- Email: [email protected]
Optical anisotropy and diamagnetic energy shifts in InP–GaP lateral quantum wells
Journal of Luminescence 151 (2014) 244–246
Contents lists available at ScienceDirect
Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
Optical anisotropy and diamagnetic energy shifts in InP–GaP lateral quantum wells Y.H. Shin a, Yongmin Kim a,n, J.D. Song b, Y.T. Lee c, H. Saito d, D. Nakamura e, Y.H. Matsuda e, S. Takeyama e a
Department of Applied Physics, Institute of Nanosensors and Biotechnology, Dankook University, Yongin 448-701, Republic of Korea Korea Institute of Science and Technology, Seoul 136-791, Republic of Korea c School of Information and Communications, Gwangju Institute of Science and Technology, Gwangju 500-712, Republic of Korea d Department of Applied Physics, The University of Tokyo, Tokyo 113-8654, Japan e Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan b
art ic l e i nf o
a b s t r a c t
Article history: Received 25 October 2013 Received in revised form 17 February 2014 Accepted 25 February 2014 Available online 11 March 2014
Linearly polarized photoluminescence (PL) measurements were made from InP–GaP lateral multiple quantum wells induced by composition modulation along the lateral direction. At B ¼0, two prominent emission peaks emerged, which are identified as transitions from In-rich well and Ga-rich barrier regions. Both transitions are strongly linear polarized parallel to the [110] crystal direction. While rotating PL orientation from [110] to [1–10] direction, the well and barrier transitions show red- and blue-shifts, respectively, due to the different valence states. In high magnetic fields, the two peaks exhibit different diamagnetic energy shifts mainly because of the effective-mass difference in the In-rich and Ga-rich alternate regions along the lateral direction. & 2014 Elsevier B.V. All rights reserved.
Keywords: Lateral composition modulation InP–GaP short period superlattice Optical anisotropy Diamagnetic energy shift
Lateral composition modulation (LCM) in compound semiconductor, [1,2] which can be formed during the growth of short period superlattice (SPS), has been investigated for more than last two decades because of its unique physical properties, such as the formation mechanism of LCM, bandgap reduction and optical anisotropy. Such physical properties also occur in an ordered alloy of GaInP2, which can be explained by the inherent nature of its crystal structure [3]. Although an ordered alloy exhibits the similar physical properties like optical anisotropy, the properties in the alloy originate from different reasons that is associated with those in semiconductor, including vertical/lateral multiple quantum wells (MQW) and superlattices. In a heterostructure that contains different cation and anion (AB–A0 B0 structure) in each side of junctions, the reduced crystal symmetry causes the optical anisotropy [4]. For a heterostructure with a common anion and a different cation (AB–A0 B structure), there is a uniform agreement that the in-plane optical anisotropy occurs due to the coherency strain field, which causes the heavy- and light-hole mixing [5,6]. The quantum confined Pockels effect that shows enhanced optical anisotropy induced by externally applied electric field was also investigated in various semiconductor heterostructures [7–9].
n
Corresponding author. E-mail address: [email protected] (Y. Kim).
http://dx.doi.org/10.1016/j.jlumin.2014.02.036 0022-2313 & 2014 Elsevier B.V. All rights reserved.
