Band-like Inhomogeneity in Bulk ZnGeP₂ Crystals, and Composition and Influence on Optical Properties

Abstract

The influence of intrinsic impurities on the formation of band-like inhomogeneities in ZGP single crystals containing two highly volatile elements has been analyzed. It has been shown that the formation of growth bands occurs due to the accumulation of binary phosphides at the crystallization front and is accompanied by the formation of pores in the near-wall region of the ingot. A connection between near-wall pore formation and the presence of growth bands in ZGP has been established. X-ray spectrometry revealed differences in the chemical compositions of “light” and “dark” growth striations, with significant deviations from stoichiometry in these regions. The dark bands exhibited a higher phosphorus content compared to the light bands and showed an increased germanium content in the light bands. Differences in the orientation of crystallographic axes were observed between the light and dark regions. It has been shown that samples containing inclusions of band-like inhomogeneity significantly distort the profile of the radiation passing through and generated in the crystal and lead to pronounced astigmatism. However, in contrast to the extremely negative influence of banded inhomogeneity on the optical properties of single crystals, the influence of growth striations on the radiation resistance of crystals is minimal.

1. Introduction

Zinc germanium phosphide (ZnGeP₂, ZGP), a diamond-like semiconductor with a tetragonal chalcopyrite structure from the A²B⁴C⁵₂ group, exhibits outstanding nonlinear and linear optical properties [1] and is used in nonlinear optical devices to generate powerful coherent radiation in the 3–8 μm range through optical parametric generation (OPG) from a solid-state pump laser generating radiation of around 2 μm. Such devices can be used in medicine, atmospheric monitoring, special applications, etc. [2]. When growing optical-quality crystals, special attention is paid to their defectiveness since the properties of crystals depend, to a greater or lesser extent, on their defect structure. In this case, they try to discover what the real structures of the grown crystals are, the reasons for individual manifestations of this structure, and the effect it has on the properties intended for use. The answer to the last question reveals significant technical, methodological, and material costs, as well as the development of methods and their use to eliminate the defect that affects the application of crystals.

Growth striations are inclusions of intrinsic impurity atoms or doping components that arise due to a violation of the uniform distribution of impurity atoms in the volume of the crystalline matrix. The formation of growth striations during the growth of single crystals of complex semiconductors containing volatile components, even with congruent melting, can be accompanied by a deviation from stoichiometry for a particular substance due to the evaporation of the elements that make up the crystal during the synthesis and growth stages. If the material contains two highly volatile components, it is practically impossible to grow a stoichiometric crystal.

All of the aforementioned factors contributing to the formation of growth striations are fully applicable to zinc germanium phosphide (ZnGeP₂) single crystals. ZnGeP₂ contains two highly volatile elements (zinc and phosphorus), and the ternary Zn-Ge-P system, in addition to ZnGeP₂, has a large number of binary compounds, making the obtaining of homogeneous crystals with the desired optical characteristics a non-trivial task.

Currently, the most common method for synthesizing ZnGeP₂ is a modified two-temperature synthesis method with an increase in the temperature of the cold zone after the reaction [3]. Zinc and germanium are located in the hot zone, and phosphorus is in the cold zone. The temperature of the hot zone during synthesis is approximately 1000 °C, and the temperature of the cold zone is approximately 500 °C [4]. In the final stage of synthesis, the temperature of the cold zone is increased and equated to the temperature of the hot zone to avoid the condensation of volatile binary phosphides. This method allows for the synthesis of a rather large volume of material in a single process (up to 500 g), while the one-temperature synthesis method of ZnGeP₂ allows for the synthesis of no more than 25 g of the ternary compound in a single process [5]. Moreover, the one-temperature synthesis method is often accompanied by explosions of ampoules due to the high pressure of phosphorus at elevated temperatures. The synthesis of the crystalline compound ZnGeP₂, in any of its variants (horizontal one-temperature or two-temperature [6,7]), involves various technical arrangements and modes; the reactions occurring during the synthesis of ZnGeP₂ and their sequence are the same for all implementations. The synthesis of the ZnGeP₂ compound goes through the stage of formation of binary phosphides, which form in different temperature ranges: in the range of 480–550 °C, molten zinc reacts with phosphorus vapor. In this case, a compound with a low content is formed [4].

