Influence of carrier localization on high-carrierdensity effects in AlGaN quantum wells Jūras Mickevičius,1,* Jonas Jurkevičius,1 Gintautas Tamulaitis,1 Michael S. Shur,2 Max Shatalov,3 Jinwei Yang,3 and Remis Gaska3 1
Institute of Applied Research and Semiconductor Physics Department, Vilnius University, Saulėtekio al. 9 – III, Vilnius, LT-10222, Lithuania 2 Department of ECE and CIE, Rensselaer Polytechnic Institute, Troy, New York 12180, USA 3 Sensor Electronic Technology, Inc., 1195 Atlas Road, Columbia, South Carolina 29209, USA * [email protected]
Abstract: The influence of carrier localization on photoluminescence efficiency droop and stimulated emission is studied in AlGaN multiple quantum wells with different strength of carrier localization. We observe that carrier delocalization at low temperatures predominantly enhances the nonradiative recombination and causes the droop, while the main effect of the delocalization at elevated temperatures is enhancement of PL efficiency due to increasing contribution of bimolecular recombination of free carriers. When the carrier thermal energy exceeds the dispersion of the potential fluctuations causing the carrier localization, the droop is caused by stimulated carrier recombination. ©2014 Optical Society of America OCIS codes: (160.4760) Optical properties; (160.6000) Semiconductor materials; (250.5230) Photoluminescence.
References and links 1.
S. Chichibu, T. Azuhata, T. Sota, and S. Nakamura, “Spontaneous emission of localized excitons in InGaN single and multiquantum well structures,” Appl. Phys. Lett. 69(27), 4188–4190 (1996). 2. C. J. Collins, A. V. Sampath, G. A. Garett, W. L. Sarney, H. Shen, M. Wraback, A. Yu. Nikiforov, G. S. Cargill III, and V. Dierolf, “Enhanced room-temperature luminescence efficiency through carrier localization in AlxGa1xN alloys,” Appl. Phys. Lett. 86(3), 031916 (2005). 3. S. Hammersley, D. Watson-Parris, P. Dawson, M. J. Godfrey, T. J. Badcock, M. J. Kappers, C. McAleese, R. A. Oliver, and C. J. Humphreys, “The consequences of high injected carrier densities on carrier localization and efficiency droop in InGaN/GaN quantum well structures,” J. Appl. Phys. 111(8), 083512 (2012). 4. N. I. Bochkareva, Y. T. Rebane, and Y. G. Shreter, “Efficiency droop and incomplete carrier localization in InGaN/GaN quantum well light-emitting diodes,” Appl. Phys. Lett. 103(19), 191101 (2013). 5. J. Wang, L. Wang, W. Zhao, Z. Hao, and Y. Luo, “Understanding efficiency droop effect in InGaN/GaN multiple-quantum-well blue light-emitting diodes with different degree of carrier localization,” Appl. Phys. Lett. 97(20), 201112 (2010). 6. Y. Lin, Y. Zhang, Z. Liu, L. Su, J. Zhang, T. Wei, and Z. Chen, “Spatially resolved study of quantum efficiency droop in InGaN light-emitting diodes,” Appl. Phys. Lett. 101(25), 252103 (2012). 7. J. Mickevičius, G. Tamulaitis, M. Shur, M. Shatalov, J. Yang, and R. Gaska, “Correlation between carrier localization and efficiency droop in AlGaN epilayers,” Appl. Phys. Lett. 103(1), 011906 (2013). 8. J. Mickevičius, J. Jurkevičius, K. Kazlauskas, A. Žukauskas, G. Tamulaitis, M. S. Shur, M. Shatalov, J. Yang, and R. Gaska, “Stimulated emission in AlGaN/AlGaN quantum wells with different Al content,” Appl. Phys. Lett. 100(8), 081902 (2012). 9. J. Mickevičius, J. Jurkevičius, K. Kazlauskas, A. Žukauskas, G. Tamulaitis, M. S. Shur, M. Shatalov, J. Yang, and R. Gaska, “Stimulated emission due to localized and delocalized carriers in Al0.35Ga0.65N/Al0.49Ga0.51N quantum wells,” Appl. Phys. Lett. 101(4), 041912 (2012). 10. J. Holst, A. Kaschner, U. Gfug, A. Hoffmann, C. Thomsen, F. Bertram, T. Riemann, D. Rudloff, P. Fischer, J. Christen, R. Averbeck, H. Riechert, M. Heuken, M. Schwambera, and O. Schon, “Comparison of the mechanism of optical amplification in InGaN/GaN heterostructures grown by molecular beam epitaxy and MOCVD,” Phys. Status Solidi A 180, 327–332 (2000). 11. M. Strassburg, A. Hoffmann, J. Holst, J. Christen, T. Riemann, F. Bertram, and P. Fischer, “The origin of the PL photoluminescence Stokes shift in ternary group-III nitrides: field effects and localization,” Phys. Status Solidi C 0(6), 1835–1845 (2003).