Mascarenhas et al. [10] reported parameters of GaP–InP LCM structure wherein the band edges, and the effective-masses of carriers in the conduction electron, heavy-hole, light-hole and spin-orbit split-off bands at the zone center were shown in detail. In this work, we present photoluminescence (PL) spectra of linearly polarized optical transitions that were obtained from InP– GaP LCM structure which was induced during the growth of short period superlattice (SPS) by using a molecular beam epitaxy technique. At B ¼0 T, we observed two main optical transitions, one from the Ga-rich barrier and the other from the In-rich well, both of which show blue- and red-shifts while switching the orientation of the probe polarizer from [1–10] to [110] crystal direction. In the presence of magnetic field up to 50 T, the amount of the diamagnetic energy shifts of two peaks from In- and Ga-rich regions can be estimated as the effective-reduced-mass ratio of excitons in the laterally modulated structure. The sample used for this study was prepared by using the molecular beam epitaxy (MBE) technique. The InP–GaP SPS was grown directly on a GaAs substrate without buffer and capping layers. The growth temperature of the sample was 490 1C and the SPS layers consisted of 659 pairs of GaP (2.9 Å) and InP (3.1 Å). Details of the growth methods, parameters and electron microscope images can be found elsewhere [11]. As seen in this reference, the average thicknesses of In-rich well and Ga-rich barrier are 90 Å. The sample temperature for PL measurements
Y.H. Shin et al. / Journal of Luminescence 151 (2014) 244–246
was maintained at 5 K by using a closed-cycle refrigerator. A 532 nm line of a Nd-YAG laser was used as the excitation source for PL measurements and a polarization rotator was located in front of the laser to vary the laser polarization. For PL emission measurements at zero magnetic field, an additional probe polarizer was located in front of a 50 cm spectrometer equipped with a liquid nitrogen cooled charge coupled device detector. Both excitation and emission polarizations were varied from parallel to perpendicular to the [110] crystal direction. For a pulsed magnetic field, PL measurements at T¼4 K, sample was positioned at the end of an optical fiber of 1.0 mm diameter and then immersed in a liquid helium dewar. A plastic polarizer is inserted between the optical fiber and sample along [1–10] direction. Fig. 1 inset shows a schematic of SPS sample structure as a consequence of the growth wherein LCM was achieved along the [110] direction. As seen in Fig. 1, PL intensities in the absence of probe polarization are anisotropic by changing the direction of polarization of the incident laser. When the incident polarization is parallel to the [110] direction, it has the maximum PL intensity, whereas it is minimum when parallel to the [1–10] direction. The peak positions, however, do not change with the orientation of the incident polarization. This means that the [110] direction is an easy axis of the formation of transition dipole oscillators which maximizes light absorption that causes the maximum PL emission [5]. Because of no appreciable changes in the PL transition energies with respect to the changing incident polarizations, we set the direction of the incident laser polarization to [110] direction and proceeded further experiments for linear polarized PL emissions at B¼ 0 T. The experimental values of the peak transition energies in Fig. 1 are Eg ðwellÞ ¼ 1:7886 eV and Eg ðbarrierÞ ¼ 1:9437 eV and these values are quite comparable to the calculated values [10]. Fig. 2 displays polarization dependence of the PL emission spectra. It shows the maximum emission intensities when the probe polarizer is parallel to the [1–10] direction and the minimum when the polarizer is parallel to the [110] direction. Such an optical anisotropy with respect to the polarization direction is due to the strong heavy- and light-hole mixing caused by biaxial strain along the lateral MQW direction. An interesting phenomenon in the PL spectra observed is that the peak transition energies of the In-rich well and the Ga-rich barrier show opposite spectral-shift behavior by changing the polarization directions. Such spectral shifts were first reported by Mascarenhas et al. [13] wherein the well transition shows 10 meV blue-shift whereas the barrier transition undergoes 1 meV redshift while rotating the PL polarization from [1–10] to [110] direction. In our case, the spectral shifts are opposite from Ref. [13]. When the probe polarizer changes its direction from [1–10] to [110] direction, the barrier transition shows 5 meV blue-shift whereas the well transition exhibits 4 meV red-shift. The main difference of our sample and Ref. [13] is the existence of InGaP buffer layer. As mentioned above, our sample does not contain buffer layer whereas the sample in Ref. [13] has InGaP buffer layer between the substrate and InP–GaP laterally modulated structure. Such difference may alter the spectral energy shifts in the well and the barrier. Mattila et al. [12] reported the dependence of the valence band energy levels with respect to the crystal direction, wherein the energygap increases when the direction changes from [1–10] to [110]. Such a behavior of energygap increase is consistent with our the Ga-rich barrier transition in Fig. 2. Therefore, one plausible reason for such spectral shifts is the recombination from the conduction band electron to different valence holes. According to Ref. [10], the lowest valence band in the InP–GaP LCM structure in the well region is the heavy-hole state whereas that in the barrier region is the light-hole state. Recombination between electrons in the conduction band and holes in the light-hole band in the
245
Fig. 1. Incident laser polarization dependence of PL Spectra. Solid (left axis) and broken (right axis) lines correspond to laser polarization along [110] and [1–10] directions, respectively. Two peaks at 1.9437 eV and 1.7886 eV are identified as the transitions from Ga-rich barrier and In-rich well regions, respectively, of InP–GaP LCM MQWs. The inset is a schematic of the sample structure. The modulation period is about 180 Å. Therefore, both well and barrier thicknesses are 90 Å.
