Magneto-photoluminescence study of radiative recombination in CuInSe2 single crystals

Journal of Physics and Chemistry of Solids 64 (2003) 2011–2016 www.elsevier.com/locate/jpcs

Magneto-photoluminescence study of radiative recombination in CuInSe2 single crystals M.V. Yakusheva,*, Y. Feofanova, R.W. Martina, R.D. Tomlinsonb, A.V. Mudryic a

Department of Physics and Applied Physics, Strathclyde University, Glasgow G4 0NG, UK b Department of Physics, University of Salford, Salford M54WT, UK c Institute of Solid State and Semiconductor Physics, National Academy of Science of Belarus, 220 072 Minsk, P.Brovki 17, Belarus

Abstract Radiative recombination processes in CuInSe2 (CIS) single crystals grown by vertical Bridgman technique were studied using photoluminescence, photoluminescence excitation and magneto-PL. The PL and PLE spectra were measured as functions of temperature (varying from 4.2 to 300 K), excitation intensity, magnetic field (up to 10 T) and the elemental composition. The PL spectra taken at 4.2 K exhibited a complicated structure with a number of sharp peaks in the near-band-edge region associated with free (EA ¼ 1:0416 eV; EB ¼ 1:0447 eV) and bound excitons (EM1 ¼ 1:0386 eV; EM2 ¼ 1:0353 eV; EM3 ¼ 1:0341 eV; EM4 ¼ 1:0324 eV and EM5 ¼ 1:0278 eV) and free-to-bound recombination bands. The binding energies of the bound-excitons were derived. The nature of the defects associated with these excitons and the other observed bands is discussed. A non-linear blue shift toward higher energies was observed in magnetic field for all PL peaks. This shift is in agreement with the exciton energy calculated as a function of field. Field-induced splitting (4.5 meV at 10 T) of a deep band (0.972 eV) band was observed. q 2003 Elsevier Ltd. All rights reserved. Keywords: D. Optical properties

1. Introduction The ternary chalcopyrite compound CuInSe2 (CIS) has a unique combination of physical properties with a band-gap ðEg Þ near 1.05 eV and an absorption coefficient ðaÞ exceeding 105 cm21. These qualities make CIS a very promising material for a new generation of thin-film solar cells [1]. Despite numerous attempts to define an accurate value of the band-gap using various techniques, including optical absorption (OA), photoluminescence (PL), photoreflectance (PR) and optical reflection (OR) reliable values of this parameter were obtained only recently [2 – 8]. The nature of the valence band splitting was also determined and Eg was estimated in a wide temperature range [2,3,7]. In this paper we report new experimental data on free and bound excitons in high-quality CIS single crystals obtained by PL * Corresponding author. Tel.: þ44-141-548-3374; fax: þ 44-141552-2891. E-mail address: [email protected] (M.V. Yakushev).

and photoluminescence excitation (PLE) spectroscopy. We also present the first results, to the best of our knowledge, of a study of the magnetic field dependence of the free and bound excitons in CIS crystals at 4.2 K.

2. Experimental details High quality CIS single crystals were grown using the vertical Bridgman technique. The crystals were of p-type conductivity and had carrier concentrations in the range 1 £ 10 16 – 7 £ 1016 cm23 and mobilities from 50 to 120 cm22 V21 s21. The Cu/In ratio, derived from the elemental composition measured using energy dispersive X-ray analysis (EDX), varied from 0.94 to 1.15 and the content of Se was measured to be , 50%. PL and PLE spectra were measured from cleaved surfaces of the crystals. The 488 nm Arþ laser line and a 400 W halogen tungsten lamp were used to generate PL and measure PLE, respectively. PL measurements were carried out using a ˚ /mm dispersion. 0.6 m diffraction monochromator with 26 A

0022-3697/03/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0022-3697(03)00090-8

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A 0.3 m diffraction monochromator was used for the PLE measurements. The PL and PLE signals were detected by liquid nitrogen cooled Ge p-i-n detector. Magneto-optical studies were carried out using a super conducting magnet in a liquid helium bath cryostat, allowing magnetic fields up to 10 T at 4.2 K. Fibre optics were used to transport the 805 nm diode laser excitation to the sample and the PL to the entrance slits of a 0.3 m diffraction monochromator. The spectral resolution in the PL and MPL measurements was 0.1 and 0.5 meV, respectively.

