Chapter 10
Recombination
Les hommes discutent, la nature agit.
Men argue, nature acts.
Voltaire
Abstract The various mechanisms and statistics of carrier recombination in semiconductors including band-band, excitonic, band-impurity (Shockley-Read-Hall kinetics) and Auger recombination
are explained. Also recombination at extended defects and surfaces is treated. Using the diffusionrecombination theory, the one-dimensional carrier profiles for typical situations in experiments and
devices are derived.
10.1 Introduction
In thermodynamic nonequilibrium excess charges can be present in the semiconductor. They can be
created by carrier injection through contacts, an electron beam or the absorption of light with wavelength
smaller than the band gap. After the external excitation is turned off, the semiconductor will return to the
equilibrium state. The relaxation of carriers into energetically lower states (and energy release) is called
recombination. The term stems from the electron recombining with the hole created after absorption
of a photon. However, there are other recombination mechanisms. A dedicated textbook is [937].
In the simplest picture an excitation generates carriers with a rate G (carriers per unit volume and
unit time). In the steady state (after all turn-on effects) a constant excess charge n carrier density
is present. Then the generation exactly compensates the recombination processes. The principle of
detailed balance even says that each microscopic process is balanced by its reverse process. If the time
constant of the latter is τ , n is given by n = G τ . This follows from the steady-state solution ˙
n = 0 of
dn
dt
= G −
n
τ
.
(10.1)
In the literature two limiting cases have been discussed, the relaxation and the lifetime semiconductor,
depending on the relation of two time constants. The one time constant τ 0 is the relaxation time constant
due to recombination as discussed in the following. The smaller τ 0 is, the faster excited electrons
and holes recombine and ‘disappear’. Fast lifetimes are typically present in direct semiconductors
(compared to indirect ones), semiconductors with high defect density and amorphous semiconductors.
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_10
303
Recombination
Les hommes discutent, la nature agit.
Men argue, nature acts.
Voltaire
Abstract The various mechanisms and statistics of carrier recombination in semiconductors including band-band, excitonic, band-impurity (Shockley-Read-Hall kinetics) and Auger recombination
are explained. Also recombination at extended defects and surfaces is treated. Using the diffusionrecombination theory, the one-dimensional carrier profiles for typical situations in experiments and
devices are derived.
10.1 Introduction
In thermodynamic nonequilibrium excess charges can be present in the semiconductor. They can be
created by carrier injection through contacts, an electron beam or the absorption of light with wavelength
smaller than the band gap. After the external excitation is turned off, the semiconductor will return to the
equilibrium state. The relaxation of carriers into energetically lower states (and energy release) is called
recombination. The term stems from the electron recombining with the hole created after absorption
of a photon. However, there are other recombination mechanisms. A dedicated textbook is [937].
In the simplest picture an excitation generates carriers with a rate G (carriers per unit volume and
unit time). In the steady state (after all turn-on effects) a constant excess charge n carrier density
is present. Then the generation exactly compensates the recombination processes. The principle of
detailed balance even says that each microscopic process is balanced by its reverse process. If the time
constant of the latter is τ , n is given by n = G τ . This follows from the steady-state solution ˙
n = 0 of
dn
dt
= G −
n
τ
.
(10.1)
In the literature two limiting cases have been discussed, the relaxation and the lifetime semiconductor,
depending on the relation of two time constants. The one time constant τ 0 is the relaxation time constant
due to recombination as discussed in the following. The smaller τ 0 is, the faster excited electrons
and holes recombine and ‘disappear’. Fast lifetimes are typically present in direct semiconductors
(compared to indirect ones), semiconductors with high defect density and amorphous semiconductors.
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_10
303