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Crystalline gallium oxide nanowires: intensive blue light emitters
22 September 2000
Chemical Physics Letters 328 Ž2000. 5–9 www.elsevier.nlrlocatercplett
Crystalline gallium oxide nanowires: intensive blue light emitters X.C. Wu ) , W.H. Song, W.D. Huang, M.H. Pu, B. Zhao, Y.P. Sun, J.J. Du Laboratory of Internal Friction and Defects in Solid, Institute of Solid State Physics, Academia Sinica, Hefei 230031, PR China Received 17 May 2000; in final form 4 August 2000
Abstract Gallium oxide nanowires ŽGaONWs; diameter, ca. 60 nm; length, hundreds of micrometers. have been synthesized by a carbothermal reduction reaction. The nanowires have been confirmed as crystalline b-Ga 2 O 3 by powder X-ray diffraction and selected area electronic diffraction. The GaONWs can emit stable and high brightness blue light at 446 nm Ž2.78 eV. under excitation at 378 nm Ž3.28 eV., which may have potential applications in one-dimensional optoelectronic nanodevices. q 2000 Published by Elsevier Science B.V.
1. Introduction Nanostructured materials possess unique electronic w1,2x, optical w3–5x and magnetic properties w6x compared with those in traditional bulk materials due to their quantum size effects. Their nanoscale dimensions may allow novel structures that could serve as potential building blocks for field-emission electron sources w7x, electronic w8x and optoelectronic devices w9x. For instance, GaAs and InAs nanowires have found applications in developing one-dimensional high-speed field effect transistors, or laser working at low-threshold current density and high gain w10x. With the development of mesoscopic science and integrated optical technology, it is important to synthesize optical nanowires that can meet the demands for further applications. Gallium oxide, b-Ga 2 O 3 , is a wide band gap Ž Eg s 4.9 eV. w11x compound which has long been known to exhibit both conduction )
Corresponding author. Current address: Institute of Solid State Physics, Academia Sinica, P.O. Box 1129, Heifei 230031, PR China. Fax: q86-551-5591434; e-mail: [email protected]
w12,13x and luminescence properties w14,15x. Therefore, the GaONWs may have potential applications in one-dimensional optoelectronic nanodevices. The fabrication and structure of crystalline Ga 2 O 3 nanowires were once reported, but the nanowires were synthesized by physical evaporation, and the photoluminescence ŽPL. was not dealt with w16x. In this Letter, we report the carbothermal reduction synthesis, characterization and PL properties of the GaONWs. The growth process and PL mechanism of the GaONWs have been discussed.
2. Experimental The gallium oxide powders were mixed with graphite according to the weight ratio of 1:1.5 and ground for 1 h. The mixtures were put in an alumina boat, and then the boat was covered with ceramic plates, placed in the center of the tube furnace, and remained at 9808C for 2 h in flowing nitrogen atmosphere Ž20 mlrmin.. Wool-like products depositing on the inner wall of the alumina boat and ceramic
0009-2614r00r$ - see front matter q 2000 Published by Elsevier Science B.V. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 8 8 9 - 7
6
X.C. Wu et al.r Chemical Physics Letters 328 (2000) 5–9
plates were collected for characterization and measurement. X-ray powder diffraction patterns of the products were obtained with Philips PW 1700 X-ray diffractometer with CuK a radiation. Transmission electron microscopy ŽTEM. images of the products were taken with a JEM-200CX transmission electron microscope. Photoluminescence ŽPL. spectra were measured in a Hitachi 850 fluorescence spectrophotometer with a Xe lamp at room temperature. The excitation wavelengths were 378 and 266 nm, and the corresponding filter wavelengths were 430 and 310 nm.