3. Results and discussion Typical PL spectra of the near-band-edge region (from 0.80 to 1.10 eV), taken at 4.2 K for three samples, cut from CIS ingots with different Cu/In ratios, are presented in Fig. 1. It can be seen that although the spectra look quite different they have many common features. Every spectrum contains high-energy lines A and B, at about 1.0416 and 1.0447 eV, with full width at half maxima (FWHM) of about 0.8 – 1.0 meV. These lines are due to radiative recombination of the free A and B excitons, corresponding to two sub-bands of the valence band split by the tetragonal crystalline field in CIS [4,7]. Assuming that the exciton binding energy is about 7 – 7.5 meV [2,9] and that the energy of the A free exciton (ground state n ¼ 1) is about 1.0416 eV we can derive the band-gap energy as Eg ¼ 1.0491 eV. Sharp peaks with FWHM from 0.3 to 1.0 meV can also be seen in the lower energy regions of the PL spectra: M1 at

Fig. 1. PL spectra measured at 4.2 K from CIS single crystals with different Cu/In ratio.

1.0386 eV, M2 at 1.0353 eV, M3 at 1.0341 eV, M4 at 1.0324 eV and M5 at 1.0278 eV. We attribute these lines to recombination of the excitons bound at shallow donors and acceptors, which in our opinion are neutral. A number of broad lines attributed to non-equilibrium charge carrier recombination on deep defects can be observed in spectral region below 1.02 eV. It can be seen that the patterns of the M1– M5 peaks and that of the broader bands (N at 1.002 eV, P at 0.972 eV, K at 0.901 eV etc) are very different for each crystal and depend on the elemental composition. The relative intensities, temperature dependencies and excitation power dependencies of the M1 – M5 lines and the broader PL bands in the different samples allow the bands located in the region from 1.05 to 0.80 eV to be attributed to radiative recombination on different independent defects. The interpretation of the low energy group of the three K-bands seems to be the easiest. The higher energy band K at 0.901 eV is the narrowest amongst the three K-bands and is accompanied by two others (KLO at 0.872 eV and K2LO at 0.845 eV) which we attribute to simultaneous excitation of one and two longitudinal optical (LO) phonons. The spectral separations of the K peaks are 29 and 27 meV, which is close to the LO phonon energy (29 meV) obtained from Raman scattering experiments on CIS single crystals [10]. It was assumed in Ref. [4] that the K line results from a transition of electrons from the conduction band to an acceptor level (e, A) and such interpretation is not contradicted by our results. Using the band-gap of 1.0491 eV, estimated earlier, the acceptor level ionisation energy is 148 meV. Using the known values for intrinsic defect ionisation energies in CIS [11] we can suggest interstitial selenium (Sei) as the acceptor. It should be mentioned, that for Cu rich samples with Cu/In , 1.15 an additional peak with a maximum at 0.909 eV was observed on the high energy side of K, and is accompanied by one and two LO phonon replicas. The relatively small blue-shift (about 7 meV) from the K line and the similarity in shape of the two peaks indicates a similar origin and suggests that copper atoms are involved in modifying the electronic structure of the luminescence centres responsible for the K peak. The formation of selenium interstitial-copper interstitial complexes (Sei – Cui) is thought to be responsible for the appearance of the additional band at 0.909 eV. The P band along with it’s LO phonon replica and the N band are the most likely to originate from (e, A) transitions. The P band could be associated with the anti-site acceptor-type defect copper on indium site (CuIn). Such a defect generates a band-gap level at about 77 meV. The N band we associate with copper vacancies ðVCu Þ with a level at 49 meV. The 2 – 3 meV (, kT/2) shift of the P and N maxima towards higher energy on raising the temperature from 4.2 to 70 K can be taken as an experimental confirmation that the mechanisms of both the P and N transitions are (e, A).:No considerable shifts in the K, N and P peak positions were observed for variations

M.V. Yakushev et al. / Journal of Physics and Chemistry of Solids 64 (2003) 2011–2016 Table 1 The binding (EbA for acceptors and EbD for donors) and ionisation (EA for acceptors and ED for donors) energies of the M1– M5 excitons bands observed in the PL spectra from CIS Line Energy Binding Defect (eV) energy (meV)

