66
3 Crystals
(a)
(b)
Fig. 3.44 a Near-neighbor distance (
√
3 a 0 /4) of In x Ga 1−x As as measured by standard X-ray diffraction (Bragg reflection, solid squares) and VCA approximation (dash-dotted line). Near-neighbor Ga–As and In–As distances as determined
by EXAFS (extended X-ray absorption fine structure, solid squares). Dashed lines are guides to the eye. Data from [255]. b
Second-neighbor distances for In x Ga 1−x As as determined from EXAFS, top: anion–anion distance (for As–As), bottom:
cation–cation distance (for In–In, Ga–Ga, and Ga–In). Solid lines in both plots are the VCA (a 0 /
√
2). Data from [256]
Fig. 3.45 Theoretical
values (T = 0 K) for the
cell-internal parameter u as
a function of the
composition for group-III
nitride alloys. The solid
lines are quadratic curves
(bowing parameter b is
shown) through the points
for x = 0, 0.5, and 1.0.
Data from [257]
and BC, is indeed fulfilled
a 0 (A x B 1−x C) = a 0 (BC) + x [a 0 (AC) − a 0 (BC)] .
(3.27)
In reality, the bond length of the AC and BC bonds changes rather little (Fig. 3.44a) such that the
atoms in the alloy suffer a displacement from their average position and the lattice is deformed on
the nanoscopic scale. In a lattice of the type In x Ga 1−x As the anions suffer the largest displacement
since their position adjusts to the local cation environment. For In x Ga 1−x As a bimodal distribution,
according to the As–Ga–As and As–In–As configurations, is observed (Fig. 3.44b). The cation–cation
second-neighbor distances are fairly close to the VCA.
While the average lattice parameter in alloys changes linearly with composition, the cell-internal
parameter u (for wurtzite structures, see Sect. 3.4.5) exhibits a nonlinear behavior as shown in Fig. 3.45.
3 Crystals
(a)
(b)
Fig. 3.44 a Near-neighbor distance (
√
3 a 0 /4) of In x Ga 1−x As as measured by standard X-ray diffraction (Bragg reflection, solid squares) and VCA approximation (dash-dotted line). Near-neighbor Ga–As and In–As distances as determined
by EXAFS (extended X-ray absorption fine structure, solid squares). Dashed lines are guides to the eye. Data from [255]. b
Second-neighbor distances for In x Ga 1−x As as determined from EXAFS, top: anion–anion distance (for As–As), bottom:
cation–cation distance (for In–In, Ga–Ga, and Ga–In). Solid lines in both plots are the VCA (a 0 /
√
2). Data from [256]
Fig. 3.45 Theoretical
values (T = 0 K) for the
cell-internal parameter u as
a function of the
composition for group-III
nitride alloys. The solid
lines are quadratic curves
(bowing parameter b is
shown) through the points
for x = 0, 0.5, and 1.0.
Data from [257]
and BC, is indeed fulfilled
a 0 (A x B 1−x C) = a 0 (BC) + x [a 0 (AC) − a 0 (BC)] .
(3.27)
In reality, the bond length of the AC and BC bonds changes rather little (Fig. 3.44a) such that the
atoms in the alloy suffer a displacement from their average position and the lattice is deformed on
the nanoscopic scale. In a lattice of the type In x Ga 1−x As the anions suffer the largest displacement
since their position adjusts to the local cation environment. For In x Ga 1−x As a bimodal distribution,
according to the As–Ga–As and As–In–As configurations, is observed (Fig. 3.44b). The cation–cation
second-neighbor distances are fairly close to the VCA.
While the average lattice parameter in alloys changes linearly with composition, the cell-internal
parameter u (for wurtzite structures, see Sect. 3.4.5) exhibits a nonlinear behavior as shown in Fig. 3.45.