Recombination rates in green-yellow InGaN-based multiple quantum wells with AlGaN interlayers

InGaN-based multiple quantum wells (MQWs) are used as the active region for the highest efficiency violet-blue light-emitting diodes (LEDs) and laser diodes.¹ They can also emit at green to red wavelengths by increasing the In content in the quantum well (QWs) (x ≥ 0.20).² InGaN emitters that can cover the visible spectrum are of interest for solid-state lighting to create color temperature tunable white sources. Also, there is a growing interest for micro-LEDs that emit at these wavelengths and operate at low to moderate current densities for efficient and large color gamut emissive displays.^1,3–5 However, efficiencies at longer wavelengths are lower than in the blue, which limits their utility; this problem is called the “green gap.”^3,6 Several reasons are typically given for the green gap, which include lattice mismatch and defect formation,^7,8 phase separation,^9,10 carrier localization due to fluctuations in InGaN composition,^11–13 low growth temperatures,^14,15 and low electron-hole wavefunction overlap due to spontaneous and piezoelectric polarization.^16–18 

It has been shown that employing Al_yGa_1 − yN or Al_yIn_1 − yN interlayers (ILs) grown on top In_xGa_1 − xN QWs can remarkably improve efficiencies at green to red wavelengths. These structures have high efficiencies,^19–22 and the efficiency improvement becomes greater as the wavelength increases up to red wavelengths.²⁰ Various studies have been conducted to understand the role of the AlGaN IL on the enhancement, and there are several findings. First, the AlGaN IL caps the InGaN QWs more efficiently than a GaN cap and barrier, and the QWs have higher In content and sharper heterointerfaces.^19,23,24 The IL capping effect also enables both higher growth temperatures of subsequent GaN barriers and improves the crystal quality of the InGaN QWs to produce higher efficiencies.^24,25 Another positive effect is strain compensation enabled by the growth of the tensile strained AlGaN ILs directly on the compressively strained InGaN QWs.^21,26–28 At a particular AlGaN IL composition and thickness, the relaxation of the InGaN QWs is minimized, leading to nearly pseudomorphic growth of the MQW structure to the underlying GaN template, which, in turn, reduces defect formation and increases radiative efficiency.²¹ Finally, by introducing an AlGaN IL, the polarization-induced electric fields and band tilting of the quantum wells (QWs) change.²⁹ While this can lead to lower electron and hole wavefunction overlap and lower radiative rates, it can also redshift the emission without increasing the indium composition. Quantifying the positive effects that AlGaN ILs have on the recombination rates is yet to be explored.

In this article, the nonradiative and radiative recombination rates vs carrier density in green-yellow InGaN-based MQWs with an AlGaN IL are determined. By quantitatively determining and decoupling the separate recombination mechanisms (Shockley-Read-Hall, radiative, and Auger), one can more clearly identify the beneficial effects of the IL on efficiency. The recombination rates are found by transforming the radiative efficiency, absorption, and differential carrier lifetime measurements under photoluminescence. By varying the Al composition in the AlGaN IL, the relaxation of the layers due to strain and the wavefunction overlap is changed within the MQW. The most efficient InGaN/AlGaN/GaN MQWs have an order of magnitude lower nonradiative recombination or Shockley-Read-Hall (SRH) rates at low carrier densities (<10¹⁷ cm⁻³) compared to the conventional InGaN/GaN MQW, which proves to be the most significant factor behind the improvement in radiative efficiency using the IL. The radiative rate, too, varies with the Al composition and is lowest for the highest efficiency samples following the trend of wavefunction overlap. However, this result is not contradictory because the reduction of the SRH recombination rate is far greater than the reduction in the radiative rate, which ultimately translates to higher efficiencies.

