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Emission of metastable excitons in PbI2
Journal of Luminescence 11(1975/76) 295—297 ~ North-Holland Publishing Company
SHORT COMMUNICATION EMISSION OF METASTABLE EXCITONS IN Pb12 V.G. PLEKHANOV, I. KUUSMANN and P. LIBLIK Institute of Physics, Academy of Sciences oft/ic Estonian SSR, 202400 Tartu USSR Received 15 October 1975 Luminescent emission greater than the band edge of Pb12 is investigated. It is proposed that the emission is from metastable excitbns, possibly from hyperbolic excitons.
Electron—hole interaction exerts a profound effect on the optical properties of the semiconductors. The excitation maxima at the fundamental absorption edge have been observed experimentally and summarized by a number of authors (see, e.g. [1]). During the past decade in the fundamental absorption spectra the excitons have been observed whose energy overlaps the band to band transitions. Some of such metastable excitons can undergo an autoionisation [2]. Phillips was the first to suggest that electrons and holes can form excitons not only near parabolic band edges but also in the vicinity of the saddle points [3]. He called them saddle point or hyperbolic excitons. The existence of hyperbolic excitons was experimentally demonstrated on the reflectance and absorption spectra of InSb and GaSe [4,5]. Of considerable interest is elucidation of the possible emission of metastable, in particular, hyperbolic excitons. The purpose of this note is to describe the results of the investigations of the emission of the exitons lying above the band edge. As it will be shown below some of such metastable excitons may be hyperbolic. Pb12 (2H polytype) single crystals with hexagonal layer structure were used as sample. This substance is most suitable for th&investigations as the reflectance and absorption spectra of these crystals have been studied in broad energy and temperature ranges [6,7] and their band structure is well known by now [8,91. According to the results of op. cit. the excitons in Pb12 are observed not only near the main edge Eg = 2.55 eV (M0 critical point) but also above it: at 2.9 eV (three-dimensional M1 critical point); 3.3 eV (M0 critical point); 3.6 eV (M1 critical point with a singularity of another type). Freshly cleaved plates with the hexagonal axes C perpendicular to the face were used in the measurements. Thewere crystals were an electron beam of 6The keV 2. The samples fixed in aexcited vacuumbycryostat (~lO~ torr). and 10 .zamm emission spectra were measured with double-prism monochromator with the reciprocal dispersion 16 A/mm, a photomultiplier FEU.7l, and a stroboscopic osdillograph (see, also [10]). An Arens prism was used as the analyser. 295
V. G. Plekhanoi’ er al. / Emission of metastable excirons
296
ncr;~
(eV
Fig. 1.
In fig. 1 the quantity ~c2Xhw at LNT (dashed line) [7] is shown. This quantity rather than e2 is directly proportional to the optical transition probabilities. At the figure the emission spectrum of the Pb!2 crystal at 80 K (solid line) displays too. Besides the well-known emission line of free excitons at ~2.5 eV [11—13]a broad and structured band with a maximum at 2.9 eV and a distinct shoulder at 3.3 eV, as also as a band at 4.0 eV can be observed in the spectrum. The peak intensity of the 2.9 eV band is 1/6 of the free exciton emission intensity, whereas their integral intensities are almost equal. The impurities cannot yield such large quantum efficiency. The emission of free excitons is polarized. The intensity with E I C is four times greater than the mtensity with E II C, which agrees well with the results of the studies on photoexcitation [11—13].The luminescence at 2.9 eV(M1 critical point) is observed with either polarisations, the intensity relation being I(E I C)/I(E II C) = 3/2. This relation is also a good agreement with the intensity relations in the reflectance spectra of these polarisations. It is possible that the observed small shift of this band is due to its complex structure. According to the selection rules the transitions A~ A~~6 at 3.3 eV (M0 critical point) are allowed only for E IC, the observed emission in this spectral region, however is polarized with E II C. The reason of this discrepance is not clear yet. The transitions near the M1 critical point at 3.6 eV are allowed for E II C and the emission within this interval has only this polarisation. To explain the nature of the band peaking at 4.0 eV some further investigation is needed. If the interpretation of the absorption (reflectance) spectra of Pb!2 made in [6— 9] is correct, the above arguments allow us to infer that in Pb12 the emission of the metastable exitons is observed not only near the M0 critical point but also near the M1 critical point, i.e. the emission of hyperbolic excitons. This conclusion, however, cannot be taken as fully proved. For hyperbolic excitons one is to expect more dis-+
V.G. Plekhanov era!. /Emission of metastable excitons
297
tinct singularities in the fundamental absorption spectra (cf. [3—5])and a considerably smaller yield of luminescence. When the energy of exciting electron beam is increased (more than 6 keV), the emission bands at 4.33; 4.70; 5.05 and 5.60 eV become observable. The interpretation of this structure is difficult as yet but it is probable that the emission at 5.05 and 5.60 eV is due to the excitons connected with the excitation of anions (see also [9]). In conclusion it is to be mentioned that the emission of metastable excitons is observed also in PbBr2 PbCl2 and InBr single crystals [14].