3. Results and discussion The X-ray powder diffraction pattern as shown in Fig. 1 can be indexed in peak position to b-Ga 2 O 3 ŽJCPDS card: No. 11-370., although the relative intensity of the peaks is not consistent with that of
bulk Ga 2 O 3 . For example, the intensity of the strongest peak 004 approaches those of peaks 104, 200, and 111 for the bulk, but the intensity of the most intensive peak 004 is obviously larger than that of other peaks for the GaONWs. A general morphology of the products as shown in Fig. 2a indicates that the nanowires, having diameters of 60 nm, have lengths of hundreds of micrometers and that slice-like crystallites are on the ends of the nanowires. Fig. 2b shows a selected area electronic diffraction ŽSAED. pattern of the crystalline GaONWs along the w011x direction. The result of the SAED is consistent with that of the XRD. Weak spots in Fig. 2b result from weak electron diffraction rather than the existence of superlattices. As shown in Fig. 3, spectrum Ža. indicates that GaONWs can emit stable and high brightness blue light at room temperature upon excitation at 378 nm Ž3.28 eV., and it peaks at about 446 nm Ž2.78 eV. in the blue range, approaching the PL peak position Ž2.85 eV. of b-Ga 2 O 3 single crystal w17x.
Fig. 1. X-ray diffraction pattern of the GaONWs.
X.C. Wu et al.r Chemical Physics Letters 328 (2000) 5–9
7
of an electron on a donor formed by oxygen vacancies and a hole on an acceptor formed by gallium vacancies w15x. Vasil’tsiv et al. once proposed that the acceptor be formed by a gallium–oxygen vacancy pair Ž VO ,VGa .X w18x. Through investigation into the temperature dependence of the blue emission upon specific excitation of the acceptor defects, Binet and Gourier agreed with the above hypothesis and put forward a PL model of the gallium oxide crystal w17x. After excitation of the acceptor, a hole on the acceptor and an electron on the donor are created according to Eq. ŽEq. Ž1..: X
Ž VO ,VGa . q VOØq hn
Fig. 2. Ža. TEM image of the GaONWs. Žb. SAED pattern of the GaONWs along w011x direction.
In fact, the luminescence can be excited at 266 nm Ž4.6 eV. or 378 nm Ž3.28 eV.. In addition to the blue emission at 448 nm Ž2.77 eV., the ultraviolet ŽUV. emission at 330 nm Ž3.76 eV. can also be observed under excitation at 266 nm, but both the PL intensities are weak as shown in Fig. 3b. Therefore the optimal excitation wavelength is 378 nm, which is longer than that Ž266 nm. of the blue emission of b-Ga 2 O 3 single crystal. The Stokes shift is only 0.5 eV in the GaONWs under the excitation at 3.28 eV, which is smaller than that Ž1.7 eV. of the b-Ga 2 O 3 single crystal. It indicates the character of the delocalized luminescence of the GaONWs. The phenomenon may be attributed to quantum size effects of the nanowires. As the dimension decreases, the donor band may be split to form polyenergetic levels and produce double excitation wavelengths according to a selective transition law. However, the remains for further investigation. In point of PL mechanism of Ga 2 O 3 , Harwig and Kellendouk once suggested that it originates from the recombination
™ Ž V ,V O
Ga
5 . q VO5
Ž 1.
and then an electron on donor VO= is captured by a hole on acceptor Ž VO ,VGa .= to form a trapped exciton, which recombines radiatively to emit a blue photon. With increasing temperature, the electrons on the donors can be detrapped to the conduction band, and the holes on acceptors can be detrapped to form hole acceptors via the valence band. The holes and electrons recombine via a self-trapped exciton to emit a UV photon. The GaONWs are prepared under reducing condition and at high temperature, and VOØ Žoxygen vacancies. and Ž VO ,VGa .X can also easily be produced, so their PL mechanism is similar to that of the gallium oxide crystal such as the emission of the GaONWs under excitation at 266 nm. Because excitation energies at 378 nm are lower than UV radiative energies, only blue emission emerges. The growth mechanism of the nanowire can be explained in terms of the vapor–solid ŽVS. mechanisms, since no droplets are observed on their ends of the nanowires. The chemical reaction may be expressed as follows: 2C Ž solid . q Ga 2 O 3 Ž solid . s Ga 2 O Ž vapor . q 2CO Ž vapor . ,
Ž 2.
Ga 2 O 3 Ž solid . q 3C Ž solid . s 2Ga Ž vapor . q 3CO Ž vapor . ,
Ž 3.
2Ga 2 O Ž vapor . q 3O 2 Ž gas . s 2Ga 2 O 3 Ž solid . ,
Ž 4.
4Ga Ž vapor . q 3O 2 Ž gas . s 2Ga 2 O 3 Ž solid . .
Ž 5.
