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Linearly polarized photoluminescence (PL) measurements were carried out on InP-GaP lateral nanowires grown using a lateral composition modulation method in pulsed magnetic fields up to ∼ 50 T. In these structures, the energy band alignment becomes type-I and type-II in In-rich wire and Ga-rich barrier regions, respectively. It is revealed that the polarization of the type-I PL is oriented along the [11̄0] crystal direction, whereas that of the type-II PL is along the [110] direction in the absence of magnetic field. These two different PL peaks exhibit anomalous energy shifts with respect to the direction of the magnetic field due to the variation of the confined energy in the exciton center of mass potential.
© 2015 Optical Society of America
1. Introduction
For the last few decade, excitons in semiconductors under high magnetic fields (B) have been studied because materials with different dimensionality exhibit a variety of exciton behaviors. The general behavior of the exciton diamagnetic shift is quadratic in low magnetic fields (ΔEdia ∼ B2) and linear in high magnetic fields (ΔEl ∼ B). This is based on the idea that, at low magnetic fields, the exciton plays a dominant role, whereas the cyclotron energy (Landau energy) becomes predominant in high fields [1]. The exciton diamagnetic shift reflects the exciton reduced mass of a given system. The exciton transition energy in magnetic fields depends greatly on the band alignment of quantum structures. It has been reported that in type-II quantum structure wherein electrons and holes are spatially separated, an external magnetic field leads to an increase in the effective reduced-masses of excitons [2].
A negative energy shift is difficult to imagine when using the features of the normal diamagnetic shift. A negative energy shift in magnetic fields is generally seen in systems with a large Zeeman energy, which can overcome the diamagnetic shift [3]. However, there are few experimental and theoretical reports on the purely negative energy shift in semiconductor quantum structures. Uchida et al. [4, 5] reported a strong negative energy shift in type-II GaP/AlP short-period superlattice (SPS) systems and neighboring confinement structure (NCS) GaP/AlP quantum wells (QWs) sandwiched between AlGaP barriers. For both SPS and NCS-QW systems, electrons and holes are confined in adjacent layers of the GaP conduction band and the AlP valence band, respectively. They claimed that the negative energy shift occurs because of the strong localization of carriers trapped in disordered potentials in type-II heterostructures.
A theoretical investigation of the negative energy shift of localized excitons was reported by Grochol et al. [6] in disordered GaAs/AlGaAs type-I QWs. They tested two different theoretical methods: a full wavefunction solution and a factorization method. They focused on the exciton center-of-mass (CM) localization potential in disordered two-dimensional QWs (2D-QWs). With increasing magnetic fields, the effective potential confining the exciton CM can become narrower and deeper, depending on the disorder potential in a given quantum structure. The negative shift of exciton transition energy is possible because the confined potential becomes deeper with increasing magnetic fields, according to the factorization method. However, they failed to confirm the negative energy shift when using the full wavefunction solution, because, in this case, the negative effect of the CM potential change was not large enough to overcome the diamagnetic shift.
In this paper, we report the magneto-PL transitions of an InP/GaP lateral nanowire structure [7] that was grown using a lateral composition modulation (LCM) growth technique [8, 9, 10, 11]. Linearly polarized PL measurements were made under pulsed magnetic fields to 50 T. We observed the normal diamagnetic shift from the direct InP nanowire transition. However, the indirect InP-GaP transition exhibits no energy shift or negative energy shift depending on the magnetic field directions.
