Optical Properties And Applications Of Germanium In Photonics
There are two of the most widely used atmospheric transparency windows in the IR region: the spectral ranges 3–5 and 8–14 µm, which correspond to the region of maximum transparency of germanium (Ge). For these ranges, a large number of optical devices have been developed and used. If in the wavelength range (λ) of 3–5 µm, optics made of silicon (Si) crystals, which is much more accessible, is used predominantly, then in the range of 8–14 µm (where Si has a high absorption), Ge elements are actively used. Crystalline germanium (single and polycrystals) is one of the classical materials for the middle and far infrared wavelength ranges. The share of its use in photonics is about 25–30% of the total consumption of this material . Ge is transparent in the range of 1.8–23 µm, however, in the region of 11–23 µm, a number of phonon absorption bands are present, which sharply limit the use of the material; there is also a transparency window in the THz range (~ 100–300 µm).
Ge impurity crystals are actively used for the manufacture of photodetectors that record infrared radiation . Their work is based on the excitation by a quantum of carrier radiation at the impurity level, which passes into the conduction band. For different IR ranges, the appropriate impurity is used. As a rule, these receivers operate at low temperatures.
Among the operational features of Ge that must be taken into account in the process of application are the lack of transparency in the visible region and the presence of an exponential dependence of the absorption coefficient on temperature.
Optical Ge single crystals are usually grown from the melt by the methods of Czochralski, Stepanov, directional solidification, etc. [7, 25, 26]. In the case when the losses on absorption and scattering in the optical system can be neglected, use cheaper polycrystalline Ge.
Creating a modern elemental base of photonics is impossible without the use of single crystals with low and ultralow content of impurities, in particular, crystals for ionizing radiation detectors require a concentration of electroactive impurities of no more than 1010 cm–3. In this case, germanium always contains background impurities, such as oxygen (the concentration of which can reach 1017 cm–3), carbon, nitrogen, etc. The presence of oxygen leads to the formation of dislocations, microdefects, and thermal donors, which, in turn, affects the lifetime of non-equilibrium charge carriers and causes radiation scattering.
Electrophysical and optical parameters of Ge are interrelated. A significant amount of research on Ge, including optical properties, is carried out by electrophysical methods, which have achieved considerable perfection in semiconductor electronics. This allows testing of Ge for IR photonics based on measurements of electrophysical parameters [27, 28].
Absorption of IR radiation in Ge has been studied by many authors, e. g. [29, 30]; however, the studies were carried out mainly in the region of fundamental absorption, or on doped samples. A number of studies were carried out calorimetrically at λ = 10.6 µm [31–33]; the results of the study of the absorption of infrared radiation in n-type Ge single crystals are presented, depending on the resistivity ρ, temperature T and wavelength λ . Figure 1 shows the frequency dependences of the absorption coefficient (β) in the region of maximum transparency 2.5–11 µm, the dependence β = f (λ), and the effect of resistivity ρ on β.
In the region of maximum transparency of Ge, the optimization of resistivity helped to reduce the value of β10,6. The measured value of β, strictly speaking, is the value of the attenuation coefficient in the samples. At present, the crystals with β = 0.015 cm–1 have been obtained, with grating absorption, βgrat = 0.01 cm–1. The surface absorption is 2βsurf = 0.0009 cm–1. These values are close to the process limit of the material [31–34]. The dependence β = f (λ) obeys the experimental expression β ~ λ1,2. The value of β depends exponentially on temperature and the main mechanism of volume loss is absorption on free charge carriers. A certain increase in β with an increase in ρ in the region of 5–50 Ohm · cm is a consequence of the increasing contribution of absorption by free holes, whose absorption cross-section in the region of 10 µm is ~16–100 times larger than that of electrons [31–33].
The studies of Ge IR absorption in the transparency region showed that by optimizing the concentration of electroactive impurities it is possible to reduce the absorption coefficient almost to the phonon limit. However, the losses can be caused not only by volume absorption, but also by surface absorption and scattering of radiation by structural defects. This, apparently, can explain a certain excess of the measured value of β10.6 over the calorimetric measurements [31–33], where only the volume absorption was recorded at λ = 10.6 µm. The same effects probably led to a decrease in the value of the coefficient γ in the measured frequency dependence β ~ λγ. . As shown in , in the region of small β values for Ge, the value γ ≈ 2.
