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undoped VO
2
. The lower panel of Fig. 11.10 elaborates the quantitative role
of the Mg doping on
T
lum
, which is seen to go monotonically from
40% to
more than 50% when the Mg content is increased from zero to 7.2 at%.
Some concomitant decrease of the distinctness of the thermochromism for
λ
∼
m is apparent from the upper panel of Fig. 11.10. Mg doping has a
secondary benefi cial effect as well, as it infl uences
>
1
μ
τ
c
favourably, as men-
tioned briefl y below.
A more detailed description of the band gap shifts in Mg-doped VO
2
fi lms
can be put forward via an evaluation of
n
and
k
for 0.3
<
λ
<
2.5
μ
m and
τ
<
τ
c
. The absorption coeffi cient
α
was then derived from
α
=
4
π
k
/
λ
. Figure
)
1/2
versus ¯
11.11 shows an evaluation of (
(as is appropriate for indi-
rect allowed band gaps; Wooten, 1972). Two band gaps appear: one shifting
from
α
¯
ω
ω
0.5 eV irre-
spective of the Mg doping. A preliminary interpretation of the two band
gaps is feasible from the band structure in the proximity of the Fermi level
for VO
2
at
∼
1.6 to 2.3 eV for rising Mg doping and another lying at
∼
τ
c
(Goodenough, 1971; Abe
et al.
, 1997) as elaborated else-
where by Li
et al.
(2012).
τ
<
11.3.4 Doped VO
2
fi lms with thermochromic switching at
room temperature
Doped VO
2
, denoted M
x
V
1−
x
O
2
, can exhibit shifted values of their 'critical'
temperature, and, at least for bulk specimens, M being W
6+
, Mo
6+
, Ta
5+
, Nb
5+
and Ru
4+
yields a lowered
τ
c
, while M being Ge
4+
, Al
3+
and Ga
3+
produces
an increased
τ
c
(Goodenough, 1971). Thin fi lms of doped VO
2
display the
1400
Mg:O
2
= 0.086
0.078
1200
0.059
0.054
1000
0.046
0.030
0
800
600
400
200
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Photon energy
ћ
w
(eV)
11.11
(
α
¯
ω
)
1/2
vs.
¯
ω
, where
α
is absorption coeffi cient and
¯
ω
is
photon energy, for Mg-doped VO
2
fi lms at
τ
<
τ
c
.
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