9.7 Band–Band Transitions
281
(a)
Energy
E X
T
E X
L
k
LPB
UPB
(b)
Fig. 9.25 a Schematic dispersion of exciton polaritons. The lower polariton branch (‘LPB’) is at small k photon-like,
at large k exciton-like. The upper branch (‘UPB’) is exciton-like at small k and photon-like at larger k. The limit of the
UPB for k → 0 is the energy of the longitudinal exciton. The dashed lines represent the pure exciton dispersions. b
Theoretical effect of spatial dispersion on the reflectance at the fundamental exciton resonance at normal incidence for
ZnSe material parameters ( T =2.8 eV, β = 1.0 × 10 −3 and a background dielectric constant of b = 8.1, damping was
set to = 10 −5 ω T ). The arrow denotes the position of ω L . The solid (dashed) line is with (without) spatial dispersion
for ˆ
D = 0.6 × 10 −5 ( ˆ
D = 0). Data from [875]
Energy
(b)
(c)
(a)
0
1
2
3
4
5
0
1
2
3
k
0
1
2
3
4
5
0
1
2
3
k
0
1
2
3
4
5
0
1
2
3
k
Fig. 9.26 Schematic polariton dispersion for a two-exciton resonance (curvature of exciton dispersion greatly exaggerated, ˆ
D = 10 −2 ) at ω T,1 = 1 and ω T,2 = 1.5 for three different oscillator strengths a f = 10 −3 , b f = 10 −2 , c
f = 10 −1 . The dashed lines in c represent the pure exciton dispersions
an exciton free layer at the semiconductor surface, additional boundary conditions and damping need
to be considered [881, 882]. The polariton dispersions of ZnO and GaN are shown in Fig. 9.27.
9.7.9 Bound-Exciton Absorption
Excitons can localize at impurities or inhomogeneities. Such excitons are called bound excitons. Here,
the absorption due to such complexes is discussed. The recombination is discussed in Sect. 10.3.2.