Evaluation of internal quantum efficiency and stimulated emission characteristics in AlGaN-based multiple quantum wells

Temperature- and EPD-dependent PL spectroscopy was performed to estimate the IQE. ^33,34) We evaluated the PL efficiency as the PL intensity per unit EPD by dividing the integrated PL intensity by the corresponding EPD. PL efficiency was obtained as a function of EPD. The maximum PL efficiency at low temperature was assumed to be 100% of the IQE, and the normalized PL efficiency was taken as the IQE. Figure 1 shows the EPD dependence of the estimated IQE at 10, 100, 200, and 300 K for the UV-A MQW. At 10 K, the estimated IQE showed a plateau around the peak of the efficiency curve. The dependence of the estimated IQE on the plateau indicated that the PL intensity increased linearly with EPD. In this scenario, NRCs were assumed to be nearly saturated. This result indicated that the maximum value of the estimated IQE reached nearly 100% at 10 K. Therefore, the estimated IQE agreed well with the absolute IQE value, and the estimated maximum IQE value at 300 K was about 30%.

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At lower EPDs, the estimated IQE increased as EPD was increased, even at 10 K, indicating that nonradiative recombination occurred, even at lower temperatures. The increase in IQE at lower EPDs reflected the filling of NRCs by photogenerated excitons. Conversely, at higher EPDs, the estimated IQE decreased as EPD was increased at all temperatures, which is called efficiency droop. Various mechanisms of efficiency droop have been proposed, ^44–52) but its cause remains unknown and there is currently no analytical model for this phenomenon. However, efficiency droop had only a small effect on the analysis of the initial IQE increase.

A rate equation model based on the radiative and nonradiative recombination processes of excitons was used to analyze the efficiency curves. ^39,40,53) The model assumes that the NRCs are saturated if they capture enough excitons and that the probability of radiative recombination is independent of the exciton density. The temporal evolution of exciton density in the model is described by the following rate equations:

$$\begin{eqnarray}&&\begin{array}{c}\frac{dn}{dt}=G-{W}_{{\rm{r}}}n-{W}_{{\rm{t}}{\rm{r}}}\left(D-N\right)n,\end{array}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&\begin{array}{c}\frac{dN}{dt}={W}_{{\rm{t}}{\rm{r}}}\left(D-N\right)n-{W}_{{\rm{n}}{\rm{r}}}N.\end{array}\end{eqnarray} \tag{ 2 }$$

Here, n is the density of the photogenerated excitons, N is the density of the excitons captured by NRCs, and D is the total density of NRCs. ${W}_{{\rm{r}}}$ is the radiative recombination rate of excitons, ${W}_{{\rm{nr}}}$ is the nonradiative recombination rate of excitons at NRCs, and ${W}_{{\rm{tr}}}\left(D-N\right)$ is the capture rate of excitons by NRCs. G is the generation rate of excitons. Solving these equations in the steady state, the IQE $\left({\eta }_{\mathrm{int}}={W}_{{\rm{r}}}n/G\right)$ is described as

$$\begin{eqnarray}&&\begin{array}{c}{\eta }_{{\rm{i}}{\rm{n}}{\rm{t}}}=\displaystyle \frac{1}{1+\tfrac{\alpha }{{I}_{{\rm{P}}{\rm{L}}}+\beta }},\end{array}\end{eqnarray} \tag{ 3 }$$

where ${I}_{{\rm{P}}{\rm{L}}}=k{W}_{{\rm{r}}}n$ is the PL intensity. Furthermore, $\alpha =k{W}_{{\rm{nr}}}D$ and $\beta =k{W}_{{\rm{r}}}{W}_{{\rm{nr}}}/{W}_{{\rm{tr}}}$ are the fitting parameters, where $k$ is a constant determined by the LEE of the samples and the detection efficiency of the experimental equipment. Therefore, parameters $\alpha$ and $\beta$ are scaled by the PL intensity.

The estimated IQE was plotted against the spectrally integrated photoluminescence (SIPL) intensity to analyze the IQE curves using Eq. (3). Figure 2 shows the SIPL intensity dependence of the estimated IQE at 10, 100, 200, and 300 K for the UV-A MQWs. The SIPL intensity was normalized so that the SIPL intensity divided by the EPD (units of kW cm⁻²) was 100 when the estimated IQE was 100%. The fits obtained using Eq. (3) (solid lines) described the low-intensity side (below a SIPL intensity of 10²) of the estimated IQE curves well at all temperatures. These results demonstrated that the increase in IQE at low carrier densities arises from the filling of NRCs. Furthermore, at 10 K, the fits agreed well with the experimental data up to the estimated IQE curve peak, indicating that at 10 K, the maximum value of IQE reached almost 100%.

