Silicon (Si)

During the past few decades, silicon has been developed to be the world's most widely produced semiconductor material, and as such is the most readily available for use in infrared systems, producing consistently high purity and sufficiently large quantities and dimensions to suit most applications. Investigations on the general optical properties of the material have been extensively reported over many years. Its refractive index and low dispersion properties are nearly as favourable as germanium. However, unlike germanium, no correlation between resistivity and transmissivity appears to exist, limiting the user to define "optical grade" material as the only procurement specification requirement available. Silicon is a robust, high melting point (1420°C) material that can be finished by ordinary glass working processes. On crystallisation it forms a diamond lattice structure that exists in either single or polycrystalline form.

Two different methods of ingot production are used to obtain a high quality monocrystalline Si substrate material: the Czochralski (Cz) crystal pulling technique, where a seeded crystal is pulled from the melt in a silica crucible and permitted to grow in a mechanically unconstrained environment, permitting precise control of the crystal orientation and shape (standard grade), and the Float Zone (Fz) refining technique (premium hyperpure grade), where a seeded molten zone is supported by surface tension between two vertical cylindrical rods of the material and passed through a heated crucible, re-orientating and refining the crystal through its travel. The most noticeable optical difference between the two grades is the presence of a significantly more pronounced absorption band at approximately 9µm (1110 cm-1) in Cz material, and a reduced absorption profile in premium hyperpure grade (Fz) material beyond 20µm, following the multi-phonon absorption region, where the material exhibits a nearly complete transparency recovery.

Absorption

Various interrelated factors determine the highly complex spectral structure of both silicon and germanium, comparative even to partially ionic II-VI semiconductors such as ZnS, ZnSe and CdTe where multi-phonon absorption is also present. The multi-phonon absorption profile exhibits a number of well-separated highly resonant absorption peaks in contrast to the fewer broader peaks exhibited by the II-VI materials.

Additionally, because of the small anharmonic (non-linear propagation) broadening of the different vibration modes, many of the individual phonon absorption features in the spectrum remain distinct. More than twenty five different two and three phonon modes of vibration have been measured and reported in silicon for this wavelength range involving all combinations of the two TO modes, two TA modes, LO mode and LA mode.

Dispersion

The refractive index of the transparent region of silicon has been reported by a number of investigators using a variety of techniques. Each of these reports has found variations in accuracy such that no coherent set of temperature dependent dispersion profiles have emerged even though high purity optical quality single crystal material was used. Consequently, the refractive index data derived for a temperature-dependent predictive dispersion model is the result of selective data across different wavelength regions. The following dispersion equation producing the best fit to this disparate data set for ambient room temperature (293K) was derived by Edwards et al with the following modified Sellmeier expression.

ir-technicallibrary-si-equation1

where λ1 = 1.1071µm, e = 1.16858x101, A = 9.39816 x 10-1 and B = 8.10461 x 10-3.

Calculated Transmission Profiles

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Calculated Multiphonon Absorption Profiles

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Temperature-dependent refractive index dispersion profiles

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Predicted far-infrared multi-phonon absorption

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Predicted electronic absorption edge

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Calculated extinction coefficient (k) profiles

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Infrared materials data

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