Disorder-based transport/models

Generally, despite the better agreement between the disorder-based models and transport measurements, it is widely believed that the charge carriers exist as po-larons rather than free s and h+ s. It should be noted that the basic disorder-based calculations yield the experimentally observed field dependence of the carrier mobility for a relatively narrow range of fields only. 

Curve fitting to c-Si device models poses several risks, because the assumptions inherent in the model are not necessarily valid in disordered semiconductor systems. Of particular note are the lack of a single uniquely definable mobility and the lack of a well defined threshold voltage. Both of these characteristics lead to inaccuracies in modeling which have led to the adoption of other transport models based on amorphous silicon (a-Si) or polysilicon (p-Si) device models. 

Percolation theory is helpful for analyzing disorder-induced M-NM transitions (recall the classical percolation model that was used to describe grain-boundary transport phenomena in Chapter 2). In this model, the M-NM transition corresponds to the percolation threshold. Perhaps the most important result comes from the very influential work by Abrahams (Abrahams et al., 1979), based on scaling arguments from quantum percolation theory. This is the prediction that no percolation occurs in a one-dimensional or two-dimensional system with nonzero disorder concentration at 0 K in the absence of a magnetic field. It has been confirmed in a mathematically rigorous way that all states will be localized in the case of disordered one-dimensional transport systems (i.e. chain structures). 

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