Open Access
Add to BibSonomy
Abstract
Optical properties and carrier dynamics of AlGaAs/AlAs asymmetric double quantum wells (ADQWs) with varied barrier thickness are studied by excitation-power-dependent photoluminescence (PL) and temperature-dependent time-resolved PL (TRPL) experiments. The origin of the transition energies derived from the time-integrated spectra is confirmed by theoretical calculation using the Schrödinger equation. The carrier kinetics and the temporal behavior of the emission in the narrow well (NW) and wide well (WW) are physically revealed with varying barrier thicknesses by the TRPL measurements. For a better understanding of the carrier transport mechanism, the electron tunneling times for the ADQWs are theoretically estimated based on a rate-equation model. The calculation indicates that the electron tunneling time decreases with increasing temperature, which may be induced by enhanced phonon-assisted scattering.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent years, ultra-short optical pulses are widely utilized in a variety of applications in fundamental sciences and engineering, such as pulsed laser deposition, micromachining [1,2], free-space communications [3], and nonlinear frequency conversion [4]. Particularly, as a possible pulsed light source, gain-switched semiconductor lasers have attracted considerable attention due to their advantages of low cost, simple operation, and compact size. The improvement of the structural and material properties of the laser diodes is an effective way to generate even shorter gain-switched pulses, which is helpful to develop semiconductor-based ultrashort pulse lasers into application-ready devices. Owing to a number of unique properties, including higher coupling efficiency between gain medium, a broader gain spectrum, enhancement of the optical confinement, and efficient transferring of carriers [5–7], the asymmetric coupled quantum wells (ACQWs) structures are good candidates for use as the active layer of semiconductor lasers. ACQWs are coupled quantum wells with different well thicknesses and/or compositions. There has been much interest in the study of the fundamental optical properties and the carrier dynamics of the ACQWs structure and their utilization in optoelectronic devices [8–12]. Due to the giant electrorefractive index change, the ACQWs are promising to realize low-voltage and high-speed compact modulators and switches [13]. In addition, tunable tunneling-induced quantum interference in ACQWs has been exploited to achieve highly efficient frequency mixing [14,15] and ultrafast all-optical switching [16]. The enhancement of carrier injection and uniform carrier distribution in the ACQWs benefiting from the conventional or anomalous tunneling mechanism [17–19], can significantly increase the recombination efficiency of the active medium. As a result, ACQW structures are utilized to reduce the efficiency drop in LED with a high current density [20–22]. Moreover, optimization of asymmetric quantum wells structure can change the dominant transport mechanism for evidently improving the performance of resonant tunneling diode (RTD) [23,24]. In gain-switching operation, the carrier recombination dynamics in the active layer play an important role in determining the transient characteristics of the output pulses [25], where carrier tunneling between the ACQWs is considered to be efficient for modifying the carrier recombination processes [17,26]. Therefore, exploring the complicated fundamental physical mechanisms of carrier tunneling in ACQWs is of great importance to further improve the active-region structure and enhance the device performance.
In this paper, the fundamental optical properties and carrier tunneling behavior of the AlGaAs/AlAs asymmetric double quantum wells (ADQWs) with different barrier thickness are investigated by excitation-power-dependent photoluminescence (PL) and temperature-dependent time-resolved PL (TRPL). The transition energies in the ADQW structure are calculated using Schrödinger equation, and the calculations show a good agreement with the energies derived from the time-integrated spectra with several well-fitted peaks. The TRPL experiments are performed to understand the carrier dynamics and the time behavior of the luminescence of the narrow well (NW) and wide well (WW) for the ADQW samples. According to the proposed rate-equation model, it is found that the electron tunneling time decreases with increasing temperature, which is ascribed to enhanced phonon-assisted scattering.
2. Materials and methods
The AlGaAs/AlAs ADQW structures used in this work were epitaxially grown on GaAs substrates using molecular beam epitaxy (MBE) system. In order to ensure the high optical quality of the materials, the temperature of growth is set near the deoxidation temperature of the wafer. The compositions of the materials were is characterized by X-ray diffraction. The sample structures are schematized in Fig. 1, which consists of a 200-nm GaAs buffer layer, a 5-nm GaAs cap layer, a 5.8-nm Al0.3Ga0.7As narrow quantum well (NW) and a 16-nm Al0.3Ga0.7As wide quantum well (WW) separated by 2 nm (Sample 1) or 15 nm (Sample 2) AlAs potential barrier. The samples mounted in a liquid helium flow cryostat with a temperature range from 5 to 300 K were optically pumped with a 1-kHz, 400-nm, 300-fs pulse laser beam with a spot diameter of around 50 µm. The TRPL signals were measured by a slow-scan-mode streak camera (C10910 Hamamatsu) with a time resolution of 20 ps.
