**Micro- and Nanotechnology of Wide Bandgap Semiconductors**

Editors

**Anna B. Piotrowska Eliana Kami ´nska Wojciech Wojtasiak**

MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin

*Editors* Anna B. Piotrowska Institute of Microelectronics and Photonics Lukasiewicz Research Network Warsaw Poland

Eliana Kaminska ´ Institute of High Pressure Physics Unipress Polish Academy of Sciences Warsaw Poland

Wojciech Wojtasiak Institute of Radioelectronics and Multimedia Techniques Faculty of Electronics and Information Technology Warsaw University of Technology Warsawa Poland

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## **Contents**


## **About the Editors**

#### **Anna B. Piotrowska**

Anna Piotrowska, graduated from the Warsaw University of Technology, Faculty of Electronics, Ph.D. and D.Sc. in Electronic Engineering, Professor in Technical Sciences. Since 1977, has been involved in research on III-V semiconductor devices at the Institute of Electron Technology, Warsaw, Poland. Research interests are: III-V semiconductor devices for photonics, high frequency, high-power and high-temperature electronics, II-VI semiconductor devices for optical and magnetic sensors; with particular emphasis on processing-properties-reliability of semiconductor devices.

#### **Eliana Kami ´nska**

Eliana Kaminska, graduated from the Warsaw University of Technology, Faculty of Electronics, Ph.D. and D.Sc. in Electronic Engineering. Since 1977, has been involved in research on III-V semiconductor devices at the Institute of Electron Technology, Warsaw, Poland. Currently at the Institute of High Pressure Physics PAS. Research interests: III-V, II-VI, and TCO semiconductors, technology and characterization of metal/semiconductor interfaces, processing of semiconductor materials for electronic and photonics devices, and structure-property-processing relationships for thin film structures and devices.

#### **Wojciech Wojtasiak**

Wojciech Wojtasiak, graduated from the Warsaw University of Technology (1984, Poland), from which he also received his Ph.D. (1998) and D.Sc. (2015). He is currently a Professor and Head of Radiocommunications and Radiolocation Division at the Institute of Radioelectronics and Multimedia Technology, Warsaw University of Technology. His research activity focuses on electro-thermal modeling of microwave power transistors, particularly GaN HEMT characterization and high-power amplifier structures. His area of interest also includes the development of front-ends for radar and wireless systems and high-frequency-stability microwave high-power solid-state sources used in precise heating systems, which were successfully commercialized. Since 1998, he has been a member of IEEE.

**Anna B. Piotrowska 1,\*, Eliana Kami ´nska 2,\* and Wojciech Wojtasiak 3,\***


Gallium Nitride and Related Wide-Bandgap Semiconductors (WBS) have constantly received a great amount of attention in recent years. The main reason behind it is that several relevant high-power/high-frequency material parameters of semiconductors such as high breakdown field and low intrinsic carrier concentration, scale advantageously with bandgap. Semiconductor devices based on WBS allow for operation under extreme conditions, like high temperatures and electric fields. A huge range of wavelengths from IR to deep UV, enabling bandgap engineering together with excellent electron transport properties, makes nitrides attractive for electronic and optoelectronic devices as well. Today, nitride-based devices are widely used in high-performing radars (mainly 3D AESA), telecommunications (LTE-A, 5G), power electronic systems, light-emitting diodes and lasers. Despite substantial progress over the last twenty years, all these devices are still the subject of intense research to reach their full potential [1–4].

In this Special Issue, eight papers are published, covering various aspects of widebandgap semiconductor device technology, from substrates through epi-growth and semiconductor doping, to novel process modules for HEMTs, vertically integrated LEDs and laser diodes, and NWs-based nanoLEDs.

K. Grabianska et al. reported on the recent progress in bulk GaN technology achieved at Unipress, Poland [5]. Two processes, namely basic ammonothermal growth and halide vapor phase epitaxy have been thoroughly investigated and their advantages, disadvantages, and prospects discussed in detail. The authors suppose that within few years high-quality 2-in. truly bulk GaN substrates will be offered in large quantities, but today the main method for mass fabrication will be HVPE with Am-GaN crystals as seeds.

M. Stepniak et al. [6] investigated the process of selective-area metalorganic vapourphase epitaxy (SA-MOVPE) of GaN and AlGaN/GaN hetereostructures intended for HEMT technology with bottom-up architecture. Excellent growth uniformity, appropriate structure profile, and precise control of compositional gradient were obtained. The applicability of the SA-MOVPE process in making GaN-based 3D nano- and microstructures for electroacoustic, electromechanic, and integrated optics devices and systems was discussed.

K. Sierakowski et al. [7] reported on high-pressure post-implant annealing of GaN at high temperatures. The thermodynamics of the process was discussed and its application for GaN processing was investigated in two aspects. First focused on GaN:Mg for p-type doping, second on GaN:Be treated as a case study for analysing mechanisms of dopant diffusion. Different configurations of the annealing process were studied in order to prevent GaN surface from decomposition. Mg activation exceeding 70% was reached together with electrical properties similar to those of MOVPE-doped GaN.

AlGaN/GaN metal-insulator-semiconductor high-electron-mobility transistors (MISHEMT) with a low-temperature epitaxy (LTE)-grown single crystalline AlN gate dielectric were demonstrated by M. Whiteside et al. [8]. Post-gate annealing effects were

**Citation:** Piotrowska, A.B.; Kami ´nska, E.; Wojtasiak, W. Micro- and Nanotechnology of Wide-Bandgap Semiconductors. *Electronics* **2021**, *10*, 507. https:// doi.org/10.3390/electronics10040507

Academic Editor: Tae-Yeon Seong

Received: 18 February 2021 Accepted: 18 February 2021 Published: 22 February 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

studied in detail showing considerable increase of 2DEG mobility and reduction of interface state density at the AlN/GaN interface after post-gate annealing. Consequently, important increase of extrinsic transconductance, reduction of reverse gate leakage, and suppression of drain current were reached in final LTE-AlN MISHEMT.

D. Gryglewski et al. proposed a novel approach to characterizing self-heating process in GaN-based HEMTs [9]. An advanced measurement system based on DeltaVGS method with implemented software enabling accurate determination of device channel temperature and thermal resistance was developed. Three types of GaN-based HEMTs were taken into consideration—commercially available GaN-on-SiC (CGH27015F and TGF2023-2-01) and GaN-on-Si (NPT2022) devices, as well as model GaN-on-Am-GaN HEMT [10]. The main advantage of the proposed approach is that it allows taking into account the self-heating effect of transistors during design of microwave devices and high-power amplifiers for systems using variable-envelope signals such as LTE-A and 5G radios.

Marcin Siekacz et al. demonstrate the applications of tunnel junctions (TJs) for new concepts of monolithic nitride-based multicolour light-emitting diode (LED) and laser diode (LD) stacks [11]. GaN-on-GaN epistructures under investigation were grown by plasma-assisted molecular beam epitaxy (PAMBE). A stack of four LDs operated at pulse mode with emission wavelength of 453 nm and two-colour (blue and green) LEDs were demonstrated. The presented design is a viable alternative to achieving III-nitride highpower pulse laser diodes for such applications such as gas sensing or LIDARs. The stack of multicolour LEDs interconnected by TJs is promising for white-colour, phosphorus-free LEDs and for LED array displays. The use of TJs simplifies the electrical connections to buried LED structures, eliminating the need of p-type contacts application.

The two next paper addressed the topic of GaN-based nanowires, promising building blocks for future generation of electronic and optoelectronic devices. These nanostructures facilitate, for instance, the integration of GaN-based devices with Si electronics. Additionally, complicated heterostructures can be grown in the form of NWs with a crystallographic quality not achievable in the case of comparable planar hetereostructures for nanoLED.

M. Sobanska et al. made use of Kelvin probe force microscopy to assess the polarity of GaN nanowires (wurtzite structures) grown by plasma-assisted Molecular Beam Epitaxy on Si (111) substrates [12]. They showed that uniformity of the polarity of GaN nanowires critically depends on substrate processing prior to the growth. Several methods of surface preparation were investigated, and their results indicated that reversal of nanowires' polarity can be prevented by growing them on a chemically uniform substrate surface, particularly on in situ formed SiN<sup>x</sup> or ex situ deposited AlOy buffers.

Anna Reszka et all. [13] reported on growth, optical and electrical properties of GaN/AlGaN Nanowire LEDs fabricated on Si (111) substrates by plasma-assisted molecular beam epitaxy (PAMBE). No catalyst was used to induce the nucleation of the NWs. The nanowire LEDs included three GaN quantum wells in the area of the p–n junction. The research focused on the influence of switching the growth polarity. Spatially and spectrally resolved cathodoluminescence spectroscopy and imaging, e-beam-induced current microscopy, the nano-probe technique, and scanning electron microscopy were used for structural analysis, and complemented by photo- and electro-luminescence characterization. The interpretation of the experimental data was supported by the results of numerical simulations of the electronic band structure. Their results proved that intentional polarity inversion between the n- and p-type parts of NWs is a potential path towards the development of efficient nanoLED NW structures.

We would like to take this opportunity to thank all authors for submitting papers to this Special Issue. We also hope that readers will find new and useful information on GaN and related semiconductors technology for high-power/high-frequency electronic and optoelectronic devices.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Review* **GaN Single Crystalline Substrates by Ammonothermal and HVPE Methods for Electronic Devices**

**Karolina Grabianska , Piotr Jaroszynski, Aneta Sidor, Michal Bockowski and Malgorzata Iwinska \***

Institute of High Pressure Physics Polish Academy of Sciences, Sokolowska 29/37, 01-142 Warsaw, Poland; kgrabianska@unipress.waw.pl (K.G.); piotr.jaroszynski28@gmail.com (P.J.); asidor@unipress.waw.pl (A.S.); bocian@unipress.waw.pl (M.B.)