#203009 - $15.00 USD Received 12 Dec 2013; revised 13 Jan 2014; accepted 20 Jan 2014; published 27 Feb 2014 (C) 2014 OSA 10 March 2014 | Vol. 22, No. S2 | DOI:10.1364/OE.22.00A491 | OPTICS EXPRESS A491
12. E. F. Pecora, W. Zhang, A. Yu. Nikiforov, L. Zhou, D. J. Smith, J. Yin, R. Paiella, L. D. Negro, and T. D. Moustakas, “Sub-250 nm room-temperature optical gain from AlGaN/AlN multiple quantum wells with strong band-structure potential fluctuations,” Appl. Phys. Lett. 100, 061111 (2012). 13. E. F. Pecora, W. Zhang, A. Yu. Nikiforov, J. Yin, R. Paiella, L. D. Negro, and T. D. Moustakas, “Sub-250 nm light emission and optical gain in AlGaN materials,” J. Appl. Phys. 113(1), 013106 (2013). 14. A. Satake, Y. Masumoto, T. Miyajima, T. Asatsuma, and M. Ikeda, “Two-dimensional exciton dynamics and gain formation processes in InxGa1-xN multiple quantum wells,” Phys. Rev. B 60(24), 16660–16666 (1999). 15. A. Žukauskas, K. Kazlauskas, G. Tamulaitis, P. Pobedinskas, S. Juršėnas, S. Miasojedovas, V. Yu. Ivanov, M. Godlewski, C. Skierbiszewski, M. Siekacz, G. Franssen, P. Perlin, T. Suski, and I. Grzegory, “Role of band potential roughness on the luminescence properties of InGaN quantum wells grown by MBE on bulk GaN substrates,” Phys. Status Solidi B 243(7), 1614–1618 (2006). 16. V. N. Jmerik, A. M. Mizerov, A. A. Sitnikova, P. S. Kop’ev, S. V. Ivanonv, E. V. Lutsenko, N. P. Tarasuk, N. V. Rzheutskii, and G. P. Yablonskii, “Low-threshold 303 nm lasing in AlGaN-based multiple-quantum well structures with an asymmetric waveguide grown by plasma-assisted molecular beam epitaxy on c-sapphire,” Appl. Phys. Lett. 96(14), 141112 (2010). 17. V. N. Jmerik, A. N. Mizerov, T. V. Shubina, A. A. Toropov, K. G. Belyaev, A. A. Sitnikova, M. A. Yagovkina, P. S. Kop'ev, E. V. Lutsenko, A. V. Danilchyk, N. V. Rzheutskii, G. P. Yablonskii, B. Monemar, and S. V. Ivanov, “Optically pumped lasing at 300.4 nm in AlGaN MQW structures grown by plasma-assisted molecular beam epitaxy on c-Al2O3,” Phys. Status Solidi A 207(6), 1313–1317 (2010). 18. P. G. Eliseev, P. Perlin, J. Lee, and M. Osinski, “"Blue” temperature-induced shift and band-tail emission in InGaN-based light sources,” Appl. Phys. Lett. 71(5), 569–571 (1997). 19. A. Bell, S. Srinivasan, C. Plumlee, H. Omiya, F. A. Ponce, J. Christen, S. Tanaka, A. Fujioka, and Y. Nakagawa, “Exciton freeze-out and thermally activated relaxation at local potential fluctuations in thick AlxGa1-xN layers,” J. Appl. Phys. 95(9), 4670–4674 (2004). 20. N. Nepal, J. Li, M. L. Nakarmi, J. Y. Lin, and H. X. Jiang, “Temperature and compositional dependence of the energy band gap of AlGaN alloys,” Appl. Phys. Lett. 87(24), 242104 (2005). 21. J. Mickevičius, G. Tamulaitis, E. Kuokštis, K. Liu, M. S. Shur, J. P. Zhang, and R. Gaska, “Well-widthdependent carrier lifetime in AlGaN/AlGaN quantum wells,” Appl. Phys. Lett. 90(13), 131907 (2007). 22. J. Mickevičius, J. Jurkevičius, M. S. Shur, J. Yang, R. Gaska, and G. Tamulaitis, “Photoluminescence efficiency droop and stimulated recombination in GaN epilayers,” Opt. Express 20(23), 25195–25200 (2012).
It is generally accepted that carrier localization results in high internal quantum efficiency (IQE) in III-nitride semiconductors [1,2]. However, as the carrier density is increased, the carriers populate the localized states with energies closer to the extended states, and the effective localization strength decreases [3,4]. Such carrier delocalization due to increasing carrier density plays an important role in the efficiency droop in InGaN quantum well (QW) structures [3,5,6] and AlGaN epilayers [7]. The stronger localizing potential fluctuations might be expected to increase the IQE. However, it also has an impact on high-carrier-density effects influencing the stimulated emission threshold [8–11] and also resulting in the efficiency droop at lower excitation levels [7]. The interrelation between localization conditions, efficiency droop, and stimulated emission threshold is quite complex. Moreover, temperature strongly affects the redistribution of carriers through the localized states, which makes the recombination processes even more complicated. Our investigations [7–9] and the data reported in literature [12,13] show that carrier localization in AlGaN, especially at high Al content, does play an important role in carrier dynamics even at room temperature. In this paper, we link the carrier localization and highdensity effects (efficiency droop and stimulated emission), which are of interest for applications of AlGaN in UV light emitters. In the samples with comparatively strong carrier localization and low internal quantum efficiency, selected for this study, this link is quite strong. Importantly, the link might also be important for the AlGaN-based emitters with less pronounced carrier localization, and it should be accounted for in the further development of AlGaN-based light-emitting diodes (LEDs) and laser diodes (LDs). The AlGaN-based multiple quantum wells (MQWs) investigated in this study were grown by a combination of conventional metal-organic chemical vapor deposition (MOCVD) and migration enhanced metal-organic chemical vapor deposition (MEMOCVD®) techniques on c-plane sapphire substrates. The samples contained ten QWs with Al molar fractions of 8% (samples A1 and A2), 18% (sample B1), and 35% (samples C1, C2, and C3). The samples
#203009 - $15.00 USD Received 12 Dec 2013; revised 13 Jan 2014; accepted 20 Jan 2014; published 27 Feb 2014 (C) 2014 OSA 10 March 2014 | Vol. 22, No. S2 | DOI:10.1364/OE.22.00A491 | OPTICS EXPRESS A492
containing the same Al content had different well widths, therefore, different strength of the carrier localization. Table 1 lists the main structural parameters of the samples under study. Table 1. The structure details of the samples under study. Sample A1 A2 B1 C1 C2 C3
Al content (%) Well Barrier 8 20 8 20 18 40 35 49 35 49 35 49
Width (nm) Well Barrier 1.9 11.5 2.9 11.5 2.5 15.0 5.0 11.5 4.1 11.5 2.5 11.5
PL Intensity (arb. units)
The photoluminescence (PL) of the samples was excited by the 4th harmonic (266 nm) of Q-switched YAG:Nd laser radiation (pulse duration 4 ns). A closed-cycle helium cryostat ensured the variation of temperature in the range from 8 to 300 K. The luminescence signal was focused into a double monochromator (Jobin Yvon HRD-1) and detected by a UVenhanced photomultiplier. The spontaneous emission properties were measured in the conventional front-surface configuration. To study the stimulated emission, the incident laser beam was focused into a long (2 mm) and narrow (150 µm) stripe on the sample edge. The light propagating along the stripe was collected and analyzed.