Fig. 1. Schematic structure of AlGaAs/AlAs ADQWs and detailed parameters of ADQWs for Sample 1 and Sample 2.
3. Results and discussion
Figures 2(a) and (b) display the time-resolved streak camera images of the AlGaAs/AlAs ADQWs for Sample 1 (S1) and Sample 2 (S2) at temperature of 5 K with the excitation power of 6 mW. The corresponding time-integrated PL spectra (blue circle line) of the ADQWs for S1 and S2 extracted from the streak-camera images are shown in Figs. 2(c) and (d), respectively. The dash dot curves show the Gaussian fitting of the three corresponding peaks in the time-integrated PL spectra. Since the pumping spot area on the sample is 2.0×10−5 cm2, the carrier density at a total incident power of 1 mW can be estimated to be 1×1021 cm-3 assuming the quantum efficiency of 50%. Noted that the photoexcited carrier density greatly surpass the Mott density (1018-1019 cm-3) of GaAs/AlGaAs quantum well [27,28]. In this case, a collective electron-hole plasma (EHP) phase is formed where the excitons finally lose their quasiparticle nature and no bound excitonic states are present due to the screening of the Coulomb interaction [29,30]. Therefore, compared with the excitons, the EHP radiative recombination plays a dominant role in the luminescence in such high-level excitation. Then, the energy levels of electrons (E) and holes (H) for WW and NW were calculated neglecting the exciton bound energy, in order to confirm the origin of the transitions for ADQW structure. Figure 3 displays the calculated energy band diagram of ADQW structure. The quantized electron and hole energy levels and wave functions of these two quantum wells were calculated using the Schrödinger equation by a finite-difference method based on the envelope-function approximation [31]. The material parameters used in the calculation are listed in Table 1[32,33]. Additionally, the band offset ratio is taken to be 62:38 for the conduction and valence bands of AlGaAs/AlAs interfaces [32]. The calculated quantized electron and hole energy levels of WW and NW are listed in Table 2. It should be noted that decreasing the barrier thickness from 15 to 2.0 nm has little effect on the calculated quantized electron and hole energy levels of each QW in this structure. This behavior is different from what is observed in the AlGaAs/GaAs CDQW’s [34,35]. In this latter case, when decreasing the barrier width, the QW ground-state energy of both holes and electrons decreases due to the interwell coupling of the confined wave functions. However, the wavefunctions of our ADQW structure behave as in the case of a single quantum well with almost no well-to-well coupling of the states even though the barrier thickness is 2.0 nm, as shown in Fig. 3. It may be related to the large difference in the width of WW and NW. The calculated and measured transition energies of ADQWs for S1 and S2 are presented in Table 3. A blueshift (19 meV) of the Peak 3 in S1 was clearly observed compared to that in S2, we suppose this to the more efficient screening of the QW potential by the charge carriers in the wide well for S1, since the barrier is narrow and more carriers accumulate in the wide well.
Fig. 2. Time- and spectra-resolved streak camera images of the AlGaAs/AlAs ADQWs for (a) Sample 1 (S1) and (b) Sample 2 (S2) with a high excitation power of 6 mW at 5 K. (c,d) Time-integrated PL spectra of the ADQWs extracted from the corresponding streak-camera images of S1 and S2 shown in (a) and (b), respectively. The green dash dot curves show the Gaussian fitting results of the three peaks in the time-integrated PL spectra.
Fig. 3. The quantized electron and hole energy levels and wave functions calculated from Schrödinger equation for the AlGaAs/AlAs ADQW structure with parameters taken from Table 1. The detailed calculated data are shown in Table 2.
Table 1. Parameters for Al0.3Ga0.7As and AlAs used in the calculation.
Table 2. Calculated quantized electron and hole energy levels of WW and NW.
Table 3. Calculated and measured transition energies of ADQWs.
