380
12 Heterostructures
(a)
(b)
Fig. 12.43 a Radiative lifetime of electron-hole pairs in polar [00.1]-oriented In 0.2 Ga 0.8 N/GaN (circles) and non-polar
[11.0]-oriented GaN/Al 0.2 Ga 0.8 N (squares) quantum wells of varying thickness. Experimental data are shown in symbols.
The solid line is the (scaled) theoretical dependence of the electron-hole overlap for (In,Ga)N/GaN QWs. The dashed
line is guide to the eye. The arrow denotes the recombination time constant in bulk GaN. Adapted from [1215, 1216].
b Low temperature PL peak recombination energy (solid squares) for ZnO/Mg 0.3 Zn 0.7 O quantum wells for various well
widths L z (barrier width L B = 5 nm). Dashed line indicates dependence for internal field of 0.9 MV/cm, horizontal
dashed line indicates recombination energy in ZnO bulk. Carrier lifetime determined from PL (circles), dashed line is
guide to the eye. Adapted from [1214]
Fig. 12.44 Measured (full
circles) and theoretical
(solid lines) confined LO
phonon energies in
70 Ge n / 74 Ge n superlattices
versus the layer thickness
(number of monolayers) n.
The dashed lines represent
a calculation that considers
intermixing at the
interfaces. On the right, the
energies of bulk modes for
isotopically pure 70 Ge and
74 Ge are shown together
with that of an
70 Ge 0.5
70 Ge 0.5 alloy.
Adapted from [1217]
320
310
300
290
280
270
20
0
30
40
10
-1
70 LO 1
70 LO 3
70 LO 5
70 LO 7
74 LO 1
74 LO 3
74 LO 5
70
Ge /
n
n
74 Ge SL
74 Ge
alloy
bulk
70 Ge
12.5 Isotope Superlattices
A special type of heterostructure is the modulation of the isotope content. The first kind of heterostructures made like this were
70 Ge n /
74 Ge n symmetric superlattices [1217]. Figure 12.44 shows phonon
energies determined from Raman spectroscopy for various layer numbers n. The modes are classified by
70 LO m and
74 LO m denoting the material in which the amplitude is maximal and m being the
number of maxima in that medium.
8 Such modes are visualized in Fig. 12.45a for a
69 GaP 16 /
71 GaP 16
superlattice. Theoretical mode energies as a function of the superlattice period are shown in Fig. 12.45b.
8 Only modes with odd m are Raman-active.
12 Heterostructures
(a)
(b)
Fig. 12.43 a Radiative lifetime of electron-hole pairs in polar [00.1]-oriented In 0.2 Ga 0.8 N/GaN (circles) and non-polar
[11.0]-oriented GaN/Al 0.2 Ga 0.8 N (squares) quantum wells of varying thickness. Experimental data are shown in symbols.
The solid line is the (scaled) theoretical dependence of the electron-hole overlap for (In,Ga)N/GaN QWs. The dashed
line is guide to the eye. The arrow denotes the recombination time constant in bulk GaN. Adapted from [1215, 1216].
b Low temperature PL peak recombination energy (solid squares) for ZnO/Mg 0.3 Zn 0.7 O quantum wells for various well
widths L z (barrier width L B = 5 nm). Dashed line indicates dependence for internal field of 0.9 MV/cm, horizontal
dashed line indicates recombination energy in ZnO bulk. Carrier lifetime determined from PL (circles), dashed line is
guide to the eye. Adapted from [1214]
Fig. 12.44 Measured (full
circles) and theoretical
(solid lines) confined LO
phonon energies in
70 Ge n / 74 Ge n superlattices
versus the layer thickness
(number of monolayers) n.
The dashed lines represent
a calculation that considers
intermixing at the
interfaces. On the right, the
energies of bulk modes for
isotopically pure 70 Ge and
74 Ge are shown together
with that of an
70 Ge 0.5
70 Ge 0.5 alloy.
Adapted from [1217]
320
310
300
290
280
270
20
0
30
40
10
-1
70 LO 1
70 LO 3
70 LO 5
70 LO 7
74 LO 1
74 LO 3
74 LO 5
70
Ge /
n
n
74 Ge SL
74 Ge
alloy
bulk
70 Ge
12.5 Isotope Superlattices
A special type of heterostructure is the modulation of the isotope content. The first kind of heterostructures made like this were
70 Ge n /
74 Ge n symmetric superlattices [1217]. Figure 12.44 shows phonon
energies determined from Raman spectroscopy for various layer numbers n. The modes are classified by
70 LO m and
74 LO m denoting the material in which the amplitude is maximal and m being the
number of maxima in that medium.
8 Such modes are visualized in Fig. 12.45a for a
69 GaP 16 /
71 GaP 16
superlattice. Theoretical mode energies as a function of the superlattice period are shown in Fig. 12.45b.
8 Only modes with odd m are Raman-active.