**\*** Correspondence: miwinska@unipress.waw.pl

Received: 6 July 2020; Accepted: 15 August 2020; Published: 19 August 2020

**Abstract:** Recent results of GaN bulk growth performed in Poland are presented. Two technologies are described in detail: halide vapor phase epitaxy and basic ammonothermal. The processes and their results (crystals and substrates) are demonstrated. Some information about wafering procedures, thus, the way from as-grown crystal to an epi-ready wafer, are shown. Results of other groups in the world are briefly presented as the background for our work.

**Keywords:** GaN; crystal growth; ammonothermal method; HVPE

#### **1. Introduction**

It seems that the lack of native wafers, of high structural quality, appropriate size, and electric properties, limits the development of GaN-based electronic devices. Highly conductive substrates are required for preparing high-power vertical transistors (i.e., the Metal-Oxide Semiconductor Field-Effect Transistor; MOSFET) or Schottky diodes. Semi-insulating GaN (SI-GaN) wafers are needed for preparing lateral devices, i.e., high electron mobility transistors (HEMTs). The nitride community is still working on the best technology for crystalizing GaN and fabricating GaN substrates. Growing GaN is, however, a rather challenging process. The compound melts at a very high temperature (exceeding 2200 ◦C) and the nitrogen pressure necessary for congruent melting is expected to be higher than 6 GPa [1–3]. GaN should, thus, be grown by other techniques requiring a lower pressure and temperature. Crystallization from the gas phase or solution has to be applied. Today, three technologies are mainly developed: sodium flux, ammonothermal, and halide vapor phase epitaxy (HVPE). The last one is the most popular one and developed by the industry. HVPE-GaN wafers are fabricated by such Japanese companies like SCIOCS by Sumitomo Chemical [4], Sumitomo Electric Industries (SEI) [5], Mitsubishi Chemical Corporation (MCC) [6], and Furukawa Metals [7]. HVPE-GaN substrates are also manufactured by Chinese Nanowin [8] and EtaResearch [9] as well as by French Lumilog by Saint Gobain [10]. All these companies sell highly conductive and semi-insulating 2-inch and even 4-inch HVPE-GaN substrates. They are all prepared from HVPE-GaN grown on foreign seeds, which lower the product's structural quality.

Companies and research institutes working on the ammonothermal method are the following: Institute of High Pressure Physics Polish Academy of Sciences (IHPP PAS; Warsaw, Poland) [11], SixPoint Materials Inc. (Buellton, CA, USA) [12], University of California Santa Barbara (Santa Barbara, CA, USA) [13], University of Stuttgart (Stuttgart, Germany), University of Erlangen (Erlangen, Germany) [14], MCC (Tsukuba, Japan) [15], Tohoku University (Sendai, Japan) [16], and Kyocera

(formerly Soraa, Inc., Santa Barbara, CA, USA/Kyoto, Japan) [17]. Two-inch as well as smaller ammonothermal GaN (Am-GaN) substrates are sold in limited quantities only by IHPP PAS [18].

The sodium flux method is mostly developed at Osaka University [19] and their GaN crystals or substrates are not available on the market. It should be, however, remarked that a 6-inch sodium flux crystal has already been demonstrated [20].

In this paper, the results of GaN bulk growth performed in Poland, at IHPP PAS, are briefly presented. Two technologies are described: HVPE and ammonothermal. Their advantages, disadvantages, and challenges are analyzed. It should be noted that no one has demonstrated a real bulk GaN crystal yielding several tens of wafers per boule. The technology allowing to reach this goal has also not been presented. The reasons for the lack of thick GaN are explained in this paper. During a growth process performed in a chosen vertical direction, crystallization occurs also in lateral directions. This, together with an anisotropy of growth, is the reason why obtaining truly bulk GaN is so difficult, even if native seeds of high structural quality are used. A few solutions that could help to further develop bulk GaN growth are, however, shown. Some information about wafering procedures, thus, the way from an as-grown crystal to an epi-ready wafer, are also demonstrated. Results presented by other groups crystallizing GaN are used as reference. The beginning of the paper focuses on the requirements for GaN substrates. Then, HVPE-GaN crystallized on foreign seeds is discussed. In the next step, the ammonothermal method is presented and analyzed. The recent progress is shown. At the end of this paper, new results of HVPE-GaN grown on native Am-GaN seeds are discussed.

#### **2. Requirements for GaN Substrates**

The most important property of a GaN substrate is its structural quality. The threading dislocation density (TDD) should be as low as possible and uniform across a wafer. In the case of GaN, the (0001) surface (c-plane) is mainly considered. Today, the lowest value of TDD, of the order of 10<sup>4</sup> cm−<sup>2</sup> , is reported for Am-GaN [21–23]. This value is two orders of magnitude lower than TDD in commercially available HVPE-GaN wafers. It is well known that TDD is well correlated with the etch pit density (EPD) [24]. In fact, EPD is a parameter much more often used when describing a GaN wafer and its properties. It is much easier and cheaper to etch a surface of a substrate, count the pits and determine their density, than to analyze dislocations by transmission electron microscopy (TEM). Additionally, if TDD is of the order of 10<sup>6</sup> cm−<sup>2</sup> or lower, it is difficult to detect dislocations by TEM. Therefore, in this paper, we refer only to values of EPD. When the (0001) GaN surface is etched three kinds of pits can be distinguished: large, medium, and small. According to Weyher et al. [24], these pits are correlated to screw, mixed, and edge dislocations, respectively. The data collected for Am-GaN and HVPE-GaN grown on Am-GaN seeds show that the density of large pits (screw dislocations) varies from 10<sup>0</sup> to 10<sup>1</sup> cm−<sup>2</sup> . In turn, the density of medium and small pits (mixed and edge dislocations) is at the level of 5 × 10<sup>4</sup> cm−<sup>2</sup> [23,25]. Figure 1 allows to compare EPD on the c-plane surface of a typical Am-GaN wafer from IHPP PAS and commercially available HVPE-GaN.

The low EPD is not the most important feature of GaN substrates. Flatness of crystallographic planes (see Figure 2) seems to be more important. It guarantees a uniform off-cut of the substrate, which, in turn, allows for epitaxial growth of any future device structure with an atomic step flow. Generally, the variation of off-cut across the surface should not be higher than 0.1◦ . This is the main and basic requirement for promoting the step flow, controlling the composition of ternary alloys in the device layers, as well as the incorporation of dopants and unwanted impurities [26–28]. For a 2-inch wafer, the required value of radius of curvature should be higher than 15 m. In commercially available HVPE-GaN substrates, the radius is at the level of 5 m, but in the case of 2-inch Am-GaN, it is usually around 30 m. The off-cut uniformity is also important for preparing an epi-ready surface of a substrate. This is also one of the most important requirements for a wafer. The surface, usually (0001) in the case of GaN, should be epi-ready, without any subsurface damage, with the value of the root means square (RMS) lower than 0.1 nm, and clean (see Figure 3).

− − **Figure 1.** Optical microscope images of (0001) surface (after etching in KOH-NaOH solution at 500 ◦C) of commercially available 2-inch: (**a**) Am-GaN wafer; medium and small pits visible; EPD = 5 <sup>×</sup> 10<sup>4</sup> cm−<sup>2</sup> (15 min etching); (**b**) HVPE-GaN; it is difficult to distinguish the size of pits; EPD <sup>=</sup> <sup>5</sup> <sup>×</sup> <sup>10</sup><sup>6</sup> cm−<sup>2</sup> (5 min etching; longer time would result in overlapping of pits and lowering the EPD); attention should be paid to different scales on both pictures; difference in pit sizes between (**a**) and (**b**) results from different etching time.

**Figure 2.** Scheme of GaN substrates with two kinds of (0001) crystallographic planes: (**a**) flat; (**b**) bent.

**Figure 3.** Example of typical atomic force microscopy image of epi-ready (0001) surface of 2-inch ammonothermal GaN wafer fabricated at IHPP PAS: (**a**) 2 µm × 2 µm area and (**b**) 5 µm × 5 µm area.

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Last but not least, there is a requirement for a GaN wafer regarding its free carrier concentration. A high, of the minimum order of 10<sup>18</sup> cm−<sup>3</sup> , and uniform value is needed if the substrate will be used for a vertical device (e.g., MOSFET). This allows to fabricate, in a relatively easy way, a stable and low-resistance ohmic contact to the bottom part of the substrate. Obviously, SI substrates with resistivity higher than 10<sup>8</sup> <sup>Ω</sup>·cm at room temperature (RT) are needed for lateral devices. − Ω∙

#### **3. HVPE-GaN Wafers—Crystallization on Foreign Seeds**

HVPE is a method of crystallization from gas phase. Figure 4 represents a scheme of a typical HVPE horizontal quartz reactor used at IHPP PAS. In a quartz tube, there are two zones with different temperatures: (i) low (800–900 ◦C), where hydrochloride (HCl) reacts with gallium (Ga) to synthesize gallium chloride (GaCl) and (ii) high (1000–1100 ◦C), where GaCl reacts with ammonia (NH3) and GaN is crystallized. All reactants are transported by a carrier gas (N2, H2, Ar, He, or their mixtures). The temperature is set with a multi-zone resistive canthal-based heater. In many cases, the resistive heating of the growth zone is replaced by RF heating. Details of such a reactor configuration were presented in many papers, e.g., [23,29,30]. Thermodynamics of GaN crystal growth process is well described in References [31,32].

**Figure 4.** Scheme of horizontal HVPE reactor working at IHPP PAS. All reactants are transported by carrier gas.

The HVPE technology demonstrates two great advantages: (i) a relatively high growth rate, which exceeds 100 µm/h and (ii) a possibility to crystallize high-purity material; concentrations of unintentional dopants (silicon, oxygen, iron) are generally of the order of 10<sup>16</sup> cm−<sup>3</sup> or even lower. A doping process with germanium or silicon to achieve highly conductive crystals as well as with carbon or iron for SI ones is well recognized and described in the literature, e.g., [33–37]. The main crystallographic growth direction in the HVPE technology is [0001] (the c-direction). GaN is predominantly crystallized on a foreign seed. It is either a gallium arsenide (GaAs) substrate with a low-temperature buffer layer of GaN or a metal-organic vapor phase epitaxy (MOVPE) GaN on sapphire template [38,39]. GaN crystallized on GaAs consists of areas (e.g., arranged in stripes) of high (10<sup>8</sup> cm−<sup>2</sup> ) and low (5 <sup>×</sup> <sup>10</sup><sup>4</sup> cm−<sup>2</sup> ) EPD [40,41]. Thus, the (0001) surface of a GaN substrate (after chemical etching of GaAs) is neither macroscopically uniform nor flat, which makes it impossible to prepare it to an epi-ready state. The bending of crystallographic planes is not observed thanks to similar thermal expansion coefficients of GaN and GaAs as well as the existence of inversion domains that reduce stress in GaN [38].

