Sub-bandgap optical absorption processes in 300-nm-thick Al_1−xIn_xN alloys grown on a c-plane GaN/sapphire template

Al_1−xIn_xN alloys have attracted a great deal of attention in applications to optoelectronic devices because their bandgap energy can be widely tuned from 6.2 eV (AlN) to 0.65 eV (InN).¹ Al_1−xIn_xN alloys with x ∼ 0.17, nearly lattice matched to GaN,² have been intensively investigated in the development of high-performing optical devices, such as the cladding layers of edge-emitting laser diodes (LDs)^3–5 and distributed Bragg reflectors (DBRs) of vertical-cavity surface-emitting lasers (VCSELs) operating at visible wavelengths.^6–10 For these devices, reduction of the sub-bandgap optical absorption (SOA) in Al_1−xIn_xN alloys is one of the primary issues faced. A thick-and-low SOA Al_1−xIn_xN layer is desirable for the cladding layers of LDs. The continuous wave operation of VCSELs with conductive Al_0.84In_0.16N/GaN DBRs suggested that a low SOA of thin (∼40 nm) Al_1−xIn_xN layers was obtained.⁶ However, SOAs and their absorption coefficients (α) in Al_1−xIn_xN thin films have not been reported yet. This is because of the challenges in growing thick and highly crystalline Al_1−xIn_xN films and detecting the SOAs on several hundred nm-thin films, as we will describe later.

Al_1−xIn_xN is known to have a large spectral broadening of absorption (emission) spectra, and a significant energy difference between the emission peak and bandgap energy (a Stokes-like shift) has been reported.^11–16 Electronic state formations in bandgaps were also observed by optical and electrical measurements.^14,17,18 These sub-bandgap electronic states possibly cause SOA, leading to internal losses in the optical waveguides of LDs and DBRs of VCSELs. However, because of the challenges in obtaining thick and highly crystalline Al_1−xIn_xN alloys, the effect of these sub-bandgap states in Al_1−xIn_xN alloys on the internal loss of these devices is unclear. Generally, the α of SOA is several orders of magnitude lower than above-bandgap optical absorption of the order of 10⁴–10⁵cm⁻¹.^19–22 Optical transmittance (OT) measurement is a representative method to determine α, but, for example, a film thickness greater than 10 μm is assumed to be required to detect the optical absorption when α ≤ 10³cm⁻¹. That is, the light penetration depth is greater than 10 μm. This is far thicker than the critical thickness of low indium content Al_1−xIn_xN alloys grown on GaN.²³ In the case of a typical spectroscopic ellipsometry (SE) system, the detection limit of α is also of the order of 10³–10⁴cm⁻¹.²⁴ Several reports have shown the absorption spectra of Al_1−xIn_xN alloys obtained by SE;^25,26 however, the accuracy of the α obtained for the SOA regions and their origins have not been reported yet. For further development of optical devices, including Al_1−xIn_xN alloys, observation and characterization of the SOAs and their InN mole fraction dependence are essential.

This study analyzes the SOA processes in 300-nm-thick Al_1−xIn_xN alloys grown on a c-plane GaN/sapphire template. Recently, Miyoshi et al. reported Al_1−xIn_xN alloys with thick and highly flat surfaces.^23,25,27 The SOA processes were observed by photothermal deflection spectroscopy (PDS), which has a high detection sensitivity for optical absorption.^{19–21,28,29} PDS measures optical absorption by detecting nonradiative recombination with heat generation. The absolute value of α is thought to be hard to determine by PDS alone because nitride semiconductors contain deep energy states leading to radiative recombination (for example, the yellow luminescence in GaN). Furthermore, to avoid the PDS signal from underlying layers (e.g., substrate), PDS usually measured the thin films grown on a transparent substrate.^{19–21,28,29} However, highly crystalline Al_1−xIn_xN thin films have often grown on GaN, and bandgaps of those alloys that were nearly lattice matched to GaN (x ∼ 0.17) were larger than the GaN.^25–27 Characterization of SOAs in Al_1−xIn_xN thin films with x ∼ 0.17 is quite important given the device applications. Thus, in this study, SOAs of Al_1−xIn_xN thin films grown on a GaN template were characterized by PDS, and the SOA's α were carefully estimated by combining PDS, OT, and SE. The x-dependence of the SOA processes was also characterized by comparing PDS and photoluminescence (PL) measurements.

