# Fundamental Studies on Crystallization and Reaching the Equilibrium Shape in Basic Ammonothermal Method: Growth on a Native Lenticular Seed

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{4}cm

^{−2}[11]. Despite many published papers devoted to crystallization [12], as well as to the properties of ammonothermal crystals [13], a detailed investigation of the basic ammonothermal growth process has never been presented. With this paper, we aim to fill this gap. By analyzing crystallization on a native seed of a lenticular shape (lens seed), thus with a varying off-cut on its surface, we aimed to answer some basic questions: (i) In which crystallographic directions does the growth proceed and which crystallographic planes play the most important role (which are formed and which disappear in time)? (ii) What are the relationships between growth rates in different crystallographic directions? (iii) What is the influence of the off-cut of the seed on the growth process? For this purpose, slices of two crystallographic non-polar planes, namely, $\left(1\overline{2}10\right)$ and $\left(\overline{1}100\right)$, of a crystal grown on a lenticular seed (also called a lens seed) were prepared and analyzed. Photo-etching (PE) under UV light, optical microscopy (OM) with Nomarski contrast and ultraviolet (UV) illumination, and X-ray topography (XRT) and high-resolution X-ray diffraction (HRXRD) were applied as the main methods for investigating structural properties, such as growth striations [14] and dislocations. Furthermore, secondary ion mass spectrometry (SIMS) was used for analyzing concentrations of impurities in all sectors of the analyzed crystal slices with different crystallographic orientations. In addition, from a part of the newly grown crystal, a $\left(0001\right)$ slice was cut that was subjected to defect selective etching (DSE) in molten eutectic KOH-NaOH in order to analyze the etch pit density (EPD). The obtained results allowed us to create a growth model of Am-GaN crystallized on a lens seed, which is of general importance for the ammonothermal growth process of GaN.

## 2. Methods

_{2}S

_{2}O

_{8}+ 0.02 M KOH) [16,17] with the addition of a 0.02 M Na

_{3}PO

_{4}component in order to increase the stability of the solution [18]. A galvanic mode (a GaN sample connected to a Pt electrode via a Ti spring) was employed for revealing electrically active inhomogeneities, such as striations. PE was performed under the illumination of a 300 W UV-enhanced Xe lamp (Oriel, Germany) [19,20]. DSE was performed on the (0001) surface in molten eutectic KOH-NaOH with 10% of MgO at 500 °C (temperature of the hot plate) for 10–20 min [21]. The dislocation density was established by counting the overall number of etch pits (EPD). The analysis was performed only in terms of the pit density and not their size. Therefore, no information on the density of different types of dislocations, namely, screw, mixed and edge, which are correlated with the pit size, was gathered [22]. As mentioned, all surfaces (epi-ready, after DSE and following PE) were characterized with a Nikon Eclipse LV100ND OM with Nomarski contrast and under UV illumination.

_{1}radiation (λ = 154.06 pm, 8.05 keV) and Mo-Kα

_{1}radiation (λ = 70.94 pm, 17.48 keV) were applied. The XRT analysis was performed in a transmission geometry (Lang technique) via exposures using $0002$ type reflections for both $\left(1\overline{2}10\right)$ and $\left(\overline{1}100\right)$ samples, as well as $\overline{3}030$ and $11\overline{2}0$ reflections for $\left(1\overline{2}10\right)$ and $\left(\overline{1}100\right)$ slices, respectively. The X-ray topographs were recorded with a high-resolution CCD camera (5.4 μm pixel size). Values of µt (µ is the linear absorption coefficient and t is the crystal thickness) were 8.6–10.3 and 8.0–9.6 for the Cu-Kα

_{1}and Mo-Kα

_{1}radiation, respectively. This meant that the XRT measurements were performed under Borrmann contrast conditions, as described in [13] and the literature referred to therein. HRXRD was applied to analyze the lattice parameters and mosaicity in various crystal regions. A Panalytical MRD system equipped with a 4 × Ge 220 Bartels monochromator (Cu-Kα

