The luminescence efficiency of AlxGa1−xN quantum dots (QDs) and quantum wells (QWs), buried in AlN cladding layers and emitting in the ultraviolet range between 234 and 310 nm, has been investigated. The growth and optical properties have been done using similar aluminum composition (varying from 0.4 to 0.75) for both QDs and QWs. In order to compare as much as possible the optical properties, the QWs were fabricated with a growth time tuned such that the QW width is similar to the average height of the QDs. The photoluminescence (PL) showed emission ranging from 4 to 5.4 eV, putting into evidence differences in terms of full width at half maximum, PL intensity, and asymmetry of the line shape between QDs and QWs. The results show shorter wavelengths and a slightly narrower PL linewidth for QWs. To determine the light emission dependence with the electric field direction in the crystal, the evolutions of the emission diagrams for all samples were recorded along two orthogonal directions, namely, the “in-plane” (growth) and the “on-side” directions, from which the light emission was collected. For the whole QDs and QWs samples' series, the shapes of the emission diagram indicate emission in both in-plane and on-side directions, as evidenced by intra-valence band mixings caused by strain effects combined with the anisotropic Coulomb interactions that are particularly contributing to the polarization at wavelengths below 260 nm. Furthermore, the degree of polarization, determined for each sample, showed good agreement with results from the literature.

The quest for the realization of compact solid state deep ultraviolet (DUV) light emitters based on the GaN-related technology is currently the subject of many investigations at the worldwide scale.1 By changing the AlxGa1−xN alloy composition in the active part [in general, a quantum well (QW) or multi-quantum well stacking] of heterostructures with sophisticated designs, one can control the light emission from 365 nm (for GaN) down to 206 nm (for AlN). Although many applications are foreseen in the UVB (between 280 and 320 nm) and UVC (below 280 nm) ranges,2 DUV AlxGa1−xN-based light emitting diodes (LEDs) still suffer from intrinsic limitations, leading to low (few percent only) wall plug efficiencies.3 In particular, due to the change from the positive value of the crystal field splitting in GaN (about +10 meV) to the negative value in AlN (about −200 meV), a change of sign in AlxGa1−xN alloys as x increases above a few percent occurs. As a consequence of its continuous decrease, the valence band maximum at the Γ point may change,4 leading to different light emission directions and polarization dependence on the electric field direction in the crystal,5 as well as to low emission intensity.6 Taking this specific property into account, it was shown that by performing adequate epitaxial growth engineering, e.g., by using short-period AlN/GaN superlattices,7 compressive strain and/or narrow quantum wells,8 and/or using high Miller index growth planes,9 strong modifications of the light polarization can be obtained that leads to improved light emission efficiency.

We have been focusing for a few years on the specific use of AlxGa1−xN quantum dots (QDs) embedded into AlyGa1−yN (y > x, y < 1) three-dimensional barrier layers. In these papers, we restricted ourselves to the (001)-oriented growth, the most widely studied one, for the purpose of reducing the fabrication costs linked to the use of other substrates' orientations on one hand and in order to avoid problems specific to the growth on exotic surfaces on the other hand. Let us first discuss the case of GaN QDs embedded into AlyGa1−yN layers. The GaN QDs are lattice-matched to the thick (i.e., 30 nm) AlyGa1−yN barrier layers as evidenced by transmission electron microscopy measurements.10 When reducing the heights of the dots, one can enhance the confinement energies of electrons and holes and limit the impact of the quantum confined Stark effect (QCSE) and the reduction of the radiative recombination rate it produces.11 This also blue shifts the light emission energy compared to what happens with large QDs. Advantage can be eventually taken of lateral confinement effects as well. Therefore, by optimizing the growth conditions and by controlling the amount of deposited GaN at the monolayer level, we have been able to fabricate LEDs emitting from the blue to the UVA region at wavelengths between 360 and 420 nm.12–16 

When increasing the y composition in the AlyGa1−yN barrier layers, one produces three different effects at first order:

  • An increase of the depths of the electron and hole confinement potentials due to the increase of the bandgap energy of AlyGa1−yN materials. This characteristic positively increases the confinement energies and the energies of the optical band to band transitions.

  • A shift of the conduction to valence band states in relation to the built-in strain effects, as the in-plane value of the lattice parameter of the AlyGa1−yN layers decreases with increasing y. This change leads to a larger lattice mismatch between the GaN and the AlyGa1−yN layers that generate a built-in strain in the GaN QDs. This built-in strain is increasing with y, and it blue shifts the bandgap energy of the QDs without altering the C6v symmetry of the Bloch states of these heterostructures. This feature has also a positive impact.

  • An increase of the QCSE in a straightforward relation with the increase of both the piezoelectric effects and the mismatch of spontaneous polarizations at the heterointerfaces when the chemical contrast (yAl − xAl) increases, i.e., the difference between the Al composition in the AlyGa1−yN cladding layers (yAl) and in the AlxGa1−xN QDs (xAl). This characteristic has to be minimized since it can have a negative effect on the total light emission intensity.

Yet, this chemical contrast appears to be a critical quantity since it should be high enough to allow the growth of QDs that is made possible by the epitaxial strain (ɛ). More precisely, ɛ is defined as the lattice mismatch between the QDs and cladding layer materials, i.e., AlxGa1−xN and AlyGa1−yN, respectively, following the expression ɛ = {a(AlyGa1−yN) − a(AlxGa1−xN)}/a(AlxGa1−xN). Therefore, one can see that as the chemical contrast between the two materials decreases, ɛ also decreases, which at some point will forbid the strain relaxation to occur through a transition from a two dimensional (2D) mode to a 3D growth mode.18 After subtle juggling with these effects during the growth stage, one can shift the emission wavelength toward shorter values. However, we have to keep in mind that the emission wavelength of one monolayer of GaN embedded into AlN barrier layers reaches a minimum value near 240 nm due to the huge long-range direct and exchange Coulomb interaction effects.17 Thus, it appears of interest to use AlxGa1−xN as a confining material for further reducing the wavelength of the emission. In such cases, however, complex and eventually unpredictable band structure effects in the different layers can be anticipated, linked to specificities of the valence band physics of AlxGa1−xN layers. In order to have substantial enough confinements of the carriers, we have then focused this work to the use of aluminum nitride barrier layers. Using such barrier layers, it is important to note that confinement effects in AlxGa1−xN QDs, as well as in AlxGa1−xN QWs, are influenced by built-in strain spontaneous polarization and piezoelectric effects. Along with these quantum physical effects typical of semiconductor heterostructures, one has to include the light–matter interaction processes, the long-range Coulomb interaction between interacting electrons and holes, and spin-related effects leading to excitonic fine structures and a distribution of the excitonic energies into bright and dark quantum states. Finally, one has to consider the anisotropy of the optical response, which is intrinsic to the wurtzite symmetry.

This paper is organized in the following way: we begin by recalling the basics of light–matter interaction in wurtzite crystals. Then, we browse the different experimental setups that are used to grow our samples and to measure their optical properties. Next, the optical properties of the series of AlxGa1−xN QDs and QWs on AlN are presented and compared, including the emission diagrams collected along the growth direction, so-called in-plane thereafter, and along its orthogonal direction, so-called on-side thereafter, and the degree of polarization as a function of the emitted wavelength.

This first section, relative to the description of the anisotropy of the optical response, is mandatory in order to grasp the physics that rules the emission diagrams that are further recorded by changing the conditions of propagation and the polarizations of the emitted photons.

In the GaN material, the hierarchy of the different band states will always be as sketched in Fig. 1(a), in the framework of the spinless description and whatever the situation of the material is, i.e., unstrained or strained by the (0001)-oriented biaxial compression. The topmost of the fundamental valence band is twofold, of the (px,py) kind and of Γ5 symmetry in the language of group theory.19,20

FIG. 1.

(a) Schematic ordering of the conduction band state (black level) and of the three valence band states (blue, green, and red levels) for unstrained or biaxially compressed GaN in the (0001) plane in the context of the spinless representation. The symmetries of the different quantum states are reported in terms of px, py, and pz states according to the standard notations (Ref. 19). The polarization of the photon leading to a dipole-allowed band to band transition is represented by dashed lines with a color code in a one-by-one relationship with the symmetry of each of the different valence band states. (b) The analog of (a) but for aluminum nitride. Please note that energy scales are not respected in these schematic representations.

FIG. 1.

(a) Schematic ordering of the conduction band state (black level) and of the three valence band states (blue, green, and red levels) for unstrained or biaxially compressed GaN in the (0001) plane in the context of the spinless representation. The symmetries of the different quantum states are reported in terms of px, py, and pz states according to the standard notations (Ref. 19). The polarization of the photon leading to a dipole-allowed band to band transition is represented by dashed lines with a color code in a one-by-one relationship with the symmetry of each of the different valence band states. (b) The analog of (a) but for aluminum nitride. Please note that energy scales are not respected in these schematic representations.

Close modal

In the case of AlN, the situation is sketched in Fig. 1(b). We remark that in this specific case, the topmost of the valence band is pz like and of Γ 1 symmetry.20 For the case of an AlxGa1−xN layer lattice-matched to an AlyGa1−yN one (with y > x), one can account for any intermediate situation regarding the different possibilities of ordering for the (px,py) couple and for the pz singlet.

