Atomistic Structure of Band-Tail States in Amorphous Silicon

The nature of the band-tail states in amorphous semiconductors is of both fundamental and applied interest. Since the seminal work of Anderson [1] it has been known that disorder induces localization of electron states. The detailed understanding of this has been a field of tremendous activity in condensed matter theory. In the parlance of amorphous semiconductors, the nature of the electron localization is determined by the microscopic structure of the band-tail and midgap eigenstates and the dependence of this structure on the energy of the state. In this Letter, we report the first explicit microscopic calculations of the band-tail states using a very large and realistic 4096 atom model of a-Si (a cube about 43 Å on a side), generated by Djordjevic, Thorpe, and Wooten [2]. A related calculation for amorphous diamond has been published recently [3]. This paper goes well beyond related earlier work [4] on 216 or fewer atom cells, which accurately modeled deep gap states, but was limited in showing their ability to model tail states. A localized-to-extended [1,5] transition occurs near both the valence and conduction band tails in a-Si, since midgap states are bound to be Anderson localized in a realistic model of a-Si and, likewise, states well into the valence or conduction bands (beyond the mobility edges) are extended. While this picture is certainly valid, it is also qualitative, and details, such as the exact nature of the mobility edge, are still controversial. Within finite-size limitations of our model, we indicate qualitative features of the transition that are robust and salient to real a-Si and that we suspect are relevant to any topologically disordered insulator. For applications, and for any transport experiments on a-Si [6], the gap and band-tail states are of interest. For example, in a lightly boron doped (p-type) sample of a-Si:H, one can expect that states much like the ones we report near the valence edge will be responsible for the conduction [7]. Any atomistic approach to computing conductivity and transport properties must start from calculations of the electron states near the Fermi level as we compute for a very large cell of a-Si for the first time in this paper. The approximations of this paper are as follows: (1) An orthogonal tight-binding Hamiltonian [8] with one s