8% Al AlGaN MQWs T = 20 K P/Pthr
2.3 1.3 0.69
(a) 3.7
3.8 35% Al AlGaN MQWs T = 20 K
P/Pthr 2.3 1.2
(b)
0.74
4.3
4.4
4.5
Photon energy (eV) Fig. 1. Edge PL spectra of AlGaN MQWs samples A1 (a) and C1 (b) measured at 20 K temperature under several excitation power densities below and above the threshold for stimulated emission. The threshold was equal to 170 kW/cm2 and 970 kW/cm2 for samples A1 and C1, respectively. The spectra were normalized and shifted for clarity. The vertical line indicates the peak positions of spontaneous luminescence bands.
The edge emission spectra were measured under the excitation power density varied from ~40 kW/cm2 to ~7 MW/cm2 in the temperature range from 20 to 300 K. Figure 1 presents several spectra measured under different excitation power densities at 20 K for samples A1 and C1. For both samples, a stimulated emission band emerges at the excitation power densities above a certain threshold. The stimulated emission threshold was equal to 170 kW/cm2 and 970 kW/cm2 for samples A1 and C1, respectively. The stimulated emission band is located on the low-energy slope of the spontaneous band in sample A1 [see Fig. 1(a)], as well as in samples A2 and B1 [not shown in Fig. 1]. This position is typical of structures with weak or no carrier localization [8]. Meanwhile, in all samples of group C (with the larger Al content of 35%) the stimulated emission band is located on the high-energy slope [see
#203009 - $15.00 USD Received 12 Dec 2013; revised 13 Jan 2014; accepted 20 Jan 2014; published 27 Feb 2014 (C) 2014 OSA 10 March 2014 | Vol. 22, No. S2 | DOI:10.1364/OE.22.00A491 | OPTICS EXPRESS A493
Fig. 1(b) for the sample C1]. As shown in previous publications on InGaN [10,11,14,15] and AlGaN [8,9,11,16,17], this position of stimulated emission peak is an indication of strong carrier localization, which affects the carrier dynamics even up to stimulated emission threshold.
0
Peak position shift (meV)
-20
AlGaN MQWs A1 σ = 13 meV A2 σ = 12 meV B1 σ = 26 meV
-40
0
-20
AlGaN MQWs C1 σ = 30 meV C2 σ = 39 meV C3 σ = 41 meV
-40
0
50
100
150
200
250
300
Temperature (K) Fig. 2. Temperature dependences of PL band peak position shift relative to the position at 8 K in AlGaN MQWs (points) for the samples listed in Table 1. Solid lines show the best fit using a simple model of carrier (exciton) hopping through localized states.
The carrier localization conditions in the AlGaN MQWs under study were estimated using the temperature dependence of the PL band peak position measured in the conventional frontsurface configuration. The points in Fig. 2 present the shift of the band peak with respect to the peak position at 8 K. All the samples exhibited non-monotonous peak shift behavior, which is similar to the so-called S-shape dependence typical of materials, where carriers move by hopping via localized states [18,19]. The S-shaped dependence at elevated temperatures can be described using a simple quantitative model linking the band shift to the fluctuations of the local potential. At nondegenerate occupation, the temperature dependence of PL peak position can be expressed as [18]: E peak ( T ) = E g ( 0 ) −
αT 2 σ 2 − . β + T k BT
(1)
Here Eg(0) is the effective band gap at T = 0, α and β are Varshni coefficients for band gap reduction with increasing temperature, and σ is the standard deviation of the Gaussian distribution of the band gap fluctuations due to the random fluctuations in Al content and/or
#203009 - $15.00 USD Received 12 Dec 2013; revised 13 Jan 2014; accepted 20 Jan 2014; published 27 Feb 2014 (C) 2014 OSA 10 March 2014 | Vol. 22, No. S2 | DOI:10.1364/OE.22.00A491 | OPTICS EXPRESS A494
QW width. The points in Fig. 2 show the dependences of the shift in the PL peak position relative to its value at 8 K. The dependences shown by solid lines were calculated according to Eq. (1) with α and β values from Ref. [20], and Eg(0) as an adjustable parameter to fit the maximum value of the calculated shift for each curve. At low temperatures, the freeze-out of carriers (excitons) takes place, and the experimental data deviate from the dependence described by Eq. (1). All the fits were quite adequate, and the corresponding values of the localization parameter σ are indicated in Fig. 2.
1.0
(a) T = 300 K
Normalized PL efficiency (arb. u.)
0.8 0.6 0.4 0.2
AlGaN MQWs A1 σ = 13 meV B1 σ = 26 meV C3 σ = 41 meV
1.0 0.8 0.6 0.4 0.2 0.0
(b) T=8K 1
10
100
1000
10000 2
Excitation power density (kW/cm ) Fig. 3. Normalized PL efficiency dependences on excitation power density in AlGaN MQWs with different localization strengths (indicated) at 300 K (a) and 8 K (b).
The relation between localization parameter σ and the properties of stimulated emission band can be observed. The stimulated emission band appears on low-energy slope in the samples with weak localization (σ ≤ 26 meV). As localization becomes stronger (σ ≥ 30 meV), the stimulated emission peak shifts to high-energy slope of the spontaneous emission band. This observation confirms that carrier localization is important in high-Alcontent AlGaN MQWs up to the carrier densities high enough for stimulated emission to occur. Using the carrier lifetime of 58 ps determined for sample C1 in Ref. [21], the carrier density corresponding to the stimulated emission threshold at room temperature is ~3 × 1019 cm−3. To analyze the links between carrier localization conditions and efficiency droop, we measured the excitation power density dependence of the spectrally integrated PL efficiency at several temperatures. The typical room temperature dependences are plotted in Fig. 3 for several samples under study. Using the data in Fig. 3, the efficiency droop onset was
#203009 - $15.00 USD Received 12 Dec 2013; revised 13 Jan 2014; accepted 20 Jan 2014; published 27 Feb 2014 (C) 2014 OSA 10 March 2014 | Vol. 22, No. S2 | DOI:10.1364/OE.22.00A491 | OPTICS EXPRESS A495
SE threshold/droop onset
estimated as the excitation power density corresponding to the highest PL efficiency and separating the initial increase in PL efficiency and its decrease (droop) above the onset.
