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Influence of Intrinsic Point Defects Incorporated from
Growth Surface on Atomic Interdiffusion and
Unintentional Compositional Gradient in AlGaN/AlN
Heterointerfaces

Yoshihiro Kangawa, Akira Kusaba, Takahiro Kawamura, Pawel Kempisty, Kana Ishisone, Mauro Boero

► To cite this version:

Yoshihiro Kangawa, Akira Kusaba, Takahiro Kawamura, Pawel Kempisty, Kana Ishisone, et al. Influence of Intrinsic Point Defects Incorporated from Growth Surface on Atomic Interdiffusion and Unintentional Compositional Gradient in AlGaN/AlN Heterointerfaces. Crystal Growth & Design, 2025, 25 (3), pp.740-746. 10.1021/acs.cgd.4c01542. hal-04940185

HAL Id: hal-04940185

https://hal.science/hal-04940185v1

Submitted on 11 Feb 2025

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Influence of intrinsic point defects incorporated from growth surface
on atomic interdiffusion and unintentional compositional gradient
in AlGaN/AlN heterointerfaces

Yoshihiro Kangawa¹, *, Akira Kusaba¹, Takahiro Kawamura²,
Pawel Kempisty³, Kana Ishisone⁴ and Mauro Boero⁵, ⁶

¹Research Institute for Applied Mechanics, Kyushu University, Fukuoka 816-8580, Japan

²Graduate School of Engineering, Mie University, Mie 514-8507, Japan

³Institute of High Pressure Physics, Polish Academy of Sciences,
Sokolowska 29/37, 01-142 Warsaw, Poland

⁴Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States

⁵University of Strasbourg CNRS, ICUBE Laboratory UMR 7357,
23 rue du Loess 67037 Strasbourg, France

⁶Institute of Materials and Systems for Sustainability, Nagoya University, Nagoya 464-8601, Japan

*Corresponding author: kangawa@riam.kyushu-u.ac.jp

Abstract:

We investigate theoretically the formation mechanisms of the unintentional compositional gradient layer occurring at AlGaN/AlN heterointerfaces during metal-organic chemical vapor deposition (MOCVD). The study of heterointerface morphology is crucial for developing AlGaN deep-ultraviolet light-emitting and laser diodes. After studying the stability of the surface reconstructions with intrinsic point defects in their sub-surface layers using an ab initio-based approach, we inspect the impact of defects on the atomic interdiffusion at the heterointerfaces by Monte Carlo simulation. The relationship between MOCVD conditions and the type of dominant intrinsic point defects is clarified. We find that (i) cation and anion vacancies complexes are dominant in the sub-surface layers above 1000 °C, and (ii) they accumulate near the AlGaN/AlN heterointerface during growth causing cation interdiffusion, i.e., formation of compositional gradient layers. Controlling the type of intrinsic point defects incorporated during the surface growth in MOCVD is a key factor to preserve atomically flat heterointerfaces.

Keywords:

Ab initio-based approach, Monte Carlo simulation, diffusion of intrinsic point defect, flatness of AlGaN/AlN
heterointerface

1. Introduction

The III-nitride semiconductors are attracting great attention as materials for light-emitting diodes (LEDs) and laser diodes (LDs) in the deep ultraviolet, visible, and infrared regions. Blue LEDs with InGaN active layers and white LEDs combining them with yellow phosphors are well-known as materials and devices components awarded the 2014 Nobel Prize in Physics. Since the InGaN/GaN system is immiscible [1-4], the heterointerface morphology or flatness has not been regarded so far as a hot topic in developing these LEDs
and LDs. Inside the material, compositional fluctuations in the InGaN active layers have been evidenced [5-7]. Conversely, AlGaN-based deep-ultraviolet LEDs and LDs, which incidentally match the absorption wavelengths of coronaviruses and bacterial RNA and DNA, have recently attracted special attention. In the AlGaN/AlN system, the mixing enthalpy, or excess energy, is small and miscible compared with the InGaN/GaN system [8, 9]. Hence, the formation of atomically flat heterointerfaces without compositional gradient layers is a key issue for this system.

