# Germanium Single Crystals for Photonics
## 1 Introduction
In the IR region of 3-5 um and 8-14 um ranges, most transparent materials are crystals and have huge operational disadvantages [9]. Among them are water-soluble alkali-halide crystals, soft, plastic crystals of the KRS group (based on toxic thallium salts), etc. It turned out that, based on a set of physical and chemical properties (transparency, hardness, mechanical and climatic resistance, etc. ), germanium turned out to be the most preferable material for a number of applications in IR technology, primarily for the optics of thermal imaging devices [1; 14]. Later, polycrystalline ZnSe was developed for this region of the spectrum, which in a number of cases has better optical properties (higher transmittance, lower absorption coefficient, transparency in the visible range) [15; 16; 17]. Nevertheless, although ZnSe displaced Ge, it could not completely replace it. The earth's crust contains 7\(\cdot\)10\({}^{-4}\)% by weight of germanium [1; 18]. It would seem that this is not a small amount, but in non-ferrous metal deposits, germanium is a much dispersed associated element, and its extraction is very difficult. The main share of Ge is extracted during the processing of zinc ores. In addition, the extraction of germanium from coal is considered economically advantageous when its content is more than 0.5 g per ton of coal. So far, only one deposit (in Belgium) has been explored in the world where germanium-containing minerals are mined. In 2021, the total world production of germanium was estimated at about 140 tons. Therefore, the price of polycrystalline zone-refined germanium usually fluctuates in the range of $1200-1300 per kg [18].  
Obviously, for the modern needs of the electronic and optical industry alone, this is extremely little, and the price of the material is quite high. In addition, there are a number of other applications of this material that are not related to photonics and electronics. In the electronic industry, germanium has been almost completely replaced by silicon, which was due to both the cost and the low thermal stability of the semiconductor properties. Currently, more than 200,000 tons/year of monocrystalline silicon are produced in the world at a price of \(\sim\)$19,000/t [18; 19]. Optical silicon is widely used in devices operating in the 3-5 um range, but in the 8-14 um region, it is practically not used due to the presence of phonon absorption peaks in this region [19; 20]. However, in the terahertz region, silicon has proven to be an extremely popular material. The use of germanium is currently effective in cases where the use of this expensive and scarce material provides a real, not only technological, but also economic effect. Since germanium does not interact with atmospheric moisture, is non-toxic, durable, has good thermal properties and a high refractive index--n = 4.0 [8], this material remains in demand in IR optics. The high hardness of Ge (6.0 on the Mohs scale) allows the formation of high-precision optical parts that are well-antireflected even by single-layer ZnS or As2S3 coatings (radiation transmission up to 98%); in addition, a wear-resistant diamond-like antireflective coating can be applied to germanium. Ge is used to manufacture semitransparent mirrors that operate both with and without interference coatings, high-precision Fabry-Perot standards, acousto-optic elements, and other components [1; 3; 7; 21; 22; 23; 24; 25; 26; 27; 28; 29]. Narrow-band interference filters are usually manufactured on Ge substrates. The most important application area of Ge is the optics of thermal imaging cameras in the wavelength range of 8-14 um, used in passive thermal imaging systems, infrared guidance systems, night vision devices, fire extinguishing systems, etc. [1; 28; 30]. Due to its low distortion and high refractive index, Ge is used to manufacture optical elements for spectroscopy that operate on the effect of multiple total internal reflection (MTIR) [2], as well as wide-angle lenses.