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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.

A band gap is an energy interval between adjacent energy bands containing no allowed bulk state.

A band offset is an interface discontinuity in a conduction band or valence band edge.^[ref]

For a chosen two-material example, let the central material A have $E_{c,A}=1$ and $E_{v,A}=0$, and the surrounding material B have $E_{c,B}=1.6$ and $E_{v,B}=-0.4$, in stipulated energy units. Define positive confinement barriers by $\Delta E_c=E_{c,B}-E_{c,A}$ and $\Delta E_v=E_{v,A}-E_{v,B}$. Then $\Delta E_c=0.6$, $\Delta E_v=0.4$, and the band gaps obeyThis identity determines the sum of the band offsets; a band gap difference alone cannot determine their partition. The chosen numbers illustrate the definition and do not specify a measured material pair.

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 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 band gap whose conduction band minimum and valence band maximum occur at the same crystal momentum, allowing an optical transition without a momentum-balancing phonon.

An electron hole is an unoccupied electron quantum state in an otherwise nearly full energy band, often the valence band. “Filled” refers to occupation of the allowed quantum states, not to filling all space with a continuous fluid of electrons. Each state, including its spin label, can hold at most one electron by the Pauli exclusion principle. The almost full energy band and its few missing occupants are therefore simpler to describe as a background plus a few electron holes. The electron hole is a quasiparticle, not a Positron inserted into the crystal.

Removing an electron of electric charge $-e$ changes the background's electric charge by $+e$. Thus an electron hole carries positive electric charge relative to that background. Promoting an electron into the conduction band creates an electron hole without changing the whole crystal's electric charge: $(-e)+(+e)=0$. An unbound pair still consists of two separate charge carriers; only a bound state of their relative motion is an exciton.

The local cartoon explains why a vacancy can move: when a neighboring electron fills it, another vacancy appears where that electron was. The vacancy has moved opposite to that particular transfer of an electron. In an extended Bloch state, use crystal momentum instead of imagining a permanently empty atomic site. For a completely filled energy band the summed electric current vanishes. Omitting one electron with group velocity ${\mathbf{v}}_v$ removes its contribution $-e{\mathbf{v}}_v$, leaving a contribution $+e{\mathbf{v}}_v$. This fixes both the positive electric charge and the velocity convention of the electron hole.

More precisely, near a parabolic valence band maximum, set its energy $E_v(0)$ as reference and define the electron hole wave vector by ${\mathbf{k}}_h=-{\mathbf{k}}_v$. ThenThe occupied electron branch has negative curvature there, while the electron hole branch has positive effective mass $m_h^{\ast }$. The velocity equality compares the electron hole with the missing Bloch state's group velocity; it does not contradict the opposite vacancy motion in a local transfer cartoon. The sign conventions are listed in Phys 460 Lecture 17.

An electron filling an electron hole removes both excitations relative to the filled-band background. Their electric charges cancel, consistent with charge conservation; the remaining electrons are still present. The released energy can leave through photon emission or other channels, including phonons. Formation of an exciton instead retains the excited electron and electron hole as a bound pair; recombination removes the pair. A valence band electron filling a nearby vacancy merely moves the electron hole and does not remove the total vacancy count.

Symmetry of the excitation spectrum under exchange of conduction band electrons and valence band holes, after choosing a central zero of energy. In a two-band model with equal effective masses and equal degeneracy factors, charge neutrality in an intrinsic semiconductor fixes the chemical potential at that central energy. Indeed the Fermi-Dirac distribution obeys $1-f(-E;\mu =0)=f(E;\mu =0)$, so excitation populations are equal at every positive energy.

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]

Isamu Akasaki chose metalorganic vapour-phase epitaxy and sapphire, which tolerated hot Ammonia. Large lattice mismatch hindered film growth. In 1985, Hiroshi Amano and Isamu Akasaki's group developed an aluminium nitride epitaxial buffer layer deposited before hotter gallium nitride growth. The buffer supplies initial growth sites; growing islands join into a continuous film. It improves growth without making the lattices identical. Isamu Akasaki separately credits Shuji Nakamura's 1991 gallium nitride buffer.^[ref]

The 1986 growth paper reports a vertical metalorganic vapour-phase epitaxy reactor, source gases mixed just before delivery to slanted sapphire, and subsequent gallium nitride growth over aluminium nitride. Surface microscopy, X-ray diffraction and photoluminescence tested different aspects of the result. Buffered and unbuffered growth supplied the comparison. Its reported preparation conditions should not be replaced by one universal buffer temperature: the later lecture's account of the first low-temperature trial and the paper's parameter study describe different stages of development.^[ref]

A magnesium acceptor impurity in gallium nitride accepts a valence band electron, leaving a mobile electron hole. Hydrogen passivation of magnesium acceptors in gallium nitride suppresses this activity. Post-growth activation restores existing impurities' electrical activity; ionization of active acceptor impurities supplies mobile electron holes. Adding magnesium alone is insufficient.^[ref]

In 1989, Hiroshi Amano, Masahiro Kito, Kazumasa Hiramatsu and Isamu Akasaki obtained p-type semiconductor conduction in magnesium-doped gallium nitride using low-energy electron beam irradiation. Hiroshi Amano recalls initially resistive samples, an unreliable hot-probe test, then Masahiro Kito's Hall effect confirmation. A junction irradiated in an M-shaped region emitted in that pattern. Treatment, carrier-sign measurement and spatial emission supplied different evidence. Earlier zinc-doped samples brightened under irradiation without becoming p-type semiconductors: brightness alone did not prove the carrier sign.^[ref]