3Zn(L) + 0.5P₄(G) → Zn₃P₂(S)

(1)

where S, L, and P denote the solid, liquid, and vapor phases, respectively.

As the temperature and phosphorus pressure increase, within the range of approximately 550–850 °C, zinc phosphide with a low phosphorus content transforms into the compound ZnP₂.

Zn₃P₂ (S) + P₄(G) → 3ZnP₂(S)

(2)

The diffusion rate of phosphorus atoms into the solid phosphide cannot be high. Therefore, during the heating of the synthesis reactor to temperatures at which the formation reaction of the ternary phosphide is possible, zinc phosphide with a low phosphorus content, Zn₃P₂, is only partially converted into ZnP₂.

At a temperature of ~750 °C, germanium phosphide can form

Ge(S) + 1/4P₄(G) →GeP(L)

(3)

The synthesis of the ternary compound begins at temperatures exceeding approximately 900 °C [8] and occurs through the following two reactions:

ZnP₂(S) + Ge(L) → 3ZnGeP₂(S, L) (volumetric)

(4)

Zn₃P₂(S) + 3GeP(L) + 1/4P₄(G) → ZnGeP₂ (S, L) (on the surface)

(5)

Subsequent growth of the ZnGeP₂ single crystal is carried out by the Bridgman method on an oriented seed (with orientation (100)); growth is performed from a previously synthesized polycrystalline melt.

According to the classification [8,9], there are two types of band inhomogeneity in crystals—type 1 bands, which are parallel to the crystallization front, and type 2 bands, which are parallel to the growth axis of the crystal.

Type 1 bands, which include those studied in this work, are parallel to the phase boundary and are primarily formed by zinc phosphides of varying valence. Type 1 growth bands appear as dark horizontal lines of varying thickness and intensity; their shape matches the crystallization front during the growth of a single crystal in a vertical furnace. Type 2 bands are not parallel to the phase boundary and are caused by non-steady-state interfacial kinetics. In single crystals of zinc germanium diphosphide grown in a vertical configuration, second-type bands are not observed.

It should be noted that growth striations are one of the most common types of bulk defects observed in ZnGeP₂ crystals. Given the significant refractive index of the material (~3), this type of defect leads to significant distortions in the distribution of the intensity of the radiation generated in the crystal and can even initiate optical breakdown. Leveling out the formation of this type of defect is a complex technological task. Despite a large number of studies devoted to identifying the mechanisms of formation of growth striations in ZnGeP₂ crystals, there is currently no comprehensive explanation for the appearance of this type of defect in crystals, and there are no effective, reproducible methods for leveling out this type of defect.

In germanium diphosphide crystals, only type 1 growth striations are found, which are parallel to the crystallization front and consist of intrinsic impurities represented by zinc phosphides of various valences, as well as, presumably, a solid solution of the excess component dissolved in the crystal matrix. Band inhomogeneity in ZnGeP₂ crystals contains information about the geometry of the crystallization front [10]. The mechanism of formation of band inhomogeneity is quite complex and depends on many factors. At the stage of single crystal growth, in addition to the evaporation of volatile components from the melt surface, there are fluctuations in the temperature field created by the error in regulating the temperature of the heating elements. Along with the oscillatory properties of the temperature control system or possible vibrations of the mechanical part of the thermal installation for the vertical Bridgman method with bottom seed placement, the cause of growth banding may be non-stationary gravitational convection arising from the horizontal (radial) temperature gradient near the crystallization front. Convection can be eliminated by providing a strictly axial heat flow, which corresponds to a flat phase interface [11]. In [12], by obtaining holographic images of band inhomogeneity in ZnGeP₂ crystals and subjecting the obtained images to mathematical analysis using Fourier series expansion, they correlated the spatial periods of band repetition with different mechanisms of their formation. Along with the oscillatory properties of the temperature control system of the heaters and the possible influence of the vibrations generated by the mechanical part of the furnace equipment, the cause of growth banding may be non-stationary gravitational convection, arising from the radial temperature gradient near the crystallization front [8].

In [13], mechanisms of the formation of growth striations are described based on the convective motion of the liquid in a temperature gradient field, and the influence of microgravity is also considered. Technical methods for controlling convective flows in the melt for growing crystals without band inhomogeneity are implemented.