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Parameters $\alpha$ and $\beta$ as a function of temperature were obtained from the fitting analysis. Figure 3(a) shows the temperature dependence of parameter $\alpha \left(=k{W}_{{\rm{nr}}}D\right).$ This parameter increased with temperature, demonstrating that the nonradiative recombination probability at NRCs, ${W}_{{\rm{n}}{\rm{r}}},$ increased with temperature; thus, the nonradiative recombination of excitons at NRCs was thermally activated.

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Because parameter $\beta \left(=k{W}_{{\rm{n}}{\rm{r}}}{W}_{{\rm{r}}}/{W}_{{\rm{t}}{\rm{r}}}\right)$ is a function of probabilities ${W}_{{\rm{r}}},$ ${W}_{{\rm{t}}{\rm{r}}},$ and ${W}_{{\rm{n}}{\rm{r}}},$ we could not evaluate the temperature dependence of these probabilities based on the temperature dependence of parameter $\beta$ alone. Consequently, ratio $\alpha /\beta \left(={W}_{{\rm{t}}{\rm{r}}}D/{W}_{{\rm{r}}}\right)$ was evaluated as a function of temperature. Figure 3(b) shows the temperature dependence of ratio $\alpha /\beta .$ The ratio increased slightly with temperature below 100 K and increased rapidly above 100 K. Similar behavior has been observed in In_x Ga_1−x N-based systems and is caused by exciton delocalization. ^39,40) It is predicted that when the excitons are localized at potential minima, where the excitons are assumed to be confined to a zero-dimensional potential, the radiative recombination probability, ${W}_{{\rm{r}}},$ is independent of temperature. ⁵⁴⁾ In contrast, the radiative recombination lifetime, ${\tau }_{{\rm{R}}}\left(={{\rm{W}}}_{{\rm{r}}}^{-1}\right),$ of extended excitons in two-dimensional systems is expected to increase linearly with temperature. ^54–56) The rapid increase in $\alpha /\beta$ above 100 K therefore primarily reflected the decrease in ${W}_{{\rm{r}}}$ caused by the delocalization of excitons with increasing temperature.

The small increase in $\alpha /\beta$ below 100 K was explained by the increase in probability ${W}_{{\rm{tr}}},$ which was the product of the capture cross-section of NRCs and the thermal velocity of excitons, and we expected that the capture cross-section would be independent of temperature. Thus, the increase in the thermal velocity of excitons caused the small increase in $\alpha /\beta .$

Figure 4 shows PL lifetimes plotted against temperature for the UV-A MQWs at excitation energy densities (EEDs) of 0.002, 0.02, 0.2, and 2 μJ cm⁻². We obtained the PL lifetimes by fitting the double-exponential function, $I\left(t\right)={I}_{{\rm{f}}}\exp \left(-t/{\tau }_{{\rm{f}}}\right)+{I}_{{\rm{s}}}\exp \left(-t/{\tau }_{{\rm{s}}}\right),$ to the PL decay profile, which was not well fitted with a single exponential function (inset in Fig. 4). The PL intensity of the faster decay component decayed more than one order of magnitude; thus, we estimated that the PL lifetime was the faster decay time of the double-exponential function (${\tau }_{{\rm{f}}}$). At all EEDs, the PL lifetime decreased as temperature was increased. The time and spectrally integrated photoluminescence (TIPL) intensity decreased as the temperature was increased, which corresponded to the decrease in IQE ($\eta$) with increasing temperature. Because the PL lifetime (${\tau }_{{\rm{P}}{\rm{L}}}$) and the nonradiative recombination lifetime (${\tau }_{{\rm{NR}}}$) are related as ${\tau }_{{\rm{P}}{\rm{L}}}={\tau }_{{\rm{n}}{\rm{r}}}\left(1-\eta \right),$ ^57,58) we can see that the decrease in the PL lifetime was caused by the decrease in the nonradiative recombination lifetime.

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The temperature dependence of radiative and nonradiative recombination dynamics are evaluated by estimating the radiative and nonradiative recombination lifetimes from the temperature dependence of the TIPL intensity and PL lifetime. The radiative and nonradiative recombination lifetimes are ${\tau }_{{\rm{R}}}={\tau }_{{\rm{P}}{\rm{L}}}/\eta$ and ${\tau }_{{\rm{NR}}}={\tau }_{{\rm{P}}{\rm{L}}}/\left(1-\eta \right),$ respectively. ^57,58) The IQE was obtained by a method similar to that in Sect. 3.1. The PL efficiency was defined as the TIPL intensity divided by the corresponding EED, and we assumed that the maximum PL efficiency at 10 K was 100% of the IQE. Thus, the IQE at 10 K was estimated to be 100% at an EED of 0.02 μJ cm⁻².

