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A semiconductor solid solution whose composition changes its band gap.

A materials scientist who studied semiconductor growth at Santa Barbara.^[ref]

Spatial variation of the valence band and conduction band edges associated with a varying electric potential. Near a semiconductor boundary it can deplete mobile charge carriers or create a semiconductor inversion layer.

When $E-\mu \gg kT$, the unit term in the denominator of the Fermi-Dirac distribution is negligible. The resulting exponentially small occupation is the Boltzmann approximation. It justifies the usual nondegenerate semiconductor carrier formulas; it fails near strongly occupied band states.

Introducing excess mobile charge carriers into a semiconductor, for example through a contact under biasing. Their subsequent motion and electron-hole recombination can change the electrical conductivity and an output electric current.

A charge-coupled device stores photoelectrons in potential wells and transfers the charge through clocked stages to an output amplifier. The transfer differs from independently addressed pixels in a hybrid infrared detector.

In an imaging charge-coupled device, absorbed photons produce mobile charge carriers in a semiconductor; collection stores an electric charge packet associated with each optical detector pixel. Closely spaced MOS capacitors allow applied electric potential differences to move the packet from site to site. Willard Sterling Boyle and George Elwood Smith described storage, transfer and detection as distinct operations, including imaging as one application.^[ref]

The useful architectural trick is that many optical detector pixels can send their electric charge to a shared output electronic amplifier. This makes repeatable conversion possible but makes fidelity depend on every transfer along the route. An active-pixel sensor made with CMOS technology instead uses circuitry at pixels to convert or buffer their signal and select it for readout; independent pixel addressing does not require transporting each packet through the whole image. This compares readout architectures, not whether either technology can use a photodiode.^[ref]

For a nondegenerate semiconductor with donor density $N_D$, no acceptors, and donor energy $E_D=E_c-E_b$, an occupied donor has two electron spin states while an empty donor has one. Its ionized fraction is therefore $N_D^{+}/N_D=[1+2e^{(E_F-E_D)/(k_{B}T)}{]}^{-1}$. The conduction-band relation $n=N_c{e}^{(E_F-E_c)/(k_{B}T)}$ gives $N_D^{+}=N_D/[1+(2n/N_c)e^{E_b/(k_{B}T)}]$. Combining charge neutrality, $n-p=N_D^{+}$, with the semiconductor mass-action law, $np=n_i^2$, proves the displayed equation.

Its left side increases strictly for $n>0$ and its right side decreases, so there is one physical solution, with $n\ge n_i$. In the freeze-out regime, holes are negligible and solving the quadratic gives $n=2N_D/[1+\sqrt{1+(8N_D/N_c)e^{E_b/(k_{B}T)}}]$. Strong dopant freeze-out reduces this to $n\simeq \sqrt{N_D{N}_c/2}{e}^{-E_b/(2k_{B}T)}$. An extrinsic plateau requires $(2N_D/N_c)e^{E_b/(k_{B}T)}\ll 1$ and $n_i\ll N_D$, not simply $k_{B}T\gg E_b$.

A compensated semiconductor contains both donor impurities and acceptor impurities. In a nondegenerate equilibrium model with both species fully ionized, charge neutrality gives $n-p=\Delta =N_D-N_A$, while the semiconductor semiconductor mass-action law gives $np=n_i^2$. Solving yieldsFor $\Delta >0$ and $n_i\ll \Delta$, $n\simeq \Delta$ and $p\simeq n_i^2/\Delta$. Numerically the minority concentration is better obtained as $n_i^2/n$ than by subtracting nearly equal numbers. If dopants are only partly ionized, replace $N_D,N_A$ in charge neutrality by their ionized concentrations and determine the chemical potential self-consistently.

The initially empty energy band above the band gap in the simple semiconductor description. Excited electrons in it can carry electric current; they can also bind to valence band electron holes as excitons.

A semiconductor used in the exciton absorption experiment in copper(I) oxide.

Before using a Maxwell–Boltzmann chemical-potential formula in a doped semiconductor, compare the carrier density to its conduction-band effective density of states. When n is much larger than $N_c$, a nondegenerate logarithmic estimate is inconsistent. Use Fermi–Dirac statistics or a controlled degenerate expansion instead. A small effective mass strongly reduces $N_c$ and raises the Fermi energy at fixed density, so even an otherwise familiar donor concentration can put the chemical potential inside the conduction band.