Compositional gradient layers have been observed in AlGaN/AlN/sapphire and AlGaN/AlN systems. Liu et al. [10] explained that the compositional gradient, termed “compositional pulling” phenomenon, is caused by the compressive stress from the underlying layer. Tsai et al. [11] reported that the surface segregation of Ga also contributes to the compositional gradient. On the other hand, Dycus et al. [12] reported that the difference in threading dislocation density, rather than compressive stress, contributes to the compositional gradient since it was observed in AlGaN/AlN/sapphire but not in AlGaN/AlN. Recently, Yoshikawa et al. [13, 14] found that the formation of the compositional gradient layer can be controlled by the growth temperature even for the same sample structure, surface morphology, and threading dislocation density. These results suggest that factors other than compressive stress, surface segregation, and threading dislocation density are responsible for the arising of the compositional gradient layer. In other words, interdiffusion during growth seems to be the key mechanism for its formation rather than thickness-related changes in Ga incorporation efficiency at the growth front. For these reasons, they called the layer an "unintentional diffusion layer" rather than a "composition-pulling layer". In this study, we theoretically analyze the types of intrinsic point defects, i.e., vacancies, incorporated during the surface growth and cation interdiffusion via vacancies near the AlGaN/AlN interface. The study focused primarily on the influence of the growth temperature on the stability of the surface reconstruction and the underlying intrinsic point defects, as well as their impact on the atomic interdiffusion near the heterointerfaces.

## 2. Computational methods

The III-nitride semiconductor LEDs and LDs are industrially fabricated by metalorganic chemical vapor deposition (MOCVD). The MOCVD is a complex process involving (1) gas-phase reactions, (2) surface reactions, and (3) interdiffusion in the solid phase. Due to this complexity, it is crucial to analyze each elementary process sequentially to clarify the whole MOCVD. Kangawa et al. [15] are developing an extensible simulator suite for CVD (eXS2-CVD), which can analyze the MOCVD process from its upstream (1) to downstream (3) mentioned above. Since this study aims at analyzing the incorporation of intrinsic point defects from the growth surface and their impact on atomic interdiffusion near the heterointerface, the focus is on the analyses of the elementary processes occurring in steps (2) and (3) above.

### 2.1. Surface phenomena analysis: Ab initio-based approach

Analyzing the gas-solid phase equilibrium is crucial to unravel the stability of surface reconstruction and the role of intrinsic point defects in the sub-surface layers under MOCVD conditions. The adsorption-desorption mechanism of an atom or molecule can be addressed by comparing the relationship between the adsorption energy of an atom (molecule) and their corresponding chemical potential in the gas phase [16, 17].

The adsorption energy of an atom (molecule) can be obtained by ab initio calculations via structural
optimization and electron density calculations. Our study makes use of the ab initio calculation package Quantum ESPRESSO (QE) [18, 19], within the density functional theory (DFT) framework with the PBE generalized gradient approximation [20] for the exchange-correlation functional. A plane wave basis set is used for the expansion of the valence electrons wavefunctions, and the cut-off energy is set to 60 and 240 Ry for wavefunctions and charge densities, respectively. Norm-conserving Troullier–Martins pseudopotentials [21] are used to account for the core-valence electrons interaction. The surface slab model used in our study consists of a 20 Å thick vacuum layer with a 5-molecular layer GaN(0001) whose bottom surface is terminated by a fictitious hydrogen with 0.75 electron (Fig. 1) to saturate dangling bonds. Here, the surface size is set to (2 x 2), i.e., a surface with an area of 35 Å² with four Ga and four N in the 1st molecular layer. The number of Monkhorst–Pack k-point sampling [22] was 3 x 3 x 1. In geometry optimization, the energy convergence threshold was set to 0.00136 eV, with a maximum force component of 0.0257 eV/Å. The obtained atomic model and electron density distribution were drawn using the visualization software VESTA [23].