All the samples are grown using metal-organic chemical vapor deposition (MOCVD) on commercial GaN on sapphire template layers. Optical reflectance measurements and X-ray diffraction (XRD) ω-2θ scans of calibration samples and the MQWs are used to determine the layer compositions and thicknesses. A series of five different InGaN/AlGaN/GaN MQWs are grown where the InGaN QWs and AlGaN ILs are grown at a fixed growth temperature of 720 °C determined by pyrometry. The GaN barrier is grown next at an increased temperature of 905 °C. Then the temperature is reduced for growth of the next InGaN QW, which is repeated 5 times. All the parameters of the growth are kept constant except for the AlGaN IL. The Al composition in the Al_yGa_1 − yN IL is varied by changing the gas phase ratio of the Al and Ga sources and are determined by fitting to XRD data to be y = 0.15, 0.26, 0.32, 0.45, and 0.58. For the In_xGa_1 − xN QWs, the In/(In + Ga) molar gas phase ratio is ∼0.50 and the targeted In composition is x = 0.22, but some samples deviate slightly resulting in x = 0.225 for y = 0.32 and x = 0.21 for y = 0.15. The use of the AlGaN IL helps in retaining In in the QW. The sample with y = 0.15 has reduced capping efficiency due to the lower Al composition IL and results in a lower In composition. For comparison, a sixth sample consisting of a 5-period InGaN/GaN conventional MQW structure with a GaN cap (y = 0) is grown. It is necessary to compare this to the IL samples to understand the improvements. For this sample, the QWs are grown at a temperature of 730 °C, and the GaN barrier is grown at a lower temperature of 830 °C to target the same amount of In in the QWs and prevent In loss. The InGaN QWs, AlGaN ILs, and GaN barriers are ∼3.2 nm, ∼1.3 nm, and ∼10.2 nm thick, respectively. The layer thicknesses and compositions are determined by fitting the XRD Ω-2θ curves along the (0002) reflection of GaN. The MQW structure and the growth sequence are detailed in previous reports.²¹ 

Characterization of the samples is executed in the following way. Reciprocal space mapping (RSM) is performed about the $(202¯5)$ reflection of the GaN template to determine the degree of relaxation of the MQWs. The relaxation is defined as (ΔQ_(x,0))⁄(ΔQ_(x,R)), where ΔQ_(x,0) is the lateral separation of the GaN peak and 0th peak of the MQW as determined by RSM along the $(2012¯5)$ reflection, and ΔQ_(x,R) is the lateral separation of GaN to a fully relaxed InGaN layer.²¹ Atomic force microscopy (AFM) is used to determine changes in the surface morphology. Photoluminescence is performed at both 8 K and room temperature with a laser diode emitting at 405 nm under continuous-wave operation at power densities varying from ∼6 W/cm² to ∼7200 W/cm² to determine the peak wavelength and radiative efficiency (η_rad) vs carrier density using a high-resolution spectrometer. At low temperatures and low carrier densities, the nonradiative recombination rates, SRH and Auger, are minimal and result in ∼100% radiative efficiency. For each sample, the room temperature efficiencies are normalized to the efficiencies measured at low carrier densities and 8 K to reveal the absolute radiative efficiency. Absorption of the laser light occurs only within the lowest bandgap InGaN QWs, so the injection efficiency is assumed as unity. Yellow-band luminescence for the samples is also measured separately and found to be negligible compared to QW emission. White light reflectance and transmission with an integrating sphere are used to determine the absorption of the samples at 405 nm, and the absorption varies between 8% and 9% for all samples.

The differential carrier lifetimes are obtained by an all-optical measurement using the methods similar to previous reports.³⁰ The MQW samples are excited with a 405 nm laser diode that is driven by combining with a bias tee a constant bias (constant carrier density) and small-signal sinusoidal bias frequencies, f, between 0.03 and 300 MHz provided by a network analyzer (NA). The emitted light from the MQW samples has a sinusoidal output that is collected using a high-speed Si avalanche photodetector and returned to the NA. The phase and amplitude differences of the input and output signals allow for the determination of the differential carrier lifetime, τ_DCL, using the small-signal response F = 1⁄(1 + j2πfτ_DCL).³¹ The differential carrier lifetime results from radiative and nonradiative recombination in the MQWs. The constant bias of the laser diode is changed to measure τ_DCL at different carrier densities.

