It is well known that TM-waves are not as effective as TE-waves in forming interference fringes in oblique incidence. In lithography, this corresponds to contrast loss when imaging with the high-NA exposure tool that employs strong off-axis illumination. One usually explains that there is an angle between electric fields of TM-waves in the resist. However, when the resist is absorptive, the calculation of reduction of contrast for TM-waves becomes rather complicated. In this paper, we show that the analytic formula for symmetric two-beam interference can be derived by straightforward full-vector approach. With the help of the Poynting vector and Poynting's theorem, aerial image in the resist can be calculated.
The contrast-reduction factor for TM-waves is thus be found to be
[formula] where k0+ is the wave vector in the resist and N0 is the complex index of refraction of the resist. When the resist is non-absorptive, the contrast loss factor for TM-waves reduces to the well-known form ε, = cos2θ0, where θ0 is the angle of refraction in the resist. It can also be shown that for TE-waves aerial image in the resist is separable in its transverse and longitudinal coordinate dependence, as is also true for TM-waves under reasonable approximations. That is, the thin-film effect can be regarded as independent of aerial image formation. This conclusion makes possible the development of an efficient methodology for optimizing the thin-film stack used in optical lithography.