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AlGaAs coupled double quantum wells with bimodal heterointerface roughness
Journal of Luminescence 132 (2012) 1183–1187
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Magnetophotoluminescence study of GaAs/AlGaAs coupled double quantum wells with bimodal heterointerface roughness E.M. Lopes a,n, J.L. Duarte b, I.F.L. Dias b, E. Laureto b, P.S.S. Guimara~ es c, A.G.S. Subtil c, A.A. Quivy d a
~ Paulo, Brazil Departamento de Fı´sica, Quı´mica e Biologia, Universidade Estadual Paulista, CP 266, CEP 19060-900, Presidente Prudente, Sao ´, Brazil Departamento de Fı´sica, Universidade Estadual de Londrina, CP 6001, CEP 86051-970, Londrina, Parana c Departamento de Fı´sica, Instituto de Ciˆencias Exatas, Universidade Federal de Minas Gerais, CP 702, CEP 30123-970, Belo Horizonte, Minas Gerais, Brazil d ~ Paulo, CP 66318, CEP 05315-970, Sao ~ Paulo, Brazil ´rio de Novos Materiais Semicondutores, Instituto de Fı´sica, Universidade de Sao Laborato b
a r t i c l e i n f o
abstract
Article history: Received 12 August 2010 Received in revised form 2 November 2011 Accepted 21 December 2011 Available online 3 January 2012
This work reports on the results of magnetophotoluminescence (MPL) measurements carried out in a sample containing two Al0.35Ga0.65As/GaAs, coupled double quantum wells (CDQWs), with inter-well barriers of different thicknesses, which have the heterointerfaces characterized by a distribution of bimodal roughness. The MPL measurements were performed at 4 K, with magnetic fields applied parallel to the growth direction, and varying from 0 to 12 T. The diamagnetic shift of the photoluminescence (PL) peaks is more sensitive to changes in the confinement potential, due to monolayer variations in the mini-well thickness, rather than to the exciton localization at the local potential fluctuations. As the magnetic field increases, the relative intensities of the two peaks in each PL band inverts, what is attributed to the reduction in the radiative lifetime of the delocalized excitons, which results in the radiative recombination, before the excitonic migration between the higher and lower energy regions in each CDQW occurs. The dependence of the full width at half maximum (FWHM) on magnetic field shows different behaviors for each PL peak, which are attributed to the different levels and correlation lengths of the potential fluctuations present in the regions associated with each recombination channel. & 2011 Elsevier B.V. All rights reserved.
Keywords: Magnetophotoluminescence Coupled double quantum wells GaAs/AlGaAs Interface disorder Potential fluctuations
1. Introduction An heterostructure that has been receiving considerable attention from the scientific community is the coupled double quantum wells (CDQWs) system, which consists of two single quantum wells (mini-wells), separated by a thin barrier (inter-well barrier) that allows the overlap of the wavefunctions in both quantum wells, due to the tunneling effect. Besides the importance of that system concerning optoelectronic applications [1–5], there is also a great interest from the academic point of view, especially in relation to the observation and understanding of new physical effects, e.g., the exciton condensation at low temperatures [6–9]. Although semiconductors growth techniques have advanced in the last decades, random variations in the width and/or in the alloy composition of the layers that make up the heterostructure are practically inevitable. Such variations generate fluctuations in the excitonic confinement potential, which strongly affects the optical properties of these heterostructures [10–15]. The analysis
n Correspondence to: Rua Oito, no 275, Park Santa Mˆonica, Osvaldo Cruz, SP, CEP 17700-000, Brazil. Tel.: þ55 18 3528 2829, 55 18 9787 7007. E-mail address: [email protected] (E.M. Lopes).
0022-2313/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jlumin.2011.12.065
of such potential fluctuations in CDQWs is not a simple extension of the potential fluctuation problem in single quantum wells (SQWs) due to the fact that in CDQWs, due to the different effective masses of electrons and holes, the inter-well barrier produces different effects on the electron and heavy-hole wave functions: while the probability of finding the heavy hole at the center of the well is strongly reduced by the insertion of a thin inter-well barrier, the square of the electronic wave function is weakly affected. This effect is responsible for the existence of a minimum in the excitonic binding energy for a narrow inter-well barrier [16] and so a mono-layer (ML) variation in the well and/or inter-well barrier thickness can substantially change the physical properties in this kind of system. However, there is little literature concerning the problem of potential fluctuations in CDQWs. A lot of important information on the optical properties of semiconductor heterostructures can be provided by experiments with magnetic fields. That kind of experiment is especially useful in the investigation of excitons confined in heterointerfaces defects [17–19]. The application of a magnetic field perpendicular to the layers of a heterostructure shifts the energy levels to higher energies (diamagnetic shift). Although the behavior of the diamagnetic shift on dimensionality in different quantum structures can be, sometimes, somewhat complicated [20,21], for SQWs
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[18,19,22] and CDQWs [23] the shift is expected to be directly proportional to the dimensionality of the spatial region where the exciton is, and the smaller the dimensionality (larger confinement) the smaller the diamagnetic shift. Therefore, if a given heterostructure is characterized by interfaces with local potential fluctuations, the excitons localized in the smaller energy states will present relatively smaller diamagnetic shifts, since they are confined more strongly than the free excitons [18,19]. We have recently published a work on the photoluminescence (PL) properties of two molecular-beam epitaxy (MBE) grown CDQWs [24]. The results showed that such CDQWs present bimodal roughness at the heterointerfaces, which splits the PL band into two peaks. The different PL lines are originated from quantum well regions where interfaces present extended islands (larger than the exciton diameter) that differ between themselves by approximately 1 ML and exhibit nanoroughness on a length scale smaller than the exciton diameter [25–28]. Samples with such interface configuration have two factors that compete to dictate the behavior of the diamagnetic shift observed: (i) the confinement generated by each CDQW region and (ii) the potential fluctuation (caused by nanoroughness and variations in the barriers composition) existent in those regions. This paper reports on an investigation about the effects on the PL properties when a magnetic field is applied normal to the layers of a sample containing two CDQWs with bimodal interface roughness. The aim of the work is to compare the exciton behavior in CDQWs, with different inter-well barrier thicknesses, which present spacial regions with different levels and correlation lengths of potential fluctuations, using the magnetophotoluminescence (MPL) technique as a probe. The diamagnetic shift observed for each PL peak is discussed in terms of the confinement generated by the effective thickness of the region where the exciton is and of the potential fluctuation degree associated with that region. The changes in the relative intensities of the peaks that compose each PL band, with increasing magnetic field, is attributed to alterations in excitonic migration between the higher and smaller energy regions in each CDQW. The full width at half maximum (FWHM) dependence on magnetic field can be explained by the degree and the extension of the potential fluctuations associated with each recombination channel.