8
X.C. Wu et al.r Chemical Physics Letters 328 (2000) 5–9
Fig. 3. Luminescence spectrum of the GaONWs under excitation at 378 and 266 nm, respectively, indicated as Ža. and Žb.; excitation spectrum of the blue emission at 446 nm. All spectra were recorded at room temperature.
The growth of the nanowires could be divided into two steps. The first step is that Ga 2 O 3 reduced by graphite at high temperature forms vapor of Ga 2 O and Ga through reactions Ž2. and Ž3.. The second step is that the vapor deposits on the alumina ceramic plate to be aggregated into nuclei. The nuclei become the center of the nanowire growth. Ga Žvapor. and Ga 2 O 3 Žvapor. are continuously deposited on the nuclei to grow in one-dimensional direction, and oxidized into b-Ga 2 O 3 by reactions Ž4. and Ž5..
toelectronic nanodevices due to the semiconducting and PL characteristics of the GaONWs.
4. Conclusions
References
b-Phase GaONWs have been successfully synthesized in large scale using a carbothermal reduction approach at 9808C in a flowing nitrogen atmosphere. They may have a potential application in nanoscale electronic transportation and in one-dimensional op-
Acknowledgements This work was supported by the National Center for R & D on Superconductivity under Contract No. 863-CD010105, National Science Foundation under Contract NSF 59872043, the Fundamental Science Bureau, Academia Sinica.
w1x N. Hamada, S. Sawada, A. Oshiyama, Phys. Rev. Lett. 68 Ž1992. 1579. w2x M. Bockrath, D.H. Cobden, P.L. Mceuen, N.G. Chopra, A. Zettl, A. Thess, R.E. Smally, Science 275 Ž1997. 1922. w3x K.E. Gonsalves, G. Carlson, S.P. Rangarajan, M. Benaissa, M. Jose-Yacaman, ´ J. Mater. Chem. 6 Ž1996. 1451.
X.C. Wu et al.r Chemical Physics Letters 328 (2000) 5–9 w4x K. Bubke, H. Gnewuch, M. Hempstead, J. Hammer, M.L.H. Green, Appl. Phys. Lett. 71 Ž1997. 1906. w5x A. Heilmann, P. Jutzi, A. Klipp, U. Kreibig, R. Neuendorf, T. Sawitowski, G. Schmid, Adv. Mater. 10 Ž1998. 398. w6x T.M. Whitney, J.S. Jiang, P.C. Searson, C.L. Chien, Science 261 Ž1993. 1316. w7x A.G. Rinzler, J.H. Hafner, P. Nikolaev, L. Lou, S.G. Kim, D. Tomanek, P. Nordlander, D.T. Colbert, R.E. Smalley, Sci´ ence 268 Ž1995. 1550. w8x K. Suenaga, C. Colliex, N. Demoncy, A. Loiseau, H. Pascard, F. Willaime, Science 278 Ž1997. 653. w9x K.E. Gonsalves, G. Carlson, S.P. Rangarajan, M. Benaissa, M. Jose-Yacaman, J. Mater. Chem. 6 Ž1996. 1451. w10x K. Hiruma, M. Yazawa, T. Katsuyama, K. Okawa, K. Haraguchi, M. Kogucchi, H. Kakibayashi, J. Appl. Phys. 77 Ž1995. 447.
9
w11x H.H. Tippins, Phys. Rev. 140 Ž1965. A316. w12x M.R. Lorenz, J.F. Woods, R.J. Gambino, J. Phys. Chem. Solids 28 Ž1967. 403. w13x T. Harwig, J. Schoonman, J. Solid State Chem. 23 Ž1978. 205. w14x W.C. Herbert, H.B. Minnier, J.J. Brown Jr., J. Electrochem. Soc. 116 Ž1969. 1019. w15x T. Harwig, F. Kellendonk, J. Solid State Chem. 24 Ž1978. 255. w16x H.Z. Zhang, Y.C. Kong, Y.Z. Wang, X. Du, Z.G. Bai, J.J. Wang, D.P. Yu, Y. Ding, Q.L. Hang, S.Q. Feng, Solid State Comm. 109 Ž1999. 677. w17x L. Binet, D. Gourier, J. Phys. Chem. Solids 59 Ž1998. 1241. w18x V.I. Vasil’ tsiv, Ya.M. Zakharko, Ya.I. Prim, Ukr. Fiz. Zh. 33 Ž1988. 1320.