Shuji Nakamura, Takashi Mukai, Masayuki Senoh and Naruhito Iwasa's 1992 thermal-activation paper established another route using annealing in nitrogen. Their companion study compared already conducting films heated in nitrogen with films heated in Ammonia: the latter became highly resistive again. Its hydrogen-complex explanation connected this atmosphere dependence to acceptor impurity passivation. These are thermal treatment and atmosphere comparisons, distinct from the earlier electron beam intervention; neither observation alone images an individual hydrogen complex.^[ref][ref]

Shuji Nakamura's two-flow metalorganic chemical vapor deposition reactor, gallium nitride buffer, thermal activation and improved indium gallium nitride growth enabled bright double heterostructure devices, followed by thinner quantum well devices.^[ref]

The original 1994 paper by Shuji Nakamura, Takashi Mukai and Masayuki Senoh describes a sapphire/gallium nitride-buffer device with zinc-doped indium gallium nitride emission and aluminium gallium nitride confinement. After nitrogen annealing, etching exposed the n-side for a separate contact. At room temperature, varied forward electric currents gave emission spectra and optical-output curves alongside a current-voltage characteristic. At $20\mathrm{mA}$: $1.5\mathrm{mW}$ output, $450\mathrm{nm}$ peak wavelength, $3.6\mathrm{V}$ terminal electric potential difference. The peak stayed nearly fixed across the current series. The paper omits a complete calibrated collection apparatus; comparisons with earlier devices change several preparation details.^[ref]

The local energy difference between the conduction and valence bands along the boundary of the first Brillouin zone. In a nearest-neighbour model it vanishes at the corner valleys and reaches $2t$ at edge midpoints; this angular variation is compatible with a globally gapless material.

Near the zone centre of many cubic semiconductors, the upper valence bands have different curvatures and hence different band effective masses. In the isotropic approximation, the $j=3/2$ states with angular-momentum projection magnitude $3/2$ along the propagation direction form the heavy-hole branch; projection magnitude $1/2$ gives the light-hole branch. A flatter downward electron dispersion corresponds to a larger positive electron hole effective mass. Crystal anisotropy, strain and confinement can mix these branches, so the labels do not imply direction-independent exact masses.

An impurity level is an electronic energy level associated with a dopant or defect in a semiconductor. A shallow donor impurity introduces a level just below the conduction band, and a shallow acceptor impurity introduces one just above the valence band. Under electrostatic band bending, these levels shift with the local band edges in the same material; their occupation is determined relative to the equilibrium chemical potential.

An indirect band gap separates a valence band maximum and a conduction band minimum at different values of crystal momentum. A near-edge radiative transition then usually needs a phonon or another momentum-transfer process in addition to the photon, whose momentum is small on the Brillouin zone scale. A direct band gap has the extrema at the same crystal momentum and more readily supports efficient band-edge light emission. A material can have direct transitions at higher energy while its smallest gap is indirect.

Quantum tunnelling between different energy bands, including transfer between the valence band and conduction band in a tunnel diode.

For nondegenerate conduction bands and valence bands, charge neutrality gives $N_c{e}^{-(E_c-{\mu }_i)/(k_{B}T)}=N_v{e}^{-({\mu }_i-E_v)/(k_{B}T)}$. Taking logarithms yieldsFor single spin-degenerate parabolic extrema this becomes $(E_c+E_v)/2+(3k_{B}T/4)\ln (m_h^{\ast }/m_e^{\ast })$. Valley multiplicities or additional hole bands belong in $N_c,N_v$ and change the logarithm. The intrinsic chemical potential lies exactly at midgap only when the two effective density of states values agree.

For an ideal MOSFET with a nondegenerate p-type semiconductor of acceptor density $N_A$, define ${\varphi }_F=(k_{B}T/e)\ln (N_A/n_i)>0$, where $n_i$ is the intrinsic carrier concentration. A positive surface electric potential ${\psi }_s$ lowers the local conduction band and valence band by $e{\psi }_s$. The surface electron density is $n_s=(n_i^2/N_A)\exp (e{\psi }_s/k_{B}T)$. Equality $n_s=N_A$ gives the conventional onset of strong inversion at ${\psi }_s=2{\varphi }_F$. The earlier crossover $n_s=p_s=n_i$ occurs at ${\psi }_s={\varphi }_F$. Neither condition requires the Fermi level to enter the conduction band.

A typical intrinsic semiconductor has a nearly full valence band ending at $E_v$ and a nearly empty conduction band starting at $E_c$, separated byAt finite temperature, the equilibrium Fermi level lies near the middle of the gap. In the nondegenerate parabolic-band approximation,where $N_c,N_v$ are the two effective density of states values. Equal densities of states put it exactly at midgap; unequal masses or valley multiplicities shift it slightly. The left panel gives the requested energy-level sketch, with doped cases for comparison.

Gallium has three valence electrons, one fewer than silicon, and acts as an acceptor impurity. A neutral acceptor can be described as a negatively charged centre binding an electron hole. Thermal release of these holes gives a p-type semiconductor.

At low temperature, the bound hole can absorb far-IR photons in transitions between acceptor levels. The simplest scalar hydrogenic acceptor state model predictsso one expects a discrete bound-hole absorption series followed by a photoionization continuum. In that idealization, the first lines would be at $3R_A^{\ast }/4$, $8R_A^{\ast }/9$ and $15R_A^{\ast }/16$, with threshold $R_A^{\ast }$.

The hole effective mass is not supplied, so the electron mass $0.2m_e$ cannot be reused to give numerical Ga line positions. In a real valence band, multiple hole bands, anisotropic masses and spin-orbit effects can split and complicate the series; acceptor spectra are generally less accurately described by one scalar hydrogenic ladder.^[ref]