Multilevel Infrared Coupling of Excitons in Quantum-Well Semiconductors

Transcription

1 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 36, NO. 11, NOVEMBER Multilevel Infrared Coupling of Excitons in Quantum-Well Semiconductors S. M. Sadeghi, J. Meyer, T. Tiedje, and M. Beaudoin Abstract We study the effects of multilevel mixing of the 1s and 2s states of the E1-HH1 and E2-HH1 excitons in the emission spectra of an undoped quantum well. This is done by investigating the E1-HH1 exciton emission spectra in the presence of an intense CO 2 laser near resonance with the transition between E1 and E2. Our results show that, depending on the frequency of the CO 2 laser, these spectra are quenched peculiarly. We explain these phenomena based on the frequency dependence of the mixing configurations of the exciton states and infrared enhancement of the nonradiative decay rates of E1-HH1 excitons. We also study the effect of the nonparabolicity of the hole subband (HH1) in the infrared mixing of the E1-HH1 and E2-HH1 excitons. Index Terms CO 2 laser, excitons, infrared coupling, intraband transitions, multilevel mixing, photoluminescence, quantum wells, quenching. I. INTRODUCTION IT HAS been known for a while that the photoluminescence (PL) spectra of an undoped quantum well (QW) can be modified using various methods. These include applying dc electric fields parallel or perpendicular to the QW plane [1] and exposing the QW to an intense far-infrared laser [2] or a microwave field [3]. The emission spectra of a QW can also be changed using an infrared laser with polarization along the QW growth direction and frequency close to that between the first (E1) and second (E2) conduction subbands [4], [23]. Since, at low carrier densities, the photo-excited electrons and holes have a strong Coulomb interaction, the transition between E1 and E2 leads to those between the E1-HH1 and E2-HH1 excitons if the sample temperature is low. Such intraband excitonic transitions have already been used to study the nondiagonal emission of the E2-HH1 exciton in an asymmetric QW [5] and the electron evolution in the conduction band of a double QW structure [6]. In this paper, for the first time we experimentally and theoretically address the effects of multilevel mixing of the exciton states in the emission spectra of an undoped QW. This is done by studying the linear PL spectra of the QW when an intense CO laser coherently drives the E1-HH1 and E2-HH1 intraband excitonic transitions. Our results show that this process leads to Manuscript received February 23, 2000; revised June 30, This work was supported by the Natural Sciences and Engineering Research Council of Canada. S. M. Sadeghi was with the Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1 Canada. He is now with the Department of Physics, University of Toronto, Toronto, ON M5S 1A7 Canada. J. Meyer and T. Tiedje are with the Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1 Canada. M. Beaudoin was with the Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1 Canada. He is now with the MBE Optoelectronics Group, Center for Solid State Electronics, Engineering Research Center, Arizona State University, Tempe, AZ USA. Publisher Item Identifier S (00)09761-X. strong quenching of the E1-HH1 emission spectrum with a peculiar dependence on the frequency of the CO laser. We explain this phenomenon in terms of the incoherent effects caused by mixing of the 1s and 2s states of the E1-HH1 and E2-HH1 excitons. We show that since the configurations of these mixing processes depend on the frequency of the CO laser, they enhance the effective nonradiative decay rates of the E1-HH1 excitons differently. This leads to a frequency-dependent quenching of the E1-HH1 exciton emission. The frequency-dependent coupling mechanisms of infrared-driven QWs can play an important role in the study of the modulation of the interband absorption spectra in QWs [7], [8], quantum confined optical Stark effects [9], and other issues related to the optical control of the interband transitions using intersubband coherent mixing [10]. These effects have been studied by ignoring the excitonic features [7], [8], considering them in a phenomenological way [11], or ignoring their energy levels and their quantum properties [12]. One important shortcoming of these treatments was that the infrared coupling of excitons became similar to that of a three-level atom where the two upper levels were optically mixed together, irrespective of the frequency and intensity of the coupling field. Based on the results of this paper, these treatments can lead to unrealistic results, if one deals with high infrared intensities and/or nonresonant