the PL from the sample to the spectrometer was transmitted by four optical fibers, with a diameter of 100 mm each. The typical power density of the excitation light at the surface of the sample was about 0.26 W/cm2 (which corresponds to the excitation power of 0.1 mW in our previous work [24]).
3. Experimental results
2. Experimental
Fig. 1 shows the PL (0 T) spectrum obtained at 4 K. Two emission bands are observed in defined positions, which are identified by comparing their energies with the values obtained through calculations based on the envelope function formalism [29] and refined with corrections for the excitonic binding energy following the Mathieu–Lefebvre–Christol (MLC) model [30] along with the approach proposed by Zhao et al. [23] for CDQWs. The MLC model is based on the idea of fractional dimensional space considering the wave function penetration at the barrier regions in a SQW, while Zhao et al. [23] proposed to extend this model for CDQWs taking into account the contribution of the inter-well barrier for the effective thickness. The PL band located at 1.595 eV is originated from recombinations at the CDQW5, while the band located at 1.645 eV is originated from recombinations at the CDQW30. For comparison, the e1-hh1 recombina˚ tion energy for a similar 40 A-thick SQW is 1.570 eV, i.e., the insertion of central inter-well barriers of 5 A˚ and 30 A˚ thickness shifts the fundamental energy levels by 25 meV and 75 meV, respectively. This occurs because in addition to the split of the SQW energy levels (into symmetric and anti-symmetric levels), there is also a shift to higher energies due to the reduction in the dimensionality. Two recombination channels can be observed in each emission band of the spectrum showed in Fig. 1 and so, in order to fit the spectrum properly, two Gaussian peaks were considered for each emission band (P1 and P2 for CDQW5 and P3 and P4 for CDQW30). This procedure has already been used in other studies [15,24,31,32], being considered appropriate for this kind of spectral analysis (see, for example, Ref. [31, p. R12]). The energy values shown in Fig. 1 were obtained through this fitting. Fig. 2 shows the PL spectra obtained at 4 K for different magnetic fields (MPL). In order to make the figure clearer the spectra are vertically shifted. One can observe the two recombination channels competing in each PL band: at low fields, the
A sample containing two GaAs CDQWs with Al0.35Ga0.65As barriers was used in this study. This configuration assures that the temperature and excitation power are very similar for both CDQWs during the measurements. The sample was grown by MBE on a GaAs substrate, without growth interruption at the ˚ heterointerfaces. First, a 5000 A-thick GaAs buffer layer was ˚ grown, followed by a 1000 A-thick Al0.35Ga0.65As layer. Next, ˚ two GaAs/Al0.35Ga0.65As CDQWs and a 300 A-thick Al0.35Ga0.65As barrier, between the two CDQWs, were grown. The first CDQW is ˚ constituted by two 40 A-thick GaAs quantum wells separated by a ˚ 5 A-thick Al0.35Ga0.65As inter-well barrier. The second CDQW is ˚ constituted by two 40 A-thick GaAs quantum wells, separated by ˚ a 30 A-thick Al0.35Ga0.65As inter-well barrier. Finally, there is a ˚ ˚ 300 A-thick Al0.35Ga0.65As barrier and a 50 A-thick GaAs cap layer. MPL measurements were performed with magnetic fields applied perpendicular to the heterointerfaces up to 12 T, at 4 K. The MPL spectra were detected using a system combining a 0.75 m grating spectrometer and a liquid-nitrogen-cooled CCD with an exposure time of 0.4 s. The excitation source was the 5145 A˚ line of an Ar þ laser. The excitation light was chopped mechanically, and the radiation was transmitted from the laser to the sample by an optical fiber, with a diameter of 400 mm, while
Fig. 1. Photoluminescence spectrum obtained at 4 K and 0 T. The dotted lines represent the four Gaussian peaks used to fit the experimental data (open circles) while the solid line corresponds to the total fit.
E.M. Lopes et al. / Journal of Luminescence 132 (2012) 1183–1187
Fig. 2. PL spectra at 4 K for several values of magnetic fields between 0 T and 12 T. The spectra are vertically shifted for clarity.
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Fig. 4. Full width at half maximum (FWHM) of the PL peaks as a function of magnetic field intensity at 4 K.
peaks P1 and P4, the FWHM presents a small increase; for the peak P2, a slight reduction is observed, and, for the peak P3, the FWHM does not present significant variation for the magnetic field intensities used.
