# Germanium Single Crystals for Photonics
## 5 Optical Damage of Germanium at a Wavelength of 10.6 \(\upmu\)m  
Ge is a classic semiconductor with a band gap of 0.67 eV [2]. The band gap of germanium is indirect [2], thanks to the various nonlinear effects occurring when intense laser radiation interacts with Ge. The experiments were carried out on a powerful pulsed CO2 laser setup, shown in Figure 5 (pulse duration up to 5 \(\upmu\)s; pulse energy up to 820 J). The laser parameters are described in detail in [79]. The 3000 mm-long laser resonator was formed by a concave mirror made of oxygen-free copper with a curvature radius of 40,000 mm and a parallel-plane transparent plate made of single-crystal germanium as an output mirror. A single-layer, antireflective coating (arsenic trisulfide--As2S3; Fresnel reflection from the germanium surface--R = 0.36) was applied to the outer surface of the output mirror. The capabilities of the laser installation, unlike most studies of optical damage, made it possible to conduct studies by exposing the crystal to a laser beam of a centimeter cross-section. The data obtained differed significantly from the results obtained by focusing the radiation of relatively low-power lasers into a spot with an area of less than 1 mm\({}^{2}\). Figure 6 shows the typical shape of the laser pulse measured by a photodetector based on the photon drag effect of holes in germanium (1 \(\upmu\)s/div). The operation of this photodetector is reported in detail in Section 8 [80]. Figure 4: Dependence of the frequencies \(\upnu\) of the peaks of the phonon absorption of the isotopically pure germanium single crystals on the mass number of the isotope, M. Reprinted with permission from Ref. [48]. 2015, Pleiades Publishing, Ltd. In the range of power densities of \(I=10^{7}\)-4-\(10^{8}\) W/cm\({}^{2}\), the dynamics of propagation of a high-power CO\({}_{2}\) laser pulse through a single-crystal germanium plate was studied [5; 6], and nonlinear losses during the passage of the peak part of the laser pulse were determined. At \(I=20\)-50 MW/cm\({}^{2}\), low-threshold optical breakdown of air occurs near the surface of the crystal [5; 6; 81]. The effect of the leading edge of the laser pulse leads to the appearance of nonequilibrium charge carriers in the surface layer of the crystal, which absorb radiation. In [5; 6], nonlinear radiation losses were studied on a group of base crystals, transparent in the region of 10 \(\upmu\)m and used for the manufacture of transparent optics of CO\({}_{2}\) lasers. The radiation losses on them grow exponentially with the decreasing width of the forbidden zone of the crystal. The experimental dependence is described by Formula (2):  
\[I_{2}=\frac{(1-R)I_{1}}{\exp\left(1-\Delta E_{g}/2 kT\right)}, \tag{2}\]  
where \(T\)-2.5\(\cdot 10^{4}\) K; \(\Delta E_{g}\) is the band gap; \(R\) is the reflection coefficient; \(k\) is the Boltzmann constant; \(I_{1}\) is the peak power density of the laser pulse; and \(I_{2}\) is the power density of the laser pulse transmitted through the crystal. The intensity of radiation passing through Ge decreases only twofold after 5-10 pulses, and damage is localized exclusively in the near-surface layer. This indicates that Ge is capable of withstanding significant radiation overloads without catastrophic destruction, and the material is of considerable interest for the optics of powerful-pulsed CO\({}_{2}\) lasers [82]. Figure 5: Experimental setup for studying the characteristics of pulsed electric discharge CO\({}_{2}\) lasers and the effect of their radiation on materials. Laser cuvettes with Brewster windows made of NaCl single crystals with a diameter of 300 mm. Reprinted with permission from Ref. [5]. 2015, [PERSON]. Figure 6: Laser pulse shape measured by a photodetector based on the photon drag effect of holes in germanium. The morphology of damage to Ge after exposure to radiation from a powerful-pulsed CO\({}_{2}\) laser was studied using methods of light and electron microscopy, as well as X-ray tomography [5].