Type of defect

M1 M2 M3 M4 M5

Donor 21 Donor 45 Donor 53 Acceptor 153 Acceptor 230

1.0386 1.0353 1.0341 1.0324 1.0278

3 6.3 7.5 9.2 13.8

Cui InCu Ini Sei (or CuIn) CuSe (or VIn)

Ionisation energy (meV)

of excitation power over three orders of magnitude. This also confirms the (e, A) type transition for P, N and K bands. In the sample with the greatest excess of copper the M1 line, which is in the spectral region associated with bound exciton lines, becomes quite intense. The intensity of this line is small for the samples with reduced Cu/In ratios. This allows us to attribute M1 to a copper related defect, which is likely to be the shallow neutral donor interstitial copper atom (Cui). The exciton binding or dissociation energies (EbA for acceptors and EbD for donors) for the sharp M1 – M5 peaks were derived as the difference between their energy and that of the free exciton A. The derived dissociation energies for the M1 – M5 excitons are shown in Table 1. Dissociation energies close to the above values were also derived by analysing the intensity decrease of each M-line at the temperature increased from 4.2 to 80 K. Assuming these experimental values of dissociation energies for M1 – M5 centres and taking into account their relation with the ionisation energy of neutral donors ðED Þ and acceptors ðEA Þ (EbD ¼ 0:14ED [12] and EbA ¼ 0:06EA [13], respectively), allows estimates to be made for ED and EA and subsequent

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comparison with the known values for the corresponding defect energy levels in CIS crystals [11]. We presume that Cui, InCu and Ini are the most probable shallow neutral donors responsible for the M1, M2 and M3 peaks, respectively. We also presume that the neutral acceptors Sei (or CuIn) and CuSe (or VIn) could be responsible for the M4 and M5 lines, respectively. Fig. 2 shows PL and PLE spectra of the exciton region measured from high quality CIS single crystals with elemental compositions close to ideal stochiometry (Cu/In ,1.03), with a spectral resolution of about 0.5 meV. The detection energy was about 1.0 eV (N band) for the PLE experiments. The A and B free exciton peaks are well resolved in these spectra. To our knowledge this is the first report of well resolved A and B peaks in CIS PLE spectra. The PLE data complement our previous experiments on optical reflection and absorption [6,7], confirming the free excitonic nature of the A and B lines. We observed good agreement between the PLE spectra and earlier absorption spectra [6]. To obtain some additional information on the excitonic transitions in CIS crystals magneto-photoluminescence (MPL) experiments were carried out. The magnetic field dependencies of PL spectra measured from the CIS samples with Cu/In ,0.94 are shown in Fig. 3. The total energy shifts measured over 10 T are 2.5 meV for the free exciton A and 2.1 and 1.9 meV for the bound excitons M2 and M4. It should be noted that the conditions for the MPL experiments were quite different from those used for the earlier PL. The excitation laser beam was delivered to the sample surface using optical fibre and was not focused on the sample. This has resulted in a wider spectral FWHM of the excitonic emission measured in the MPL experiments. The shift of the free and bound excitons A, M2 and M4 can be clearly seen in Fig. 4(a) and (b) plots their peak energies as a function of the magnetic field. As expected the blue shift with

Fig. 2. PL and PLE spectra of the A and B free excitons. PLE spectra were measured at Edet ,1.00 eV from a single crystal with Cu/In ,1.03.

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Fig. 3. Effect of magnetic field on the PL spectra from CIS single crystal with Cu/In ratio 0.94.

increasing magnetic field is non-linear and occurs at different rates for the different peaks. The maximum average shift is observed for the free exciton peak A ,0.25 meV/T, whereas for bound excitons the shift is smaller: for the M2 it is ,0.21 meV/T and for M4 is ,0.19 meV/T, i.e. the shift depends on the depth of the excitonic states in the band-gap. The FWHM of all the excitonic lines is of about 4 meV, independent of magnetic field and probably too large to

permit observation of any splitting of the A, M2 and M4 lines. It is important to note that MPL experiments, carried out for different orientation of the magnetic field vector with respect to crystallographic axis (B ’ c and Bkc), resulted in the same blue spectral shift of the peaks in magnetic field and did not reveal any anisotropy. The obtained MPL data can be modeled using a calculation of the energy levels of a neutral hydrogen-like

Fig. 4. (a) PL spectra from CIS single crystal, without and under magnetic field up to 10 T at 4.2 K; (b) energy shift of the excitonic peaks A, M2, M4 under magnetic field. The solid line shows the calculated energy shift for the A exciton.