Fig. 2. The probe polarization dependence of the PL transition spectra. By rotating the probe polarization orientation, the PL transitions change not only the intensities but also the peak transition energies. The peak position corresponding to the well and barrier regions shows red- and blue-shift, respectively, while changing the polarization orientation.
barrier region causes the blue-shift as seen in Ref. [12], whereas the recombination to the heavy-hole band in the well region may cause the red-shift. The effective-masses of the valence holes in In-rich and Ga-rich regions are known to be different [10]. Taking into account the inherent modulation in the sample, we propose that the different effective-masses may lead to the different diamagnetic energy shifts in the presence of strong magnetic field. Fig. 3 shows the diamagnetic shifts of the well and barrier transitions in magnetic fields up to 50 T. The inset displays PL spectra at B ¼0 T and 49 T. A theoretical calculation for the exciton diamagnetic shift is generally complicated because the interaction energy related to the magnetic field has a cylindrical symmetry while the Coulomb energy has spherical symmetry. Numerical approximations of Schrödinger equation for a hydrogen-like bound system for low and high magnetic fields are available in comparison to the Coulomb energy [14]. In this case, the ratio between the magnetic energy ðℏωc =2Þ and effective Rydberg energy (Ryn), which is called
246
Y.H. Shin et al. / Journal of Luminescence 151 (2014) 244–246
and that of the light hole in the barrier is mnlh ¼ 0:080m0 . By using theses values, the effective reduced mass can be estimated as
Fig. 3. The relative energy shift in pulsed magnetic fields. The linear fittings at high magnetic fields are 0.28B meV/T and 0.10B meV/T for the barrier and well transitions, respectively. The inset shows PL spectra at B¼ 0 T and 49 T.
the
γ¼
γ parameter plays an important role
1 ℏωc 2
, 16π 2 ℏ3 ϵ2 ϵ20 B Ryn ¼ mn2 e3
ð1Þ
where ωc ¼ eB=mn is the cyclotron frequency, Ryn ¼ mn e4 = 32π 2 ℏ2 ϵ2 ϵ20 is the effective Rydberg energy, and mn and ϵ are the effective mass and dielectric constant of the given system. When γ 5 1 (low field limit), the term that contains magnetic field in Schrödinger equation can be treated as a perturbation and the diamagnetic energy shift is proportional to B2 =mn3 . In the case of high field limit, γ b 1, where the Coulomb interaction can be treated as a perturbation, the transition energy follows a Landaulike-level, E p 12 eB=mn . Hence, in the first order approximation, the transition energy is proportional to the magnetic field and inversely proportional to the effective mass. Because the sample used for this study is an undoped system, the observed PL transitions are mainly due to the formation of excitons. Above approximations are based on the hydrogen-like bound state in semiconductors. For a free exciton in high magnetic fields, though an electron is bound to a hole, both electron and hole move freely. Therefore, the Schrödinger equation should contain the motion of the center of gravity by changing the effective mass to the exciton reduced-mass, 1=μ ¼ 1=mne þ 1=mnh . For the high field limit, based on γ b 1 approximation, we attempted to make a linear fit for the peak PL transition energies. As shown in Fig. 3, the high field linear fitting for the barrier and the well transitions is ΔE 0:28B meV=T and 0:10B meV/T, respectively. The transition ratio between the well and the barrier is inversely proportional to the ratio of the effective reduced masses,
