities. The Seebeck coefficient is a transport property: density of states alone does not determine it, since carrier motion and scattering also matter. Its usefulness extends beyond temperature sensing to diagnosing which carriers transport electric charge. ^[ref].

A quantum dot of InAs embedded in gallium arsenide confines injected electrons and electron holes. Strain-driven island formation supplies dots with lateral dimensions of order tens of nanometres and heights of a few nanometres. In an electrically driven implementation, a dot lies in a junction's intrinsic region. Selecting one dot spatially and one radiative line spectrally turns discrete exciton recombination into a single-photon source. Pulsed injection must avoid re-excitation during the same collection window.

The pioneering electrically driven device used an areal dot density around $5\times 10^8\mathrm{c}{\mathrm{m}}^{-2}$, a GaAs p-i-n structure and an aperture selecting individual-dot light.^[ref]

A semiconductor has an electronic band gap and a conductivity strongly affected by temperature, impurities and carrier injection. Optical absorption can create mobile electrons and holes, enabling a photodiode.

The useful feature of a semiconductor is that its charge carrier population can be controlled. Semiconductor doping changes the supply of mobile electrons or electron holes; carrier injection changes their population away from thermal equilibrium. A transistor turns that control into an electronic amplifier: a small input signal controls a larger flow of supplied energy.

For a uniform semiconductor in a weak electric field, a simple drift model writes its electrical conductivity asHere $q>0$ is the elementary charge, $n,p$ are the number densities of mobile electrons and electron holes, and ${\mu }_n,{\mu }_p$ their positive charge carrier mobilities. The two contributions add because opposite electric charges drift in opposite directions and therefore carry electric current in the same direction. This model assumes fixed temperature and mobilities and omits diffusion from density gradients.

An original dimensionless example isolates the effect of carrier injection. Suppose initially $p\ll n=n_0$ and ${\mu }_n=2{\mu }_p$. Adding equal excess populations $\Delta n=\Delta p=0.1n_0$ gives $\Delta \sigma /{\sigma }_0=0.15$, even though the added electron holes remain a minority carrier population. A semiconductor can respond strongly to a small injected population without changing its underlying band gap.

Ionizing radiation creates electron-hole pairs in a depleted semiconductor. An applied electric field collects their charge, allowing precise energy spectroscopy when charge loss and electronic noise are controlled.

In thermal equilibrium, nondegenerate conduction electrons and valence electron holes share one chemical potential. Multiplying $n=N_c{e}^{-(E_c-\mu )/(k_{B}T)}$ by $p=N_v{e}^{-(\mu -E_v)/(k_{B}T)}$ cancels that chemical potential:This relation remains valid with semiconductor doping under the stated assumptions. Equality of the two individual densities, $n=p=n_i$, additionally requires the intrinsic neutral case. Separate electron and hole quasi-Fermi levels in nonequilibrium need not obey this equilibrium product.

With one parabolic valley and two spin states at each band edge, the prefactor multiplying $(k_{B}T{)}^3$ in the product is $4(m_c{m}_h{)}^{3/2}/(2\pi {\hslash }^2{)}^3$. Both populations must be nondegenerate; the Pauli reduction of the pinned-edge mass-action product quantifies a failure of the classical approximation.

Nevill Francis Mott's 1977 lecture discusses silicon deposited in a glow discharge. Injected electrons provided a drift-mobility readout; electrical conductivity and temperature dependence tested localized-state transport and excitation toward a mobility edge. Varying temperature distinguishes transport regimes. The lecture gives no contact geometry or timing circuit here, so none is inferred. Its Figure 2 is schematic, not measured data.^[ref]

This evidence motivates a transport question beyond the closed-chain eigenvalue problem: how does a prepared charge disturbance move under the conditions of a real sample? The numerical figures above supply neither drift-mobility measurements nor a model of the deposition process. Finite-size concentration alone cannot reproduce an experimental electrical conductivity curve.

Finite temperature permits phonon-assisted hopping between localized eigenstates or thermal excitation toward a mobility edge; localized states therefore need not imply zero measured electrical conductivity at every nonzero temperature.^[ref]

Real dephasing destroys the relative wave phases needed for long-path interference. Observing coherent confinement requires the distance over which those wave phases survive to be long enough to explore the localized region, and the sample to be large enough to resolve it. Temperature alone is not an automatic switch: the actual inelastic processes set the relevant scales. Static elastic wave scattering preserves coherence within each realization. Loss of the ensemble-averaged coherent field through random wave phases is therefore not, by itself, physical dephasing of an individual sample.