The chemical potential $\mu$ of an atom (molecule) in the gas phase can be computed according to the following equation based on statistical thermodynamics.

$$ \mu = -k_B T \ln(g k_B T / p \times \zeta_{trans} \zeta_{rot} \zeta_{vibr}), \quad (1) $$

$$ \zeta_{trans} = (2\pi m k_B T / h^2)^{3/2}, \quad (2) $$

$$ \zeta_{rot} = (1/\pi\sigma)\{8\pi^3 (I_A I_B \dots)^{1/n} k_B T / h^2\}^{n/2}, \quad (3) $$

$$ \zeta_{vibr} = \prod_{i}^{3N-3-n} \{1 - \exp(-hv_i/k_B T)\}^{-1}, \quad (4) $$

where $\zeta_{trans}$, $\zeta_{rot}$, and $\zeta_{vibr}$ are the partition functions of the translational, the rotational, and the vibrational motion, respectively. Here, $k_B$ is the Boltzmann's constant, $T$ is the temperature, $g$ is the degree of degeneracy of the electron energy level, $p$ is the partial pressure of the molecule, $m$ is the mass of a molecule, $h$ is the Planck's constant, $\sigma$ is the symmetric factor, $I_i$ is the moment of inertia, $n$ is the degree of freedom of the rotation, $N$ is the number of atoms in the molecule, $i$ is the degree of freedom for the vibration, and $v$ is the frequency. $I_i$ is written as

$$ I_i = m_i r^2. \quad (5) $$

being $m_i$ the reduced mass and $r$ the radius of gyration. For further details, see Ref. 17.

When this method is applied to multiple atoms or elements on the GaN surfaces under MOCVD conditions, the Gibbs free energy $G$ of the reconstructed surface is given by the following equation [24]:

$$ G = E_{slab}^{recon} - (E_{slab}^{ideal} + n_{Ga}^{ad} \mu_{Ga}^{gas} + \frac{1}{2} n_{N}^{ad} \mu_{N2}^{gas} + \frac{1}{2} n_{H}^{ad} \mu_{H2}^{gas}), \quad (6) $$

$$ \mu_i^{gas} = E_i^{gas} + \mu_i, \quad (7) $$

where $E_{slab}^{recon}$ and $E_{slab}^{ideal}$ are the total energies of the reconstructed and ideal surfaces, respectively; $E_i^{gas}$ is the total energy of an atom or molecule $i$ in the gas phase; $\mu_i$ is the chemical potential of an atom or molecule $i$; $n_i^{ad}$ is the number of atoms $i$ on the reconstructed surface.

## 2.2. Solid phase interdiffusion analysis: Monte Carlo simulation

The formula below gives the average time $\tau$ for an atom to move to a neighboring lattice site by overcoming the diffusion barrier $\Delta E^a$ [25].
$$ \tau = \frac{1}{P_{\text{diff}}}, \qquad (8) $$

$$ P_{\text{diff}} = 2k_B T / \{ \exp(-\Delta E^a / k_B T) \}, \qquad (9) $$

Here, $P_{\text{diff}}$ is the diffusion probability to move to the neighboring lattice site. The diffusion barriers $\Delta E^a$ of Ga vacancy $V_{\text{III}}$, N vacancy $V_N$, and their complex $V_{\text{III}}-V_N$ in the bulk GaN are reported to be 2.5 eV [26], 2.7 eV [26], and 2.2 ~ 3.3 eV [27], respectively. The typical MOCVD growth temperature of GaN is 1050 °C. When these values are substituted into Equations 8 and 9, $\tau$ turns out to be 6 µs ~ 0.1 s. The general deposition time for an LED and LD cladding layer ranges from a few to a few tens of minutes. During this time, vacancy diffusion across the underlying quantum well seems to progress appreciably. The degradation mechanism of the InGaN/GaN heterointerface has been discussed in a former work [28], suggesting vacancy diffusion at relatively low temperatures (930~960 °C). Based on this consideration, this study analyzed the contribution of vacancy diffusion to the heterointerface morphology using metropolis Monte Carlo (MC) simulation [15] rather than kinetic MC approach [25].

