- Email: [email protected]
CdS interface grown by rf magnetron sputtering
November 1998
Materials Letters 37 Ž1998. 281–284
S diffusion at the CdTerCdS interface grown by rf magnetron sputtering ) R. Castro-Rodrıguez , P. Bartolo Perez, D. Perez-Delgado, F. Caballero-Briones, ´ J.L. Pena ˜ Applied Physics Department, CINVESTAV-PN Merida, A.P. 73-Cordemex, CP 97310, Merida, Yucatan, ´ ´ Mexico Received 10 November 1997; revised 4 March 1998; accepted 11 May 1998
Abstract CdTe films were grown by radio-frequency magnetron sputtering Žrf-sputtering. on CdS substrates in the growth temperature range between 250 and 4008C. The stoichiometry of the CdTerCdS interface was observed by the Auger electron spectroscopy ŽAES., and Auger depth profiles demonstrate that the CdTerCdS interface was not abrupt. The mechanism of the interface diffusion as well as the parameters necessary for its description were determined. q 1998 Elsevier Science B.V. All rights reserved. PACS: 66.30.N; 68.35.F; 81.15.E; 81.05.E; 84.60.J Keywords: Solar cells; CdTerCdS; Films; Sputtering
1. Introduction CdTe-based polycrystalline solar cells are among the top contenders for terrestrial solar applications, and several companies are already involved in developing modules based on this material w1,2x. The most successful device structure for this material is a heterostructure with a CdS windows layer. In spite of the large lattice mismatch between CdTe and CdS Ž; 10%. w3x, different crystal structure Žcubic vs. hexagonal., and difference in the electron affinity, cells using CdTe prepared by a variety of low cost
)
Corresponding author. Fax: q52-99-81-29-17
technique w4x have shown efficiencies greater than 10% with the highest reported efficiency being 15.8% w5,6x. In view of the difficulty of forming a complete microscopic model for growth of CdTerCdS interface, it is interesting to examine first empirically how film growth proceeds. Understanding the properties of the CdTerCdS interface is crucial for improving CdTerCdS device performance. That is why investigation of the diffusion process for to obtain information about the mechanism of S transmission through CdTerCdS interface might be of interest. In this work we utilize Auger electron spectroscopy ŽAES. technique to study the mobility of S in CdTerCdS interface grown by radio-frequency sputtering Žrf-sputtering..
00167-577Xr98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X Ž 9 8 . 0 0 1 0 6 - 2
282
R. Castro-Rodrıguez et al.r Materials Letters 37 (1998) 281–284 ´
2. Experimental details
3. Experimental results and discussion
The substrates used were SnO 2 :F Žfluorine-doped tin oxide. coated borosilicate Ž7059. glass purchased from Solarex. A thin layer of CdS was deposited on the substrate by chemical bath deposition ŽCBD. using a modification of a process described in the literature w7–9x. Specifically, after thorough cleaning with 1% Liquinox soap and deionized ŽDI. water, the substrate were placed in a stirred and covered jacketed beaker at 898C with 550 ml DI water, 8 ml of 0.033 M cadmium acetate, 5.3 ml of 1 M ammonium acetate, 15 ml of 15 M ammonia, and 8 ml of 0.667 M thiourea. The thiourea was added in 4 aliquots of 2 ml, 10 min apart to minimize homogeneous growth ˚ in the solution. The resultant films were 1000 A thick, highly adherent, and had an index of refraction of 2.3. The CdTerCdS interface were prepared by using a commercial magnetron rf-sputtering system ŽCooke Vacuum Products, USA.. The home-made sputtering target was a 2-in. diameter pressed CdTe Ž99.999% purity.. High-purity Ar Ž99.999%. was introduced through a mass flow controller after the vacuum chamber was evacuated to about 2 = 10y6 Torr. The gas pressure was monitored with a precision ionization gauge and kept at 7.5 = 10y3 Torr during deposition. The rf power Ž13.56 MHz. was introduced through an rf power supply ŽRF Plasma Products, USA. with an automatic matching network which could be tuned for minimum reflected power. Before deposition, the target was presputtered to remove any contaminants and eliminate any differential sputtering effects. The presputtering time was 20 min and the deposition time of the CdTe film was 40 min. Films were deposited at substrate temperature of 250, 350 and 4008C, respectively. The composition of the films around the CdTerCdS interface was investigated by Auger electron spectroscopy ŽAES.. The AES analysis were performed in an system ESCArSAM Perkin-Elmer PHI-560 equipped with a double pass cylindrical mirror analyzer. The samples were chemically cleaning by immersion in methanol with 3% bromine for 1 min before this analysis. The atomic concentration were estimated analyzing a region of the films by an electron beam of 10 mm, and using sensitivity factor of SCd s 1, STe s 0.662 and SS s 0.8 w10,11x.
