Efficient Computation of Multidimensional Lambertian Optical Absorption

Abstract

Approximate analytic expressions are given for the absorption of light emanating from a nonuniformly illuminated Lambertian surface into an absorptive layer having a spatially uniform coefficient of absorption, α. This situation is particularly relevant for silicon solar cells, which have deliberately textured surfaces and grid fingers that create nonuniform illumination. The approach uses Fourier superposition to represent spatial variation in the plane of the surface, represented by a series of wavenumbers in each axis. It is observed that the absorption rate and flux density at any given distance, z, into the layer is given by an effective wavenumber, keff, that is the root-sum-square of the wavenumbers in the two axes. This allows for simple analytic expressions that, for each Fourier component, depend only on the dimensionless terms keffz and αz. This Fourier-superposition approach is computationally efficient compared with ray tracing, and is particularly effective when the nonuniform illumination is periodic and symmetric in each axis, in which case the Fourier superposition becomes a cosine series of spatial harmonics. An example illustrates the good fidelity that can be obtained using as few as ten harmonics in each axis.