Figures 2(a)–2(c) show the diffusion models for $V_{\text{III}}$, $V_N$, and $V_{\text{III}}-V_N$. Cation (anion) vacancies in these models move toward neighbor cation (anion) sites. Interstitials and anti-site defects are neglected because they are significantly less stable than cation (anion) vacancies. Moreover, the total number of vacancies in the simulated system was kept constant to 2,600 vacancies in the 260,000-atom system, according to the mass conservation law. This means vacancies are incorporated from the growth surface and are not newly generated within the crystal. Table 1 shows the energy differences in vacancy formation between GaN and AlN [29, 30]. Charged vacancies in n-type semiconductors are accounted for in our mMC simulations. Table 1 indicates that cation vacancies prefer the AlN-rich to the GaN-rich region, while anion vacancies prefer the GaN-rich region rather than the AlN-rich one. For more recent values, refer to Ref. 31. In the mMC simulation, the transition probability $P$ was calculated according to the equation.

$$ P(x \to x') = \frac{\exp(-\frac{\Delta E(x \to x')}{k_B T})}{1 + \exp(-\Delta E(x \to x')/k_B T)}, \qquad (10) $$

where $\Delta E(x \to x')$ is the difference in formation energy before and after the vacancy diffusion. If vacancies exist in the AlGaN layers, their formation energy was calculated by linear interpolation. This simulation used a 100 x 100 x 26 atomic-pair system consisting of 9 layers of AlN/8 layers of $Al_{0.5}Ga_{0.5}N/9$ layers of AlN. The periodic boundary conditions along the three dimensions are imposed. Hereafter, 100 x 100 x 26 = 260,000 attempts are identified as 1 Monte Carlo step (MCS).

### 3. Results and Discussion

#### 3.1. Surface phase diagram considering intrinsic point defects in the sub-surface layers

As already acknowledged, charged defects become stable when the Fermi level is higher than the defect level. Thus, when calculating the formation energy of point defects in a bulk, it is common wisdom to transfer the charge between the electron reservoir at the Fermi level and the point defect according to their respective levels [32]. In contrast, this study considers the formation of intrinsic point defects in the sub-surface layer. In this case, the excess charge on the surface dangling bonds acts as an electron reservoir. Figure 3 shows the atomic arrangements and charge transfer near $V_{\text{III}}$ due to its incorporation. The electron density decreases in
the blue region and increases in the yellow region. When $V_{III}$ is introduced, the N atom directly above is displaced along the [0001] direction, and Ga atoms bonded to it are displaced along the [000-1] direction (red arrows in Fig. 3). This rearranges the dangling bonds above the N and below the Ga sites. Furthermore, a charges transfer occurs from the Ga dangling bonds to the N dangling bonds around $V_{III}$, since they prefer the latter to the former. As a result, a spontaneously charged intrinsic point defect is formed in the sub-surface layers. The stability of the surface systems, which considers the charge transfer between the surface and underlying intrinsic point defects, is discussed below.

The surface phase diagram in GaN MOCVD is shown in Figure 4. In the case of GaN (0001) w/o intrinsic point defects (Fig. 4(a)), the 3Ga-H surface appears at low temperature and high $H_2$ partial pressure conditions. Here, 3 of 4 Ga atoms on the topmost layer are terminated by hydrogen in the 3Ga-H surface reconstruction. This electrically neutral surface reconstruction satisfies the electron counting (EC) rule [33]. Conversely, ideal surfaces with excess charge arise at high temperatures and low $H_2$ partial pressures. This is because the energy gain due to the H desorption exceeds the surface energy loss because of deviations from the EC rule. In the system containing $V_{III}$ in Fig. 4(b), the stable region of the ideal surface is expanded. This might be due to the charge transfer between the surface and the intrinsic point defects (see Fig. 3), which suppresses deviations from the EC rule. In the systems containing $V_N$ (Fig. 4(c)) and $V_{III}-V_N$ (Fig. 4(d)), the $Ga_{ad}$ and Ga-NH$_2$ surface reconstructions appear in the low-temperature region. The former is a surface on which a Ga atom is adsorbed on the H3 site (see Fig. 1), while the latter is a surface on which an NH$_2$ is adsorbed on a topmost Ga. Figure 5(a)-(c) shows the electron density distribution of the ideal surface w/o $V_{III}-V_N$, w/ $V_{III}-V_N$, and the Ga-NH$_2$ surface w/ $V_{III}-V_N$, respectively. When an $V_{III}-V_N$ is incorporated into the ideal surface model (Fig. 5(b)), N, highlighted by the yellow arrow, is displaced along [0001], whereas the neighbor Ga are displaced along [000-1]. The adsorption of NH$_2$ on Ga (Fig. 5(c)) displaces the Ga to [0001], and the local atomic structure gets closer to the standard lattice. This seems to have stabilized the NH$_2$-attached surface more than the hydrogen-attached surface. The results in Fig. 4(c) can be rationalized in an analogous way.

