Electron Hole · aiwiki.page

An electron hole, usually called a hole, is the absence of an electron from an otherwise filled or nearly filled set of electronic states. In semiconductors, holes most commonly occur in the valence band and behave as mobile quasiparticles with positive electric charge. Describing the unoccupied states as holes makes it possible to represent the collective behavior of many remaining electrons in terms of a relatively small number of positive charge carriers. A hole is not an independent elementary particle or a physical gap in the crystal. (fab.cba.mit.edu)

Physical meaning

In a crystalline solid, electronic states form allowed energy bands. The electronic band structure determines which states electrons can occupy and how they respond to external forces. In the ideal zero-temperature picture of an ordinary semiconductor, the valence band is filled and the conduction band is empty, with a band gap between them. Exciting an electron from the valence band into the conduction band leaves an unoccupied valence-band state: a hole. (ocw.mit.edu)

A completely filled band carries no net ordinary conduction current because the current contributions of its occupied states cancel. Removing one electron removes its contribution to that cancellation. Relative to the filled-band reference, the resulting change can be described as the contribution of a positive carrier with charge $+e$ , where $e$ is the elementary charge. This is why an absence of a negatively charged electron can act electrically like a positive particle. (fab.cba.mit.edu)

A local illustration imagines an electron filling an empty bond and leaving another bond unoccupied; the vacancy appears to move opposite to the electron. This is a useful analogy, but in a clean crystal the relevant electronic states extend throughout the lattice. Hole motion is therefore fundamentally a description of changing occupations of quantum states, not necessarily a sequence of localized jumps between atoms. (ocw.mit.edu)

Energy and effective mass

A hole has an energy measured relative to a chosen filled-band reference. For a missing electron with valence-band energy $E_v(\mathbf{k})$ , its excitation energy relative to the valence-band maximum $E_{v,\max}$ can be written as

E_h=E_{v,\max}-E_v(\mathbf{k}).

Thus, the top of the electron valence band corresponds to the bottom of the hole energy dispersion. Holes near that maximum can consequently behave like particles with positive effective mass, even though the underlying electron band has downward curvature. (ocw.mit.edu)

For a simple one-dimensional parabolic band near its maximum,

E_v(k)\approx E_{v,\max} -\frac{\hbar^2(k-k_0)^2}{2m_h^*},

where $m_h^*$ is the hole effective mass and $\hbar$ is the reduced Planck constant. Equivalently,

\frac{1}{m_h^*} =-\frac{1}{\hbar^2}\frac{d^2E_v}{dk^2}.

Effective mass describes the response to forces within the crystal; it is not the rest mass of a new elementary particle. In three dimensions it can depend on direction and may require a tensor rather than a single scalar value. (archive.nptel.ac.in)

Many common semiconductors have heavy-hole and light-hole valence-band branches. These names distinguish different band curvatures and effective masses, not different charges. Their behavior becomes more complicated in confined structures, where confinement can split and mix the branches. Consequently, a single hole mass is an approximation whose usefulness depends on the material and experimental conditions. (web.mit.edu)

Formation and carrier populations

Holes can be produced by thermal excitation, absorption of a sufficiently energetic photon, or electrical processes that generate or inject carriers. An interband excitation produces both a conduction-band electron and a valence-band hole—an electron–hole pair. Generating such a pair does not itself change the material’s total electric charge. (archive.nptel.ac.in)

Semiconductor doping provides another way to control the hole population. An acceptor impurity can accept an electron from the valence band, leaving a mobile hole while becoming negatively charged. Boron is a common acceptor in silicon. In p-type material, holes are the majority carriers; in n-type material, they are minority carriers. The label “p-type” does not mean that the semiconductor as a whole must have a net positive charge. (fab.cba.mit.edu)

Transport and electric current

Holes contribute to electric current through both drift and diffusion. Drift is driven by an electric field, whereas diffusion results from a spatial variation in carrier concentration. In the low-field drift–diffusion approximation,

\mathbf{J}_p =e p\mu_p\mathbf{E}-eD_p\nabla p,

where $p$ is the hole number density, $\mu_p$ the hole mobility, $D_p$ the diffusion coefficient, and $\mathbf{J}_p$ the hole current density. Positive hole drift is along the electric field; hole diffusion is toward lower hole concentration. (ocw.mit.edu)

Mobility is not determined by effective mass alone. Scattering by lattice vibrations, impurities, and other carriers also affects transport. The simple drift–diffusion description must therefore be modified when fields are strong or when confinement and other quantum effects become important. (archive.nptel.ac.in)

Recombination and excitons

A conduction-band electron can occupy an empty valence-band state, eliminating both the conduction electron and the hole as excitations. This process is called electron–hole recombination. The released energy may appear as light or be transferred through nonradiative processes. Recombination mechanisms include radiative transitions, defect-assisted transitions, and Auger processes, in which energy is transferred to another carrier. (archive.nptel.ac.in)

An electron and a hole can also form a bound state called an exciton. Because their charges cancel, the pair is electrically neutral overall. “Electron–hole pair” does not necessarily mean “exciton”: the electron and hole may instead be unbound carriers. (archive.nptel.ac.in)

Role in semiconductor devices

The generation, motion, and recombination of holes are central to semiconductor electronics and optoelectronics:

P–N junctions: electron and hole transport, together with recombination, governs junction behavior.
Light-emitting devices: radiative electron–hole recombination produces light in light-emitting diodes and semiconductor lasers.
Solar cells: absorbed light produces carriers whose collection competes with recombination; mobility and carrier lifetime influence device performance.
Confined semiconductor structures: holes can be collected in thin layers and confined to effectively two-dimensional systems. (archive.nptel.ac.in)

Distinction from a positron

A hole must not be confused with a positron. A positron is the electron’s antiparticle; a semiconductor hole is a missing electronic occupation defined relative to a material’s filled-band reference. Both have positive charge, but a hole’s dispersion and effective mass are properties of its host crystal. Filling a hole is a transition between material electronic states, not electron–positron annihilation. (nobelprize.org)

References

Semiconductor Materials and Devicesfab.cba.mit.edu
Complete 2004 Lecture Notesocw.mit.edu
Lecture 5: Quantum Mechanics for Heterostructuresocw.mit.edu
Physics of Semiconductor Devices: Electrons and Holesarchive.nptel.ac.in
Semiconductor Physics: Effective Massarchive.nptel.ac.in
Semiconductor Physics Lecture Notesweb.mit.edu
Quantum Condensed Matter Physics Supplementary Notessp.phy.cam.ac.uk
Semiconductor Physics: Electron–Hole Pair Generation and Recombinationarchive.nptel.ac.in
Introduction to Low-Dimensional Systemssp.phy.cam.ac.uk
012 Microelectronic Devices and Circuits, Lecture 3ocw.mit.edu
Lecture 18: Motion and Recombination of Electrons and Holesethz.ch