2. Experimental methods
The InP-GaP lateral nanowires used in this study were prepared using the molecular beam epitaxy technique. Fig. 1(a) shows a schematic of the sample structure wherein three layers of lateral nanowires are aligned along the [11̄0] direction. The sample growth sequence is as follows: Initially, n-type Al0.6Ga0.4As (100 nm), n-type GaAs (100 nm) and undoped InGaP (100 nm) buffer layers were sequentially grown. Three pairs of layers consisting of thirty pairs of undoped InP(0.31 nm)-GaP(0.29 nm) monolayer short period superlattices (SPSs) and a 20-nm-thick undoped InGaP stopping layer were grown on top of the buffer layer. A 300-nm InGaP-alloy capping layer was deposited on the uppermost lateral nanowire. The growth temperature of the SPSs was 490 °C. At this temperature, the SPSs undergo phase separation and, as a consequence, LCM-induced InP-GaP nanowires were formed along the [11̄0] direction [8, 9, 10, 11]. Each lateral superlattice layer was separated by a 20-nm undoped InGaP layer. The buffer, stopping, and capping layers are disordered InGaP alloy layers. More specific details regarding the growth methods and parameters (and electron microscope images) can be found elsewhere [12].
Fig. 1 (a) A schematic of the sample structure consists of three InP-GaP lateral nanowire layers. (b) Experimental set up for optical spectroscopic measurements. A multi-mode optical fiber carries laser light to and photoluminescence signal from the sample located at the center of the magnet. Fast ICCD detector system made it possible to take a PL spectrum during transient magnetic field pulse. The inset on the right corner depicts the Voigt geometry by using a small right-angle prism.
The sample temperature for the PL measurements at B = 0 was maintained at 5 K using a closed-cycle refrigerator. The 532-nm line from a Nd-YAG laser was used as the excitation source for the PL measurements, and a 50-cm spectrometer equipped with a liquid-nitrogen-cooled charge-coupled device was used as the detector. A polarization rotator was located in front of the laser to vary the polarization of the incident laser light; a probe polarizer was located in front of the spectrometer. Both pump and probe polarizations were varied from the [110] to the [11̄0] crystal directions. For the pulsed magnetic field PL measurements at T = 4.2 K, the sample was immersed in a liquid helium dewar that was positioned at the center of the magnet (Fig. 1(b)) for Faraday geometry, which is parallel to the [001] crystal direction. A multi-mode optical fiber of 1.0 mm in diameter was used to excite the sample and to collect the PL emission from the sample. A plastic polarizer (Polaroid polarizer film) was located between the optical fiber and the sample. For the Voigt geometry, which is parallel to the [110] and [11̄0] crystal directions, a miniature right-angle prism was used to turn the laser beam and the PL signal 90° between the optical fiber and the sample. The plastic linear polarizer was sandwiched between the sample and the right-angle prism.
3. Results and discussion
3.1. Photoluminescence transitions at B=0
Figure 2 shows the unpolarized PL spectra for two different directions of polarization of the incident laser in the absence of the probe polarizer in front of the spectrometer. In this experimental setup, only the laser polarization was varied, and the detected PL signal was nonpolarized. When the laser polarization is parallel to the [110] crystal direction, we obtain the maximum PL emission intensity; whereas, it is at a minimum when parallel to the [11̄0] direction. There are no appreciable changes in the PL transition energies while rotating the incident laser polarizations. The peak centered at 1.887 eV is associated with the nanowires; the peak at 1.938 eV corresponds to the transition from the InGaP alloy layers (capping and stopping layers). It has been reported that the incident-laser-polarization-dependent intensity anisotropy arises from the different absorption efficiencies along the different crystal directions [10, 11]. After finding the maximum peak intensity, which is the [110] crystal direction, we fixed the incident laser polarization and performed further PL experiments with the linear polarizer in front of the spectrometer so as to measure the anisotropic PL emission spectra.
Fig. 2 Unpolarized PL spectra with respect to the incident laser polarization. Two peaks at 1.8869 eV and 1.9384 eV are identified as the transitions from InP-GaP nanowires and InGaP cap and stopping layers, respectively.
