# Germanium Single Crystals for Photonics
## 2 Absorption and Scattering of Germanium in the IR Region of the Spectrum  
Many authors [2; 23; 57] have studied the absorption of IR radiation in Ge; the initial studies were mainly conducted in the field of fundamental absorption or on doped samples. The advent of CO\({}_{2}\) lasers stimulated studies of the absorption coefficient (\(\beta\)) at a wavelength of 10.6 \(\upmu\)m. A physically permissible level of the absorption coefficient was revealed and technologically confirmed for practical use. The papers [10; 11; 58] present the results of a study of infrared radiation absorption in n-type Ge single crystals depending on the specific electrical resistance (\(\rho\)), temperature (T), and wavelength (\(\lambda\)) [59]. Figure 2 shows the frequency dependencies of the absorption coefficient in the region of maximum transparency (2.5-11) \(\upmu\)m, the spectral dependence of absorption, and the effect of specific resistance on absorption [5]. In the region of maximum transparency of Ge, optimization of the specific resistance allowed a reduction in the value of \(\beta\). The measured value of \(\beta\), strictly speaking, is the value of the attenuation coefficient in the samples (except for the use of the calorimetric method, which allows for obtaining data only on absorption, but this method allows for measuring the value of \(\beta\) only at the wavelength of the laser used). At present, crystals  
Figure 2: Dependence of the absorption coefficient of n-type germanium in the region of maximum transparency: (**a**) on the wavelength \(\lambda\) (\(\upmu\)m): 1. \(\rho\) = 0.03 Ohm\(\cdot\)cm; 2. \(\rho\) = 1.0 Ohm\(\cdot\)cm; 3. \(\rho\) = 2.0 Ohm\(\cdot\)cm; 4. \(\rho\) = 2.5 Ohm\(\cdot\)cm; 5. \(\rho\) = 3.0 Ohm\(\cdot\)cm; 6. \(\rho\) = 5.5 Ohm\(\cdot\)cm; (**b**) at \(\lambda\) = 10.6 \(\upmu\)m on the specific resistance, T\({}_{1}\) = 297 K, T\({}_{2}\) = 220 K; (**c**) on the temperature (\(\lambda\) = 10.6 \(\upmu\)m): \(\rho_{1}\) = 0.03 Ohm\(\cdot\)cm; \(\rho_{2}\) = 2.5 Ohm\(\cdot\)cm. Reprinted with permission from Ref. [5]. 2015, Rogalin V.E. with \(\beta\) = 0.015 cm\({}^{-1}\), with lattice absorption \(\beta_{\rm{grat}}\) = 0.01 cm\({}^{-1}\) have been obtained. It was possible to bring surface absorption to \(\beta_{\rm{surf}}\) = 0.0009 cm\({}^{-1}\). These values are close to the technological (phonon) limit of the material's capabilities [10; 11; 58; 59]. The dependence \(\beta\) = f (\(\lambda\)) obeys the experimental expression \(\beta\)\(\sim\)\(\lambda^{1.2}\) measured by us. The value of \(\beta\) depends exponentially on temperature, and the main mechanism of losses in the volume is absorption on free charge carriers. Studies of the IR absorption of Ge in the region of maximum transparency have shown that by optimizing the concentration of electroactive impurities, it was possible to reduce the absorption coefficient almost to the phonon limit. This is ensured by the constancy of the ratio of the product of the concentration of electrons and holes and thus reducing the concentration of holes (the absorption cross-section of which, in the 10 \(\mu\)m region, is \(\sim\)16-100 times greater than that of the electrons [10; 58; 59; 11]). For the production of IR optics from germanium, exclusively crystals of the electron conductivity type are specially grown in the range of specific electrical resistance values of \(\sim\)5-40 Ohm\(\cdot\)cm [22]. It can also be noted that the use of germanium under elevated temperature conditions requires values \(\sim\) in the range of 4-10 Ohm\(\cdot\)cm. It has been established that doping germanium with silicon increases the temperature stability of transmission, in which a decrease occurs with increasing temperature already at 45-60 \({}^{\circ}\)C [22]. However, optical losses can be caused not only by volume absorption but also by surface absorption, as well as by scattering of radiation by structural defects.