X-ray diffraction topography is considered an informative method for studying linear and bulk defects in single-crystalline and polycrystalline materials [14].

In [15], the structure of a ZnGeP₂ crystal, grown by the vertical Bridgman method, was investigated using high-resolution X-ray diffractometry and transmission topography based on the Borrmann method. The dominant defects identified were growth bands and dislocations. The observed growth bands were of two types. Type 1 was caused by sharp fluctuations in the temperature and pulling rate in the growth zone. The type 2 growth bands could form due to segregation processes or unsteady gravitational convection near the crystallization front. The obtained data showed that foreign impurities were practically absent, meaning the growth bands were caused by point defects under conditions of a concave, non-flat crystallization front. Toward the end of the ingot formation, these point defects accumulated, leading to the deformation of the ZnGeP₂ single crystal and increased dislocation generation.

In [16], the authors investigated the influence of crystal lattice quality on the optical damage threshold of single crystals. For this purpose, they studied single crystals grown under different technological conditions. The main research focus was on analyzing the effect of the crystal lattice quality on the optical damage threshold of ZGP (ZnGeP₂) single crystals.

This article presents the results of the observations and studies of processes observed during the synthesis and growth of ZnGeP₂ crystals that lead to the appearance of this type of defect, as well as recommendations for growing ZnGeP₂ crystals free from band inhomogeneities. The following mechanism for the formation of wall pores and their relationship with growth bands is also proposed, which has not been previously studied.

2. Experimental Samples

For the study of band inhomogeneities, four typical single crystals containing these inhomogeneities were selected. The crystals were grown using the vertical Bridgman method with (100)-oriented seeds. The grown crystals measured 190 × 50 mm. Longitudinal plates were cut from the central part of the crystals and examined for the presence of bands through visual inspection and Schlieren imaging. From each such plate, a 40 × 15 mm section containing the most distinct and wide growth bands was selected.

The plates were cut from these single crystals along the growth axis using wire sawing, ensuring that the side surface orientation corresponded to the (100) plane. They were then ground and polished on a 4PD-200 polishing and finishing machine. The plates were sequentially numbered from 1 to 4.

The index following the plate number denotes a light “L” or dark “D” area of the single crystal plate. The presence of growth striations was determined by obtaining shadow images in transmitted visible light (the shadow images of the experimental samples are presented in Figure 1).

All four samples of ZGP single crystals were grown by the vertical Bridgman method on an oriented seed with a (100) orientation similar to that described in [4]. A crucible with a seed and a polycrystalline mass was placed in a vacuum ampoule. The ampoule was placed in a vertical furnace with an axial gradient. Figure 2 presents information about the axial and radial temperature distribution during the growth of ZnGeP₂ crystals.

The material for all single crystals was pre-synthesized by a modified two-temperature synthesis method with an increase in the temperature of the cold zone after the reaction, similar to that done in [4].

Through the study of shadow images of longitudinal sections of single crystals with band inclusions and the appearance of monocrystalline boules, a direct dependence of pore formation at the crystal–crucible wall interface on the presence of growth striations in the crystal was established. Porous inclusions in zinc germanium diphosphide single crystals are located in the peripheral part of the single crystal and form wall cavities. In the upper third of the monocrystalline cylinder, the wall pores form vertical, elongated channels (Figure 3). It was noted that in ZnGeP₂ single crystals without pores at the crystal–crucible wall interface, there are no band inhomogeneities. A typical appearance of a single crystal ingot without growth striations is shown in Figure 4.

A connection has been established between the formation of wall pores and the presence of growth striations in ZGP. This connection lies in the fact that during the crystallization of a melt layer enriched with impurities and binary phosphides (“dark” band), additional heat is released, which leads to the formation of a vapor bubble. The bubble rises above the layer in which it was formed and is captured by the next layer (“light” band), with a lower impurity content. The main contribution to the formation of bubbles is made by the wall region, the temperature of which is higher than in the bulk of the melt, and the roughness of the crucible walls serves as centers of vapor formation. This effect is clearly demonstrated in Figure 5. From Figure 5, it can be seen that the bubbles and pores in the wall region of the ingot are concentrated in the “light bands”.