The results of Fig. 1a,b show that the films consisted of cadmium and tellurium at the 1.26, 1.1 and 0.9 mm depth, and of sulfur, cadmium, and tellurium at the 1.36, 1.2 and 1.0 mm for films deposited at substrate temperature of 250, 350 and 4008C, respectively. Fig. 2a–c show that the interface between the CdTe layer and CdS was not abrupt and alloys of sulfur and tellurium were formed at the CdTerCdS interface. This gradual interface due to interdiffusion represents reduced lattice mismatch and lower interface defect density, resulting in improved cell efficiency w12x. The thickness of the interfaces was about 0.09, 0.16 and 0.18 mm for films deposited at substrate temperature of 250, 350 and 4008C, respectively. The ratio of peak-to-peak intensities between the sulfur, cadmium and tellurium peaks of the films indicated that the interfa-
Fig. 1. AES data obtained from CdTerCdS interface grown at Ts s 2508C, Ts s 3508C and Ts s 4008C respectively. Ža. The curves obtained at the 1.26 mm, 1.1 mm and 0.9 mm depth, respectively. Žb. The curves obtained at the 1.36 mm, 1.2 mm and 1.0 mm depth, respectively.
R. Castro-Rodrıguez et al.r Materials Letters 37 (1998) 281–284 ´
283
and X j2 Ž t s constant. ; exp Ž yEarkT .
Ž 2.
where C0 is the concentration of diffusing atoms at the source surface ŽCdTerCdS interface., X j is the distance from the interface, D 1 is the coefficient of volume diffusion, C j is the concentration of the element at a distance from interface equal to X j and Ea is the activation energy of diffusion. The dependence of X j2 s f Ž1rT ., was determined on the basis of experimental Auger profiles for tgrown s 40 min, using the experimental S Auger profiles on the CdTerCdS interface. This allowed us to evaluate the coefficient of S volume diffusion into CdTe 2
D 1 s X j2 Ž erfc C jrC0 . r4 t
Fig. 2. Auger depth profiles of CdTe interface grown at substrate temperature of Ža. 2508C, Žb. 3508C and Žc. 4008C, respectively. The d 0 indicates the depth at t s 0.
Ž 3.
Žwhen Ts s 2508C, D 1 f 4.39 = 10y1 3 cm2 sy1 , for Ts s 3508C, D1 f 6.84 = 10y1 5 cm2 sy1 , and for Ts s 4008C, D 1 f 9.13 = 10y1 5 cm2 sy1 . and the activation energy of this process Ž Ea .. For the range of temperatures 250–4008C Ea had a value ; 0.142 eV. Knowing D 1 and Ea gives us the possibility of writing down the general equation of temperature
cial layer might be a CdS-rich ternary phase ŽCdS1y xTe x . as show in Fig. 1b. As one can see from the curves in Fig. 2a–c, the Cd and Te distribution profiles at the CdTerCdS interface practically does not chance during the formation of the CdTerCdS interface. This demonstrates that the component of S but not the components of CdTe, by penetration into the CdTe film promote the expansion of the CdTerCdS interface. For determination of the mechanism of penetration of S by diffusion into CdTe at the CdTerCdS interface we examined the profiles of the S distribution in CdTe film Žsee Fig. 2.. From Fig. 2a–c one can see that experimental Auger profiles look like typical diffusion profiles corresponding to classical diffusion correlation w13,14x C1 s C0 erfc X jr2 Ž D 1 t . X j Ž T s constant. ; t 1r2
1r2
Ž 1.
Fig. 3. Temperature dependence of the diffusion coefficient of interface expansion of CdTerCdS interface in slow diffusion for t s 40 min.
