High-quality CuInSe2 single crystals were studied using polarization resolved photoluminescence (PL) and magnetophotoluminescence (MPL). The emission lines related to the first (n=2) excited states for the A and B free excitons were observed in the PL and MPL spectra at 1.0481 meV and 1.0516 meV, respectively. The spectral positions of these lines were used to estimate accurate values for the A and B exciton binding energies (8.5 meV and 8.4 meV, respectively), Bohr radii (7.5 nm), band gaps (E-g(A)=1.050 eV and E-g(B)=1.054 eV), and the static dielectric constant (11.3) assuming the hydrogenic model

Faugeras, C.

Karotki, A. V.

Luckert, F.

Martin, R. W.

Mudryi, A. V.

Yakushev, M. V.

English

M. V. Yakushev

F. Luckert

C. Faugeras

A. V. Karotki

A. V. Mudryi

R. W. Martin

Crossref

Applied Physics Letters

Excited states of the free excitons in CuInSe2 single crystals

Name not available

University of Strathclyde Institutional Repository

Strathprints Institutional RepositoryYakushev, M. V. and Luckert, F. and Faugeras, C. and Karotki, A. V. and Mudryi, A. V. and Martin,R. W. (2010) Excited states of the free excitons in CuInSe2 single crystals. Applied Physics Letters,97 (15). -. ISSN 0003-6951Strathprints is designed to allow users to access the research output of the University of Strathclyde.Copyright c© and Moral Rights for the papers on this site are retained by the individual authorsand/or other copyright owners. You may not engage in further distribution of the material for anyprofitmaking activities or any commercial gain. You may freely distribute both the url (http://strathprints.strath.ac.uk/) and the content of this paper for research or study, educational, ornot-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to Strathprints administrator:mailto:strathprints@strath.ac.ukhttp://strathprints.strath.ac.uk/Excited states of the free excitons in CuInSe2 single crystalsM. V. Yakushev,1,a F. Luckert,1 C. Faugeras,2 A. V. Karotki,3 A. V. Mudryi,3 andR. W. Martin11Department of Physics, SUPA, Strathclyde University, G4 0NG Glasgow, United Kingdom2LNCMI, CNRS, UJF, UPS, INSA, BP 166, 38042 Grenoble Cedex 9, France3Scientific-Practical Material Research Centre of the Belarus National Academy of Science, P.Brovki 19,220072 Minsk, BelarusReceived 27 August 2010; accepted 25 September 2010; published online 14 October 2010High-quality CuInSe2 single crystals were studied using polarization resolved photoluminescencePL and magnetophotoluminescence MPL. The emission lines related to the first n=2 excitedstates for the A and B free excitons were observed in the PL and MPL spectra at 1.0481 meV and1.0516 meV, respectively. The spectral positions of these lines were used to estimate accurate valuesfor the A and B exciton binding energies 8.5 meV and 8.4 meV, respectively, Bohr radii 7.5 nm,band gaps EgA=1.050 eV and EgB=1.054 eV, and the static dielectric constant 11.3 assuming thehydrogenic model. © 2010 American Institute of Physics. doi:10.1063/1.3502603Solar cells with CuInSe2-based absorber layers are theleading thin-film technology in terms of conversion efficien-cies, reaching 20%,1 and stability. CuInSe2 has a direct bandgap near 1.05 eV and an absorption coefficient exceeding105 cm−1, one of the highest among known semiconductors.Despite a considerable amount of research the evolution ofthe conversion efficiency is showing a tendency to saturatewell below the theoretical limit of about 30% for a one-junction solar cell2 suggesting a lack of fundamental under-standing of these materials.A key milestone in the understanding and application ofevery semiconductor material is the unambiguous observa-tion of free excitons and their excited states. Resolving boththe ground and excited states of the free excitonic transitionsis a reliable way to accurately determine such parameters asthe band-gap Eg.3 Despite many studies of the optical prop-erties of CuInSe2 dating back nearly 40 years4 only very fewreports suggest resolution of the A and B free excitonicstates.5–8 No reliable information on their excited states hasyet been reported and therefore the band-gap cannot be con-sidered to be accurately known.Previous experimental attempts to determine the free ex-citon binding energies Eb in CuInSe2 have been carried outby analyzing either the temperature quenching of the exci-tonic photoluminescence PL emission intensity7,9 or dia-magnetic shifts under the influence of magnetic fields.10 Thequenching characteristics of the A and B excitons are rathercomplex due to the small energy splitting and proximity ofshallow bound excitons and thus values of Eb determined bythis