ΔEb eB=μb μw 0:28 ¼ 2:80; ¼ ¼ ¼ ΔEw eB=μw μb 0:10
ð2Þ
where μw and μb are effective reduced masses of well and barrier, respectively. In Ref. [11], the values of the effective masses of the conduction electrons in the well and the barrier are mnew ¼ 0:105m0 and mneb ¼ 0:095 m0 , respectively, where m0 is the electron rest mass. The effective masses of the heavy-hole in the well are mnhh ¼ 1:926m0
μw ¼
mnew mnhh C 0:100m0 mnew þ mnhh
ð3Þ
μb ¼
mneb mnlh C 0:043m0 mneb þ mnlh
ð4Þ
The ratio of the reduced effective-mass is μw =μb ¼ 2:330, which is close to our experimental value of 2.8. Such a small discrepancy may occur because our sample differs from the ideal system used for theoretical calculation. In summary, we report the effect of effective-mass modulation in the valence band and abnormal optical anisotropy from a InP– GaP lateral MQWs by using photoluminescence transitions under strong magnetic fields. At zero magnetic field, transitions from well and barrier emerge with strong optical anisotropy in peak intensities and peak transition energies. While changing the PL polarization from [1–10] to [110] direction, the well transition energy shows blue-shift whereas the barrier transition exhibits red-shift. This may due to the complicated energy level mixing of the valence hole states. The conduction electrons in the well and the barrier recombine with the heavy-holes and light-holes, respectively, which may lead to opposite energy shift in crossed polarization direction. Magnetophotoluminescence measurements were made in pulsed magnetic fields up to 50 T. The deference of the diamagnetic energy-shifts between the well and the barrier transitions is due to the modulation of the effective-mass in the valence band.
Acknowledgments This research was supported by the Converging Research Center Program through the Ministry of Education, Science and Technology (grant number 2013K000180). JDS acknowledges support from the KIST institutional program including dream project and partially by 2012K001280 and GRL Program through MEST. YK would like to thank Prof. K. H. Lee at DKU for critical reading. References [1] K.C. Hsieh, J.N. Baillargeon, K.Y. Cheng, Appl. Phys. Lett. 57 (1990) 2244. [2] K.W. Park, C.Y. Park, Y.T. Lee, Appl. Phys. Lett. 101 (2012) 051903, and references therein. [3] S.-H. Wei, in: A. Mascarenhas (Ed.), Spontaneous Ordering in Semiconductor Alloys, Kluwer Academic/Plenum Publishers, New York, 2002, Chap. 15, pp. 423–450, and references therein. [4] O. Krebs, P. Voisin, Phys. Rev. Lett. 77 (1996) 1829. [5] P.J. Pearah, A.C. Chen, A.M. Moy, K.-C. Hsieh, K.-Y. Cheng, IEEE J. Quantum Elect. 30 (1994) 608. [6] Y. Zhang, A. Mascarenhas, Phys. Rev. B 57 (1998) 12245. [7] G. Landwehr, D.R. Yakovlev, M. Keim, G. Reuscher, W. Ossau, Superlattice Microst. 27 (2000) 515. [8] P. Yu, J. Wu, B.-F. Zhu, Phys. Rev. B 73 (2006) 235328. [9] A.A. Toropov, E.L. Ivechenko, O. Krebs, S. Cortez, P. Voisin, Phys. Rev. B 63 (2000) 035302. [10] A. Mascarenhas, R.G. Alonso, G.S. Horner, S. Froyen, K.C. Hsieh, K.Y. Cheng, Phys. Rev. B 48 (1993) 4907. [11] J.D. Song, Y.-W. Ok, J.M. Kim, Y.T. Lee, T.-Y. Seong, J. Appl. Phys. 90 (2001) 5086. [12] T. Mattila, L.-W. Wang, Alex Zunger, Phys. Rev. B 59 (1999) 15270. [13] A. Mascarenhas, R.G. Alonso, G.S. Horner, S. Froyen, K.C. Hsieh, K.Y. Cheng, Superlattices Microstruct. 12 (1992) 57. [14] N. Miura, Physics of Semiconductors in High Magnetic Fields, Oxford University Press, New York, 2008, Chap. 2, pp. 52–63.