3
10
2
10
1
10
0
10
0.0
0.5
1.0
1.5
2.0
kT/σ Fig. 4. Ratio of thresholds for stimulated emission and droop onset as a function of the ratio of thermal energy to dispersion of potential fluctuations for 6 different samples at various temperatures. The solid line indicates the ratio between stimulated emission threshold and droop onset equal to 1.
When comparing the stimulated emission threshold and droop onset dependences on localization parameter, several peculiarities were noticed. At low temperatures, the stimulated emission threshold is always at much higher excitations than the droop onset. Meanwhile, at 300 K, the values of droop onset and stimulated emission threshold are quite close, except for the strongest localization. Moreover, at low temperatures, the value of the ratio between the stimulated emission threshold and droop onset is above ~40 and steadily increases with localization parameter σ. The increase in temperature results in a decrease of the ratio for the MQWs with the weakest localization, while having no significant influence in the samples with the strongest localization. To summarize these trends, we plotted the ratio of the thresholds for stimulated emission and droop onset as a function of the ratio of the thermal energy to the dispersion of potential fluctuations [see Fig. 4]. Each point in Fig. 4 corresponds either to a different sample with a different σ value in the range from 12 to 41 meV or to a different temperature (20, 100, 180, or 300 K). Despite the strong scattering of the points in Fig. 4, which is expected, first of all, due to different carrier lifetimes in different samples, the plot reveals a clear trend: i) as the ratio kT/σ increases (either because of smaller σ or larger T) up to 1, the ratio of the thresholds for stimulated emission and droop onset becomes smaller, and ii) the efficiency droop and stimulated emission occurs at the same excitation power density, when kT becomes larger than σ. This is an indication that the dominating droop origin in AlGaN with low band gap fluctuations at high temperatures might be caused by stimulated emission. It is worth noting that the light amplification by stimulated emission of radiation (i.e., the LASER effect) might be not observed in AlGaN MQWs and, especially, in epilayers, because the amplification due to stimulated emission is overcompensated by the light losses due to scattering and absorption by dislocations (abundant in AlGaN, especially in high-Alcontent AlGaN). For LEDs, it is important that the stimulated emission, though being ineffective in the light amplification, effectively decreases the useful light output of an LED. As pointed out in our previous study on the droop in GaN [22], the total (spontaneous and stimulated) light emission efficiency might increase at increasing excitation intensity but the front-surface emission efficiency, which is actually important for LED operation in the current injection mode, decreases.
#203009 - $15.00 USD Received 12 Dec 2013; revised 13 Jan 2014; accepted 20 Jan 2014; published 27 Feb 2014 (C) 2014 OSA 10 March 2014 | Vol. 22, No. S2 | DOI:10.1364/OE.22.00A491 | OPTICS EXPRESS A496
For AlGaN MQWs with low kT/σ, the droop has to have a different origin related to the carrier (exciton) localization. As shown above, the carrier localization might play a significant role in the carrier dynamics up to the nonequilibrium carrier densities sufficient for stimulated carrier recombination to occur. It is important that the delocalization of the nonequilibrium carriers influences the carrier density in two ways, having opposite sign effects on the PL efficiency. The delocalization enhances the luminescence efficiency, since the free carriers recombine via bimolecular-type transitions with the rate proportional to the square of the carrier density, while the radiative recombination of the localized carriers is linear (like that of excitons). In our study, we selected low-efficiency samples to exclude the saturation of nonradiative recombination as a possible origin of the photoluminescence efficiency increase. Therefore, the enhancement due to increasing contribution of bimolecular recombination remains the only plausible explanation of such an increase, which we observe in a wide range of excitation intensities at room temperature, and which is gradually overwhelmed by the droop as the temperature is decreased. The droop might be caused by the increased ability of the carriers to move by hopping via the shallow localized states, and to reach the recombination centers, where they recombine nonradiatively. The overall influence of the carrier delocalization at room and low temperatures can be explained by the different occupancy of the localized states. At low temperatures, most of the carriers populate the localized states. After the localized states are predominantly filled-in, the further increase in the carrier generation rate results in generation of predominantly free carriers, which can move longer distances, reach nonradiative recombination centers and recombine there. As a result, the droop is observed. At elevated temperatures, trapping of the free carriers becomes more pronounced, since the carrier distribution becomes broader and localized states for trapping are available even at high carrier densities. The contribution of the bimolecular recombination increases due to increasing fraction of the free carriers, while frequent trapping-detrapping decreases the distance the free carriers move during their lifetime. As a result, the PL efficiency increases up to the carrier densities sufficient for stimulated recombination causing the efficiency droop. In conclusion, it is observed that delocalization i) increases the PL efficiency by increasing the contribution of bimolecular recombination of free carriers, and ii) causes the PL droop by enhancement of nonradiative recombination. The study of the competition between these two opposite-sign effects revealed that the ratio kT/σ might be treated as the parameter indicating the predominant origin of PL droop in AlGaN-based MQWs. In AlGaN MQWs with low band gap fluctuations at high temperatures (kT/σ > 1), the droop is caused by stimulated emission. For kT/σ < 1, the droop occurs due to enhancement of nonradiative recombination as the localized states are populated and an increasing fraction of carriers become free at elevated excitation intensities. Acknowledgments The work at VU was funded by the European Social Fund under the Global Grant measure project VP1-3.1-ŠMM-07-K-02-014. The work at RPI was supported primarily by the Engineering Research Centers Program (ERC) of the National Science Foundation under NSF Cooperative Agreement No. EEC-0812056 and in part by New York State under NYSTAR contract C090145 and by I/UCRC “CONNECTION ONE” (award 11347230).