coupling. In fact, some of the shortcomings of the atomic-like treatment of infrared-coupled QWs have already been reported in [13]. To explain the physics behind the nondiagonal intraband excitonic transitions between the 1s (2s) state of E1-HH1 and the 2s (1s) state of E2-HH1 excitons, we address in this paper the effects of the holes dispersion in the infrared excitonic coupling of QWs. We show that these transitions are possible because of the nonparabolicity of the HH1 subband. In fact, the nonparabolic dispersion makes the states of the excitons asymmetric, making the nondiagonal transitions possible. We estimate the dipole moment associated with these transitions using our experimental results. II. EXPERIMENTAL DETAILS AND RESULTS In this section, we study experimentally how the interband emission spectra of undoped QWs are changed in the presence of intense radiation from a CO laser. The sample was grown by molecular-beam epitaxy (MBE) on a nominally undoped semi-insulating GaAs substrate. It contained nm undoped wells (GaAs) sandwiched between 18.1-nm barriers (Al Ga As). A buffer layer consisting of 440-nm GaAs followed by a smoothing superlattice separated this structure from the (100) plane of the substrate. The calculated /00$ IEEE

2 1268 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 36, NO. 11, NOVEMBER 2000 Fig. 1. Schematic energy diagram of the conduction and valence subbands of the sample at 77K. The valence band offset is 143 mev and the energy spacing between LH1 and HH2 is 10 mev. energies of the electron and hole subbands in this structure at 77K are shown in Fig. 1. Here the conduction band has two subbands (E1 and E2) with energy spacing of 121 mev, and the first two valence subbands (HH1 and LH1) are separated by about 19 mev. Two edges of the sample were polished at 45, making a wave-guide geometry, and then mounted on a cold finger. Pulses from tunable hybrid CO laser, having a 500-ns width and 1 MW/cm intensity, were focused onto one of the polished sides of the sample. To pump the QW, a frequency-doubled Nd : YAG laser with 2.34-eV photon energy and 70-ps pulse width was used. This laser was focused at the surface of the QW within the area affected by the CO laser. The peak intensity of these laser pulses was 10 W/cm, giving rise to a carrier density of about cm. The PL emission was dispersed in a 0.25-m double monochromator and detected by a GaAs photomultiplier tube. The PL spectra of the QW in the absence of the CO laser for three different trials at 77K are shown in Fig. 2 (open circles). At this temperature, the main peaks in these spectra are caused by the emission of free excitons. The low-energy tails, however, are the signs of the excitons localized by the layer interface roughness and other imperfections of the QW [14]. Because various lateral regions of the sample were not identical in terms of the interface morphology, the spectra in Fig. 2 (open circles) are slightly different. In order to study the dynamics of the emission spectra in the presence of the intraband excitonic coupling, we exposed the sample to three frequencies of the CO laser corresponding to 130-, 121-, and 117-meV photon energies. Considering the electronic energy scheme of the QW, this laser was detuned by about 9, 0, and 4 mev from the E1 E2 transition (Fig. 3). As Fig. 2 shows (filled circles), when the CO laser was polarized along the growth direction (p-polarization), the emission spectra of the infrared-coupled QW evolve as follows. 1) For the near resonance case, corresponding to 121-meV photon energy of the CO laser [Fig. 2(b)], we see a large amount of quenching around the frequency of the spectrum peak. When the laser photon energies increase by 9 mev ( mev), we still see significant quenching around this frequency [Fig. 2(a)]. However, as Fig. 2(c) shows, for a 117-meV photon energy ( mev), the amount of quenching is much less. This is in contrast to our expectations from the electronic or atomic-like Fig. 2. PL spectra of the QW in the absence (open circles) and presence (filled circles) of the CO laser with 1 MW/cm intensity and (a) 130-, (b) 121-, and (c) 117-meV photon energies. The solid and dotted lines represent the results of the theory in the absence and presence of the CO laser, respectively. In (a), = (( )=2) for the dotted line and =0for the dashed line. " refers to the CO photon energy. Fig. 3. Schematic diagrams of the electronic or atomic-like picture of infrared intraband coupling of the QW. (a) 1 9 mev. (b) 1 0. (c) 1 04 mev. The two-sided arrows refer the CO laser and the one-sided arrows to the LO-phonon decay process. picture (Fig. 3), where we expected more quenching in Fig. 2(c) ( mev) than in Fig. 2(a) ( mev). In fact, this shows that the coupling process is not symmetric with respect to the detuning of the infrared field from the E1 E2 transition. This is in contrast with previous studies of the quantum-confined Stark effect [12] and modulation of the interband absorption spectra of QWs [7], [8], [10], [11], where the detuning of the infrared laser from the intersubband transitions was considered symmetric, similar to the optical coupling of two atomic levels. This effect will be discussed in detail in the following sections. 