Contents lists available at ScienceDirect
Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
Optical anisotropy and diamagnetic energy shifts in InP–GaP lateral quantum wells Y.H. Shin a, Yongmin Kim a,n, J.D. Song b, Y.T. Lee c, H. Saito d, D. Nakamura e, Y.H. Matsuda e, S. Takeyama e a
Department of Applied Physics, Institute of Nanosensors and Biotechnology, Dankook University, Yongin 448-701, Republic of Korea Korea Institute of Science and Technology, Seoul 136-791, Republic of Korea c School of Information and Communications, Gwangju Institute of Science and Technology, Gwangju 500-712, Republic of Korea d Department of Applied Physics, The University of Tokyo, Tokyo 113-8654, Japan e Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan b
art ic l e i nf o
a b s t r a c t
Article history: Received 25 October 2013 Received in revised form 17 February 2014 Accepted 25 February 2014 Available online 11 March 2014
Linearly polarized photoluminescence (PL) measurements were made from InP–GaP lateral multiple quantum wells induced by composition modulation along the lateral direction. At B ¼0, two prominent emission peaks emerged, which are identified as transitions from In-rich well and Ga-rich barrier regions. Both transitions are strongly linear polarized parallel to the [110] crystal direction. While rotating PL orientation from [110] to [1–10] direction, the well and barrier transitions show red- and blue-shifts, respectively, due to the different valence states. In high magnetic fields, the two peaks exhibit different diamagnetic energy shifts mainly because of the effective-mass difference in the In-rich and Ga-rich alternate regions along the lateral direction. & 2014 Elsevier B.V. All rights reserved.
Keywords: Lateral composition modulation InP–GaP short period superlattice Optical anisotropy Diamagnetic energy shift
Lateral composition modulation (LCM) in compound semiconductor, [1,2] which can be formed during the growth of short period superlattice (SPS), has been investigated for more than last two decades because of its unique physical properties, such as the formation mechanism of LCM, bandgap reduction and optical anisotropy. Such physical properties also occur in an ordered alloy of GaInP2, which can be explained by the inherent nature of its crystal structure [3]. Although an ordered alloy exhibits the similar physical properties like optical anisotropy, the properties in the alloy originate from different reasons that is associated with those in semiconductor, including vertical/lateral multiple quantum wells (MQW) and superlattices. In a heterostructure that contains different cation and anion (AB–A0 B0 structure) in each side of junctions, the reduced crystal symmetry causes the optical anisotropy [4]. For a heterostructure with a common anion and a different cation (AB–A0 B structure), there is a uniform agreement that the in-plane optical anisotropy occurs due to the coherency strain field, which causes the heavy- and light-hole mixing [5,6]. The quantum confined Pockels effect that shows enhanced optical anisotropy induced by externally applied electric field was also investigated in various semiconductor heterostructures [7–9].
n
Corresponding author. E-mail address: [email protected] (Y. Kim).
http://dx.doi.org/10.1016/j.jlumin.2014.02.036 0022-2313 & 2014 Elsevier B.V. All rights reserved.