Approximately 300-nm-thick Al_1−xIn_xN alloys, with x ranging from 0.114 to 0.185, were grown by metal-organic chemical vapor deposition (MOCVD) on a 2.2-μm-thick c-plane GaN/sapphire template.²³ InN mole fractions were estimated by high-resolution x-ray diffraction 2θ−ω scan. A 2.2-μm-thick GaN/sapphire template without an Al_1−xIn_xN layer was also prepared as a reference. The detailed growth procedures and the structural characterizations of the Al_1−xIn_xN samples have been described elsewhere.²³ To estimate α in the sub-bandgap region of a 2.2-μm-thick GaN template, the PDS and OT of a 350-μm-thick undoped GaN substrate grown by hydride vapor phase epitaxy (HVPE) were measured. The threading dislocation density (TDD) and background electron density of the GaN substrate were approximately 1.0 × 10⁶cm⁻² and 1.0 × 10¹⁷ cm⁻³, respectively. The SE measurements were conducted using an SE system (SOPRA ES4G) with a rotating polarizer at room temperature. An Xe lamp was used as the light source, and the incident angle was set to 75°. PL measurements were conducted using the fourth harmonic generation of an Nd:YAG laser with an excitation wavelength of 266 nm. The PL signal was dispersed by a monochromator with a focal length of 500 mm and detected using a photomultiplier tube. The energy resolution of the system is estimated to be 7.3 meV. In the PDS measurement, a monochromatic excitation source was obtained using an Xe lamp dispersed by a monochromator with a focal length of 120 mm. The slit width of the monochromator was set to 0.5 mm when the measured wavelength was shorter than 400 nm and 2.0 mm when the measured wavelength was longer than 400 nm. The energy resolutions of the system were estimated to be 10 and 50 meV for slit widths of 0.5 and 2.0 mm, respectively. The excitation light was chopped at 17 Hz using an optical chopper. A He–Ne laser with a wavelength of 632.8 nm was utilized as a probe beam. The sample was immersed in n-hexane, which has a significant temperature dependence on the refractive index change (dn/dT).^28,29 A probe laser beam was passed close to the sample surface in a parallel direction (transverse PDS). The deflection of the probe laser beam by nonradiative recombination via sub-bandgap states with heat generation was detected by a position-sensitive detector (PSD) and lock-in amplifier. A 632.8-nm bandpass filter was installed before a PSD. The theoretical detection limit for α of transverse PDS was approximately 1 cm⁻¹ in the case of a 100-nm-thick sample.³⁰ 

Figure 1 shows the room-temperature PDS spectra of the Al_1−xIn_xN alloys and the GaN template without the Al_1−xIn_xN layer. The peak at approximately 2.0 eV originates from the excitation light. The S_PDS above 3.4 eV was saturated because of the band-to-band optical absorption of the GaN templates [from Eq. (1), the S_PDS becomes constant when $α 1 d 1+ α 2 d 2>1$]. The bandgaps of the Al_1−xIn_xN layers were larger than 3.4 eV (see Table I) and did not appear in the PDS spectra. Below 3.4 eV, the S_PDS increased by depositing the Al_1−xIn_xN layers. The S_PDS of the GaN template was the lowest among these samples. This indicated that $α 1 d 1> α 2 d 2$⁠. At photon energies less than 3.4 eV, $α 1 d 1+ α 2 d 2<1$ is valid. In this case, Eq. (1) can be approximated as $( α 1 d 1+ α 2 d 2) P 0ηκ( 1 − R 0)$⁠, and the difference in the S_PDS among the measured samples originates from the differences in the α of the Al_1−xIn_xN thin layers if $α 1 d 1> α 2 d 2$⁠. To obtain the SOA spectra of Al_1−xIn_xN layers, we estimated the α of the GaN template and Al_1−xIn_xN layers using OT, PDS, and SE measurements.

