Energetics of Interstitial Hydrogen and Hydrogen Diffusion in Realistic Models of a-Si:H
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Energetics of Interstitial Hydrogen and Hydrogen Diffusion in Realistic Models of a-Si:H P. A. Fedders Department of Physics, Washington University, St. Louis, Mo 63130 ABSTRACT In order to determine the mechanism or mechanisms of hydrogen transport in a-Si:H one must identify the reactions that bring deeply bonded H (on dangling bonds) to the transport band which is some form of interstitial hydrogen. Further, one must have reliable estimates of the energy difference between these deep states and transport states as well as the barrier energies among transport sites. In this paper we consider all of these ingredients in order to partially explain how hydrogen migrates in a-Si:H. INTRODUCTION The essentially universal view of hydrogen transport in a-Si:H is that deeply bonded H (at a dangling bonds site) is thermally excited to a band of spatially dense transport sites and then hops among these sites until it fall back into another deeply bonded site [1]. In order to determine the mechanism or mechanisms of hydrogen migration in a-Si:H, one needs to identify the possible reactions which put a hydrogen atom or molecule in a transport band and one needs to accurately determine the energies of the various possible sites for hydrogen atoms or molecules that are relevant in the possible reactions. Finally one must also know the barrier energies between the transport sites. Most calculations of hydrogen transport activation energies consider only neutral defect states. As it turns out, this may ignore the most promising (lowest energy) pathways for diffusion. The recent work of Branz [2] on the charge state of the diffusing hydrogen (or doping of the sample) has made it more imperative to consider all possible charge states of both the diffusing hydrogen and the (presumed) dangling bond states from which the hydrogen originates. Also the work of Beyer [3] strongly suggests a rather complex doping dependence of the diffusion activation energy of H. Virtually all calculations of the energies of hydrogen configurations use too small a supercell and/or too few points in k-space. This leads to errors of a number of tenths of an electron volt. In this work we first address the reaction paths and then report on accurate calculations of the energy levels of relevant hydrogen configurations. This includes both the dangling bonds states as well as interstitial atomic and molecular H sites as candidates for the transport band. REACTION PATHS As noted, we shall first consider the reaction paths possible for a hydrogen atom or molecule to reach a transport band. We assume that the hydrogen starts out by passivating what would otherwise be a Si dangling bond and the H atom or molecule then goes to a higher energy transport site. We assume that this transport site is an interstitial site of some sort but this includes T-like sites, bond centered sites, or even floating bond sites. The details of these sites will be discussed in the next section. Consider the electronic energy level sketch in figure 1 which includes the valence and condu
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