Chemical Physics Letters 328 Ž2000. 5–9 www.elsevier.nlrlocatercplett
Crystalline gallium oxide nanowires: intensive blue light emitters X.C. Wu ) , W.H. Song, W.D. Huang, M.H. Pu, B. Zhao, Y.P. Sun, J.J. Du Laboratory of Internal Friction and Defects in Solid, Institute of Solid State Physics, Academia Sinica, Hefei 230031, PR China Received 17 May 2000; in final form 4 August 2000
Abstract Gallium oxide nanowires ŽGaONWs; diameter, ca. 60 nm; length, hundreds of micrometers. have been synthesized by a carbothermal reduction reaction. The nanowires have been confirmed as crystalline b-Ga 2 O 3 by powder X-ray diffraction and selected area electronic diffraction. The GaONWs can emit stable and high brightness blue light at 446 nm Ž2.78 eV. under excitation at 378 nm Ž3.28 eV., which may have potential applications in one-dimensional optoelectronic nanodevices. q 2000 Published by Elsevier Science B.V.
1. Introduction Nanostructured materials possess unique electronic w1,2x, optical w3–5x and magnetic properties w6x compared with those in traditional bulk materials due to their quantum size effects. Their nanoscale dimensions may allow novel structures that could serve as potential building blocks for field-emission electron sources w7x, electronic w8x and optoelectronic devices w9x. For instance, GaAs and InAs nanowires have found applications in developing one-dimensional high-speed field effect transistors, or laser working at low-threshold current density and high gain w10x. With the development of mesoscopic science and integrated optical technology, it is important to synthesize optical nanowires that can meet the demands for further applications. Gallium oxide, b-Ga 2 O 3 , is a wide band gap Ž Eg s 4.9 eV. w11x compound which has long been known to exhibit both conduction )
Corresponding author. Current address: Institute of Solid State Physics, Academia Sinica, P.O. Box 1129, Heifei 230031, PR China. Fax: q86-551-5591434; e-mail: [email protected]
w12,13x and luminescence properties w14,15x. Therefore, the GaONWs may have potential applications in one-dimensional optoelectronic nanodevices. The fabrication and structure of crystalline Ga 2 O 3 nanowires were once reported, but the nanowires were synthesized by physical evaporation, and the photoluminescence ŽPL. was not dealt with w16x. In this Letter, we report the carbothermal reduction synthesis, characterization and PL properties of the GaONWs. The growth process and PL mechanism of the GaONWs have been discussed.
2. Experimental The gallium oxide powders were mixed with graphite according to the weight ratio of 1:1.5 and ground for 1 h. The mixtures were put in an alumina boat, and then the boat was covered with ceramic plates, placed in the center of the tube furnace, and remained at 9808C for 2 h in flowing nitrogen atmosphere Ž20 mlrmin.. Wool-like products depositing on the inner wall of the alumina boat and ceramic
0009-2614r00r$ - see front matter q 2000 Published by Elsevier Science B.V. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 8 8 9 - 7
6
X.C. Wu et al.r Chemical Physics Letters 328 (2000) 5–9
plates were collected for characterization and measurement. X-ray powder diffraction patterns of the products were obtained with Philips PW 1700 X-ray diffractometer with CuK a radiation. Transmission electron microscopy ŽTEM. images of the products were taken with a JEM-200CX transmission electron microscope. Photoluminescence ŽPL. spectra were measured in a Hitachi 850 fluorescence spectrophotometer with a Xe lamp at room temperature. The excitation wavelengths were 378 and 266 nm, and the corresponding filter wavelengths were 430 and 310 nm.
3. Results and discussion The X-ray powder diffraction pattern as shown in Fig. 1 can be indexed in peak position to b-Ga 2 O 3 ŽJCPDS card: No. 11-370., although the relative intensity of the peaks is not consistent with that of
bulk Ga 2 O 3 . For example, the intensity of the strongest peak 004 approaches those of peaks 104, 200, and 111 for the bulk, but the intensity of the most intensive peak 004 is obviously larger than that of other peaks for the GaONWs. A general morphology of the products as shown in Fig. 2a indicates that the nanowires, having diameters of 60 nm, have lengths of hundreds of micrometers and that slice-like crystallites are on the ends of the nanowires. Fig. 2b shows a selected area electronic diffraction ŽSAED. pattern of the crystalline GaONWs along the w011x direction. The result of the SAED is consistent with that of the XRD. Weak spots in Fig. 2b result from weak electron diffraction rather than the existence of superlattices. As shown in Fig. 3, spectrum Ža. indicates that GaONWs can emit stable and high brightness blue light at room temperature upon excitation at 378 nm Ž3.28 eV., and it peaks at about 446 nm Ž2.78 eV. in the blue range, approaching the PL peak position Ž2.85 eV. of b-Ga 2 O 3 single crystal w17x.