Figure 3 displays PL emission spectra with two different polarizations at B = 0 (T = 5 K); it shows maximum emission intensities when the probe polarizer is parallel to the [11̄0] direction and minimum emission intensities when the polarizer is parallel to the [110] direction. The polarization degree (ρ(%)) of the nanowire transition is estimated as,
where I[ijk] is the integral intensity of the PL emission along the [ijk] direction. Transition energies from both the nanowires and the capping layers exhibit blue-shift while rotating the polarization direction from the [11̄0] to the [110] crystal directions. This energy-shift with respect to the polarization direction is caused by the valence band offset in the quantum structure [7, 13]. Rich et al. [7] reported experimental and theoretical studies of linearly polarized cathodoluminescence (CL) from (In-rich)P-(Ga-rich)P lateral quantum wires, which have a similar lateral structures to that of our sample. According to their calculated results, the energy band structure of the (In-rich)P nanowire region is direct band-gap (type-I) at the Γ-point, whereas that of the (Ga-rich)P barrier region is the indirect (type-II) X-point valence band with respect to the InP conduction band. Moreover, they also found that the coherent strain along the lateral direction and quantum size effect induce heavy- and light-hole mixing by the in the valence band structure [7, 14] in such a way that the valence band of the In- and Ga-rich regions consist mostly of the heavy- hole (96%) and light-hole (94%) bands, respectively. In a strain-induced quantum structure together with the valence band mixing is responsible for linear polarization in the respective PL emission. Therefore, as seen in Fig. 3, the peak at 1.8863 eV ([11̄0] direction) and the peak at 1.8897 eV ([110] direction) are associated with the transitions from the In-rich conduction band to either the In-rich valence band (direct) or the Ga-rich valence band (spatially indirect), respectively. The energy difference between the type I and the type II bands is due to the physical band structure. According to the calculated result from Rich et al., the energy splitting between type I and II is ∼ 6 meV, which is slightly larger than our experimental value of 3.4 meV.Fig. 3 The linearly polarized PL transition spectra. By rotating the probe polarizer, the PL transitions change not only the intensities but also the peak transition energies. For the nanowire transitions, the higher intensity peak at 1.8863 eV along [11̄0] direction corresponds to the direct transition in InP nanowire region whereas the lower intensity at 1.8897 eV ([110] direction) is associate with the InP conduction band to the GaP valence band indirect transition. The inset shows the schematic of the band alignments of the sample and the arrows indicate the transitions of the type-I (blue arrow)) and type-II (red arrow).
3.2. Photoluminescence transitions at B>0
The main issue of this paper is to focus the PL transitions in the nanowire in high magnetic fields using pulse magnets. As seen in Fig. 4, we performed the PL measurements in three different magnetic field directions (with respect to the crystal axis) and in two polarization directions for each magnetic field direction. The left and the right columns correspond to the polarized PL spectra along the [110] (direct transition) and the [11̄0] (indirect transition) directions, respectively. Additionally, the first (Faraday geometry), second, and the third rows (Voigt geometry) correspond to the magnetic field along the [001], [11̄0], and [110] crystal directions, respectively. Figures 4(d)–(f) show that the type-I nanowire transition exhibits the high energy shift (blue-shift). However, for the [110] direction in the left column in Figs. 4(a)–4(c), the type-II nanowire PL transitions show different features. For Faraday geometry in Fig. 4(a), PL intensity gradually diminishes with an increasing magnetic field, and it eventually vanished at roughly 30 T, without any indication of high energy shifts. In the B//[11̄0] direction in Fig. 4(b) for the nanowire PL transition, there is no observed change up to 50 T. However, the B//[110] direction in Fig. 4(c) exhibits a discernible change in the presence of magnetic field.
Fig. 4 PL spectra from nanowires in various pulsed magnetic fields and polarization directions. Figures (a) ∼ (c) correspond to PL along the [110] direction and (d) ∼ (f) along the [11̄0] direction with three different magnetic field directions.