The temperature dependence of the radiative recombination lifetime at EEDs of 0.002, 0.02, 0.2, and 2 μJ cm⁻² is shown in Fig. 5(a). Below about 100 K, the radiative recombination lifetime was independent of temperature at all EEDs. The temperature-independence of the radiative recombination lifetime is a characteristic of localized (zero-dimensional) excitons. ⁵⁴⁾ Thus, these results showed that the majority of excitons were localized below 100 K. At temperatures above 100 K, the radiative recombination lifetime at all the EEDs increased with temperature almost linearly $\left({\tau }_{{\rm{R}}}\propto {T}^{0.9 \tilde 1.2}\right).$ Because this linear increase is characteristic of extended (two-dimensional) excitons, ^54–56) the excitons became increasingly delocalized as the temperature was increased above 100 K.

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The temperature dependence of the nonradiative recombination lifetime at EEDs of 0.002, 0.02, 0.2, and 2 μJ cm⁻² is shown in Fig. 5(b). The nonradiative recombination lifetime decreased monotonically with increasing temperature at all EEDs. The temperature dependence of the nonradiative recombination lifetime was analyzed by using a simple model of the nonradiative recombination process, in which NRCs capture the delocalized excitons. ^34,59) In the model, the reciprocal of the nonradiative recombination lifetime is written as

$$\begin{eqnarray}&&\begin{array}{c}{\tau }_{{\rm{N}}{\rm{R}}}^{-1}=\sigma {v}_{{\rm{t}}{\rm{h}}}D\exp \left(-\displaystyle \frac{{T}_{0}}{T}\right)=A\sqrt{T}\exp \left(-\displaystyle \frac{{T}_{0}}{T}\right),\end{array}\end{eqnarray} \tag{ 4 }$$

where $\sigma$ is the capture cross-section of NRCs, ${v}_{{\rm{t}}{\rm{h}}}$ is the thermal velocity of excitons, $D$ is the density of NRCs, and ${T}_{0}$ is the degree of localization at a given temperature. Because the thermal velocity is proportional to $\sqrt{T},$ coefficient $\sigma {v}_{{\rm{th}}}D$ can be written as $A\sqrt{T},$ where $A$ is a constant. Hence, the reciprocal of the nonradiative recombination lifetime is expressed by the right-hand side of Eq. (4). The results of the fit obtained using Eq. (4) are shown as solid lines in Fig. 5(b). The model described by Eq. (4) is based on the exciton delocalization process; therefore, the experimental data were fitted well at temperatures above 100 K because the excitons were assumed to be delocalized in this temperature range. The solid lines agreed well with the nonradiative recombination lifetimes measured for temperatures above 100 K at all EEDs. These results suggested that the simple model in Eq. (4) could explain the nonradiative recombination process of extended (delocalized) excitons. We interpreted the disagreement between the solid lines and the experimental data at low temperatures as reflecting the nonradiative recombination process of localized excitons. More work is required to reveal the mechanism of the nonradiative recombination process of localized excitons.

According to the fitting, parameter A was estimated to be 0.27, 0.21, 0.21, and 0.20 ns⁻¹ K⁻¹ at 0.002, 0.02, 0.2, and 2 μJ cm⁻², respectively, and ${T}_{0}$ was estimated to be 120, 120, 108, and 20 K at 0.002, 0.02, 0.2, and 2 μJ cm⁻², respectively. The filling of NRCs explained the decrease in parameter A because the effective density of NRCs decreased as the density of photogenerated excitons increased. The decrease in parameter ${T}_{0}$ was also explained by the decrease in exciton localization owing to the localized states filling as the density of photogenerated excitons increased.

First, we discuss the temperature dependence of parameter ratio $\alpha /\beta \left(={W}_{{\rm{t}}{\rm{r}}}D/{W}_{{\rm{r}}}\right).$ Ratio $\alpha /\beta$ represents the probability that the excitons are captured by NRCs in addition to the radiative recombination. Therefore, a ratio of less than 1 indicates that radiative recombination is dominant, whereas a ratio of more than 1 indicates that nonradiative recombination is dominant. Figure 6 shows ratio $\alpha /\beta$ plotted against temperature. Open squares indicate ratio $\alpha /\beta$ calculated with the rate equation. The ratio was greater than 1 at temperatures above 100 K, which showed that the nonradiative recombination process was dominant even at 100 K. To improve the IQE, it is necessary to decrease the ratio at room temperature. Consequently, the temperature dependence of $\alpha /\beta$ indicated that the IQE could be increased by suppressing the decrease in the radiative recombination probability and reducing the NRC density. Thus, exciton localization should help to increase the IQE.