method cannot be considered as reliable. The techniquebased on the analysis of the exciton line diamagnetic shift isvalid within the weak field approximation, which limits theaccuracy of Eb.10,11 These issues are reflected in the consid-erable scatter of the EbA values in the literature, ranging from4.3 to 39.1 meV Refs. 6, 7, 9, 10, and 12–14 resulting inscattered values of the band gap. It is advantageous to deter-mine Eb from the spectral positions of the PL lines of the freeexciton ground and excited states as this does not involveany other material parameters. This gives one an opportunityto clarify the static dielectric constant , which also reveals aconsiderable scatter in the literature from 16 Ref. 15 to 9.3Ref. 16, assuming published values of the effective massesare correct and the validity of the hydrogenic model.In this letter, PL and reflectance RF data on CuInSe2bulk crystals, grown from the melt, are used to resolve awide range of excitonic transitions, including the A and Bfree excitonic excited states. The quality of the crystal isdemonstrated by the improved resolution and intensity of thefree excitonic transitions. Polarization and magnetic field de-pendent spectra are used to probe the symmetry and clarifythe assignments. The spectral positions of PL lines related toexcited states were used to calculate accurate values of theband gap and dielectric constant, as well as the binding en-ergies, and Bohr radii aB of the A and B free excitons inCuInSe2.Bulk single crystals of CuInSe2 were cleaved from themiddle part of an ingot grown by the vertical Bridgman tech-nique using a near stoichiometric mix of the high purity el-ements Cu, In, and Se.17 The elemental composition of thecrystals, measured by energy dispersive X-ray analysisEDX was close to ideal stoichiometry Cu: 24.9, In: 24.9,and Se: 50.2 at. %. The orientation of the three major cubicstructure crystallographic axes 001, 010, and 100 of thesamples was established by analysis of x-ray Laue patterns.Cleaved surfaces of the crystals were examined using PL andRF at 6 K at Strathclyde and magneto-PL MPL at 4.2 K atthe Grenoble High Magnetic Field Laboratory GHMFL.Magnetic fields up to 20 T were directed perpendicular to cBc, which is the tetragonal distortion direction in thecrystalline lattice. Both the PL and the MPL measurementsemployed the unpolarized 514 nm line of an Ar+ laser as anexcitation source while the RF measurements used a 100 Wtungsten halogen lamp. The spectral resolution was deter-mined as 0.07 meV for the RF, 0.8 meV for the polarizationresolved PL at 6.5 K, and 0.14 meV for the PL and MPL at4.2 K. The spectral position of the lines was determined withan accuracy of 0.2 meV. More details on the experimental setups can be found elsewhere.9,10,12The near band gap region of the PL and RF spectra takenin CuInSe2 at 4.2K and 6K, respectively, using nonpolarizedaAuthor to whom correspondence should be addressed. Electronic mail:michael.yakushev@strath.ac.uk.APPLIED PHYSICS LETTERS 97, 152110 20100003-6951/2010/9715/152110/3/$30.00 © 2010 American Institute of Physics97, 152110-1Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsplight, are shown in Figs. 1a and 1b, respectively. The RFspectrum reveals two prominent resonances, associated withthe A and B free excitons, confirming that the lines at 1.0417eV and 1.0453 eV in the PL spectra are related to the A andB free excitons, respectively.7,8 The A exciton energy, deter-mined in this paper 1.0417 eV, is very close to that re-ported by Chatrophorn et al.7 for single crystals 1.0418 eVbut higher then the values measured by Schön et al.6 forsingle crystals 1.0406 eV and Niki et al.5 for epitaxial lay-ers 1.0386 eV. The difference can be explained by the in-fluence of intrinsic defects due to deviations from the idealstoichiometry19 and strain in the epitaxial layer due to a mis-match in the CuInSe2 and GaAs lattice parameters.8 In addi-tion to the free exciton lines the spectrum shows several wellresolved lines M1–M7 which have been previously attributedto bound excitons and their excited states.7–9The chalcopyrite structure of CuInSe2 can be derivedfrom the sphalerite zinc blende structure of ZnSe by the or-dered replacement of Zn either with Cu or In. These twononequivalent replacements result in two different lengthsfor the chemical bonds Cu–Se and In–Se creating a tetrago-nal distortion18 splitting the triply degenerated valence bandat the  point of the Brillouin zone in ZnSe into the threesub-bands A, B, and C. In terms of the quasicubic model20this splitting can be described as the simultaneous influenceof the noncubic crystal-field