We present a combined theoretical and experimental study of the anisotropy in the optical absorption of V‐shaped quantum wires. By means of realistic band structure calculations for these structures, we show that detailed information on the heavy‐ and light‐hole states can be singled out from the anisotropy spectra independently of the electron confinement, thus allowing accurate valence band spectroscopy

CINGOLANI R.

FASOLINO A.

GOLDONI G.

MOLINARI E.

RINALDI R.

ROSSI, FAUSTO

English

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05 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEValence band spectroscopy in V-grooved quantum wires / GOLDONI G.; ROSSI F.; MOLINARI E.; FASOLINO A.;RINALDI R.; CINGOLANI R.. - In: APPLIED PHYSICS LETTERS. - ISSN 0003-6951. - 69:20(1996), pp. 2965-2967.OriginalValence band spectroscopy in V-grooved quantum wiresaip_postprintPublisher:PublishedDOI:10.1063/1.117745Terms of use:openAccessPublisher copyright-(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/1405278 since:AIP American Institute of PhysicsValence band spectroscopy in Vgrooved quantum wiresG. Goldoni, F. Rossi, E. Molinari, A. Fasolino, R. Rinaldi et al.  Citation: Appl. Phys. Lett. 69, 2965 (1996); doi: 10.1063/1.117745 View online: http://dx.doi.org/10.1063/1.117745 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v69/i20 Published by the American Institute of Physics.  Related ArticlesImaging ambipolar diffusion of photocarriers in GaAs thin films J. Appl. Phys. 111, 123720 (2012) Visible light emission and energy transfer processes in Sm-doped nitride films J. Appl. Phys. 111, 123105 (2012) Structural and optical properties of InAs/AlAsSb quantum dots with GaAs(Sb) cladding layers Appl. Phys. Lett. 100, 243108 (2012) The electronic band structure of GaBiAs/GaAs layers: Influence of strain and band anti-crossing J. Appl. Phys. 111, 113108 (2012) Growth of AlN/SiC/AlN quantum wells on Si(111) by molecular beam epitaxy Appl. Phys. Lett. 100, 232112 (2012)  Additional information on Appl. Phys. Lett.Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors Downloaded 06 Jul 2012 to 192.167.204.100. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionsValence band spectroscopy in V-grooved quantum wiresG. Goldoni,a) F. Rossi, and E. MolinariIstituto Nazionale di Fisica della Materia (INFM) and Dipartimento di Fisica, Universita` di Modena,Via Campi 213/A, I-41100 Modena, ItalyA. FasolinoInstitute of Theoretical Physics, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen,The Netherlands, and Istituto Nazionale di Fisica della Materia (INFM) and Dipartimento di Fisica,Universita` di Modena, Via Campi 213/A, I-41100 Modena, ItalyR. Rinaldi and R. CingolaniIstituto Nazionale di Fisica della Materia (INFM) and Dipartimento di Scienza dei Materiali,Universita` di Lecce, Via Arnesano, I-73100 Lecce, Italy~Received 9 July 1996; accepted for publication 5 September 1996!We present a combined theoretical and experimental study of the anisotropy in the opticalabsorption of V-shaped quantum wires. By means of realistic band structure calculations for thesestructures, we show that detailed information on the heavy- and light-hole states can be singled outfrom the anisotropy spectra independently of the electron confinement, thus allowing accuratevalence band spectroscopy. © 1996 American Institute of Physics. @S0003-6951~96!04646-3#In semiconductor quantum wires, the anisotropic absorp-tion of light linearly polarized parallel or perpendicular to thewire axis has long been recognized to be the effect of thequasi-one-dimensional ~quasi-1D! character of electronicstates, combined with heavy- and light-hole ~HH and LH!mixing.1,2 The observation of optical anisotropy has sincebeen considered as evidence of the 1D character of nano-structured materials.3 However, even in samples showing thebest optical properties, the interpretation of optical spectra isdifficult owing to the large broadening of the peaks, which iscomparable to the typical inter-subband splittings, and to thelack of realistic band structure calculations, so far limited towires with model geometries.2,4–6 Moreover, theconfinement-induced blueshift is dominated by the light ef-fective mass of conduction electrons, and information con-cerning hole states are even more