The α in the sub-bandgap region of a 350-μm-thick GaN substrate was directly obtained by OT measurements to complement the PDS spectra. Subsequently, the absorption spectra of the 2.2-μm-thick GaN template and GaN substrate obtained by PDS ${ α PDS ∼ S PDS / [ d ( 1 − R ) ]}$ were multiplied by a constant and scaled to those obtained by OT (α_OT). Here, R and d are the reflectivity of the n-hexane/GaN interface and the GaN film thickness, respectively. The refractive index was obtained using SE. Here, α_PDS≤ α_OT is valid because PDS only detects optical absorption leading to thermal emission, such as the nonradiative recombination with phonon emissions. When nonradiative recombination is the dominant energy relaxation process occurring after SOA (η ∼ 1), α_PDS coincides with α_OT. Figure 2 shows the sub-bandgap absorption spectra of a 2.2-μm-thick GaN template and a 350-μm-thick GaN substrate obtained by PDS and OT. Excellent agreement was observed between the α_PDS and α_OT of the GaN substrate, and α of the GaN substrate was estimated to be in the order of 10⁻¹cm⁻¹ in the range of 1.5–3.0 eV. This result indicates that η ∼ 1 is valid for the GaN substrate in the measured photon energy range. α_OT was approximately twice as large as that of HVPE-grown thick GaN with a similar electron density (1.3 × 10¹⁷cm⁻³).²² This was probably because of defect-related deep-state absorption, as observed in Ref. 22. The α_PDS of the GaN template was approximately two orders of magnitude larger than that of the GaN substrate, and η ∼ 1 is also assumed to be valid. The α_PDS of a 2.2-μm-thick GaN template was estimated to be of the order of 10¹cm⁻¹ in the range of 1.5–3.0 eV. This value also agrees well with those of MOCVD-grown c-plane GaN on sapphire substrates previously obtained by PDS.^19,20 Previous studies indicate that the hydrogen and carbon concentrations (∼10¹⁷cm⁻³) in MOCVD-grown c-plane GaN epitaxial layers on a sapphire substrate are one or two orders of magnitude higher than those in GaN layers grown on an HVPE bulk GaN.^36,37 These impurity concentrations tend to increase with increasing TDD (of the order of 10⁶cm⁻² for GaN epitaxial layers on HVPE bulk GaN and 10⁸–10⁹cm⁻² for those on a sapphire substrate).³⁶ Hydrogen-related deep states located at 2.74–2.8 eV from the conduction band minima (E_c) have been reported.^22,38,39 Several carbon-related deep states, for example, located at 1.35, 2.05, 3.0, and 3.28 eV from E_c also have been reported.^40–42 Pimptukar et al. reported that the α of ammonothermal bulk GaN is approximately two orders of magnitude larger than that of HVPE-grown bulk GaN at photon energies ranging from 2.6 to 3.3 eV. Hydrogenated gallium vacancies [(V_Ga-H)²⁻, (V_Ga-H)⁻] are expected as possible candidate sources of large SOA.²² In addition, the large SOA in a GaN template can be attributed to the point defects and/or complexes that function as nonradiative recombination centers (NRCs), such as gallium vacancy (V_Ga), N vacancy (V_N), and their complexes (V_Ga-V_N).^43,44 Chichibu et al. reported that the PL lifetime of HVPE-grown bulk GaN (TDD ∼10⁶cm⁻²) is approximately one order of magnitude longer than that of c-plan GaN epitaxial layers grown on a sapphire substrate; that is, the NRC density in HVPE-grown bulk GaN is approximately one order of magnitude lower than that in GaN on a sapphire substrate.⁴⁴ PDS also measures the SOA that leads to nonradiative carrier recombination. Thus, a high density of impurities, vacancy-type defects, and their complexes are expected to serve as the source of the large SOA observed in GaN grown on a sapphire substrate.

