Hydrogen charged state

Point defects and complexes exliibit metastability when more than one configuration can be realized in a given charge state. For example, neutral interstitial hydrogen is metastable in many semiconductors one configuration has H at a relaxed bond-centred site, bound to the crystal, and the other has H atomic-like at the tetrahedral interstitial site. 

Here, we pointed to the problem of theoretical representation, in particular, in two aspects of theory (i) the existence of highly mobile atoms at the surface such as hydrogen, which are usually not considered in the atomistic models and (ii) the importance of bandgaps and relative energy levels of electronic states, which is often distorted in local density approximations. In both respects, a quick fix to the problem is not very likely. However, as both theory and experiment continue to be developed and applied in common research projects, it can be expected that the actual understanding of the processes involved in reaction on model catalysts will substantially improve over the next 10 years. After all, the ability to trace reactions and to account for the position and charge state of each reactant is already a realization of what seemed 20 years ago a fiction rather than fact. 

The remark just made suggests that a natural place to begin our discussion of equilibrium equations is with the occupation of different charge states. Let a hydrogen in charge state i(i = +, 0, or - ) have possible minimum-energy positions in each unit cell, of volume O0, of the silicon lattice. (O0 contains two Si atoms, so our equations below will be applicable also to zincblende-type semiconductors.) To account for spin degener-ancies, vibrational excitations, etc., let us define the partition function... 

Fig. 1. Possible positions of electronic energy levels associated with hydrogen in a semiconductor. (a) normal order (acceptor above donor), allowing possible predominance of any of the charge states H+, H°, H. (b) negative-U order (donor above acceptor), H+ or H always predominant.

The case of most frequent interest to us is that where the hydrogen-free center can exist in two charge states if I is an acceptor, these will be 1° and I-. We shall continue to assume that all IH complexes are neutral (5) is then replaced by... 

The case where hydrogen can combine with a simple donor center I to form a neutral IH complex is described by equations of just the same form as (8-10), but with I replaced by 1+ and eF - ej by eY - ef, with ej now representing the donor level. More complicated cases, e.g., those involving centers with more than two charge states, can be treated by similar reasoning. 

REACTIONS CHANGING THE CHARGE STATE OF MONATOMIC HYDROGEN SPECIES... 

Fig. 2. Variation of the logarithms of the rate factors (23) and (24) for charge-state changes as the band potential, and hence the height of the hydrogen donor level eD is changed (a) relative to an equilibrium Fermi level eF for the carriers or (b) relative to an arbitrary level, when the electron and hole Fermi levels eFe and rFh, respectively, are made different by application of a reverse bias to a p-n junction.

It is not overly difficult to include the effects of interconversion of hydrogen among its charge states if these are equilibrated with the local carrier concentrations and if we continue to neglect complex formation and assume that the spatial scale of the diffusion-migration phenomena is large... 

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