In wurtzite crystals, the transition from the conduction band to the valence band of Γ 1 symmetry is possible for a photon with its electric field oriented along the 001 direction (red arrows in Figs. 1 and 2), that is to say, with a photon's propagating direction sitting in the plane orthogonal to 001 . Let this direction be arbitrarily called x. The transition from the conduction band to the valence band of Γ 5 symmetry is possible for a photon's electric field oriented along the y direction (green arrow in Figs. 1 and 2), which propagates in the x direction in the plane orthogonal to 001 . Then, the matrix element of the optical transition does not vanish for the valence band state of the py kind. In such an experimental condition, transitions from the conduction band toward either Γ 1 and Γ 5 valence bands can be detected depending on the polarization of the photon. This is a first selection rule that indicates anisotropy of the emission diagram for such experimental conditions, as sketched as a dashed ellipsoid in Fig. 2, with its principal axes plotted in red and green. A second experiment of interest requires using a photon that propagates along the 001 direction, orthogonally to the (0001) growth plane. In that case, the transition toward the Γ 5 doublet is allowed and the emission diagram is isotropic in this [(x,y) or (0001)] plane (dashed circle with blue and green principal axes in Fig. 2).

FIG. 2.

Polarizations of the photons (blue, green, and red arrows) leading to dipole-allowed transitions for the different orientations of the Poynting vector (thick brown arrows) of the photon. The shapes of the emission diagrams are given in terms of dashed lines. The letters x, y, and z represent the orientations of the international basis set.

FIG. 2.

Polarizations of the photons (blue, green, and red arrows) leading to dipole-allowed transitions for the different orientations of the Poynting vector (thick brown arrows) of the photon. The shapes of the emission diagrams are given in terms of dashed lines. The letters x, y, and z represent the orientations of the international basis set.

Close modal

The transition from the conduction band to the Γ 5 valence band is the fundamental one for the biaxially compressed GaN, whereas it is the transition from the conduction band to the Γ 1 valence band for AlN. Any in-between case is possible for AlxGa1−xN alloys, and a crossover from a transition toward the Γ 5 (for GaN) to a transition toward the Γ 1 (for AlN) topmost valence band symmetry exists in bulk materials21 and heterostructures.22 The values of the Γ 1 to Γ 5 valence band splittings are represented by a parameter that is labeled Δ1, which equals about 10 meV in unstrained GaN and between −200 and −220 meV in AlN.23–29  A crossover from the Γ 5 Γ 1 to the Γ 1 Γ 5 configuration occurs for an alloy composition between these two asymptotic cases.4,6 Such a crossover is also possible for biaxially compressed AlxGa1−xN alloys, and this transition occurs for Al compositions (xAl) that depend on their strain states, as will be described below. We will consider here (0001)-grown heterostructures embedded into AlN barrier layers themselves deposited on a pseudo-AlN substrate grown on (0001)-oriented sapphire.

In such a situation, any AlxGa1−xN layer will experience a biaxial compression in the (0001) plane. This biaxial compression adds an arithmetic (therefore positive) value to the algebraic value of the crystal field parameter Δ1. This Δ1 is positive (about 10 meV) in unstrained GaN, as stated above, and it is negative (about −200 to −220 meV) in AlN. This results in an enhancement of the energy difference between the (px,py) pair of valence band states and the pz one in a GaN layer grown on AlN: the absolute value of Δ1 increases. The situation is more complex for AlxGa1−xN layers. Let us consider here an aluminum composition high enough so that Δ1 is negative in an unstrained AlxGa1−xN layer. When increasing the value of the built-in strain, as in the case of AlxGa1−xN grown on AlN, a reduction of the algebraic magnitude of the energy splitting between the pz valence band state and the couple of states (px,py) pair occurs. It can even be suppressed (i.e., with an energy splitting equal to zero) or it can have its sign changed to a positive value. This switch from negative to positive values depends on the composition x of AlxGa1−xN, which sets the magnitude of the biaxial deformation in the case of a pseudomorphic growth of AlxGa1−xN on AlN. The xAl composition for the crossover from the Γ 5 Γ 1 to the Γ 1 Γ 5 configuration occurs at a higher Al value in the case of a compressively strained AlxGa1−xN layer with respect to the case of an unstrained layer.

Of course, the spin–orbit interaction (SO) has been neglected so far, and it is mandatory to include it for an exact description of the physics of the valence band of wurtzite crystals.23–33 In wurtzite materials, SO is represented by two parameters Δ2 and Δ3, where values in GaN and AlN are very close to each other and equal to about 5.5 and 6.2 meV, respectively.23–27 Including this interaction produces new eigenvectors: a spin-dependent linear combination of px and py states that gives an eigenvector state of Γ 9 symmetry in the language of group theory for the double group C6v,20 which is plotted in black in Fig. 3, and two eigenvectors that are both of Γ 7 symmetry still in the language of group theory for the double group C6v.20 These two eigenvectors anti-cross vs the aluminum composition, and they are, respectively, plotted in red to green and green to red in Fig. 3. They are spin-dependent linear combinations of px, py, and pz states. In general, that is to say, far from the crossover conditions, the splitting between the Γ 9 state and one of the Γ 7 ones equals 7–8 meV and the other splitting equals ∼Δ1 (corrected by strain effects in the strained material, which in our case adds a positive number to the value of Δ1 in the unstrained materials). From the coefficients that express the expansions of eigen vectors along px, py, and pz states, one can estimate the relative intensities of the different band to band transitions in terms of the relative proportions of pz states (green portion of the plots in Fig. 3) and (px,py) states (red portions of the plots in Fig. 3). To quantitatively express the energy spectrum of AlxGa1−xN layers lattice-matched (or not) to AlN, we followed the prescriptions of the theory of invariants and used the parameters of the literature.23–50 

FIG. 3.

Evolutions of the valence band states of AlxGa1−xN layers lattice-matched to AlN, which illustrates the impact of the built-in strain on the symmetry crossover of the topmost valence band near x = 0.6, instead of x = 0.1, for the unstrained situation. The black line represents the Γ 9 valence band level. The red and green lines represent the two Γ 7 levels that anti-cross for x near 0.6. The origin of the energy is taken at the maximum of the valence band in AlN. The amounts of red color represent the proportion of (px,py) states in the wavefunctions of the levels, while the amounts of green color represent the amount of the pz state. In the inset is shown the evolution of the fundamental bandgap energy of these alloys for the unstrained case (in magenta) and in the lattice-matched case (in purple).

FIG. 3.

Evolutions of the valence band states of AlxGa1−xN layers lattice-matched to AlN, which illustrates the impact of the built-in strain on the symmetry crossover of the topmost valence band near x = 0.6, instead of x = 0.1, for the unstrained situation. The black line represents the Γ 9 valence band level. The red and green lines represent the two Γ 7 levels that anti-cross for x near 0.6. The origin of the energy is taken at the maximum of the valence band in AlN. The amounts of red color represent the proportion of (px,py) states in the wavefunctions of the levels, while the amounts of green color represent the amount of the pz state. In the inset is shown the evolution of the fundamental bandgap energy of these alloys for the unstrained case (in magenta) and in the lattice-matched case (in purple).

Close modal

The evolutions of the valence band states of AlxGa1−xN layers lattice-matched to AlN have been plotted in Fig. 3. The evolution of the fundamental bandgap of these alloys has also been inserted for the unstrained situation (in magenta) and in the lattice-matching case (in purple), which illustrates the impact of the switch of symmetry of the topmost valence band based on the competing effects of chemical composition and built-in strain. The importance of the inset is also to qualitatively frame, simultaneously, the energy of the quantum dots' emission (in orange units on the left y axis) and the corresponding emission wavelength (in gray units on the right y axis).

Figure 3 has to be read from right to left: one starts with AlN lattice-matched to itself, with the topmost of the valence band built from a linear combination of quantum states of the pz type, which spectrally splits by, according to the literature,23–29 200–220 meV from the (px,py) pair (in the range of AlxGa1−xN layers with high xAl, see Fig. 1(b), spin–orbit effects can be neglected). Further decreasing xAl composition, a competition occurs between the increase of built-in strain effects (a positive number) and the reduction of the negative value of Δ1. Thus, instead of occurring at xAl ≈ 0.1 as in the case of unstrained AlxGa1−xN layers, the crossover for the switching of the valence band nature from Γ 7 to Γ 9 occurs at xAl ≈ 0.6. This is strongly impacting the light emission property: in the low xAl range, the topmost valence band is dominantly built from (px, py) states until xAl ≈ 0.5, which means efficient TE polarized light emission (i.e., propagating in the 001 direction). When the valence band is dominantly built from the pz state, that is to say, from xAl ≈ 0.7 to higher xAl values, which means TM polarized light emission, the light extraction efficiency along 001 collapses. In the range of compositions close to the anti-crossing conditions of the two Γ 7 valence band levels (the spin is now included in the discussion at this stage), the relative proportions of (1) the valence band composition in terms of states of px, py, and pz symmetries (to minimize the proportion of TM polarized emission relatively to the TE one in the crystal) and (2) the valence band splitting (to manage thermal population effects that can, for instance, enhance the proportion of TM waves relatively to TE ones at high temperature in the low xAl range) have also to be taken into account since their impact could be of the same order of magnitude. In this study, QD and QW samples grown with AlxGa1−xN nominal aluminum compositions x of 0.4, 0.6, 0.7, and 0.75 are investigated (roughly located using short dashed blue vertical lines in Fig. 3). Finally, it can be seen that the Γ 9 level (plotted in black in Fig. 3) behaves non-linearly with x. This is related to the non-vanishing value of the bowing parameter that describes the evolution of the bandgap energy of AlxGa1−xN alloys vs x.4–6 