_{1}-radiation) and a 3 × Ge 220 analyzer was used (Panalytical, Almelo, The Netherlands). For each crystal slice, symmetric and asymmetric reflections were used at six different positions to perform 2Θ/Θ-, 2Θ/ω- and ω-scans, as well as reciprocal space maps (RSMs). In order to limit the measured spot to a specific sample location, a pinhole aperture with a diameter of 1.5 mm was used. For the calculation of the lattice parameters, refraction-corrected data were applied [23]. SIMS measurements were performed in selected areas of the $\left(1\overline{2}10\right)$ and $\left(\overline{1}100\right)$ surfaces to determine the contamination of Am-GaN in the different oriented slices, as well as in different growth sectors. A CAMECA IMS6F microanalyzer was used. Molecular oxygen and cesium ions were applied as primary ions. The generated secondary ions were detected with a mass spectrometer, and the relative sensitivity factors derived from standard samples were used for quantitative calibration of the secondary ion intensities.

## 3. Results

^{4}cm

^{−2}was found in the respective topographs. This indicated that the predominant threading dislocation types in the lens-seed-grown Am-GaN crystal were edge and/or mixed-type dislocations that ran along the $\u23290001\u232a$ direction. Furthermore, similar striations were observed in the $\overline{3}030$ and $11\overline{2}0\text{}$reflections, as in the type $000\overline{2}$ reflection topographs. Likewise, in the laterally grown region (3), mainly bright diffuse contrasts were also observed for these reflections. For completeness, the $\overline{3}030$ reflection topograph of the $\left(1\overline{2}10\right)$ slice and the $11\overline{2}0\text{}$reflection topograph of the $\left(\overline{1}100\right)$ slice are shown in Appendix A.

_{//}reciprocal space direction was small and confirmed the high structural quality of these crystal regions. This was particularly the case for the $1\overline{2}10$ and $1\overline{2}12$ reflections of the a-plane sample. Furthermore, the high structural perfection in these areas, as well as the good surface quality, were evidenced by the presence of crystal truncation rods (CTRs). CTRs are dynamic X-ray scattering effects that emerge as continuous-intensity rods connecting Bragg peaks along the surface normal. In reciprocal space, CTRs are visible as broadened streaks in the q

_{⊥}-direction and become apparent due to the loss of translational invariance and crystal lattice order in the near-surface region [26,27]. A CTR was particularly prominent in the$1\overline{2}10$ reflection RSM measured at AP II of the a-plane slice. The slight tilt of the CTR in this measurement was due to an unintentional preparation-related miscut by $~$6° of the $\left(1\overline{2}10\right)$ surface. In the RSMs of the AP Vs, the CTRs were no longer as clearly visible as in the AP IIs. Different phenomena, which overlapped, were observed in these RSMs: broadening of the reflections in the q

_{//}-direction connected with mosaicity, splitting of the reflections and diffuse scattering. Patterns with significantly different appearances were observed for the GaN reflections in the RSMs of the AP Vis (area (3) with lateral growth). The reciprocal lattice points were enormously broadened by the diffusely scattered intensity. The central areas of the reflections were split. Another observation for the HRXRD measurements in the AP Vis was that the reflection positions were shifted to smaller values in reciprocal space compared with the reflection positions of the other Aps. This indicated an increase in the a-lattice parameters for these GaN crystal regions. The RSMs of Aps I and III, which are not shown, had almost the same qualitative appearance as the RSMs of the AP Iis and demonstrated the high crystalline perfection of these GaN regions. For the RSMs of the AP Ivs, which are also not shown, reflection broadening and diffuse scattering were observed, similar to the RSMs of the AP Vs. In order to determine the a- and c-lattice parameters of the different crystal regions on the $\left(1\overline{2}10\right)$ and $\left(\overline{1}100\right)$ GaN slice, HRXRD 2Θ/Θ-scans and 2Θ/ω-scans were performed from the same symmetrical and asymmetrical reflections as used for the RSMs. The measurement profiles are shown in Figure A3a,b and Figure A4a,b of Appendix B. The determined lattice parameters are reported in Table A1 and Table A2 of Appendix C. HRXRD ω-scans were also performed to allow for a quantitative analysis of the above-discussed mosaicity and diffuse scattering. The full width at half maximum (FWHM) was determined for all six investigated APs of the two crystal slices. In addition, in order to determine a kind of quantification for the weak-intensity diffuse scattering, the full width of the thousandth maximum (FWTM) was determined in each case. The ω-scans are shown in Figure A3c,d and Figure A4c,d (Appendix B). The determined values of FWHM and FWTM are listed in Table A1 and Table A2 (Appendix C).