#203009 - $15.00 USD Received 12 Dec 2013; revised 13 Jan 2014; accepted 20 Jan 2014; published 27 Feb 2014 (C) 2014 OSA 10 March 2014 | Vol. 22, No. S2 | DOI:10.1364/OE.22.00A491 | OPTICS EXPRESS A497
Institute of Applied Research and Semiconductor Physics Department, Vilnius University, Saulėtekio al. 9 – III, Vilnius, LT-10222, Lithuania 2 Department of ECE and CIE, Rensselaer Polytechnic Institute, Troy, New York 12180, USA 3 Sensor Electronic Technology, Inc., 1195 Atlas Road, Columbia, South Carolina 29209, USA * [email protected]
Abstract: The influence of carrier localization on photoluminescence efficiency droop and stimulated emission is studied in AlGaN multiple quantum wells with different strength of carrier localization. We observe that carrier delocalization at low temperatures predominantly enhances the nonradiative recombination and causes the droop, while the main effect of the delocalization at elevated temperatures is enhancement of PL efficiency due to increasing contribution of bimolecular recombination of free carriers. When the carrier thermal energy exceeds the dispersion of the potential fluctuations causing the carrier localization, the droop is caused by stimulated carrier recombination. ©2014 Optical Society of America OCIS codes: (160.4760) Optical properties; (160.6000) Semiconductor materials; (250.5230) Photoluminescence.
References and links 1.
S. Chichibu, T. Azuhata, T. Sota, and S. Nakamura, “Spontaneous emission of localized excitons in InGaN single and multiquantum well structures,” Appl. Phys. Lett. 69(27), 4188–4190 (1996). 2. C. J. Collins, A. V. Sampath, G. A. Garett, W. L. Sarney, H. Shen, M. Wraback, A. Yu. Nikiforov, G. S. Cargill III, and V. Dierolf, “Enhanced room-temperature luminescence efficiency through carrier localization in AlxGa1xN alloys,” Appl. Phys. Lett. 86(3), 031916 (2005). 3. S. Hammersley, D. Watson-Parris, P. Dawson, M. J. Godfrey, T. J. Badcock, M. J. Kappers, C. McAleese, R. A. Oliver, and C. J. Humphreys, “The consequences of high injected carrier densities on carrier localization and efficiency droop in InGaN/GaN quantum well structures,” J. Appl. Phys. 111(8), 083512 (2012). 4. N. I. Bochkareva, Y. T. Rebane, and Y. G. Shreter, “Efficiency droop and incomplete carrier localization in InGaN/GaN quantum well light-emitting diodes,” Appl. Phys. Lett. 103(19), 191101 (2013). 5. J. Wang, L. Wang, W. Zhao, Z. Hao, and Y. Luo, “Understanding efficiency droop effect in InGaN/GaN multiple-quantum-well blue light-emitting diodes with different degree of carrier localization,” Appl. Phys. Lett. 97(20), 201112 (2010). 6. Y. Lin, Y. Zhang, Z. Liu, L. Su, J. Zhang, T. Wei, and Z. Chen, “Spatially resolved study of quantum efficiency droop in InGaN light-emitting diodes,” Appl. Phys. Lett. 101(25), 252103 (2012). 7. J. Mickevičius, G. Tamulaitis, M. Shur, M. Shatalov, J. Yang, and R. Gaska, “Correlation between carrier localization and efficiency droop in AlGaN epilayers,” Appl. Phys. Lett. 103(1), 011906 (2013). 8. J. Mickevičius, J. Jurkevičius, K. Kazlauskas, A. Žukauskas, G. Tamulaitis, M. S. Shur, M. Shatalov, J. Yang, and R. Gaska, “Stimulated emission in AlGaN/AlGaN quantum wells with different Al content,” Appl. Phys. Lett. 100(8), 081902 (2012). 9. J. Mickevičius, J. Jurkevičius, K. Kazlauskas, A. Žukauskas, G. Tamulaitis, M. S. Shur, M. Shatalov, J. Yang, and R. Gaska, “Stimulated emission due to localized and delocalized carriers in Al0.35Ga0.65N/Al0.49Ga0.51N quantum wells,” Appl. Phys. Lett. 101(4), 041912 (2012). 10. J. Holst, A. Kaschner, U. Gfug, A. Hoffmann, C. Thomsen, F. Bertram, T. Riemann, D. Rudloff, P. Fischer, J. Christen, R. Averbeck, H. Riechert, M. Heuken, M. Schwambera, and O. Schon, “Comparison of the mechanism of optical amplification in InGaN/GaN heterostructures grown by molecular beam epitaxy and MOCVD,” Phys. Status Solidi A 180, 327–332 (2000). 11. M. Strassburg, A. Hoffmann, J. Holst, J. Christen, T. Riemann, F. Bertram, and P. Fischer, “The origin of the PL photoluminescence Stokes shift in ternary group-III nitrides: field effects and localization,” Phys. Status Solidi C 0(6), 1835–1845 (2003).