Unfortunately, this description does not reflect the reality of the samples under illumination since the physical objects that recombine are excitons, i.e., long-range Coulomb-interacting electron–hole pairs with fine internal structures linked to the spins of electrons and holes.19 By coupling the conduction electron-spin with the Γ 9 and Γ 7 valence band states, for example, within the context of Clebsch–Gordan algebra, one can form the eigenstates of the exciton. In the language of group theory, this leads to bright Γ1 and Γ5 excitons that are created or annihilated according to the previously formulated selection rules of the band-to-band transitions and dark Γ 2 and Γ 6 excitons that are trapping carriers and act as non-radiative recombination centers. In bulk wurtzite crystals, the theory of invariants predicts at the center of the Brillouin zone 12 excitonic states, among which 4 are singlet ( 2 Γ 2 and c levels) and 8 can be classified into 4 doublet states ( 3 Γ 5 and 1 Γ 6 levels). In low-dimensional heterostructures, from the 2D QWs to the 0D QDs, there are, in general, much more than three valence band and one conduction band states depending on depths and widths of confining potentials, effective mass, electric fields, etc. Although the predictions of light–matter interaction in terms of group theory as for bulks remains valid for (0001)-grown low-dimensional systems, the construction of the different excitonic states and wave functions is from far much more delicate and difficult. The wave functions are linear expansions over the whole set of confined conduction and valence band pairs, and the wavefunction of each of these pairs is weighted by an excitonic envelope function of the appropriate symmetry. Besides the confinement effects and the mixings they produce over the kp hamiltonian, besides the influence of the internal electric fields, electron–hole direct and exchange interactions produce large correction of the energies and initiate complex excitonic mixings. This also causes many observable effects on optical oscillator strengths.51 

The exact calculation of the excitonic energies in AlxGa1−xN QDs presents severe difficulties. Andreev and O'Reilly52 have published an accurate theory of the electronic structure of GaN/AlN QDs in the context of a multiband kp model built at the center of the Brillouin zone by extensively using the theory of invariants for the description of the Lüttinger parameters and a comparison with band structures computed by first principles approaches to obtain the numerical values of these parameters. Further using symmetry considerations, adapted and extended versions of previous investigations dedicated to bulk materials can be used for QWs or QDs.52–66 The specificity of nitride-based QDs, in contrast to other systems, such as InAs QDs, is the observation of excitonic transitions, robust bi-excitons, thanks to the huge excitonic interaction and to the enhancement of its direct and exchange contributions.53–72 For nitrides, no calculation similar to the one proposed by Lucio Claudio Andreani and Alfredo Pasquarello for GaAs/GaAlAs QWs can be found, which includes the kp description of the dispersion relations of the band structures of the confining material and barrier materials and the mismatch of dielectric constants.73 An even more sophisticated calculation was proposed with a linear expansion of the excitonic wave function over several conduction and hole confined states,74 an extension mutatis mutandis of the method used by Alfonzo Baldereschi and Nunzio Lipari to calculate accurately acceptor states in cubic semiconductors.75 

After the fabrication of the AlN template on sapphire by MOCVD (see the supplementary material), the sample was introduced into a molecular beam epitaxy (MBE) reactor for the fabrication of the active region consisting either of AlxGa1−xN QDs or of AlxGa1−xN QWs buried in AlN. At first, a 30-nm thick AlN layer was regrown on the AlN template at a temperature of 870 °C in order to prevent from the influence of a possible surface contamination layer. Next, regarding the AlxGa1−xN QD plane, it was grown at a growth rate of 0.2 ML/s and at a lower temperature Tgrowth (see Table I) using a plasma source for nitrogen operating at 300 W with a flow rate of 0.3 sccm. The deposited thickness was corresponding to an equivalent 2D deposited thickness ranging between 7 and 8 monolayers (MLs), with one ML corresponding to an average thickness of about 0.256 nm. After the deposition of the QDs, annealing was performed under vacuum at a temperature Tanneal following the process described in Refs. 76 and 77. A 30-nm thick AlN capping layer was then grown on top of the QDs. For atomic force microscopy (AFM) characterization, another plane of AlxGa1−xN QDs was deposited at the surface to get insights on the QD structural properties (see the supplementary material and Table I).

TABLE I.

Experimental temperature conditions for the growth of the AlxGa1−xN quantum dots and experimental parameters describing their composition, sizes, and areal densities.

Nominal Al composition Tgrowth (°C) Tannealing (°C) Nominal height of QDs (MLs) Diameters of QDs from AFM (nm) Height of QDs from AFM (nm) Densities (cm−2)
0.4  720  820  7.6  10 ± 5  2 ± 0.5  4.82 × 1011 
0.6  720  820  8 ± 5  1.8 ± 0.5  5.36 × 1011 
0.7  720  820  7.2  8 ± 5  1.8 ± 0.5  5.36 × 1011 
0.75  720  820  8 ± 6  2 ± 0.5  … 
Nominal Al composition Tgrowth (°C) Tannealing (°C) Nominal height of QDs (MLs) Diameters of QDs from AFM (nm) Height of QDs from AFM (nm) Densities (cm−2)
0.4  720  820  7.6  10 ± 5  2 ± 0.5  4.82 × 1011 
0.6  720  820  8 ± 5  1.8 ± 0.5  5.36 × 1011 
0.7  720  820  7.2  8 ± 5  1.8 ± 0.5  5.36 × 1011 
0.75  720  820  8 ± 6  2 ± 0.5  … 

QD samples grown with AlxGa1−xN xAl compositions of 0.4, 0.6, 0.7, and 0.75 have been studied. Table I summarizes these experimental conditions. Complementary AFM measurements, useful to determine the dimensions of the QDs and their densities, are also available in Table I. Tuning the QD composition, it was found that the 2D–3D transition under the above-mentioned growth conditions, based on the in situ reflection high-energy electron diffraction (RHEED) and the appearance of additional spotty patterns in the diagram (see the supplementary material), was becoming weak as the QD xAl composition was reaching 75%, setting up the limit for the largest xAl value in the samples' series.

In parallel, a series of QWs, with similar xAl compositions and with growth times tuned such that the heights of the QDs are similar to the QW widths, have been grown for the purpose of comparing their optical properties with those of the QDs. Similarly to the QD structures, a 30-nm thick AlN layer was first deposited at the AlN surface at a temperature of 870 °C. Then, the series of four different QW active regions, with xAl varying from 0.4 to 0.75, was grown as follows: the AlxGa1−xN layer was deposited at a growth rate of about 0.3 ML/s and at a temperature ranging between 840 and 875 °C, depending on the xAl value, with the lowest temperature for the AlxGa1−xN layer with the lowest xAl and the highest temperature for the AlxGa1−xN layer with the highest xAl. Finally, a capping layer of 30 nm of AlN was grown, and the sample was cooled down before removing it from the MBE reactor. Based on the in situ RHEED measurement, a diagram made of streaky lines was continuously observed that is characteristic of a 2D growth mode (see the supplementary material). AFM measurements have also been performed to characterize the surface morphology of the structures, showing surfaces made of surface monoatomic steps and smooth terraces, with a typical root mean square (RMS) roughness of 0.2 nm and an average width of 70 nm (see the supplementary material).

The photoluminescence (PL) spectra were recorded with the sample mounted inside a closed-cycle He cryostat operating between 8 and 300 K. A specific sample holder was fabricated for on-side emission collection. The PL was excited with the fifth harmonic (212.8 nm) of an Nd:YAG laser with passive Q-switching, resulting in a pulse width in the order of 1 ns and a repetition rate of 10 kHz. The laser average power on the sample was set to 50 μW, and the excitation beam was focused to a spot of about 30 μm in diameter. The PL was collected with an achromatic set of off-axis parabolic mirrors (OAPs). In between the OAP, the photoluminescence beam was collimated, and we placed here a half wave-plate operating between 240 and 300 nm inside a computer-controlled motorized rotation stage. The PL polarization was rotated by an angle, which is twice as big as the angle the wave-plate was rotated. A polarizer, placed just after the wave-plate, selected the vertical component in order to use the grating across its s-plane for a smooth response curve. A 60 s acquisition spectrum was recorded every 5° between 0° and 180° (half wave-plate angle). The spectrometer was a 500 mm Czerny–Turner design. The holographic grating had a ruling of 1200 grooves mm−1 and a blaze wavelength of 250 nm. The camera was a back-illuminated CCD (Andor Newton 920), providing a spectral resolution of ∼2.3 meV. All instruments were operated under Qudi software package.78 

1. Photoluminescence

The PL recorded for the Poynting vector aligned along the x direction and integrated over the (y,z) plane on the series of samples described above reveals radiative recombination bands centered from 240 nm to near 310 nm, as plotted in Fig. 4. They are the signatures of the AlxGa1−xN QDs deposited on the (0001)-oriented AlN templates. The PL intensity is maximum for a nominal xAl of the QDs of 60% (orange spectrum), i.e., when the topmost of the valence band state is still Γ 9 and the chemical contrast between the material of the dot and the AlN substrate is not too high. In the case of the sample with 40% Al content QDs, the PL intensity (dark blue spectrum) is smaller, which we attribute to a larger contribution of QCSE in relation with a higher chemical contrast and a lattice mismatch between the material of the QDs and the barrier layers. The QCSE produces a decrease of the radiative recombination rate and a redshift of the transition energy compared to what is expected for a bulk AlxGa1−xN material with an xAl of 40%, i.e., 4.2 eV vs 4.6 eV as can be seen in the inset of Fig. 3. Further increasing xAl from 60% to a nominal value of 70%, in order to switch the symmetry of the topmost valence band while still keeping a large enough lattice mismatch with AlN (to control the growth of QDs), the PL intensity drastically decreases by an order of magnitude (green spectrum). When further increasing xAl with the objective to target a value of 75%, forming QDs is not fully achieved (see the supplementary material). However, one observes a weaker inhomogeneous PL signal (magenta plot), which frames the range of control for the growth protocol of AlxGa1−xN QDs on AlN. Interestingly, the low-energy tails of the two PL bands displayed on the green and magenta plots overlap through a large energy range, which indicates competition effects between the QD sizes and the alloy composition leading to inhomogeneous PL broadening. The evolutions of the PL intensities for the “in-plane” collection (purple spheres) and for the “on-side” collection (orange spheres, Y polarization) of the light emission are plotted in the inset of Fig. 4. The in-plane collection indicates a brutal collapse of the emission intensity that is usually attributed to the switch of the symmetry of the valence band from the px, py to pz state.