By comparing the transition energies derived from time-integrated PL spectra and theoretical calculations, it is found that the highest-energy peak (Peak 1) in the PL spectrum is assigned to the interband transitions from the first quantized hole level to the first quantized electron level (ENW1 → HNW1) of the narrow well. The mid-energy peak (Peak 2) and lowest-energy peak (Peak 3) correspond to the transitions between the second quantized hole level to the second quantized electron level (EWW2 → HWW2), and the first quantized hole level to the first quantized electron level (EWW1 → HWW1) for wide well, respectively. Combining with Fig. 2(c) and (d), it can be observed clearly that under identical excitation conditions the emission of the narrow well becomes weaker with decreasing barrier thickness. The variation of intensities in the NW indicates the occurrence of the carrier transfer from NW to WW as the barrier decreases, which results in additional exhaustion of the carrier population in the NW. This is a clear indication that carrier tunneling is a relevant effect.
Figure 4(a) and (b) show the normalized excitation power dependences of PL spectra at a temperature of 5 K for S1 and S2, respectively. As it is shown, under low excitation power, only the one emission peak of the WW (Peak 3) can be observed for both samples because carriers are always trying to fill the lowest energy level. With increasing the excitation power, due to the carrier distribution becoming relatively uniform, the other emission peaks gradually appear. However, the intensity of the NW emission for S1 with a thin barrier is clearly decreased compared to the S2 with a thicker barrier under high excitation. This can be well explained by the tunneling behavior between the adjacent well through a thin barrier, that is, the electrons in the narrow well tunnel significantly to the wide one, leading to a serious suppression of the radiative emission for the narrow well. In addition, it is seen that the peak energies of the WW (Peak 3) shifted to the low-energy side with increasing excitation intensity, as shown in Fig. 4(c) and (d). Generally, there are two main factors that affect the emission energy when the excitation intensity was varied, including the band-gap shrinkage and the band-filling effect. Since the band-filling effect in a quantum well is insignificant compared with that in bulk material, band-gap shrinkage is more effective in quantum well photoluminescence under high excitation [36]. And Peak 3 in S1 have more obvious redshifts compared to those in S2. The reason for this is that the barrier layer is thick to block the carrier tunneling from NW to WW in S2, thus leading to the carrier density, giving rise to the band-gap shrinkage, in the WW in S2 is much lower than those in S1.
Fig. 4. Normalized PL spectra with offset at varied excitation powers for the Sample 1 (a) and Sample 2 (b) at temperature of 5 K. PL peaks of each QWs extracted by Gaussian fitting at different excitation powers for S1 (c) and S2 (d), respectively.
In order to clarify the carrier transfer process and relaxation dynamics of the AlGaAs/AlAs QWs, the transient spectra at different times after the excitation are extracted from the streak camera images. We can clearly see that in Figs. 5(a) and (b), at the very initial stage, the peak intensities of WW and NW are almost the same for both S1 and S2. However, the total time-integrated spectrum shows the emission of the NW from S1 is much weaker than the WW, as illustrated in Fig. 2. The comparison indicated that the electron tunneling from the NW to WW occurs through a thin barrier during the relaxation of the carriers, leading to a dramatic increase of the decay rate in the NW. As shown in Fig. 5(a) and (c), the emission peak from NW (Peak 1) for S1 disappears rapidly as time goes on. Additionally, we can see another interesting phenomenon that the intensity of the higher-energy peak in WW (Peak 2) occurs a rapid drop along with the quenching of Peak 1 in the time delays from 535 to 685 ps. However, the emission from WW (Peak 3) keeps a stable intensity without any shift of peak position, which indicates that the recombination consumption of carriers in WW can be effectively compensated through carrier tunneling effect. As a result, the emission intensity of Peak 2 in S1 is weaker than that in S2, as shown in Fig. 2(c) and (d). The behavior could be ascribed to the coupling between the E1 electron level of the narrow well (ENW1) and the E2 electron level of the wide well (EWW2), which significantly affects the carrier relaxation behavior. In this case, the majority of electrons on the first-excited subband of WW participate in nonradiative transfer instead of radiative emission. Turning to S2 (see Fig. 5(b) and (d)) where the barrier width is thick enough to suppress the coupling behavior between the adjacent well, the carrier decay in NW is comparable to that in WW. And peak positions of the emission shift toward lower energies with an increase of delay time. The transitions of each subband in WW and NW in S2 seem to be independent as almost no well-to-well coupling of the states.
Fig. 5. (a)-(b) Time-resolved transient spectra of S1 and S2 extracted from the corresponding streak-camera images at 5 K. (c)-(d) Peak energies of each QW at different time delays. (e)-(f) PL decay traces of the WW and NW for S1 and S2.
