Previous Up Next

Defect kinetics

Just as the nature of defects in amorphous silicon, also their creation and annealing behaviour has been subject of debate for a long time, and the debate is still ongoing.

Before presenting some of the initial work, I would like to illustrate a puzzling detail about light induced degradation; there is agreement that degradation is not related to the absorption process, but to charge carrier recombination. At room temperature, recombination is generally non-radiating because the generated electron hole pairs have sufficient energy to diffuse apart. Once separated, the mobile charge carriers get trapped somewhere and slip down ever deeper trap states, giving off their energy to phonons. However, as the temperature is lowered, electron hole pairs can no longer diffuse apart because the mobility decreases drastically at low temperatures. Thus, they stay closer together and there is an increasing chance for radiative recombination. Now, the surprising thing is that the degradation kinetics of the material proceed almost exactly the same at low and at high temperatures, regardless of the differences in the underlying recombination process [Stradins-1993jncs]!

Defect creation

The kinetics of defect creation were addressed by many researchers; Stutzmann was one of the first to look directly into the defect densities by ESR [Stutzmann-1984apl, Stutzmann-1985prb]. He used a setup with in-situ illumination and annealing which allowed degradation and recovery of the sample without uncertainties of the sample position that might be introduced by frequent loading and unloading cycles.

Variation of neutral defect density with exposure time for various light intensites (650 nm laser illumination at 40°C). The dashed line represents the initial value of 8x10¹⁵ cm^-3 .

Because it was already known that the creation of defects proceeds via recombination processes, Stutzmann proposed a proportionality to the free carrier densities n and p. These are in turn proportional to the ratio between the generation rate G and the already existing defect density N_D:

$frac{dN_D}{dt}~const G^2/N_D^2$

Therefore, the density of newly induced defects N_D - N₀ should follow a time dependence proportional to t^1/3:

$N_D - N_0 ~ G^{2/3} t^{1/3}$

Same data as above, presented as log-log plot of the induced defects (total number minus the initial density). The slope is almost exactly 1/3 for all of the curves.

Stutzmann's explanation appears very successful indeed. However, it applies only to the initial behaviour and does not take into account that the defect density eventually saturates. Below we will see a model that was proposed to include saturation.

Annealing of light induced defets

The figure below reproduces Stutzmann's data on annealing of light induced defects from figures 15 and 16 of the same publication as above. Before the experiment the sample was anneald in order to reach a reproducible annealed state with a defect density of 8x10¹⁵ cm^-3. Then, it was exposed to illumination until a level of 5.3x10¹⁶ cm^-3 defects was reached and subsequently the defect density was measured by ESR.

Annealing of light induced defects at different temperatures.

Stutzmann proposes a thermally activated annealing process. However, the graph shows that low and high temperature annealing apprach different saturation levels. In order to explain this observation, Stutzmann further proposes that there is not one single activation energy but a distribution of energies; at low temperatures it is unlikely that an annealing process with high activation energy will participate, we can thereforer anneal out only those defects with low activation energy.

While this idea is powerful, equilibrium models are favoured in most of the literature.

Annealing of equilibrium defects

Defect annealing was investigated by Street in the following experiment [Street-1989prb]; a high defect density N₀ was established by heating the sample to 290°C, then frozen in by rapidly cooling to room temperature. Subsequently, the sample was brought to the desired annealing temperature and the defect density N_D was monitored by ESR until the steady state density N_eq was reached. The graph below shows the normalized kinetics of this process, i.e. (N_D - N_eq)/(N₀ - N_eq).

Normalized variation of the defect density during annealing. Temperatures of 200, 225 and 250°C are represented by black, red, and green points. Full and dashed lines represent stretched and regular exponential decay, respectively.

The graph above illustrates that the defect annealing kinetics cannot be described by a simple exponential decay, but require a description in terms of stretched exponentials with a stretching parameter β.

$N_D = N_0 \exp{-t/\tau}^\beta}$

Stretched exponentials are a very general phenomenon; they are usually applied to effects that rely on a multitude of processes, each one with its own timescale. This rather fuzzy description is just what we would expect from a disordered material, and not surprisingly, it is difficult to relate the stretching parameter β to an accessible quantity.

A unified concept for the kinetics of defect creation and annealing

Based on the fact that defect creation and annealing are somehow related to hydrogen bond breaking and formation, researchers at Stanford University published a series of papers which proposed that both processes should be combined in a unified rate equation [Redfield-1988apl, Redfield-1988apl, Bube-1989jap]. Such an equation would contain a dispersive dependence on the time, illustrated by the exponential α, a defect creation term with built-in saturation, and a defect healing term. The first term should be related to illumination, while the latter is likely to scale with annealing temperature. The rather general form below assumes that light can also heal some defects, and that the temperature can also create defects.

$frac{d N_D}{dt} = (\nu t)^{-\alpha} [(c_1 G + \nu_1)(N_T - N_D ) - (c_2 G + \nu_2) N_D ]$

Applying such a generalized rate equation to Stutzmann's data, Redfield concluded that the time dependence of t^1/3 should be a mere coincidence for degradation experiments carried out at room temperature. There is a difficulty with Redfields interpretation because it is a purely empiric model that does not give any relation to microscopic processes taking place in the material.

Crandall proposed a relation between the activation energy of defect annealings and stretched exponentials kinetics [Crandall-1991prb].

Previous Up Next

Last updated August 20th, 2010