4. Discussion
Fig. 3. The magnetic-field dependence of the two energy peaks observed for the CDQW5 (solid symbols) and for the CDQW30 (open symbols).
smaller energy channels (P1 and P3) are more intense, but, as the magnetic field increases, the higher energy channels become more and more intense, and they seem to dominate the PL band at 12 T. Fig. 2 also shows a displacement of the PL bands to higher energies (blueshift) with increasing magnetic field intensity. For a more appropriate analysis, the PL spectra obtained at different magnetic fields were fitted in a similar way to that shown in Fig. 1. All the subsequent discussion will be based on the results obtained through these fits. The excitonic energy shift, as a function of the magnetic field, relative to the zero field energy, is shown in Fig. 3 for the four peaks. It shows that the peaks associated with the CDQW5 (P1 and P2) present larger shifts in comparison to the peaks associated to the CDQW30 (P3 and P4). In addition, for both CDQWs, the higher energy channels (P2 and P4) present lower shifts in comparison to the respective smaller energy channels (P1 and P3). The full width at half maximum (FWHM) as a function of the magnetic field, at 4 K, is shown in Fig. 4 for the four emission peaks. In general, the FWHM associated to each peak presents different behaviors as the intensity of the magnetic field increases: for the
As the interfaces profile will be of fundamental importance for the interpretation of the MPL spectra properties, we will present, initially, a brief discussion concerning the origin of the two emission peaks observed for each CDQW in Fig. 1. A detailed discussion regarding the PL spectra properties at 0 T can be found in our previous work [24]. Literature presents several works that use the so called bimodal interface roughness model to explain a series of effects observed in semiconductor heterostructures, especially the split of the PL band in two or more peaks [24–28]. That model suggests that the different PL channels are due to the existence of extended terraces (larger than the exciton diameter) at the heterointerfaces, which give origin to quantum well regions that differ among themselves by approximately one ML. In addition, those regions can exhibit a certain distribution of nanoroughness on a length scale smaller than the exciton diameter. In experiments where a magnetic field is applied perpendicular to the layers of a semiconductor heterostructure a general trend is the shift of the energy levels to higher energies, known as diamagnetic shift [22,23,33]. This shift is attributed to the increase in the oscillator strength with increasing magnetic field (B//z), due to the reduction of the excitonic wave function extension in the xy plane [34]. Generally, in the case of SQWs, the diamagnetic shift decreases with decreasing well width, which is the expected behavior when the system dimensionality is reduced in this kind of structure [18,19,22,23]. Table 1 shows dimensions for the mini-wells and for the interwell barrier, which result in the best match between the theoretical (performed as before) and the experimental values for each PL peak, at low temperatures. Theoretical results obtained for Lef and for the system dimensionality (a) of each CDQW region, calculated following the approximation suggested by Zhao et al. [23], are also shown (those results are in excellent agreement with experimental values obtained through the fit of the diamagnetic shift curves of each PL peak showed in Fig. 3 [35]).
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Table 1 Theoretical values for the: CDQWs’s dimensions that best agree with the experimentally measured PL peaks, system dimensionality (a) and effective width (Lef). Peak
˚ Mini-wells (A)
˚ Inter-well barrier (A)
a
˚ Lef (A)
P1 P2 P3 P4
42.8 40.0 40.0 37.2
7.8 7.8 32.8 32.8
2.39 2.38 2.34 2.33
110.3 106.1 89.2 86.6
In an attempt to explain the differences in the diamagnetic shift of the four PL peaks (see Fig. 3), we will consider the confinement generated by each region of the mini-wells interfaces: (i) for the same CDQW, the higher diamagnetic shift is observed for the peak related to the mini-well regions that present a one ML larger width (higher a), and (ii) between the two studied CDQWs, the diamagnetic shift is higher for the system, which has the weaker carrier confinement, i.e., the CDQW5. An important result is the fact that the change in the confinement generated by the variation in the mini-wells thickness is the dominant effect for the diamagnetic shift differentiation between the channels observed for a same CDQW. In our previous work [24], different potential fluctuation levels (PFL) were observed for the four channels that compose the PL spectrum of our sample: (i) P1 and P4 are associated to channels that present intermediate PFL; (ii) P2 is associated to a channel practically free from fluctuations and (iii) P3 is originated from a channel that presents the higher PFL among them (moreover, the carriers, which recombine through this channel experience an absolute minimum (deeper), present in the confinement potential). The PFL associated with each emission peak can be ranked, in a descending order, in the following way: PFL3 4PFL1 4PFL4 4PFL2. As discussed previously, the excitons localized in the states generated by the fluctuations in the confinement potential of SQWs should present relatively lower diamagnetic shifts, since they will be more strongly confined than the free excitons [18,19]. In this context, higher diamagnetic shifts would be observed for P2 in CDQW5 and for P4 in CDQW30, since they present lower PFL when compared to P1 and P3, respectively. However, this is not what happens. P1 presents higher diamagnetic shift than P2, and P3 has higher shift than P4, showing that the effect of the confinement due to the variation of one ML in the mini-well (or inter-well barrier) thickness has greater influence than the excitonic localization in the local potential fluctuations, even if these are of great magnitude, as in the case of the P3 channel. To our knowledge