As mentioned earlier, the second kind of seeds are MOVPE-GaN/sapphire templates [39,42,43]. In this case, stress induced by the difference in thermal expansion coefficients of new-grown thick HVPE-GaN and sapphire results in a well-controlled self-separation of GaN during the cooling

process. This way, free-standing (FS) crystals are obtained. Substrates prepared from them will have macroscopically flat c-plane surfaces, uniform EPD of the order of 5 <sup>×</sup> <sup>10</sup><sup>6</sup> cm−<sup>2</sup> , but bent crystallographic planes. The last results from the difference between the lattice constants and thermal expansion coefficients of sapphire and GaN. The value of the bowing radius of crystallographic planes of a typical GaN substrate does not exceed 10 m. It is not possible to prepare an epi-ready surface with a uniform off-cut. The substrates are plastically deformed and have dislocation bundles creating a cellular network [44].

In the authors' opinion, the HVPE technology requires a fresh approach. The only way to further develop GaN substrates is GaN-on-GaN crystallization. Since there are no native HVPE-GaN seeds of high structural quality, the ones prepared by the ammonothermal method can be very useful.

#### **4. Ammonothermal Crystal Growth of GaN**

The scheme of the ammonothermal growth is the following: polycrystalline GaN (feedstock) is dissolved in supercritical ammonia enriched with mineralizers in the first zone of a high-pressure autoclave. The dissolved feedstock is transported to the second zone, where the solution is supersaturated and crystallization of GaN on native seeds takes place. An appropriate temperature gradient applied between the dissolution and crystallization zones enables the convective mass transport. Mineralizers are added to ammonia in order to accelerate its dissociation and enhance the solubility of GaN. The growth is proceeded in a different environment: basic or acidic, depending on the type of mineralizer. The ammonobasic process makes use of alkali metals or their amides, while in ammonoacidic growth, halide compounds are present. A negative temperature coefficient of solubility is observed in the ammonobasic approach [45,46]. As a consequence, the chemical transport of GaN is directed from the low-temperature solubility zone (with the feedstock) to the high-temperature crystallization one (with the seeds). The pressure of ammonia in the reactor is usually between 100 and 600 MPa and the typical growth temperature is in the range 400–750 ◦C [47].

Schemes of the high-pressure autoclave and a time-temperature relation of the two temperature zones applied for the basic ammonothermal crystallization developed at IHPP PAS are presented in Figure 5a,b, respectively. Red and green curves (see Figure 5b) represent, respectively, the temperature of the feedstock and growth zones. At the beginning, the zone with feedstock is heated and the material starts to dissolve in ammonia. Herein, the feedstock temperature is higher than the temperature of the crystal growth zone. During the dissolution stage, a back etching process occurs; the seeds are etched and they couple with the solution; a full contact is maintained between the surfaces of the GaN seeds and ammonia. Then, the crystal growth zone is heated to a temperature higher than that in the feedstock zone. In turn, the temperature of the feedstock zone decreases and the crystal growth starts. After a few months, the autoclave is cooled down, ammonia is released, and the crystals can be removed.

The basic ammonothermal growth at IHPP PAS consists of two parts [11]: (i) increase of the size of the seeds; they can be gradually enlarged (in diameter) by taking advantage of the lateral growth phenomena in non-polar and/or semi-polar directions and (ii) seed multiplication, which is concentrated on crystallization mainly in the vertical direction (in the [000-1] direction), after the growth process, the crystals are sliced perpendicularly to the growth direction and they can either increase the population of seeds used for subsequent growth runs or be subject to the wafering process (substrate fabrication). It should be remarked that the crystallization in the [0001] direction is treated as parasitic with an unstable morphology. In order to avoid the growth in this direction, specially prepared holders are used for the seeds. As a result, the (000-1) surface or side surfaces (non-polar and semi-polar) can be exposed for growth, while the (0001) face is always masked.

**Figure 5.** Scheme of: (**a**) high pressure ammonothermal autoclave; (**b**) temperature-time profiles of feedstock (red curve) and crystal growth zones (green curve) during a typical ammonothermal crystallization process at IHPP PAS.

One of the most important factors limiting Am-GaN growth in the [000-1] direction (seed multiplication) is associated with the anisotropy of growth as well as crystallization that occurs in the lateral directions at the edges of the crystal. It was shown [11] that the kinds and concentrations of impurities incorporated into GaN growing on the non-polar (11–20) and (10–10) facets and on the (000-1) plane are vastly different. This causes stress and finally leads to a plastic deformation of the growing Am-GaN crystals and appearance of cracks close to the edges [11]. Changing the shape of a seed from an irregular (hexagonal) to a round one (see Figure 6) as well as masking its edges with a metal border allowed us to grow stress-free and crack-free GaN. Both the formation of side facets as well as uncontrolled growth in the lateral directions were hindered. The border effectively counteracts the crystallization in all unwanted lateral directions. Only one facet, the (000-1) plane, was crystallized. It should be noted that it is much easier to provide a metal border around the growing crystal when the seed is round. Therefore, there were no cracks visible in the round-shaped crystals. Applying this new shape allowed to increase the yield of an ammonothermal crystal growth process. Before, cracks from the edges had been able to propagate to the center of a crystal during wafering procedures. The quantity of substrates obtained from crystals had been low. Thus, the lack of cracks at the edges seems very important from the point of view of GaN substrate production. It should be noted that each crystal after the growth process is subject to a significant mechanical treatment. Firstly, slicing is performed, and the Am-GaN seed is retrieved. It can be re-used in an ammonothermal crystallization run. In turn, the new-obtained crystal is misoriented and ground. Then, it is cut into a round shape. The primary and secondary flats are formed. Furthermore, edge grinding is performed. Next, the crystal is lapped and polished. At the end, its (0001) surface is prepared to an epi-ready state by chemo-mechanical polishing (CMP) and cleaning.

Today, one ammonothermal growth process allows to obtain a few tens of crystals with a diameter larger than 2.1-inch (see Figure 7a) and of high structural quality. This, in turn, enables to fabricate high structural quality (crystallographically flat and with low EPD) 2-inch GaN wafers (see Figure 7b). Unintentionally doped Am-GaN is n-type with free carrier concentration in the range 1 <sup>×</sup> <sup>10</sup><sup>18</sup> – 2 <sup>×</sup> 10<sup>19</sup> cm−<sup>3</sup> [11]. The main unintentionally incorporated donor is oxygen. No intentional n-type doping is performed. Doping with Mn allows to compensate the oxygen donors and crystallize material with high resistivity (exceeding 10<sup>12</sup> <sup>Ω</sup>·cm at 300 ◦C) [11].

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**Figure 6.** Examples of as-grown Am-GaN crystals of different shape: (**a**) 'old' hexagonal (**b**) 'new' round.

**Figure 7.** (**a**) Am-GaN as-grown crystals from one crystal growth process; grid 1 mm; (**b**) 2-inch ammonothermal GaN substrate; primary flat (PF) and secondary flat (SF) are marked.

#### **5. HVPE-GaN on Native Ammonothermal GaN Seeds**

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− − One of the important disadvantages of the ammonothermal crystal growth process is the low growth rate. The average value in the [000-1] direction is between 1 and 2 µm/h. Thus, as already mentioned, the ammonothermal method can be used as the source of seeds for HVPE growth. The first results of such a hybrid approach: HVPE-GaN growth on Am-GaN, were presented by IHPP PAS in 2013 [48]. Then, similar work was shown by MCC [49], and later, many other papers were published. They are summarized in References [23,50]. The growth of unintentionally doped HVPE-GaN on an Am-GaN seed proceeds in a hillock mode (see Figure 8a) with an average rate higher than 100 µm/h. The very high structural quality of an Am-GaN seed can be preserved in an HVPE layer (see Figure 8b). Doping processes performed to obtain highly conductive crystals (silicon or germanium) or SI ones (iron, carbon, or manganese), were also examined for HVPE-GaN grown on Am-GaN seeds. Crystals of high structural quality and required electrical properties were obtained. The free carrier concentration exceeded 1 <sup>×</sup> <sup>10</sup><sup>19</sup> cm−<sup>3</sup> [50]. It should be mentioned that in the case of highly resistive HVPE-GaN crystals doped with carbon or manganese, resistivity higher than 10<sup>9</sup> <sup>Ω</sup>·cm at 300 ◦<sup>C</sup> was detected [37]. It is a very important result, since the operating temperature of high power-high frequency electronic devices based on SI-GaN substrates is at least 300 ◦C.

**Figure 8.** HVPE-GaN grown on Am-GaN seed at IHPP PAS: (**a**) morphology; one central hillock is well visible; (**b**) X-ray rocking curve of Am-GaN seed and FS HVPE-GaN layer; full with half maximum (FWHM) for (00.2) reflection keeps the same value as Am-GaN seed: 43 arcsec and 50 arcsec, respectively.

It was observed that during the homoepitaxial crystallization of HVPE-GaN in the [0001] direction the non-polar and semi-polar growth of "wings" (laterally-grown material) leads to the formation of large stress close to the edges of the growing crystal. The reason for this is a different incorporation of dopants (mainly oxygen) into HVPE-GaN grown in the [0001] than in lateral directions. This leads, in turn, to different lattice parameters of the crystallized material [23,51,52]. The stress from the edges is much more significant than the one generated by the lattice mismatch between the seed and the deposited layer. Avoiding lateral growth during crystallization in the [0001] direction seems essential for developing the GaN bulk growth technology.