Figure 5 shows the PL peak energy in different magnetic fields. In this figure, we do not include the peak energy shift for the cases of Figs. 4(a) and 4(b) because they do not exhibit any energy shift up to 50 T. The type-I transitions in Figs. 4(d)–4(f) show the typical diamagnetic shift, which is proportional to B2. The transition in Fig. 4(f) is significantly larger than the transition in 4(d) and 4(e). This result indicates that the exciton reduced-masses of type-I are anisotropic with different crystal directions, and that the exciton wavefunction is anisotropic and expanded along the direction of the quantum wire. The nanowire transition in (c), which is indirect type-II, exhibits a negative energy shift to 25 T, and thereafter, changes to a positive shift.
Fig. 5 Peak position vs. magnetic fields with different polarizations. Transitions along [11̄0] direction, three field dependent peak shifts show normal diamagnetic shift (ΔE ∝ B2). However, the diamagnetic shift along [110] direction with B//[11̄0] direction clearly show negative shift to 25 T and turn it to positive thereafter. Two other transitions along B//[11̄0] and [100] are not displayed because they did not show any diamagnetic shift at all to 50 T.
The negative energy shift in an applied magnetic field is an unusual phenomenon, and there are, as yet, no rigorous theoretical explanations of it. Grochol et al. [6] tested their theoretical models on energy shifts in disordered GaAs-AlGaAs two-dimensional (2D) type-I quantum wells (QWs) using simplified wavefunction factorization and full-solution approaches. For a quantum well with an ideally smooth interface, the motion of the two-dimensional exciton decouples into relative and center of mass (CM) motions and the relative motion plays an important role in magnetic fields. However, an effective CM potential caused exciton localization at the disordered interfaces couples with the relative motion and plays an important role in the presence of magnetic field. Calculated results from both factorization and full-solution methods indicate that the potential becomes narrower and deeper with an increasing magnetic field. As the CM potential becomes deeper, the confined energy level decreases with increasing magnetic fields as depicted in the inset of Fig. 6. According to calculations in [6], even though the CM confined energy decreases, a negative energy shift occurs only in the case of the factorization method. They could not obtain a rigorous answer for the negative energy shift in disordered type-I 2D QWs by using a full wavefunction solution. Exciton CM motion is important under magnetic fields, as it leads to an enhancement of exciton reduced-mass at the transition point from exciton to magnetoexciton in a type-II QW, as discussed in [2], wherein an electron and a hole are spatially separated. However, in this study, the authors did not indicate the negative energy shift in type-II QWs with smooth interfaces [2].
Fig. 6 Magnetic length ( ) vs. magnetic fields. The magnetic length, which affect the CM motion, drastically diminishes with increasing magnetic fields. The inset depicts the CM potential change in magnetic fields. The CM confined energy level decreases as the magnetic field is increased [6] indicated by the arrow.
Experimental evidence of the negative energy shift was reported by Uchida et al. [4, 5] in GaP/AlP type-II SPS systems and type-II GaP-AlP neighboring confinement structures (NCSs) sandwiched between AlGaP barriers. An admixture of deposited atoms could be formed at the interfaces, where excitons are localized to the disorder potentials. The negative energy shift arises from a delocalization process under magnetic fields parallel to the growth direction. However, in the presence of a magnetic field perpendicular to the growth direction (the B in-plane direction) they obtained a negligibly small (but positive) diamagnetic shift. They claim that a spatially separated electron and hole bound state (type-II exciton) transition localized at the interface is responsible for the negative energy shift. Small energy shifts in the in-plane magnetic field result because the in-plane magnetic field cannot affect the exciton wavefunction in type-II alignment.
The LCM-induced lateral nanowire sample used in this study is a system with the SPS structure along the growth direction and composition modulation along the lateral direction. Because the LCM occurs spontaneously, the potential modulation along the lateral direction is sinusoidal, with an appreciable amount of disorder. Therefore, excitons in lateral nanowires can easily be localized in disorder potentials. The localized exciton state in the LCM lateral nanowires was studied using the band filling effect. Rich et al. [7] reported on the excitation current dependence of the cathodoluminescence (CL) emissions, in which the formation of the disorder-localized excitons in the lateral nanowires at low excitation currents turned into delocalized band excitons as the excitation current increases. However, the transition in InGaP alloy layers forming the capping and buffer layers did not show any energy shift while the excitation currents changed. Although not shown here, we obtained the same band filling effect of lateral nanowires in excitation-laser-power-dependent photoluminescence measurements.