this finding was not reported before. Following the competition between the two emission peaks for each PL band with increasing magnetic field will be discussed (Fig. 2). At a null field, P1 presents more intense emission than P2 but, as the magnetic field is increased, P2 gains intensity faster than P1 and, at 12 T, P2 is the most intense peak in the CDQW5 PL band. Although that behavior is not so evident for the peaks, which compose the CDQW30 PL band, the spectral fitting showed that the effect is very similar. That behavior can be explained by analyzing the magnetic field influence on the excitonic migration between the different regions of each CDQW. At 0 T, the delocalized excitons generated in the higher energy regions can migrate to the lower energy regions, that process being responsible for the higher intensity of P1. With the reduction of the excitonic wave function extension in the well plane (and the consequent increase in the oscillator force) due to the magnetic field application [33], the probability of radiative recombinations to occur is increased and so the excitons from the higher energy regions have higher probability of recombining before migrating to the lower energy regions, thus stopping contributing to the P1 intensity and
contributing to the P2 intensity. This behavior is not so evident between the CDQW30 peaks due to its higher oscillator strength; in this case, with increasing magnetic field, the reduction of excitonic wavefunction extension is not so effective and, as a consequence, the effect of reducing excitonic migration from higher energy regions to the lower ones is also less effective, resulting in a less pronunciated competition between the intensities of the peaks for this CDQW. The dependence of the FWHM on the magnetic field, shown in Fig. 4, is quite different among the four peaks. To understand the experimental results, which show that the FWHM of one peak (P2) decreases with increasing magnetic field, those of other two (P4 and P1) increases, and that of another (P3) is practically constant, we will consider a model recently developed by Bansal et al. [36]. To apply that model, which was primarily developed for single quantum wells, to double quantum wells, we have also used the methodology proposed by Zhao et al. [23], which allows to consider a system of two coupled quantum wells as a single quantum well system, with effective width Lef (Table 1). According to Bansal et al. [36], the fact that the linewidth sometimes shows an increase and sometimes a decrease with increasing B can be understood by postulating the existence of two correlation lengths for the interface fluctuations, one (w1) much smaller than the exciton size and the other one (w2) of the order of the exciton size. In the case of lateral correlation w1 (w1 5 aB) the FWHM is proportional to (w1/aB) and in the case of lateral correlation w2 (w2 aB) the FWHM is proportional to (aB/ w2). So, it is expected that, for w1 lateral correlation lengths an increase in the magnetic field (what implies in the excitonic wave function shrinkage) results in a FWHM increase; on the other hand, for w2 an increase in the magnetic field (and a consequent aB decrease) should result in a reduction of the FWHM. It is also expected that lateral correlations of type w2 affect more intensely thicker wells, differently from the lateral correlations of type w1, which affect more intensely thinner wells. Fig. 4 shows that the P2 FWHM decreases as the magnetic field increases. As discussed previously, P2 is associated with regions with lower PFL, and originates from a CDQW with larger effective ˚ Then, global fluctuations (of larger extenwidth (Lef ¼106.1 A). sion) should have a stronger effect on that well and, hence, with the reduction of the excitonic wave function extension by the magnetic field, the FWHM decreases. On the other hand, although PFL4 is small, P4 is associated with the well of smaller effective width; hence, the local fluctuations should be decisive for a FWHM increase. Therefore, with an increase in magnetic field, and the consequent excitonic diameter reduction, the P4 FWHM increases. For P1, which is associated with a region of relatively high PFL (PFL1 4PFL4 4PFL2), the behavior is that expected: the FWHM increases with increasing magnetic field. The behavior of P3 FWHM is the only one that does not follow exactly that model: the FWHM value is practically constant for the whole range of the applied magnetic field. We attribute that behavior to the fact that the local PFL associated to P3 is very high (P3 FWHM at null field is twice the P1 FWHM), what makes the magnetic field variation weakly affect the FWHM already extremely large at null field.
5. Conclusions In this work, we carried out a study on the effects of the application of magnetic fields on the emission properties of two GaAs/Al0.35Ga0.65 CDQWs with different inter-well barriers, grown on the same substrate. Each CDQW presents two emission channels, which are attributed to the existence of bimodal roughness in the heterointerfaces. Theoretical predictions for CDQWs agree with the experimental results in the sense that the higher
E.M. Lopes et al. / Journal of Luminescence 132 (2012) 1183–1187
the system dimensionality the higher the diamagnetic shift. Alterations on the confinement potential, generated by variations in the effective thickness of each mini-well, affect the diamagnetic shift more strongly than the excitonic localization at the local potential fluctuations. The changes in the relative intensities of the peaks that compose each PL band, with increasing magnetic field, are attributed to the radiative lifetime reduction of the delocalized excitons, what makes the radiative recombination occur before the excitonic migration from the higher energy regions to the lower energy regions in each CDQW takes place. The dependence of the FWHM as a function of the magnetic field is explained by considering the different levels and correlation lengths of the potential fluctuations existents in the spatial regions associated to each recombination channel.