With the advent of the technology of forming optical components by high-temperature deformation, an attempt was made to carry out this process in the manufacture of germanium optics. It was found  that plastic deformation causes an increase in the absorption coefficient of germanium crystals, since changes in the absorption spectrum and conductivity indicate that the dislocations resulting from this at a temperature of 300 K have acceptor properties.
In the presence of scattering, the Bouguer-Lambert law for weakening light is followed not strictly, and the known formulas relating transmittance and attenuation in the case of noticeable scattering become incorrect. The differences are the higher, the higher the ratio of the probabilities of photon scattering and absorption in a unit-length layer, and the higher the ratio of crystal length to its diameter .
For a number of applications, primarily in thermal imaging (receiving, processing and transmitting images), scattering causes a decrease in image contrast and resolution . In this range, small-angle Mie scattering takes place and the fraction of scattered radiation can reach 20% or more, depending on the characteristics of germanium. Ge polycrystals scatter light several times more intensely than single crystals. The corresponding loss coefficients βp Ge – (10–3 – 10–1 cm–1) are included in the light attenuation (extinction) coefficients, in many samples they are comparable with the extinction coefficients themselves and often exceed β [9, 12, 13].
The scattering of radiation in Ge is associated with the appearance of growth thermoelastic stresses, impurity inhomogeneity, and structural defects. The scattering maximum is observed in doped single and polycrystals with a large number of defects (low-angle boundaries, inclusions, block structure) . High-temperature annealing of Ge leads to a decrease in the intensity of light scattering several times, which indicates a change in the size and shape of scattering inhomogeneities, and, possibly, their partial decay. During heat treatment of germanium, two processes take place: dissociation of oxygen complexes with antimony during heat treatment (with removal of antimony from an impurity cloud) and an increase in oxygen clouds due to oxygen diffusion. These results indicate possible ways to reduce the light loss associated with scattering. This is a long-term high-temperature annealing, the use of ultrapure raw materials, and, above all, the improvement of Ge growing technologies [4, 9].
The presence of a sharp temperature dependence β limits the use of Ge in continuous lasers. Ge windows perform satisfactorily at power densities of 100–250 W / cm2 if their effective cooling is ensured . However, the use of Ge in continuous lasers is limited because of the appearance of optical elements from polycrystalline zinc selenide, which has better optical strength.
The relationship between the structure and electrical conductivity (and, consequently, absorption) of not only single crystals, but also optical polycrystals of Ge (GPO) and highly pure germanium (HPG) has been revealed. The electrical conductivity of GPO decreases with a decrease in the size of crystallites, which is associated with a decrease in the mobility of charge carriers caused by their scattering at the boundaries of crystallites. In HPG, the electrical conductivity increases with decreasing crystallite size, and the lifetime of non-equilibrium charge carriers in it decreases due to an increase in the concentration of surface electronic states [36, 37].
Dislocation free and low dislocation HPG is grown for the production of radiation-resistant photoelectric detectors of ionizing radiation, where crystals with a content of linear defects (of the order of 100 cm–2) and a concentration of electroactive impurities at the level of 109–1010 cm–3 are required. One of the harmful impurities that influence the defect structure and properties of Ge crystals is oxygen [O] [38–41]. Oxygen in germanium, as a rule, is an atomic interstitial, optically active impurity. The complexes formed by [O] in germanium are due to the presence of Ge-O-Ge quasimolecules, as well as various GeOx precipitates, the sizes, concentrations, shape of which depend on the total concentration of [O], growing conditions, heat treatment. The authors of [38––41] identified a relationship between concentration [O] and dislocation density, determined the content of optically active [O] in Ge crystals of various grades, and found that the content of [O] has a noticeable effect on the structural perfection of HPG and the parameters of devices manufactured on based on, e. g., detectors.
The content of optically active [O] in Ge of various grades is determined by the method of IR-Fourier transform spectroscopy based on the position of the absorption bands in the phonon zone (Fig. 2). Regulation of the content of [O] in the Ge matrix is often achieved by doping with rare earth elements . It was shown that in Ge doped with a series of lanthanides, they actively bind [O] into electrically neutral complexes, formally reducing the concentration of optically active [O] in the matrix by almost an order.
Modern technologies for growing germanium with low oxygen content in crystals should provide oxygen concentration at a level of 1015 cm–3, which implies growing in the atmosphere with the partial pressure of [О] in the gas phase not exceeding 1.53 · 10–23 atm (∼1.50 · 10–18 Pa) . With the growth of Ge from the melt and the presence of oxygen in the gas phase, Ge oxidation reaction occurs with the formation of heterogeneous GeO2 inclusions in the melt, which are not only a source of dislocations, but also an increase in radiation losses.
