Editing Semiconductor (section)

=== Charge carriers (electrons and holes) ===
{{Main article|Electron hole}}

The partial filling of the states at the bottom of the conduction band can be understood as adding electrons to that band. The electrons do not stay indefinitely (due to the natural thermal [[recombination (physics)|recombination]]) but they can move around for some time. The actual concentration of electrons is typically very dilute, and so (unlike in metals) it is possible to think of the electrons in the conduction band of a semiconductor as a sort of classical [[ideal gas]], where the electrons fly around freely without being subject to the [[Pauli exclusion principle]]. In most semiconductors, the conduction bands have a parabolic [[dispersion relation]], and so these electrons respond to forces (electric field, magnetic field, etc.) much as they would in a vacuum, though with a different [[effective mass (solid-state physics)|effective mass]].<ref name="Kittel"/> Because the electrons behave like an ideal gas, one may also think about conduction in very simplistic terms such as the [[Drude model]], and introduce concepts such as [[electron mobility]].

For partial filling at the top of the valence band, it is helpful to introduce the concept of an [[electron hole]]. Although the electrons in the valence band are always moving around, a completely full valence band is inert, not conducting any current. If an electron is taken out of the valence band, then the trajectory that the electron would normally have taken is now missing its charge. For the purposes of electric current, this combination of the full valence band, minus the electron, can be converted into a picture of a completely empty band containing a positively charged particle that moves in the same way as the electron. Combined with the ''negative'' effective mass of the electrons at the top of the valence band, we arrive at a picture of a positively charged particle that responds to electric and magnetic fields just as a normal positively charged particle would do in a vacuum, again with some positive effective mass.<ref name=" Kittel"/> This particle is called a hole, and the collection of holes in the valence band can again be understood in simple classical terms (as with the electrons in the conduction band).

==== Carrier generation and recombination ====
{{Main article|Carrier generation and recombination}}

When [[ionizing radiation]] strikes a semiconductor, it may excite an electron out of its energy level and consequently leave a hole. This process is known as [[carrier generation and recombination|''electron-hole pair generation'']]. Electron-hole pairs are constantly generated from [[thermal energy]] as well, in the absence of any external energy source.

Electron-hole pairs are also apt to recombine. [[Conservation of energy]] demands that these recombination events, in which an electron loses an amount of [[energy]] larger than the [[band gap]], be accompanied by the emission of thermal energy (in the form of [[phonon]]s) or radiation (in the form of [[photon]]s).

In some states, the generation and recombination of electron–hole pairs are in equipoise. The number of electron-hole pairs in the [[steady state]] at a given temperature is determined by [[quantum statistical mechanics]]. The precise [[quantum mechanics|quantum mechanical]] mechanisms of generation and recombination are governed by the [[conservation of energy]] and [[conservation of momentum]].

As the probability that electrons and holes meet together is proportional to the product of their numbers, the product is in the steady-state nearly constant at a given temperature, providing that there is no significant electric field (which might "flush" carriers of both types, or move them from neighbor regions containing more of them to meet together) or externally driven pair generation. The product is a function of the temperature, as the probability of getting enough thermal energy to produce a pair increases with temperature, being approximately {{nowrap|exp(−''E''<sub>G</sub>/''kT'')}}, where ''k'' is the [[Boltzmann constant]], ''T'' is the absolute temperature and ''E''<sub>G</sub> is bandgap.

The probability of meeting is increased by carrier traps&nbsp;– impurities or dislocations which can trap an electron or hole and hold it until a pair is completed. Such carrier traps are sometimes purposely added to reduce the time needed to reach the steady-state.<ref>{{cite book |last1=Louis Nashelsky |first1=Robert L.Boylestad |title=Electronic Devices and Circuit Theory |year=2006 |publisher=Prentice-Hall of India Private Limited |location=India |isbn=978-81-203-2967-6 |pages=7–10 |edition=9th}}</ref>