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Next, we compare the analyses of the efficiency curves and the recombination dynamics. Parameter ratio $\alpha /\beta$ is expressed as $\alpha /\beta ={W}_{{\rm{tr}}}D/{W}_{{\rm{r}}},$ and probability ${W}_{{\rm{tr}}}$ is the product of the NRC capture cross-section and the thermal velocity of excitons. Thus, the parameter ratio $\alpha /\beta$ represents the same physical quantity as parameter $A\sqrt{T}{\tau }_{{\rm{R}}}.$ The closed symbols in Fig. 6 show the temperature dependence of parameter $A\sqrt{T}{\tau }_{{\rm{R}}}$ at EEDs of 0.002, 0.02, 0.2, and 2 μJ cm⁻². At all EEDs, the behavior of $A\sqrt{{\rm{T}}}{\tau }_{{\rm{R}}}$ agreed with that of parameter ratio $\alpha /\beta ,$ but particularly at 0.02 μJ cm⁻², at which the IQE was estimated to be 100% at low temperatures, parameter $A\sqrt{T}{\tau }_{{\rm{R}}}$ agreed quantitatively with $\alpha /\beta .$ The quantitative agreement demonstrated that the rate equation analysis based on radiative and nonradiative exciton recombination, including the filling of NRCs, was valid for Al_x Ga_1−x N-based UV-A MQWs and that exciton recombination processes should be considered when analyzing the IQE.

Finally, we discuss the EED dependence of parameter $A\sqrt{T}{\tau }_{{\rm{R}}}.$ Parameter $A\sqrt{T}{\tau }_{{\rm{R}}}$ decreased as the EED was increased and this decrease was larger at higher temperatures (Fig. 6). Because parameter $A$ decreased only slightly from 0.27 to 0.21 as the EED was increased from 0.002 to 2 μJ cm⁻², the decrease in parameter $A\sqrt{T}{\tau }_{{\rm{R}}}$ primarily corresponded to the decrease in radiative recombination lifetime ${\tau }_{{\rm{R}}}$ [Fig. 5(a)]. The decrease in ${\tau }_{{\rm{R}}}$ was larger at higher temperatures, similar to the decrease in $A\sqrt{T}{\tau }_{{\rm{R}}}.$ In other words, the increase in EED slowed the increase in ${\tau }_{{\rm{R}}}$ with temperature. Because the increase in ${\tau }_{{\rm{R}}}$ was caused by the exciton delocalization, the exciton delocalization was suppressed with increasing exciton density. A plausible explanation for this result was that excitons were redistributed as the EED was increased. At lower EEDs, the excitons remained in the local potential minima. With increasing exciton density, the local potential minima were filled and the excitons traveled further to reach vacant localized states. Although the long-distance redistribution of excitons populated various localized states, the exciton population of the lowest localized states increased substantially because the probability of exciton delocalization from the deeper localized states was low. Therefore, the rate of exciton delocalization was predicted to decrease with increasing EED. A similar explanation has been proposed for Al_x Ga_1−x N epilayers, ⁶⁰⁾ In_x Ga_1−x N/GaN quantum wells, ⁶¹⁾ and InAs/AlAs quantum dots. ⁶²⁾

In the following section, we assess the optical properties of UV-C MQWs. Figure 7 shows the temperature dependence of the PL spectra for the UV-C1 MQWs at an EPD of 60 kW cm⁻². The PL spectra were measured with a back-scattering configuration. At 10 K, the PL peak from the well layers was observed around 283 nm. The PL peak at about 266 nm arose from the emission from the barrier layer and/or OCL. The wavelength of both PL peaks shifted toward the longer-wavelength side as the temperature was increased. The Bose–Einstein expression describes the temperature dependence of the PL peak wavelength; ⁶³⁾ thus, the PL redshift should reflect the temperature-dependent decrease of the bandgap. Even at 750 K, a clear PL peak from the well layers was visible around 295 nm.

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We evaluated the IQE to investigate the thermal stability of the radiative recombination process. Figure 8 shows the temperature dependence of the estimated IQE for the UV-C1 MQWs as a function of EPD. The estimated IQE was normalized to the maximum value at 10 K. The estimated IQEs from 10 to 300 K and from 300 to 750 K were measured using different cryostats and calibrated with values measured at 300 K. To prevent sample damage, the PL was not measured from 350 to 750 K at higher EPDs. At all temperatures, the estimated IQE increased and subsequently decreased as the EPD was increased. The initial increase in IQE at 10 K showed that the nonradiative recombination process occurred even at 10 K. However, at lower EPDs, the efficiency curve remained almost unchanged between 10 and 50 K, suggesting that the majority of nonradiative recombination pathways were inactive below 50 K. Hence, the assumption that the maximum estimated IQE at 10 K was almost 100% was also appropriate.

