170
6 Band Structure
Fig. 6.47 Band gap of
Cd x Hg 1−x Te for various
alloy compositions and
temperatures. On the right,
the schematic band
structure of (Hg,Cd)Te with
positive, zero and negative
band gap is shown.
Adapted from [531],
reprinted under a Creative
Commons Attribution (CC
BY 4.0) licence
6.12 Strain Effects on the Band Structure
A mechanical strain (or equivalently stress) causes changes in the bond lengths. Accordingly, the band
structure is affected. These effects have been exhaustively treated in [533, 534]. For small strain,
typically 0.01 the shift of the band edges is linear with the strain, for large strain it becomes
nonlinear [535]. Often homogeneous strain is assumed, the effect of inhomogeneous strain is discussed
in [536].
6.12.1 Strain Effect on Band Edges
In a direct-gap zincblende material the position of the conduction-band edge is only affected by the
hydrostatic component of the strain
E C = E
0
C + a c
xx + yy + zz
= E
0
C + a c Tr(() ,
(6.55)
where a c < 0 is the conduction-band hydrostatic deformation potential and E
0
C is the conduction-band
edge of the unstrained material. Similarly, the valence-band edge is
E V = E
0
V + a v Tr(() ,
(6.56)
where a v > 0 is the valence-band hydrostatic deformation potential. Therefore the band gap
increases by
g = a Tr(() = a
xx + yy + zz
,
(6.57)
with a = a C − a V . Such linear behavior upon hydrostatic pressure has been found for many semiconductors and is shown in Fig. 6.48a for Ga 0.92 In 0.08 As. The anomaly for N-doping is discussed below
in Sect. 6.12.3. In Fig.6.49 the dependence of the direct and indirect gaps of GaAs is shown. The
dependence of the direct gap on pressure is non-linear, that on the density is linear [537].
Biaxial and shear strains affect the valence bands and lead to shifts and splitting of the heavy and
light holes at the -point:
E v,hh/lh = E
0
v ± E
(6.58a)
6 Band Structure
Fig. 6.47 Band gap of
Cd x Hg 1−x Te for various
alloy compositions and
temperatures. On the right,
the schematic band
structure of (Hg,Cd)Te with
positive, zero and negative
band gap is shown.
Adapted from [531],
reprinted under a Creative
Commons Attribution (CC
BY 4.0) licence
6.12 Strain Effects on the Band Structure
A mechanical strain (or equivalently stress) causes changes in the bond lengths. Accordingly, the band
structure is affected. These effects have been exhaustively treated in [533, 534]. For small strain,
typically 0.01 the shift of the band edges is linear with the strain, for large strain it becomes
nonlinear [535]. Often homogeneous strain is assumed, the effect of inhomogeneous strain is discussed
in [536].
6.12.1 Strain Effect on Band Edges
In a direct-gap zincblende material the position of the conduction-band edge is only affected by the
hydrostatic component of the strain
E C = E
0
C + a c
xx + yy + zz
= E
0
C + a c Tr(() ,
(6.55)
where a c < 0 is the conduction-band hydrostatic deformation potential and E
0
C is the conduction-band
edge of the unstrained material. Similarly, the valence-band edge is
E V = E
0
V + a v Tr(() ,
(6.56)
where a v > 0 is the valence-band hydrostatic deformation potential. Therefore the band gap
increases by
g = a Tr(() = a
xx + yy + zz
,
(6.57)
with a = a C − a V . Such linear behavior upon hydrostatic pressure has been found for many semiconductors and is shown in Fig. 6.48a for Ga 0.92 In 0.08 As. The anomaly for N-doping is discussed below
in Sect. 6.12.3. In Fig.6.49 the dependence of the direct and indirect gaps of GaAs is shown. The
dependence of the direct gap on pressure is non-linear, that on the density is linear [537].
Biaxial and shear strains affect the valence bands and lead to shifts and splitting of the heavy and
light holes at the -point:
E v,hh/lh = E
0
v ± E
(6.58a)