The reason for the effect of finite substrate is the following: In reality, the substrate is always finite. In the regular multi-layer substrate MOM modeling, we assume it is infinitely extended in the horizontal direction. The infinite substrate will create surface waves. When the thickness of substrate is thin, the surface wave is relatively small. When it is thick, the surface wave is becoming significant. For the finite substrate case, the surface wave will hit the boundary of the finite substrate, part of the power will be radiated out. However, part of it will bounce back to the patch. Normally, the bounced back power should be small and it will not affect the input impedance. However, when the thickness is too large or the size of the finite substrate is too small, the bounced power may be big enough to change the behaviour of the input impedance.