R. Castro-Rodrıguez et al.r Materials Letters 37 (1998) 281–284 ´
284
dependence of the effective coefficient of S volume diffusion at the CdTerCdS interface. When Ts s 250–4008C, this formula is D 1 s D 0 exp Ž yEarkT .
Ž 4.
fur diffusion at temperatures and coefficients of Ts s 2508C, D 1 f 4.39 = 10y1 3 cm2 sy1 , Ts s 3508C, D 1 f 6.84 = 10y1 5 cm2 sy1 , and Ts s 4008C, D1 f 9.13 = 10y1 5 cm2 sy1 , makes the dominant contribution to this process.
where D 0 ; 1.02 = 10y1 3 cm2 sy1 .
Ž 5.
as we can see in Fig. 3. The Ea value is approximated equal to the migration energy of Cd vacancies into CdTe Ž D MmŽ VS . s 155 meV.. This value of D Mm has been calculated by Khalal et al. w15x for several II–VI semiconductor multilayers. This suggest that in the case the S diffusion at the CdTerCdS interface is limited by VCd migration into the CdTe lattice. We do not observe in the diffusion profiles any behavior that corresponds to a diffusion along the grain boundaries ŽGB.. This is based on the following points: Ži.
Žii.
Atomic force microscopy data demonstrate that the grain structure does not change. The grain diameter and the grain size distribution are very similar in all samples. In the Auger profiles we did not noticed a display typical of the GB diffusion effect, such as sulfide accumulated at the grain surface Žsurface of CdTe..
4. Conclusions We can conclude that the CdTerCdS interfaces are not abrupt. A gradually changing hetero-interface structure decreases the lattice mismatch, mismatchinduced interface states and tunneling current, and optical loss due to the gradual change in index. AES measurements also indicated that the interfacial layers within the CdTerCdS interface could be CdS-rich ternary phase ŽCdS1y xTe x ., and the broadening of the CdTerCdS interface is caused by diffusion. Sul-
Acknowledgements The authors would like to thank Mr. Roberto Sanchez, Wilian Cauich, Oswaldo Gomez, Victor Rejon ´ and Mario Herrera for the technical support. This work was supported by CONACYT-SEP ŽMexico. under project number 2367P-E. References w1x A.A. Brikman, CdTe-based solar cells, in: Capper ŽEd.., Properties of narrow gap cadmium-based compounds, INSPEC, England, 1994. w2x S.P. Albright, B. Ackerman, J.F. Jordan, IEEE Transaction on Electron Devices 37 Ž1990. 434. w3x A. Fischer, Z. Feng, E. Bykov, G. Contreras-Puentes, A. Compaan, F. de Landa Castillo-Alvarado, J. Avedano, ˜ A. Mason, Appl. Phys. Lett. 70 Ž24. Ž1997. 3239. w4x T.L. Chu, S.S. Chu, Prog. Photovolt. Rest. Appl. 1 Ž1993. 31. w5x T.L. Chu, S.S. Chu, J. Britt, C. Ferekides, Q.C. Wu, J. Appl. Phys. 70 Ž1991. 2688. w6x J. Britt, C. Ferekides, Appl. Phys. Lett. 62 Ž22. Ž1993. 2851. w7x T. Chu, S. Chu, Final letter report to the National Renewable Energy Laboratory, EAT-3-13159-01-104149, Oct. 1993. w8x M. Hsu, R. Jih, P. Lin, H. Ueng, Y. Hsu, H. Hwang, J. Appl. Phys. 59 Ž1986. 6307. w9x Y.S. Tyan, Solar Cells 23 Ž1988. 19. w10x M. Zapata Torres, Physics Doctoral Thesis 1995, Department of Applied Physics, Cinvestav IPN-Merida. ´ w11x L.E. Davis, N.C. MacDonald, P.W. Palmberg, G.E. Riach, R.E. Weber, Handbook of Auger Electron Spectroscopy, Perkin-Elmer, Eden Prairie, 1978. w12x Z.C. Feng, H.C. Chou, A. Rohatgi, G.K. Lim, A.T.S. Wee, K.L. Tan, J. Appl. Phys. 79 Ž4. Ž1996. 2152. w13x J.P. Stark, Diffusion in Solid State, Energia, Moscow, 1980. w14x J.C. Fisher, J. Appl. Phys. 22 Ž1951. 74. w15x K. Khalal, A.C. Chami, E. Ligeon, J. Fontanille, A. Hamoundi, G. Berard, J. Cibert, J. Appl. Phys. 76 Ž6. Ž1995. 3706.