Figures 3(a) and 3(b) show the refractive index and absorption spectra of the Al_1−xIn_xN alloys obtained by SE analysis. α was obtained from the extinction coefficient. The tanΨ and cosΔ spectra were fitted by the dielectric function model called Adachi's critical point model⁴⁵ as shown in Figs. 3(c)–3(e). The effect of surface roughness was considered based on Bruggeman's effective medium approximation.²⁴ The details of the SE analyses are described elsewhere.^46,47 The bandgap energies, surface roughness (d_s), and broadening parameters of band-to-band transition (Γ) obtained by the spectral fitting are summarized in Table I. The accuracy of the bandgap energy values obtained using this dielectric function model was confirmed in our previous studies.^46,47 The sample with x = 0.185 exhibited the largest α in the sub-bandgap region among the measured samples. Samples with x = 0.114 and 0.144 showed lower α than x = 0.185, but those in the sub-bandgap region (<3.0 eV) were close to or below the detection limit of our SE system (∼3.0 × 10³cm⁻¹). Thus, the accuracies of these values were investigated by combining the PDS measurements. In our study, the best spectral fitting could not be achieved for the sample with x = 0.183 possibly because of the near-the-surface polycrystalline phase of Al_1−xIn_xN. In this series of samples, surface roughness estimated by atomic force microscopy (AFM) drastically increased when x exceeded approximately 0.17 because of the in-plane compressive strain.²³ The observed large surface roughness could be attributed to a columnar polycrystalline phase near the surface of Al_1−xIn_xN. The In composition of this polycrystalline upper layer (∼100 nm) is a few percent lower than that in the epitaxially grown underlying layer.²³ This same phenomenon was observed and reported by several groups.^48,49 Because of such a degraded upper layer in Al_1−xIn_xN, the SE spectra cannot be easily fitted by the same multilayer model used for the other samples. The surface roughness of x = 0.183 is the largest among the measured samples.²³ This indicates that the effect of the near-the-surface polycrystalline layer on the SE spectra was the largest among all the measured samples. The d_s of x = 0.185 estimated by SE is approximately three times larger than that of low In content samples (x = 0.114 and 0.144). Thus, we expected that the same dielectric function model (and/or multilayer model structure) used for the other samples could not adapted for x = 0.183. Here, the d_s's are approximately one order of magnitude larger than those estimated by AFM. It was reported that there is a linear relationship between the surface roughness obtained by AFM and SE, and those obtained by SE tended to be larger than those obtained by AFM.^24,26,50

The $α PDS$ of Al_1−xIn_xN alloys $( ∼ S { PDS / [ d 1 ( 1 − R 0 ) ] − α 2 d 2})$ are plotted in Fig. 4 and were scaled to the α of x = 0.185 obtained by SE. α₂ is the SOA spectrum of the GaN template obtained in Fig. 2. R₀ of x = 0.185 was used to obtain the α_PDS of x = 0.183. The α_PDS agreed well with that estimated by SE for the sample with x = 0.185. The relations of α among the samples obtained by PDS and SE also agreed well. This indicates that η ∼ 1 is also valid for these Al_1−xIn_xN samples. Here, in samples with x = 0.114 and 0.144, the α_PDS spectra deviate from the α estimated by SE. In SE analysis, optical absorption by deep energy states is not included in the dielectric function model. The spectral shape of α is determined by the dielectric function for the band-to-band optical transition. Thus, the slopes of the α derived from SE are similar among the samples. In a sample with x = 0.185, large spectral broadening (Γ in Table I) was obtained by the spectral fitting and it is the cause of the large SOA [the absorption spectrum tail extends to the sub-bandgap energy region as shown in Fig. 3(b)]. A large Γ was probably because of the indium-related near-band-edge (NBE) localized states observed in Al_1−xIn_xN alloys.^{11–15,36,37,51} Thus, the spectral shape of α_PDS agrees well with that estimated by SE in x = 0.185. In contrast, samples with x = 0.114 and 0.144 have wider bandgap energies and lower Γ than those with x = 0.185. This indicates that the effect of NBE localized states on α is smaller than with x = 0.185 in a measured photon energy range of PDS. Furthermore, αs in the sub-bandgap energy region of these samples are close to or below the detection limit of the SE system. Thus, absorption spectral shapes obtained by PDS are expected to be more accurate than by SE in samples of x = 0.114 and 0.144. By combining the PDS and SE, α of the SOAs in the range of 1.5–3.0 eV were estimated to be 0.6–7.0 × 10³cm⁻¹. Based on this result, the αd of 300-nm-thick Al_1−xIn_xN layers were estimated to be 0.21–2.3 × 10⁻¹ for 1.55–3.0 eV from the α_PDS. These are 2–10 times larger than those of the underlying GaN template (αd was estimated to be 0.88–1.1 × 10⁻²) below the GaN bandgap (∼3.0 eV), and $α 1 d 1> α 2 d 2$ was valid for all samples.