#203009 - $15.00 USD Received 12 Dec 2013; revised 13 Jan 2014; accepted 20 Jan 2014; published 27 Feb 2014 (C) 2014 OSA 10 March 2014 | Vol. 22, No. S2 | DOI:10.1364/OE.22.00A491 | OPTICS EXPRESS A491
12. E. F. Pecora, W. Zhang, A. Yu. Nikiforov, L. Zhou, D. J. Smith, J. Yin, R. Paiella, L. D. Negro, and T. D. Moustakas, “Sub-250 nm room-temperature optical gain from AlGaN/AlN multiple quantum wells with strong band-structure potential fluctuations,” Appl. Phys. Lett. 100, 061111 (2012). 13. E. F. Pecora, W. Zhang, A. Yu. Nikiforov, J. Yin, R. Paiella, L. D. Negro, and T. D. Moustakas, “Sub-250 nm light emission and optical gain in AlGaN materials,” J. Appl. Phys. 113(1), 013106 (2013). 14. A. Satake, Y. Masumoto, T. Miyajima, T. Asatsuma, and M. Ikeda, “Two-dimensional exciton dynamics and gain formation processes in InxGa1-xN multiple quantum wells,” Phys. Rev. B 60(24), 16660–16666 (1999). 15. A. Žukauskas, K. Kazlauskas, G. Tamulaitis, P. Pobedinskas, S. Juršėnas, S. Miasojedovas, V. Yu. Ivanov, M. Godlewski, C. Skierbiszewski, M. Siekacz, G. Franssen, P. Perlin, T. Suski, and I. Grzegory, “Role of band potential roughness on the luminescence properties of InGaN quantum wells grown by MBE on bulk GaN substrates,” Phys. Status Solidi B 243(7), 1614–1618 (2006). 16. V. N. Jmerik, A. M. Mizerov, A. A. Sitnikova, P. S. Kop’ev, S. V. Ivanonv, E. V. Lutsenko, N. P. Tarasuk, N. V. Rzheutskii, and G. P. Yablonskii, “Low-threshold 303 nm lasing in AlGaN-based multiple-quantum well structures with an asymmetric waveguide grown by plasma-assisted molecular beam epitaxy on c-sapphire,” Appl. Phys. Lett. 96(14), 141112 (2010). 17. V. N. Jmerik, A. N. Mizerov, T. V. Shubina, A. A. Toropov, K. G. Belyaev, A. A. Sitnikova, M. A. Yagovkina, P. S. Kop'ev, E. V. Lutsenko, A. V. Danilchyk, N. V. Rzheutskii, G. P. Yablonskii, B. Monemar, and S. V. Ivanov, “Optically pumped lasing at 300.4 nm in AlGaN MQW structures grown by plasma-assisted molecular beam epitaxy on c-Al2O3,” Phys. Status Solidi A 207(6), 1313–1317 (2010). 18. P. G. Eliseev, P. Perlin, J. Lee, and M. Osinski, “"Blue” temperature-induced shift and band-tail emission in InGaN-based light sources,” Appl. Phys. Lett. 71(5), 569–571 (1997). 19. A. Bell, S. Srinivasan, C. Plumlee, H. Omiya, F. A. Ponce, J. Christen, S. Tanaka, A. Fujioka, and Y. Nakagawa, “Exciton freeze-out and thermally activated relaxation at local potential fluctuations in thick AlxGa1-xN layers,” J. Appl. Phys. 95(9), 4670–4674 (2004). 20. N. Nepal, J. Li, M. L. Nakarmi, J. Y. Lin, and H. X. Jiang, “Temperature and compositional dependence of the energy band gap of AlGaN alloys,” Appl. Phys. Lett. 87(24), 242104 (2005). 21. J. Mickevičius, G. Tamulaitis, E. Kuokštis, K. Liu, M. S. Shur, J. P. Zhang, and R. Gaska, “Well-widthdependent carrier lifetime in AlGaN/AlGaN quantum wells,” Appl. Phys. Lett. 90(13), 131907 (2007). 22. J. Mickevičius, J. Jurkevičius, M. S. Shur, J. Yang, R. Gaska, and G. Tamulaitis, “Photoluminescence efficiency droop and stimulated recombination in GaN epilayers,” Opt. Express 20(23), 25195–25200 (2012).
It is generally accepted that carrier localization results in high internal quantum efficiency (IQE) in III-nitride semiconductors [1,2]. However, as the carrier density is increased, the carriers populate the localized states with energies closer to the extended states, and the effective localization strength decreases [3,4]. Such carrier delocalization due to increasing carrier density plays an important role in the efficiency droop in InGaN quantum well (QW) structures [3,5,6] and AlGaN epilayers [7]. The stronger localizing potential fluctuations might be expected to increase the IQE. However, it also has an impact on high-carrier-density effects influencing the stimulated emission threshold [8–11] and also resulting in the efficiency droop at lower excitation levels [7]. The interrelation between localization conditions, efficiency droop, and stimulated emission threshold is quite complex. Moreover, temperature strongly affects the redistribution of carriers through the localized states, which makes the recombination processes even more complicated. Our investigations [7–9] and the data reported in literature [12,13] show that carrier localization in AlGaN, especially at high Al content, does play an important role in carrier dynamics even at room temperature. In this paper, we link the carrier localization and highdensity effects (efficiency droop and stimulated emission), which are of interest for applications of AlGaN in UV light emitters. In the samples with comparatively strong carrier localization and low internal quantum efficiency, selected for this study, this link is quite strong. Importantly, the link might also be important for the AlGaN-based emitters with less pronounced carrier localization, and it should be accounted for in the further development of AlGaN-based light-emitting diodes (LEDs) and laser diodes (LDs). The AlGaN-based multiple quantum wells (MQWs) investigated in this study were grown by a combination of conventional metal-organic chemical vapor deposition (MOCVD) and migration enhanced metal-organic chemical vapor deposition (MEMOCVD®) techniques on c-plane sapphire substrates. The samples contained ten QWs with Al molar fractions of 8% (samples A1 and A2), 18% (sample B1), and 35% (samples C1, C2, and C3). The samples
#203009 - $15.00 USD Received 12 Dec 2013; revised 13 Jan 2014; accepted 20 Jan 2014; published 27 Feb 2014 (C) 2014 OSA 10 March 2014 | Vol. 22, No. S2 | DOI:10.1364/OE.22.00A491 | OPTICS EXPRESS A492
containing the same Al content had different well widths, therefore, different strength of the carrier localization. Table 1 lists the main structural parameters of the samples under study. Table 1. The structure details of the samples under study. Sample A1 A2 B1 C1 C2 C3
Al content (%) Well Barrier 8 20 8 20 18 40 35 49 35 49 35 49
Width (nm) Well Barrier 1.9 11.5 2.9 11.5 2.5 15.0 5.0 11.5 4.1 11.5 2.5 11.5
PL Intensity (arb. units)
The photoluminescence (PL) of the samples was excited by the 4th harmonic (266 nm) of Q-switched YAG:Nd laser radiation (pulse duration 4 ns). A closed-cycle helium cryostat ensured the variation of temperature in the range from 8 to 300 K. The luminescence signal was focused into a double monochromator (Jobin Yvon HRD-1) and detected by a UVenhanced photomultiplier. The spontaneous emission properties were measured in the conventional front-surface configuration. To study the stimulated emission, the incident laser beam was focused into a long (2 mm) and narrow (150 µm) stripe on the sample edge. The light propagating along the stripe was collected and analyzed.