The corresponding PL decay traces of S1 and S2 are exhibited in Fig. 5(e) and (f), and the decay constants are obtained from exponential fitting included the standard deviation (dash curves). It is observed that the decay trace of NW for S1 shows a fast decay time of 80(±0.5) ps, and the one of WW exhibits a slow decay time of 472(±5.5) ps. However, for S2 shown in Fig. 5(f), the PL lifetime is almost independent of the well width without interwell coupling. That is, the carrier tunneling from NW to WW is more effective in the increase of the PL decay time of WW when the barriers are thin. In S2, the TRPL traces of WW and NW have a comparable fast-decay time of 40(±0.56) ps and 32(±0.26) ps, respectively, followed by a slow decay component of around 200 ps. The TRPL in S2 shows a characteristic of bimolecular recombination, which is similar to the form of the EHP emission at high excitation densities reported in [30,37]. The shortening of the PL lifetime at early delay times can be assigned to the fast radiative decay of a degenerate electron-hole plasma [30].
Streak-camera images at different temperatures were measured to investigate the temperature-dependent carrier dynamics in the ADQWs for a better understanding of the underlying physical mechanism. The streak-camera images of the S1 at different temperatures of 10, 20, 75, and 300 K with the excitation power of 6 mW are shown in Figs. 6(a)-(d). The corresponding time-integrated PL spectra and spectrally-integrated PL decay traces extracted from the streak-camera images are also plotted in Fig. 6. The PL decay curve of NW at 10 K shows a fast decay time of 60(±0.36) ps due to the tunneling of electrons from the NW to the WW. As the temperature rises up to 20 and 75 K, it is seen that the emission peak from NW vanished, leaving only the emission peak from WW with a much larger decay time. It is well known that the thermal escape or thermally activated nonradiative recombination of the carriers in the NW would not likely be dominated at such low temperatures [38], which is experimentally confirmed as indicated in Fig. 7. The emission of the NW is comparable to that of the WW with almost the same PL decay rate when the barrier is thick at 75 K. Therefore, the disappearance of the NW luminescence is a direct consequence of the enhancement of electrons tunneling. The carrier recombination in coupled QWs taking tunneling behavior into account can be described with rate equations as below [39,8]:
Fig. 6. (a)-(d) The streak-camera images of Sample 1 at different temperatures of 10, 20, 75, and 300 K. (e)-(h) The time-integrated PL spectra extracted from the corresponding streak-camera images. The dash curves show the Gaussian fitting results of the peaks in the time-integrated PL spectra. (i)-(l) The spectrally-integrated PL decay traces of NW and WW extracted from the corresponding streak-camera images. The decay constants obtained from exponential fittings (red dashed curves) of the PL traces are given.
Fig. 7. Time- and spectral-resolved PL measurement results of Sample 2 at temperature of 75 and 300 K.
Here, nW and nN are the carrier densities in WW and NW, respectively. The PL decay time τW and τN include the radiative and nonradiative recombination processes. Laser light absorption generates carriers in WW and NW at the generation rates, GW and GN, respectively. δ(t) is a delta function. TNW is the tunneling time from NW to WW. Using the steady-state solutions of the Eqs. (1) and (2), the PL intensity ratio can be described as Eq. (3). At the temperature of 5 K, the integrated PL intensity ratio IW/IN of the two QWs was obtained to be around 3.94 from the Gaussian fitting result shown in Fig. 2(c). The decay times τW and τN of WW and NW are given in Fig. 5(e) as 472(±5.5) and 80(±0.5) ps, respectively. Considering the almost same PL intensity of each peak at the very initial stage after the excitation (shown in Fig. 5(a)), the ratio of generation rate GW/GN = 2 is obtained. Note that the generation rate here is approximatively considered as the total effect of carrier generation and capture in the different wells. According to Eq. (3), the carrier tunneling time TNW can be assessed to be around 124 (±1.2) ps based on the experimental results that GW/GN = 2, IW/IN = 3.94, τW = 472(±5.5) ps, τN = 80(±0.5) ps. Similarly, the TNW at the temperature of 10 K can be estimated to be 76(±0.81) ps, with the experimental results of GW/GN = 2, IW/IN = 4.36, τW = 374(±3.3) ps, τN = 60(±0.36) ps.