Mascarenhas et al. [10] reported parameters of GaP–InP LCM structure wherein the band edges, and the effective-masses of carriers in the conduction electron, heavy-hole, light-hole and spin-orbit split-off bands at the zone center were shown in detail. In this work, we present photoluminescence (PL) spectra of linearly polarized optical transitions that were obtained from InP– GaP LCM structure which was induced during the growth of short period superlattice (SPS) by using a molecular beam epitaxy technique. At B ¼0 T, we observed two main optical transitions, one from the Ga-rich barrier and the other from the In-rich well, both of which show blue- and red-shifts while switching the orientation of the probe polarizer from [1–10] to [110] crystal direction. In the presence of magnetic field up to 50 T, the amount of the diamagnetic energy shifts of two peaks from In- and Ga-rich regions can be estimated as the effective-reduced-mass ratio of excitons in the laterally modulated structure. The sample used for this study was prepared by using the molecular beam epitaxy (MBE) technique. The InP–GaP SPS was grown directly on a GaAs substrate without buffer and capping layers. The growth temperature of the sample was 490 1C and the SPS layers consisted of 659 pairs of GaP (2.9 Å) and InP (3.1 Å). Details of the growth methods, parameters and electron microscope images can be found elsewhere [11]. As seen in this reference, the average thicknesses of In-rich well and Ga-rich barrier are 90 Å. The sample temperature for PL measurements
Y.H. Shin et al. / Journal of Luminescence 151 (2014) 244–246
was maintained at 5 K by using a closed-cycle refrigerator. A 532 nm line of a Nd-YAG laser was used as the excitation source for PL measurements and a polarization rotator was located in front of the laser to vary the laser polarization. For PL emission measurements at zero magnetic field, an additional probe polarizer was located in front of a 50 cm spectrometer equipped with a liquid nitrogen cooled charge coupled device detector. Both excitation and emission polarizations were varied from parallel to perpendicular to the [110] crystal direction. For a pulsed magnetic field, PL measurements at T¼4 K, sample was positioned at the end of an optical fiber of 1.0 mm diameter and then immersed in a liquid helium dewar. A plastic polarizer is inserted between the optical fiber and sample along [1–10] direction. Fig. 1 inset shows a schematic of SPS sample structure as a consequence of the growth wherein LCM was achieved along the [110] direction. As seen in Fig. 1, PL intensities in the absence of probe polarization are anisotropic by changing the direction of polarization of the incident laser. When the incident polarization is parallel to the [110] direction, it has the maximum PL intensity, whereas it is minimum when parallel to the [1–10] direction. The peak positions, however, do not change with the orientation of the incident polarization. This means that the [110] direction is an easy axis of the formation of transition dipole oscillators which maximizes light absorption that causes the maximum PL emission [5]. Because of no appreciable changes in the PL transition energies with respect to the changing incident polarizations, we set the direction of the incident laser polarization to [110] direction and proceeded further experiments for linear polarized PL emissions at B¼ 0 T. The experimental values of the peak transition energies in Fig. 1 are Eg ðwellÞ ¼ 1:7886 eV and Eg ðbarrierÞ ¼ 1:9437 eV and these values are quite comparable to the calculated values [10]. Fig. 2 displays polarization dependence of the PL emission spectra. It shows the maximum emission intensities when the probe polarizer is parallel to the [1–10] direction and the minimum when the polarizer is parallel to the [110] direction. Such an optical anisotropy with respect to the polarization direction is due to the strong heavy- and light-hole mixing caused by biaxial strain along the lateral MQW direction. An interesting phenomenon in the PL spectra observed is that the peak transition energies of the In-rich well and the Ga-rich barrier show opposite spectral-shift behavior by changing the polarization directions. Such spectral shifts were first reported by Mascarenhas et al. [13] wherein the well transition shows 10 meV blue-shift whereas the barrier transition undergoes 1 meV redshift while rotating the PL polarization from [1–10] to [110] direction. In our case, the spectral shifts are opposite from Ref. [13]. When the probe polarizer changes its direction from [1–10] to [110] direction, the barrier transition shows 5 meV blue-shift whereas the well transition exhibits 4 meV red-shift. The main difference of our sample and Ref. [13] is the existence of InGaP buffer layer. As mentioned above, our sample does not contain buffer layer whereas the sample in Ref. [13] has InGaP buffer layer between the substrate and InP–GaP laterally modulated structure. Such difference may alter the spectral energy shifts in the well and the barrier. Mattila et al. [12] reported the dependence of the valence band energy levels with respect to the crystal direction, wherein the energygap increases when the direction changes from [1–10] to [110]. Such a behavior of energygap increase is consistent with our the Ga-rich barrier transition in Fig. 2. Therefore, one plausible reason for such spectral shifts is the recombination from the conduction band electron to different valence holes. According to Ref. [10], the lowest valence band in the InP–GaP LCM structure in the well region is the heavy-hole state whereas that in the barrier region is the light-hole state. Recombination between electrons in the conduction band and holes in the light-hole band in the
245
Fig. 1. Incident laser polarization dependence of PL Spectra. Solid (left axis) and broken (right axis) lines correspond to laser polarization along [110] and [1–10] directions, respectively. Two peaks at 1.9437 eV and 1.7886 eV are identified as the transitions from Ga-rich barrier and In-rich well regions, respectively, of InP–GaP LCM MQWs. The inset is a schematic of the sample structure. The modulation period is about 180 Å. Therefore, both well and barrier thicknesses are 90 Å.