^{17}cm

^{−3}in all the analyzed areas. Metals such as Mg, Mn, Fe and Zn that were observed in the basic ammonothermal GaN came from ceramic and metal elements (i.e., holders) of the autoclave in the crystal growth zone. The SIMS measurements were also performed in sub-areas (2a) and (2b). The highest concentrations of H, Na and O were noted for area (2b). Furthermore, the lowest H and O concentrations were measured for area (2a).

^{4}cm

^{−2}(see Figure 10a). Halfway between the center and the edge of the crystal in m1 and a1, the EPD decreased to 7.6×10

^{3}cm

^{−2}and 1.6×10

^{4}cm

^{−2}, respectively (see Figure 10b,c). At the edge of the sample in m2 and a2, the EPD decreased even more and was equal to 2.8 × 10

^{3}cm

^{−}

^{2}and 4.4 × 10

^{3}cm

^{−2}, respectively (see Figure 10d,e).

## 4. Discussion

_{(3-4)}= (a

_{(3)}− a

_{(4)})/(a

_{(4)})

_{(3)}and a

_{(4)}are the values of the a-lattice parameters measured in areas (3) and (4), respectively. The calculated Δε

_{(3-4)}was equal to 2.0 × 10

^{−4}and 3.8 × 10

^{−4}for the $\left(\overline{1}100\right)$ and $\left(1\overline{2}10\right)$ slices, respectively. These values were relatively high and may have had a strong impact on the structural quality of the crystal. Moreover, such a mismatch could lead to structural deterioration in both areas at the edge grown in lateral and vertical directions. The difference in the lattice parameters measured in area (3) and (4) was caused by varying concentrations of unintentionally incorporated impurities. It is especially visible in the case of O, whose concentration was higher in area (3) than in area (4), as verified using SIMS. This also affected the free carrier concentration and, as a result, led to faster photo-etching of area (3). The strong influence of the lattice parameter mismatch on the strain in the crystal was described by Lucznik et al. [28] and Amilusik et al. [29] for the homoepitaxial growth of HVPE-GaN. Thus, the presence of strong strain between the mentioned areas was most probably the cause of the appearance of cracks in layer (4), as shown in Figure 3a,b. However, no cracks were observed in the crystal’s volume after the growth. They appeared during the preparation of the slices as a result of strain relaxation.

^{−2}(where I is the X-ray intensity and q is the deviation of the scattering vector H from the reciprocal lattice vector G) [31]. This diffuse scattering, called Huang diffuse scattering, is due to the far field of elastic distortions around defects and occurs at relatively small wave vectors. In the $1\overline{2}10$ reflection, a small range at higher wave vectors additionally indicated another decrease according to I~q

^{−4}and originated in the vicinity of defects where the distortions were strong. This kind of diffuse scattering is named Stokes–Wilson scattering [32]. Huang and Stokes-Wilson diffuse scattering are clear indicators of point defects and their clusters. This clearly confirmed the strongly increased incorporation of impurities, as was also detected by other methods, e.g., SIMS. Moreover, based on these HRXRD observations, the bright diffuse contrasts for the laterally grown GaN crystal regions (3) in the XRT images (Figure 6, Figure 7, Figure A1 and Figure A2) could be clearly explained by the diffuse scattering.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**X-ray topograph of the $\left(1\overline{2}10\right)$ slice imaged using the $\overline{3}030$ reflection (Mo-Kα

_{1}radiation).