Fig. 1. X-ray diffraction pattern of the GaONWs.
X.C. Wu et al.r Chemical Physics Letters 328 (2000) 5–9
7
of an electron on a donor formed by oxygen vacancies and a hole on an acceptor formed by gallium vacancies w15x. Vasil’tsiv et al. once proposed that the acceptor be formed by a gallium–oxygen vacancy pair Ž VO ,VGa .X w18x. Through investigation into the temperature dependence of the blue emission upon specific excitation of the acceptor defects, Binet and Gourier agreed with the above hypothesis and put forward a PL model of the gallium oxide crystal w17x. After excitation of the acceptor, a hole on the acceptor and an electron on the donor are created according to Eq. ŽEq. Ž1..: X
Ž VO ,VGa . q VOØq hn
Fig. 2. Ža. TEM image of the GaONWs. Žb. SAED pattern of the GaONWs along w011x direction.
In fact, the luminescence can be excited at 266 nm Ž4.6 eV. or 378 nm Ž3.28 eV.. In addition to the blue emission at 448 nm Ž2.77 eV., the ultraviolet ŽUV. emission at 330 nm Ž3.76 eV. can also be observed under excitation at 266 nm, but both the PL intensities are weak as shown in Fig. 3b. Therefore the optimal excitation wavelength is 378 nm, which is longer than that Ž266 nm. of the blue emission of b-Ga 2 O 3 single crystal. The Stokes shift is only 0.5 eV in the GaONWs under the excitation at 3.28 eV, which is smaller than that Ž1.7 eV. of the b-Ga 2 O 3 single crystal. It indicates the character of the delocalized luminescence of the GaONWs. The phenomenon may be attributed to quantum size effects of the nanowires. As the dimension decreases, the donor band may be split to form polyenergetic levels and produce double excitation wavelengths according to a selective transition law. However, the remains for further investigation. In point of PL mechanism of Ga 2 O 3 , Harwig and Kellendouk once suggested that it originates from the recombination
™ Ž V ,V O
Ga
5 . q VO5
Ž 1.
and then an electron on donor VO= is captured by a hole on acceptor Ž VO ,VGa .= to form a trapped exciton, which recombines radiatively to emit a blue photon. With increasing temperature, the electrons on the donors can be detrapped to the conduction band, and the holes on acceptors can be detrapped to form hole acceptors via the valence band. The holes and electrons recombine via a self-trapped exciton to emit a UV photon. The GaONWs are prepared under reducing condition and at high temperature, and VOØ Žoxygen vacancies. and Ž VO ,VGa .X can also easily be produced, so their PL mechanism is similar to that of the gallium oxide crystal such as the emission of the GaONWs under excitation at 266 nm. Because excitation energies at 378 nm are lower than UV radiative energies, only blue emission emerges. The growth mechanism of the nanowire can be explained in terms of the vapor–solid ŽVS. mechanisms, since no droplets are observed on their ends of the nanowires. The chemical reaction may be expressed as follows: 2C Ž solid . q Ga 2 O 3 Ž solid . s Ga 2 O Ž vapor . q 2CO Ž vapor . ,
Ž 2.
Ga 2 O 3 Ž solid . q 3C Ž solid . s 2Ga Ž vapor . q 3CO Ž vapor . ,
Ž 3.
2Ga 2 O Ž vapor . q 3O 2 Ž gas . s 2Ga 2 O 3 Ž solid . ,
Ž 4.
4Ga Ž vapor . q 3O 2 Ž gas . s 2Ga 2 O 3 Ž solid . .
Ž 5.