The detailed data including decay times, tunneling times, and integrated PL intensity ratio at different temperatures for S1 are summarized in Table 4. The lifetimes of NW at 20 and 75 K are supposed to be below the resolution limit of < 20 ps. Noted that TNW* in Table 4 shows the tunneling times are calculated following the relation reported in [40], which are in good agreement with the calculations based on the rate equations model. As the temperature is up to 300 K, the TNW and TNW* are estimated as 135 and 126 ps. However, we inferred the real tunneling time is smaller than the calculations. It is probably related to the nonradiative recombination processes that our simple calculation has neglected, so does to the model in Ref.41. It is well known the nonradiative decay channels play a major role in the recombination processes at such a high temperature. Therefore, the observed NW PL decay rate in S1 is a sum of the tunneling rate, the radiative and nonradiative recombination rate.
Table 4. PL decay times, the resulting tunneling times and integrated PL intensity ratio at different temperatures for S1.
The experimental results show that, at relatively low temperatures (see Fig. 6), the PL decay time of WW increases with the increase of temperature. There are two factors that will make such a phenomenon. Firstly, the radiative recombination processes are generally slowed down with the increase of temperature [41,42]. Secondly, the tunneling rate will increase obviously with the increase of temperature, which is in agreement with the calculated tunneling time showing a decrease with elevated temperature using rate equations above. The tunneling effect is dominated in our study. It is known that the phonon-assisted tunneling behavior is sensitive to temperature, and the phonon-assisted scattering time shows an increase with decreasing temperature [43]. The energy difference (ΔE) between the ground levels of NW and WW in our sample is estimated to be around 70 meV, which is larger than twice the longitudinal-optical phonon energy of 34 meV for Al0.3Ga0.7As [44]. This benefits a further decrease in the electron tunneling time in the phonon-absorption scenario. Therefore, the enhancement of electron tunneling with increasing the temperature indicates a phonon-absorption mechanism may exist in the carrier tunneling process in our case. The effect of increasing temperature is also to provide more phonons, enhancing the scattering and reducing the contrast between emission and absorption [45].
As the temperature increases up to 300 K, the PL lifetime is also independent of the well width in S2 (see Fig. 7(f)). Therefore, the faster decay of PL lifetime in narrow well in S1 also can be attribute to the tunneling effect. Although the thermal escape or thermally activated nonradiative recombination of the carriers cannot be ignored in quantum well, resulting in the difficulty to estimate the tunneling time accurately, the tunneling behavior is still observed to influence the PL lifetime during the relaxation process in S1. In addition, we can see that the PL lifetimes of NW and WW in S1 are much longer than those in S2, resulting from the fast spontaneous radiative recombination is suppressed by the carrier relaxation between the coupling quantum well, which can significantly enhance the possibility of the population inversion in the optical pumping scheme. This behavior is very useful for the design of powerful QW lasers. Moreover, the carrier tunneling between the coupled ADQWs is effective to modify the carrier recombination processes, which is of great significance to influence the characteristics of devices. Therefore, these results in this paper are expected to provide essential reference in designing coupled ADQW-based devices.
4. Conclusion
In summary, the carrier dynamics in AlGaAs/AlAs QWs with varied-well-thickness of 5.8 nm (NW) and 16 nm (WW) separated by different barrier width grown by MBE were systematically investigated by excitation-power-dependent PL and temperature-dependent TRPL. In order to confirm the origin of the transitions extracted from the time-integrated spectra through Gaussian fitting, the subband energy levels were calculated using the Schrödinger equation. Moreover, the carrier dynamics and recombination processes are clarified by the excitation power and temperature dependences of the luminescence. The PL lifetime decreasing with the increase of temperature is independent of the well width when the barrier is thick. The fast decay of the NW emission gives clear evidence of carrier tunneling from NW to WW in the coupled ADQWs. The tunneling times are extracted based on a set of rate equations, showing a negative correlation with temperature. The increase of tunneling rate with increasing temperature can be explained by the phonon-absorption mechanism in the carrier tunneling process. Although the recombination channels become more complicated at room temperature, the tunneling behavior is still observed to influence the PL lifetime during the relaxation process. The coupling between the ADQWs is effective to modifying the carrier recombination processes, resulting in the longer PL lifetime of QWs, which can be of great significance to influence the characteristics of devices. This work is useful in understanding the carrier dynamics of ADQWs and provides a guidance to design and fabricate ADQW-based high-performance devices.
Funding
National Natural Science Foundation of China (61874044, 61975225, 62035014); Japan Society for the Promotion of Science (21H01361); Science and Technology Commission of Shanghai Municipal (21DZ1101102).
