97
Electronic Properties of Strain-Engineered Semiconductors
the Hamiltonian of Luttinger and Kohn [22], and that allows us to determine
the effective masses and lifting of degeneration of the band. The Hamiltonian
may be expressed as
0
2
2
0
2
3
2
0
3
2
2
0
2
2
2
2
3
2
2
0
2
3
2
2
2
0
H
P Q
S
R
S
R
S
P Q
R
Q
S
R
P Q
S
S
Q
R
S
P Q
R
S
S
Q
S
R
P
R
S
Q
S
P
BP =
+
−
−
−
−
−
−
+
−
−
−
−
−
−
(4.15)
with
,
2
,
2
2
2
P
qa Tr
Q
q
b
v
x x
y y
z z
(
)
( )
= −
ε
=−
ε + ε + ε
3
2
,
(
)
2
2
2
R
qb
i qd
S
qd
i
xx
yy
xy
zx
yz
(
)
= −
ε + ε − ε
=− ε − ε
where the front coefficients b and d are the potentials of deformation of the
valence band and are specific to material considered. These are shown for Si
in Table 4.1 [26].
In unstrained Si, the heavy-hole (HH) and the light-hole (LH) bands are
degenerate at the Γ point as shown in Figure 4.5. The eigen states at the
Γ point split into two groups due to spin-orbit coupling and are classified by J = 3/2 and J = 1/2 and degenerated in to HH (J = 3/2, M J = ±3/2)
TABLE 4.1
Deformation Potential of the Valence Band of Si
Theoretical (eV)
Experimental (eV)
Δ 0
—
0.04
a v
2.46
1.80
b
–2.35
–2.10 ± 0.10
d
–5.32
–4.85 ± 0.15
Source: Kasper, E., and D. J. Paul, Silicon Quantum Integrated
Circuit, Springer-Verlag, Berlin, Heidelberg, 2005.
Electronic Properties of Strain-Engineered Semiconductors
the Hamiltonian of Luttinger and Kohn [22], and that allows us to determine
the effective masses and lifting of degeneration of the band. The Hamiltonian
may be expressed as
0
2
2
0
2
3
2
0
3
2
2
0
2
2
2
2
3
2
2
0
2
3
2
2
2
0
H
P Q
S
R
S
R
S
P Q
R
Q
S
R
P Q
S
S
Q
R
S
P Q
R
S
S
Q
S
R
P
R
S
Q
S
P
BP =
+
−
−
−
−
−
−
+
−
−
−
−
−
−
(4.15)
with
,
2
,
2
2
2
P
qa Tr
Q
q
b
v
x x
y y
z z
(
)
( )
= −
ε
=−
ε + ε + ε
3
2
,
(
)
2
2
2
R
qb
i qd
S
qd
i
xx
yy
xy
zx
yz
(
)
= −
ε + ε − ε
=− ε − ε
where the front coefficients b and d are the potentials of deformation of the
valence band and are specific to material considered. These are shown for Si
in Table 4.1 [26].
In unstrained Si, the heavy-hole (HH) and the light-hole (LH) bands are
degenerate at the Γ point as shown in Figure 4.5. The eigen states at the
Γ point split into two groups due to spin-orbit coupling and are classified by J = 3/2 and J = 1/2 and degenerated in to HH (J = 3/2, M J = ±3/2)
TABLE 4.1
Deformation Potential of the Valence Band of Si
Theoretical (eV)
Experimental (eV)
Δ 0
—
0.04
a v
2.46
1.80
b
–2.35
–2.10 ± 0.10
d
–5.32
–4.85 ± 0.15
Source: Kasper, E., and D. J. Paul, Silicon Quantum Integrated
Circuit, Springer-Verlag, Berlin, Heidelberg, 2005.