Infrared material absorption theory
The design of any infrared filtering system requires the selection of materials based upon knowledge of the optical, mechanical and thermal properties available. Frequently, the selection of suitable materials results from compromises between these various properties as no single material will possess the ideal characteristics required to suit the wide variety of applications.
All of the observed intrinsic absorption characteristics present in the spectrum of an infrared optical material can be classified by three fundamental processes involving interaction between the material and the incident electromagnetic radiation, namely; electronic absorption, lattice or phonon absorption and free-carrier absorption.
The electronic absorption characteristics observed towards the higher frequency end of the infrared spectrum are the result of interaction between the incident radiation and the motions of electrons or holes within the material. Only electromagnetic radiation with sufficient energy to cause an electron to transfer between the valence band and conduction band (hf) will be absorbed by this mechanism. The various transitions of these electrons define the position of the short wavelength absorption edge. The resulting spectrum provides information on the width of the energy band-gap of the material, and through spectral anomalies, can indicate the presence of impurities.
The lattice absorption characteristics observed at the lower frequency regions, in the middle to far-infrared wavelength range, define the long wavelength transparency limit of the material, and are the result of the interactive coupling between the motions of thermally induced vibrations of the constituent atoms of the substrate crystal lattice and the incident radiation. Hence, all materials are bounded by limiting regions of absorption caused by atomic vibrations in the far-infrared (>10µm), and motions of electrons and/or holes in the short-wave visible regions. In the interband region, the frequency of the incident radiation has insufficient energy (E=hf) to transfer electrons to the conduction band and cause absorption; here the material is essentially loss-free.
In addition to the fundamental electronic and lattice absorption process, free-carrier absorption in semiconductors can be present. This involves electronic transitions between initial and final states within the same energy band. The absorption or emission of the resulting photons is accompanied by scattering by optical or acoustic-mode phonon vibrations or by charged impurities.
These intrinsic absorption properties of semiconductors and insulators define the transparency of the material. To be transmitted in the region between the electronic and lattice absorptions, the incident radiation must have a lower frequency than the band-gap (Eg) of the material. This is defined by the short wavelength semiconductor edge at λ = hc/eEg, preventing electrons transferring to the conduction band. The generalised profile of the electronic absorption edge is known as the Urbach tail where the exponentially increasing absorption coefficient follows the general relationship: