We present a model for determining the optical absorption spectrum and optical absorption profile for any layer in a one-dimensional thin-film multilayer structure, based on the coherent interference between light waves in the structure. We show how partially coherent and incoherent layers may be incorporated into the calculation by means of an appropriate integration. The work is an extension of previously published work regarding a particle (photon) model for absorption in such structures. We use a structure that is typical of an a-Si:H-based photovoltaic cell as an example, and find the optical absorption profile in the a-Si:H layer of this cell using the photon model and the coherence (wave) model presented in this paper. We find that the former is strictly monotonic with position in the layer, while the latter has a slight oscillatory character. We propose a simple model for determining the absorption profile in the a-Si:H layer when one or more layers in the structure are partially coherent or incoherent, including the a-Si:H layer itself. The absorption profile for such a case lies between the profiles for the cases of incoherence and coherence. The determination of such absorption profiles is very important in solar cell simulation, where the optical generation rate of electron-hole pairs must be known at each point in the a-Si:H layer. We stress that, although we have presented results specifically for an a-Si:H-based cell, the model is general and can be applied to any thin-film multilayer structure. It should be particularly useful for determining optical generation rate profiles of electron-hole pairs for use in photovoltaic device simulations.

A technique for calculating the optical generation rate of electron-hole pairs (EHPs) in the absorber layers of a multilayer photovoltaic cell is described, taking into account the multiple internal reflections that typically occur in such multilayer cells. The technique is based on the assumption that all multiply reflected and transmitted light, within the cell, combines incoherently and enables the determination of the EHP generation rate at every position within the absorber layers. This, in turn, yields the optical generation rate profile - a quantity that is needed in one-dimensional computer simulations of solar cells. Calculations pertaining to a typical a-Si:H-based solar cell indicate that ignoring the effect of front layers, such as glass and transparent conducting oxides (TCOs), has a significant effect on the calculated optical generation rate profile. Also, calculations suggest that the TCO in a typical glass/TCO/a-Si:H solar cell should have a real refractive index of ~2.0, in good agreement with the observed fact that ZnO is a good TCO for these types of cells.

Stepwise local error control using local extrapolation in Runge-Kutta methods is well-known. In this paper, we introduce an algorithm, designated RKrvQz, that is capable of controlling local and global errors in a stepwise manner. The algorithm utilizes three Runge-Kutta methods, of orders r, v and z, with r < v z. Local error is controlled in the usual way using local extrapolation, whereas global error is controlled using a technique we have termed 'quenching', which exploits the availability of a very high order solution and the use of a 'safety factor', often present in local extrapolation methods. An example using RK34Q8 gives a clear indication of the effectiveness of the method.

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We determine the Rolle function in Lagrange polynomial approximation using a suitable differential equation. We then propose a device for improving the Lagrange approximation by exploiting our knowledge of the Rolle function.