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Spectroscopic ellipsometry measurements on a germanium crystal at a photon energy of 1.5 eV show

that the real and imaginary parts of the complex relative permittivity are 21.56 and 2.772 respectively.

Find the complex refractive index. What is the reflectance and absorption coefficient at this wavelength?

How do your calculations match with the experimental values of n = 4.653 and K = 0.298, R = 0.419 and

α = 4.53 × 106 m-1 ?

a. Show that the attenuation coefficient a due to free carrier absorption is given by

α ω ε

ε

σ =



=

 

 

c n c n

r

o

1

Free carrier absorption

where ω is the angular frequency of the EM radiation, ε

r″ is the imaginary part of the relative

permittivity, n is the refractive index and σ is the conductivity due to free carriers in the sample.

b. Intrinsic germanium has a conductivity of about 2.1 Ω-1 m-1. Calculate the imaginary part εr″ of the

relative permittivity at a wavelength of 20 μm. Find the attenuation coefficient α due to free carrier

absorption. The refractive index of germanium at the specified wavelength is n = 4.

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