Interest to Ge has increased due to the development of global satellite networks, as well as other telecommunication projects . For the on-board power supply of satellites, which are the basis of such projects, radiation-resistant photoelectric converters (PEC) with high efficiency are required. Such elements are noticeably more expensive than widely used silicon, but, in this case, they are used due to greater efficiency. PEC with efficiency more than 39% are based on epitaxial AIII – BV GaInP / GaInAs / Ge on Ge substrates. The necessary requirements for Ge are low dislocation density (at the level of ~200–250 cm–2), the absence of dislocation defects such as low-angle boundaries, and a crystal diameter of 100 mm and above [40, 41].
Currently, various devices using X-ray radiation are widely applied. High-quality single crystals with relatively high reflectivity are used as X-ray monochromators. They are split in such a way that the surface is parallel to the diffraction planes. The monochromatic radiation received in this way is always to a certain extent polarized. The degree of polarization of the radiation depends on the perfection of the monochromator crystal. Undoped Ge is used for these purposes due to the high level of perfection of the crystals achieved .
Ge has a high radiation resistance . Ge samples were irradiated with γ rays of 60Co at 3 800 rad · s–1 (108 rad dose), fast electrons with an energy of 1 MeV, in a nuclear reactor with a stream of slow and fast (up to 30%) neutrons at T = 200 °C. The transmittance changed only after treatment in the reactor. Irradiation with thermal neutrons in Ge gives rise to Ga and As atoms, which are absorbing electroactive impurities.
Most of the data on Ge is obtained on the material of natural isotopic composition: Ge’s atomic number is 32, its atomic mass is 72.59; it consists of a mixture of stable isotopes with mass numbers of 70, 72, 73, 74, 76. Isotope separation is a technically complex and expensive process, and therefore there is little data on the effect of the isotopic composition on the physical properties of Ge. In , the effect was studied on 70Ge and 74Ge isotopes and it was shown that at low temperatures the heat conduction of isotopically pure Ge is by 8.5 times higher than that of Ge of natural composition.
Phonon absorption significantly limits the use of Ge [20, 34]. It is well studied, the position of the absorption bands in the natural spectra of the Ge composition is practically the constant of the material. However, on the 70Ge and 74Ge samples, an isotopic shift of these bands was observed in the 12–14 µm region  (Fig. 2) (the experiments were performed on the same samples as in ). The influence of crystallographic orientation and growing technology on the position of the maxima of the phonon absorption bands was not revealed. Absorption grating peaks at frequencies ν – 850, 755, 650 cm–1, observed in natural Ge composition, are shifted in monoisotopic crystals. Moreover, in the 70Ge crystals, an increase in the frequency of the absorption band, ν, is observed, and in74Ge, ν decreases as compared to crystals of natural isotopic composition. The shift exceeds the measurement error and can be used for rapid assessment of the Ge isotopic composition.
Ge is a classical semiconductor with a band gap of 0.67 eV . This contributes to various nonlinear effects in the interaction of intense radiation with Ge.
In the power density range, I = 107–4 · 108 W / cm2, the pulse propagation dynamics of a CO2 laser was studied , nonlinear losses were determined during the passage of the peak part of the laser pulse. At I = 20–50 MW / cm2, optical breakdown of air occurs near the crystal surface. The action of the leading edge of a pulse generates the appearance of hot non-equilibrium charge carriers in the crystal that absorb radiation. Nonlinear radiation losses on them grow exponentially with decreasing width of the forbidden band of the crystal. Experimental dependence is transformed into the expression:
where Т ~ 2,5 · 104 K; ΔEg is the width of the forbidden zone; R is the reflection coefficient; k is the Boltzmann constant; I1 is the peak power density of the laser pulse; I2 is the power density of a laser pulse emitted from a crystal.
The intensity of the signal passing through the Ge decreases only twice after 5–10 pulses, and the damage is localized exclusively in the surface layer, i. e., Ge, as a material capable of withstanding significant radiation overload without catastrophic destruction, represents considerable interest for the pulsed CO2 laser optics.