2) In the presence of the CO laser, the low-energy tails of the spectra of Fig. 2(b) and (c) are not quenched significantly, but that of Fig. 2(a) is quenched. To verify the role played by the CO laser polarization in these dynamics, we tried the experiments using the same CO laser

3 SADEGHI et al.: MULTILEVEL INFRARED COUPLING OF EXCITONS IN QUANTUM-WELL SEMICONDUCTORS 1269 Fig. 4. PL spectrum of the QW in the presence of the CO laser with s-polarization. All other specifications are the same as those in Fig. 2(b). The lines here are for eyeguide. pulses but with in-plane (or s) polarization. Under similar conditions as those of Fig. 2(b) the PL spectrum evolved as shown in Fig. 4. Here the effect of the CO laser is a slight quenching and some red shifting. These may be attributed to free carrier excitations, second-order effects of the infrared-qw interaction, and infrared mixing of hole subbands and hole transitions. III. INTRABAND EXCITONIC TRANSITION IN QWS AND THE EFFECTS OF HOLE DISPERSION To analyze the experimental results, it is important to consider the mechanisms responsible for the emission processes in QWs. These processes dependon the photo-excited carrier densities and energies and the sample temperature. As shown in [15], when the photo-excited carriers have large kinetic energies, the emission process may not necessarily be the result of the population of the exciton states, but rather due to the contribution of the Coulomb interaction to the photon-assisted electron-hole radiative recombination. As shown in [16], however, at low carrier densities and low temperatures the emission process can be attributed to the population of exciton states. The results presented in this paper were obtained at very low carrier densities and at 77K; therefore, we attribute them to the generation of excitons. The theoretical development presented in this section is based on this consideration (exciton population) and can consistently describe the experimental results, as shown in the next section. Since the photo-excited carrier densities are considered low and the well thickness is small (7.3 nm), in the absence of the CO laser only the E1-HH1 excitons are generated. Also, in the presence of this laser, we can ignore the optical transitions between the hole subbands. This is because 1) for an infrared laser with polarization along the growth direction, the dipole moments associated with the hole intersubband transitions are very small [17] and 2) when this laser is near resonance with the transition between E1 and E2, it is very off-resonance from those between the hole subbands (see Fig. 1). As a result, while the electrons are excited into E2 by the CO laser, the holes remain in HH1. The electrons in E2 have a Coulomb interaction with the holes in HH1, generating the E2-HH1 excitons. 1 The selection rules for transitions between the E1-HH1 and E2-HH1 excitons only allow transitions between heavy- or light-hole exciton 1 Note that in some literature such transitions are called Photoinduced intersubband transitions, see [18] and [24]. states with the same orbital angular momenta. Therefore, the excitonic states involved in the coupling process are and ( 1 and 2). Although the E1-HH1 and E2-HH2 excitons have been studied in the past extensively, we are not aware of any theoretical investigation of the E2-HH1 excitons. The existing experimental studies, however, have revealed some of the basic properties of these excitons. For example, in [18] and [24], the binding energies of the 1s states of the E2-HH1 excitons were found to be similar to those of the E1-HH1 excitons. This has been confirmed by at least two more independent studies [5], [19]. It is also consistent with our experimental observations where we expected to see maximum change in the PL emission when the CO laser photon energies were similar to that between E1 and E2. As a result, in our analysis we consider the energy spacing between E1 and E2 similar to that between the 1s states of the E1-HH1 and E2-HH1 excitons. We also consider that the binding energies of the 1s and 2s states of these excitons