# Germanium Single Crystals for Photonics
## 4 Isotopic Shift of Fundamental Absorption Bands of Germanium in the IR Region  
The vast majority of data on the physical and chemical properties of Ge were obtained using a material with a natural isotopic composition: Ge (atomic number 32, atomic mass 72.59) consists of a mixture of five stable isotopes with mass numbers 70, 72, 73, 74, 76. The separation of isotopes is a technically complex and expensive process; therefore; there are few data on the influence of isotopic composition on the physicochemical properties of Ge. In work [47], the influence of isotopically purity was studied on the isotopes \({}^{70}\)Ge and \({}^{74}\)Ge, and it was shown that isotopically pure germanium at low temperatures has a thermal conductivity 8.5 times higher than natural Ge. Phonon absorption significantly limits the use of Ge in optics [10; 11; 59]. The residual absorption of radiation in the IR region and thermal conductivity are largely determined by one physical phenomenon--the behavior of the atoms of the crystal lattice, in other words, phonon processes. They have been well studied; the position of the absorption bands in the spectra of Ge of natural composition is practically a constant of the material. However, on \({}^{70}\)Ge and \({}^{74}\)Ge samples, an isotopic shift of these bands in the region of 12-14 \(\upmu\)m was detected [48] (these measurements were carried out on the same samples as in [47]). This fact was subsequently confirmed for the remaining germanium isotopes, \({}^{72}\)Ge, \({}^{73}\)Ge, \({}^{76}\)Ge [49], and the area of study of absorption bands was expanded to 40 \(\upmu\)m, due to which it was possible to significantly expand the number of absorption peaks considered (up to 16). In this series of experiments, another technology for obtaining pure germanium isotopes was already used, but this did not affect the results obtained (Figure 3). It should be noted that the influence of crystallographic orientation and growth technology on the position of the phonon absorption band maxima was also not revealed. Lattice absorption peaks at frequencies \(\upgamma\)--850, 755, 650 cm\({}^{-1}\), etc., observed in Ge of natural composition, shifted in monoisotopic crystals, depending on the mass composition of the single crystal. In this case, in \({}^{70}\)Ge and \({}^{72}\)Ge crystals, an increase in the frequency of the absorption band, \(\upnu\), is observed, while in \({}^{73}\)Ge, \({}^{74}\)Ge, \({}^{76}\)Ge, \(\upnu\) decreases compared to crystals of natural composition. This shift, although small, exceeds the measurement error and can be used for express assessment of the isotopic composition of Ge. Figure 4 shows the dependence of the frequencies \(\upnu\) of the peaks of the phonon absorption of isotopically pure germanium single crystals on the mass number of the isotope, M. In the general case, the shift of the absorption bands was approximated by the following expression (1):  
\[\
u=1.6\
u_{0}e^{-k\upmu\upmu}, \tag{1}\]  
where \(\
u_{0}\) is the frequency of the maximum of the corresponding phonon absorption band of natural germanium; M is the mass number of the isotope; and \(k\) is a power coefficient in the range 0.0062-0.0072. This equation was obtained by processing the experimental data presented in Figure 4.  
Absorption peaks corresponding to frequencies shown in Figures 3 and 4 [49] can be characterized as corresponding to two-phonon absorption at critical points of the Brillouin zone (active IR modes). Increasing the operating efficiency of acousto-optical IR modulators based on germanium is largely determined by the increase in the speed and power of devices. The relatively high absorption coefficient of germanium suggests the presence of good heat dissipation during operation of the devices. The efficiency of heat dissipation can be increased by using isotopically pure germanium.