The methods of light and electron microscopy and X-ray tomography investigated the morphology of Ge damage after exposure to radiation of the high-power pulsed CO2 laser . The studies were carried out on commercially available Ge of GMO brand, processed according to optical technology, and on dislocation-free crystals, chemically polished, according to the technology used in microelectronics. It was established that in the range of amplitude values of the radiation power density of 2 · 106–4 · 108 W / cm2 two main types of damage are realized. At I < 4 · 107 W / cm2, foci of local microfracture of the surface layer are observed. Local microfractures arising at I < 4 · 107 W / cm2 due to breakdown on either absorbing micro-inhomogeneities of a crystal or on defects in optical processing are the result of microexplosions forming craters. The effect of radiation at I ≥ 4 · 107 W / cm2 leads to the melting of a layer with a depth of 1–3 µm, which is explained by the avalanche breakdown of non-equilibrium charge carriers of the near-surface Ge layer, which prevents the crystal volume from being affected by ultra-threshold intensity. The nature of the impact, leading to the destruction of only the surface layer of the optical element, allows you to completely restore the elements made of Ge by repolishing.
In the range of 2.6–5 µm, the effects of two-photon [48, 49] and three-photon absorption  are superimposed on the nonlinear absorption process. Nonlinear absorption of radiation from a high-power non-chain pulsed HF laser was studied on Ge of various thickness and specific resistance . Depending on the composition of the mixture (SF6 : C2H6 or SF6 : C6D12), the laser generated radiation in the range of 2.7–3 µm (HF laser), or 3.7–4.1 µm (DF laser). The generation spectrum of the HF laser was a set of 18 different lines in the range of λ = 2,6–3 µm (average ℏω = 0.4397 eV, corresponding to λ = 2.82 µm). Pulse width at half-height ~150 ns; maximum energy Е ≈ 5 J; the energy distribution is close to uniform.
In the case of low intensities of irradiation with a HF laser (I = 0.3 MW / cm2), in the absence of damage to the samples, a substantially nonlinear character of the transmission of radiation through Ge is observed. Figure 3 shows the dependences of the transmission of Ge (h = 1 mm) on the radiation density of HF and DF lasers, respectively, and Fig. 4. shows dependence of the concentration of nonequilibrium free carriers generated in the process of two-photon absorption over depth (calculated at time t ≈ 200 ns). Nonlinear absorption of the DF laser radiation in Ge was observed at a significantly higher radiation intensity I > 10 MW / cm2.
The transmittance of Ge in the nonlinearity region decreases noticeably with increasing sample thickness and crystal specific resistance. The power of the transmitted pulse noticeably decreases, the shape is strongly deformed, there is a noticeable shortening of the front edge. The two-photon absorption coefficient of Ge К2 = 55 ± 10 cm / GW was obtained. The effect of pulse parameters on the dynamics of the passage of a HF laser pulse through a Ge with a thickness of h = 0.03–0.55 cm is analyzed.
The intensity distribution I(z) over the thickness of Ge varies greatly within the duration of the laser pulse. The generated carriers are concentrated in a thin layer near the entrance surface of the crystal (see Fig. 4.), i. e. the main processes of nonlinear absorption occur in a layer with a thickness of less than 50 microns. The emerged peculiar nonlinear filter, as well as at λ = 10.6 µm, prevents the destruction of the volume of the material even when trying to tightly focus the laser energy into the depth of the crystal. This circumstance testifies to the great importance of nonlinear absorption processes occurring in the surface layer, e. g., the value of the recombination coefficient of free carriers on the surface may exceed by several orders of magnitude. Special doping of the surface layer can noticeably change the magnitude of the nonlinear transmission of the entire Ge sample.
Other nonlinear effects are observed in Ge . The optical constants of materials are determined by the equation
P = ε0(χ(1) E + χ(2) E + χ(3) E + ...),
where P is the electric polarization induced by the electromagnetic wave, Е is the field strength, χ is the susceptibility tensor of the medium.
In linear optics, only the first term of the equation is taken into account, but when working with high-power laser radiation, it is no longer possible to neglect non-linear effects determined by other members of the equation. In crystals with a diamond structure (in particular, Ge), χ(2) = 0 at all times. For Ge, χ(3) = 1.5·10–10 units CGSE. This allows the use of Ge for the effective reversal of the wave front . In the Ge plate installed in the cavity of a CO2 laser, a phase-conjugate reflection of 10.6 µm from phase gratings arising in counterpropagating waves was obtained. The reflection coefficient reached 20%. The beam reflected by such a mirror goes back along the same optical path. The use of this effect makes it possible to obtain diffraction divergence of the radiation of a high-power laser with inhomogeneities in the active medium and in optical elements.