Room-temperature PL spectra of the Al_1−xIn_xN alloys and GaN templates are shown in Fig. 5(a). Broad emission peaks, which were shifted to the lower energy side with increasing x, located in the range of 3.4–4.5 eV were observed. The Stokes-like shift estimated from the difference between the bandgaps and those PL peak energies (Table I) is plotted in Fig. 5(b). The Stokes-like shifts were estimated to be 0.5–0.6 eV, which were comparable with those reported in previous works (most of them were in the range of 0.4–0.9 eV when x = 0.1–0.2).^{11–14,51–55} Thus, we conclude that these peaks originate from the NBE emission of Al_1−xIn_xN alloys. The NBE emissions of x = 0.183 and 0.185 overlapped with the PL peak of the GaN template. Spectral tails were observed at both high and low energy sides of the GaN NBE peak, and these tails tended to decay with increasing x; however, estimating the PL peak energies was challenging. Comparing the PL spectra of Al_1−xIn_xN alloys with the GaN template confirmed that broad emissions at approximately 2.2 eV originated from the GaN template. The PL spectral shapes were similar to the emission spectra reported in the previous works obtained by cathode luminescence (CL), and the distinct deep-state emissions of Al_1−xIn_xN were not observed.^51,56 Here, a part of the NBE emission of the Al_1−xIn_xN alloys was absorbed by the underlying GaN. The light extraction efficiency from the Al_1−xIn_xN layer to air for photon energy ranging from 3.5 to 5.0 eV (higher than GaN bandgap) was roughly estimated by the following equation considering the multiple reflection; $I 0 2( 1 − R s)( 1 + R i) ∑ m = 1 ∞ ( R s R i ) m − 1$⁠. To simplify the calculation, we only considered the light beam parallel to the c-axis (wave vector k//c) [see the inset of Fig. 5(c)]. I₀ is the initial PL intensity generated in the Al_1−xIn_xN layer and assumed to be constant (I₀ = 1). R_s and R_i are the reflectivity at the air/Al_1−xIn_xN and Al_1−xIn_xN/GaN interfaces, respectively. As shown in Fig. 5(c), approximately 30%–35% of the PL extracted from the Al_1−xIn_xN layer to air contributes to the signal. In this photon energy range, the difference among the light extraction efficiencies of the samples was estimated to be less than 5%. Thus, although, the comparison of the NBE emission intensity among the measured samples was not straightforward, the NBE emission of Al_1−xIn_xN alloys decreased with increasing x. Figure 6 shows the x-dependence of the integrated PDS signal intensities (I_PDS) of the Al_1−xIn_xN alloys. PDS signals in the range of 1.55–3.0 eV were integrated. Conversely, I_PDS increased with x; in particular, I_PDS drastically increased when x exceeded approximately 0.17, which is the lattice-matched composition to the underlying GaN/sapphire template. Here, light scattering by the polycrystalline phase and/or large surface roughness observed in x = 0.183 and 0.185 did not enhance the PDS signal. Recently, Li et al. reported that point defect densities, such as cation vacancy (V_III), divacancy (V_III–V_N), and their oxygen complexes that work as nonradiative recombination centers in Al_1−xIn_xN alloys grown on c-plane GaN drastically increased when x exceeded 0.17–0.18 because of the reduction in growth temperature and change of stress from tensile to compressive.^51,56 They also reported that the room-temperature CL intensity of Al_1−xIn_xN emission tended to decrease with increasing x.⁵⁶ Aluminum vacancy (V_Al) and its complex with oxygen substitution at nitrogen sites (V_Al–O_N) are expected to form deep energy states leading to SOA in AlN.^57,58 V_Al or (V_Al–O_N) and their V_N complexes were speculated to be the origins of the SOA at ∼2.9 eV.⁵⁸ An optical absorption band at ∼4.0 eV, with α ranging from 10¹ to 10³cm⁻¹, was observed when the oxygen density exceeded 10¹⁹ cm⁻³, and (V_Al–O_N) was expected to be the origin of this SOA feature of AlN.^57,58 Carbon-related SOA (α ∼ 50 cm⁻¹ when carbon concentration is 7 × 10¹⁷ cm⁻³) at ∼4.7 eV in AlN was also reported, and the carbon substituted at the nitrogen sites (C_N⁻) was expected to be a source of this SOA.⁵⁹ High densities of oxygen and carbon impurities (of the order of 10¹⁹ and 10¹⁷ cm⁻³, respectively) were incorporated in the Al_1−xIn_xN alloys grown under the same growth condition in the same MOCVD reactor.⁶⁰ These results suggest that V_Al and its oxygen complexes are also possible candidates that cause SOA, which increases with increasing x, in the Al_1−xIn_xN alloys. According to previous studies, NBE extended states are also formed by impurities such as O_N and C_N, point defects, and their complexes in Al_1−xIn_xN alloys,^56,61 and these NBE extended states can be plausible origins of the observed large Γ and large SOA in the x = 0.185 sample. The full width at half maxima (FWHM) of the (102) and (002) x-ray diffraction ω-rocking curves (XRCs) of our samples were almost constant.²³ Among the series of samples, the sample with x = 0.114 showed a significantly large FWHM value of (102), i.e., the largest edge-type TDD.²³ However, the sample showed the largest NBE emission intensity of PL and relatively low I_PDS among the measured samples. Thus, the increase in I_PDS in these samples primarily originated from the sub-bandgap states related to the impurities, vacancy-type defects, and their complexes rather than the threading dislocations.