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant Nos. 61874044, 61975225 and 62035014), Science and Technology Commission of Shanghai Municipal (21DZ1101102), the Strategic Priority Research Program of ECNU of China, the Research Funds of MoE Nanophotonics and Advanced Instrument Engineering Research Center, and the Fundamental Research Funds for the Central Universities. This work was also partly supported by KAKENHI No. 21H01361 from JSPS, in Japan.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. M. Kraus, M. A. Ahmed, A. Michalowski, A. Voss, R. Weber, and T. Graf, “Microdrilling in steel using ultrashort pulsed laser beams with radial and azimuthal polarization,” Opt. Express 18(21), 22305–22313 (2010). [CrossRef]
2. M. Pervolaraki, Ph. Komninou, J. Kioseoglou, A. Othonos, and J. Giapintzakis, “Ultrafast pulsed laser deposition of carbon nanostructures: structural and optical characterization,” Appl. Surf. Sci. 278, 101–105 (2013). [CrossRef]
3. F. Feng, I. H. White, and T. D. Wilkinson, “Free space communications with beam steering a two-electrode tapered laser diode using liquid-crystal SLM,” J. Lightwave Technol. 31(12), 2001–2007 (2013). [CrossRef]
4. K. Kowalewski, J. Zembek, V. Envid, and D. C. Brown, “201 W picosecond green laser using a mode-locked fiber laser driven cryogenic Yb:YAG amplifier system,” Opt. Lett. 37(22), 4633–4635 (2012). [CrossRef]
5. J. Zhang, L. Cai, B. Zhang, S. Li, F. Lin, J. Shang, D. Wang, K. Lin, J. Yu, and Q. Wang, “Low threshold lasing of GaN-based vertical cavity surface emitting lasers with an asymmetric coupled quantum well active region,” Appl. Phys. Lett. 93(19), 191118 (2008). [CrossRef]
6. J. Wang, J. -. Leburton, F. H. Julien, and A. Saar, “Design and performance optimization of optically-pumped mid-infrared intersubband semiconductor lasers,” IEEE Photonics Technol. Lett. 8(8), 1001–1003 (1996). [CrossRef]
7. Y. Nomura, H. Sugimoto, S. Maruno, Y. Morishita, O. Wada, and T. Ogama, “Gain switching of an AlGaAs/GaAs laser with an asymmetric double quantum well,” Appl. Phys. Lett. 57(25), 2672–2674 (1990). [CrossRef]
8. T. Tada, A. Yamaguchi, T. Ninomiya, H. Uchiki, T. Kobayashi, and T. Yao, “Tunneling process in AlAs/GaAs double quantum wells studied by photoluminescence,” J. Appl. Phys. 63(11), 5491–5494 (1988). [CrossRef]
9. A. T. Roberts, A. Mohanta, H. O. Everitt, J. H. Leach, D. Van Den Broeck, A. M. Hosalli, T. Paskova, and S. M. Bedair, “Spectroscopic investigation of coupling among asymmetric InGaN/GaN multiple quantum wells grown on non-polar a-plane GaN substrates,” Appl. Phys. Lett. 103(18), 181106 (2013). [CrossRef]
10. G. Livescu, A. M. Fox, D. A. B. Miller, T. Sizer, W. H. Knox, A. C. Gossard, and J. H. English, “Resonantly enhanced electron tunneling rates in quantum wells,” Phys. Rev. Lett. 63(4), 438–441 (1989). [CrossRef]
11. Ph. Roussignol, A. Vinattieri, L. Carraresi, M. Colocci, and A. Fasolino, “Resonance effects in the carrier-tunneling dynamics in asymmetric coupled quantum wells,” Phys. Rev. B 44(16), 8873–8879 (1991). [CrossRef]
12. S. Ten, M. F. Krol, B. P. McGinnis, M. J. Hayduk, G. Khitrova, and N. Peyghambarian, “Temperature- and carrier-density-dependent electron tunneling kinetics in (Ga,In)As/(Al,In)As asymmetric double quantum wells,” J. Appl. Phys. 79(3), 1526–1531 (1996). [CrossRef]