difficult to extract from thespectra.The aim of this letter is to show, by a combination ofoptical measurements and band structure calculations, that inrealistic structures the details of the optical anisotropy can betraced to HH and LH states and, therefore, allow for a spec-troscopy of hole states. We shall focus on quasi-1D struc-tures obtained by epitaxial growth on non-planar substrates~V-shaped wires!7–9, which rank among the best availablesamples from the point of view of optical properties.Our samples are arrays of GaAs quantum wires embed-ded in ~GaAs!8~AlAs!4 superlattices ~SL!, grown by molecu-lar beam epitaxy ~MBE! on V-grooved substrates obtainedby holographic lithography and wet etching. In our case, thethickness of the crescent-shape wire which self-organizes atthe bottom of the V-groove —as obtained by transmissionelectronic microscopy ~TEM! analysis— is approximately80 Å. More details on sample parameters are reported inRef. 10.In Fig. 1a we show the low-temperature ~10 K! photolu-minescence excitation ~PLE! spectra ~thin lines! for thea!Electronic mail: goldoni@unimo.itAppl. Phys. Lett. 69 (20), 11 November 1996 0003-6951/96/69(20Downloaded 06 Jul 2012 to 192.167.204.100. Redistribution subject to AIPsample just described. The spectra are obtained with lightpolarized along the wire axis and perpendicular to it ~and tothe growth direction!. We shall focus on the excitonic con-tinuum, i.e., the energy range above 1.575 eV. The broadpeaks in PLE spectra are very different from the singularitieswhich one would naively expect from the ideal joint densityof states ~DOS! of quasi-1D electrons and holes, because ofthe relatively small intersubband splittings compared to theinhomogeneous broadening11 and the effects of Coulombinteraction12, so that the interpretation is not easy. As weshall demonstrate, however, additional information can begained by considering the optical anisotropy between the twoFIG. 1. a! Low-temperature PLE spectra measured with incoming lightlinearly polarized perpendicular to the wire axis ~thin solid line!, parallel tothe wire axis ~dotted line!, and relative anisotropy ~thick solid line!. b!Calculated absorption spectra with light linearly polarized perpendicular tothe wire axis ~thin solid line!, parallel to the wire axis ~dotted line!, parallelto the z direction ~dashed line!, and relative anisotropy ~thick solid line!.2965)/2965/3/$10.00 © 1996 American Institute of Physics license or copyright; see http://apl.aip.org/about/rights_and_permissionspolarizations ~thick line in Fig. 1a!, defined as100*(I i2I')/I i , where I i , I' are the PLE intensities for thetwo polarizations. In this range of energy, the anisotropy liesin the range 10–20%, but goes through a deep minimumaround 1.59–1.60 eV, where it is almost suppressed.We have performed realistic band structure calculationswithin the envelope function approximation. The HH–LHmixing was modelled by the Luttinger Hamiltonian13, withproper account of crystallographic directions14. As in Ref.10, the wire potential profile was extracted from a TEM mi-crograph of the sample. In the present complex geometry, thecommon approach of first solving the Schro¨dinger equationfor uncoupled HHs and LHs and then using them as a basisset to represent the Luttinger Hamiltonian, results in a verylarge computation due to the poor convergence with respectto the number of subbands included in the basis. To over-come this difficulty, our approach is to set up a basis set fromthe eigenstates of only one type of particle, with a fictitiousmass to be specified later, confined in the V-shaped wirepotential. These are obtained numerically in terms of a planewave expansion as in Ref. 10. In this scheme the additionalcost in the calculation of matrix elements of the LuttingerHamiltonian is more than compensated, because only onetype of particle needs to be calculated, and, more important,the convergence can be improved by properly choosing thefictitious mass. In practice, we find it efficient to choose avalue close to the HH mass15.Band parameters are taken from GaAs bulk values. Theonly unknown parameters are the barrier heights for conduc-tion and valence electrons: in fact, the embedding short pe-riod superlattice ~SL! is modeled by a homogeneous barrierwith an effective