Like in the case of the ammonothermal process, growth in the lateral directions on the edges of the seed can also be eliminated in HVPE by using a metal ring (e.g., molybdenum). It increases the dissociation of ammonia. The supersaturation close to the edges of the crystal with the ring decreases. No growth takes place in the lateral directions. Unfortunately, the side facets are still formed. The main issue is to find such growth conditions that will allow to form only the side facets that grow faster than the material in the [0001] direction. Then, they will disappear and the crystal will increase its lateral size by growing only in the [0001] direction. According to a hypothesis by Professor Zlatko Sitar from North Carolina State University (USA) [53], such conditions may be achieved by controlling the thermal field around a crystal. It has to reach its final shape by adapting to this field rather than taking the hexagonal habit. The equilibrium shape can be overpowered by a proper design of the thermal field. In this case, the crystal will follow the thermal field and grow in a direction perpendicular to the isotherms. The idea is schematically shown in Figure 9. Such an approach was presented by HexaTech for aluminum nitride (AlN) growth by physical transport deposition (PVT) [54]. Obviously, the formation of supersaturation in the PVT and HVPE methods varies significantly. The supersaturation is the difference of thermodynamic potentials at the interface between a crystal and its environment. In the case of PVT it is almost unambiguous with the temperature distribution on the growing surface. In HVPE, reactions of all vapor species have to be considered. It should, however, be stated that if the equilibrium crystal shape of GaN can be overcome, it will be a transformative achievement for the HVPE technology. It has never been demonstrated before and will allow to grow true bulk GaN crystals of high purity, eventually yielding several tens of wafers per boule. To this day, the formation of side facets has not been defeated and they are still created during HVPE-GaN growth in the [0001] direction. In spite of this, MCC has already demonstrated 4-mm-thick HVPE-GaN-on-Am-GaN [22] and IHPP PAS showed 3-mm-thick HVPE-GaN-on-Am-GaN (see Figure 9b) [55].

**Figure 9.** (**a**) Scheme of temperature distribution close to the growing crystal surface: it may allow for controlled crystal expansion and prevent crystallization on the sidewalls; (**b**) three-mm-thick HVPE-GaN grown on Ammono-GaN; equilibrium hexagonal crystal habit is well visible; c-plane is reduced; grid 1 mm.

#### **6. Conclusions**

The growth of high structural quality bulk GaN crystals can only be performed using GaN-on-GaN technology. Today, the main method for mass fabrication of GaN crystals is HVPE. This is due to its high growth rate and purity. The process repeatability is also the highest. Ammonothermal method can provide seeds for HVPE growth. However, if the ammonothermal technology is improved, it will become a great competitor for HVPE. It should be remembered that during one ammonothermal process, a few tens of crystals can be grown. Table 1 summarizes the advantages and disadvantages of the two methods presented in this paper. Most probably, the economy will decide which technology will be applied in the future.



**Author Contributions:** K.G.—crystal growth experiments, characterization, preparing the manuscript; P.J., crystal growth experiments, characterization; A.S.—wafering, characterization; M.B.—supervision, review and editing; M.I.—review and editing. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by TEAM TECH program of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund (POIR.04.04.00-00-5CEB/17-00) as well as by the Polish National Science Center through project No. 2018/29/B/ST5/00338.

**Acknowledgments:** The authors are grateful to Tomasz Sochacki, Boleslaw Lucznik, and Michal Fijalkowski for helpful scientific discussions.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

*Article*

## **Growth Uniformity in Selective Area Epitaxy of AlGaN/GaN Heterostructures for the Application in Semiconductor Devices**

**Michał St ˛epniak \* , Mateusz Wo´sko , Joanna Prazmowska-Czajka, Andrzej Stafiniak, ˙ Dariusz Przybylski and Regina Paszkiewicz**

Faculty of Microsystem Electronics and Photonics, Wrocław University of Science and Technology, Wybrzeze Wyspia ´nskiego 27, 50-370 Wrocław, Poland; mateusz.wosko@pwr.edu.pl (M.W.); ˙ joanna.prazmowska@pwr.edu.pl (J.P.-C.); andrzej.stafiniak@pwr.edu.pl (A.S.); dariusz.przybylski@pwr.edu.pl (D.P.); regina.paszkiewicz@pwr.edu.pl (R.P.) **\*** Correspondence: michal.stepniak@pwr.edu.pl

Received: 6 November 2020; Accepted: 9 December 2020; Published: 12 December 2020

**Abstract:** The design of modern semiconductor devices often requires the fabrication of threedimensional (3D) structures to integrate microelectronic components with photonic, micromechanical, or sensor systems within one semiconductor substrate. It is a technologically challenging task, as a strictly defined profile of the device structure is obligatory. This can be achieved either by chemical etching or selective deposition on a masked substrate. In this paper, the growth uniformity of AlGaN/GaN heterostructures during selective-area metalorganic vapour-phase epitaxy (SA-MOVPE) was studied. Such structures are typically used in order to fabricate high-electron-mobility transistors (HEMT). The semiconductor material was deposited through 200 µm long stripe-shaped open windows in a SiO<sup>2</sup> mask on GaN/sapphire templates. The window width was varied from 5 µm to 160 µm, whereas mask width separating particular windows varied from 5 µm to 40 µm. The experiment was repeated for three samples differing in GaN layer thickness: 150 nm, 250 nm, and 500 nm. Based on theoretical models of the selective growth, a sufficiently uniform thickness of epitaxially grown AlGaN/GaN heterostructure has been achieved by selecting the window half-width that is smaller than the diffusion length of the precursor molecules. A Ga diffusion length of 15 µm was experimentally extracted by measuring the epitaxial material agglomeration in windows in the dielectric mask. Measurements were conducted while using optical profilometry.

**Keywords:** selective area growth; selective epitaxy; AlGaN/GaN heterostructures; gallium nitride; edge effects; effective diffusion length; MOVPE

#### **1. Introduction**

Group III nitrides, including (Al, In, Ga)N compounds, gained importance at the turn of the 20th and 21st centuries, especially in the field of optoelectronics and high power electronics. Gallium nitride is characterised by a wide band gap (3.4 eV) [1], high chemical and temperature stability [2] and large piezoelectric coefficients [3]. Its unique properties make it a material of choice for many advanced semiconductor devices, such as: high temperature devices, high electron mobility transistors (HEMT), microwave instruments, facet lasers, electroacoustic transducers and electromechanical resonators, field emitters or integrated optics devices. Those devices consist of 3D structures, such as U-shaped and V-shaped grooves, mesa structures, nanowire matrices or planar waveguides, which can be produced in two ways. In top-down architecture, the epitaxial layer is spatially patterned by wet or dry chemical etching, whereas, in bottom-up architecture, structures are selectively grown while using dielectric masks. Because of this, it is possible to integrate many opto-electro-mechanical devices

within one semiconductor substrate, which is required in order to achieve compactness, high stability, and efficiency, as well as minimise losses in modern, technologically advanced semiconductor devices [4].

Metalorganic vapour-phase epitaxy (MOVPE) is the most popular method that is used industrially to produce high quality gallium nitride layers. The possibility of precise control of several process parameters allows for the fabrication of sophisticated planar nano- and microstructures. The use of SA-MOVPE to get 3D semiconductor epitaxial growth on the nano- and micro scale is a promising, but challenging, approach. Numerous factors have to be addressed in the technological process. First of all, conducting epitaxy on a masked substrate causes heterogeneous layer growth in the window area. This phenomenon is called the edge effect and it results from excessive accumulation of epitaxial material adjacent to the dielectric mask. This is also associated with a different growth rate of a structure relative to non-selective deposition [4]. Homogeneous structure growth along the window area is necessary for keeping continuous metallization for the contact layer and close fitting between semiconductor components.

Two mechanisms of mass transport into the window area could be distinguished during the MOVPE process: vapour-phase diffusion and surface diffusion. The diffusion length of precursor molecules in vapour is several orders of magnitude greater than the surface diffusion length of the adatoms [5]. It was proved, for the first time, by Gibbon regarding InP selective deposition [6]. Mass diffusion is caused by precursor concentration gradient between masked and unmasked substrate surface. The Laplace Equation (1) describes the precursor concentration *ϕ* in the steady state

$$
\nabla^2 \varphi = 0.\tag{1}
$$

The mass flux to the substrate surface is balanced by molecule incorporation into grown layer, as local thermodynamic equilibrium can be established in the vicinity of the growth interface [7]. This can be formulated by a combination of Fick's first law and Langmuir adsorption model (2) [6]

$$-\left(D\nabla\varphi\right)\cdot\overrightarrow{n}^{\flat}=k\varphi\tag{2}$$

where *<sup>D</sup>* is diffusion coefficient, *<sup>k</sup>* is surface reaction rate, and −→*<sup>n</sup>* refers to the normal vector. Assuming that no crystal growth occurs on the dielectric mask, the reaction rate on masked substrate is equal to zero (3)

$$-\left(D\nabla\varphi\right)\cdot\overrightarrow{n}^{\flat}=0\text{ (on }mask\text{)}.\tag{3}$$

The ratio *D*/*k* is the key factor influencing the shape of the structure profile in the window area. It used to be called the effective lateral diffusion length of precursor molecules *λe f f* [4,8–10]. Molecules are incorporated with similar probability into the epitaxial structure within the whole window area when the effective diffusion length is greater than the half-width of the window. Otherwise, the uneven accumulation of epitaxial material will be observed [4–6,8–18]. Surface diffusion additionally influences structure shape adjacent to the mask. The overall participation of surface diffusion in the profile of an epitaxial structure increases with the thickness of the deposited layer [14,19]. The diffusion length is strongly dependent on the composition and material parameters of the precursors in the reactor chamber, as well as the carrier gas type [5] and process parameters, such as pressure or temperature [4]. The effective diffusion length is primarily affected by the group III precursors concentration, as group V molecules have a minor influence on the growth rate [20].