FIG. 4.

Low temperature plot of the PL intensities for the QD sample series showing the energies, the full width at half maximum, the asymmetry of the PL line shape, and the difference in intensities for an unpolarized collection of the emitted light. Inset: Evolution of the photoluminescence intensities for the in-plane collection and the on-side collection of the light emission.

FIG. 4.

Low temperature plot of the PL intensities for the QD sample series showing the energies, the full width at half maximum, the asymmetry of the PL line shape, and the difference in intensities for an unpolarized collection of the emitted light. Inset: Evolution of the photoluminescence intensities for the in-plane collection and the on-side collection of the light emission.

Close modal

The experiments are made in different geometrical conditions, the plane of QDs being located very near the surface of emission for the in-plane excitation/collection. For the on-side collection, one excites QDs from the cleaved surface orthogonal to the growth plane, therefore probing the structure in depth along the growth plane. Consequently, the light emission is recorded after the recombination of carriers either in QDs located close to the surface, i.e., 30 nm below the surface, for light collected in-plane or in QDs buried much deeper, i.e., up to several hundreds of nm, along the x direction inside the crystal from light collected on-side. Thus, in this latter case, the emitted light is extracted after some propagation in a medium where it can be reabsorbed, and/or the electron–hole pairs photo-created may recombine non-radiatively. The non-radiative recombination rate increases with the Al composition of QDs and is higher for an xAl of 75%, as seen by the collapse of the PL intensity of the QDs with this Al composition. Indeed, such a collapse cannot be attributed from bona fide to the QCSE as the sizes of the QDs are fairly similar and the chemical contrast between the AlN barrier material and the AlxGa1−xN QDs decreases while increasing the xAl value up to 0.7–0.75.

To go one step further, we have performed a line-shape analysis of these asymmetric PL bands using a couple of gaussian functions,
P L ( E ) = i = 1 , 2 A i 2 π σ i exp [ ( E E i 2 σ i ) 2 ] .
(1)

From this equation, and for each gaussian function, it is straightforward to determine from the σis the corresponding full width at half maximum (FWHM). In that case, the FWHM is equal to ≈2.355σ.

The results of the fitting procedure are summarized in Table II.

TABLE II.

Fits of the PL line shapes using a couple of Gaussian functions. The parameters of the Gaussian functions are indicated in the text, and the values of the full width at half maximum (FWHM) are indicated as well as the emission wavelengths (λ). For the sample with AlxGa1−xN QDs made with an xAl nominal composition of 0.75, the fit using one Gaussian is also given.

Nominal alloy composition A1 σ1 (meV) E1 (eV) A2 σ2 (meV) E2 (eV) A1/A2 FWHM1 (meV) FWHM2 (meV) 〈λ〉 (nm)
Ga0.6Al0.4 0.234  115  4.157  0.122  179  3.990  1.63  270  421  310–298 
Ga0.4Al0.6 0.141  78  4.758  0.117  109  4.651  1.21  183  257  266–260 
Ga0.3Al0.7 0.131  81  5.093  0.124  118  4.967  1.06  192  278  249–243 
Ga0.25Al0.75 0.202  96  4.995  0.099  148  4.832  2.04  226  349  256–248 
Ga0.25Al0.75 0.253a  111a  4.972a  …  …  …  …  261a  …  249 
Nominal alloy composition A1 σ1 (meV) E1 (eV) A2 σ2 (meV) E2 (eV) A1/A2 FWHM1 (meV) FWHM2 (meV) 〈λ〉 (nm)
Ga0.6Al0.4 0.234  115  4.157  0.122  179  3.990  1.63  270  421  310–298 
Ga0.4Al0.6 0.141  78  4.758  0.117  109  4.651  1.21  183  257  266–260 
Ga0.3Al0.7 0.131  81  5.093  0.124  118  4.967  1.06  192  278  249–243 
Ga0.25Al0.75 0.202  96  4.995  0.099  148  4.832  2.04  226  349  256–248 
Ga0.25Al0.75 0.253a  111a  4.972a  …  …  …  …  261a  …  249 
a

One gaussian fit.

The lines are always very broad due to at least a triple contribution to a disorder among the different nano-objects that are examined:

  • a spatial distribution of the (Al,Ga)N alloy composition among the different QDs,

  • a variability of the size of the QDs as indicated by the AFM measurements, and

  • spatial inhomogeneities of the QCSE due to the QDs' variability in composition and size.

For the Al0.75Ga0.25N QDs case, we have added the result of the line-shape fitting with one gaussian function. This is the situation of the smallest discrepancy between both procedures. When one records a two-band PL signal, the low-energy band is weaker and broader and cannot be attributed to a phonon replica of the high-energy band. This is most probably the signature of a structural defect or a bimodal growth through the QDs assembly or both.79 

2. Emission diagrams for QDs embedded into AlN

The dependence of the low temperature emission diagrams of the AlxGa1−xN QDs (lattice-matched to aluminum nitride embedded into AlN barrier layers) with the aluminum composition is reported in Fig. 5. In these experimental conditions, the Poynting vector of the emitted photon is oriented along x in agreement with the convention of Fig. 2. The y direction is taken vertical, while the z direction is horizontal. The long (resp. short) axes of the emission diagram are switched from y (resp. z) to z (resp. y) when the xAl composition increases and the orientation of the emission diagrams are rotated by 90°. This is what is expected from the simplified description of the situation in terms of the ordering of the valence band states for AlxGa1−xN layers lattice-matched to AlN: for values of xAl larger than 0.6, the valence band maximum switches from Γ 5 (px and py in the spinless description) to Γ 1 (pz in the spinless description). However, the emission diagram is significantly at variance with this behavior, and it can be fitted by the following equation:
a Γ 1 co s 2 ( θ ) + b Γ 5 si n 2 ( θ ) ,
where θ is the angle between the direction of the electric field probed by the setup with z and where values of the (aΓ1,bΓ5) ratios would be predicted in advance by a kp calculation. None of the components of the (aΓ1,bΓ5) couple ever vanish and at the maximum of stress induced valence band mixing of the two Γ 7 states, the on-side emission is isotropic, that is to say, aΓ1 ≈ bΓ5, as expected in such a coupling condition for a bulk wurzitic semiconductor.19,23 This indicates a deviation from the simple description in terms of valence band physics and the importance of excitonic effects. For xAl = 0.40, xAl = 0.60, and xAl = 0.70, the values of the (aΓ1, bΓ5) ratio are (0.49, 1); (0.98, 1); and (1, 0.86). We estimate an error of about 0.03–0.05 in the determination of aΓ1 and bΓ5 values.
FIG. 5.

Evolution of the low temperature emission diagrams of the AlxGa1−xN quantum dots lattice-matched to aluminum nitride embedded into AlN barrier layers. In Figs. 5(a)–5(c), the Poynting vector of the emitted photon is oriented along z in agreement with the convention of Fig. 2; the y direction is taken vertically, while the x direction is taken horizontally. These are the conditions of collection of light named in-plane collection. The shapes of the emission diagram indicate emission in both x and y directions, as evidenced by intra-valence band mixings by the localized quantum dot confining potential. In Figs. 5(d)–5(f), the Poynting vector of the emitted photon is oriented along x in agreement with the convention of Fig. 2. These are the conditions of collection of light named on-side collection.

FIG. 5.

Evolution of the low temperature emission diagrams of the AlxGa1−xN quantum dots lattice-matched to aluminum nitride embedded into AlN barrier layers. In Figs. 5(a)–5(c), the Poynting vector of the emitted photon is oriented along z in agreement with the convention of Fig. 2; the y direction is taken vertically, while the x direction is taken horizontally. These are the conditions of collection of light named in-plane collection. The shapes of the emission diagram indicate emission in both x and y directions, as evidenced by intra-valence band mixings by the localized quantum dot confining potential. In Figs. 5(d)–5(f), the Poynting vector of the emitted photon is oriented along x in agreement with the convention of Fig. 2. These are the conditions of collection of light named on-side collection.

Close modal

The emission diagram could not be precisely measured for the sample with xAl = 0.75, which indicates that this technology of AlxGa1−xN QDs is not mature enough under these growth conditions to reach emission wavelengths shorter than 245 nm. However, although the signal to noise ratio was too high for this sample to be shown here, the intensity of the light emission was found to be roughly identical for the y and z polarizations. As a general trend, a lack of purity in the emission diagrams is found in terms of strict domination either by bΓ5 for xAl = 0.40 or by aΓ1 for xAl = 0.70.

Please note that the alloy disorder has also to be considered, which leads to linewidth that can be intrinsically larger than the valence band splittings, in particular, near the maximum of strain-induced coupling,80 that is to say, in the 50%–70% region of aluminum composition (see Fig. 4.33 in Ref. 19). However, this disorder blurs the predictions of the kp calculation, which do not include this effect in Fig. 3.