band offset. The conduction band offsetwas taken to be 150 meV, a value that was independentlyproved to reproduce PLE and magnetoluminescenceexperiments10. The criterium for the choice of the valenceband offset is a by-product of the present work and will bediscussed below.The calculated absorption spectra and the relative opticalanisotropy, obtained from the full band structure within thedipole approximation, are shown in Fig. 1b. A Gaussianbroadening of 64.5 meV has been included. The anisotropy~thick line! shows a minimum, and then reaches a value of;20 %. The comparison with experiments is quite favour-able for energies around the minimum, while the agreementworsens in the high energy range, where the calculated an-isotropy drops rapidly and finally changes sign. This discrep-ancy might be due to our ‘‘effective’’ description of the bar-riers which affects particularly the higher-lying hole states.As for the calculated absorption spectra, apart from aredshift of the continuum onset with respect to the experi-mental curves ~which is within the uncertainty in the wiregeometry!, the main difference lies in the relative intensitiesof the two broad features at 1.59 eV and 1.61 eV in the ex-periment. This might be due to the Coulomb interaction,which is neglected in the present calculation, and causes achange in the excitonic continuum. Note, however, thatwhile each single polarization is significantly changed byexcitonic effects, the relative anisotropy seems to be muchless affected.2966 Appl. Phys. Lett., Vol. 69, No. 20, 11 November 1996Downloaded 06 Jul 2012 to 192.167.204.100. Redistribution subject to AThe suppression of the optical anisotropy at;1.59 meV is due to states which are mainly of LH charac-ter: As an indication of the role of LH states, we also show inFig. 1b the calculated absorption spectra for light linearlypolarized parallel to the growth direction (z direction!. Al-though measurements with this polarization are actually dif-ficult because of the small active volume, it is instructive tocalculate, since z-polarized light only couples with the LHcomponent of hole states.2 Figure 1b shows that the mini-mum in anisotropy actually lies in the range where thez-polarized absorption ~and therefore the LH character! has asudden increase.Due to the large DOS, the electron and hole states atk50 (k is the 1D wave vector along the wire axis! aremainly responsible for the features in the spectra. Due to thequasi-1D confinement provided by the wire barriers, and incontrast to the case of quantum wells, these states are ofmixed HH and LH character.2 Figure 2 shows the calculatedHH character of k50 hole states ~labeled by the quantumnumber nh) vs the confinement energy.16 Even in a stronglyconfined system as the present V-shaped wire, the groundstate is almost a pure HH state ~92%); the transition involv-ing this hole state (nh51) and the first electron state(ne51) is mainly responsible for the first peak in the calcu-lated spectrum.17 The excited hole states show an increas-ingly mixed HH–LH character, so that the classification inHH and LH states, familiar from quantum wells, becomesinappropriate. Simultaneous to the decrease in the HH char-acter, the wave functions of excited states become more andmore extended along the ‘‘wings’’ of the wire, in analogy tothe simpler case of conduction electrons10, and, conse-quently, they couple to excited electron subbands, mostlywith ne5nh); starting from the nh52 level in Fig. 2, theycontribute to the broad features above ;1.59 in the calcuFIG. 2. Percentage of HH character for the lowest hole subbands at k50 vssubband energy. The arrow indicates the first state which is mainly(56 %) of LH character. Insets: total charge density, and HH- and LH-projected charge densities for the state indicated with the arrow (nh513).Darker regions correspond to larger values of the charge density; thin linesrepresent the potential profile used in the calculation. In-plane axes are innm ~note the different scale in the two directions!. For clarity, in the threepanels grey levels are set to different scales.Goldoni et al.IP license or copyright; see http://apl.aip.org/about/rights_and_permissionslated spectra. However, this progression is interrupted by thestate indicated with an arrow in Fig. 2. This state is