Acknowledgement The authors thank Prof. Ch.B. Lushchik, Drs. G.S. Zavt and V.V. Hizhnyakov for stimulating discussions. References Li]
R.S. Knox, Theory of excitons, New York, London, 1963. 121 M. Cardona and G. Harbeke, Phys. Rev. Letters 8 (1962) 90; E.R. Ilmas, R.A. Kink, G.G. Liidja and Ch.B. Lushchik, Izvestlja AN SSSR, ser. fiz. 29 (1965) 27. 131 J.C. Phillips, Solid State Physiscs 18 (1966) p. 55. [4] V.L. Shaklee, J.E. Rove and M. Cardona, Phys. Rev. 174 (1968) 828. [51V.K. Subashiev and Le-Khac-Bink, JETP Letters 12 (1970) 139. [6] D.L. Greenaway and G.Harbeke, J. Phys. Soc. Japan, Suppl. 21(1966)151. [7] Ch. Gähwiller and G. Harbeke, Phys. Rev. 185 (1969) 1141; E. Tosatti and G. Harbeke, Nuovo Cimento 22B (1974) 87. 18] E. Doni and G. Grosso and G. Spavieri, Solid State Comm. 11(1972)493. [9] I.Ch. Schlüter and M. Schltiter, Phys. Rev. B9 (1974) 1652. [10] IL. Kuusmann, P.H. Liblik and Ch.B. Lushchik, JETP Letters 21(1975)161. [11] R. Kleim and F. Raga, J. Phys. Chem. Solids 30(1969)2213. [12] lB. Blonsky and I.S. Gorban, Fiz. tverd. tela 15 (1973) 3664. 113] F. Levy, A. Mercier and J.-F. Voitchovsky, Solid State Comm. 15(1974) 819. 1141 IL. Kuusmann, PH. Liblik and V.G. Plekhanov, Fiz. tverd. tela, to be published.
SHORT COMMUNICATION EMISSION OF METASTABLE EXCITONS IN Pb12 V.G. PLEKHANOV, I. KUUSMANN and P. LIBLIK Institute of Physics, Academy of Sciences oft/ic Estonian SSR, 202400 Tartu USSR Received 15 October 1975 Luminescent emission greater than the band edge of Pb12 is investigated. It is proposed that the emission is from metastable excitbns, possibly from hyperbolic excitons.
Electron—hole interaction exerts a profound effect on the optical properties of the semiconductors. The excitation maxima at the fundamental absorption edge have been observed experimentally and summarized by a number of authors (see, e.g. [1]). During the past decade in the fundamental absorption spectra the excitons have been observed whose energy overlaps the band to band transitions. Some of such metastable excitons can undergo an autoionisation [2]. Phillips was the first to suggest that electrons and holes can form excitons not only near parabolic band edges but also in the vicinity of the saddle points [3]. He called them saddle point or hyperbolic excitons. The existence of hyperbolic excitons was experimentally demonstrated on the reflectance and absorption spectra of InSb and GaSe [4,5]. Of considerable interest is elucidation of the possible emission of metastable, in particular, hyperbolic excitons. The purpose of this note is to describe the results of the investigations of the emission of the exitons lying above the band edge. As it will be shown below some of such metastable excitons may be hyperbolic. Pb12 (2H polytype) single crystals with hexagonal layer structure were used as sample. This substance is most suitable for th&investigations as the reflectance and absorption spectra of these crystals have been studied in broad energy and temperature ranges [6,7] and their band structure is well known by now [8,91. According to the results of op. cit. the excitons in Pb12 are observed not only near the main edge Eg = 2.55 eV (M0 critical point) but also above it: at 2.9 eV (three-dimensional M1 critical point); 3.3 eV (M0 critical point); 3.6 eV (M1 critical point with a singularity of another type). Freshly cleaved plates with the hexagonal axes C perpendicular to the face were used in the measurements. Thewere crystals were an electron beam of 6The keV 2. The samples fixed in aexcited vacuumbycryostat (~lO~ torr). and 10 .zamm emission spectra were measured with double-prism monochromator with the reciprocal dispersion 16 A/mm, a photomultiplier FEU.7l, and a stroboscopic osdillograph (see, also [10]). An Arens prism was used as the analyser. 295
V. G. Plekhanoi’ er al. / Emission of metastable excirons
296
ncr;~
(eV
Fig. 1.