The photon-drag effect of current carriers in semiconductors is used in photoreceivers (PR) for recording high-power pulsed laser radiation . When high-power electromagnetic radiation is absorbed, not only energy is transmitted to the free carrier, but also a photon momentum, the redistribution of which leads to the formation of a directed flow of charge carriers in the crystal. Such receivers for λ = 10.6 µm are usually made of p-type Ge. The quantum of CO2 laser radiation hν = 0.117 eV is absorbed in Ge mainly due to the intraband transition between the subbands of holes with heavy and light masses. In this case, the hole perceives both the energy and the momentum of the photon. The condition for fulfilling the laws of conservation of energy and momentum makes it necessary to move holes relative to the lattice in the direction of radiation propagation, which contributes to the appearance between the ends of the crystal rod potential difference, the photon drag EMF (V). The main parameters of the PR are: time resolution up to 10–10 s, large dynamic range (10–107 W / cm2), operation at room temperature, sensitivity of the order of 0.1–1 V / MW. The time constant (τ) is described by the formula
τ = nc / L,
where: L is the length of the working crystal of the photodetector; n is the refractive index; c is the speed of light.
The advantages of such PRs include: high noise immunity, stability of parameters, the ability to produce receivers with large apertures. The maximum V is ensured by optimizing the crystal by the parameters: ρ, S, L. At room temperature, the optimal values are ρ ≈ 1–10 Ohm · cm, L = 4–6 cm, and the area of the receiving platform corresponds to the minimum possible cross-section of the laser beam .
The acoustooptic effect  is also a nonlinear effect widely used in photonics. The devices based on this effect are used to modulate and scan light. The passage of an acoustic wave in a photoelastic medium induces changes in the instantaneous value of the refractive index, which leads to the formation of a phase grating with a period equal to the acoustic wavelength and amplitude proportional to the amplitude of the acoustic wave and the photoelastic constant of the crystal. Ge is one of the main materials for use in acoustooptics of the middle and far infrared range, in particular, in CO2 lasers, due to the good physicochemical properties and high values of the refractive index and photoelastic constants . Acoustooptic modulators for CO2 lasers are commercially available (see, e. g., ). The high thermal conductivity of Ge makes it possible to create thermostable constructions of acousto-optic devices based on Ge crystal, which consume tens of watts of control power with a diffraction efficiency at a wavelength of 10.6 µm more than 90% . Th devices are usually water-cooled. In modern technics, the laser Ge-based acoustooptic modulators are used in free-electron lasers for pulsed radiation control .
The most recent trend in modern photonics is the creation of Ge-based devices for modulating infrared radiation: modulation by introducing moderate levels of excess carriers into Ge by exciting diode laser radiation ; modulation in waveguide Ge structures on Si substrates by controlling the absorption of free carriers [59, 60].
Recently, the possibility of using germanium in the terahertz (THz) range of the electromagnetic spectrum (~3 mm – 30 µm, 3 cm–1 – 300 cm–1)  is being considered. The optical properties of pure and doped Ge in the THz range were studied in . In the THz range, active elements of acoustooptic devices made of Ge are of interest . Ge can be used for use in multispectral infrared imaging devices of the IR + THz range, as well as in THz range lasers pumped by a CO2 laser.
Ge transmittance spectra with different ρ are shown in Fig.5. The results showed a noticeable increase in the absorption of doped Ge in the THz range, compared with the undoped (ρ = 47 Ohm · cm). An increase in the impurity concentration, both electron and hole, leads to an increase in absorption. If in the region of 25–50 µm, the effect of ρ on the transmittance of Ge (Sb) is not noticeable, then in the region of ≥220 µm it is observed firsthand.
The main absorption in the THz region occurs on free charge carriers (self and impurity). If we compare the results for Ge (the region λ ~ 160–220 µm) and the data for Si , then they show that the attenuation coefficient in the region of 160–220 µm approximately coincides, and is ~ 0.5 cm–1.
By contrast to the IR range, minimal losses of ~0.5 cm–1 in the THz region are observed in intrinsic crystals. Fresnel reflection losses can be largely compensated by creating periodic relief structures on the surface with a high degree of regularity and a period less than the radiation wavelength. Therefore, optical products from undoped single-crystal Ge can be effectively used to control the radiation in the THz region.