3. Influence of Band Inhomogeneity on the Optical Properties of ZnGeP₂ and the Geometry of the Laser Beam in the IR Spectral Range

A characteristic feature of zinc germanium diphosphide single crystals with band inhomogeneity inclusions is the change in geometry of the beam of transmitted or generated radiation. Figure 6 shows a block diagram of a setup for recording the intensity distribution of laser radiation from a Ho:YAG laser at a wavelength of 2.1 μm in the far field after passing through a single crystal containing band inhomogeneity inclusions.

When laser radiation passes through a monocrystalline plate containing growth striations, the beam shape is distorted due to the different refractive index between the dark and light areas of the crystal [12]. To visualize the change in the geometric parameters of the laser beam, Figure 7 shows the images obtained using a Pyrocam III, allowing us to assess the degree of distortion of the beam’s geometric shape.

It is interesting that such crystal structure defects as growth striations lead to a distortion of the beam profile generated in the crystal during parametric generation. Figure 8 shows an image of the generated beam obtained using an OPG based on an optical element with band inhomogeneity. As can be seen, there is a pronounced astigmatism.

4. Methods for Investigating Experimental Samples

The qualitative and semi-quantitative compositions of the dark and light areas of the plates cut from crystals with banded inhomogeneity were studied using a sequential Shimadzu XRF 1800 (Shimadzu Corporation, Kyoto, Japan) wavelength dispersive X-ray fluorescence spectrometer. X-ray fluorescence analysis allowed us to determine the qualitative and semi-quantitative compositions of the zinc germanium diphosphide single crystals, thereby enabling us to evaluate the relative quantity of matrix elements in the growth bands and light areas of the single crystal without inclusions. Studies of elemental compositions were carried out at the Tomsk Materials Science Centre for Collective Use (NR TSU, Tomsk, Russia).

The phase composition and crystal orientation of the investigated samples were determined using X-ray diffraction analysis. The samples were studied on a DRON-8N X-ray powder diffractometer with a copper X-ray tube at a wavelength of 1.541862 Å, which was equipped with a Goebel mirror on a primary X-ray beam and a high-speed semiconductor position-sensitive detector Mythen 2R1D (Dectris, Baden, Switzerland) at the “Nanotech” Common Center for Collective Use (ISPMS SB RAS, Tomsk, Russia). The maximum power of the X-ray tube was 800 W. The diffractometer was equipped with a vertical goniometer with a scanning speed of 10°/min. The minimum step of the goniometer on the 2θ scale was 0.005°. For measuring XRD patterns in monocrystals, the X-ray tube power was reduced, and a scintillation NaI detector was applied. Measurements were carried out at a voltage of 10 kV and a current of 5 mA. The XRD patterns were measured using the θF-θD and Ω modes. The θF-θD-patterns were measured within a 2θ range of 30–70°, while the Ω-patterns were measured within an Ω range of −7–7°; the scanning step was 0.02°, and the acquisition time was 1 s. To determine the laser-induced damage thresholds (LIDTs) of the dark and light regions of the crystals, the standard R-on-1 method was used. A Ho:YAG laser with continuous-wave thulium fiber laser pumping was used as a source for testing the radiation with a wavelength of 2.097 μm. The Ho:YAG laser operated in an active Q-switching mode with a pulse repetition rate of 20 kHz and a pulse duration of 35 ns. The amplitude of nanosecond pulses, their duration, and energy, as well as the beam diameter, were stable with constant pumping (random variations in the pulse amplitude did not exceed 5%). The LIDT study was conducted with an exposure duration τ_ex = 5 s. The sample was exposed to packets of laser pulses with a fixed-energy density level that did not cause damage to the crystal surface. Then, the energy density level was increased in steps of ~0.1 J/cm². When visible damage appeared on one of the surfaces of the nonlinear element, the experiment was stopped. Then, the sample was moved 0.5 mm in height or width using a two-coordinate stage; the experiment was repeated 5 times. The probability of optical breakdown was obtained by constructing a graph of the cumulative probability as a function of the optical breakdown energy density. The value of the optical breakdown threshold (W_0d) was taken as the value of the energy density corresponding to the approximation of the probability of optical breakdown to zero [17]. According to the international standard ISO 11146, the energy density of laser radiation was determined by the following expression:

W = 8 P_av/(fπd²)

(6)

where d is the diameter of the laser beam.