**Figure A2.**X-ray topograph of the $\left(\overline{1}100\right)$ slice imaged using the$11\overline{2}0$ reflection (Cu-Kα

_{1}radiation).

^{4}cm

^{−2}. Striations and dislocation refraction at the seed and growth sector boundaries were likewise visible in the $\overline{3}030$ and$11\overline{2}0$ reflections, as described in the type $000\overline{2}$ reflection topographs.

## Appendix B

**Figure A3.**HRXRD scans performed for the $\left(1\overline{2}10\right)$ slice: (

**a**) 2θ/θ scan for reflection $1\overline{2}10$, (

**b**) 2θ/ω-scan for reflection $1\overline{2}12$, (

**c**) ω -scan for reflection $1\overline{2}10$ and (

**d**) ω-scan for reflection $1\overline{2}12$. Analysis positions (APs) and growth areas: AP I—area (4)—center of the seed, AP II—area (4)—in the middle of the radius, AP III—area (1)—seed, AP IV—area (4)—close to the edge of the crystal, AP V—area (2) and AP VI—area (3).

**Figure A4.**HRXRD scans performed for the $\left(\overline{1}100\right)$ slice: (

**a**) 2θ/θ-scan for reflection $\overline{3}300$, (

**b**) 2θ/ω-scan for reflection $\overline{2}201$, (

**c**) ω-scan for reflection $\overline{3}300$. and (

**d**) ω-scan for reflection $\overline{2}201$. Analysis positions (APs) and growth areas: AP I—area (4)—center of the seed, AP II—area (4)—in the middle of the radius, AP III—area (1)—seed, AP IV—area (4)—close to the edge of the crystal, AP V—area (2) and AP VI—area (3).

## Appendix C

**Table A1.**Results of the HRXRD lattice parameters and ω -scan FWHM and FWTM measurements of the $\left(1\overline{2}10\right)$ slice. Measurement positions: AP I—area (4)—center of the seed, AP II—area (4)—in the middle of the radius, AP III—area (1)—seed, AP IV—area (4)—close to the edge of the crystal, AP V—area (2) and AP VI—area (3).

AP/Area | a (pm) | c (pm) | ω$\text{}\mathbf{FWHM}\text{}1\overline{2}10\text{}\left(\mathbf{arcsec}\right)$ | $\mathbf{\omega}\text{}\mathbf{FWHM}\text{}1\overline{2}12\text{}\left(\mathbf{arcsec}\right)$ | $\mathbf{\omega}\text{}\mathbf{FWTM}\text{}1\overline{2}10\text{}\left(\mathbf{arcsec}\right)$ | $\mathbf{\omega}\text{}\mathbf{FWTM}\text{}1\overline{2}12\text{}\left(\mathbf{arcsec}\right)$ |
---|---|---|---|---|---|---|

I/(4) | 318.953 | 518.725 | 7.81 | 8.89 | 25 | 32 |

II/(4) | 318.956 | 518.728 | 6.80 | 8.86 | 24 | 31 |

III/(1) | 318.958 | 518.806 | 6.98 | 18.18 | 27 | 42 |

IV/(4) | 318.958 | 518.825 | 8.35 | 22.46 | 391 | 605 |

V/(2) | 318.970 | 518.741 | 16.27 | 13.07 | 66 | 209 |

VI/(3) | 319.078 | 518.567 | 15.48 | 62.21 | 1152 | 1793 |

**Table A2.**Results of the HRXRD lattice parameters and ω -scan FWHM and FWTM measurements of the $\left(\overline{1}100\right)$ slice. Measurement positions: AP I—area (4)—center of the seed, AP II—area (4)—in the middle of the radius, AP III—area (1)—seed, AP IV—area (4)—close to the edge of the crystal, AP V—area (2) and AP VI—area (3).