Sérgio P. Machado coauthored research on molecular orbital.^[ref]

A molecular orbital is a one-electron spatial wavefunction for the combined atomic nuclei of a molecule. For a normalized molecular orbital, the Born rule gives the position probability density $|\psi (\mathbf{r}){|}^2$, with ${\int }_{{\mathbb{R}}^3}|\psi {|}^2{d}^3\mathbf{r}=1$. The molecular orbital is the amplitude, rather than its squared modulus or a classical trajectory.

Seth Neddermeyer and Carl David Anderson studied the penetrating component of cosmic rays, contributing to identification of the muon. Measurements of particle energy loss in dense absorbers revealed events that were too penetrating to fit the expected behavior of electrons at the measured momentum. Comparing track curvature and penetration supplied evidence about particle mass. The result showed why similar-looking charged tracks could belong to physically different particles.^[ref]

A physicist.^[ref]

In 1986, Akira Tonomura and collaborators coated a ferromagnet shaped as a torus with superconducting niobium and copper. A cooled stage held it in a 150 kV field-emission electron microscope. An electron biprism overlapped object and reference waves; film holograms were reconstructed optically. Room-temperature leakage screening selected samples; varying copper thickness tested electron penetration.^[ref]

Below the superconducting transition, through-hole and outside electron waves differed in wave phase by zero or $\pi$ modulo $2\pi$. Warming through it changed the interference reversibly. Leakage and coherent-penetration bounds do not prove zero magnetic field.^[ref]

Why these two phases? The shield's superconducting flux quantum is $h/(2e)$, whereas the probing electron has electric charge $-e$. Substituting $\Phi =Nh/(2e)$ givesAn odd $N$ therefore moves a carrier fringe by half its spacing; an even $N$ leaves it unchanged modulo a full spacing. The phase quantization provides an internal check on the superconducting enclosure. It does not mean that zero wave phase proves zero trapped magnetic flux.^[ref]

The readout is electron holography in the off-axis holography geometry: a known tilted reference converts an unknown relative wave phase into a spatial carrier displacement. Reconstructing a magnetic wave phase assumes stable reference phase, adequate coherence and a calibrated carrier; electrostatic charging and material traversal can also shift wave phase. Optical wave phase amplification rescales the displayed fringe displacement. The experiment's shielding and comparison tests support the magnetic inference; an interferogram by itself measures the total relative wave phase, rather than separately certifying every contribution. The ideal field-free model describes the limiting geometry, while finite leakage and penetration remain questions of experimental bounds.

Shin'ichirō Tomonaga developed a relativistically consistent formulation of quantum electrodynamics and a method of renormalization. The physical problem was that naive corrections to an electron's interaction with the electromagnetic field produced divergent intermediate expressions. Relating the theory's parameters to measured mass and electric charge allowed finite predictions to be extracted. His own recollections explain how the relativistic formulation and the treatment of those divergences developed into a calculable quantum theory.^[ref]

A physicist.^[ref]

The Shockley-Queisser limit is the radiative conversion-efficiency bound for an ideal single-junction solar cell, with one collected electron-electron hole pair per absorbed above-gap photon, carrier thermalization, and radiative recombination required by the reverse optical process. Photons below the band gap are not absorbed, while excess photon energy above it is thermalized. Maximizing the electrical power over the operating electric potential difference and then the band gap gives a ceiling of roughly thirty percent for ordinary unconcentrated sunlight; its precise value depends on the incident spectrum, cell temperature and emission geometry. The original calculation by William Shockley and Hans-Joachim Queisser obtained approximately $30\%$ at $1.1\mathrm{eV}$ for a $6000\mathrm{K}$ blackbody source and a cell at $300\mathrm{K}$.^[ref]

Let $q>0$ be the magnitude of each transferred electric charge, and let arrivals form a Homogeneous Poisson process of rate $\lambda$. Extend the stream over past and future times when considering stationary filtering. For electrons, $q=e$, the elementary charge. Choose the positive electric current direction to follow these transfers, so $I=q\lambda >0$ is its mean magnitude. If $N_T$ counts arrivals in a gate of duration $T>0$, thenThe gate's transferred electric charge is $Q_T=q{N}_T$, and its average electric current is ${\overline{i}}_T=Q_T/T$. Scaling the expected value and variance givesMore arrivals increase the absolute fluctuation but decrease its size relative to the mean. For an original count example with $\lambda T=4$, the mean count and its variance are both $4$, the standard deviation is $2$, and the relative standard deviation is $1/2$. The probability of no transfer is $e^{-4}\approx 0.01832$; the probability of four is $4^4{e}^{-4}/4!\approx 0.19537$. A constant arrival rate does not prescribe four arrivals in every gate.