5. Results and Discussion

The data from the X-ray fluorescence analysis of the samples are presented in the form of histograms for better visualization of the differences in the concentrations of the main elements constituting the material in the dark and light areas (bands) of the monocrystalline sample. The columns of the histograms denoting the percentage content of a chemical element in the measured area of a particular sample were denoted according to the type of bands: “L” corresponds to the light area of the monocrystalline plate, and “D” corresponds to the dark area of the monocrystalline plate (Figure 9 and Figure 10). The measurement error in determining the concentration of chemical elements did not exceed 0.2%.

The histograms of the relative content of atoms forming ZGP clearly illustrate the differences in the contents of elements in the dark and light areas of the longitudinal sections of monocrystalline plates. For all four studied samples, an increased content of P was observed in the dark band regions. In particular, for sample No. 1, the content of P in the dark bands was more than ~3.5% higher than in the light bands, as can be seen from Figure 8 and Figure 9. For sample No. 2, the content of P in the dark band was 0.1% higher than in the light band. For sample No. 3, the content of P in the dark bands was 2% higher than in the light ones. For sample No. 4, the content of P in the dark band was 1% higher compared to the content of P in the light band. The obtained data are in good agreement with the shadow patterns obtained in the transmitted visible light. With an increase in the difference in the phosphorus content, the contrast of the growth bands present in the single crystal increases. Thus, the samples of single crystals numbered 1 and 3, Figure 9 and Figure 10, in the dark areas of which the highest content of phosphorus was found, demonstrate a high contrast of dark areas in visible light, as well. As can be seen, sample number 1, Figure 10, has another distinctive feature—an increased content of germanium in the light areas (the difference in the content of Ge was ~4% compared to the content of germanium in the dark bands). In general, in all studied samples, an increased content of Ge was observed in the light bands (the difference in the content of Ge with the dark bands is ~0.5–1.5% for samples No. 2–4). The increased content of germanium may have a positive effect on the transparency of zinc germanium diphosphide in the near IR and visible spectral regions due to a decrease in the content of V_Zn⁻ vacancies [18]. In addition, it is worth noting the sharp boundary between the dark and light areas; such a picture is possibly the result of a decrease in the affinity between the crystal matrix with an increased content of germanium and its own impurity inclusions, as a result of which the distribution coefficient of the impurity-saturated layer increases abruptly, crystallizing faster than in crystals with a lower content of germanium.

X-ray diffraction measurements were performed on experimental sample No. 1 to assess the difference in the crystallographic orientation angle relative to the scanning plane between the dark and light bands of the single crystal.

Where the angles 2θ (the rotation angle of the X-ray detector relative to the source of the diffractometer) and Ω (the rotation angle of the sample stage with the experimental sample) were measured, the measurement error for the angles Ω and 2θ was 0.001°. If the studied crystallographic plane is parallel to the face of the sample from which the reflection is taken, then the angle Ω will be exactly half of the angle 2θ. Any deviations in the angle Ω from this ratio indicate that the face of the sample is rotated at a certain angle relative to the studied crystallographic plane. This deviation can be calculated according to the expression 2θ–2Ω.

We obtained diffractograms from the points located in the light bands of the sample and the dark bands of the sample. Figure 11 shows the results of the diffractogram measurements in the light and dark bands of sample No. 1 in the middle of the sample, as schematically shown on the axis. Spectra were obtained along the 2θ axis, and scanning was also performed at a single angle Ω to determine the deviation of the crystallographic plane (100) of the single crystal from the studied surface in different regions of the sample.

For this sample, the reflection from the (100) crystallographic plane should correspond to an angle of 32.67° on the 2θ axis. To determine the deviation of this crystallographic plane of the single crystal from the studied surface, Ω-scans of the light and dark bands of the sample were taken, respectively (Figure 11a,b). As a result of this scanning, it became clear that the studied region in the light band is rotated relative to the (100) crystallographic plane by −1.05° (Figure 11a). Further, an Ω-scan was taken in the dark band in the central part of the single crystal. The result is shown in Figure 11b—the angle Ω was −1.1° (the value differs from the angle Ω for the light area by 0.05°). Taking into account the rotation angles Ω, 2θ scans were performed in the light and dark areas, as shown in Figure 11. The result of the 2θ scans for the light and dark bands can be seen in Figure 11c. Figure 11c presents a single image since the results of the scans for the light and dark bands were identical. In the diffractogram, two orders of reflection from one family of planes are clearly observed. The reflection angle of the first order 2θ was 32.74°.

