Optical absorption of thin film on a Lambertian reflector substrate

A formula is derived for calculating the optical absorption of thin films deposited on a Lambertian reflector substrate. It is shown that compared with the case of flat reflecting substrate, the incoherent absorption is enhanced by a factor of
m\epsilon_{1}
in the weak absorption limit, where ε
1
is the real part of the film dielectric constant and
m \simeq 2
is a slightly varying function of ε
1
. For a 0.5-µm a-SiH
x
(bandgap 1.7 eV) solar cell with a Lambertian reflector substrate, the total absorption in terms of the short-circuit current is calculated to be 18.63 mA/cm
²
.