Fig. 2. The probe polarization dependence of the PL transition spectra. By rotating the probe polarization orientation, the PL transitions change not only the intensities but also the peak transition energies. The peak position corresponding to the well and barrier regions shows red- and blue-shift, respectively, while changing the polarization orientation.
barrier region causes the blue-shift as seen in Ref. [12], whereas the recombination to the heavy-hole band in the well region may cause the red-shift. The effective-masses of the valence holes in In-rich and Ga-rich regions are known to be different [10]. Taking into account the inherent modulation in the sample, we propose that the different effective-masses may lead to the different diamagnetic energy shifts in the presence of strong magnetic field. Fig. 3 shows the diamagnetic shifts of the well and barrier transitions in magnetic fields up to 50 T. The inset displays PL spectra at B ¼0 T and 49 T. A theoretical calculation for the exciton diamagnetic shift is generally complicated because the interaction energy related to the magnetic field has a cylindrical symmetry while the Coulomb energy has spherical symmetry. Numerical approximations of Schrödinger equation for a hydrogen-like bound system for low and high magnetic fields are available in comparison to the Coulomb energy [14]. In this case, the ratio between the magnetic energy ðℏωc =2Þ and effective Rydberg energy (Ryn), which is called
246
Y.H. Shin et al. / Journal of Luminescence 151 (2014) 244–246
and that of the light hole in the barrier is mnlh ¼ 0:080m0 . By using theses values, the effective reduced mass can be estimated as
Fig. 3. The relative energy shift in pulsed magnetic fields. The linear fittings at high magnetic fields are 0.28B meV/T and 0.10B meV/T for the barrier and well transitions, respectively. The inset shows PL spectra at B¼ 0 T and 49 T.
the
γ¼
γ parameter plays an important role
1 ℏωc 2
, 16π 2 ℏ3 ϵ2 ϵ20 B Ryn ¼ mn2 e3
ð1Þ
where ωc ¼ eB=mn is the cyclotron frequency, Ryn ¼ mn e4 = 32π 2 ℏ2 ϵ2 ϵ20 is the effective Rydberg energy, and mn and ϵ are the effective mass and dielectric constant of the given system. When γ 5 1 (low field limit), the term that contains magnetic field in Schrödinger equation can be treated as a perturbation and the diamagnetic energy shift is proportional to B2 =mn3 . In the case of high field limit, γ b 1, where the Coulomb interaction can be treated as a perturbation, the transition energy follows a Landaulike-level, E p 12 eB=mn . Hence, in the first order approximation, the transition energy is proportional to the magnetic field and inversely proportional to the effective mass. Because the sample used for this study is an undoped system, the observed PL transitions are mainly due to the formation of excitons. Above approximations are based on the hydrogen-like bound state in semiconductors. For a free exciton in high magnetic fields, though an electron is bound to a hole, both electron and hole move freely. Therefore, the Schrödinger equation should contain the motion of the center of gravity by changing the effective mass to the exciton reduced-mass, 1=μ ¼ 1=mne þ 1=mnh . For the high field limit, based on γ b 1 approximation, we attempted to make a linear fit for the peak PL transition energies. As shown in Fig. 3, the high field linear fitting for the barrier and the well transitions is ΔE 0:28B meV=T and 0:10B meV/T, respectively. The transition ratio between the well and the barrier is inversely proportional to the ratio of the effective reduced masses,
