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Figure 2. Room-temperature conductivity as a function of crystalline volume fraction for a series of undoped nc-Si:H. Reprinted with permission from [11], K. Shimakawa, J. Non-Cryst. Solids 266-269, 223 (2000). © 2000, Elsevier Science.

Figure 3. Room-temperature Hall mobility as a function of crystalline volume fraction in undoped nc-Si:H. Reprinted with permission from [11], K. Shimakawa, J. Non-Cryst. Solids 266-269, 223 (2000). © 2000, Elsevier Science.

crystallites. Unfortunately, however, as shown in Figure 4, a series of experimental data of the Hall mobility is shown to depend on the crystallite size as 8y with y ~ 0.3 [11]. This sublinear dependence of /xH has been explained by the following way [11]: At the same Xc, the area of a disordered zone (DZ) (and hence the number of localized states in region B) can be regarded to be proportional to the surface to volume ratio RSV. Since /xH is expected to be inversely proportional to the area of DZs, we get /xH a R—V. As RSV is proportional to 8a/8fi, where a = 2.0 and fi = 3.0 in Euclid space dimension and a < 2 and fi < 3.0 in fractal space, the relation of /xH a 8y gives y = fi — a.

In Euclid space dimension, we get y = 1. This can be also easily understood by the following way. Imagine a cubic length 8 = L in Euclid space. The total surface area for this cubic is 6L2. When it is divided into eight parts, that is, 8 = L/2, the total surface area is 12L2. The total surface area (grain boundary) is thus expected to be inversely proportional to 8, when the volume is kept the same L3. However, if we consider a and fi in the fractal dimensions, one gets the sublinear dependence. In fact, the fractal dimensions of fi ~ 1.9 and a ~ 1.6 are predicted from a computer simulation for metallic clusters growing in thin films [27], which gives /xH a 80 3.

Next, the excess optical absorption in fundamental absorption region is discussed. A larger optical absorption coefficient for nc-Si:H than for crystalline silicon (c-Si) from the infrared to the blue region has been reported [5, 28, 29]. This is an advantage for using solar cells, because many more photons can be absorbed in the films. An example of this difference is shown in Figure 5. Three solid lines are the experimental data for a-Si:H, nc-Si:H, and c-Si. Why such an excess optical absorption is observed in ^c-Si:H is still a matter of debate. Although a scattering of light is suggested to be an origin of the enhanced optical absorption [29], Shi-makawa [11] took the EMA, in an alternative way, to explain the excess absorption. The results obtained from EMA for Xc = 0.8 and D = 3 are shown by open circles. The frequency (energy)-independent refractive index, n0 = 3.9 for c-Si and n1 = 3.2 for a-Si:H which can be given as the root of real part of optical dielectric constant, are used in the

Figure 4. Hall mobility at room temperature as a function of grain size. Reprinted with permission from [11], K. Shimakawa, J. Non-Cryst. Solids 266-269, 223 (2000). © 2000, Elsevier Science.

Figure 4. Hall mobility at room temperature as a function of grain size. Reprinted with permission from [11], K. Shimakawa, J. Non-Cryst. Solids 266-269, 223 (2000). © 2000, Elsevier Science.

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