and spin-orbit interactions,which in CuInSe2 determine the spectral splitting of the A-Band B-C bands, respectively. The tetragonal distortion ,given by 1−c /2a, where c and a are the lattice constants, hasa small negative value 0.52% in the samples studied here.This results in a small and positive value of the crystal fieldsplitting cf, which inverts the valence sub-band sequencein CuInSe2 and gives the uppermost A sub-band the 6vsymmetry.The region of the free excitonic transitions is examinedmore closely using PL spectra measured with a linear polar-izer oriented either along E c or perpendicular Ec tothe c—axis of the crystalline lattice as shown in Fig. 2a.The A and B free exciton transitions are resolved at 1.0417and 1.0453 eV in the unpolarized spectrum.7,8It is clear that the A free exciton emission is predomi-nantly polarized Ec, reaching a maximum intensity IA atthis polarization as reported for electro-reflectance21 and PLRef. 22 spectra. This is consistent with the selection rulesfor an A excitonic transition involving the 6v symmetry ofthe top valence sub-band and the 6c symmetry of the con-duction band. According to the quasi-cubic model,20 the the-oretical ratio of IA / IA intensities should reach 9.21 In our PLexperiment the value of IA / IA is 7.1, approaching the theo-retical value more closely than the earlier reported value of 5for electroreflectance.21 The B exciton line does not changeas dramatically with polarization as the A exciton line. Itsintensity is almost unchanged, which is consistent with theselection rules for a transition between the 7v symmetry Bvalence sub-band and the 6c symmetry conduction band forboth the Ec and E c polarizations.21 However, it is notedthat its width is reduced from about 2.2 meV in the nonpo-larized spectrum down to 1.1 meV for the Ec polarization.The lines related to the excited states A and B of thefree excitons become visible to higher energy in Fig. 2. Theirintensities are weak but the polarized spectra aid their iden-tification. For the E c polarization the reduced strength ofthe A exciton ground and excited transitions improves thevisibility of the excited state line of the B exciton and alsoclarifies the A n=2 contribution to the high-energy tail ofthe B exciton line. Conversely, for the Ec polarization, thenarrowing of the B exciton line allows the line related to theA excited state, to be more clearly resolved as shown in Fig.2a. The straight line emphasizes its presence.The excited state lines can also be seen in the unpolar-ized PL spectra taken at higher excitation density as shownin Fig. 2b. In particular the separation of B from the otherlines allows it to be resolved more clearly, whereas A is notso well resolved due to the proximity of the B line. In orderto determine their spectral positions this unpolarized PLspectrum has been fitted with Lorentz shape curves of A, B,A, and B. The spectral positions of the excitonic lines fittedwith Lorentzians are shown in Table I. Further evidence forthe excited state nature of the weaker features A and B inthe PL spectra is provided by the MPL spectra in Fig. 3a.The spectra show the B exciton lines shifting toward higherFIG. 1. Color online Near band-gap regions in a RF and b PL spectrafor CuInSe2 single crystals taken at 6 K and 4.2 K, respectively, showinglines of free and bound excitons.FIG. 2. Color online a Near band-gap regions in PL spectra for CuInSe2single crystals taken at unpolarized, polarized Ec and E c conditions at 6K offset for clarity; b the A and B free exciton region of the unpolarizedPL spectra in CuInSe2 single crystals fitted with A, B, A, and B Lorentzshape curves.152110-2 Yakushev et al. Appl. Phys. Lett. 97, 152110 2010Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jspenergies and splitting into two components. At higher ener-gies the spectra also reveal components of the A and Bn=2 excited states. These features are more easily seen atmagnetic fields above 2 T, for which the effective excitonsize and the Bohr radius are reduced. In addition the fieldcauses an increase in binding energy, rendering the excitonsmore stable. The dependence of the spectral positions of theB n=1, A, and B n=2 lines on the magnetic field atBc are shown in Fig. 3b. The A line is seen to splitnoticeably into two components, which converge to 1.0481eV as the field reduces to zero. At 2 T the B line, related tothe excited state, can also be seen in Fig. 3a. According tothe hydrogenic model for simple parabolic bands in a directband gap material the spectral position En of a free excitonline in the nth excited state is, as follows:11En = Eg − Eb = Eg − 13.6m02n2, 