Drift-mobility measurements and mobility edges in disordered silicons

Abstract

Published electron and hole drift-mobility measurements in hydrogenated amorphous silicon (a-Si:H), amorphous silicon alloys (a-SiGe:H and a-SiC:H), and microcrystalline silicon (µc-Si:H) are analysed in terms of the exponential bandtail trapping model. A three-parameter model was employed using an exponential bandtail width E, the band mobility µ 0 , and the attempt-toescape frequency ν. Low-temperature measurements indicate a value around µ 0 = 1 cm 2 V −1 s −1 for both the conduction and valence bands over the entire range of materials. High temperature-measurements for electrons in a-Si:H suggest a larger value of 7 cm 2 V −1 s −1 . These properties and those of the frequency ν are discussed as possible attributes of a mobility edge.

Hole drift-mobility measurements in microcrystalline silicon

“…However, the physical significance of is not well established, and even the assumption that its value is independent of trap level energy has been challenged. 20 Our estimates of the valence band mobility 0 Ϸ 1-2 cm 2 / V s for c-Si: H are similar in magnitude to estimates of 0 for holes and for electrons in a-Si: H and a-SiGe: H. 18 Bandtail widths associated with these estimates in a-Si: H vary from 20 to 50 meV, and estimates of vary over several orders of magnitude. The near constancy of 0 across such a broad range of materials suggests to us that 0 is a fundamental property of band transport and of the mobility edge for disordered silicon-based materials, and perhaps even more broadly.…”

“…One paperreporting temperature-dependent ambipolar diffusion lengths 16 -estimates an exponential valence bandtail width of 26 meV, which seems reasonably consistent with the estimates of 31-32 meV in the present work. These valence bandtail widths for c-Si: H are substantially lower than those ͑40-50 meV͒ reported for a-Si: H. 9,10 While this seems unsurprising, these valence bandtails are actually wider than conduction bandtails ͑20-25 meV͒ in a-Si: H. 18 In this context, it may be useful to make one observation regarding the microscopic character of bandtail states in c -Si: H. Theoretical studies of bandtail states near a mobility edge, such as those probed by drift-mobility measurements, show that these states are not strongly localized on a defective configuration of a few atoms, but are spread over a broad region 13 and possibly with an intricate "spongelike" spatial structure. 19 It is interesting that the attempt-to-escape frequency estimates Ϸ 10 9 s −1 for bandtail-trapped holes in c-Si: H are lower than most values reported for holes in a-Si: H ͑ Ϸ 10 11 -10 12 s −1 ͒.…”

Temperature dependence of the electron diffusion coefficient in electrolyte-filledTiO2nanoparticle films: Evidence against multiple trapping in exponential conduction-band tails

“…7,25 As has been noted in many of the earlier papers, 6,15,21,26-29 these aspects of the diffusion measurements over the range of light intensities or open-circuit photovoltages investigated are consistent with an "exponential conduction-band tail multiple-trapping" model; the properties of this model are well-known owing to its extensive application to amorphous silicon. 30,31 The exponential conduction-band tail ͑CBT͒ model assumes the existence of a "transport edge" E C within the electronic density of states g͑E͒ of the conduction band. Electrons occupying states above the transport edge are assumed to have a well-defined electron diffusion coefficient D 0 ; this edge plays the same role in the multiple-trapping model as does the ordinary conduction-band edge in a homogeneous crystalline material.…”

Carrier drift-mobilities and solar cell models for amorphous and nanocrystalline silicon

“…This assumption sets the value for the density of bandtail traps 0 V g at E V (see Appendix 1). Second, the conduction bandtail is neglected; at about 22 meV [8], the conduction bandtail in a-Si:H is sufficiently narrow that this neglect is justified near room-temperature. The assumption should be reassessed for work at low temperatures below about 225 K or for a-SiGe:H alloys, which have broader conduction bandtails [9].…”

“…To facilitate such constraints, in Appendix 1 we give the expressions for calculating the drift-mobility based on the values of the bandtail parameters; the calculations can then be checked for consistency with the experimental results. Electron and hole drift-mobilities for a-Si:H and related materials have been reviewed fairly recently [8]. For a-Si:H, the 7-parameter model has been tested by comparing its predictions with the temperature-dependent properties of nip cells of varying thickness; the results are presented in Fig.…”