Acknowledgments The authors would like to acknowledge the financial support granted by the Brazilian agencies: Fundac- a~ o de Amparo a Pesquisa do Estado de Sa~ o Paulo (FAPESP), Coordenac- a~ o de Aperfeicoamento de Pessoal de Nı´vel Superior (CAPES), Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico (CNPq), Fundac- a~ o Arauca´ria de Apoio ao Desenvolvimento Cientı´fico e Tecnolo´gico do Parana´ (Fundac- a~ o Arauca´ria), and Fundac- a~ o Banco do Brasil (FBB). References [1] X.G. Peralta, S.J. Allen, M.C. Wanke, N.E. Harff, J.A. Simmons, M.P. Lilly, J.L. Reno, P.J. Burke, J.P. Eisenstein, Appl. Phys. Lett. 81 (2002) 1627. [2] X.G.P. Grish, Terahertz Plasmon Modes in Grating Coupled Double Quantum Well Field Effect Transistors, Ph.D. Thesis, University of California, Santa Barbara, 2002. ¨ ¨ [3] P. Janes, P. Holmstrom, U. Ekenberg, IEEE J. Quantum Electron. 38 (2002) 178. [4] H. Yoshikda, T. Simoyama, V.A. Gopal, J. Kasai, T. Mozume, H. Ishikawa, IEICE Trans. Electron. E87C (7) (2004) 1134. [5] M. Miura, S. Katayama, Sci. Technol. Adv. Mater. (2006) 286. [6] L.V. Butov, A.C. Gossard, D.B. Chemla, Nature 418 (2002) 751. [7] D. Snoke, S. Denev, Y. Liu, L. Pfeiffer, K. West, Nature 418 (2002) 754.
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Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
Magnetophotoluminescence study of GaAs/AlGaAs coupled double quantum wells with bimodal heterointerface roughness E.M. Lopes a,n, J.L. Duarte b, I.F.L. Dias b, E. Laureto b, P.S.S. Guimara~ es c, A.G.S. Subtil c, A.A. Quivy d a
~ Paulo, Brazil Departamento de Fı´sica, Quı´mica e Biologia, Universidade Estadual Paulista, CP 266, CEP 19060-900, Presidente Prudente, Sao ´, Brazil Departamento de Fı´sica, Universidade Estadual de Londrina, CP 6001, CEP 86051-970, Londrina, Parana c Departamento de Fı´sica, Instituto de Ciˆencias Exatas, Universidade Federal de Minas Gerais, CP 702, CEP 30123-970, Belo Horizonte, Minas Gerais, Brazil d ~ Paulo, CP 66318, CEP 05315-970, Sao ~ Paulo, Brazil ´rio de Novos Materiais Semicondutores, Instituto de Fı´sica, Universidade de Sao Laborato b
a r t i c l e i n f o
abstract
Article history: Received 12 August 2010 Received in revised form 2 November 2011 Accepted 21 December 2011 Available online 3 January 2012
This work reports on the results of magnetophotoluminescence (MPL) measurements carried out in a sample containing two Al0.35Ga0.65As/GaAs, coupled double quantum wells (CDQWs), with inter-well barriers of different thicknesses, which have the heterointerfaces characterized by a distribution of bimodal roughness. The MPL measurements were performed at 4 K, with magnetic fields applied parallel to the growth direction, and varying from 0 to 12 T. The diamagnetic shift of the photoluminescence (PL) peaks is more sensitive to changes in the confinement potential, due to monolayer variations in the mini-well thickness, rather than to the exciton localization at the local potential fluctuations. As the magnetic field increases, the relative intensities of the two peaks in each PL band inverts, what is attributed to the reduction in the radiative lifetime of the delocalized excitons, which results in the radiative recombination, before the excitonic migration between the higher and lower energy regions in each CDQW occurs. The dependence of the full width at half maximum (FWHM) on magnetic field shows different behaviors for each PL peak, which are attributed to the different levels and correlation lengths of the potential fluctuations present in the regions associated with each recombination channel. & 2011 Elsevier B.V. All rights reserved.
Keywords: Magnetophotoluminescence Coupled double quantum wells GaAs/AlGaAs Interface disorder Potential fluctuations
1. Introduction An heterostructure that has been receiving considerable attention from the scientific community is the coupled double quantum wells (CDQWs) system, which consists of two single quantum wells (mini-wells), separated by a thin barrier (inter-well barrier) that allows the overlap of the wavefunctions in both quantum wells, due to the tunneling effect. Besides the importance of that system concerning optoelectronic applications [1–5], there is also a great interest from the academic point of view, especially in relation to the observation and understanding of new physical effects, e.g., the exciton condensation at low temperatures [6–9]. Although semiconductors growth techniques have advanced in the last decades, random variations in the width and/or in the alloy composition of the layers that make up the heterostructure are practically inevitable. Such variations generate fluctuations in the excitonic confinement potential, which strongly affects the optical properties of these heterostructures [10–15]. The analysis
n Correspondence to: Rua Oito, no 275, Park Santa Mˆonica, Osvaldo Cruz, SP, CEP 17700-000, Brazil. Tel.: þ55 18 3528 2829, 55 18 9787 7007. E-mail address: [email protected] (E.M. Lopes).