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The maximum IQE was estimated as 53% at 300 K and 16% at 750 K (Fig. 8). The well-resolved PL spectrum and the high IQE at 750 K showed that the radiative recombination was effective even at 750 K, which demonstrated that the radiative recombination probability was high and nonradiative recombination was well-suppressed. Thus, the excitonic optical transition was dominant in the radiative recombination, even at 750 K, owing to the stability of the excitons in Al_x Ga_1−x N-based UV-C MQWs at these high temperatures. ^22,64)

Figure 9 shows the EPD dependence of the PL spectra for UV-C1 MQWs at (a) 10 and (b) 295 K in the edge-emission configuration. Even though the edge-emission configuration was used, the PL signal was collected from the sample surface as well as from the sample edge. At lower EPDs, only spontaneous emission (SPE) with interference ripples was observed at both temperatures. As the EPD was increased, the narrow line from the STE appeared at the shorter-wavelength side of the SPE at both temperatures, and the estimated PL peak wavelengths of the STE were 277 nm at 10 K and 274 nm at 295 K. Figures 9(c) and 9(d) show the EPD dependence of the integrated PL intensity at 10 and 295 K, respectively. At both temperatures, the integrated PL intensity increased linearly as the EPD was increased to the threshold EPD (P_th), whereas above P_th, the integrated PL intensity increased superlinearly with the EPD. The superlinear increase in the integrated PL intensity supported our attribution of the narrow line to the STE. Thus, we estimated the threshold EPD for STE to be approximately 13 kW cm⁻² at 10 K and 69 kW cm⁻² at 295 K.

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Figure 10(a) shows the temperature dependence of the threshold EPD for STE. The increase in threshold EPD with increasing temperature was small from 10 to 200 K and from 250 to 295 K, whereas the increase was rapid between 200 and 250 K. The threshold EPDs were 32 kW cm⁻² at 200 K and 59 kW cm⁻² at 250 K. The temperature dependence of the peak wavelength for the STE spectra around the threshold EPD is shown in Fig. 10(b). Although the peak wavelength remained almost constant as the temperature was increased from 10 to 200 K, the PL peak wavelength shifted suddenly at the same time as the rapid increase in the threshold EPD occurred between 200 and 250 K. Thus, we focused on the STE spectra near the threshold EPD. Figures 11(a) and 11(b) show the PL spectra near the threshold EPDs at 250 and 200 K, respectively. The PL spectrum at 200 K (blue line) contained a narrow peak, whereas the PL spectrum at 250 K (red line) contained a broad peak. The difference in the STE spectra reflected the change in the shape of the optical gain spectrum between 200 and 250 K. These results indicated that the STE mechanism changed between 200 and 250 K.

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To determine the mechanism of the STE as a function of temperature, we estimated the Mott transition density of excitons. The Mott transition density for Al_0.45Ga_0.55N was estimated as ${n}_{{\rm{M}}}$ ∼ 3 × 10¹⁸ cm⁻³, from ${n}_{{\rm{M}}}=1/\left\{4\pi {\left({a}_{{\rm{e}}{\rm{x}}}{r}_{{\rm{s}}}\right)}^{3}/3\right\},$ where ${a}_{{\rm{e}}{\rm{x}}}$ is the exciton Bohr radius and ${r}_{{\rm{s}}}$ is a dimensionless quantity. To estimate the Mott transition density, ${a}_{{\rm{e}}{\rm{x}}}$ was estimated by linear interpolation between the effective masses of electrons and holes, the dielectric constant between GaN and AlN, and using ${r}_{{\rm{s}}}=2.$ ⁶⁵⁾ The threshold EPD of 59 kW cm⁻² at 250 K corresponded to a carrier density of roughly 7 × 10¹⁸ cm⁻³. The carrier density was estimated from the EPD assuming that the absorption coefficient was 10⁵ cm⁻¹ and the decay time constant was 1 ns. Thus, the threshold carrier densities for the STE at ≥250 K were more than twice the Mott transition density, whereas those at ≤200 K were less than or near the Mott transition density. The temperature dependence of the STE spectra and the threshold EPD suggested that the STE at 250 K and above resulted from degenerate EHP. Furthermore, excitonic transitions were likely involved in the STE at 200 K and below. Consequently, we proposed that between 200 and 250 K, the mechanism of optical gain formation changed from excitonic transitions to EHP. ⁴²⁾ It was unclear why the STE appeared at the higher-energy side of the SPE, although the exciton localization may have contributed to this behavior. ⁶⁶⁾

In III-nitride semiconductors, the exciton-related mechanisms of optical gain formation have mainly been reported for GaN epilayers ^67–69) and In_x Ga_1−x N-based MQWs ⁶⁶⁾ and epilayers, ⁷⁰⁾ whereas excitonic STE has not been reported in Al_x Ga_1−x N-based systems. Even though the mechanism of optical gain formation is unknown, we demonstrated that STE occurred from excitonic processes in Al_x Ga_1−x N-based UV-C MQWs. The threshold carrier density of the excitonic STE was one or two orders of magnitude lower than that of the EHP-based STE. The excitonic gain should help to decrease the threshold current density of LDs.