We have grown complementary series samples for which the active part of the light emitter is a QW instead of a plane of QDs, as described above in Sec. III. Our objective was to measure their emission energy vs the nominal xAl value and to record their emission diagrams for both the in-plane and on-side configurations. The optical properties of the AlxGa1−xN/AlN QW samples have been determined as well as their emission diagrams, similarly to the measurements performed for the AlxGa1−xN/AlN QD samples. We remind that, as detailed in Sec. III, the growth conditions have been chosen so that the nominal xAl compositions in the AlxGa1−xN QW sample series are similar to those of the AlxGa1−xN QDs series, and the QW thicknesses are found between 7 and 8 MLs, corresponding to the QD heights given in Table I. Thus, at the first order, the QCSEs are identical, and at the second order, they only differ from form factors linked to the specific shapes of the confining elements.

1. Photoluminescence for conditions of in-plane collection of photons

The evolution of the low temperature PL recorded for in-plane polarization of the emitted photons is shown in Fig. 6. The emission diagrams are perfectly circular. We remark an asymmetrical shape of the PL band with a low-energy tail that smoothly decreases over about two decades and then vanishes at an energy of about 400–500 meV below the energy of the maximum intensity of the PL emission. The PL features of the different QW samples significantly overlap except for the QW grown with xAl = 0.40. We can, at this stage, anticipate that this characteristic will have consequences on the selection rules, as well as consequences on the overall shapes of the emission diagrams. Indeed, such an overlap occurs for xAl compositions in the 60%–75% range of maximum mixing of the valence band states. In the series of QWs, the emission wavelengths at the maximum PL intensity decrease down to a minimum value of 234 nm for xAl = 75%. This is at a shorter wavelength than for the QDs grown with a similar nominal composition of xAl. It can be noted that the photo-excitation wavelength is 213 nm, that is to say, below-barrier excitation. The partial transparency of the AlN permits to deal with low photoexcitation densities, and this produces the interference fringes observed in the PL spectra, which are originating from the air/AlGaN/sapphire structure of the samples.

FIG. 6.

Low temperature plot of the PL spectra of the QW samples series showing the energies, the full width at half maximum, the asymmetry of the PL line shape, and the difference in intensities for the in-plane collection of the emitted light.

FIG. 6.

Low temperature plot of the PL spectra of the QW samples series showing the energies, the full width at half maximum, the asymmetry of the PL line shape, and the difference in intensities for the in-plane collection of the emitted light.

Close modal

From a logarithmic plot of the spectral dependence of the intensities of the low-energy PL tails, we obtain typical localization energies in the 100 meV range, which increases for higher xAl. The values of the localization energies are jointly attributed to the random alloy disorder in the cation sublattice of AlxGa1−xN (see, for instance, Fig. 4.33 of Ref. 18) and to fluctuations of the well widths. In addition, from bona fide, the low range of growth temperatures for the AlxGa1−xN growth, required by MBE, could also set up a limit to the growth of high efficiency aluminum-rich AlxGa1−xN materials.

On another hand, we remark that the FWHMs of the PL peaks are smaller for these QW samples than those obtained for the QDs samples with similar xAl. This is illustrated in Fig. 7, where the PL spectra of AlxGa1−xN QDs (full lines) and QWs (dotted lines) have been plotted for the four nominal xAl compositions of interest here.

FIG. 7.

PL spectra of AlxGa1−xN QDs/AlN (dotted lines) and AlxGa1−xN QWs/AlN (full lines) for the four nominal xAl composition values of 0.4, 0.6, 0.7, and 0.75 (also reported in the figure). Please note that some of the PL spectra for the QDs samples have been shifted in energy so that, given a nominal xAl composition, the maximum of the PL peak of both QDs and QW coincides.

FIG. 7.

PL spectra of AlxGa1−xN QDs/AlN (dotted lines) and AlxGa1−xN QWs/AlN (full lines) for the four nominal xAl composition values of 0.4, 0.6, 0.7, and 0.75 (also reported in the figure). Please note that some of the PL spectra for the QDs samples have been shifted in energy so that, given a nominal xAl composition, the maximum of the PL peak of both QDs and QW coincides.

Close modal

At this point, it can be emphasized that, for the AlxGa1−xN QWs, the decrease of the PL intensity with increasing xAl is smaller than for the QDs. The PL intensity recorded in similar excitation conditions decreases by a factor 20 for the QDs (see the inset in Fig. 4) for emission wavelengths ranging between 298 and 248 nm. It also decreases by a factor of 20 for the QWs, but for shorter emission wavelengths ranging between 276 and 234 nm. Noteworthy, in the 276–249 nm range, the decrease in the QW PL intensity is of factor 2 only. This is the evidence of more non-radiative recombination channels in the AlxGa1−xN QD samples as the nominal xAl composition increases more than the AlxGa1−xN QW ones.

2. Emission diagrams for QWs embedded into AlN

The PL spectra collected for both on-side polarizations (dashed lines for E//z and full lines for E//y) are plotted in Fig. 8. There is a substantial disorder in the composition of the QWs and in the well width, which is evidenced by the overlaps of the PL features corresponding to the nominal xAl compositions of 60%, 70%, and 75%.

FIG. 8.

Low temperature plot of the PL spectra for the QW samples series recorded for the on-side collection of the emitted light in the case of E//y (solid lines) and E//z (dotted lines) polarization conditions. The color code is shared with Figs. 6 and 7.

FIG. 8.

Low temperature plot of the PL spectra for the QW samples series recorded for the on-side collection of the emitted light in the case of E//y (solid lines) and E//z (dotted lines) polarization conditions. The color code is shared with Figs. 6 and 7.

Close modal

The emission diagrams recorded for the four QW samples at 8 K are reported in Fig. 9. The shapes of the emission diagrams are significantly at variance and can be fitted by an equation of the form aΓ1 cos2(θ) + bΓ5 sin2(θ), where values of the (aΓ1, bΓ5) ratio would be predicted in advance by a kp calculation. None of the components of the (aΓ1, bΓ5) couple ever vanishes, including the QW with an xAl composition of 40%. This result is again the experimental evidence of a deviation from the simple description in terms of valence band physics and shows the importance of excitonic effects. For xAl = 0.40, 0.60, 0.70, and 0.75, the values of the (aΓ1, bΓ5) ratio are (0.7, 1); (0.84, 1); (0.88, 1); and (1, 0.87), respectively.

FIG. 9.

Evolution of the low temperature emission diagrams of AlxGa1−xN quantum wells lattice-matched to aluminum nitride embedded into AlN barrier layers. The diagrams have been recorded in the on-side conditions of collection of light. The Poynting vector of the emitted photon is oriented along x in agreement with the convention of Fig. 2; the y direction is taken vertically, while the z direction is taken horizontally. The shape of the emission diagram indicates emission in both y and z directions, as evidenced by intravalence band mixings.

FIG. 9.

Evolution of the low temperature emission diagrams of AlxGa1−xN quantum wells lattice-matched to aluminum nitride embedded into AlN barrier layers. The diagrams have been recorded in the on-side conditions of collection of light. The Poynting vector of the emitted photon is oriented along x in agreement with the convention of Fig. 2; the y direction is taken vertically, while the z direction is taken horizontally. The shape of the emission diagram indicates emission in both y and z directions, as evidenced by intravalence band mixings.

Close modal

There are similar reasons that explain the general trend observed for both AlxGa1−xN QDs and QWs in these xAl composition ranges. First, the lack of purity of the emission diagrams in terms of strict dominations of either bΓ5 (for instance, for xAl = 0.40) or aΓ1 (for instance, for xAl = 0.75) should be pointed out. There are at least two main physical reasons to this result:

  • First, there are significant overlaps of the PL features for samples grown with xAl of 60%, 70%, and 75%. This characteristic means that for these QWs, the nature of the PL band is mixed in terms of contributions of valence band states of Γ 7 and Γ 9 symmetries in the xAl percentage region near the crossover of the valence band levels. Thus, none of the components of the (aΓ1,bΓ5) couple in the measured emission diagrams ever passes by zero. At the maximum xAl composition, the pz nature of the fundamental valence band is reached, leading to aΓ1 > bΓ5. One can safely anticipate that an emission diagram where a Γ 1 b Γ 5 can be obtained if growing an AlxGa1−xN QW active region with a higher xAl value, while this option could be bottlenecked by lattice-mismatch effects for QDs, as discussed earlier.

  • The long-range direct and short range exchange Coulomb interactions are large in group III-element nitrides and in their heterostructures. Coulombic effects produce mixings of the confined states that impact the selection rules of the simple kp calculation.

Finally, we have plotted in Fig. 10 the degree of polarization DOP = I y I z I y + I z measured on these samples (Iy and Iz being the integrated intensity for y and z polarizations). This plot allows comparing our data with some recent data of the literature. More precisely, the detailed data reported in Ref. 81 have been selected for comparison. However, it should be noticed that samples differ from a work to another: in particular, the samples of Ref. 81 have been grown on AlyGa1−yN templates of varying Al compositions. This modifies the strain effects and makes the relationship between the xAl composition in the AlxGa1−xN QW layer and the emission wavelength slightly at variance with our results. In addition, no bowing in the (Al,Ga)N composition dependence of the bandgap is considered in Ref. 81, and both electroluminescence (EL) and PL data are presented: EL spectra have been obtained under different conditions of carrier injections and for the PL under different photoexcitation densities, which are noticeably higher than ours. In our work, smaller photo-excitation densities have been used, as well as photo-excitation conditions that are below the bandgap energy of the AlN barrier layers. Within these experimental differences, i.e., sample design, light collection conditions, and data processing and interpretations, a reasonable agreement between the DOP of all the samples, grown by either MBE or MOVPE (Ref. 81), can be observed, although the DOP variation is less abrupt in the MBE case. In addition, a complementary Al0.3Ga0.7N QD sample buried into Al0.7Ga0.3N cladding layers grown on an AlN template has been studied, as described in the supplementary material. The orange sphere corresponds to this sample. The emission wavelength was measured at 288 nm, and the value of the (aΓ1, bΓ5) ratio is (0.53, 1), which corresponds to a DOP of 0.32.