A semiconductor whose mobile charge carrier population requires Fermi-Dirac statistics rather than a dilute Maxwell-Boltzmann distribution. In a strongly degenerate n-type semiconductor, the Fermi level lies inside the conduction band; in a strongly degenerate p-type semiconductor, it lies inside the valence band. The occupied and empty quantum states on opposite sides of a tunnel diode can then overlap in energy. Heavy semiconductor doping both changes these occupations and narrows the depletion region; a narrow barrier and accessible final quantum states serve different roles.

A double heterostructure sandwiches one semiconductor between two layers of another, for example gallium arsenide between aluminium gallium arsenide layers. Suitable band offsets confine injected charge carriers centrally.^[ref]

A doped semiconductor at frequencies far below its bound-electron resonances can haveFor a weakly absorbing nonmagnetic half-space adjacent to vacuum, the normal-incidence optical reflectance is minimized near refractive-index matching, ${ϵ}_r\simeq 1$. When ${ϵ}_b>1$ and ${\gamma }_c$ is small this gives ${\omega }_{\min }\simeq {\omega }_{pc}/\sqrt{{ϵ}_b-1}$. The zero of the real part of ${ϵ}_r$, near ${\omega }_{pc}/\sqrt{{ϵ}_b}$, is a distinct frequency. Increasing the carrier density shifts the minimum to shorter wavelength if the carrier effective mass and background response remain fixed. With appreciable loss, the minimum must be found from the full complex Fresnel equations.

Official University of Illinois semiconductor-device lecture slides. Slide 26 distinguishes carrier-counting, conductivity and cyclotron effective masses, and gives the multiple-valley density-of-states effective mass for silicon. This is useful when interpreting a supplied scalar mass in an elementary semiconductor model.

The effective density of states of a parabolic semiconductor band is its density of states integrated against a thermal Boltzmann factor measured from its edge. For one spin-degenerate valley,These quantities have units of number per volume, unlike the energy-resolved density of states. In a nondegenerate semiconductor, $n=N_c{e}^{-(E_c-\mu )/(k_{B}T)}$ and $p=N_v{e}^{-(\mu -E_v)/(k_{B}T)}$; multiple equivalent valleys add their contributions.

An electrical conductor supports mobile charge carriers and hence an electric current under a field. In a band description, a partially filled band or available overlapping bands supply nearby accessible states. The contrast with a band insulator depends on band filling as well as spectral gaps; semiconductors provide carriers through thermal excitation or doping.

An electron-hole pair consists of an excited electron and the unoccupied valence state described as an electron hole. Promoting a valence electron across a semiconductor band gap creates such a pair without changing the total electric charge. The carriers can separate under an electric field, or undergo electron-hole recombination. A bound electron-hole pair is an exciton; an arbitrary unbound pair need not be an exciton.

A semiconductor state is approximated by a slowly varying envelope multiplying a cell-periodic Bloch function from a selected band. effective masses govern the envelope equation. Interband optical matrix elements then factor approximately into a cell-scale momentum matrix element and an envelope overlap; abrupt interfaces, band mixing and nonparabolicity limit the separation.

An exciton is a bound state of an electron and an electron hole. Their opposite electric charges attract through the Coulomb potential, producing a neutral quasiparticle with internal relative motion and motion of its center of mass. In a semiconductor, promoting an electron from the valence band into the conduction band leaves an electron hole; the pair can occupy either an exciton bound state or an unbound scattering state. Merely creating the two charge carriers does not establish binding. A neutral exciton can transport excitation energy without transporting net electric charge. Coupling this material excitation strongly to a photon can form a polariton.

The striking optical consequence is that an exciton optical transition can absorb a photon with less energy than the threshold for creating unbound electrons and electron holes. The difference is the exciton binding energy, not an extra one-electron energy band inside the band gap. The Wannier-Mott exciton supplies a useful large-radius model; the Frenkel exciton describes the opposite, tightly localized limit.^[ref]