A crucial aspect of the selective area epitaxy (SAE) of AlGaN/GaN heterostructures is a horizontal gradient of the AlxGa1-xN composition that is caused by the difference in the diffusion lengths of Al and Ga molecules. Compositional variation is primarily derived by vapour-phase diffusion [9,19]. Based on Lennard–Jones potential theory, diffusion length is assumed to be inversely proportional to the square of the Lennard–Jones theorem length σ [4]. The effective diffusion length of Al molecules is expected to be smaller than the effective diffusion length of Ga molecules when using TMAl (trimethylaluminium) and TMGa (trimethylgallium) as precursors for AlGaN deposition, as σ is longer in TMAl than in TMGa [21]. This leads to a larger concentration of Al adjacent to the mask when compared to the window center. Precise control of compositional variation is substantial for the fabrication of highly efficient optoelectronic devices while using multiple quantum wells (MQWs), as the application of MQWs causes a decrease of carrier lifetime and an increase of radiative recombination efficiency [15,19]. On the other hand, compositional uniformity is required in the heterojunction band-gap engineering for the application of HEMT or planar waveguides.

There were researches that were conducted for both rectangular [5,6,8–10,15,16] and hexagonal windows in the mask [11–13,22]. All of them showed that the edge effect is strongly dependent on the structure geometry and configuration of the dielectric mask. According to Hara, the profile of selectively grown layer can be described as (4) [16]

$$h\_{\mathbf{x}} = (h\_{\text{edge}} - h\_{\text{planar}}) \exp\left(-\mathbf{x} \cdot \lambda\_{\text{eff}}^{-1}\right) + h\_{\text{planar}} \tag{4}$$

where *h<sup>x</sup>* refers to layer thickness at the distance *x* from the mask edge, *hedge* is the layer thickness adjacent to the mask, and *hplanar* indicates the thickness of the non-selectively deposited epitaxial layer under the same growth conditions. Equation (4) allows for the calculation of the effective diffusion length based on the measurements of the epitaxial material agglomeration in windows in the dielectric mask. By dividing both sides of Equation (4) by *hplanar*, an equation describing growth rate enhancement (GRE) at the distance *x* from the mask edge is obtained:

$$GRE\_{\rm x} = (GRE\_{edge} - 1) \exp\left(-\mathbf{x} \cdot \lambda\_{eff}^{-1}\right) + 1. \tag{5}$$

In order to maximize the GRE value difference, window half-width as the distance from the mask edge was chosen:

$$\text{GRE}\_{\text{center}} = (\text{GRE}\_{\text{edge}} - 1) \exp\left(-w \cdot (2\lambda\_{eff})^{-1}\right) + 1. \tag{6}$$

The effective diffusion length *λe f f* can be then calculated by

$$\lambda\_{eff} = -\frac{w}{2\ln\left(\frac{GRE\_{catter} - 1}{GRE\_{ckey} - 1}\right)} = -\frac{w}{2\ln\left(\gamma\right)}\tag{7}$$

where

$$\gamma = \frac{GRE\_{center} - 1}{GRE\_{edge} - 1}.\tag{8}$$

The effective diffusion length has been estimated so far either by calculation while using the Hara Equation (4) [10,16,18] or by fitting mathematical models to the experimental data (simulations) [4–6,8,9,11,14,17]. Published research overwhelmingly focused on the selective epitaxy of GaAs and its ternary compounds. This paper presents a new method for the estimation of the precursor molecules diffusion length according to the relative height difference between the edge and center of the grown heterostructure.

#### **2. Materials and Methods**

The test structures were deposited on GaN/sapphire templates while using an AIXTRON CCS 3 × 2 ′′ epitaxial system. Figure 1 shows the layers scheme of the investigated structures. An undoped GaN buffer layer with a total thickness of 1950 nm was grown prior to selective epitaxy. Trimethylgallium (TMGa) and ammonia (NH3) with different molar ratios were used as precursors for GaN growth with H<sup>2</sup> as a carrier gas. Next, a 400 nm thick SiO<sup>2</sup> mask was deposited by PECVD (plasma enhanced chemical vapour deposition), followed by UV photolithography. The selective epitaxy of AlGaN/GaN heterostructures with AlN cladding and cap layers was conducted at 1060 ◦C and pressure of 10 kPa with NH<sup>3</sup> flow of 67 mmol·min−<sup>1</sup> , and TMGa and TMAl flow of 65 µmol·min−<sup>1</sup>

and 8.6 µmol·min−<sup>1</sup> , respectively. The selected conditions ensured that the epitaxial layer was deposited in the mass-transport limited growth regime [23]. Three samples differing in GaN thickness (150 nm, 250 nm, and 500 nm) were successfully fabricated. Epitaxial lateral overgrowth was not observed.

**Figure 1.** Layer scheme of the investigated structures.

Figure 2 presents the configuration of the SiO<sup>2</sup> mask. Selective epitaxy was conducted in windows of different width *w* (from 5 µm to 160 µm) and length of 200 µm. The distance between windows (mask width *m*) varied from 5 µm to 40 µm. The rectangular heterostructure deposited selectively between two dielectric masks could be used as the active region of a high electron mobility transistor [24].

**Figure 2.** Configuration of the dielectric mask (*m*) and open windows (*w*).

The measurements of the epitaxial material agglomeration in windows in the dielectric mask were conducted while using Taylor Hobson Talysurf CCI optical profilometer. Coherence correlation interferometry was used as a measurement technique with 0.01 nm vertical and 0.6 µm lateral resolution. The layers profile has been determined after the removal of the dielectric mask. The whole structure was covered with a 10 nm layer of gold in order to increase the measurement accuracy. This caused an increase in the reflection coefficient and reduction of the optical beam interference

on the heterostructure. Additional measurements were performed while using Bruker Multimode V Atomic Force Microscope for measurements accuracy comparison. The data presented in this study are available in the Supplementary Materials. Measurement data have been divided into three sets depending on the thickness of the GaN layer (150 nm, 250 nm and 500 nm).

#### **3. Results and Discussion**

Figure 3 shows a part of the AlGaN/GaN heterostructure profile with the 500 nm thick GaN layer. The abscissa axis shows the profile width, whereas the ordinate axis shows the profile height relative to the GaN buffer layer surface. Increased material accumulation adjacent to the dielectric mask was observed. Fluctuations in the material growth rate at the mask edge were evaluated in dependence of the surface of the masked and exposed area, based on the obtained profiles. The overall layer profile was assembled of fragments that were measured separately. A separate calibration of the structure height reference point was conducted for each part. This resulted in a nonuniform buffer surface layer level that is visible in Figure 3. Additionally, the substrate deformed due to stresses that arose in the deposited layer.

**Figure 3.** Part of the AlGaN/GaN heterostructure profile with 500 nm thick GaN layer.

The following parameters were calculated for each window separately (Figure 4) in order to eliminate measurement errors that result from substrate deformation:


$$
\sigma = \frac{h\_{\text{edge}}}{h\_{\text{center}}} - \mathbf{1}[\text{\textquotedblleft}] \tag{9}
$$

A detailed analysis of the measured profile was conducted for the sample with a 500 nm thick GaN layer. Figure 5 (variable window width) and Figure 6 (variable mask width) present growth rate enhancement as a function of location relative to the window center. The presented results are cross-sections of selected test structures. Figure 5 shows that, with increasing window width, for a constant mask width and layer thickness, the height of the epitaxial structure decreases significantly and the edge growth factor increases. The average structure height at the window center for a 5 µm wide window is almost twice as large as for a 160 µm wide window. The shape of the profile is similar for different window widths. When reducing the size of the window, the structure edges are brought closer, without a significant change in the shape of the profile. For narrow windows (*w* < 20 µm), structure edges overlap, which results in a nearly uniform layer surface.

**Figure 4.** Parameters characterising the test structures.

**Figure 5.** Growth rate enhancement (GRE) as a function of location relative to the window center (layer thickness 500 nm). Variable window width *w*, constant mask width *m* = 20 µm.

Figure 6 shows that, with increasing mask width, for a constant window width and layer thickness, the height of the epitaxial structure increases with a slight change in the shape of the profile.

The GRE of the epitaxial structure as a function of window width is presented in Figure 7 (adjacent to the mask) and in Figure 8 (in the window center). GRE decreases exponentially with increasing windows width. This agrees with previous findings by Tanaka [11], and it can be easily understood, as the same amount of material has to be deposited on a larger area. The vertical dimensions of the layer are also affected by the surrounding mask width. The structure height increases with increasing mask width. All of the approximation curves were fitted to the measurement data while using orthogonal distance regression method with the value of the adjusted R-squared over 0.99.

**Figure 6.** GRE as a function of location relative to the window center (layer thickness 500 nm). Variable mask width *m*, constant window width *w* = 80 µm.

**Figure 7.** GRE as a function of the window width adjacent to the mask *GREedge* = *f*(*w*) (layer thickness 500 nm).

**Figure 8.** GRE as a function of the window width in the window center *GREcenter* = *f*(*w*) (layer thickness 500 nm).

The relation between GRE and window width can be expressed as (10)

$$\text{GRE}(w) = \text{GRE}\_0 + \text{GRE}\_{\text{ex}} \cdot \exp\left(-\lambda\_{eff}^{-1} \cdot w\right) \tag{10}$$

where *GRE*<sup>0</sup> refers to the minimal growth rate enhancement for a window width much greater than the effective diffusion length (*w* ≫ *λe f f*), and *GREex* is the excess growth rate enhancement dependent on the window width. The effective diffusion length *λe f f* defines the steepness of the relation between the GRE and the window width. Greater *λe f f* means that the epitaxial material diffusing from the mask will be distributed over a larger area. Table 1 depics the values of *GRE*0, *GREex*, and *λe f f* for different mask widths. Error margins have been estimated as the statistical error of the orthogonal distance regression method.

