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Based on effective media
approximation (EMA) model, the effective dielectric constants for a
multi-component thin film can be expressed as:
where fa,
fb,
ea,
and eb are volume fractions and dielectric constants
for components a and b, respectively. e is an effective dielectric
constant for the composite with component a and b, which can be expressed as e=(n2-k2)-2nki.
n and k are the refractive index and the extinction coefficient,
respectively.
For dielectric films such
as SiO2 and TiO2,
there is no significant absorption (k=0), therefore, above equation can be
simplified as:
where na and nb are refractive index for component a and b, respectively. n is the effective refractive
index for the film.