are 10 and 2 mev, respectively. To understand the mechanisms responsible for the phenomena seen in Fig. 2, we should now consider coupling of the and excitons by the CO laser. Considering the intensity and frequencies of the CO laser used in this experiment and the QW parameters, this can lead to three effective coupling configurations. As shown in Fig. 5(b), when the CO laser is nearly resonant with the E1 E2 transition, the coupling between and exciton is dominant ( system). However, when the laser photon energy is larger than the E1 E2 transition energy, can be coupled to both and [Fig. 5(a)]. In the case of smaller photon energies, can be mixed with and [Fig. 5(c)]. We call these two configurations and, respectively. Note that in the and systems, only decays by emitting LO-phonons. In the case of the system, however, both and emit LO-phonons. We explain in the following how these lead to the frequency-dependent quenching processes seen in Fig. 2. Note also that because the interband excitations were low, the PL spectra were mostly caused by the decay of the excitons. To analyze the experimental results, we adopt here a phenomenological approach in which the equations of motion of a driven system with a,,or configuration are given by [20] Here is the QW Hamiltonian in the absence of the CO laser and is the interaction term between this laser and the QW with either of these configurations. is the density matrix of the excitonic system, and and refer to the incoherent radiative and nonradiative decay processes of the system, respectively. Since the photo-excited carrier density is low ( cm ), the incoherent many-body effects caused by the carrier carrier and carrier exciton scattering processes can be ignored. Therefore, refers mostly to scattering of excitons with (1)

4 1270 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 36, NO. 11, NOVEMBER 2000 Here, refers to the radiation frequency, is a coefficient related to the thermal distribution of the E1-HH1 excitons, and is the positive frequency part of the interband polarization given by (8) Fig. 5. Schematic diagrams of the infrared intraband excitonic coupling in a system similar to that in Fig. 2. Here (a) refers to V (1 9 mev), (b) to 4 (1 0), and (c) to 3 configuration (1 04 mev). Other specifications are the same as those in Fig. 3. phonons and the potential fluctuations caused by layer interface roughness. The excitons are scattered by acoustic phonons and the excitons by LO-phonons. The latter is very fast and leads to ionization of these excitons. in (1) is the generation rate of the excitons caused by the Nd : YAG laser. in (1) is the Hamiltonian of the CO interaction with the QW. For the systems considered here, they are given by Here, refers to the electric dipole moments associated with the diagonal transition between and, and to those of the nondiagonal transitions between and ( ). Note that the nondiagonal dipole moments are caused by the asymmetry of the exciton states caused by the nonparabolicity of the hole subbands. To see this, note that these moments are related to the following: where Here, and refer to the envelope function of the excitons and to that of the holes with spin. Note that (5) is simplified after imposing all intraband selection rules, i.e., the initial and final states are either heavy or light hole-like and have the same orbital angular momenta. If one assumes that the hole dispersion is parabolic, then the right side of (5) becomes zero, causing to be zero. Having from (1), one can find the emission spectra of the coupled QW using (2) (3) (4) (5) (6) (7) Here, is the dipole moment for the transition between the ground state ( ) and. is the Laplace transform of with respect to. Since the CO pulse width is much larger than the characteristic dephasing time of the system, we can solve (1) in the steady state ( ). IV. FREQUENCY-DEPENDENT QUENCHING OF THE EXCITON EMISSION SPECTRA Our experimental results in Section II showed that when a CO laser coupled the E1-HH1 and E2-HH1 exciton states, the emission spectra of the E1-HH1 excitons were peculiarly quenched. In the preceding section, we presented a model that put into consideration the various configurations caused by the coupling of the 1s and 2s states of E1-HH1 and E2-HH1 excitons by a CO laser. In this section, we apply this model to the experimental results. To do this, note that at 77K, the free excitons are dominant [21], and therefore they play major roles in the system dynamics. To describe the distribution of the binding energies of such excitons, we use a Gaussian envelope function. Adding this distribution to that of the less significant localized excitons can lead to a