Further, two scans were performed in the left part of the sample, as shown in Figure 12. The Ω-scan taken in the light area can be seen in Figure 12a. In this case, the angle Ω was −0.85°. The Ω-scan taken in the dark band can be seen in Figure 12b. In this case, the angle Ω was −0.9° (the value differs from the angle Ω for the light area by 0.05°).

Taking into account the angle Ω, a diffractogram was obtained, shown in Figure 12c. In this case, only the first order of reflection of the (100) plane can be seen. Its reflection angle 2θ was 32.68°.

Such behavior indicates a certain misorientation of the crystallographic planes in the dark and light areas relative to each other. The results of X-ray diffraction, indicating that the crystallographic planes in a bulk single crystal of zinc germanium diphosphide have different deviations from the studied crystallographic plane (100) in the dark and light areas, may be associated with the presence of a large number of crystal structure defects, which formed as a result of the accumulation of impurity compounds. Crystals with banded inhomogeneity, when radiation passes through heterogeneous layers, work like a diffraction grating, having a different refractive index, distorting the passing radiation.

Thus, the following facts were established in the course of this work:

(1)

A misorientation of the crystal lattice in the dark and light bands of ZnGeP₂ single crystals relative to each other was recorded (the value of the relative misorientation of the (100) plane is 0.05°).

(2)

An increase in the content of P in the dark bands relative to the phosphorus content in the light bands of ZnGeP₂ single crystals was established. On average, the difference in phosphorus content was 1–3%.

(3)

A direct dependence of pore formation at the crystal–crucible wall boundary on the presence of growth bands in the crystal was established. Porous inclusions in zinc germanium diphosphide single crystals are located on the peripheral part of the single crystal and form wall cavities. In the upper third of the monocrystalline cylinder, wall pores form vertical, elongated channels. It was noted that in ZnGeP₂ single crystals without pores at the crystal–crucible wall boundary, there are no banded inhomogeneities. Moreover, pores usually form in the region of light bands.

To explain the observed dependencies, let us consider the process of synthesis and growth of ZnGeP₂ single crystals. The growth process is preceded by heating a polycrystalline charge consisting of small, fused ZnGeP₂ crystals. The growth charge intensively absorbs gaseous phosphorus, which is present in the growth ampoule as an additive, providing backpressure and contributing to a decrease in the evaporation of volatile components. This is due to the fact that the mass of the monocrystalline ingot after the growth process, as a rule, is greater than the calculated value obtained based on the mass of the loaded charge by about 2 g. The only option for increasing the mass of single crystals is the absorption of phosphorus charged into the ampoule to create back pressure. The absorbed phosphorus in the final ZnGeP₂ single crystal can be represented in the form of a solid solution; a similar phenomenon was observed during the growth of germanium phosphides [19] or is consumed for the formation of ZnP₂ according to Expression (7). Thus, the polycrystalline mass of zinc germanium diphosphide formed at the material stage absorbs 0.25 g of phosphorus for every 100 g of mass. Further, the phosphorus-saturated polycrystalline charge melts, and after the homogenization stage, the crucible with the melt is pulled through the gradient zone. At a temperature of ~1173 K, the following reaction occurs:

2Zn₃P₂(S) + P₄(G) → 3ZnP₂↑

(7)

Also, dissociation reactions occur in the melt within the temperature range of 1173–1335 K [20].

ZnGeP₂ = ZnP₂ + Ge

(8)

3ZnP₂ = Zn₃P₂ + P₄↑

(9)

Zn₃P₂ = 3Zn↑ + 1/2P₄↑

(10)

P₄↑ = 2P₂↑

(11)

All of the reactions presented above also result in the formation of a vapor phase consisting of the melt’s components (P, Zn, ZnP₂, and Zn₃P₂). It is likely that the wall-bound pores are subsequently formed from these vapor components.

