Electron-Hole Liquid

a condensed state of a nonequilibrium electron-hole plasma in a semiconductor (seePLASMA, SOLID-STATE). An electron-hole liquid is formed when the density of the electrons and holes exceeds some critical value that is a function of temperature. The electrons and holes may be free or may be bound together to form excitons.

The critical density n_cr is easily attained by, for example, injecting carriers into a semiconductor or exposing a semiconductor to light. When n_cr is attained, the system of nonequilibrium charge carriers undergoes a phase transition similar to a gas-liquid transition. As a result, the system separates into the following two phases: droplets of a relatively dense electron-hole liquid and free carriers; the droplets are surrounded by an exciton gas. When the phase transition occurs, the density and crystal structure of the semiconductor are virtually unaffected.

In contrast to ordinary liquids, an electron-hole liquid contains no heavy particles, that is, no ions or atomic nuclei. Therefore, an electron-hole liquid has pronounced quantum properties. Such a liquid cannot be solidified but remains a liquid down to the lowest temperatures (seeQUANTUM FLUID). It cannot be a molecular liquid; that is, it cannot consist of excitons or of exciton molecules. Instead, an electron-hole liquid is composed of quasi-free electrons and holes; that is, it is similar to a liquid metal.

Coulomb interactions bind the particles in an electron-hole liquid. The interactions are weakened by the permittivity of the crystal. Therefore, in comparison with the case of ordinary liquids, the binding energies ℰ₀ and densities n₀ of the particles in an electron-hole liquid are very low; ℰ₀ ~ 10²–10^–1 electron volt, and n₀ ~ 10^–7–10^–19 cm^–3. By order of magnitude, the range of temperatures Tat which an electron-hole liquid may exist is given by the relation T ≤ (0.1 ℰ₀/k) ~ 10–100°K, where k is the Boltzmann constant.

The diameter of an electron-hole droplet is usually ~ 1–10 micrometers. However, droplets with a diameter of up to 1 mm have been observed. The droplets may be accelerated to speeds of up to the speed of sound in a crystal. In other words, electron-hole droplets are mobile regions of high conductivity (as in a metal) in a crystal that, at low T, is virtually nonconducting.

An electron-hole liquid may be regarded as “blobs” of excitation energy introduced into a crystal. When electrons and holes recombine, some of the energy is released in the form of electromagnetic radiation—that is, as a result of radiative transitions—so that the liquid is a strong source of light.

Electron-hole liquids have been most comprehensively studied in Ge and Si. However, evidence for the existence of such liquids has also been found in other semiconductors.