AP/Area | a (pm) | c (pm) | ω$\text{}\mathbf{FWHM}\text{}\overline{3}300\text{}\left(\mathbf{arcsec}\right)$ | ω$\text{}\mathbf{FWHM}\text{}\overline{2}201\text{}\left(\mathbf{arcsec}\right)$ | ω$\text{}\mathbf{FWTM}\text{}\overline{3}300\text{}\left(\mathbf{arcsec}\right)$ | ω$\text{}\mathbf{FWTM}\text{}\overline{2}201\text{}\left(\mathbf{arcsec}\right)$ |
---|---|---|---|---|---|---|

I/(4) | 318.934 | 519.299 | 13.43 | 20.92 | 66 | 89 |

II/(4) | 318.932 | 519.412 | 9.68 | 31.31 | 30 | 72 |

III/(1) | 318.931 | 519.136 | 11.48 | 20.66 | 49 | 71 |

IV/(4) | 318.937 | 519.172 | 10.22 | 32.94 | 114 | 73 |

V/(2) | 319.003 | 519.518 | 26.64 | 33.84 | 73 | 981 |

VI/(3) | 319.002 | 520.066 | 16.52 | 73.55 | 1008 | 1353 |

## Appendix D

**Figure A5.**Log–log plot of diffuse scattering intensity measured around the $1\overline{2}10$ reflection on the $\left(1\overline{2}10\right)$ a-plane slice. The intensity decreases according to I~q

^{−2}and I~q

^{−4}were observed, indicating Huang and Stokes–Wilson diffuse scattering, respectively (I—X-ray intensity, q—deviation of the scattering vector H from the reciprocal lattice vector G).

**Figure A6.**Log–log plot of the diffuse scattering intensity measured around the $\overline{3}300$ reflection on the $\left(\overline{1}100\right)$ m-plane slice. Huang diffuse scattering was identified since the intensity decreased according to I~q

^{−2}(I—X-ray intensity, q—deviation of the scattering vector H from the reciprocal lattice vector G).

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**Figure 1.**Selected and specially prepared Am-GaN seed with a lenticular shape: (

**a**) top view of the $\left(000\overline{1}\right)$ plane; (

**b**) side view. The thickness of the seed at its center was 4.1 mm; radii of the surface curvature varied between 21 and 25 mm; grid line 1 mm.

**Figure 2.**(

**a**) Top view of a hexagonal Am-GaN crystal grown on a lens seed; white dashed lines indicate the location of slicing for samples with non-polar planes; white solid trapezoid represents a sample (see

**b**) obtained by cutting a slice in the $\left(000\overline{1}\right)$ plane. (

**b**) Slice of the sample that was cut and prepared for DSE; view on the $\left(0001\right)$ plane; EPD was determined at indicated points; grid line 1 mm.

**Figure 3.**Slices of an Am-GaN crystal grown on the lenticular seed. OM images gathered under UV illumination: (

**a**) $\left(1\overline{2}10\right)$ plane and (

**b**)$\left(\overline{1}100\right)$ plane. Five areas separated by clear interfaces were named with Arabic numerals in brackets: (0)—pre-seed; (1)—lens seed; (2)—area of the $\left(000\overline{1}\right)$ plane recovery; two sub-areas: (2a) and (2b), differing in the intensity of UV luminescence, were distinguished; (3)—area of lateral growth; (4) area of GaN grown in the $\left[000\overline{1}\right]$ direction. One crack was clearly visible. Roman numerals (I–VI) were used to represent the six locations of HRXRD and SIMS measurements called “analysis points (APs)”.

