8.8 Hopping Transport
247
Fig. 8.25 Temperature
dependence of conductivity
of a hydrogenated
amorphous Si thin film,
plotted as ln ξ vs. ln T
(8.50). Solid lines are linear
fits for constant s according
to (8.50) as labelled.
Adapted from [801]
0.0
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
ln
4.8
5.0
5.2
5.4
5.6
5.8
ln(T
150
200
250
300
T
100
a-Si:H
s=0.54±0.05
s=1.08±0.14
Fig. 8.26 Schematic
density of states of
amorphous semiconductor
with band tails and deep
levels. The localized
(delocalized) states are
shown in dark (light) grey.
The mobility edges for
electrons and holes are
indicated by dashed lines
E V
E C
DOS (arb. units)
localized
delocalized
delocalized
E F
Energy
From (8.45) one can rewrite for ξ = d(ln σ(T ))/d ln T ,
ln ξ = ln s + s ln T 0 − s ln T .
(8.50)
Thus in a plot of ln ξ vs. ln T , the exponent s can be determined from the slope. As can be seen in
Fig. 8.25, for the conductivity of a hydrogenated amorphous silicon thin film the transition of hopping
mechanism from Efros–Shklovskii variable range hopping (s ≈ 1/2) to next neighbor hopping (s ≈ 1)
takes place around T = 220 K, as discussed in detail in [801].
8.9 Transport in Amorphous Semiconductors
Many models have been presented for the carrier transport in amorphous semiconductors [203]. The
most important concept is that of a mobility edge, an energy separating localized from delocalized states
[547, 548, 802]. This is schematically depicted in Fig. 8.26. The carrier transport between localized
states is mediated via tunneling (hopping) which has been described in the previous section (Sect. 8.8).
The localization of carriers in random lattices has been treated by Anderson [782] and reviewed in
[780]. If the degree of disorder surpasses a certain value, diffusion is suppressed (at T = 0) and
conductivity vanishes altogether (Anderson metal–insulator transition).
247
Fig. 8.25 Temperature
dependence of conductivity
of a hydrogenated
amorphous Si thin film,
plotted as ln ξ vs. ln T
(8.50). Solid lines are linear
fits for constant s according
to (8.50) as labelled.
Adapted from [801]
0.0
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
ln
4.8
5.0
5.2
5.4
5.6
5.8
ln(T
150
200
250
300
T
100
a-Si:H
s=0.54±0.05
s=1.08±0.14
Fig. 8.26 Schematic
density of states of
amorphous semiconductor
with band tails and deep
levels. The localized
(delocalized) states are
shown in dark (light) grey.
The mobility edges for
electrons and holes are
indicated by dashed lines
E V
E C
DOS (arb. units)
localized
delocalized
delocalized
E F
Energy
From (8.45) one can rewrite for ξ = d(ln σ(T ))/d ln T ,
ln ξ = ln s + s ln T 0 − s ln T .
(8.50)
Thus in a plot of ln ξ vs. ln T , the exponent s can be determined from the slope. As can be seen in
Fig. 8.25, for the conductivity of a hydrogenated amorphous silicon thin film the transition of hopping
mechanism from Efros–Shklovskii variable range hopping (s ≈ 1/2) to next neighbor hopping (s ≈ 1)
takes place around T = 220 K, as discussed in detail in [801].
8.9 Transport in Amorphous Semiconductors
Many models have been presented for the carrier transport in amorphous semiconductors [203]. The
most important concept is that of a mobility edge, an energy separating localized from delocalized states
[547, 548, 802]. This is schematically depicted in Fig. 8.26. The carrier transport between localized
states is mediated via tunneling (hopping) which has been described in the previous section (Sect. 8.8).
The localization of carriers in random lattices has been treated by Anderson [782] and reviewed in
[780]. If the degree of disorder surpasses a certain value, diffusion is suppressed (at T = 0) and
conductivity vanishes altogether (Anderson metal–insulator transition).