Figure 1(a) shows the radiative efficiency (η_rad) vs input power densities for all the samples. The η_rad is defined as the radiative rate divided by the total recombination rate,³² and it varies significantly with the IL Al composition. The samples with an IL of y ≥ 0.26 are of higher efficiency, and the y = 0.26 sample has the highest efficiency. A closer look at the sample grouping of y ≥ 0.26 shows a gradual decrease in efficiency with increasing Al composition. A couple of factors are contributing to this trend. First, variations in the In composition in the QWs can lead to differences in the defect formation. For example, the y = 0.32 sample has the highest In composition, emits at longer wavelengths [see Fig. 1(c)], and is subject to higher strain that promotes defect formation. Second, as the Al in the IL increases, differences in the wavefunction overlap, and hence, differences in radiative recombination rate will occur as discussed below. The inclusion of the AlGaN IL results in a marked improvement in efficiency as reported by others,^19,21 and the Al composition necessitates tuning to achieve the highest efficiencies.

Figure 1(b) shows the differential carrier lifetimes vs input power densities for all the samples. τ_DCL is the shortest for the InGaN/GaN conventional MQW structure and slightly improve for y = 0.15. For MQW structures with y = 0.26 and y = 0.32, the τ_DCL are the longest and approximately an order of magnitude longer than the conventional structure when compared at the lower power densities where the SRH recombination dominates. As the power density (carrier density) increases, there is the expected drop in the τ_DCL as the radiative rate starts to dominate the overall carrier lifetimes. The τ_DCL has a consistent and expected relationship with η_rad, where at low carrier densities τ_DCL becomes longer as the η_rad increases.

The peak wavelength vs input power density is shown in Fig. 1(c). The peak wavelength shifts from yellow at low carrier densities to deep green at the highest. Carrier screening is the main cause of this blueshift as the carriers screen the polarization charge in the quantum well. The MQWs with y ≥ 0.26 show a more significant and consistent blueshift than the y = 0 and 0.15 MQWs. The y = 0 and 0.15 samples have the shorter lifetimes and, therefore, require higher powers before a significant number of carriers can begin screening. This is observed in Figs. 1(b) and 1(c) where the wavelength shift increases at ∼200–300 W/cm² where τ_DCL is beginning to be determined more by radiative recombination. Other possible causes that could also contribute to the blueshift are carrier delocalization from In fluctuations and QW to QW variations.

The steady-state carrier density, N, and subsequently the radiative rate, R_R, and nonradiative generation rate, R_NR, as functions of N are determined from the η_rad, τ_DCL, and absorption data using the method detailed in Ref. 33. Figure 2 shows the result of this transformation where R_R and R_NR are normalized to N^a (a = 1, 2, or 3) to determine the radiative and nonradiative A, B, and C coefficients. Note that these coefficients are a misnomer because the recombination rates vary with carrier density, but using this convention allows one to compare to previously reported data measured at specific carrier densities. Figure 2(a) shows R_NR/N vs N for all the samples. At low carrier densities, R_NR/N is constant and is equivalent to the SRH A coefficient assuming R_NR= AN (N ≤ 10¹⁷cm⁻³).³⁴ The R_NR/N is the largest for the conventional InGaN/GaN MQW structure at ∼3 × 10⁷ s⁻¹. With the introduction of an AlGaN IL, the R_NR/N reduces, and at y = 0.26, it is a minimum at ∼3 × 10⁶s⁻¹. At y = 0.32, it is nearly the same. The R_NR/N increases with further increases in the IL Al composition, closely following an inverse relationship to radiative efficiency.