**Figure 4.**Images of the $\left(1\overline{2}10\right)$ slice of an Am-GaN crystal after the PE: (

**a**) View of the entire sample; white rectangles (A–D) indicate the sectors chosen for further detailed analysis. (

**b**) Sector A; (

**c**) sector B; (

**d**) sector C; (

**e**) sector D. Crystallographic planes parallel to the visible striations and their angle of inclination to the $\left(000\overline{1}\right)$ plane are marked: the $\left(\overline{1}01\overline{2}\right)$ plane and 43.1°, the $\left(\overline{1}01\overline{1}\right)$ plane and 61.9°, and the $\left(\overline{1}010\right)$ plane and 90°; interfaces between different areas of the crystal (see

**a**) are marked with white dashed lines.

**Figure 5.**Images of the $\left(\overline{1}\overline{1}00\right)$ slice of an Am-GaN crystal after the PE: (

**a**) View of the entire sample; white rectangles (A–D) indicate sectors for further detailed analysis. (

**b**) Sector A; (

**c**) sector B; (

**d**) sector C; (

**e**) sector D. Crystallographic planes parallel to the visible striations and their angle of inclination to the $\left(000\overline{1}\right)$ plane are marked: the $\left(\overline{1}\overline{1}2\overline{4}\right)$ plane and 39.1°, the $\left(\overline{1}\overline{1}2\overline{2}\right)$ plane and 58.4°, and the $\left(\overline{1}\overline{1}2\overline{3}\right)$ plane and 47.3°; the interfaces between different areas of the crystal (see Figure 3a) are marked with white dashed lines.

**Figure 6.**X-ray topographs of the $\left(1\overline{2}10\right)$ slice. For the imaging, the $000\overline{2}$ reflection (Cu-Kα

_{1}radiation) was used. (

**a**) Overview topograph of the $\left(1\overline{2}10\right)$ plane; five areas separated by clear interfaces were visible, as seen in Figure 3a,b; one crack was also present. Magnified images of sectors presented in Figure 6a: (

**b**) sector A, where dislocations from area (1) went almost straight to area (4), and (

**c**) sector B, with two-stage dislocation refraction in area (2) (considered as the sum of areas 2a and 2b) and one stage refraction from area (1) to (3).

**Figure 7.**X-ray topographs of the $\left(\overline{1}100\right)$ slice. To image the $000\overline{2}$ reflection, Cu-Kα

_{1}radiation was used: (

**a**) overview topograph of the $\left(\overline{1}100\right)$ plane; five areas separated by clear interfaces were visible, as in Figure 3a,b; one crack was also present. Magnified images of sectors presented in Figure 7a: (

**b**) sector C, where the dislocations from area (1) went straight to area (4) and the two-stage dislocation refraction in area (2) (considered as the sum of areas 2a and 2b); (

**c**) sector D, where the two-stage dislocation refraction went from area (1) to area (3).

**Figure 8.**RSMs of the symmetrical $1\overline{2}10$ reflection and the asymmetrical $1\overline{2}12$ reflection performed on the $\left(1\overline{2}10\right)$ slice. Positions of the crystal truncation rods (CTRs) are indicated on the maps.

**Figure 9.**RSMs of the symmetrical $\overline{3}300$ reflection and the asymmetrical $\overline{2}201$ reflection performed on the $\left(\overline{1}100\right)$ slice. Positions of the crystal truncation rods (CTR) are indicated on the maps.

**Figure 10.**DIC optical images of the $\left(0001\right)$ plane after the DSE; the EPD at five points indicated in Figure 2b: (

**a**) c, (

**b**) m1, (

**c**) m2, (

**d**) a1 and (

**e**) a2; white squares indicate areas of the EPD estimation.

**Figure 11.**Model of Am-GaN growth on a lenticular seed along the $\left[000\overline{1}\right]$ and $\left[\overline{1}010\right]$ directions with a view of the $\left(1\overline{2}10\right)$ plane: (

**a**) the first stage of the growth—recovery of the $\left(000\overline{1}\right)$ plane and formation of the $\left(\overline{1}01\overline{2}\right)$ semi-polar plane; (

**b**) growth on the recovered $\left(000\overline{1}\right)$ plane and growth on the $\left(\overline{1}01\overline{2}\right)$ plane; (

**c**) growth on the $\left(000\overline{1}\right)$, $\left(\overline{1}01\overline{2}\right)$, $\left(\overline{1}01\overline{1}\right)$ and $\left(\overline{1}010\right)$ planes; (

**d**) expansion of the $\left(\overline{1}010\right)$ plane and transition from growth of the $\left(\overline{1}01\overline{2}\right)$ to the $\left(\overline{1}01\overline{1}\right)$ plane.

