Hydrogen Diffusion Studies

Experimental measurements of DH in a-Si H using SIMS were first performed by Carlson and Magee (1978). A sample is grown that contains a thin layer in which a small amount (=1-3 at. %) of the bonded hydrogen is replaced with deuterium. When annealed at elevated temperatures, the deuterium diffuses into the top and bottom layers and the deuterium profile is measured using SIMS. The diffusion coefficient is obtained by subtracting the control profile from the annealed profile and fitting the concentration values to the expression, valid for diffusion from a semiinfinite source into a semi-infinite half-plane (Crank, 1956), 

The concentration profile studies find that the hydrogen diffusion coefficient in a-Si H is thermally activated, as shown in Fig. 17 (Street et al., 1987). Over the temperature range of 130 to 300°C, the diffusion data is described by the Arhennius expression 

The lower activation energy may arise from a smaller binding energy for a hydrogen atom located on the surface of a column, compared to in the bulk. It is known that the surface of the columns contain polymerically bonded hydrogen (Knights and Lujan, 1979), which will have a bonding structure that differs from that found in the bulk of CVD-quality a-Si H. 

An important point regarding the hydrogen diffusion data described above is that the diffusion coefficient is not uniquely defined but rather depends on the time for which the sample is annealed. This is clearly shown in Fig. 14 where DH is plotted against anneal time in hours for a 10 2[B2H6]/[SiH4] doped sample, annealed at 200°C (Street etal., 1987b). The diffusion coefficient decreases by nearly a factor of five as the annealing time is increased from 10 min to nearly 200 hours. DH can be approximately described by a power law, 

If Dh is indeed time dependent as in eq. (5) it is not obvious that C(x, t) will follow an error function expression as in eq. (3) or that H will be thermally activated as in eq. (4). We now show that eqs. (3) and (4) still apply with a time dependent diffusion coefficient, by making a coordinate transformation (Kakalios and Jackson, 1988). The one-dimensional diffusion equation 

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ScHoj- H 300-600 T] measurements, hydrogen diffusion studied Weaver (1972b)... 

SmHj LuH 0.17 h 173-425 hydrogen diffusion studied Barrere and Tran (1971)... 

For completeness it should be mentioned that the passivation of gold, presumably via the same AuH complex, has also been studied in p-type silicon, where it is the donor rather than the acceptor level of gold that is active (Hansen et al., 1984). Though no profiles were reported in this work, apparent hydrogen diffusion coefficients inferred by these authors are of the same order as the Pearton (1985) points of Fig. 16 at temperatures 110°C and below. 

Contrary to silicon, very little work has been done in germanium regarding quantitative hydrogen diffusion or electric field drift studies. Such experiments may be complicated by the fact that ultra-pure germanium becomes intrinsic already at temperatures near 200 K. It would be worthwhile to explore the possibility of using lightly doped germanium for such studies in order to explore Fermi level dependent effects. 

As for silicon, secondary ion mass spectrometry (SIMS) is the most widely used profiling analysis technique for deuterium diffusion studies in III-V compounds. Deuterium advantageously replaces hydrogen for lowering the detection limit. The investigations of donor and acceptor neutralization effects have been usually performed through electrical measurements, low temperature photoluminescence, photothermal ionization spectroscopy (PTIS) and infrared absorption spectroscopy. These spectroscopic investigations will be treated in a separated part of this chapter. 

Lastly, we studied the effect of 7-stress on the effective time to steady state and the corresponding magnitude of the peak hydrogen concentration. We found that a negative T -stress (which is the case for axial pipeline cracks) reduces both the effective time to steady state and the peak hydrogen concentration relative to the case in which the T -stress effect is omitted in a boundary layer formulation under small scale yielding conditions. This reduction is due to the associated decrease of the hydrostatic stress ahead of the crack tip. It should be noted that the presented effective non-dimensional time to steady state r is independent of the hydrogen diffusion coefficient D 9. Therefore, the actual time to steady state is inversely proportional to the diffusion coefficient (r l/ ). 

Graham CM (1981) Experimental hydrogen isotope studies. Diffusion of hydrogen in hydrous minerals, and stable isotope exchange in metamorphic rocks. Contrib Mineral Petrol 76 216-228 Hoefs J (2004) Stable isotope geochemistry. S" Edition. Springer, Berlin... 

The method can be used for studies on hydrogen diffusion and trapping in metals, which, for example, are relevant within the field of hydrogen-related stress corrosion cracking. Critical hydrogen concentrations for various types of cracking can be assessed. 

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