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C. Stratified Medium

In this appendix we investigate the wave propagation phenomenon in a stratified medium, i.e., in a stack of homogeneous planar layers with parallel interfaces [11, pp. 51-70]. The derivation is motivated by two reasons. The results show not only the operation principle of the simulation methods suited for planar topography as described in Section 5.2, but also yield the boundary conditions for the differential method in case of multiple planar layers below the simulation domain (cf. Chapter 6). Furthermore, the analytical expressions can be used to check the numerical results obtained with the differential method in case of a planar homogeneous resist.

The appendix is organized as follows. We start with the description of the electric field and then derive expressions for the magnetic field. Introducing a compact matrix notation provides an elegant mathematical formalism. Especially the factorization of the so-called propagation matrix of one layer is exploited in the treatment of a stack of homogeneous planar layers.


Heinrich Kirchauer, Institute for Microelectronics, TU Vienna