In Sects. 3.7 and 3.8, we report the results of our latest experiments. Recently, we performed optically pumped STE measurements for a UV-C2 MQW that had an optimally positioned quantum well region. The UV-C2 MQW structure was sandwiched between the upper and bottom Al_0.50Ga_0.50N OCLs. The sample was also grown on a c-plane sapphire substrate following deposition of a 4 μm thick AlN layer and a 2 μm thick Al_0.63Ga_0.37N cladding layer. The MQW structure consisted of three periods of 2 nm thick Al_0.32Ga_0.68N well layers separated by 7 nm thick Al_0.50Ga_0.50N barrier layers. The thicknesses of the upper and bottom OCLs were 85 and 40 nm, respectively. All the layers were intentionally undoped.

Figure 12 shows the EPD dependence of the PL spectra at 295 K for the UV-C2 MQWs. At EPDs less than 11 kW cm⁻², the SPE from the well layers dominated the spectra. The SPE had a peak wavelength around 274 nm. A narrow line corresponding to the STE emerged on the shorter-wavelength side of the SPE and increased superlinearly as the EPD was increased. The peak wavelength and linewidth of the STE were estimated to be 271.6 and 1.76 nm (29.5 meV), respectively. The integrated PL intensity increased linearly below the threshold EPD and superlinearly above the threshold EPD (inset in Fig. 12). For the STE, the threshold EPD was estimated to be 26 kW cm⁻², which was about 2.6 times smaller than the threshold EPD for the UV-C1 MQWs (see Sect. 3.6).

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Figure 13(a) shows the temperature dependence of the peak shift of the STE spectrum relative to the peak at 10 K for the UV-C2 MQWs near the threshold EPD, indicated by the closed circles. Below 200 K, the position of the STE peak varied slightly, and then shifted toward the lower-energy values as the temperature was increased further. Because the peak wavelength of the SPE exhibited a similar trend, the peak shift was attributed to the temperature-dependent decrease of the bandgap. The linewidth (FWHM) of the STE spectrum for the UV-C2 MQWs around the threshold EPD as a function of temperature is shown by the closed circles in Fig. 13(b). The linewidth of the STE broadened gradually and showed no rapid change as the temperature was increased. The temperature dependence of the peak shift and linewidth showed no major changes in the shape of the optical gain spectrum as the temperature was increased, suggesting that the mechanism of optical gain formation was unchanged as the temperature was increased to 295 K. The open squares in Figs. 13(a) and 13(b) indicate the peak shift and linewidth, respectively, of the STE spectrum for the UV-C1 MQWs. ⁴²⁾ A sudden blue shift and rapid broadening of the STE spectrum were observed simultaneously between 200 and 250 K, which probably reflected the change in the mechanism of optical gain formation from the excitonic transition process to EHP recombination between 200 and 250 K. Therefore, the temperature dependence of the peak shift and linewidth for the UV-C2 MQWs suggested that excitonic processes contributed to the optical gain formation up to room temperature.

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We examined the temperature dependence of the threshold EPD for the STE. Figure 14 shows the temperature dependence of the threshold EPD and threshold carrier density for the STE for the UV-C2 MQWs, indicated by the closed circles. At 10 K, the estimated threshold EPD was 11 kW cm⁻², which was similar to the value at 10 K obtained for the UV-C1 MQWs (13 kW cm⁻²). As the temperature was increased, the threshold EPD showed almost no change up to 200 K and increased only slightly above 200 K. At 295 K, the threshold EPD was estimated to be 26 kW cm⁻². The threshold EPDs for the UV-C1 MQWs are shown by the open squares in Fig. 14 for comparison. ⁴²⁾ The threshold EPD for the UV-C1 MQW increased suddenly in the temperature range of 200–250 K, which probably reflected the change in the mechanism of optical gain formation from the excitonic transition process to EHP recombination. This observation confirmed that the optical gain formation in the UV-C2 MQWs resulted from the excitonic transition process at room temperature.

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The threshold carrier density at 295 K was estimated from the threshold EPD to be 3.6 × 10¹⁸ cm⁻³, which was close to the Mott transition density of approximately 3 × 10¹⁸ cm⁻³. The threshold carrier densities below or close to the Mott transition density indicated that the excitons were stable around the threshold carrier density, and thus the STE at room temperature was excitonic in origin for the UV-C2 MQWs.