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system in a magnetic field [14] and also compared to MPL results measured for other semiconductors with a similar energy-band structure, specifically GaN [15,16]. At the highest field used in this work the cyclotron energy is approximately twice the excitonic binding energy (,7 meV) and we are in an intermediate field range. At much higher fields the shift of the excitonic ground state can be expressed as   e"B 1 1 e"B DE ¼ þ : ð1Þ ¼ p p 2 mc mv 2m

no splitting of sharp bound exciton peaks has also been observed whilst deeper levels were observed to split into two or three components ðDE=B , 0:20 meV=TÞ: At the present time modifications to the experimental arrangement are being carried out in order to try and obtaining narrower PL lines for the free and bound exciton peaks and hopefully resolve the spin-splittings.

where m is the reduced effective mass. Using the reported values for the effective mass of the hole mph ¼ 0:73m0 [17] and electron mpe ¼ 0:09m0 [18] for CIS crystals gives a blue-shift of about 0.7 meV/T, dominated by the lighter electron mass. At low magnetic field an approximately quadratic diamagnetic energy shift is expected, which we estimate as ,2 £ 1022 meV/T2 for CIS. Between these extremes we calculate the energy shift using the variational model of Ref. [14]. The result is shown for the A exciton in the inset (b) of Fig. 4. A slight reduction to the above value for the electron effective mass (to 0.08 m0 ) gives excellent agreement with the measured points (similar agreement is obtained by slightly reducing the binding energy, to 6 meV). The magnetic field induced energy shift for the bound excitons M2 and M4 is not too dissimilar to that for A due to the small exciton binding energies in CIS [2,9]. Comparison can be made with wurtzitic GaN, where the effective masses of electron and hole in GaN are 0.22 m0 and ,0.75 m0 ; respectively, [15]. Having a similar band structure but an electron mass reduced by a factor of 2, the magnetic field induced energy shift is expected to be approximately half that for CIS. The Zeeman splitting of the excitonic ground state in a magnetic field is given by

Well-resolved A and B free exciton lines were observed in both the PL and PLE measurements at 4.2 K. Along with these lines the PL spectra measured from samples with Cu/In ratio from 0.94 to 1.15 revealed a number of peaks. The sharp emission lines M1 – M5 were attributed to the excitons, bound at different shallow neutral defects. The broader bands P, N and K were assigned to the free-to-bound (e, A) transitions at different deep PL centres. A non-linear increase in the energy of all PL peaks was detected in magnetic field up to 10 T and could be modelled using a variational model for excitonic states. Splitting of the P band (4.5 meV at 10 T), associated with deep defects was observed.

dE ¼ gmj mB B;

ð2Þ

where mB is the Bohr magneton, mj is the magnetic quantum number, and g the Lande factor. According to Refs. [15,16] magnetic field line splitting coefficients for free excitons (A, B, C) in GaN are , 0.17 meV/T, for neutral donors , 0.10 meV/T, for neutral acceptors , 0.12 meV/T. The g-factor for donors is ,1.708 and for acceptors , 2.040. Using these values as a guide we estimate that the spin-splitting of the free and bound excitonic levels in CIS is unlikely to exceed 0.30 – 0.35 meV/T. Therefore the measured value of the FWHM (,4 meV at 4.2 K) of the excitonic transition at MPL measurements is probably insufficient to resolve the spinsplitting of the A, M2 and M4 lines. However, a sign of splitting was observed for a deeper energy state (band P, which is shown in Fig. 3), indicating a higher g-factor for deeper states. In particular for the P band, with a peak at 0.972 eV, the observed splitting was DE , 4.5 meV for B ¼ 10 T (0.45 meV/T). The obtained results qualitatively agree with the MPL data reported for CuGaS2 [19], where

4. Conclusion

Acknowledgements This work was supported by the grants EPSRC R74116, Royal Society and INTAS 01-283.

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