13. T. Arakawa, T. Toya, M. Ushigome, K. Yamaguchi, T. Ide, and K. Tada, “InGaAs/InAlAs five-layer asymmetric coupled quantum well exhibiting giant electrorefractive index change,” Jpn. J. Appl. Phys. 50, 032204 (2011). [CrossRef]
14. H. Sun, S. Fan, H. Zhang, and S. Gong, “Tunneling-induced high-efficiency four-wave mixing in asymmetric quantum wells,” Phys. Rev. B 87(23), 235310 (2013). [CrossRef]
15. E. Dupont, Z. R. Wasilewski, and H. C. Liu, “Terahertz emission in asymmetric quantum wells by frequency mixing of midinfrared waves,” IEEE J. Quantum Electron. 42(11), 1157–1174 (2006). [CrossRef]
16. H. Wu, J. Gao, J. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95(5), 057401 (2005). [CrossRef]
17. G. Weng, B. Zhang, M. Liang, X. Lv, J. Zhang, L. Ying, Z. Qiu, H. Yaguchi, S. Kuboya, K. Onabe, S. Chen, and H. Akiyama, “Optical properties and carrier dynamics in asymmetric coupled InGaN multiple quantum wells,” Funct. Mater. Lett. 6, 1350021 (2013). [CrossRef]
18. J. Zhang, L. Cai, B. Zhang, X. Hu, F. Jiang, J. Yu, and Q. Wang, “Efficient hole transport in asymmetric coupled InGaN multiple quantum wells,” Appl. Phys. Lett. 95(16), 161110 (2009). [CrossRef]
19. X. Ji, F. Yang, J. Wang, R. Duan, K. Ding, Y. Zeng, G. Wang, and J. Li, “Luminescence distribution and hole transport in asymmetric InGaN multiple-quantum well light-emitting diodes,” J. Semicond. 31(9), 094009 (2010). [CrossRef]
20. X. Ni, Q. Fan, R. Shimada, Ü. Özgür, and H. Morkoçb, “Reduction of efficiency droop in InGaN light emitting diodes by coupled quantum wells,” Appl. Phys. Lett. 93(17), 171113 (2008). [CrossRef]
21. G. Verzellesi, D. Saguatti, M. Meneghini, F. Bertazzi, M. Goano, G. Meneghesso, and E. Zanoni, “Efficiency droop in InGaN/GaN blue light-emitting diodes: physical mechanisms and remedies,” J. Appl. Phys. 114(7), 071101 (2013). [CrossRef]
22. L. Zhu, W. Liu, F. Zeng, Y. Gao, B. Liu, Y. Lu, and Z. Chen, “Efficiency droop improvement in InGaN/GaN light-emitting diodes by graded-composition multiple quantum wells,” IEEE Photonics J. 5(2), 8200208 (2013). [CrossRef]
23. L. Yang, Y. Li, Y. Wang, S. Xu, and Y. Hao, “Asymmetric quantum-well structures for AlGaN/GaN/AlGaN resonant tunneling diodes,” J. Appl. Phys. 119(16), 164501 (2016). [CrossRef]
24. Y. Liu, B. Gao, M. Gong, and R. Shi, “Modeling and optimization of a double-well double-barrier GaN/AlGaN/GaN/AlGaN resonant tunneling diode,” J. Appl. Phys. 121(21), 215701 (2017). [CrossRef]
25. S. Chen, T. Nakamura, T. Ito, X. Bao, H. Nakamae, G. Weng, X. Hu, M. Yoshita, H. Akiyama, J. Liu, M. Ikeda, and H. Yang, “Picosecond tunable gain-switched blue pulses from GaN laser diodes with nanosecond current injections,” Opt. Express 25(12), 13046–13054 (2017). [CrossRef]
26. G. Weng, S. Chen, B. Zhang, X. Hu, S. Kuboya, and K. Onabe, “Dynamics of carrier tunneling and recombination in asymmetric coupled InGaN multiple quantum wells,” Opt. Express 25(20), 24745–24755 (2017). [CrossRef]
27. A. John Peter, “Metal-insulator transitions due to shallow donors in a GaAs/AlGaAs quantum well,” Phys. E (Amsterdam, Neth.) 42(2), 91–94 (2009). [CrossRef]
28. M. Carras, V. Berger, X. Marcadet, and B. Vinter, “Experimental evidence of a Mott transition in highly doped two-dimensional confined structures,” Phys. Rev. B 70(23), 233310 (2004). [CrossRef]
