Amorphous semiconductors, such as hydrogenated amorphous silicon (a-Si:H) and amorphous indium gallium zinc oxide (a-IGZO) have been central to the development of thin film transistors (TFTs) for large-area electronic applications such as displays. This is a result of the exceptional material uniformity that can be achieved when depositing over very large areas (~10 m2). This means that all TFTs are essentially identical over an entire large display panel. However, there is a technological price to pay – the carrier mobility is generally less in amorphous semiconductors compared to their crystalline equivalent.The origin of this reduced carrier mobility is a result of a key difference in the density of states between crystalline semiconductors and their amorphous counterparts. The long-range order of a crystalline lattice means that all carrier states in the conduction and valence bands exist over long distances. These ‘extended states’ are associated with generally high mobility carriers. However, there is no long-range order in amorphous semiconductors, but only short-range order over one to two bond lengths associated with local atomic coordination requirements (and to some degree a medium-range order over a few bond lengths). The result is that the bottom of the conduction band and top of the valence band gain ‘tail’ states which are localized in nature.Not only do these localized states frequently dominate (or at least significantly affect) conduction in amorphous semiconductors and hence the switching characteristics of TFTs, but they also have a role to play in other important processes such as hysteresis and bias stress instability. But what are these localized band tail states, how should we think about them in the context of conduction and how do they relate to extended states?These questions are revisited from the starting point that there is a perturbation in the delocalized charge concentration with position in an amorphous semiconductor compared to its crystalline counterpart, and this can be quantified as a spatially varying excess charge concentration (where a deficit is just a negative excess). The rate of spatial variation is long relative to the rate of change in the electron wavefunction, and reflects the short- and medium-range order distances. Charge conservation means that that this excess charge concentration will have a mean of zero and a Gaussian probability distribution is assumed. A model using this as a starting point has been created which reproduces band tails and which provides new insights into their physics which are discussed.
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