Figure 6 shows the surface phase diagram of the system containing intrinsic point defects. A $Ga_{ad}$ surface containing $V_N$ appears at low temperatures, the ideal surface containing $V_{III}$ at about 900 °C, and the ideal surface containing $V_{III}-V_N$ above 1000 °C. This means that the dominant intrinsic point defect type changes from $V_N$ to $V_{III}$ to $V_{III}-V_N$ as the temperature increases. The next paragraph will focus on the impact of each intrinsic point defect diffusion on the formation of compositional gradient layers in AlGaN/AlN heterointerfaces.

## 3.2. Interdiffusion via intrinsic point defects near heterointerfaces

Figure 7(a) shows the Ga composition distribution in an AlN/AlGaN/AlN system after $V_N$ diffusion at 1000 °C. Anion vacancies in the AlN cladding layer move toward the AlGaN quantum well (Fig. 7(d)) because the anion vacancy prefers the GaN-rich region to the AlN-rich region (see Table 1). As expected, N vacancy diffusion does not contribute to the cation diffusion. Thus, an atomically flat heterointerface is preserved. Figure 7(b) shows the Ga composition distribution in an AlN/AlGaN/AlN system after $V_{III}$ diffusion. Cation vacancies in the AlGaN quantum well move toward the AlN cladding layer (Fig. 7(e))
because cation vacancy prefers the AlN-rich region rather than the GaN-rich one (see Table 1). This implies that the exchange of cation vacancies in the AlGaN layer and Al in the AlN layer occurred. In this process, the Ga in the AlGaN layer rarely diffuses into the AlN layer, so there is little change in the Ga composition of the AlN side of the heterointerfaces. The Al (Ga) composition on the AlGaN side of the heterointerface only increases (decreases) after $V_{III}$ diffusion.

The Ga composition distribution in an AlN/AlGaN/AlN system after $V_{III}-V_N$ diffusion is shown in Figure 7(c). In this case, $V_{III}-V_N$ accumulates near the heterointerfaces because cation vacancy prefers the AlN-rich side, while anion vacancy prefers the Ga-rich one. Because the cation vacancy diffusion barrier is smaller than that of the N vacancy [27], the cation vacancy moves around the N vacancy and promotes Ga atoms diffusion from the AlGaN layer toward the AlN layer. As a result, the Ga content on the AlGaN layer side of the heterointerface decreases, and the Ga amount on the AlN layer side increases (Fig. 7(c)). Furthermore, the change in Ga composition on the lower side (left side in the figure) of the AlGaN quantum well is more significant than that on the upper side (right side in the figure). This is because of the asymmetric nature of the atomic configurations: one cation is below the $V_N$ and three above. On the AlGaN side of the heterointerfaces, specifically, there are three cation sites at the lower interface and one cation site at the upper interface, so the probability of Ga diffusion at each interface is different. Figure 8 shows the influence of temperature on Ga composition distribution in the system after $V_{III}-V_N$ diffusion. The figure shows that the decrease in the diffusion frequency of $V_{III}-V_N$ accompanying the decrease in temperature does not contribute to preserve the heterointerface flatness. Thus, the change in the type of intrinsic point defects due to the decrease in temperature becomes a key factor, not the decrease in diffusion frequency due to the reduction in temperature.

These results indicate that the type of intrinsic point defects that contribute significantly to the degradation of heterointerface flatness are $V_{III}-V_N$, followed by $V_{III}$, with no contribution from $V_N$. This means that the heterointerface flatness is maintained by thin film deposition at temperatures below 900~1000 °C (see Fig. 6). In experiments, Yoshikawa et al. [13] reported that the thickness of the layer where the uncontrolled interdiffusion occurs can be considerably decreased by deposition conditions below 1000 °C. Our theoretical findings give a rationalization of the physical and chemical phenomena occurring, thus providing valuable guidelines for experiments.