A plot of R_R/N² vs N for all samples is shown in Fig. 2(b). R_R/N² is equivalent to the radiative recombination B coefficient assuming R_R= BN². Determining B is, of course, an oversimplification of the radiative rate because it can have a substantial variation with N. While R_R/N² is relatively constant at N ≤ 4 × 10¹⁸ cm⁻³ for the y ≥ 0.26 samples, at high carrier densities, R_R/N² drops because of phase-space filling where the radiative rate becomes monomolecular instead of bimolecular.^33,35 For the y = 0 (no IL) and y = 0.15 samples, the decrease in R_R/N² is more severe vs N, either due to the phase-space filling in conjunction with carrier delocalization and QW to QW variations or possibly due to carrier escape in shallower QWs (GaN barriers) compared to the QWs with AlGaN ILs.³⁶ Additionally, there are other, subtle variations. For example, R_R/N² for the y = 0.26 and 0.32 samples exhibit a slight rise at high carrier densities before phase-space filling occurs at N ∼ 5 × 10¹⁸/cm³ and R_R/N² drops. Understanding the second order dependencies of R_R vs N requires further study.

Figure 2(c) shows a plot of R_NR/N³ vs N for all samples. The R_NR/N³ is equivalent to the nonradiative Auger C coefficient assuming R_NR= CN³ at very high N where Auger recombination dominates.³² This cubed dependence is not perfect, again, because of the phase-space filling at high carrier densities, so R_NR ∼N^p, where p < 3.^33,35 The decrease of R_NR/N³ vs increasing N matches well with previously published reports. All the MQWs with AlGaN ILs have lower C coefficients compared to the standard MQW. Also, the samples with lowest A coefficients also have the lowest C coefficient and could be caused by reduced point-defect induced Auger-like recombination.³⁷ To accurately compare C coefficients to others, the measurements need to be taken at even higher N (>10¹⁹ cm⁻³), which is left for future work. Here, the focus is on A and B coefficients that dominate at low and moderate carrier densities, which is the operating point for micro-LEDs in displays.⁴ 

RSMs are used to determine the relaxation of the MQW and connect it with the trends observed in the recombination rates. The relaxation of the MQWs from the RSMs and the A coefficient (R_NR/N) at N = 4 × 10¹⁶ cm⁻³ from Fig. 2(a) is plotted vs the IL Al composition in Fig. 3. The relaxation is highest for the MQW without an IL and decreases with the addition of the AlGaN IL. The relaxation is the lowest at 0.27% for y = 0.32, which is approximately 10 times smaller than the conventional InGaN/GaN structure. Both the relaxation and A coefficient, in general, show the same trend where they decrease with increasing IL Al composition, and then beyond an optimum IL Al composition, they both increase again. A similar trend was previously reported where the relaxation is minimum at an optimum AlGaN IL thickness with a fixed Al composition due to strain compensation, which leads to reduction of defect density.²¹ Note that the relaxation falls out of the trend (dotted line) because of In differences (for example, at y = 0.15, the In is lower and less susceptible to relaxation) and due to differences in growth variations from sample to sample captured by the large spot size of the RSM.

The large reduction of A coefficient from the conventional InGaN MQW to the AlGaN capped MQWs is due to two factors: First, the better material quality achieved due to higher barrier growth temperature, and second, the reduction in strain relaxation. For samples with y ≥ 0.26, the growth conditions are the same, and the A coefficient variation is due mainly due to strain relaxation variation. Therefore, controlling the strain relaxation and material quality of the MQW are contributing factors to control SHR recombination and reduce the A coefficient.

AFM is performed to image the MQW surface and understand whether morphological changes are present. Figure 4 shows AFM images of the MQW samples. Excluding pits, the root mean square roughness is approximately the same for all the samples. However, for the y = 0 sample [Fig. 4(a)], the pits emanating from threading dislocations are large and intersect one another, and at times forming larger and less geometric shapes.³⁸ Indium inclusions can also be observed on the surface as shown in previous reports.³⁹ Figure 4(b) shows the Al_0.15Ga_0.85N IL MQW structure with improved surface morphology. The size of the pits becomes smaller, instances of intersecting pits are reduced, and the In inclusion disappears. As the Al composition in the Al_yGa_1 − yN IL is increased to y ≥ 0.26, the surface morphology improves even more. Figures 4(c) and 4(d) show AFM images of the Al_0.26Ga_0.74N IL and Al_0.32Ga_0.68N IL capped MQWs. The pits around the threading dislocations are much smaller, well formed, and hexagonal in shape. The AFM images for y = 0.45 and 0.58 look similar (data not shown).

