Reflectivity of absorbing layers

Consider a ray of light incident on a thin absorbing film of BARC sandwiched between two semi-inflnite media, namely, photoresist and the silicon wafer substrate (Fig. 9.12). 

Using a similar approach as in the case of the top antireflection coating above, and assuming normal incidence at the boundary between two media, for instance medium 1 (photoresist) and medium 2 (BARC), the reflection (rj2) and transmission (ti2) coefficients are given by the Fresnel equations above [Eqs. (9.5) and (9.6)]. Multiplication of the reflection amplitude with its complex conjugate yields 

Equation (9.24) can be simplified by the use of the following expressions for some of the terms  

Therefore, the refleetivity from the BARC layer is then conveniently expressed as 

For the limiting case of the infinitely thick layer 2 (photoresist), 

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