8
X.C. Wu et al.r Chemical Physics Letters 328 (2000) 5–9
Fig. 3. Luminescence spectrum of the GaONWs under excitation at 378 and 266 nm, respectively, indicated as Ža. and Žb.; excitation spectrum of the blue emission at 446 nm. All spectra were recorded at room temperature.
The growth of the nanowires could be divided into two steps. The first step is that Ga 2 O 3 reduced by graphite at high temperature forms vapor of Ga 2 O and Ga through reactions Ž2. and Ž3.. The second step is that the vapor deposits on the alumina ceramic plate to be aggregated into nuclei. The nuclei become the center of the nanowire growth. Ga Žvapor. and Ga 2 O 3 Žvapor. are continuously deposited on the nuclei to grow in one-dimensional direction, and oxidized into b-Ga 2 O 3 by reactions Ž4. and Ž5..
toelectronic nanodevices due to the semiconducting and PL characteristics of the GaONWs.
4. Conclusions
References
b-Phase GaONWs have been successfully synthesized in large scale using a carbothermal reduction approach at 9808C in a flowing nitrogen atmosphere. They may have a potential application in nanoscale electronic transportation and in one-dimensional op-
Acknowledgements This work was supported by the National Center for R & D on Superconductivity under Contract No. 863-CD010105, National Science Foundation under Contract NSF 59872043, the Fundamental Science Bureau, Academia Sinica.
w1x N. Hamada, S. Sawada, A. Oshiyama, Phys. Rev. Lett. 68 Ž1992. 1579. w2x M. Bockrath, D.H. Cobden, P.L. Mceuen, N.G. Chopra, A. Zettl, A. Thess, R.E. Smally, Science 275 Ž1997. 1922. w3x K.E. Gonsalves, G. Carlson, S.P. Rangarajan, M. Benaissa, M. Jose-Yacaman, ´ J. Mater. Chem. 6 Ž1996. 1451.
X.C. Wu et al.r Chemical Physics Letters 328 (2000) 5–9 w4x K. Bubke, H. Gnewuch, M. Hempstead, J. Hammer, M.L.H. Green, Appl. Phys. Lett. 71 Ž1997. 1906. w5x A. Heilmann, P. Jutzi, A. Klipp, U. Kreibig, R. Neuendorf, T. Sawitowski, G. Schmid, Adv. Mater. 10 Ž1998. 398. w6x T.M. Whitney, J.S. Jiang, P.C. Searson, C.L. Chien, Science 261 Ž1993. 1316. w7x A.G. Rinzler, J.H. Hafner, P. Nikolaev, L. Lou, S.G. Kim, D. Tomanek, P. Nordlander, D.T. Colbert, R.E. Smalley, Sci´ ence 268 Ž1995. 1550. w8x K. Suenaga, C. Colliex, N. Demoncy, A. Loiseau, H. Pascard, F. Willaime, Science 278 Ž1997. 653. w9x K.E. Gonsalves, G. Carlson, S.P. Rangarajan, M. Benaissa, M. Jose-Yacaman, J. Mater. Chem. 6 Ž1996. 1451. w10x K. Hiruma, M. Yazawa, T. Katsuyama, K. Okawa, K. Haraguchi, M. Kogucchi, H. Kakibayashi, J. Appl. Phys. 77 Ž1995. 447.
9
w11x H.H. Tippins, Phys. Rev. 140 Ž1965. A316. w12x M.R. Lorenz, J.F. Woods, R.J. Gambino, J. Phys. Chem. Solids 28 Ž1967. 403. w13x T. Harwig, J. Schoonman, J. Solid State Chem. 23 Ž1978. 205. w14x W.C. Herbert, H.B. Minnier, J.J. Brown Jr., J. Electrochem. Soc. 116 Ž1969. 1019. w15x T. Harwig, F. Kellendonk, J. Solid State Chem. 24 Ž1978. 255. w16x H.Z. Zhang, Y.C. Kong, Y.Z. Wang, X. Du, Z.G. Bai, J.J. Wang, D.P. Yu, Y. Ding, Q.L. Hang, S.Q. Feng, Solid State Comm. 109 Ž1999. 677. w17x L. Binet, D. Gourier, J. Phys. Chem. Solids 59 Ž1998. 1241. w18x V.I. Vasil’ tsiv, Ya.M. Zakharko, Ya.I. Prim, Ukr. Fiz. Zh. 33 Ž1988. 1320.