The AFMs show that the surface morphology can be controlled by using an AlGaN IL. First, the AlGaN IL caps the QW to prevent In inclusions formed during GaN barrier growth. Second, high In-content InGaN QWs are more susceptible to pit formation,³⁸ and the tensile AlGaN IL compensates the compressive strain in the QW to suppress ill-formed pits. This improvement in surface morphology with AlGaN ILs follows the trend of increased efficiency and reduced SRH recombination and is consistent with previous reports.^24,39 Careful formation of pits has been shown as a method to reduce nonradiative recombination^40,41 and could also be playing a role in the A coefficient. It should also be noted that some claim V-pits also help with hole injection and radiative efficiency.⁴² While this study's measurement technique removes injection efficiency as a variable, it cannot be discounted that well-formed V-pits also help with radiative efficiency.

Figure 5(a) plots the B coefficient vs the Al composition in the IL at low carrier densities (N = 1 × 10¹⁷ cm⁻³) so that carrier screening and phase-space filling are minimized. B coefficients vary ∼2 times across the samples, first decreasing with increasing Al composition and then increasing with a minimum at y = 0.26. Some insight into the variation can be gained by investigating the elements that constitute the radiative rate and B coefficient. The radiative rate can be expressed as

where E_eh is the transition energy, $|e^⋅peh|2$ is the momentum matrix element, I is the electron-hole wavefunction overlap, and ℒ(E_eh) is the linewidth broadening.⁴³ The first two terms (E_eh and $|e^⋅peh|2$⁠) should vary slightly for this set. The last two terms, however, can be significantly different across the samples.

To gain a better understanding of the different radiative rates for these sets of samples, the wavefunction overlap, I, vs Al composition found using the nextnano³ Schrödinger-Poisson solver⁴⁴ is shown in Fig. 5(b). A complete set (blue circles) is plotted, assuming abrupt heterointerfaces, no carrier screening, and pseudomorphic layers to GaN. The overlap increases with increasing Al composition, because the AlGaN layer shifts the electron wavefunction closer to the hole wavefunction. In general, this trend qualitatively matches the trend observed for the B coefficient for samples with y ≥ 0.26 showing that overlap is a significant factor.

To better qualitatively match the trend of B coefficient to overlap at lower Al compositions, one needs to consider the abruptness of the heterointerfaces. In reality, a significant amount of Al in the IL is necessary to prevent In loss and achieve abrupt heterointerfaces. Indeed, conventional InGaN/GaN MQWs have been shown to have compositional grading at the heterointerfaces.^24,45 To verify that this grading will improve the trend, the overlap is also calculated [red triangle at y = 0 in Fig. 5(b)] where a compositionally graded 0.4 nm thick In_xGa_1 − xN layer is inserted above the QW at the QW-barrier interface. The thickness of this layer is equally subtracted from the InGaN QW and the GaN barrier, and x is linearly varied from 0.11 to 0. This results in a significant increase in the overlap from 8.7% to 9.94%. For the y = 0.15 sample, the QW has lower In, and it is also likely that interface grading and higher overlap are present. This suggests that less abrupt interfaces and larger overlaps are factors in the larger B coefficients for y ≤ 0.15. It should be noted that all these simulations are performed with ideal situations and show qualitative agreement, but to quantitatively determine B, other effects should be included such as carrier screening for overlap and relaxation and In fluctuations for linewidth broadening. It should be noted that the A coefficient also depends on the overlap at approximately to the power of 1⁴⁶ and has a similar Al composition trend suggesting that it is also a contributing (smaller) factor in addition to stain relaxation.