1where =memh /me+mh is the reduced mass of exciton, m0 isthe free electron mass, me is an effective electron, and mh aneffective hole masses, and  is the static dielectric constantof the material. From the spectral separation of the groundn=1 and excited n=2 states, shown in Table I, the bind-ing energies of the A and B excitons have been calculatedusing the formulaEb =43 EFEn = 2 − EFEn = 1 , 2and are shown in Table II. Accurate values of the A and Bband gaps are also calculated using Eg=En=1+Eb andshown in Table II. Assuming literature values of the effectivemasses for the electron and hole in CuInSe2 me=0.09m0 andmh=0.71m0, respectively23, the static dielectric constant inCuInSe2 was calculated to be =11.3 using Eq. 1. TheBohr radii for the A and B free excitons have also beencalculated as: aB=aBHm0 /, where aBH is the Bohr radius forhydrogen. The calculated values of aB are shown in Table II.In conclusion, high quality CuInSe2 single crystals werestudied by PL spectroscopy, employing polarization andmagnetic field dependence to clarify the properties of thefree exciton transitions. The lines related to the first n=2excited states for the A and B free excitons at EAn=2=1.0481 eV and EBn=2=1.0516 eV, respectively, havebeen observed in the PL and MPL spectra. Accurate valuesof the A and B exciton binding energies EbA=8.5 and EbB=8.4 meV have been established. These are then used toestimate Bohr radii aB of 7.5 nm for both excitons, a 6 Kband gap of 1.050 eV for the A exciton and of 1.054 eV forthe B exciton as well as the value of 11.3 for the staticdielectric constant. A standard hydrogenic model is assumed.This work was supported by the EPSRC Grant No. EP/E026451/1, the Royal Society Grant No. IJP 2008/R1,BCFR Grant No. F09MC-003, “Nanomaterials and nano-technology” 6.17, and EC-EuroMagNetII-228043.1I. Repins, M. A. Contreras, B. Egaas, C. DeHart, J. Scharf, C. L. Perkins,B. To, and R. Noufi, Prog. Photovolt. Res. Appl. 16, 235 2008.2W. Shockley and H. J. Queisser, J. Appl. Phys. 32, 510 1961.3M. Smith, G. D. Chen, J. Y. Lin, H. X. Jiang, M. A. Khan, C. J. Sun, Q.Chen, and J. W. Yang, J. Appl. Phys. 79, 7001 1996.4J. L. Shay and J. H. Wernick, Ternary Chalcopyrite Semiconductors-Growth, Electronic Properties, and Applications Pergamon, New York,1975.5S. Niki, H. Shibata, P. J. Fons, A. Yamada, A. Obara, Y. Makita, T.Kurafuji, S. Chichibu, and H. Nakanishi, Appl. Phys. Lett. 67, 12891995.6J. H. Schön and E. Bucher, Appl. Phys. Lett. 73, 211 1998.7S. Chatraphorn, K. Yoodee, P. Songpongs, C. Chityuttakan, K. Sayavong,S. Wongmanerod, and P. O. Holtz, Jpn. J. Appl. Phys., Part 2 37, L2691998.8A. V. Mudryi, I. V. Bodnar, I. A. Viktorov, V. F. Gremenok, M. V. Yaku-shev, R. D. Tomlinson, A. E. Hill, and R. D. Pilkington, Appl. Phys. Lett.77, 2542 2000.9M. V. Yakushev, R. W. Martin, and A. V. Mudryi, Phys. Status Solidi C 6,1082 2009.10M. V. Yakushev, R. W. Martin, A. Babinski, and A. V. Mudryi, Phys.Status Solidi C 6, 1086 2009.11C. F. Klingshirn, Semiconductor Optics Springer, New York, 1997.12M. V. Yakushev, Y. Feofanov, R. W. Martin, R. D. Tomlinson, and A. V.Mudryi, J. Phys. Chem. Solids 64, 2011 2003.13M. A. Abdulaev, Sov. Phys. Semicond. 26, 1196 1992.14L. Nemerenco, Moldavian J. Phys. Sci. 4, 438 2005.15G. Riede, H. Subotta, H. Neumann, and X. N. Hoang, Solid State Com-mun. 28, 449 1978.16P. W. Yu, J. Appl. Phys. 47, 677 1976.17R. D. Tomlinson, Sol. Cells 16, 17 1986.18J. E. Jaffe and A. Zunger, Phys. Rev. B 29, 1882 1984.19M. V. Yakushev, A. V. Mudryi, and R. D. Tomlinson, Appl. Phys. Lett.82, 3233 2003.20J. E. Rowe and J. L. Shay, Phys. Rev. B 3, 451 1971.21J. L. Shay, H. M. Tell, H. M. Kasper, and L. M. Schiavone, Phys. Rev. B7, 4485 1973.22K. Hönes, M. Eickenberg, S. Siebentritt, and C. Persson, Appl. Phys. Lett.93, 092102 2008.23H. Neumann, Sol. Cells 16, 317 1986.TABLE I. The spectral positions of the excitonic lines fitted with Lorentz-ians.Excitons A B A Bh eV 1.0417 1.0453 1.0481 1.0516FIG. 3. Color online a The evolution of the B ground n=1 state excitonand the A and B excited n=2 states under the influence of magneticfields at Bc, b dependence of the spectral positions of the lines related tothe ground B and A and B excited states of free excitons on the magneticfield strength.TABLE II. The band gaps, binding energies Eb, and Bohr radii aB of the Aand B excitons.ExcitonsEbmeVaBnmEgeVA 8.5 7.5 1.0502B 8.4 7.5 1.0537152110-3 Yakushev et al. Appl. Phys. Lett. 97, 152110 2010Author complimentary copy. 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Excited states of the free excitons in CuInSe2 single crystals

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