Substrate/overlayer model
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A homogeneous overlayer uniformally covers a homogeneous substrate. At least one XPS peak distinguishes the substrate material from the overlayer. An example would be the oxide layer on a silicon substrate. If we assume that the photoelectron inelastic mean free path is the same in both the substrate and overlayer, the intensity of an XPS peak characteristic of the substrate (e.g. the metallic component of the Si 2p envelope) would vary with the photoemission angle as :
Setting
and solving the integral
Let us note that IS0λ represents the intensity obtained from the substrate in the absence of an overlayer. Continuing,
so that 
can be obtained from the slope of 
vs 
Similarly, one obtains for the intensity of a peak characteristic of the overlayer :
where IL0λ represents the intensity obtained from a thick sample of the overlayer material.