ΔEb eB=μb μw 0:28 ¼ 2:80; ¼ ¼ ¼ ΔEw eB=μw μb 0:10
ð2Þ
where μw and μb are effective reduced masses of well and barrier, respectively. In Ref. [11], the values of the effective masses of the conduction electrons in the well and the barrier are mnew ¼ 0:105m0 and mneb ¼ 0:095 m0 , respectively, where m0 is the electron rest mass. The effective masses of the heavy-hole in the well are mnhh ¼ 1:926m0
μw ¼
mnew mnhh C 0:100m0 mnew þ mnhh
ð3Þ
μb ¼
mneb mnlh C 0:043m0 mneb þ mnlh
ð4Þ
The ratio of the reduced effective-mass is μw =μb ¼ 2:330, which is close to our experimental value of 2.8. Such a small discrepancy may occur because our sample differs from the ideal system used for theoretical calculation. In summary, we report the effect of effective-mass modulation in the valence band and abnormal optical anisotropy from a InP– GaP lateral MQWs by using photoluminescence transitions under strong magnetic fields. At zero magnetic field, transitions from well and barrier emerge with strong optical anisotropy in peak intensities and peak transition energies. While changing the PL polarization from [1–10] to [110] direction, the well transition energy shows blue-shift whereas the barrier transition exhibits red-shift. This may due to the complicated energy level mixing of the valence hole states. The conduction electrons in the well and the barrier recombine with the heavy-holes and light-holes, respectively, which may lead to opposite energy shift in crossed polarization direction. Magnetophotoluminescence measurements were made in pulsed magnetic fields up to 50 T. The deference of the diamagnetic energy-shifts between the well and the barrier transitions is due to the modulation of the effective-mass in the valence band.
Acknowledgments This research was supported by the Converging Research Center Program through the Ministry of Education, Science and Technology (grant number 2013K000180). JDS acknowledges support from the KIST institutional program including dream project and partially by 2012K001280 and GRL Program through MEST. YK would like to thank Prof. K. H. Lee at DKU for critical reading. References [1] K.C. Hsieh, J.N. Baillargeon, K.Y. Cheng, Appl. Phys. Lett. 57 (1990) 2244. [2] K.W. Park, C.Y. Park, Y.T. Lee, Appl. Phys. Lett. 101 (2012) 051903, and references therein. [3] S.-H. Wei, in: A. Mascarenhas (Ed.), Spontaneous Ordering in Semiconductor Alloys, Kluwer Academic/Plenum Publishers, New York, 2002, Chap. 15, pp. 423–450, and references therein. [4] O. Krebs, P. Voisin, Phys. Rev. Lett. 77 (1996) 1829. [5] P.J. Pearah, A.C. Chen, A.M. Moy, K.-C. Hsieh, K.-Y. Cheng, IEEE J. Quantum Elect. 30 (1994) 608. [6] Y. Zhang, A. Mascarenhas, Phys. Rev. B 57 (1998) 12245. [7] G. Landwehr, D.R. Yakovlev, M. Keim, G. Reuscher, W. Ossau, Superlattice Microst. 27 (2000) 515. [8] P. Yu, J. Wu, B.-F. Zhu, Phys. Rev. B 73 (2006) 235328. [9] A.A. Toropov, E.L. Ivechenko, O. Krebs, S. Cortez, P. Voisin, Phys. Rev. B 63 (2000) 035302. [10] A. Mascarenhas, R.G. Alonso, G.S. Horner, S. Froyen, K.C. Hsieh, K.Y. Cheng, Phys. Rev. B 48 (1993) 4907. [11] J.D. Song, Y.-W. Ok, J.M. Kim, Y.T. Lee, T.-Y. Seong, J. Appl. Phys. 90 (2001) 5086. [12] T. Mattila, L.-W. Wang, Alex Zunger, Phys. Rev. B 59 (1999) 15270. [13] A. Mascarenhas, R.G. Alonso, G.S. Horner, S. Froyen, K.C. Hsieh, K.Y. Cheng, Superlattices Microstruct. 12 (1992) 57. [14] N. Miura, Physics of Semiconductors in High Magnetic Fields, Oxford University Press, New York, 2008, Chap. 2, pp. 52–63.