8% Al AlGaN MQWs T = 20 K P/Pthr
2.3 1.3 0.69
(a) 3.7
3.8 35% Al AlGaN MQWs T = 20 K
P/Pthr 2.3 1.2
(b)
0.74
4.3
4.4
4.5
Photon energy (eV) Fig. 1. Edge PL spectra of AlGaN MQWs samples A1 (a) and C1 (b) measured at 20 K temperature under several excitation power densities below and above the threshold for stimulated emission. The threshold was equal to 170 kW/cm2 and 970 kW/cm2 for samples A1 and C1, respectively. The spectra were normalized and shifted for clarity. The vertical line indicates the peak positions of spontaneous luminescence bands.
The edge emission spectra were measured under the excitation power density varied from ~40 kW/cm2 to ~7 MW/cm2 in the temperature range from 20 to 300 K. Figure 1 presents several spectra measured under different excitation power densities at 20 K for samples A1 and C1. For both samples, a stimulated emission band emerges at the excitation power densities above a certain threshold. The stimulated emission threshold was equal to 170 kW/cm2 and 970 kW/cm2 for samples A1 and C1, respectively. The stimulated emission band is located on the low-energy slope of the spontaneous band in sample A1 [see Fig. 1(a)], as well as in samples A2 and B1 [not shown in Fig. 1]. This position is typical of structures with weak or no carrier localization [8]. Meanwhile, in all samples of group C (with the larger Al content of 35%) the stimulated emission band is located on the high-energy slope [see
#203009 - $15.00 USD Received 12 Dec 2013; revised 13 Jan 2014; accepted 20 Jan 2014; published 27 Feb 2014 (C) 2014 OSA 10 March 2014 | Vol. 22, No. S2 | DOI:10.1364/OE.22.00A491 | OPTICS EXPRESS A493
Fig. 1(b) for the sample C1]. As shown in previous publications on InGaN [10,11,14,15] and AlGaN [8,9,11,16,17], this position of stimulated emission peak is an indication of strong carrier localization, which affects the carrier dynamics even up to stimulated emission threshold.
0
Peak position shift (meV)
-20
AlGaN MQWs A1 σ = 13 meV A2 σ = 12 meV B1 σ = 26 meV
-40
0
-20
AlGaN MQWs C1 σ = 30 meV C2 σ = 39 meV C3 σ = 41 meV
-40
0
50
100
150
200
250
300
Temperature (K) Fig. 2. Temperature dependences of PL band peak position shift relative to the position at 8 K in AlGaN MQWs (points) for the samples listed in Table 1. Solid lines show the best fit using a simple model of carrier (exciton) hopping through localized states.
The carrier localization conditions in the AlGaN MQWs under study were estimated using the temperature dependence of the PL band peak position measured in the conventional frontsurface configuration. The points in Fig. 2 present the shift of the band peak with respect to the peak position at 8 K. All the samples exhibited non-monotonous peak shift behavior, which is similar to the so-called S-shape dependence typical of materials, where carriers move by hopping via localized states [18,19]. The S-shaped dependence at elevated temperatures can be described using a simple quantitative model linking the band shift to the fluctuations of the local potential. At nondegenerate occupation, the temperature dependence of PL peak position can be expressed as [18]: E peak ( T ) = E g ( 0 ) −
αT 2 σ 2 − . β + T k BT
(1)
Here Eg(0) is the effective band gap at T = 0, α and β are Varshni coefficients for band gap reduction with increasing temperature, and σ is the standard deviation of the Gaussian distribution of the band gap fluctuations due to the random fluctuations in Al content and/or
#203009 - $15.00 USD Received 12 Dec 2013; revised 13 Jan 2014; accepted 20 Jan 2014; published 27 Feb 2014 (C) 2014 OSA 10 March 2014 | Vol. 22, No. S2 | DOI:10.1364/OE.22.00A491 | OPTICS EXPRESS A494
QW width. The points in Fig. 2 show the dependences of the shift in the PL peak position relative to its value at 8 K. The dependences shown by solid lines were calculated according to Eq. (1) with α and β values from Ref. [20], and Eg(0) as an adjustable parameter to fit the maximum value of the calculated shift for each curve. At low temperatures, the freeze-out of carriers (excitons) takes place, and the experimental data deviate from the dependence described by Eq. (1). All the fits were quite adequate, and the corresponding values of the localization parameter σ are indicated in Fig. 2.
1.0
(a) T = 300 K
Normalized PL efficiency (arb. u.)
0.8 0.6 0.4 0.2
AlGaN MQWs A1 σ = 13 meV B1 σ = 26 meV C3 σ = 41 meV
1.0 0.8 0.6 0.4 0.2 0.0
(b) T=8K 1
10
100
1000
10000 2
Excitation power density (kW/cm ) Fig. 3. Normalized PL efficiency dependences on excitation power density in AlGaN MQWs with different localization strengths (indicated) at 300 K (a) and 8 K (b).
The relation between localization parameter σ and the properties of stimulated emission band can be observed. The stimulated emission band appears on low-energy slope in the samples with weak localization (σ ≤ 26 meV). As localization becomes stronger (σ ≥ 30 meV), the stimulated emission peak shifts to high-energy slope of the spontaneous emission band. This observation confirms that carrier localization is important in high-Alcontent AlGaN MQWs up to the carrier densities high enough for stimulated emission to occur. Using the carrier lifetime of 58 ps determined for sample C1 in Ref. [21], the carrier density corresponding to the stimulated emission threshold at room temperature is ~3 × 1019 cm−3. To analyze the links between carrier localization conditions and efficiency droop, we measured the excitation power density dependence of the spectrally integrated PL efficiency at several temperatures. The typical room temperature dependences are plotted in Fig. 3 for several samples under study. Using the data in Fig. 3, the efficiency droop onset was
#203009 - $15.00 USD Received 12 Dec 2013; revised 13 Jan 2014; accepted 20 Jan 2014; published 27 Feb 2014 (C) 2014 OSA 10 March 2014 | Vol. 22, No. S2 | DOI:10.1364/OE.22.00A491 | OPTICS EXPRESS A495
SE threshold/droop onset
estimated as the excitation power density corresponding to the highest PL efficiency and separating the initial increase in PL efficiency and its decrease (droop) above the onset.