FIG. 10.

Degree of polarization measured in our AlxGa1−xN QD and QW samples (red spheres for QDs and black ones for QWs). Experimental results recorded on samples grown by MOVPE (body-centered spotted open circles), taken from Ref. 81, are also shown. The orange sphere corresponds to an Al0.3Ga0.7N QD sample described in the supplementary material. The QDs were grown in an Al0.7Ga0.3N cladding layer grown on an AlN template. The emission wavelength occurs at 288 nm.

FIG. 10.

Degree of polarization measured in our AlxGa1−xN QD and QW samples (red spheres for QDs and black ones for QWs). Experimental results recorded on samples grown by MOVPE (body-centered spotted open circles), taken from Ref. 81, are also shown. The orange sphere corresponds to an Al0.3Ga0.7N QD sample described in the supplementary material. The QDs were grown in an Al0.7Ga0.3N cladding layer grown on an AlN template. The emission wavelength occurs at 288 nm.

Close modal

Our experimental observations indicate that, similarly with what has been theoretically reported for the case of QWs, the continuity conditions of the densities of probabilities and of the current of probability at the heterointerfaces, combined with the anisotropic Coulomb interaction, produce complex mixings of the confined valence band states. This characteristic leads to the non-vanishing of one of the components of the (aΓ1, bΓ5) couple and permits to understand the final shape of the emission diagrams.51,73,74 Beyond the simple description of any level in terms of one conduction band and one valence band, it becomes mandatory to express the wave function of the exciton in terms of a linear expansion along all the conduction and valence band states (eventually also including resonant ones). This is mandatory when the effects of the Coulombic terms cannot be treated as a perturbation of the confined electron and hole states. Intraband mixings, in particular, those among the Bloch valence band states (as in the case of our QW samples), weighted by their associated envelope functions, have been found mandatory to include for interpreting the selection rules in more cases than for computing binding energies and wave functions of acceptors in cubic semiconductors.74 Deformations potentials of acceptors in bulks are also influenced by mixings of the valence bands, and they substantially differ from band deformation potentials.82,83 The ratio between the one-phonon replica oscillator strength and the zero phonon one is also very sensitive to mixings of confined valence band states in AlxGa1−xN QWs.74 In the specific case of (Ga,In)N-based QWs, it has been recently evidenced, by David and Weisbuch,84 that sophisticated numerical investigations, where both random alloy disorder and Coulomb interaction are treated,85 in the Schrödinger equation are mandatory for describing the physics of nitride QWs with disordered confining layers.

Electric dipole moments of excitonic complex in nitride-based QDs grown on (0001)-oriented AlN templates are oriented along the c axis,86 and the effects demonstrated in QWs are also to be observed in the series of samples studied here. Compared with the case of QWs, the theoretical description of the electronic structure of QDs is complexified by the distribution of size and the disorder in the AlxGa1−xN confining material. These effects add complementary and in-homogenously distributed breakings of translation symmetry in the growth plane. Thus, a theoretical description of the electronic structure of AlxGa1−xN/AlN QWs and QDs in the context of an approach similar to the one proposed in Refs. 84 and 85 is found to be mandatory in order to explain the experimental shapes and orientations of emission diagrams recorded perpendicularly to the (0001)-oriented growth plane.

An in-depth investigation of the optical properties of a series of samples made of AlxGa1−xN quantum dots (QDs) or a quantum well (QW) active region has been done. The samples consist of a QD or QW plane, with an AlxGa1−xN deposited thickness of about 2 nm, encapsulated in AlN cladding layers, grown by molecular beam epitaxy on an AlN template deposited by metal organic chemical vapor deposition on a (0001)-oriented sapphire substrate. In both QD and QW cases, the series consists of four samples, each sample being made of an AlxGa1−xN layer with an aluminum composition xAl varying from 0.4, 0.6, 0.7, and 0.75. Both the QDs and QWs are lattice-matched to AlN. Using low temperature (8 K) photoluminescence measurements, the emission diagrams of the samples, under both in-plane and on-side conditions, have been determined. The emission diagrams measured for the on-side conditions exhibit anisotropy of the light emission depending on the electric field polarization condition. However, independently of the AlxGa1−xN composition xAl, the anisotropy, along with the degree of polarization, is found to be limited, an effect that cannot be interpreted within the simple context of a kp band-to-band model. This characteristic is the experimental indication of the influence of the Coulomb interaction and exciton mixings that substantially contribute to the polarization of the emission, in particular, in the deep UVC range at wavelengths below 260 nm. The results show the occurrence of the band crossover at high xAl composition above 70%. In addition, the degree of polarization calculated from the measurements gave comparable results, including both QDs and QWs, with data previously reported in the literature for MOCVD grown heterostructures. Noteworthy, the onset of non-radiative recombination processes for the highest xAl values (xAl ≥ 0.7), used to fabricate AlxGa1−xN QDs with emitting wavelengths shorter than 260 nm, is setting a limit in the growth of QDs as localization centers within the present epitaxial process. When compared with the results recorded on the AlxGa1−xN QW series of samples, it appears that the QW technology brings more flexibility to reach shorter wavelengths range, i.e., below 245 nm, compared to their AlxGa1−xN QD counterpart, along with increased radiative efficiency.

The supplementary material describes the structural properties of the AlN based layers and nanostructures investigated in this study. At first, the growth conditions for the fabrication of the AlN templates are given, along with the characterizations by x-ray diffraction and atomic force microscopy (AFM) measurements. In the second section, the in situ investigation of the quantum well (QW) and quantum dot (QD) heterostructures by reflection high energy electron diffraction (RHEED) is described. In particular, the different RHEED diagrams are compared as a function of the sample's active region design. Finally, in the last part, the morphological properties of the samples are presented with typical AFM images and surface profiles obtained for both AlxGa1−xN QDs and QW structures.

Alexandra Ibanez acknowledges the support of the French National Research Agency through the ANR Project ANR-22-CE51-0035 “DOPALGAN” for the funding of her Ph.D. grant. We acknowledge the support by the French National Research Agency through ANR Projects ANR-20-CE09-0027 “DILEMMA” and GANEX (ANR-11-LABX-0014). GANEX belongs to the publicly funded “Investissements d’Avenir” program managed by the French ANR agency. The authors would like to thank A. Courville, D. Lefebvre, M. Portail, B. Poulet, A. Rousseau, and S. Vézian for their invaluable technical and scientific assistance.

The authors have no conflicts to disclose.

Alexandra Ibanez: Data curation (equal); Formal analysis (supporting); Investigation (equal); Methodology (equal); Writing – review & editing (equal). Nikita Nikitskiy: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). Aly Zaiter: Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Methodology (supporting); Writing – review & editing (equal). Pierre Valvin: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). Wilfried Desrat: Conceptualization (supporting); Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Methodology (supporting); Writing – review & editing (equal). Thomas Cohen: Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Methodology (supporting); Writing – review & editing (equal). M. Ajmal Khan: Conceptualization (supporting); Data curation (supporting); Investigation (supporting); Methodology (supporting); Writing – review & editing (equal). Guillaume Cassabois: Conceptualization (supporting); Data curation (supporting); Formal analysis (supporting); Funding acquisition (supporting); Investigation (supporting); Methodology (supporting); Project administration (supporting); Resources (supporting); Supervision (supporting); Validation (supporting); Writing – review & editing (equal). Hideki Hirayama: Conceptualization (supporting); Funding acquisition (supporting); Investigation (supporting); Methodology (supporting); Project administration (supporting); Resources (supporting); Supervision (supporting); Writing – review & editing (equal). Patrice Genevet: Funding acquisition (supporting); Investigation (supporting); Project administration (supporting); Resources (supporting); Supervision (supporting); Writing – review & editing (equal). Julien Brault: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Bernard Gil: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and its supplementary material.