The crystallization front pushes the inherent impurities (P, Zn, ZnP₂, and Zn₃P₂) towards the phase boundary. These impurities can be present in the melt as a solid, liquid, or vapor phase. The impurity-enriched layer of melt begins to compress under the action of the crystallization front from below and the pressure of the melt column from above. The high viscosity of the melt likely prevents gas bubbles (the vapor phase of the impurity) from floating up under the action of Archimedes’ force. The impurity concentration in front of the crystallization front gradually increases, and the impurity layer is compressed. With an increase in impurity concentration, the distribution coefficient of the impurity also increases. Upon reaching critical conditions, the distribution coefficient of the impurity becomes greater than unity, as a result of which the impurity is captured by the crystallization front.

Due to the accumulation of impurity in the melt in front of the crystallization front, there is a local decrease in the crystallization temperature of the melt, and the impurity is captured by the crystallization front, resulting in the formation of a layer with a higher impurity content in the volume of the crystal, which, in a cross-section, looks like a dark band, taking the shape of a crystallization front.

During the crystallization of a layer with a high impurity content, energy is released, which increases the local temperature of the adjacent layer of melt, which can lead to more intensive vaporization of some excess amount of impurity with the formation of a gas bubble consisting of a mixture of phosphorus and zinc diphosphide.

The shape of the crystallization front significantly affects the distribution of gas inclusions in a growing single crystal [21]. Thus, if the shape of the crystallization front is close to planar, then gas bubbles are pressed against the crystallization front until reaching a critical size and are captured by the crystallization front. With a convex crystallization front, gas bubbles begin to move along the crystallization front, shifting towards the wall region. If the crystallization front has a concave shape, then the gas bubbles formed during the growth process are repelled to the center of the growing crystal.

However, in real growth processes of ZnGeP₂ single crystals, even with the implementation of a concave crystallization front, gas inclusions are located only near the crucible wall, which is also evident from the results presented in this article (see Figure 3, Figure 5 and Figure 13). This behavior is due to the fact that the wall region is the main contributor to the formation of vapor bubbles. Gas bubbles in a superheated liquid, which is the melt, are formed mainly in the regions adjacent to the crucible wall due to the higher temperature of the melt and the constant supply of heat using the furnace heating element [22]. This is evident in Figure 2, which shows the radial temperature distribution at the crystallization front. In the wall region, the melt temperature is 1.5–2 degrees Celsius higher than in the central part of the ingot. Also, vapor formation in the wall region is stimulated by the micro-roughness of the growth crucible, which acts as a vapor nucleation site [22].

Apparently, overheating the melt in the wall region and the presence of nucleation sites lead to an intensification of the evaporation process of volatile impurity components of the melt and the formation of bubbles. In turn, in the central part of the ingot, the absence of nucleation sites leads to the absence of vapor phases in the melt.

When a melt layer enriched with impurities crystallizes, heat is released, which, together with the heat of the heater and the developed relief of the crucible surface in the wall region, leads to the formation of a vapor inclusion bubble. This bubble has a lower density than the crystallized impurity-enriched layer, so the bubble will be above the crystallizing impurity-enriched layer from which it was formed. As a result, the vapor-phase bubble is captured by the next layer of the crystallizing substance, which will be less enriched with impurities, and it looks like a light area in a banded crystal.

As the mass of the melt decreases, the pressure of the liquid column decreases, and some of the gas bubbles can float to the surface, forming elongated vertical pores (Figure 3). However, due to the high viscosity of the melt, vapor bubbles can only float to the surface when there are 10–15 mm left to the melt surface, which is also observed during the growth of ZnGeP₂ single crystals. This value was obtained empirically by measuring the length of elongated vertical pores at the top of the monocrystalline boules.

Obviously, gravitational convection, arising from the radial temperature gradient near the crystallization front, also contributes to the movement of the vapor-phase bubble. The radial gradient arises due to the temperature difference between the melt in the central and peripheral parts. The melt in the wall region is slightly hotter due to the shorter distance from the heating element.