The sensitivity matrix *X* (11) has been calculated in order to analyse the influence of the parameters *GRE*0, *GREex*, and *λe f f* on the absolute growth rate enhancement

$$X = \frac{\partial \text{GRE}(w)}{\partial \theta} \tag{11}$$

where *θ* is a vector of parameters: *GRE*0, *GREex*, and *λe f f* . The values of sensitivity to particular parameters may vary significantly, thus the dimensionless normalized sensitivity matrix *X<sup>n</sup>* (12) was calculated by the multiplication of sensitivity matrix *X* and normalization diagonal matrix *D<sup>n</sup>*

$$X\_{\mathfrak{n}} = X D\_{\mathfrak{n}}.\tag{12}$$

Matrix *D<sup>n</sup>* satisfies the Equation (13)

$$\mathbf{D}\_{\mathbf{il}} = ((\mathbf{X}^T \mathbf{X}) \circ \mathbf{I})^{-0.5} \tag{13}$$

where *I* is the identity matrix and ◦ denotes the Hadamard product. Normalized sensitivity to *GRE*0, *GREex*, and *λe f f* as a function of window width, for a constant mask width *m* = 40 µm, is presented in Figure 9. GRE at the window edge was considered. The value of *GRE*<sup>0</sup> is independent of window width and it has a dominant influence on growth rate enhancement for windows that are much broader than the effective diffusion length (*w* ≫ *λe f f*) (14)

$$\lim\_{w \to \infty} GRE(w) = GRE\_0. \tag{14}$$

Window center will not be affected by lateral diffusion provided that *w* ≫ *λe f f* , thus *GRE*<sup>0</sup> = 1 at the window center.

Excess growth rate enhancement *GREex* has the greatest impact on absolute GRE for windows that are narrower than effective diffusion length. It is related to the constant amount of material that has to be deposited on a variable surface area. Reducing window width leads to higher GRE, as the same amount of epitaxial material has to be deposited on a smaller area (15)

$$\lim\_{w \to 0} GRE(w) = GRE\_0 + GRE\_{\text{ex}} \tag{15}$$

Effective diffusion length influences GRE the most for a window width equal to *λe f f* .

**Figure 9.** Normalized sensitivity of GRE to *GRE*0, *GREex* and *λe f f* as a function of window width, for a constant mask width *m* = 40 µm (at the window edge).

Figure 10 presents the *γ* ratio as a function of window width. For windows that are narrower than 20 µm, *γ* is equal to one. This indicates uniform growth within the whole window area, as the structure height at the window edge is equal to the structure height at the window center. Because of this, Hara Equation (4) cannot be used for estimating the effective diffusion length in this range (*w* < *λe f f*). For wide windows, *γ* approaches zero. It means that layer at the window center is equal in height to the layer deposited non-selectively, thus window center was not affected by mass diffusing from the dielectric mask.

Figure 11 presents the effective diffusion length that was calculated using the Hara Equation (4) for different window and mask widths. Window widths that were smaller than 20 µm were not included. It can be easily seen that *λe f f* calculated while using Equation (4) depends on both window and mask width. Effective diffusion length decreases exponentially with an increasing window width. Offset values for different mask widths are within error margin of *λe f f* estimated while using Equation (10) at the window edge, thus Equation (10) is coherent with Equation (4) and Equation (4) should be used only to windows that are much wider than the exact value of the effective diffusion length (here: *w* > 4*λe f f*). Table 1 illustrates the offset values. For similar process conditions, *λe f f* of

about 30 µm has been reported [4,11,25]. It is expected that the effective diffusion length will decrease with decreasing temperature [4,9,19,25] and increasing pressure [4,5,9,19,25]. Similarly, an increase in the temperature causes an increase in the effective diffusion length [4,8,25]. Therefore, the calculated values of the effective diffusion length are in agreement with previous reports.


**Table 1.** Estimated parameters of the *GRE* = *f*(*w*) relation at the window edge and at the window center for different mask widths.

**Figure 11.** Theoretical effective diffusion length as a function of window width, for different mask widths *λe f f* = *f*(*w*) (Hara Equation (4)).

Figure 12 presents the effective diffusion length that was calculated using Equation (10) at the window edge and center as a function of the mask width. Both of the relations are linear and they share the same intercept equal to 15 µm that can be interpreted as the lateral vapour diffusion length of Ga *λGa*, independent of the mask configuration and structure geometry. Slopes of approximation lines are equal to 0.5 µm−<sup>1</sup> and 0.3 µm−<sup>1</sup> for the window center and window edge, respectively. Therefore, Equation (10) can be transformed into Equations (16) and (17).

$$\text{GRE}(w) = \text{GRE}\_0 + \text{GRE}\_{\text{ex}} \cdot \exp\left(-(\lambda\_{\text{Gal}} + 0.3m)^{-1} \cdot w\right) \text{(at the window edge)} \tag{16}$$

$$\text{GRE}(w) = \text{GRE}\_0 + \text{GRE}\_{\text{ex}} \cdot \exp\left(-(\lambda\_{\text{Ga}} + 0.5m)^{-1} \cdot w\right) \text{(at the window center)}\tag{17}$$

**Figure 12.** Effective diffusion length at the window edge and the window center as a function of the mask width *λe f f* = *f*(*m*).

Figure 13 presents the edge growth factor as a function of window width. It can be seen that the larger the window width and the greater the distance between windows, the greater the difference in structure height between the edge and the window center. This effect is also visible in Figure 3, showing the layer altitude profile. An increased agglomeration of epitaxial material adjacent to the mask may not be observed for narrow windows, while more intense layer growth will be seen throughout the entire window area. This increase will be faster for smaller window area and larger mask area.

**Figure 13.** Edge growth factor as a function of window width *σ* = *f*(*w*) (layer thickness 500 nm).

Uniform layer growth will be observed, provided that the distance between the mask center and window center will be smaller than the effective diffusion length (18)

$$0.5m + 0.5w < \lambda\_{eff}.\tag{18}$$

When considering Equation (17), this condition can be expressed as

$$w < \Im \lambda\_{Ga}.$$

Figure 13 marks a value of 2*λGa*. It can be seen that, for a window width smaller than 2*λGa*, nearly uniform layer growth was observed. In order to compare measurement accuracy, a heterostructure with a 250 nm thick GaN layer was additionally profiled while using atomic force microscope (AFM). Edge growth factor as a function of window width calculated using different profiling methods is presented in Figure 14. Optical profilometer and AFM both have similar accuracy regarding window widths satisfying the condition (19).

GRE as a function of location relative to the window center for a constant window and mask width and different nominal GaN layer thickness is presented in Figure 15. Figure 16 presents the edge growth factor as a function of the mask surface to the window surface ratio for three different GaN layer thicknesses. Figures 15 and 16 suggest that GRE is independent of the structure thickness, thus growth uniformity cannot be achieved by the modification of the deposition time or the mask configuration. The edge growth factor can be minimised by selection of the sufficiently narrow dielectric mask, but uniform front of crystallization for a constant window width can only be achieved by modification of the diffusion length of precursor molecules. This can be achieved by a variation of the process parameters, such as temperature or pressure [4].

**Figure 14.** Edge growth factor as a function of window width *σ* = *f*(*w*) (layer thickness 250 nm); comparison of optical profilometer and atomic force microscope (AFM).

**Figure 15.** GRE as a function of location relative to the window center. Variable nominal GaN layer thickness, constant window width *w* = 80 µm, and mask width *m* = 20 µm.

**Figure 16.** Edge growth factor as a function of the mask surface to the window surface ratio *σ* = *f*( *m w* ). Constant mask width *m* = 40 µm.

#### **4. Conclusions**

Control of the growth uniformity in selecive area epitaxy is a crucial aspect regarding the fabrication of the modern semiconductor devices. It applies to both the structure profile and compositional gradient. In this paper, a uniform front of crystallization of AlGaN/GaN heterostructure was achieved by the selection of the window half-width smaller than the Ga diffusion length of 15 µm. Ga diffusion length was estimated at 1060 ◦C and a pressure of 100 mbar based on the relative height difference between the edge and the center of the grown heterostructure. It was presented that uniform layer growth cannot be achieved by the modification of the mask configuration or the deposition time.

#### **Supplementary Materials:** Measurement data are available online at http://www.mdpi.com/2079-9292/9/12/ 2129/s1 .

**Author Contributions:** Conceptualization, M.S.; Methodology, M.S., M.W., J.P.-C., A.S. and D.P.; Validation, M.W. and R.P.; Formal analysis, M.S.; Investigation, M.S.; Resources, R.P.; Data curation, M.S.; Writing—original draft preparation, M.S.; Writing—review and editing, M.W. and R.P.; Visualization, M.S.; Supervision, M.W. and R.P.; Project administration, R.P.; Funding acquisition R.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was co-financed by the National Centre for Research and Development grants TECHMATSTRATEG No. 1/346922/4/NCBR/2017, Polish National Agency for Academic Exchange under the contract PPN/BIL/2018/1/00137 and Wroclaw University of Science and Technology subsidy. This work was accomplished thanks to the product indicators and result indicators achieved within the projects co-financed by the European Union within the European Regional Development Fund, through a grant from the Innovative Economy (POIG.01.01.02-00-008/08-05) and by the National Centre for Research and Development through the Applied Research Program Grant No. 178782 and Grant LIDER No. 027/533/L-5/13/NCBR/2014.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Review* **High Pressure Processing of Ion Implanted GaN**

**Kacper Sierakowski 1,\* , Rafal Jakiela <sup>2</sup> , Boleslaw Lucznik <sup>1</sup> , Pawel Kwiatkowski <sup>1</sup> , Malgorzata Iwinska <sup>1</sup> , Marcin Turek <sup>3</sup> , Hideki Sakurai 4,5 , Tetsu Kachi <sup>4</sup> and Michal Bockowski 1,4**


Received: 27 July 2020; Accepted: 19 August 2020; Published: 26 August 2020

**Abstract:** It is well known that ion implantation is one of the basic tools for semiconductor device fabrication. The implantation process itself damages, however, the crystallographic lattice of the semiconductor. Such damage can be removed by proper post-implantation annealing of the implanted material. Annealing also allows electrical activation of the dopant and creates areas of different electrical types in a semiconductor. However, such thermal treatment is particularly challenging in the case of gallium nitride since it decomposes at relatively low temperature (~800 ◦C) at atmospheric pressure. In order to remove the implantation damage in a GaN crystal structure, as well as activate the implanted dopants at ultra-high pressure, annealing process is proposed. It will be described in detail in this paper. P-type GaN implanted with magnesium will be briefly discussed. A possibility to analyze diffusion of any dopant in GaN will be proposed and demonstrated on the example of beryllium.