**Figure 12.**Model of Am-GaN growth on a lenticular seed along the $\left[000\overline{1}\right]$ and $\left[\overline{1}\overline{1}20\right]$ directions with a view of the $\left(\overline{1}100\right)$ plane: (

**a**) the first stage of the growth—recovery of the $\left(000\overline{1}\right)$ plane and formation of the semi-polar $\left(\overline{1}\overline{1}2\overline{4}\right)$ plane; (

**b**) growth on the recovered $\left(000\overline{1}\right)$ plane and growth on the $\left(\overline{1}\overline{1}2\overline{4}\right)$ plane; (

**c**) growth on the $\left(000\overline{1}\right)$ and $\left(\overline{1}\overline{1}2\overline{4}\right)$ planes with a transition between the $\left(\overline{1}\overline{1}2\overline{4}\right)$ and $\left(\overline{1}\overline{1}2\overline{2}\right)$ semi-polar planes and the formation of the $\left(0001\right)$ plane; (

**d**) growth on the $\left(000\overline{1}\right)$ and $\left(\overline{1}\overline{1}2\overline{2}\right)$ planes with the transition between the $\left(\overline{1}\overline{1}2\overline{4}\right)$ and $\left(\overline{1}\overline{1}2\overline{3}\right)$ semi-polar planes and the expansion of the $\left(0001\right)$ plane.

**Figure 13.**Predicted behavior of interface C for a longer growth process and the resulting shape of the crystal: (

**a**) view on the $\left(1\overline{2}10\right)$ plane and (

**b**) view on the $\left(\overline{1}100\right)$ plane.

**Table 1.**Concentrations of the main impurities (donors and acceptors) measured using SIMS on the $\left(1\overline{2}10\right)$ slice at six analysis points (APs) (indicated as Roman numerals in circles in Figure 3a) and the corresponding growth areas (indicated as Arabian numerals in brackets in Figure 3a).

$\left(1\overline{2}10\right)\phantom{\rule{0ex}{0ex}}\mathbf{AP}/\mathbf{Area}$ | [H] (cm ^{−3}) | [O] (cm ^{−3}) | [Si] (cm ^{−3}) | [Na] (cm ^{−3}) | [Mg] (cm ^{−3}) | [Fe] (cm ^{−3}) | [Mn] (cm ^{−3}) | [Zn] (cm ^{−3}) |
---|---|---|---|---|---|---|---|---|

III/(1) | 1.6 × 10^{19} | 9.7 × 10^{18} | 1.1 × 10^{17} | 6.1 × 10^{16} | 1.0 × 10^{17} | 1.9 × 10^{15} | 1.0 × 10^{17} | 2.8 × 10^{17} |

V/(2a) | 2.6 × 10^{18} | 2.3 × 10^{18} | 1.9 × 10^{17} | 8.3 × 10^{16} | 6.3 × 10^{15} | 2.4 × 10^{14} | 8.0 × 10^{15} | 9.1 × 10^{16} |

V/(2b) | 2.9 × 10^{19} | 8.9 × 10^{18} | 2.6 × 10^{17} | 4.5 × 10^{17} | 2.0 × 10^{16} | 3.9 × 10^{14} | 2.3 × 10^{16} | 1.3 × 10^{17} |

I/(4) | 1.3 × 10^{19} | 4.4 × 10^{18} | 1.0 × 10^{17} | 1.8 × 10^{16} | 2.8 × 10^{16} | 2.5 × 10^{14} | 2.7 × 10^{16} | 1.0 × 10^{17} |

IV/(4) | 1.1 × 10^{19} | 3.8 × 10^{18} | 8.7 × 10^{17} | 1.7 × 10^{16} | 2.4 × 10^{16} | 6.3 × 10^{14} | 2.2 × 10^{16} | 1.0 × 10^{17} |

VI/(3) | 1.2 × 10^{20} | 6.1 × 10^{18} | 4.8 × 10^{17} | 1.1 × 10^{18} | 6.4 × 10^{16} | 7.2 × 10^{15} | 1.3 × 10^{17} | 1.3 × 10^{17} |

**Table 2.**Concentrations of the main impurities (donors and acceptors) measured using SIMS on the $\left(\overline{1}100\right)$ slice at six analysis points (APs) (indicated as Roman numerals in circles in Figure 3b) and the corresponding growth areas (indicated as Arabian numerals in brackets in Figure 3b).

