8.3 Low-Field Transport
231
(a)
(b)
Fig. 8.4 a Electronic barrier ( b ) for (hole) transport at a grain boundary (GB). b Average hole mobility in polysilicon, experimental data (symbols) and theoretical model (solid line). The dependence for monocrystalline silicon is
shown for comparison as dashed line. Adapted from [730]
8.3.8 Grain Boundary Scattering
The lowering of mobility due to transport across grain boundaries is an important effect in polycrystalline materials, such as poly-silicon for solar cells or thin film transistors [730–733]. Grain boundaries
contain electronic traps whose filling depends on the doping of the bulk of the grains. Charges will be
trapped in the grain boundaries and a depletion layer will be created.
2 At low doping the grains are
fully depleted and all free carriers are trapped in the grain boundaries. This means low conductivity,
however, no electronic barrier to transport exists. At intermediate doping, traps are partially filled and
the partial depletion of the grain leads to the creation of an electronic barrier b (Fig. 8.4a) hindering
transport since it must be overcome via thermionic emission. At high doping the traps are completely
filled and the barrier vanishes again. Accordingly the mobility goes through a minimum as a function
of the doping concentration (Fig. 8.4b) [730]. In [734] these data have been modeled with a 20 nm
grain size, the value found in [730] from TEM analysis.
The expression for the limitation of the mobility due to scattering at grain boundaries is given by
[733, 735]
μ GB =
e L G
√
8m ∗ πk
T
−1/2 exp
−
b
kT
,
(8.25)
where L G is the grain size.
8.3.9 Alloy Scattering
The random population of lattice sites represents disorder from a perfectly periodic lattice. The charge
carrier mobility in an alloy A x B 1−x due to scattering in this potential is proportional to the alloy
scattering potential [590],
μ alloy =
2 e
3π m ∗ x (1 − x) ((U ) 2
kT
n
1 + exp(E F /kT )
,
(8.26)
2 The following arguments may only be followed once the concept of depletion layers and band bending is understood,
see Sect. 21.2.1.
231
(a)
(b)
Fig. 8.4 a Electronic barrier ( b ) for (hole) transport at a grain boundary (GB). b Average hole mobility in polysilicon, experimental data (symbols) and theoretical model (solid line). The dependence for monocrystalline silicon is
shown for comparison as dashed line. Adapted from [730]
8.3.8 Grain Boundary Scattering
The lowering of mobility due to transport across grain boundaries is an important effect in polycrystalline materials, such as poly-silicon for solar cells or thin film transistors [730–733]. Grain boundaries
contain electronic traps whose filling depends on the doping of the bulk of the grains. Charges will be
trapped in the grain boundaries and a depletion layer will be created.
2 At low doping the grains are
fully depleted and all free carriers are trapped in the grain boundaries. This means low conductivity,
however, no electronic barrier to transport exists. At intermediate doping, traps are partially filled and
the partial depletion of the grain leads to the creation of an electronic barrier b (Fig. 8.4a) hindering
transport since it must be overcome via thermionic emission. At high doping the traps are completely
filled and the barrier vanishes again. Accordingly the mobility goes through a minimum as a function
of the doping concentration (Fig. 8.4b) [730]. In [734] these data have been modeled with a 20 nm
grain size, the value found in [730] from TEM analysis.
The expression for the limitation of the mobility due to scattering at grain boundaries is given by
[733, 735]
μ GB =
e L G
√
8m ∗ πk
T
−1/2 exp
−
b
kT
,
(8.25)
where L G is the grain size.
8.3.9 Alloy Scattering
The random population of lattice sites represents disorder from a perfectly periodic lattice. The charge
carrier mobility in an alloy A x B 1−x due to scattering in this potential is proportional to the alloy
scattering potential [590],
μ alloy =
2 e
3π m ∗ x (1 − x) ((U ) 2
kT
n
1 + exp(E F /kT )
,
(8.26)
2 The following arguments may only be followed once the concept of depletion layers and band bending is understood,
see Sect. 21.2.1.