The SOA processes in 300-nm-thick Al_1−xIn_xN alloys grown on a c-plane GaN/sapphire template were investigated using PDS, SE, and PL measurements. The dominant energy relaxation processes occurring after SOA in Al_1−xIn_xN alloys are thermal emissions, such as nonradiative recombination with phonon emissions. The α for the SOA were estimated to be 0.6–7.0 × 10³cm⁻¹ by combining PDS and SE. The SOAs drastically increased when x exceeded approximately 0.17, probably originating from the sub-bandgap states (and/or NBE extended sates) formed by impurities, vacancy-type defects, and their complexes. Using PDS, the SOA of thinner and lower α Al_1−xIn_xN alloys can also be analyzed by adjusting the sample structure.

This work was partly supported by the Grants-in-Aid for Young Research (No. 20K15182), Scientific Research C (No. 22K04956), Japan Society for Promotion of Science [JSPS KAKENHI], MEXT “Program for research and development of next-generation semiconductor to realize energy-saving society” Program Grant No. JPJ005357, Naito Research Fund, Nitto Foundation, and Toyota Riken scholar.

The authors have no conflicts to disclose.

Daichi Imai: Conceptualization (equal); Data curation (equal); Formal analysis (lead); Funding acquisition (equal); Investigation (lead); Methodology (lead); Supervision (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Yuto Murakami: Data curation (equal); Formal analysis (equal); Investigation (equal); Validation (equal). Hayata Toyoda: Data curation (equal); Formal analysis (equal); Investigation (equal); Validation (equal). Kouki Noda: Data curation (equal); Formal analysis (supporting); Investigation (supporting). Kyosuke Masaki: Data curation (supporting); Investigation (supporting). Kazutoshi Kubo: Data curation (supporting); Investigation (supporting). Mayu Nomura: Formal analysis (supporting); Investigation (supporting). Makoto Miyoshi: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Resources (equal); Supervision (equal). Takao Miyajima: Conceptualization (supporting); Investigation (supporting); Methodology (supporting); Supervision (equal). Tetsuya Takeuchi: Conceptualization (equal); Funding acquisition (equal); Investigation (supporting); Resources (supporting); Supervision (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.