In fig. 1 the quantity ~c2Xhw at LNT (dashed line) [7] is shown. This quantity rather than e2 is directly proportional to the optical transition probabilities. At the figure the emission spectrum of the Pb!2 crystal at 80 K (solid line) displays too. Besides the well-known emission line of free excitons at ~2.5 eV [11—13]a broad and structured band with a maximum at 2.9 eV and a distinct shoulder at 3.3 eV, as also as a band at 4.0 eV can be observed in the spectrum. The peak intensity of the 2.9 eV band is 1/6 of the free exciton emission intensity, whereas their integral intensities are almost equal. The impurities cannot yield such large quantum efficiency. The emission of free excitons is polarized. The intensity with E I C is four times greater than the mtensity with E II C, which agrees well with the results of the studies on photoexcitation [11—13].The luminescence at 2.9 eV(M1 critical point) is observed with either polarisations, the intensity relation being I(E I C)/I(E II C) = 3/2. This relation is also a good agreement with the intensity relations in the reflectance spectra of these polarisations. It is possible that the observed small shift of this band is due to its complex structure. According to the selection rules the transitions A~ A~~6 at 3.3 eV (M0 critical point) are allowed only for E IC, the observed emission in this spectral region, however is polarized with E II C. The reason of this discrepance is not clear yet. The transitions near the M1 critical point at 3.6 eV are allowed for E II C and the emission within this interval has only this polarisation. To explain the nature of the band peaking at 4.0 eV some further investigation is needed. If the interpretation of the absorption (reflectance) spectra of Pb!2 made in [6— 9] is correct, the above arguments allow us to infer that in Pb12 the emission of the metastable exitons is observed not only near the M0 critical point but also near the M1 critical point, i.e. the emission of hyperbolic excitons. This conclusion, however, cannot be taken as fully proved. For hyperbolic excitons one is to expect more dis-+
V.G. Plekhanov era!. /Emission of metastable excitons
297
tinct singularities in the fundamental absorption spectra (cf. [3—5])and a considerably smaller yield of luminescence. When the energy of exciting electron beam is increased (more than 6 keV), the emission bands at 4.33; 4.70; 5.05 and 5.60 eV become observable. The interpretation of this structure is difficult as yet but it is probable that the emission at 5.05 and 5.60 eV is due to the excitons connected with the excitation of anions (see also [9]). In conclusion it is to be mentioned that the emission of metastable excitons is observed also in PbBr2 PbCl2 and InBr single crystals [14].
Acknowledgement The authors thank Prof. Ch.B. Lushchik, Drs. G.S. Zavt and V.V. Hizhnyakov for stimulating discussions. References Li]
R.S. Knox, Theory of excitons, New York, London, 1963. 121 M. Cardona and G. Harbeke, Phys. Rev. Letters 8 (1962) 90; E.R. Ilmas, R.A. Kink, G.G. Liidja and Ch.B. Lushchik, Izvestlja AN SSSR, ser. fiz. 29 (1965) 27. 131 J.C. Phillips, Solid State Physiscs 18 (1966) p. 55. [4] V.L. Shaklee, J.E. Rove and M. Cardona, Phys. Rev. 174 (1968) 828. [51V.K. Subashiev and Le-Khac-Bink, JETP Letters 12 (1970) 139. [6] D.L. Greenaway and G.Harbeke, J. Phys. Soc. Japan, Suppl. 21(1966)151. [7] Ch. Gähwiller and G. Harbeke, Phys. Rev. 185 (1969) 1141; E. Tosatti and G. Harbeke, Nuovo Cimento 22B (1974) 87. 18] E. Doni and G. Grosso and G. Spavieri, Solid State Comm. 11(1972)493. [9] I.Ch. Schlüter and M. Schltiter, Phys. Rev. B9 (1974) 1652. [10] IL. Kuusmann, P.H. Liblik and Ch.B. Lushchik, JETP Letters 21(1975)161. [11] R. Kleim and F. Raga, J. Phys. Chem. Solids 30(1969)2213. [12] lB. Blonsky and I.S. Gorban, Fiz. tverd. tela 15 (1973) 3664. 113] F. Levy, A. Mercier and J.-F. Voitchovsky, Solid State Comm. 15(1974) 819. 1141 IL. Kuusmann, PH. Liblik and V.G. Plekhanov, Fiz. tverd. tela, to be published.