**Keywords:** ion implantation; gallium nitride; thermodynamics; ultra-high-pressure annealing; diffusion; diffusion coefficients

#### **1. Introduction**

Electronic devices prepared by GaN-on-GaN technology are still at the beginning of their road to commercialization. Two different technologies can be applied for preparing GaN-on-GaN vertical devices (e.g., metal–oxide–semiconductor field-effect transistor (MOSFET)). The structure can be grown by epitaxial techniques with some procedures, such as regrowth and/or etching, needed due to the device architecture, or by ion implantation [1,2]. The latter approach seems to be much less demanding and more perspective. The implantation process has been commonly applied in semiconductors for selective area n- and p-type doping. Such approach allows one to reduce the device size and to control the electric field configuration in devices. However, the implantation process destroys the crystal structure of the material. In order to rebuild it, appropriate (for a given compound) temperature treating is required. The temperature required to remove the damage is around 50–70% of the melting temperature of a given compound [3]. Temperature treatment is also important in order to activate the implanted ions [4–6]. In case of Mg, the sole process of implantation of ions into GaN does not result in p-type conductivity at room temperature [7]. The reason for this is not only the rather high ionization energy of Mg in GaN. The implantation process results in introducing defects that compensate the implanted dopant. It was assumed that they were nitrogen vacancies. Uedono et al. showed that these defects were coupled gallium and nitrogen vacancies [8]. It was also presented that annealing at temperature higher than 1100 ◦C allows one to decrease the defect density. It should be stressed that GaN loses its thermal stability close to 800 ◦C at atmospheric pressure [9]. Therefore, annealing it at higher temperature results in surface decomposition. It is possible to apply an AlN capping layer in order to protect the surface. However, it was suggested that during annealing vacancy-type defects agglomerate near the interface between the AlN cap and GaN [8]. Therefore, the best approach is to avoid using a capping layer. One of the possible solutions is to anneal implanted GaN at much higher temperature but, then, also at high nitrogen pressure. Such technology is called the ultra-high-pressure annealing (UHPA). UHPA is strictly derived from the well-known high nitrogen pressure solution (HNPS) growth technology of GaN [10]. First GaN monocrystals of the highest structural quality were obtained by the HNPS method [11]. They were grown from a solution of atomic nitrogen in liquid gallium (Ga) at temperature of the order of 1500 ◦C and nitrogen (N2) pressure of 1 GPa. If Ga is removed from such a system, it is possible to anneal any material in the temperature and pressure conditions described above. This is the foundation of the UHPA technology. Today, it serves to anneal implanted GaN (see, e.g., [12–16]) as well as different kinds of glasses and foams (see, e.g., [17–21]).

In this paper, the basis of applying the UHPA technology only for GaN is described. At the beginning, the thermodynamics of this process is briefly explained. Next, the UHPA configuration is presented and analyzed. P-type GaN implanted with magnesium (Mg) is discussed based on recent results obtained in cooperation with Nagoya University in Japan. Then, application of the UHPA technology for analyzing the diffusion mechanism of beryllium (Be) in GaN is demonstrated. It is treated as a case study since the presented approach allows one to examine the diffusion of any element in GaN. A summary is given at the end of this paper.

#### **2. Thermodynamic Basics**

In 1984, Karpinski et al. [9] determined the pressure–temperature (p–T) equilibrium curve for the GaN-Ga-N<sup>2</sup> system. This curve is presented in Figure 1a. The p–T area where GaN exists is clearly seen. Figure 1b shows the Gibbs free energy (G) as a function of temperature for GaN and its constituent, N<sup>2</sup> [11]. With increasing temperature, the G curves decrease. It happens faster in the case of N2. Thus, at atmospheric pressure at around 800 ◦C, the G curves for GaN and N<sup>2</sup> intersect and GaN loses its thermodynamic stability. Increasing the N<sup>2</sup> pressure shifts the Gibbs free energy of nitrogen into higher ranges, according to the equation:

$$\mathbf{G} = \mathbf{U} + \mathbf{p}\mathbf{V}\text{-TS} \tag{1}$$

where U represents the internal energy, V-volume, and S-entropy.

Then, the stability region of GaN is extended. Thus, high nitrogen pressure (in fact nitrogen activity) stabilizes the existence of GaN at higher temperature. It should be, however, remembered that GaN is a binary compound and at very high temperature Ga vapor pressure is also required to secure GaN against decomposition.

**Figure 1.** (**a**) Experimental p–T equilibrium curve for the GaN-Ga-N<sup>2</sup> system [9]; (**b**) Gibbs free energy (G) for GaN and N<sup>2</sup> ; visible temperature shift of GaN stability area if N<sup>2</sup> pressure is increased [11].

#### **3. Ultra-High-Pressure Annealing Process**

During the UHPA process, a GaN sample is placed in a crucible. The crucible is then positioned in a resistive furnace and in a high-pressure reactor. In such a configuration, annealing of GaN at nitrogen rich conditions can be performed. If no changes are introduced, the compound will only have contact with the N<sup>2</sup> gas phase. However, as already mentioned, Ga vapor might be needed for protecting GaN against decomposition during annealing at relatively high temperature. The presence of Ga vapor can be provided in two ways: (1) the GaN sample is covered by GaN powder; (2) the GaN sample is placed close to a Ga droplet. The first solution bases on the assumption that the GaN powder decomposes faster than the GaN sample and, therefore, Ga vapor is above the annealed sample. The second way is more elegant and bases on the assumption that the Ga droplet evaporates and, therefore, Ga vapor is close to the surface of the annealed sample. In this paper, examination of the three described configurations: only in N2, with GaN powder, and with a Ga droplet, will be presented. They are shown in Figure 2. For each UHPA process, two GaN samples of high structural quality were prepared: one with the (0001) surface and the second one with the (000-1) surface prepared to an epi-ready state. Figure 3 shows atomic force microscopy (AFM) images of the mentioned surfaces. In both cases, values of the root mean square (RMS) were lower than 0.1 nm. GaN samples grown by halide vapor phase epitaxy (HVPE-GaN) were used (for details see [22]). This material is characterized by high structural quality with threading dislocation density of the order of 5 × 10 4 cm−<sup>2</sup> , flat crystallographic planes (bowing radius higher than 20 m) as well as high purity (donor and acceptor concentration lower than 10<sup>17</sup> cm−<sup>3</sup> ).

**Figure 2.** Three configurations for annealing HVPE-GaN samples with exposed (0001) and (000-1) surfaces: (**a**) in N<sup>2</sup> rich conditions; samples have direct contact only with N<sup>2</sup> (configuration A); (**b**) covered by polycrystalline GaN powder (configuration B); (**c**) close to Ga droplet (configuration C); the samples are placed in a crucible (represented by blue box in the figure), resistive heater and high pressure autoclave (reactor).

Figure 4 demonstrates AFM images of the samples' surfaces after annealing at 1400 ◦C under N<sup>2</sup> pressure of 0.7 GPa for 15 min. A lower value of RMS (of the order of 0.5 nm) was noted for samples covered with GaN powder. Multiple atomic steps were clearly visible. The samples annealed at nitrogen rich conditions and placed close to the gallium droplet (configurations A and C in Figure 2, respectively) demonstrated higher RMS close to 1 nm. In the case of samples annealed in configuration A, Ga droplets and pinholes were detected. The samples annealed in configuration C showed areas without steps but with small beads. These results showed that only annealing in configuration B did not lead to GaN surface decomposition. Thus, this configuration was chosen for annealing implanted GaN.

**Figure 3.** AFM images of HVPE-GaN surfaces: (**a**) (0001); (**b**) (000-1); RMS = 0.1 nm.

**Figure 4.** AFM images of the samples' surfaces: (0001)—left column and (000-1)—right column, respectively, annealed in three configurations presented in Figure 2; annealing: (**a**) configuration A—only in N<sup>2</sup> ; (**b**) configuration B—covered by GaN powder; (**c**) configuration C—with Ga droplet close to the samples' surfaces.

#### **4. P-Type GaN by Mg Implantation**

As mentioned, the implantation process has been commonly applied for controlling the selective area doping of both n- and p-type regions, which allow one to reduce the device size and control the electric field configuration in devices. In the case of GaN, high n-type carrier concentration has already been demonstrated by using a relatively large ion dosage [4,23]. Obtaining highly conductive p-type after ion implantation still remains a challenge. Recently, a very effective activation by UHPA of Mg-implanted p-type GaN has been announced [24]. Investigating Mg diffusion during the UHPA process also started [25–27].

Magnesium was implanted into n-type GaN deposited by metalorganic vapor phase epitaxy (MOVPE). The 2-µm-thick MOVPE layer was grown on an HVPE-GaN substrate. The ion implantation process was performed at room temperature. A 300-nm-deep box-shaped profile with Mg concentration of 10<sup>19</sup> cm−<sup>3</sup> was obtained. The UHPA process was performed at 1400 ◦C for 5 min under N<sup>2</sup> pressure of 1 GPa. The sample was covered by polycrystalline GaN powder. Figure 5a shows Mg profiles after implantation and after annealing. The diffusion of Mg into the sample (up to 1 µm) was observed. The average Mg concentration in a 1-µm-thick layer was of the order of 10 18 cm−<sup>3</sup> . AC Hall measurements, described in detail in [24], demonstrated that the layer is p-type GaN with hole concentration of 10 17 cm−<sup>3</sup> and mobility 25 cm<sup>2</sup> V −1 s <sup>−</sup><sup>1</sup> at room temperature (see Figure 5b). A comparison of electrical results between the p-type GaN resulting from implantation followed by UHPA and an MOVPE-GaN layer doped with Mg [28] showed that the same results can be obtained by both methods.