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of such potential fluctuations in CDQWs is not a simple extension of the potential fluctuation problem in single quantum wells (SQWs) due to the fact that in CDQWs, due to the different effective masses of electrons and holes, the inter-well barrier produces different effects on the electron and heavy-hole wave functions: while the probability of finding the heavy hole at the center of the well is strongly reduced by the insertion of a thin inter-well barrier, the square of the electronic wave function is weakly affected. This effect is responsible for the existence of a minimum in the excitonic binding energy for a narrow inter-well barrier [16] and so a mono-layer (ML) variation in the well and/or inter-well barrier thickness can substantially change the physical properties in this kind of system. However, there is little literature concerning the problem of potential fluctuations in CDQWs. A lot of important information on the optical properties of semiconductor heterostructures can be provided by experiments with magnetic fields. That kind of experiment is especially useful in the investigation of excitons confined in heterointerfaces defects [17–19]. The application of a magnetic field perpendicular to the layers of a heterostructure shifts the energy levels to higher energies (diamagnetic shift). Although the behavior of the diamagnetic shift on dimensionality in different quantum structures can be, sometimes, somewhat complicated [20,21], for SQWs
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[18,19,22] and CDQWs [23] the shift is expected to be directly proportional to the dimensionality of the spatial region where the exciton is, and the smaller the dimensionality (larger confinement) the smaller the diamagnetic shift. Therefore, if a given heterostructure is characterized by interfaces with local potential fluctuations, the excitons localized in the smaller energy states will present relatively smaller diamagnetic shifts, since they are confined more strongly than the free excitons [18,19]. We have recently published a work on the photoluminescence (PL) properties of two molecular-beam epitaxy (MBE) grown CDQWs [24]. The results showed that such CDQWs present bimodal roughness at the heterointerfaces, which splits the PL band into two peaks. The different PL lines are originated from quantum well regions where interfaces present extended islands (larger than the exciton diameter) that differ between themselves by approximately 1 ML and exhibit nanoroughness on a length scale smaller than the exciton diameter [25–28]. Samples with such interface configuration have two factors that compete to dictate the behavior of the diamagnetic shift observed: (i) the confinement generated by each CDQW region and (ii) the potential fluctuation (caused by nanoroughness and variations in the barriers composition) existent in those regions. This paper reports on an investigation about the effects on the PL properties when a magnetic field is applied normal to the layers of a sample containing two CDQWs with bimodal interface roughness. The aim of the work is to compare the exciton behavior in CDQWs, with different inter-well barrier thicknesses, which present spacial regions with different levels and correlation lengths of potential fluctuations, using the magnetophotoluminescence (MPL) technique as a probe. The diamagnetic shift observed for each PL peak is discussed in terms of the confinement generated by the effective thickness of the region where the exciton is and of the potential fluctuation degree associated with that region. The changes in the relative intensities of the peaks that compose each PL band, with increasing magnetic field, is attributed to alterations in excitonic migration between the higher and smaller energy regions in each CDQW. The full width at half maximum (FWHM) dependence on magnetic field can be explained by the degree and the extension of the potential fluctuations associated with each recombination channel.
the PL from the sample to the spectrometer was transmitted by four optical fibers, with a diameter of 100 mm each. The typical power density of the excitation light at the surface of the sample was about 0.26 W/cm2 (which corresponds to the excitation power of 0.1 mW in our previous work [24]).
3. Experimental results
2. Experimental
Fig. 1 shows the PL (0 T) spectrum obtained at 4 K. Two emission bands are observed in defined positions, which are identified by comparing their energies with the values obtained through calculations based on the envelope function formalism [29] and refined with corrections for the excitonic binding energy following the Mathieu–Lefebvre–Christol (MLC) model [30] along with the approach proposed by Zhao et al. [23] for CDQWs. The MLC model is based on the idea of fractional dimensional space considering the wave function penetration at the barrier regions in a SQW, while Zhao et al. [23] proposed to extend this model for CDQWs taking into account the contribution of the inter-well barrier for the effective thickness. The PL band located at 1.595 eV is originated from recombinations at the CDQW5, while the band located at 1.645 eV is originated from recombinations at the CDQW30. For comparison, the e1-hh1 recombina˚ tion energy for a similar 40 A-thick SQW is 1.570 eV, i.e., the insertion of central inter-well barriers of 5 A˚ and 30 A˚ thickness shifts the fundamental energy levels by 25 meV and 75 meV, respectively. This occurs because in addition to the split of the SQW energy levels (into symmetric and anti-symmetric levels), there is also a shift to higher energies due to the reduction in the dimensionality. Two recombination channels can be observed in each emission band of the spectrum showed in Fig. 1 and so, in order to fit the spectrum properly, two Gaussian peaks were considered for each emission band (P1 and P2 for CDQW5 and P3 and P4 for CDQW30). This procedure has already been used in other studies [15,24,31,32], being considered appropriate for this kind of spectral analysis (see, for example, Ref. [31, p. R12]). The energy values shown in Fig. 1 were obtained through this fitting. Fig. 2 shows the PL spectra obtained at 4 K for different magnetic fields (MPL). In order to make the figure clearer the spectra are vertically shifted. One can observe the two recombination channels competing in each PL band: at low fields, the
A sample containing two GaAs CDQWs with Al0.35Ga0.65As barriers was used in this study. This configuration assures that the temperature and excitation power are very similar for both CDQWs during the measurements. The sample was grown by MBE on a GaAs substrate, without growth interruption at the ˚ heterointerfaces. First, a 5000 A-thick GaAs buffer layer was ˚ grown, followed by a 1000 A-thick Al0.35Ga0.65As layer. Next, ˚ two GaAs/Al0.35Ga0.65As CDQWs and a 300 A-thick Al0.35Ga0.65As barrier, between the two CDQWs, were grown. The first CDQW is ˚ constituted by two 40 A-thick GaAs quantum wells separated by a ˚ 5 A-thick Al0.35Ga0.65As inter-well barrier. The second CDQW is ˚ constituted by two 40 A-thick GaAs quantum wells, separated by ˚ a 30 A-thick Al0.35Ga0.65As inter-well barrier. Finally, there is a ˚ ˚ 300 A-thick Al0.35Ga0.65As barrier and a 50 A-thick GaAs cap layer. MPL measurements were performed with magnetic fields applied perpendicular to the heterointerfaces up to 12 T, at 4 K. The MPL spectra were detected using a system combining a 0.75 m grating spectrometer and a liquid-nitrogen-cooled CCD with an exposure time of 0.4 s. The excitation source was the 5145 A˚ line of an Ar þ laser. The excitation light was chopped mechanically, and the radiation was transmitted from the laser to the sample by an optical fiber, with a diameter of 400 mm, while
Fig. 1. Photoluminescence spectrum obtained at 4 K and 0 T. The dotted lines represent the four Gaussian peaks used to fit the experimental data (open circles) while the solid line corresponds to the total fit.