Recently, we performed optically pumped STE measurements above room temperature up to 550 K for a UV-C3 MQW. The UV-C3 MQW structure was sandwiched between the upper and bottom Al_0.50Ga_0.50N OCLs. The sample was also grown on a c-plane sapphire substrate following deposition of a 4 μm thick AlN layer and a 2 μm thick Al_0.63Ga_0.37N cladding layer. The MQW structure consisted of three periods of 2 nm thick Al_0.32Ga_0.68N well layers separated by 7 nm thick Al_0.50Ga_0.50N barrier layers. The thickness of the upper and bottom OCLs was 62 nm. All the layers were intentionally undoped.

Figure 15(a) shows the EPD dependence of the PL spectra at 295 K for the UV-C3 MQWs. At EPDs of 4.5 and 11 kW cm⁻², the spectra were governed by SPE from the well layers. The peak wavelength of the SPE was located around 281 nm. With increasing EPD, a narrow line due to the STE appeared at the shorter-wavelength side of the SPE peak. The peak wavelength of the STE was estimated to be 279 nm and the FWHM was estimated to be 18.5 meV. Figure 15(b) shows the EPD dependence of integrated PL intensity at 295 K. The integrated PL intensity increased linearly with EPD up to the threshold EPD, and the superlinear increase in the integrated PL intensity occurred above the threshold EPD. The threshold EPD was estimated to be 18.5 kW cm⁻². According to the previous reports, the minimum value of the threshold EPD for STE was 3 kW cm⁻² for Al_x Ga_1−x N-based UV-C MQWs on AlN bulk substrates. ⁷¹⁾ On the other hand, the minimum value was 61 kW cm⁻² on sapphire substrates. ⁷²⁾ Therefore, the threshold EPD of 18.5 kW cm⁻² for STE is the lowest value reported to date for Al_x Ga_1−x N-based UV-C MQWs on sapphire substrates.

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To evaluate the thermal stability of the formation process of optical gain, we performed temperature-dependent STE measurements. Figure 16 shows the EPD dependence of the PL spectra at (a) 400, (b) 450, (c) 500, and (d) 550 K. At each temperature, the broad SPE peak was observed at lower EPDs and the narrow line of the STE appeared on the shorter-wavelength side of the SPE peak with increasing EPD. In particular, the STE was clearly visible, even at 550 K. The separations between the STE and SPE peaks at 500 and 550 K were about twice those at 450 K and below. Figure 17(a) shows the temperature dependence of the peak energy of the STE and the SPE. The closed circles and triangles indicate the peak energies of the STE (E_STE) and the SPE (E_SPE), respectively. The E_SPE shifted toward the lower-energy side with increasing temperature, which reflected the temperature-dependent shrinkage of the bandgap energy. In contrast, E_STE was blue shifted with increasing temperature from 450 and 500 K. The closed squares in Fig. 17(a) show the energy separation between E_STE and E_SPE as a function of temperature. Although the energy separation varied slightly, it was almost independent of temperature up to 450 K, and then increased rapidly between 450 and 500 K. Thus, the peak of the optical gain spectrum shifted suddenly with increasing temperature from 450 to 500 K. Figure 17(b) shows the FWHM of the STE peak around the threshold EPD as a function of temperature. The FWHM of the STE peak was almost unchanged with increasing temperature up to 450 K, and then the STE peak broadened above 450 K. Consequently, the optical gain spectrum broadened significantly above 450 K. These observations unambiguously indicated that the STE features changed between 450 and 500 K. Thus, the origin of STE at 500 K and above was different from that at 450 K and below, and the mechanism of the optical gain formation changed between 450 and 500 K.

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Figures 18(a) and 18(b) show the temperature dependence of the threshold EPD for STE on a linear scale and a logarithmic scale, respectively. The closed squares indicate the threshold EPD for the UV-C3 MQWs. The results for the UV-C1 and UV-C2 MQWs are also shown for comparison by closed triangles and circles, respectively. The threshold EPDs up to 500 K were estimated from the EPD dependence of the integrated PL intensity. Although the threshold EPD at 550 K could not be estimated from the integrated PL intensity, it was estimated from the spectral feature in Fig. 16(d) as between 124 and 143 kW cm⁻². The threshold EPD increased slightly with increasing temperature from 295 to 450 K, and then a rapid increase occurred above 450 K [Fig. 18(a)]. We observed the rapid increase in the threshold EPD with increasing temperature above 200 K for the UV-C1 MQWs [closed triangles, Fig. 18(a)], which was explained by a change in the mechanism of optical gain formation. ⁴²⁾ Moreover, the slope of the threshold EPD on the logarithmic scale above 500 K was steeper than that below 450 K [Fig. 18(b)]. Because the slope of the threshold EPD depended on the thermal stability of STE, the change in the slope indicated a change in the thermal stability of the optical gain formation process and implied a change in the mechanism of the optical gain formation. Therefore, the temperature dependence of the threshold EPD supported the change in the mechanism of optical gain formation between 450 and 500 K.