The B coefficients (or R_R/N²) found in this work match well to the trends of previous reports.^47,48 Although B varies with N [Fig. 2(b)], the common way to compare B coefficients in the literature is to use values at a specific carrier density where B is nearly constant and LEDs typically operate. Figure 6 plots the B coefficient vs transition energy for the samples investigated here at N = 3 × 10¹⁸ cm⁻³ and samples emitting at higher energies (in the near ultraviolet to green) from Refs. 47 and 48. The B coefficient decreases with decreasing transition energy, following the trend of the other reports. Using Eq. (1) provides an insight into this trend. All the terms for radiative efficiency in Eq. (1) decrease with decreasing transition energy (higher In). The first two terms on the right-hand side are obvious but sometimes ignored, and I is decreasing because of the increased charge separation from the higher In composition in the QWs attributed to the polarization-induced band tilting that shifts the electron and hole wavefunctions further from one another. Linewidth broadening occurs due to carrier scattering (homogenous) and alloy and thickness variations (inhomogenous). The broadening is generally greater for higher In-content QWs and is manifest in broader emission spectra and a reduction in the radiative rate.

This decrease in B coefficient with decreasing energies is one known cause of the green gap in InGaN-based emitters. In the simple ABC efficiency model, the radiative efficiency can be expressed as

This equation shows that at low to moderate carrier densities (CN³ not significant), the radiative efficiency is a strong function of the ratio of the coefficients B/A. InGaN-based QWs operating at green gap wavelengths are more sensitive to SHR recombination (A coefficient) because of the lower B coefficients. For the green gap energies, there is a decrease in B, as shown in Fig. 6, and a proclivity to create defects and increase A due to lattice-mismatch strain. Both A and B move in the wrong direction with increased In in the QWs, which causes the lower efficiency.

Finally, Eqs. (1) and (2) can be used to connect the efficiencies shown in Fig. 1(a) to the recombination rates shown in Fig. 2 for this set of MQWs. By improving the material quality and controlling the strain with the inclusion of the AlGaN IL in the MQW, the A coefficient decreases. The AlGaN IL also affects overlap and leads to a decrease in the A and B coefficients for the best samples. However, the decrease in A is much larger than the decrease in B (∼10 times vs ∼2 times) and, therefore, results in an increase in the radiative efficiency at y = 0.26 and y = 0.32. It is interesting that the best A coefficient (3 × 10⁶ s⁻¹) measured in this study for green-yellow emitting InGaN-based MQWs is similar to the A coefficients measured for InGaN-based MQW emitters with higher transition energies in the green (520 nm, A = 3 × 10⁶/cm⁻³)⁴⁸ and blue (470 nm, A = 4 × 10⁶ cm⁻³)⁴⁷ even with less indium in the QWs. However, comparisons of the B coefficient show a much larger difference (Fig. 6). This suggests that the principal cause behind lower efficiency in the long-wavelength InGaN-based QW emitters (green gap) is a severe reduction of the spontaneous emission rate as long as the A coefficient is controlled, as is possible with the AlGaN IL. Further studies need to be done where similar IL capped MQWs are grown on semipolar GaN templates to see whether the high efficiency green gap emitter can be realized.^49,50 This work shows that by measuring the recombination rates, as opposed to efficiency alone, one can more clearly identify the underlying physics and target areas for improvement.

To conclude, radiative and nonradiative recombination rates are determined in InGaN/AlGaN/GaN MQWs grown with different IL Al compositions emitting in green-yellow by transforming measurements on radiative efficiency, absorption, and differential carrier lifetimes. Relaxation and, therefore, defect formation can be affected by the IL Al composition. For the most pseudomorphic structures, the A coefficient is an order of magnitude smaller than that of the conventional InGaN/GaN MQW structure. While this also leads to a decrease in the B coefficient too due to the overlap, the decrease in A is greater and leads to an overall improvement in the radiative efficiency. These recombination rate measurements confirm that if the SRH recombination is controlled, then the severe reduction of radiative recombination with an increased emitting wavelength is one of the main challenges in realizing high efficiency InGaN-based MQW emitters in the green gap.

The authors would like to acknowledge funding from the U.S. National Science Foundation (NSF) (Award Nos. 1408051, 1505122, and 1708227), and the Daniel E. ‘39 and Patricia M. Smith Endowed Chair Professorship Fund (N.T.).