of mainlyLH character ~56 %!, and for brevity it will be indicatedbelow as the LH state. Although this is a highly excited state(nh513), its wave function, shown in the insets, is localizedin the center of the wire. Therefore, due to the large overlap,this state couples primarily with the first conduction subband(ne51), making a contribution to the low energy part of thespectrum. The large LH component, moreover, makes thatthe intensity for the two polarizations is reversed with re-spect to the strongly HH ground state, causing the dip in theanisotropy at 1.59 meV. We have checked, in a set of wireswith different thicknesses at the bottom of the V-groove anddifferent barrier compositions, that a more or less pro-nounced dip in the anisotropy is always present in the lowenergy range of the spectrum, extending over a range com-parable to the linewidth of the broadened spectra, and super-imposed to a background of an otherwise large and positiveanisotropy.An immediate consequence of the above reasoning isthat, since both the ground HH state and the LH state couplewith the lowest electron subband, the difference in energybetween the onset of the continuum and the position of thedip in the anisotropy is a direct measure of the energy split-ting between the ground HH and the first LH states, indepen-dent of the electron confinement. This splitting, which in theexperiment of Fig. 1a is ;16 meV, has been used in ourcalculation to estimate the effective valence band offset; itsvalue was finally taken as 85 meV.18In conclusion we have shown by realistic band structurecalculations that the optical anisotropy of V-shaped quantumwires contains detailed information on the valence subbands,Appl. Phys. Lett., Vol. 69, No. 20, 11 November 1996Downloaded 06 Jul 2012 to 192.167.204.100. Redistribution subject to AIPwhich can be singled out from the conduction electron con-tribution, allowing for a spectroscopy of the hole states.1P. C. Sercel and K. J. Vahala, Appl. Phys. Lett. 57, 545 ~1990!.2U. Bockelmann and G. Bastard, Phys. Rev. B 45, 1688 ~1992!.3For a review see: R. Cingolani and R. Rinaldi, Riv. Nuovo Cimento 16, 1~1993!; see also: R. Rinaldi et al., Phys. Rev. B 50, 11 795 ~1994!.4D. S. Citrin and Y. -C. Chang, Phys. Rev. B 40, 5507 ~1989!; IEEE J.Quantum Electron. 29, 97 ~1993!.5H. Ando, S. Nojima, and H. Kanbe, J. Appl. Phys. 74, 6383 ~1993!.6G. Goldoni and A. Fasolino, Phys. Rev. B 52, 14 118 ~1995!.7E. Kapon, D. M. Hwang, and R. Bhat, Phys. Rev. Lett. 63, 430 ~1989!.8M. Gailhanou, T. Baumbach, U. Marti, P. L. Silva, F. K. Reinhart, and M.Ilegems, Appl. Phys. Lett. 62, 1623 ~1993!.9S. Tiwari, G. D. Pettit, K. R. Milkove, F. Legoues, R. J. Davis, and J. M.Woodall, Appl. Phys. Lett. 64, 3536 ~1994!.10R. Rinaldi, R. Cingolani, M. Lepore, M. Ferrara, I. M. Catalano, F. Rossi,L. Rota, E. Molinari, P. Lugli, U. Marti, D. Martin, F. Morier-Gemoud, P.Ruterana, and F. K. Reinhart, Phys. Rev. Lett. 73, 2899 ~1994!.11E. Molinari, F. Rossi, L. Rota, P. Lugli, R. Rinaldi, M. Lepore, and R.Cingolani, in Proceedings of the 22nd International Conference on thePhysics of Semiconductors, edited by D. J. Lockwood ~World Scientific,Singapore, 1994!, p. 1707.12F. Rossi and E. Molinari, Phys. Rev. Lett. 76, 3642 ~1996!; Phys. Rev. B53, 16 462 ~1996!.13 J. M. Luttinger, Phys. Rev. 102, 1030 ~1956!.14 J. -B. Xia, Phys. Rev. B 43, 9856 ~1991!.15The choice of such fictitious mass is purely dictated by computationalconvenience: once convergence is achieved, it does not affect the finalresults in any way.16The angular momentum quantization axis is chosen along the direction ofstrongest confinement, i.e. the @001# growth direction.17To help with the interpretation of the theoretical spectra we record herethe electron confinement energy of the three lowest subbands ne51,2,3:43.3 meV, 57.3 meV, and 65.3 meV. The band gap is 1.519 eV.18To give an idea of the precision of this assessment, a variation of thevalence band offset of 615 meV shifts the HH–LH splitting of61.3 meV.2967Goldoni et al. license or copyright; see http://apl.aip.org/about/rights_and_permissions

Valence band spectroscopy in V-grooved quantum wires

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Valence band spectroscopy in V-grooved quantum wires

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