318
10 Recombination
Fig. 10.18 Schematic
representation of 1 LO
exciton scattering of an
exciton at K = 0 to an
intermediate state with
K ≈ 0 and subsequent
radiative decay.
represents the phonon
energy and E 1 the energy
of the emitted photon
K
n=1
n=2
n=3
h ph
E 1
E
continuum
disorder potential (arrow in Fig. 10.17b). At low temperatures excitons are frozen in local potential
minima and have a non-thermal (non-Boltzmann) population. With increasing temperature they can
overcome energy barriers and thermalize, leading to a shift of the recombination peak to lower energies.
Further increase of temperature populates higher levels and leads to a shift of the recombination peak to
higher energies. Superimposed is the red-shift due to the band gap shrinkage. This so-called “S”-shape
effect of E(T ) is discussed in Sect. 12.4 in detail with regard to exciton localization in a quantum well
disorder potential.
For x = 0.06 only a single photoluminescence peak is observed for the alloy (σ = 8.5 meV). The
(D
0 ,X) peak is the dominant for the Mg x Zn 1−x O alloys at low temperatures even in the presence of
large alloy broadening (Fig. 10.16(b)). The peak changes its nature from (D
0 ,X) at low temperatures
to X A at room temperature. In between, first exciton thermalization (red-shift) in the disorder potential
and subsequently exciton ionization from the donors (blue-shift, arrow in Fig. 10.17c) are observed
[977]. Such exciton ionization from impurities has also been observed for (Al,Ga)N:Si [628, 989].
10.4 Phonon Replica
The momentum selection rule for free-exciton recombination allows only excitons with K ≈ 0 (for
K, cf. (9.49)) to recombine. The fine structure of this recombination is connected to polariton effects
(cf. Sect. 9.7.8). Excitons with large K can recombine if a phonon or several phonons are involved
[990] that provide the necessary momentum q = K 1 − K 2 , with K 1 (K 2 ) being the wavevector of
the initial (intermediate) exciton state (Fig. 10.18). A so-called zero-phonon line at energy E 0 is then
accompanied by phonon replica below E 0 at integer multiples (at low temperature) of the (LO) phonon
energy ph
E n = E 0 − n ph .
(10.31)
Phonon replicas have been observed in many polar semiconductors such as CdS [991] and ZnSe [992].
A sequence of such phonon replica, as observed in GaN [993], is depicted in Fig. 10.19a.
The lineshape of the n-th phonon-assisted line is proportional to the exciton population at a given
excess energy, which is proportional to the density of states and the Boltzmann distribution function [994]
I n (E ex ) ∝
E ex exp
−
E ex
kT
w n (E ex ) .
(10.32)
10 Recombination
Fig. 10.18 Schematic
representation of 1 LO
exciton scattering of an
exciton at K = 0 to an
intermediate state with
K ≈ 0 and subsequent
radiative decay.
represents the phonon
energy and E 1 the energy
of the emitted photon
K
n=1
n=2
n=3
h ph
E 1
E
continuum
disorder potential (arrow in Fig. 10.17b). At low temperatures excitons are frozen in local potential
minima and have a non-thermal (non-Boltzmann) population. With increasing temperature they can
overcome energy barriers and thermalize, leading to a shift of the recombination peak to lower energies.
Further increase of temperature populates higher levels and leads to a shift of the recombination peak to
higher energies. Superimposed is the red-shift due to the band gap shrinkage. This so-called “S”-shape
effect of E(T ) is discussed in Sect. 12.4 in detail with regard to exciton localization in a quantum well
disorder potential.
For x = 0.06 only a single photoluminescence peak is observed for the alloy (σ = 8.5 meV). The
(D
0 ,X) peak is the dominant for the Mg x Zn 1−x O alloys at low temperatures even in the presence of
large alloy broadening (Fig. 10.16(b)). The peak changes its nature from (D
0 ,X) at low temperatures
to X A at room temperature. In between, first exciton thermalization (red-shift) in the disorder potential
and subsequently exciton ionization from the donors (blue-shift, arrow in Fig. 10.17c) are observed
[977]. Such exciton ionization from impurities has also been observed for (Al,Ga)N:Si [628, 989].
10.4 Phonon Replica
The momentum selection rule for free-exciton recombination allows only excitons with K ≈ 0 (for
K, cf. (9.49)) to recombine. The fine structure of this recombination is connected to polariton effects
(cf. Sect. 9.7.8). Excitons with large K can recombine if a phonon or several phonons are involved
[990] that provide the necessary momentum q = K 1 − K 2 , with K 1 (K 2 ) being the wavevector of
the initial (intermediate) exciton state (Fig. 10.18). A so-called zero-phonon line at energy E 0 is then
accompanied by phonon replica below E 0 at integer multiples (at low temperature) of the (LO) phonon
energy ph
E n = E 0 − n ph .
(10.31)
Phonon replicas have been observed in many polar semiconductors such as CdS [991] and ZnSe [992].
A sequence of such phonon replica, as observed in GaN [993], is depicted in Fig. 10.19a.
The lineshape of the n-th phonon-assisted line is proportional to the exciton population at a given
excess energy, which is proportional to the density of states and the Boltzmann distribution function [994]
I n (E ex ) ∝
E ex exp
−
E ex
kT
w n (E ex ) .
(10.32)