$\left(\overline{1}100\right)\phantom{\rule{0ex}{0ex}}\mathbf{AP}/\mathbf{Area}$ | [H] (cm ^{−3}) | [O] (cm ^{−3}) | [Si] (cm ^{−3}) | [Na] (cm ^{−3}) | [Mg] (cm ^{−3}) | [Fe] (cm ^{−3}) | [Mn] (cm ^{−3}) | [Zn] (cm ^{−3}) |
---|---|---|---|---|---|---|---|---|

III/(1) | 1.2 × 10^{19} | 9.6 × 10^{18} | 9.2 × 10^{16} | 4.0 × 10^{16} | 5.4 × 10^{16} | 1.9 × 10^{15} | 7.2 × 10^{16} | 2.4 × 10^{17} |

V/(2a) | 2.6 × 10^{18} | 1.3 × 10^{18} | 2.7 × 10^{17} | 3.1 × 10^{16} | 4.1 × 10^{15} | 4.9 × 10^{14} | 7.6 × 10^{15} | 1.2 × 10^{17} |

V/(2b) | 2.1 × 10^{19} | 1.0 × 10^{19} | 1.5 × 10^{17} | 8.0 × 10^{16} | 2.8 × 10^{16} | 8.8 × 10^{14} | 3.1 × 10^{16} | 1.1 × 10^{17} |

I/(4) | 6.4 × 10^{18} | 4.2 × 10^{18} | 6.9 × 10^{16} | 1.6 × 10^{16} | 2.1 × 10^{16} | 5.9 × 10^{14} | 1.9 × 10^{16} | 9.8 × 10^{16} |

IV/(4) | 4.3 × 10^{18} | 3.1 × 10^{18} | 5.1 × 10^{16} | 1.2 × 10^{16} | 1.5 × 10^{16} | 7.5 × 10^{14} | 1.3 × 10^{16} | 9.8 × 10^{16} |

VI/(3) | 1.3 × 10^{20} | 9.8 × 10^{18} | 5.6 × 10^{17} | 1.9 × 10^{18} | 7.9 × 10^{16} | 8.1 × 10^{15} | 1.5 × 10^{17} | 2.2 × 10^{17} |

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**MDPI and ACS Style**

Sochacki, T.; Kucharski, R.; Grabianska, K.; Weyher, J.L.; Iwinska, M.; Bockowski, M.; Kirste, L.
Fundamental Studies on Crystallization and Reaching the Equilibrium Shape in Basic Ammonothermal Method: Growth on a Native Lenticular Seed. *Materials* **2022**, *15*, 4621.
https://doi.org/10.3390/ma15134621

**AMA Style**

Sochacki T, Kucharski R, Grabianska K, Weyher JL, Iwinska M, Bockowski M, Kirste L.
Fundamental Studies on Crystallization and Reaching the Equilibrium Shape in Basic Ammonothermal Method: Growth on a Native Lenticular Seed. *Materials*. 2022; 15(13):4621.
https://doi.org/10.3390/ma15134621

**Chicago/Turabian Style**

Sochacki, Tomasz, Robert Kucharski, Karolina Grabianska, Jan L. Weyher, Malgorzata Iwinska, Michal Bockowski, and Lutz Kirste.
2022. "Fundamental Studies on Crystallization and Reaching the Equilibrium Shape in Basic Ammonothermal Method: Growth on a Native Lenticular Seed" *Materials* 15, no. 13: 4621.
https://doi.org/10.3390/ma15134621