1.
M.
Kneissl
,
T.-Y.
Seong
,
J.
Han
, and
H.
Amano
,
Nat. Photonics
13
,
233
244
(
2019
).
2.
Y.
Muramoto
,
M.
Kimura
, and
S.
Nouda
,
Semicond. Sci. Technol.
29
,
084004
(
2014
).
3.
C. J.
Zollner
,
S. P.
DenBaars
,
J. S.
Speck
, and
S.
Nakamura
,
Semicond. Sci. Technol.
36
,
123001
(
2021
).
4.
M.
Leroux
,
S.
Dalmasso
,
F.
Natali
,
S.
Helin
,
C.
Touzi
,
S.
Laügt
,
M.
Passerel
,
F.
Omnes
,
F.
Semond
,
J.
Massies
, and
P.
Gibart
,
Phys. Status Solidi B
234
,
887
891
(
2002
).
5.
K. B.
Nam
,
J.
Li
,
M. L.
Nakarmi
,
J. Y.
Lin
, and
H. X.
Jiang
,
Appl. Phys. Lett.
84
,
5264
5266
(
2004
).
6.
Y.
Taniyasu
and
M.
Kasu
,
Appl. Phys. Lett.
99
,
251112
(
2011
).
7.
B.
Neuschl
,
J.
Helbing
,
M.
Knab
,
H.
Lauer
,
M.
Madel
,
K.
Thonke
,
T.
Meisch
,
K.
Forghani
,
F.
Scholz
, and
M.
Feneberg
,
J. Appl. Phys.
116
,
113506
(
2014
).
8.
C.
Reich
,
M.
Guttmann
,
M.
Feneberg
,
T.
Wernicke
,
F.
Mehnke
,
C.
Kuhn
,
J.
Rass
,
M.
Lapeyrade
,
S.
Einfeldt
,
A.
Knauer
,
V.
Kueller
,
M.
Weyers
,
R.
Goldhahn
, and
M.
Kneissl
,
Appl. Phys. Lett.
107
,
142101
(
2015
).
9.
H.
Kobayashi
,
S.
Ichikawa
,
M.
Funato
, and
Y.
Kawakami
,
Adv. Opt. Mater.
7
,
1900860
(
2019
).
10.
M.
Korytov
,
J. A.
Budagosky
,
J.
Brault
,
T.
Huault
,
M.
Benaissa
,
T.
Neisius
,
J.-L.
Rouvière
, and
P.
Vennéguès
,
J. Appl. Phys.
111
,
084309
(
2012
).
11.
L. I.
Schiff
,
Quantum Mechanics
(
McGraw Hill
,
New York
,
1955
).
12.
J.
Brault
,
B.
Damilano
,
A.
Kahouli
,
S.
Chenot
,
M.
Leroux
,
B.
Vinter
, and
J.
Massies
,
J. Cryst. Growth
363
,
282
286
(
2013
).
13.
J.
Brault
,
B.
Damilano
,
B.
Vinter
,
P.
Vennéguès
,
M.
Leroux
,
A.
Kahouli
, and
J.
Massies
,
Jpn. J. Appl. Phys.
52
,
08JG01
(
2013
).
14.
J.
Brault
,
D.
Rosales
,
B.
Damilano
,
M.
Leroux
,
A.
Courville
,
M.
Korytov
,
S.
Chenot
,
P.
Vennéguès
,
B.
Vinter
,
P.
de Mierry
,
A.
Kahouli
,
J.
Massies
,
T.
Bretagnon
, and
B.
Gil
,
Semicond. Sci. Technol.
29
,
084001
(
2014
).
15.
J.
Brault
,
S.
Matta
,
T.-H.
Ngo
,
M.
Korytov
,
D.
Rosales
,
B.
Damilano
,
M.
Leroux
,
P.
Vennéguès
,
M.
Al Khalfioui
,
A.
Courville
,
O.
Tottereau
,
J.
Massies
, and
B.
Gil
,
Jpn. J. Appl. Phys.
55
,
05FG06
(
2016
).
16.
J.
Brault
,
S.
Matta
,
T.-H.
Ngo
,
D.
Rosales
,
M.
Leroux
,
B.
Damilano
,
M.
Al Khalfioui
,
F.
Tendille
,
S.
Chenot
,
P.
De Mierry
,
J.
Massies
, and
B.
Gil
,
Mater. Sci. Semicond. Process.
55
,
95
101
(
2016
).
17.
A. A.
Toropov
,
E. A.
Evropeitsev
,
M. O.
Nestoklon
,
D. S.
Smirnov
,
T. V.
Shubina
,
V. K.
Kaibyshev
,
G. V.
Budkin
,
V. N.
Jmerik
,
D. V.
Nechaev
,
S.
Rouvimov
,
S. V.
Ivanov
, and
B.
Gil
,
Nano Lett.
20
,
158
165
(
2020
).
18.
B.
Damilano
,
J.
Brault
, and
J.
Massies
,
J. Appl. Phys.
118
,
024304
(
2015
).
19.
B.
Gil
,
Physics of Wurtzite Nitrides and Oxides: Passport to Devices
(
Springer International Publishing
,
Cham
,
2014
). ISSN: 0933-033X; ISBN: 978-3-319-06804-6; ISSN: 2196-2812 (electronic); ISBN: 978-3-319-06805-3 (eBook).
20.
G. F.
Koster
,
J. O.
Dimmock
,
R. G.
Wheeler
, and
H.
Statz
,
Properties of the Thirty-Two Point Groups
(
MIT Press
,
Cambridge
,
1964
).
21.
M.
Suzuki
and
T.
Uenoyama
, “
Chapter A6.2
,” in
Properties, Processing, and Applications of Gallium Nitride and Related Semiconductors
, EMIS Data Review Series No. 23, edited by
J. H.
Edgar
,
S.
Strite
,
I.
Akasaki
,
H.
Amano
, and
C.
Wetzel
(
Institution of Electrical Engineering
,
London
,
1999
), pp.
168
171
, ISBN: 0 85296 953 8.
22.
P. A.
Shields
,
R. J.
Nicholas
,
N.
Grandjean
, and
J.
Massies
,
Phys. Rev. B
63
,
245319
(
2001
).
23.
B.
Gil
,
O.
Briot
, and
R.-L.
Aulombard
,
Phys. Rev. B
52
,
R17028
R17031
(
1995
).
24.
M.
Tchounkeu
,
O.
Briot
,
B.
Gil
,
J. P.
Alexis
, and
R.-L.
Aulombard
,
J. Appl. Phys.
80
,
5352
5360
(
1996
).
25.
S.
Chichibu
,
A.
Shikanai
,
T.
Azuhata
,
T.
Sota
,
A.
Kuramata
,
K.
Horin
, and
S.
Nakamura
,
Appl. Phys. Lett.
68
,
3766
3768
(
1996
).
26.
K.
Kornitzer
,
T.
Ebner
,
K.
Thonke
,
R.
Sauer
,
C.
Kirchner
,
V.
Schwegler
,
M.
Kamp
,
M.
Leszczynski
,
I.
Grzegory
, and
S.
Porowski
,
Phys. Rev. B
60
,
1471
1473
(
1999
).
27.
K.
Torii
,
T.
Deguchi
,
T.
Sota
,
K.
Suzuki
,
S.
Chichibu
, and
S.
Nakamura
,
Phys. Rev. B
60
,
4723
4730
(
1999
).
28.
E.
Silveira
,
J. A.
Freitas
, Jr.
,
O. J.
Glembocki
,
G. A.
Slack
, and
L. J.
Schowalter
,
Phys. Rev. B
71
,
041201
(
2005
).
29.
H.
Ikeda
,
T.
Okamura
,
K.
Matsukawa
,
T.
Sota
,
M.
Sugawara
,
T.
Hoshi
,
P.
Cantu
,
R.
Sharma
,
J. F.
Kaeding
,
S.
Keller
,
U. K.
Mishra
,
K.
Kosaka
,
K.
Asai
,
S.
Sumiya
,
T.
Shibata
,
M.
Tanaka
,
J. S.
Speck
,
S. P.
DenBaars
,
S.
Nakamura
,
T.
Koyama
,
T.
Onuma
, and
S. F.
Chichibu
,
J. Appl. Phys.
102
,
123707
(
2007
); Erratum J. Appl. Phys. 103, 089901 (2008).
30.
G.
Rossbach
,
M.
Feneberg
,
M.
Roppischer
,
C.
Werner
,
N.
Esser
,
C.
Cobet
,
T.
Meisch
,
K.
Thonke
,
A.
Dadgar
,
J.
Blasing
,
A.
Krost
, and
R.
Goldhahn
,
Phys. Rev. B
83
,
195202
(
2011
).
31.
D. G.
Thomas
and
J. J.
Hopfield
,
Phys. Rev.
116
,
573
582
(
1959
).
32.
V. B.
Sandomirskii
,
Fiz. Tverd. Tela
6
,
324
(
1964
) [Sov. Phys. Solids State 6, 261 (1964)].
33.
B.
Gil
,
F.
Hamdani
, and
H.
Morkoç
,
Phys. Rev. B
54
,
7678
7681
(
1996
).
34.
H.
Lahreche
,
M.
Leroux
,
M.
Laugt
,
M.
Vaille
,
B.
Beaumont
, and
P.
Gibart
,
J. Appl. Phys.
87
,
577
583
(
2000
).
35.
G. L.
Bir
and
G. E.
Pikus
,
Symmetry and Strain-Induced Effects in Semiconductors
(
John Wiley & Sons
,
1974
), ISBN: 0470073217.
36.
K.
Cho
,
Phys. Rev. B
14
,
4463
4482
(
1976
).
37.
A.
Kobayashi
,
O. F.
Sankey
,
S. M.
Volz
, and
J. D.
Dow
,
Phys. Rev. B
28
,
935
945
(
1983
).
38.
M.
Suzuki
,
T.
Uenoyama
, and
A.
Yanase
,
Phys. Rev. B
52
,
8132
8139
(
1995
).
39.
S. L.
Chuang
and
C. S.
Chang
,
Phys. Rev. B
54
,
2491
2504
(
1996
).
40.
K.
Kim
,
W. R. L.
Lambrecht
, and
B.
Segall
,
Phys. Rev. B
53
,
16310
16326
(
1996