### 4. Conclusions

This study clarified the types of intrinsic point defects incorporated from the growth surface in the III-nitrides MOCVD and their role. We also elucidated the mechanism by which these defects degrade the flatness of the heterointerface due to atomic interdiffusion within the solid. In other words, we have found that the key to maintaining the flatness of the heterointerface is not to reduce the atomic interdiffusion frequency due to a decrease in temperature but to control the type of intrinsic point defect by MOCVD conditions. This knowledge cannot be obtained by analyzing only surface phenomena or solid phase interdiffusion but by combining the two. The development of AlGaN deep-ultraviolet LEDs and LDs is underway [34-38]. If the flatness of the heterointerface can be maintained based on the findings of this research, even higher brightness can be expected.
Acknowledgments

This work was partially supported by JSPS KAKENHI Grant Number JP24H00432, JST SICORP Grant Number JPMJSC22C1, and Special Projects by Institute for Molecular Science (IMS program 23-IMS-C135 and 24-IMS-C131). One of the authors, K. I., thanks for the support from the Collaborative Research Program of the Research Institute for Applied Mechanics, Kyushu University (2023EC-ME-1). M. B. thanks for support GENCI (Grand Equipment National de Calcul Intensif; Grant Number A0160906092) and fruitful discussions with A. Oshiyama, K. Shiraishi and H. Amano. Y. K. thanks students K. Tateyama, R. Shimauchi, M. Miyaguchi and R. Murakami for their help in data analyses.

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<figure><img src="image_2.png" /><figcaption>Fig. 1. Schematic of slab model. V<sub>III</sub> and V<sub>N</sub> show cation and anion vacancy sites, respectively.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2. Schematic of (a) V<sub>III</sub>, (b) V<sub>N</sub>, and (c) V<sub>III</sub>-V<sub>N</sub> diffusion models.</figcaption></figure>
<table><caption>Table 1

Difference in vacancy formation energy between GaN and AlN [29, 30]. n-type material is considered.</caption><thead><tr><td>Type of defect</td><td>Formation energy difference</td></tr></thead><tbody><tr><td>V<sub>III</sub>(GaN) - V<sub>III</sub>(AlN)</td><td>2.2 eV</td></tr><tr><td>V<sub>N</sub>(GaN) - V<sub>N</sub>(AlN)</td><td>- 1.9 eV</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>Fig. 3. Atomic arrangements near V<sub>III</sub> in the ideal surface model (a) before and (b) after optimization. The topmost Ga and underlying N are displaced (see red arrows in (b)). V<sub>III</sub> formation, i.e., the comparison between the models w/ and w/o Ga at the dotted circle, decreases the electron density in the blue region and increases in the yellow region in (b).</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 4. Surface phase diagram in GaN MOCVD: (a) w/o vacancy, (b) w/ $V_{III}$, (c) w/ $V_N$, and (d) w/ $V_{III}-V_N$. The vertical axis shows the partial pressure of $H_2$ in the dilute gas ($H_2+N_2$). Calculation conditions: The partial pressure of the Ga source (trimethylgallium) is $1.0 \times 10^{-4}$ atm, that of ammonia is 0.2 atm, and the total pressure is 1.0 atm.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5. Cross-sectional view of electron density distribution: (a) ideal surface w/o $V_{III}-V_N$, (b) that w/ $V_{III}-V_N$, and (c) Ga-NH$_2$ surface w/ $V_{III}-V_N$. The dotted circles show $V_{III}-V_N$.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 6. Surface phase diagram of GaN w/ intrinsic point defects under MOCVD conditions. The calculation conditions are the same as in Fig. 4. The defects-free model is not considered.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 7. (a), (b) and (c) are Ga composition distributions in AlN/AlGaN/AlN system after V<sub>N</sub>, V<sub>III</sub>, and V<sub>III-VN</sub> diffusion, respectively. (d), (e) and (f) are vacancy concentration distributions in AlN/AlGaN/AlN system after V<sub>N</sub>, V<sub>III</sub>, and V<sub>III-VN</sub> diffusion, respectively. The temperature was set to 1000 °C in the simulations.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Fig. 8. Influence of temperature on Ga composition distribution in AlN/AlGaN/AlN system after V<sub>III</sub>-V<sub>N</sub> diffusion. The change in Ga composition on the lower side (left side in the figure) of the AlGaN quantum well is more significant than that on the upper side (right side).</figcaption></figure>