**Figure 5.** (**a**) Comparison of Mg profile after implantation and UHPA; (**b**) temperature-dependent hole concentration for samples processed by Mg ion implantation and UHPA compared to MOVPE-GaN doped with Mg; modified from Sakurai et al. [24] with permission of AIP Publishing.

No doubt, achieving efficient p-type conductivity in Mg-implanted GaN depends on post-implantation annealing conditions. Up to now, p-type GaN with 70% activated Mg atoms was obtained only by UHPA at 1400 ◦C [24]. Conventional annealing at atmospheric pressure and 1300 ◦C (with an AlN cup sputtered on GaN surface) allowed us to obtain activation of Mg atoms at the level of 25% [2]. Additionally, atomic-resolution transmission electron microscopy analysis showed that interstitial-type extended defects and inversion domains with Mg segregation formed during the conventional annealing [29]. These defects are not observed in the samples treated by UHPA [26,27].

#### **5. Di**ff**usion Mechanism of Beryllium in GaN—Case Study**

As can be remarked, the UHPA leads to diffusion of implanted dopants in GaN. It seems that such experiments allow one to analyze the diffusion phenomenon in GaN and determine the diffusion coefficients of any dopant. In what follows, we will analyze the diffusion of Be in GaN. Unintentionally doped HVPE-GaN layers deposited on ammonothermal GaN substrates [30] were used as samples for ion implantation. Implantation of Be ions was performed with a dose of 2.9 × 10 15 cm−<sup>2</sup> at energy of 200 keV, without the use of a through film and at room temperature. UHPA was applied as post-implantation annealing. It was performed at nitrogen pressure of 1 GPa, temperature varying in the range 1200–1400 ◦C and for two different times: 15 and 30 min.

Secondary ion mass spectrometry (SIMS) measurements allowed us to examine the depth profiles of Be. Results for samples as-implanted and annealed for 15 and 30 min are presented in Figure 6. Only Be profiles are shown. No significant changes were observed in the case of other elements. Concentrations of oxygen and silicon in HVPE-GaN used for implantation were lower than 10 17 cm−<sup>3</sup> . It should be noted that all other elements apart from Be, especially atmospheric impurities like hydrogen and carbon, were below the SIMS background level. The data presented in Figure 6 indicate that: (1) the detection limit of Be is 10 15 cm−<sup>3</sup> ; (2) annealing at 1200 ◦C and 1400 ◦C changes the Be profile; Be reaches the depth of 8 µm at 1400 ◦C; (3) diffusion profiles exhibit a characteristic kink (marked in Figure 6); (4) in the sample annealed at 1400 ◦C, the Be reservoir remains at the depth of the maximum concentration of the as-implanted sample; it indicates that the top of the layer, around 1 µm from the surface, can be regarded as an infinite source of Be dopant for all annealing conditions.

**Figure 6.** Results of SIMS measurements. Be depth profiles for samples as-implanted and annealed in the temperature range 1200 ◦C–1400 ◦C for: (**a**) 15 min; examples of the kink are marked, (**b**) 30 min; gray curves are error function (erfc) function fitting; black dotted lines indicate the concentration level of the kink in the profile.

If an infinite source of a species is used, the diffusion profiles (concentration *C* of the examined species) are described by a complementary error function (erfc):

$$\mathcal{C}(\mathbf{x},t) = \mathcal{C}\_{S} \text{erfc}\left(\frac{\mathbf{x}}{\sqrt{4Dt}}\right) \tag{2}$$

where *C<sup>S</sup>* is the maximum concentration of the diffused species, corresponding to the surface concentration in the case of infinite source experiment; *D* is the diffusion coefficient; t is annealing time; *x* is the depth from the source of the species. Fitting curves were determined based on the erfc function. They are also presented in Figure 6. *C<sup>S</sup>* and *D* were used as fitting parameters. Magnitudes of the diffusion coefficients obtained from the fitting of Equation (1) changed significantly from 4 × 10 −12 cm<sup>2</sup> s −1 to 6 × 10 −11 cm<sup>2</sup> s −1 for 1200 ◦C and 1400 ◦C, respectively. However, it is clearly

seen that the erfc relation is well fitted only to the upper parts of the SIMS profiles (above the characteristic kink). Therefore, the diffusion coefficients calculated in such a way are valid for high Be concentration. A drop (kink) in the Be depth profile appears at a certain Be concentration. This concentration increases when the annealing temperature rises. Such a deviation from the erfc fitting in the profile indicates a change in the diffusion coefficient. For a system, in which *D* of a species is concertation-dependent, the method described by Matano [31] is applied. According to this approach the standard Fick's law equation is transformed into:

$$\frac{\partial \mathbf{C}}{\partial t} = \frac{\partial}{\partial \mathbf{x}} D \left( \frac{\partial \mathbf{C}}{\partial \mathbf{x}} \right) \tag{3}$$

where *t* and *x* are time and depth variables, respectively.

A following variable: η = *x*/*t 1*/*2* , can be applied if the boundary conditions are known. This results in a dependence of concentration only on η instead of *x* and *t*. Then, the equation can be integrated with respect to η between *C* = 0 and *C* = *C<sup>l</sup>* , where *C<sup>l</sup>* is a specific value of concentration. Since the analyzed experimental profile is plotted for a specific diffusion time, *t* can be treated as constant when η is replaced by *x* and *t*. For *C* equal to 0, *dC*/*dx* is also equal 0. Therefore, the final equation for the diffusion coefficient is the following:

$$D\left(\mathbb{C}^1\right) = -\frac{1}{2t} \left(\frac{d\mathbf{x}}{d\mathbb{C}}\right) \int\_{\mathbb{C}^1}^{\mathbb{C}\_1} \mathbf{x} d\mathbb{C} \tag{4}$$

This way, the diffusion coefficient for concentration *C<sup>1</sup>* can be derived from a dopant depth profile by transforming the plot from a *C(x)* to *x(C)* function and then integrating. Beryllium depth profiles transformed using Equation (4) are presented in Figure 7a,b for 15-min and 30-min annealing processes, respectively. The Matano method (also known as Boltzmann–Matano method [32]) allowed us to determine the diffusion coefficients for lower concentrations of Be, where there is a divergence between the erfc fit and the SIMS data. Values of the diffusion coefficients are indicated by lines in Figure 7.

**Figure 7.** Matano analysis of Be depth profiles according to Equation (3) for samples annealed for: (**a**) 15 min and (**b**) 30 min; lines indicate the diffusion coefficients for low concentration of Be; two peaks are visible for high Be concentrations; they may result from the departure from the Matano analysis at the initial Be profile.

The diffusion coefficients calculated from Equation (2), based on the erfc fit and the ones derived from the Matano analysis for both annealing durations, are presented as a function of 1000/*T* in Figure 8. A classical Arrhenius equation was used to fit the dependence of the diffusion coefficients on inverse temperature:

$$D = D\_0 \exp\left(\frac{-E\_A}{kT}\right) \tag{5}$$

**Figure 8.** Diffusion coefficients of Be atoms in GaN as a function of inverse temperature; Arrhenius plot from erfc fitting (red filled triangles and line) and Matano analysis (black filled circles and line).

Results of such fitting, prepared for data from the erfc and Matano analysis, are also presented in Figure 8.

The temperature-independent pre-exponent factor *D0*, as well as the activation energy for both Be diffusion mechanisms, was determined from Equation (2) using the erfc fitting and the Matano analysis. The results are presented in Table 1.

**Table 1.** Temperature-independent pre-exponent factor *D<sup>0</sup>* and the activation energy for the Be diffusion.


All the results presented in the above suggest two mechanisms, fast and slow, of Be diffusion in GaN. The first process is most probably a pure interstitial mechanism through octahedral lattice sites (for details, see [33]). The slower one is an interstitial–substitutional diffusion mechanism involving Ga vacancies and tetrahedral lattice sites. The ratio of atoms involved in both mechanisms depends on the concentration of Ga vacancies. Such a result shows that controlling the Ga vacancy concentration can influence the rate of diffusion of the Be dopant in GaN.

#### **6. Summary**

The UHPA technology and its application for GaN was presented. Different configurations of the annealing process were studied in order to prevent GaN surface, both (0001) and (000-1), from decomposition. The experiments performed at 1400 ◦C involved placing GaN samples in N<sup>2</sup> rich conditions, close to a Ga droplet, covered by polycrystalline GaN powder. Only the last configurations resulted in surfaces with visible atomic steps. Therefore, UHPA can be successfully applied for GaN

samples without the need to place a cap layer. The described annealing technology, preceded with Mg ion implantation, results in p-type GaN with the dopant activation exceeding 70% and electrical properties similar to those of MOVPE-doped GaN. This makes UHPA a very promising technology for fabricating devices with selectively doped areas. The high temperature applied in UHPA allows one to study the diffusion process of different elements in GaN. This was presented in the example of Be. Both the diffusion coefficients, as well as two different mechanisms of diffusion, were determined.

**Author Contributions:** K.S.—crystal growth experiments, UHPA experiments, characterization, preparing the manuscript; R.J.—SIMS measurements, theoretical analysis; B.L.—UHPA experiments, characterization; P.K.—UHPA experiments; M.I.—review and editing; M.T.—Be implantation; T.K., H.S.—Mg implantation, Hall and SIMS measurements, supervision, review and editing; M.B.—UHPA experiments, supervision, review and editing. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the Polish National Science Center through projects No. 2018/29/B/ST5/00338, as well as by the TEAM TECH program of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund (POIR.04.04.00-00-5CEB/17-00). This work was also supported by MEXT "Research and development of next-generation semiconductor to realize energy-saving society" Program Grant Number JPJ005357.

**Acknowledgments:** The authors are also grateful to Anna Feduniewicz-Zmuda for performing the AFM analysis and helpful discussions. The authors would also like to thank Tetsuo Narita of Toyota Central R&D Labs., Inc. for valuable discussions.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
