A rigorous mathematical model for H transport in, and evolution from, amorphous hydrogenated material was described. The model improved upon previous evolution models by including 3 discrete H energy levels (1 mobile level, 2 independent trap levels) in the film, and by explicitly simulating adsorption/desorption processes at the surface. This multi-energy level model, with a floating boundary condition at the surface, was used to simulate 2 types of evolution experiment (temperature programmed, isothermal). The results of both types of experiment, for glow discharge deposited films, were modelled by using the same energetics; with trap depths that were 1.5 and 1.8 to 1.9eV below the transport level, and with 20 to 30% of the H residing in deep traps. These results differed from previous predictions, which had suggested that H in deep traps was more tightly bound; 2.1 to 3.4eV below the transport level. The difference of 0.3 to 0.4eV which was observed here between the 2 trap energy levels agreed well with published bonding energies that were estimated by using  ab initio  quantum-mechanical calculations. The difference in trap energies was also similar to the measured defect formation activation energy of 0.2 to 0.5eV; thus suggesting that the defect formation mechanism in amorphous hydrogenated material might involve H motion between the 2 energy levels. A combination of these results with quantum-mechanical calculations of various H energy levels in crystalline Si suggested that interstitial hopping might not be the primary H transport mechanism.

A.J.Franz, M.Mavrikakis, J.L.Gland: Physical Review B, 1998, 57[7], 3927-38