good fit to the emission spectra (solid lines in Fig. 2). Note that localization of the E1-HH1 excitons increases their binding energies [14]. Therefore, the energy separation between E1-HH1 and E2-HH1 could become larger than that between E1 and E2. This is in contrast to the case of free excitons, where these two energy spacings are nearly equal [18], [24]. We consider the widths of the homogeneously broadened localized and free E1-HH1 excitons equal to 0.4 and 1 mev, respectively [22]. We also consider the width of the E2-HH1 exciton equal to 5 mev. This includes the very fast decay of such excitons by emission of LO-phonons and the contribution of the layer interface roughness. The results of the theory for the emission spectra in the presence of the CO laser are shown in Fig. 2 (dotted lines). As Fig. 2(b) shows, considering a resonant configuration for the free excitons (main peak) leads to a fairly good match with the experiment if we assume the nonradiative decay rates of excitons equal to 0.15 ps. Such a fast decay is expected since, in such a system, the CO laser effectively remove excitons from their E1-HH1 radiative into E2-HH1 nonradiative states. The E2-HH1 states decay very fast into electrons with large wavevectors in E1 (intersubband transition) and holes at the top of the valence band. The electrons in E1 then undergo intrasubband transitions by emitting LO-phonons. Note that the near-resonance CO laser can slow down this process. This is because the effective masses of E1 and E2 are similar for small wave-vectors. Therefore, the CO radiation can reexcite the electrons into E2, increasing their energy relaxation time in E1. For the case of Fig. 2(a), however, since the CO photon energy is relatively higher, the effective coupling configurations of the

5 SADEGHI et al.: MULTILEVEL INFRARED COUPLING OF EXCITONS IN QUANTUM-WELL SEMICONDUCTORS 1271 free excitons are types. In these systems, both and decay very fast by emitting LO-phonons; therefore, we expect to see an effective quenching process. Using the parameters of Fig. 2(b), we find a good fit to the Fig. 2(a) spectrum, assuming nm. If one considers (assuming parabolic dispersion for HH1), the spectrum undergoes insignificant quenching [Fig. 2(a), dashed line], in contrast to experimental observations. To see the consistency of the theory and estimated parameters, we apply them to the system of Fig. 2(c) without any fitting parameter. Here, since the field is detuned by 4 mev from the to transition, the system has a configuration. As the dotted line in Fig. 2(c) shows, the result is in reasonable agreement with the experiment. To explain the dynamics of the low-energy tails (localized excitons), note that, as mentioned before, here the energy spacing between the E1-HH1 and E2-HH1 exciton states can be larger than those between the free excitons. Therefore, in the case of Fig. 2(a), since the CO photon energy is also large (130 mev), the system can still have a or configuration. In the case of Fig. 1(b) and (c), however, the coupling configuration becomes type with insignificant quenching. This and the fact that localized excitons have a small width lead to larger quenching in the tail of Fig. 2(a) than those in Fig. 2(b) and (c). V. CONCLUSION In conclusion, we studied the multilevel mixing of the exciton states associated with the first and second conduction subbands in the presence of a CO laser near resonance with the transition between these two subbands. We showed that this mixing led to quenching of the emission spectra of the QW with a peculiar dependence on the frequency of the CO laser. We attributed this to the fact that the configurations of the mixed exciton states depend on this laser frequency. We also showed the hole dispersions may play an important role in the intraband mixing of excitons. ACKNOWLEDGMENT The authors are grateful to J. F. Young for very constructive discussion and M. K. Y. Hughes for providing them technical support. REFERENCES [1] H.-J. Polland, L. Schultheis, J. Kuhl, E. O. Gobel, and C. W. Tu, Lifetime enhancement of two-dimensional excitons by quantum-confined Stark effect, Phys. Rev. Lett., vol. 55, pp , [2] S. M. Quinlan, A. Nikroo, M. S. Sherwin, M. Sundaram, and A. C. Gossard, Photoluminescence from Al Ga As/GaAs quantum wells quenched by intense far-infrared radiation, Phys. Rev. B, vol. 45, pp , [3] B. M. Ashkinadze, E. Cohen, A. Ron, and L. N. Pfeiffer, Microwave modulation of exciton luminescence in GaAs/Al Ga As quantum wells, Phys. Rev. B, vol. 47, pp , [4] S. M. Sadeghi and J. 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Beaudoin, photograph and biography not available at the time of publication.