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Fig. 2. PL spectra at 4 K for several values of magnetic fields between 0 T and 12 T. The spectra are vertically shifted for clarity.
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Fig. 4. Full width at half maximum (FWHM) of the PL peaks as a function of magnetic field intensity at 4 K.
peaks P1 and P4, the FWHM presents a small increase; for the peak P2, a slight reduction is observed, and, for the peak P3, the FWHM does not present significant variation for the magnetic field intensities used.
4. Discussion
Fig. 3. The magnetic-field dependence of the two energy peaks observed for the CDQW5 (solid symbols) and for the CDQW30 (open symbols).
smaller energy channels (P1 and P3) are more intense, but, as the magnetic field increases, the higher energy channels become more and more intense, and they seem to dominate the PL band at 12 T. Fig. 2 also shows a displacement of the PL bands to higher energies (blueshift) with increasing magnetic field intensity. For a more appropriate analysis, the PL spectra obtained at different magnetic fields were fitted in a similar way to that shown in Fig. 1. All the subsequent discussion will be based on the results obtained through these fits. The excitonic energy shift, as a function of the magnetic field, relative to the zero field energy, is shown in Fig. 3 for the four peaks. It shows that the peaks associated with the CDQW5 (P1 and P2) present larger shifts in comparison to the peaks associated to the CDQW30 (P3 and P4). In addition, for both CDQWs, the higher energy channels (P2 and P4) present lower shifts in comparison to the respective smaller energy channels (P1 and P3). The full width at half maximum (FWHM) as a function of the magnetic field, at 4 K, is shown in Fig. 4 for the four emission peaks. In general, the FWHM associated to each peak presents different behaviors as the intensity of the magnetic field increases: for the
As the interfaces profile will be of fundamental importance for the interpretation of the MPL spectra properties, we will present, initially, a brief discussion concerning the origin of the two emission peaks observed for each CDQW in Fig. 1. A detailed discussion regarding the PL spectra properties at 0 T can be found in our previous work [24]. Literature presents several works that use the so called bimodal interface roughness model to explain a series of effects observed in semiconductor heterostructures, especially the split of the PL band in two or more peaks [24–28]. That model suggests that the different PL channels are due to the existence of extended terraces (larger than the exciton diameter) at the heterointerfaces, which give origin to quantum well regions that differ among themselves by approximately one ML. In addition, those regions can exhibit a certain distribution of nanoroughness on a length scale smaller than the exciton diameter. In experiments where a magnetic field is applied perpendicular to the layers of a semiconductor heterostructure a general trend is the shift of the energy levels to higher energies, known as diamagnetic shift [22,23,33]. This shift is attributed to the increase in the oscillator strength with increasing magnetic field (B//z), due to the reduction of the excitonic wave function extension in the xy plane [34]. Generally, in the case of SQWs, the diamagnetic shift decreases with decreasing well width, which is the expected behavior when the system dimensionality is reduced in this kind of structure [18,19,22,23]. Table 1 shows dimensions for the mini-wells and for the interwell barrier, which result in the best match between the theoretical (performed as before) and the experimental values for each PL peak, at low temperatures. Theoretical results obtained for Lef and for the system dimensionality (a) of each CDQW region, calculated following the approximation suggested by Zhao et al. [23], are also shown (those results are in excellent agreement with experimental values obtained through the fit of the diamagnetic shift curves of each PL peak showed in Fig. 3 [35]).
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Table 1 Theoretical values for the: CDQWs’s dimensions that best agree with the experimentally measured PL peaks, system dimensionality (a) and effective width (Lef). Peak
˚ Mini-wells (A)
˚ Inter-well barrier (A)
a
˚ Lef (A)
P1 P2 P3 P4
42.8 40.0 40.0 37.2
7.8 7.8 32.8 32.8
2.39 2.38 2.34 2.33
110.3 106.1 89.2 86.6
In an attempt to explain the differences in the diamagnetic shift of the four PL peaks (see Fig. 3), we will consider the confinement generated by each region of the mini-wells interfaces: (i) for the same CDQW, the higher diamagnetic shift is observed for the peak related to the mini-well regions that present a one ML larger width (higher a), and (ii) between the two studied CDQWs, the diamagnetic shift is higher for the system, which has the weaker carrier confinement, i.e., the CDQW5. An important result is the fact that the change in the confinement generated by the variation in the mini-wells thickness is the dominant effect for the diamagnetic shift differentiation between the channels observed for a same CDQW. In our previous work [24], different potential fluctuation levels (PFL) were observed for the four channels that compose the PL spectrum of our sample: (i) P1 and P4 are associated to channels that present intermediate PFL; (ii) P2 is associated to a channel practically free from fluctuations and (iii) P3 is originated from a channel that presents the higher PFL among them (moreover, the carriers, which recombine through this channel experience an absolute minimum (deeper), present in the confinement potential). The PFL associated with each emission peak can be ranked, in a descending order, in the following way: PFL3 4PFL1 4PFL4 4PFL2. As discussed previously, the excitons localized in the states generated by the fluctuations in the confinement potential of SQWs should present relatively lower diamagnetic shifts, since they will be more strongly confined than the free excitons [18,19]. In this context, higher diamagnetic shifts would be observed for P2 in CDQW5 and for P4 in CDQW30, since they present lower PFL when compared to P1 and P3, respectively. However, this is not what happens. P1 presents higher diamagnetic shift than P2, and P3 has higher shift than P4, showing that the effect of the confinement due