Figure 13 presents a schematic representation of the mechanism of banded inhomogeneity formation in zinc germanium diphosphide crystals. From the moment the crucible with the melt is pulled through the temperature gradient zone of the furnace, a crystallization front arises in the melt. This front is considered a moving monolayer of the crystallizing substance, moving from bottom to top, opposite to the pulling direction. At the crystallization front, the crystal lattice is constructed. Before the crystallization front, as it moves, molecules of impurity compounds accumulate (in this case, these are double compounds of zinc and germanium with phosphorus, such as phosphides). Due to the differences in the crystal lattice of zinc germanium diphosphide and the double phosphides, a certain amount of impurity atoms gradually accumulate in front of the crystallization front. As a result of the movement of the crystallization front, the impurity-enriched layer is gradually compressed, and the impurity concentration increases, which ultimately leads to the capture of the impurity layer by the crystal lattice. The layer of substance enriched with impurity atoms, due to the significant difference in their physical properties from the properties of the main substance, looks like a dark band in a thin section. At the same time, in the layer enriched with impurity atoms, in the near-wall region, the impurities dissociate due to the higher temperature in the near-wall region. The high viscosity of the melt prevents the vapor-phase bubbles formed in the impurity layer due to the dissociation of impurities from floating to the surface from a significant depth, which leads to their capture by the growing crystal. The vapor-phase bubbles captured in this way form so-called near-wall pores and look like spherical depressions on the outer surface of the single crystal. However, when the crystallization front approaches the outer edge of the crucible, the viscosity of the melt can no longer prevent the vapor phase from floating to the surface of the melt, as a result of which the bubbles in the upper third of the crystal form extended vertical pore channels.

The negative impact of banded inhomogeneity on the optical properties of zinc germanium diphosphide single crystals is obvious and unquestionable. However, a completely different picture is observed when studying the influence of growth bands on the radiation resistance of zinc germanium diphosphide single crystals. The results of the conducted studies on the influence of banded inhomogeneity on radiation resistance (Figure 14) demonstrate a weak dependence of the optical damage threshold on the presence or absence of banded inhomogeneity in the crystal volume. For tests to determine the optical damage threshold, experimental sample No. 3 was selected (Figure 1). Using sample No. 3, LIDT values were obtained for the light and dark bands.

Figure 14 shows the dependence of the LIDT on the energy density of incident laser radiation. This graph illustrates the differences in the optical damage thresholds of two regions of the single-crystal plate: D—dark region (growth band) and L—light region (crystal matrix). The differences in the LIDT values of the samples in the two regions of the crystal are minimal. For instance, for the dark region of the single-crystal plate 3L, the energy density at which the probability of optical damage becomes zero is 1.15 J/cm², while for the light region of the single-crystal plate 3D, this value is 1.18 J/cm².

6. Conclusions

This study analyzed the impact of intrinsic impurities on the formation of bulk inhomogeneities in zinc germanium phosphide (ZGP) single crystals, which contain two highly volatile elements. It was demonstrated that the formation of growth striations is due to the accumulation of binary phosphides at the crystallization front, accompanied by the formation of pores in the near-wall region of the ingot.

X-ray spectrometry revealed differences in the chemical composition of “light” and “dark” growth striations, with significant deviations from stoichiometry apparent in these regions. The dark bands exhibited a higher phosphorus content (approximately 0.5–2%) compared to the light bands. Additionally, all the studied samples showed an increased germanium content in the light bands (a difference in germanium content with dark bands of approximately 0.5–1.5%). Differences in the orientations of the crystallographic axes were observed between the light and dark regions.

The formation of near-wall pores was linked to the presence of growth striations in ZGP. When a melt layer enriched with impurities and binary phosphides (“dark band”) crystallizes, additional heat is released, leading to the formation of a vapor bubble. This bubble rises above the layer in which it formed and is captured by the subsequent layer (“light band”) with a lower impurity content. The near-wall region, with its higher temperature compared to the bulk of the melt and the roughness of the crucible walls serving as nucleation sites for vapor formation, contributes significantly to bubble formation.

Samples containing inclusions of banded inhomogeneity significantly distort the profile of the transmitted and generated radiation in the crystal, leading to pronounced astigmatism. However, in contrast to the extremely negative influence of banded inhomogeneity on the optical properties of single crystals, the influence of growth striations on the radiation resistance of crystals is minimal, which requires further study.