These are fluctuations of a time average, not the variance of an ideal instantaneous electric current. A model of point transfers has arbitrarily sharp impulses; it acquires a finite measured variance only after specifying a gate or linear filter. Actual collection pulses have finite duration and electrical circuits have finite response times.

For an original model, set $q=1.602176634\times 10^{-19}\mathrm{C}$, $I=1\mu \mathrm{A}$, $R_F=100\mathrm{k}\Omega$, $G=10$, and the exponential low-pass filter's $\tau =100\mu \mathrm{s}$. Assume an ideal detector without charge multiplication and omit all additive noise for this calculation. ThenDoubling $I$ doubles the voltage variance and multiplies its standard deviation by $\sqrt{2}$. Halving $\tau$ also doubles the variance, provided the detector remains approximately white throughout the enlarged passband. Using $f_c$ in place of $B_{\mathrm{n}}$ underestimates the variance by the factor $2/\pi$. These are calculated predictions, not measured values or settings claimed for the laboratory below.

To read the dimensionless figure, set $a=\lambda \tau$ and $x=\tau i_{\mathrm{filtered}}/q$, with frequency $\nu =f\tau$ in cycles per unit $t/\tau$. A gate of duration $\tau$ has count mean and variance $a$. The continuously filtered $x$ instead hasThe count and the filtered electric current are different observables. The factor $1/2$ comes from the exponential weighting, not from non-Poisson arrivals. The dimensionless count illustration is a separate choice of rate; it does not assert that the $1\mu \mathrm{A}$ example has only four electrons per $100\mu \mathrm{s}$.

Shree Sowndarya S. V. coauthored research on radical.^[ref]

A radical has one or more unpaired electrons. In a simple atomic orbital or molecular orbital occupancy picture, an unpaired electron occupies a spatial orbital without an opposite-spin partner in that orbital. A dot such as ${\mathrm{H}}^{\bullet }$ marks this electronic property; it does not mean a missing electron or positive electric charge. Free radicals can be neutral or charged. Terminology also has a boundary: metal ions exhibiting paramagnetism are not normally called free radicals just because they have unpaired electrons.

Shuji Nakamura is an electrical engineer whose work helped make efficient blue light-emitting diodes possible using gallium nitride and indium gallium nitride. His work combined improved material growth, activation of p-type semiconductor and the design of an emitting active layer.^[ref]

One crucial result concerned hydrogen binding to magnesium acceptor impurities in gallium nitride. The resulting complexes suppress their electrical activity; thermal treatment can remove that passivation. In an emitting semiconductor heterostructure, injected electrons and holes recombine in an active layer with a smaller band gap than the surrounding material, helping confine the carriers where light is produced. This connects material chemistry with an operating electronic device.^[ref]

Sigma donation transfers electron density from an occupied ligand orbital into a metal acceptor orbital with the appropriate symmetry along the bond axis. CO uses an occupied carbon-centered $5\sigma$ orbital. Backdonation can occur simultaneously.

Attach two statistical flux quanta ${\Phi }_0=h/e$ per electron at density $n_s$. For $B>0$, $B^{\ast }=B-2n_s{\Phi }_0=B(1-2\nu )$ and the signed effective filling is ${\nu }^{\ast }=n_s{\Phi }_0/B^{\ast }=\nu /(1-2\nu )$. Inversion gives $\nu ={\nu }^{\ast }/(2{\nu }^{\ast }+1)$. Integer ${\nu }^{\ast }=p$ gives $p/(2p+1)$, while ${\nu }^{\ast }=-p$ gives $p/(2p-1)$. Using nonnegative effective filling instead requires explicitly tracking the effective-field sign. At half filling the mean effective field vanishes.

A theoretical condensed matter physicist who coauthored a microscopic study of interacting electrons in an antidot-based interferometer using the Aharonov-Bohm effect. The calculation treats the electrostatic potential self-consistently, linking charge rearrangement and Coulomb blockade to conductance oscillations. It shows why an observed magnetic-field period need not be explained by counting magnetic flux through one rigid geometric area.^[ref]

At very high temperatures, photodisintegration and proton, neutron and alpha captures rearrange silicon-group material through networks approaching quasi-statistical equilibrium. The result is an iron-group mixture determined by electron fraction and weak-reaction timescales. Direct silicon-plus-silicon fusion is not the usual mechanism. The approach to maximal nuclear binding energy per nucleon ends sustained hydrostatic fusion power.