to the variation of one ML in the mini-well (or inter-well barrier) thickness has greater influence than the excitonic localization in the local potential fluctuations, even if these are of great magnitude, as in the case of the P3 channel. To our knowledge this finding was not reported before. Following the competition between the two emission peaks for each PL band with increasing magnetic field will be discussed (Fig. 2). At a null field, P1 presents more intense emission than P2 but, as the magnetic field is increased, P2 gains intensity faster than P1 and, at 12 T, P2 is the most intense peak in the CDQW5 PL band. Although that behavior is not so evident for the peaks, which compose the CDQW30 PL band, the spectral fitting showed that the effect is very similar. That behavior can be explained by analyzing the magnetic field influence on the excitonic migration between the different regions of each CDQW. At 0 T, the delocalized excitons generated in the higher energy regions can migrate to the lower energy regions, that process being responsible for the higher intensity of P1. With the reduction of the excitonic wave function extension in the well plane (and the consequent increase in the oscillator force) due to the magnetic field application [33], the probability of radiative recombinations to occur is increased and so the excitons from the higher energy regions have higher probability of recombining before migrating to the lower energy regions, thus stopping contributing to the P1 intensity and
contributing to the P2 intensity. This behavior is not so evident between the CDQW30 peaks due to its higher oscillator strength; in this case, with increasing magnetic field, the reduction of excitonic wavefunction extension is not so effective and, as a consequence, the effect of reducing excitonic migration from higher energy regions to the lower ones is also less effective, resulting in a less pronunciated competition between the intensities of the peaks for this CDQW. The dependence of the FWHM on the magnetic field, shown in Fig. 4, is quite different among the four peaks. To understand the experimental results, which show that the FWHM of one peak (P2) decreases with increasing magnetic field, those of other two (P4 and P1) increases, and that of another (P3) is practically constant, we will consider a model recently developed by Bansal et al. [36]. To apply that model, which was primarily developed for single quantum wells, to double quantum wells, we have also used the methodology proposed by Zhao et al. [23], which allows to consider a system of two coupled quantum wells as a single quantum well system, with effective width Lef (Table 1). According to Bansal et al. [36], the fact that the linewidth sometimes shows an increase and sometimes a decrease with increasing B can be understood by postulating the existence of two correlation lengths for the interface fluctuations, one (w1) much smaller than the exciton size and the other one (w2) of the order of the exciton size. In the case of lateral correlation w1 (w1 5 aB) the FWHM is proportional to (w1/aB) and in the case of lateral correlation w2 (w2 aB) the FWHM is proportional to (aB/ w2). So, it is expected that, for w1 lateral correlation lengths an increase in the magnetic field (what implies in the excitonic wave function shrinkage) results in a FWHM increase; on the other hand, for w2 an increase in the magnetic field (and a consequent aB decrease) should result in a reduction of the FWHM. It is also expected that lateral correlations of type w2 affect more intensely thicker wells, differently from the lateral correlations of type w1, which affect more intensely thinner wells. Fig. 4 shows that the P2 FWHM decreases as the magnetic field increases. As discussed previously, P2 is associated with regions with lower PFL, and originates from a CDQW with larger effective ˚ Then, global fluctuations (of larger extenwidth (Lef ¼106.1 A). sion) should have a stronger effect on that well and, hence, with the reduction of the excitonic wave function extension by the magnetic field, the FWHM decreases. On the other hand, although PFL4 is small, P4 is associated with the well of smaller effective width; hence, the local fluctuations should be decisive for a FWHM increase. Therefore, with an increase in magnetic field, and the consequent excitonic diameter reduction, the P4 FWHM increases. For P1, which is associated with a region of relatively high PFL (PFL1 4PFL4 4PFL2), the behavior is that expected: the FWHM increases with increasing magnetic field. The behavior of P3 FWHM is the only one that does not follow exactly that model: the FWHM value is practically constant for the whole range of the applied magnetic field. We attribute that behavior to the fact that the local PFL associated to P3 is very high (P3 FWHM at null field is twice the P1 FWHM), what makes the magnetic field variation weakly affect the FWHM already extremely large at null field.
5. Conclusions In this work, we carried out a study on the effects of the application of magnetic fields on the emission properties of two GaAs/Al0.35Ga0.65 CDQWs with different inter-well barriers, grown on the same substrate. Each CDQW presents two emission channels, which are attributed to the existence of bimodal roughness in the heterointerfaces. Theoretical predictions for CDQWs agree with the experimental results in the sense that the higher
E.M. Lopes et al. / Journal of Luminescence 132 (2012) 1183–1187
the system dimensionality the higher the diamagnetic shift. Alterations on the confinement potential, generated by variations in the effective thickness of each mini-well, affect the diamagnetic shift more strongly than the excitonic localization at the local potential fluctuations. The changes in the relative intensities of the peaks that compose each PL band, with increasing magnetic field, are attributed to the radiative lifetime reduction of the delocalized excitons, what makes the radiative recombination occur before the excitonic migration from the higher energy regions to the lower energy regions in each CDQW takes place. The dependence of the FWHM as a function of the magnetic field is explained by considering the different levels and correlation lengths of the potential fluctuations existents in the spatial regions associated to each recombination channel.
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