The type-I transitions as seen in Figs. 4(d)–(f) always exhibit normal diamagnetic shifts. However, the type-II transition within the nanowires shows no diamagnetic shift as exhibited in Figs. 4(a) and (b) or negative energy shift in Fig. 4(c), which are similar to the results from Uchida et al. [4, 5] under in-plane and perpendicular magnetic fields. For our lateral nanowire type-II excitons, electrons and holes are spatially separated. The cases of Figs. 4(a) and (b) are similar to those of an in-plane magnetic field applied to a type-II QW without a diamagnetic shift. However, the case in Fig. 4(c), in which the magnetic field is oriented along the [110] crystal direction, corresponds to that of perpendicular magnetic fields applied to a conventional type-II QW associated with the negative energy shift [4, 5]. Therefore, we claim that the negative energy shifts are strongly associated with the localized excitons at the interface in type-II quantum wells because the confined CM energy level in type-II structure decreases enough to overcome the normal diamagnetic shift.
The positive turnover occurred above ∼ 25 T is due to the competition between the reduction of the CM confined energy level (negative shift) and the normal diamagnetic shift (positive shift). As seen in Fig. 6, the magnetic length, that strongly affect the CM motion drastically decreases in the low field region. The CM potential is quadratic for small B because it can be obtained from the second order perturbation theory [6]. Therefore, at high magnetic fields where the perturbation is no longer valid, the diamagnetic energy dominates in the exciton transition, which makes positive turnover in high field limit. They also claim that the amount of the diamagnetic energy shift decreases with increasing disorder strength (e.g., Fig. 6 in [6]). Therefore, a strongly disorder system requires higher magnetic field to make the positive turnover than a weakly disordered system. Softening of the localization can be made by aid of thermal energy. Localized carriers in the strongly disordered potentials at low temperature become weakly localized with increasing temperature because of the obtained thermal energy. In magneto-PL experiments observed at 20 K, Uchida et al. [4, 5] found that the strong negative shift at 4 K turns to positive at such elevated temperatures. The positive turnover after 25 T in Fig. 5 can be attributed to carrier localization in the relatively weak disorder potential compared to the results from [4] and [5] at low temperature (T = 4.2 K).
4. Conclusion
We studied the PL transition energies of InP-GaP LCM-induced lateral nanowires in high magnetic fields. At zero magnetic field, two PL peaks associated with the InGaP capping layer and the InP-GaP nanowires, respectively, were observed. Both peaks show strong PL emission anisotropy along the [110] and the [11̄0] crystal directions. The type-I and the type-II band alignments are responsible for the anisotropic PL emissions in the nanowires. Under magnetic fields, the type-I transition, which is emission along the [11̄0] crystal direction, shows the normal diamagnetic shift (∼ B2). When the magnetic field is applied along the [001] or the [11̄0] direction, the type-II transitions do not exhibit any diamagnetic shift. However, along the [110] magnetic field direction, the type-II transition exhibits a negative energy shift at fields up to roughly 25 T and then changes to a positive shift. To date, there is no rigorous theoretical model explaining the negative energy shift. However, it is most plausible that the negative energy shift observed in our system is associated with the diminishing confined CM potential energy of spatially separated electrons and holes localized at interface disorders in type-II heterostructures.
Acknowledgments
Work at Dankook University was supported by the Leading Foreign Research Institute Recruitment Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (MEST No. 2014-039452)(YK), and NRF-2010-0022383 (BKC). JDS acknowledges support from the KIST institutional program of flag-ship and partial support by NRF-2013M3C1A3065033.
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