); Erratum: Phys. Rev. B 56, 7018 (1997).
41.
K.
Kim
,
W. R. L.
Lambrecht
,
B.
Segall
, and
M.
van Schilfgaarde
,
Phys. Rev. B
56
,
7363
7375
(
1997
).
42.
M.
Kumagai
,
S. L.
Chuang
, and
H.
Ando
,
Phys. Rev. B
57
,
15303
15314
(
1998
).
43.
P.
Rinke
,
M.
Winkelnkemper
,
A.
Qteish
,
D.
Bimberg
,
J.
Neugebauer
, and
M.
Scheffler
,
Phys. Rev. B
77
,
075202
(
2008
).
44.
R. G.
Banal
,
M.
Funato
, and
Y.
Kawakami
,
Phys. Rev. B
79
,
R121308
(
2009
).
45.
T.
Kolbe
,
A.
Knauer
,
C.
Chua
,
Z.
Yang
,
S.
Einfeldt
,
P.
Vogt
,
N. M.
Johnson
,
M.
Weyers
, and
M.
Kneissl
,
Appl. Phys. Lett.
97
,
171105
(
2010
).
46.
J. E.
Northrup
,
C. L.
Chua
,
Z.
Yang
,
T.
Wunderer
,
M.
Kneissl
,
N. M.
Johnson
, and
T.
Kolbe
,
Appl. Phys. Lett.
100
,
021101
(
2012
).
47.
M.
Feneberg
,
M.
Winkler
,
J.
Klamser
,
J.
Stellmach
,
M.
Frentrup
,
S.
Ploch
,
F.
Mehnke
,
T.
Wernicke
,
M.
Kneissl
, and
R.
Goldhahn
,
Appl. Phys. Lett.
106
,
182102
(
2015
).
48.
H.
Wang
,
L.
Fu
,
H. M.
Lu
,
X. N.
Kang
,
J. J.
Wu
,
F. J.
Xu
, and
T. J.
Yu
,
Opt. Express
27
,
A436
(
2019
) and references therein.
49.
S.-H.
Park
,
J.
Kim
,
D.
Ahn
, and
E.
Yoon
,
Phys. E: Low-Dimensional Syst. Nanostruct.
120
,
114112
(
2020
).
50.
Y.
Chen
,
J.
Ben
,
F.
Xu
,
J.
Li
,
Y.
Chen
,
X.
Sun
, and
D.
Li
,
Fundam. Res.
1
,
717
734
(
2021
).
51.
G. E. W.
Bauer
and
T.
Ando
,
Phys. Rev. B
38
,
6015
(
1988
).
52.
A. D.
Andreev
and
E. P.
O’Reilly
,
Phys. Rev. B
62
,
15851
15870
(
2000
).
53.
R.
Ishii
,
A.
Kaneta
,
M.
Funato
, and
Y.
Kawakami
,
Phys. Rev. B
81
,
155202
(
2010
).
54.
R.
Ishii
,
A.
Kaneta
,
M.
Funato
, and
Y.
Kawakami
,
Phys. Rev. B
87
,
235201
(
2013
).
55.
S.
Kako
,
K.
Hoshino
,
S.
Iwamoto
,
S.
Ishida
, and
Y.
Arakawa
,
Appl. Phys. Lett.
85
,
64
66
(
2004
).
56.
C.
Santori
,
S.
Gotzinger
,
Y.
Yamamoto
,
S.
Kako
,
K.
Hoshino
, and
Y.
Arakawa
,
Appl. Phys. Lett.
87
,
051916
(
2005
).
57.
S.
Kako
,
C.
Santori
,
K.
Hoshino
,
S.
Gotzinger
,
Y.
Yamamoto
, and
Y.
Arakawa
,
Nat. Mater.
5
,
887
892
(
2006
).
58.
F.
Rol
,
S.
Founta
,
H.
Mariette
,
B.
Daudin
,
L. S.
Dang
,
J.
Bleuse
,
D.
Peyrade
,
J.-M.
Gerard
, and
B.
Gayral
,
Phys. Rev. B
75
,
125306
(
2007
).
59.
D.
Simeonov
,
A.
Dussaigne
,
R.
Butte
, and
N.
Grandjean
,
Phys. Rev. B
77
,
075306
(
2008
).
60.
F. S.
Cheregi
,
A.
Vinattieri
,
E.
Feltin
,
D.
Simeonov
,
J.-F.
Carlin
,
R.
Butte
,
N.
Grandjean
, and
M.
Gurioli
,
Phys. Rev. B
77
,
125342
(
2008
).
61.
J.
Renard
,
R.
Songmuang
,
G.
Tourbot
,
C.
Bougerol
,
B.
Daudin
, and
B.
Gayral
,
Phys. Rev. B
80
,
121305(R)
(
2009
).
62.
C.
Kindel
,
S.
Kako
,
T.
Kawano
,
H.
Oishi
,
Y.
Arakawa
,
G.
Honig
,
M.
Winkelnkemper
,
A.
Schliwa
,
A.
Hoffmann
, and
D.
Bimberg
,
Phys. Rev. B
81
,
241309
(
2010
).
63.
D.
Rosales
,
T.
Bretagnon
,
B.
Gil
,
A.
Kahouli
,
J.
Brault
,
B.
Damilano
,
J.
Massies
,
M. V.
Durnev
, and
A. V.
Kavokin
,
Phys. Rev. B
88
,
125437
(
2013
).
64.
S.
Sergent
,
S.
Kako
,
M.
Burger
,
D. J.
As
, and
Y.
Arakawa
,
Appl. Phys. Lett.
103
,
151109
(
2013
).
65.
M. J.
Holmes
,
K.
Choi
,
S.
Kako
,
M.
Arita
, and
Y.
Arakawa
,
Nano Lett.
14
,
982
986
(
2014
).
66.
Y.
Arakawa
and
M. J.
Holmes
,
Appl. Phys. Rev.
7
,
0210309
(
2020
) and references therein.
67.
B.
Gil
and
O.
Briot
,
Phys. Rev. B
55
,
2530
(
1997
).
68.
M.
Julier
,
J.
Campo
,
B.
Gil
,
J. P.
Lascaray
, and
S.
Nakamura
,
Phys. Rev. B
57
,
R6791
R6794
(
1998
).
69.
R.
Ishii
,
A.
Yoshikawa
,
K.
Nagase
,
M.
Funato
, and
Y.
Kawakami
,
AIP Adv.
10
,
125014
(
2020
).
70.
M.
Feneberg
,
M. F.
Romero
,
B.
Neuschl
,
K.
Thonke
,
M.
Röppischer
,
C.
Cobet
,
N.
Esser
,
M.
Bickermann
, and
R.
Goldhahn
,
Appl. Phys. Lett.
102
,
052112
(
2013
).
71.
R.
Ishii
,
M.
Funato
, and
Y.
Kawakami
,
Phys. Rev. B
102
,
155202
(
2020
).
72.
Y.
Chen
,
B.
Gil
,
P.
Lefebvre
, and
H.
Mathieu
,
Phys. Rev. B
37
,
6429
6432
(
1988
).
73.
L. C.
Andreani
and
A.
Pasquarello
,
Phys. Rev. B
42
,
8928
8938
(
1990
).
74.
E. P.
Pokatilov
,
D. L.
Nika
,
V. M.
Fomin
, and
J. T.
Devreese
,
Phys. Rev. B
77
,
125328
(
2008
).
75.
A.
Baldereschi
and
N. O.
Lipari
,
Phys. Rev. Lett.
25
,
373
376
(
1970
); Phys. Rev. B 8, 2697 (1973).
76.
S.
Matta
,
J.
Brault
,
T. H.
Ngo
,
B.
Damilano
,
M.
Korytov
,
P.
Vennéguès
,
M.
Nemoz
,
J.
Massies
,
M.
Leroux
, and
B.
Gil
,
J. Appl. Phys.
122
,
085706
(
2017
).
77.
J.
Brault
,
M.
Al Khalfioui
,
S.
Matta
,
B.
Damilano
,
M.
Leroux
,
S.
Chenot
,
M.
Korytov
,
J. E.
Nkeck
,
P.
Vennéguès
,
J. Y.
Duboz
,
J.
Massies
, and
B.
Gil
,
Semicond. Sci. Technol.
33
,
075007
(
2018
).
78.
J. M.
Binder
,
A.
Stark
,
N.
Tomek
,
J.
Scheuer
,
F.
Frank
,
K. D.
Jahnke
,
C.
Müller
,
S.
Schmitt
,
M. H.
Metsch
,
T.
Unden
,
T.
Gehring
,
A.
Huck
,
U. L.
Andersen
,
L. J.
Rogers
, and
F.
Jelezko
,
SoftwareX
6
,
85
90
(
2017
).
79.
J.
Cañas
,
A.
Harikumar
,
S. T.
Purcell
,
N.
Rochat
,
A.
Grenier
,
A.
Jannaud
,
E.
Bellet-Amalric
,
F.
Donatini
, and
E.
Monroy
, “AlGaN/AlN Stranski-Krastanov quantum dots for highly efficient electron beam pumped emitters: The role of miniaturization and composition to attain far UV-C emission,” arXiv:2305.15825 (2023).
80.
S.
Ohno
,
S.
Adachi
,
R.
Kaji
,
S.
Muto
, and
H.
Sasakura
,
Appl. Phys. Lett.
98
,
161912
(
2011
).
81.
M.
Guttmann
,
F.
Mehnke
,
B.
Belde
,
F.
Wolf
,
C.
Reich
,
L.
Sulmoni
,
T.
Wernicke
, and
M.
Kneissl
,
Jpn. J. Appl. Phys.
58
,
SCCB20
(
2019
).
82.
M.
Schmidt
,
Phys. Status Solidi B
79
,
533
538
(
1977
).
83.
H.
Mathieu
,
J.
Camassel
, and
F. B.
Chekroun
,
Phys. Rev. B
29
,
3438
3448
(
1984
).
84.
A.
David
and
C.
Weisbuch
,
Phys. Rev. Res.
4
,
043004
(
2022
).
85.
A.
David
,
Phys. Rev. Appl.
15
,
054015
(
2021
).
86.
G.
Hönig
,
S.
Rodt
,
G.
Callsen
,
I. A.
Ostapenko
,
T.
Kure
,
A.
Schliwa
,
C.
Kindel
,
D.
Bimberg
,
A.
Hoffmann
,
S.
Kako
, and
Y.
Arakawa
,
Phys. Rev. B
88
,
045309
(
2013
).

Supplementary Material