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To discuss the temperature dependence of the mechanism of the optical gain formation, we calculated the Mott transition density of excitons and compared it with the estimated value of the threshold carrier density. In Figs. 18(a) and 18(b), the Mott transition density of $3\times {10}^{18}$ cm⁻³ for Al_0.32Ga_0.68N is shown by the dotted line and the right-hand y-axes indicate the threshold carrier density estimated from the threshold EPD. The threshold carrier densities at 500 and 550 K were estimated to be $8\times {10}^{18}$ and $1.5\mbox{--}1.7\times {10}^{19}$ cm⁻³, respectively. These values were more than twice the Mott transition density. Thus, the excitonic transition processes may not contribute to the optical gain formation at 500 K and above. The optical gain formation at 500 K and above originated from the degenerate EHP. In contrast, the threshold carrier density at 450 K was estimated to be $4\times {10}^{18}$ cm⁻³, and thus the threshold carrier densities at 450 K and below were close to or less than the Mott transition density. Consequently, the excitonic transition processes can contribute to the optical gain formation at 450 K and below. The exciton resonance has been observed up to 750 K in the PL excitation spectra of Al_x Ga_1−x N-based MQWs with an emission wavelength of a similar spectral range at the same EPD. ²²⁾ Therefore, the excitonic transition processes were involved with the optical gain formation at 450 K and below.

Next, we evaluate the thermal stability of the STE from the temperature dependence of the threshold EPD. The temperature dependence of the threshold EPD is usually analyzed by the empirical equation, ${I}_{{\rm{t}}{\rm{h}}}\left(T\right)={I}_{{\rm{t}}{\rm{h}}0}\exp \left(T/{T}_{0}\right),$ where ${I}_{{\rm{t}}{\rm{h}}0}$ is a constant and ${T}_{0}$ is the characteristic temperature. The dashed lines in Fig. 18(b) indicate the results of fits using the empirical equation. The characteristic temperature was estimated to be ${T}_{0}=310$ K at 295–450 K and ${T}_{0}=72$ K above 450 K for the UV-C3 MQWs; ${T}_{0}=205$ K at 10–200 K and ${T}_{0}=82$ K above 200 K for the UV-C1 MQWs; and ${T}_{0}=325$ K at 10–295 K for the UV-C2 MQWs, which was similar to the characteristic temperature for the UV-C3 MQWs at 295–450 K. The UV-C2 MQWs had the same structure as the UV-C3 MQWs, except for the thickness of the OCLs. Thus, the origin of the STE and its thermal stability at temperatures below 295 K for the UV-C3 MQWs were expected to be similar to those of the UV-C2 MQWs. Therefore, the characteristic temperature of the UV-C3 MQWs at temperatures between 10 and 450 K was estimated to be 310–325 K. The characteristic temperature of ${T}_{0}=310$ K around room temperature was more than twice that reported for Al_x Ga_1−x N-based UV-A LDs. ⁷³⁾ The large characteristic temperature indicated the high thermal stability of the optical gain formation process. Therefore, these observations demonstrated excitonic STE with a low threshold and high thermal stability at room temperature.

Finally, we performed optically pumped lasing measurements with a high spectral resolution for the UV-C3 MQWs with a cavity length of 27 μm to confirm the lasing action due to the excitonic gain formation mechanism. Figure 19 shows the EPD of the PL spectra at 295 K. At the EPD of 11 kW cm⁻², only a broad PL band of SPE was observed at approximately 281 nm. A narrow emission band with fine structures appeared at the shorter-wavelength side of the SPE with increasing EPD. The peak wavelength of the narrow band was estimated to be approximately 279 nm. The narrow band increased superlinearly with increasing EPD. The fine structures were clearly resolved at EPDs of 35 kW cm⁻² and above. The separation between the structures was estimated to be approximately 0.54 nm. The longitudinal mode spacing of a Fabry–Pérot cavity is expressed as ${\rm{\Delta }}\lambda \tilde {\lambda }^{2}/2d{n}_{{\rm{e}}{\rm{f}}{\rm{f}}},$ where $d$ is the cavity length and ${n}_{{\rm{e}}{\rm{f}}{\rm{f}}}$ is an effective refractive index. The longitudinal mode spacing was estimated using ${n}_{{\rm{e}}{\rm{f}}{\rm{f}}}$ ∼ 2.5 ^74,75) to be 0.58 nm for a cavity length of 27 μm and was roughly consistent with the spacing between the fine structures. Thus, the fine structure was attributed to the longitudinal cavity mode. Based on the superlinear increase in the PL intensity and the clearly resolved fine structures, the narrow band was attributed to the lasing spectra. Therefore, these observations confirmed that excitonic lasing occurred at room temperature.

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