29. G. Weng, J. Tian, S. Chen, J. Yan, H. Zhang, Y. Liu, C. Zhao, X. Hu, X. Luo, J. Tao, S. Chen, Z. Zhu, J. Chu, and H. Akiyama, “Electron-hole plasma lasing dynamics in CsPbClmBr3-m microplate lasers,” ACS Photonics 8(3), 787–797 (2021). [CrossRef]
30. L. Kappei, J. Szczytko, F. Morier-Genoud, and B. Deveaud, “Direct observation of the Mott transition in an optically excited semiconductor quantum well,” Phys. Rev. Lett. 94(14), 147403 (2005). [CrossRef]
31. S. F.-P. Paul and H. Fouckhardt, “An improved shooting approach for solving the time-independent Schrödinger equation for III/V QW structures,” Phys. Lett. A 286(2-3), 199–204 (2001). [CrossRef]
32. N. Watanabe and H. Kawai, “Single and coupled double-well GaAs/AlGaAs and energy-dependent light-hole mass,” J. Appl. Phys. 60(10), 3696–3698 (1986). [CrossRef]
33. I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, “Band parameters for III–V compound semiconductors and their alloys,” J. Appl. Phys. 89(11), 5815–5875 (2001). [CrossRef]
34. E.M. Lopes, J.L. Duarte, L.C. Pocas, I.F.L. Dias, E. Laureto, A.A. Quivy, and T.E. Lamas, “Exciton behavior in GaAs/AlGaAs coupled double quantum wells with interface disorder,” J. Lumin. 130(3), 460–465 (2010). [CrossRef]
35. D. Atkinson, G. Parry, and E J Austin, “Modelling of electroabsorption in coupled quantum wells with applications to low-voltage optical modulation,” Semicond. Sci. Technol. 5(6), 516–524 (1990). [CrossRef]
36. H. Kawai, K. Kaneko, and N. Watanabe, “Photoluminescence of AlGaAs/GaAs quantum wells grown by metalorganic chemical vapor deposition,” J. Appl. Phys. 56(2), 463–467 (1984). [CrossRef]
37. S. JurSenas, M. Strumskis, A. iukausk, and A. I. Ekimov, “Surface recombination of nonequilibrium electron-hole plasma in laser-modified semiconductor-doped glasses,” Solid State Commun. 87(6), 577–580 (1993). [CrossRef]
38. D. Y. Oberli, J. Shah, T. C. Damen, C. W. Tu, T. Y. Chang, D. A. B. Miller, J. E. Henry, R. F. Kopf, N. Sauer, and A. E. DiGiovanni, “Direct measurement of resonant and nonresonant tunneling times in asymmetric coupled quantum wells,” Phys. Rev. B 40(5), 3028–3031 (1989). [CrossRef]
39. G. Weng, Y. Liu, S. Chen, T. Ito, X. Hu, C. Zhao, J. Liu, J. Chu, and H. Akiyama, “Quantitative study of electron tunneling dynamics in asymmetric coupled InGaN/GaN quantum wells,” Appl. Opt. 59(20), 6231–6236 (2020). [CrossRef]
40. M. Nido, M. G. W. Alexander, W. W. Rühle, T. Schweizer, and K. Kohler, “Nonresonant electron and hole tunneling times in GaAs/Al0.35Ga0.65As asymmetric double quantum wells,” Appl. Phys. Lett. 56(4), 355–357 (1990). [CrossRef]
41. J. Feldmann, G. Peter, E. O. Göbel, P. Dawson, K. Moore, C. Foxon, and R. J. Elliott, “Linewidth dependence of radiative exciton lifetimes in quantum wells,” Phys. Rev. Lett. 59(20), 2337–2340 (1987). [CrossRef]
42. M. Tsuchiya, T. Matsusue, and H. Sakaki, “Tunneling escape rate of electrons from quantum well in double-barrier heterostructures,” Phys. Rev. Lett. 59(20), 2356–2359 (1987). [CrossRef]
43. A. F. M. Anwar and Kevin R. Lefebvre, “Electron escape via polar optical-phonon interaction and tunneling from biased quantum wells,” Phys. Rev. B 57(8), 4584–4590 (1998). [CrossRef]
44. S. Adachi, “GaAs, AlAs, and AlxGa1−xAs: Material parameters for use in research and device applications,” J. Appl. Phys. 58(3), R1–R29 (1985). [CrossRef]
45. T. Weil and B. Vinter, “Calculation of phonon-assisted tunneling between two quantum wells,” J. Appl. Phys. 60(9), 3227–3231 (1986). [CrossRef]