3
10
2
10
1
10
0
10
0.0
0.5
1.0
1.5
2.0
kT/σ Fig. 4. Ratio of thresholds for stimulated emission and droop onset as a function of the ratio of thermal energy to dispersion of potential fluctuations for 6 different samples at various temperatures. The solid line indicates the ratio between stimulated emission threshold and droop onset equal to 1.
When comparing the stimulated emission threshold and droop onset dependences on localization parameter, several peculiarities were noticed. At low temperatures, the stimulated emission threshold is always at much higher excitations than the droop onset. Meanwhile, at 300 K, the values of droop onset and stimulated emission threshold are quite close, except for the strongest localization. Moreover, at low temperatures, the value of the ratio between the stimulated emission threshold and droop onset is above ~40 and steadily increases with localization parameter σ. The increase in temperature results in a decrease of the ratio for the MQWs with the weakest localization, while having no significant influence in the samples with the strongest localization. To summarize these trends, we plotted the ratio of the thresholds for stimulated emission and droop onset as a function of the ratio of the thermal energy to the dispersion of potential fluctuations [see Fig. 4]. Each point in Fig. 4 corresponds either to a different sample with a different σ value in the range from 12 to 41 meV or to a different temperature (20, 100, 180, or 300 K). Despite the strong scattering of the points in Fig. 4, which is expected, first of all, due to different carrier lifetimes in different samples, the plot reveals a clear trend: i) as the ratio kT/σ increases (either because of smaller σ or larger T) up to 1, the ratio of the thresholds for stimulated emission and droop onset becomes smaller, and ii) the efficiency droop and stimulated emission occurs at the same excitation power density, when kT becomes larger than σ. This is an indication that the dominating droop origin in AlGaN with low band gap fluctuations at high temperatures might be caused by stimulated emission. It is worth noting that the light amplification by stimulated emission of radiation (i.e., the LASER effect) might be not observed in AlGaN MQWs and, especially, in epilayers, because the amplification due to stimulated emission is overcompensated by the light losses due to scattering and absorption by dislocations (abundant in AlGaN, especially in high-Alcontent AlGaN). For LEDs, it is important that the stimulated emission, though being ineffective in the light amplification, effectively decreases the useful light output of an LED. As pointed out in our previous study on the droop in GaN [22], the total (spontaneous and stimulated) light emission efficiency might increase at increasing excitation intensity but the front-surface emission efficiency, which is actually important for LED operation in the current injection mode, decreases.
#203009 - $15.00 USD Received 12 Dec 2013; revised 13 Jan 2014; accepted 20 Jan 2014; published 27 Feb 2014 (C) 2014 OSA 10 March 2014 | Vol. 22, No. S2 | DOI:10.1364/OE.22.00A491 | OPTICS EXPRESS A496
For AlGaN MQWs with low kT/σ, the droop has to have a different origin related to the carrier (exciton) localization. As shown above, the carrier localization might play a significant role in the carrier dynamics up to the nonequilibrium carrier densities sufficient for stimulated carrier recombination to occur. It is important that the delocalization of the nonequilibrium carriers influences the carrier density in two ways, having opposite sign effects on the PL efficiency. The delocalization enhances the luminescence efficiency, since the free carriers recombine via bimolecular-type transitions with the rate proportional to the square of the carrier density, while the radiative recombination of the localized carriers is linear (like that of excitons). In our study, we selected low-efficiency samples to exclude the saturation of nonradiative recombination as a possible origin of the photoluminescence efficiency increase. Therefore, the enhancement due to increasing contribution of bimolecular recombination remains the only plausible explanation of such an increase, which we observe in a wide range of excitation intensities at room temperature, and which is gradually overwhelmed by the droop as the temperature is decreased. The droop might be caused by the increased ability of the carriers to move by hopping via the shallow localized states, and to reach the recombination centers, where they recombine nonradiatively. The overall influence of the carrier delocalization at room and low temperatures can be explained by the different occupancy of the localized states. At low temperatures, most of the carriers populate the localized states. After the localized states are predominantly filled-in, the further increase in the carrier generation rate results in generation of predominantly free carriers, which can move longer distances, reach nonradiative recombination centers and recombine there. As a result, the droop is observed. At elevated temperatures, trapping of the free carriers becomes more pronounced, since the carrier distribution becomes broader and localized states for trapping are available even at high carrier densities. The contribution of the bimolecular recombination increases due to increasing fraction of the free carriers, while frequent trapping-detrapping decreases the distance the free carriers move during their lifetime. As a result, the PL efficiency increases up to the carrier densities sufficient for stimulated recombination causing the efficiency droop. In conclusion, it is observed that delocalization i) increases the PL efficiency by increasing the contribution of bimolecular recombination of free carriers, and ii) causes the PL droop by enhancement of nonradiative recombination. The study of the competition between these two opposite-sign effects revealed that the ratio kT/σ might be treated as the parameter indicating the predominant origin of PL droop in AlGaN-based MQWs. In AlGaN MQWs with low band gap fluctuations at high temperatures (kT/σ > 1), the droop is caused by stimulated emission. For kT/σ < 1, the droop occurs due to enhancement of nonradiative recombination as the localized states are populated and an increasing fraction of carriers become free at elevated excitation intensities. Acknowledgments The work at VU was funded by the European Social Fund under the Global Grant measure project VP1-3.1-ŠMM-07-K-02-014. The work at RPI was supported primarily by the Engineering Research Centers Program (ERC) of the National Science Foundation under NSF Cooperative Agreement No. EEC-0812056 and in part by New York State under NYSTAR contract C090145 and by I/UCRC “CONNECTION ONE” (award 11347230).
#203009 - $15.00 USD Received 12 Dec 2013; revised 13 Jan 2014; accepted 20 Jan 2014; published 27 Feb 2014 (C) 2014 OSA 10 March 2014 | Vol. 22, No. S2 | DOI:10.1364/OE.22.00A491 | OPTICS EXPRESS A497