Materials Letters 37 Ž1998. 281–284
S diffusion at the CdTerCdS interface grown by rf magnetron sputtering ) R. Castro-Rodrıguez , P. Bartolo Perez, D. Perez-Delgado, F. Caballero-Briones, ´ J.L. Pena ˜ Applied Physics Department, CINVESTAV-PN Merida, A.P. 73-Cordemex, CP 97310, Merida, Yucatan, ´ ´ Mexico Received 10 November 1997; revised 4 March 1998; accepted 11 May 1998
Abstract CdTe films were grown by radio-frequency magnetron sputtering Žrf-sputtering. on CdS substrates in the growth temperature range between 250 and 4008C. The stoichiometry of the CdTerCdS interface was observed by the Auger electron spectroscopy ŽAES., and Auger depth profiles demonstrate that the CdTerCdS interface was not abrupt. The mechanism of the interface diffusion as well as the parameters necessary for its description were determined. q 1998 Elsevier Science B.V. All rights reserved. PACS: 66.30.N; 68.35.F; 81.15.E; 81.05.E; 84.60.J Keywords: Solar cells; CdTerCdS; Films; Sputtering
1. Introduction CdTe-based polycrystalline solar cells are among the top contenders for terrestrial solar applications, and several companies are already involved in developing modules based on this material w1,2x. The most successful device structure for this material is a heterostructure with a CdS windows layer. In spite of the large lattice mismatch between CdTe and CdS Ž; 10%. w3x, different crystal structure Žcubic vs. hexagonal., and difference in the electron affinity, cells using CdTe prepared by a variety of low cost
)
Corresponding author. Fax: q52-99-81-29-17
technique w4x have shown efficiencies greater than 10% with the highest reported efficiency being 15.8% w5,6x. In view of the difficulty of forming a complete microscopic model for growth of CdTerCdS interface, it is interesting to examine first empirically how film growth proceeds. Understanding the properties of the CdTerCdS interface is crucial for improving CdTerCdS device performance. That is why investigation of the diffusion process for to obtain information about the mechanism of S transmission through CdTerCdS interface might be of interest. In this work we utilize Auger electron spectroscopy ŽAES. technique to study the mobility of S in CdTerCdS interface grown by radio-frequency sputtering Žrf-sputtering..
00167-577Xr98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X Ž 9 8 . 0 0 1 0 6 - 2
282
R. Castro-Rodrıguez et al.r Materials Letters 37 (1998) 281–284 ´
2. Experimental details
3. Experimental results and discussion
The substrates used were SnO 2 :F Žfluorine-doped tin oxide. coated borosilicate Ž7059. glass purchased from Solarex. A thin layer of CdS was deposited on the substrate by chemical bath deposition ŽCBD. using a modification of a process described in the literature w7–9x. Specifically, after thorough cleaning with 1% Liquinox soap and deionized ŽDI. water, the substrate were placed in a stirred and covered jacketed beaker at 898C with 550 ml DI water, 8 ml of 0.033 M cadmium acetate, 5.3 ml of 1 M ammonium acetate, 15 ml of 15 M ammonia, and 8 ml of 0.667 M thiourea. The thiourea was added in 4 aliquots of 2 ml, 10 min apart to minimize homogeneous growth ˚ in the solution. The resultant films were 1000 A thick, highly adherent, and had an index of refraction of 2.3. The CdTerCdS interface were prepared by using a commercial magnetron rf-sputtering system ŽCooke Vacuum Products, USA.. The home-made sputtering target was a 2-in. diameter pressed CdTe Ž99.999% purity.. High-purity Ar Ž99.999%. was introduced through a mass flow controller after the vacuum chamber was evacuated to about 2 = 10y6 Torr. The gas pressure was monitored with a precision ionization gauge and kept at 7.5 = 10y3 Torr during deposition. The rf power Ž13.56 MHz. was introduced through an rf power supply ŽRF Plasma Products, USA. with an automatic matching network which could be tuned for minimum reflected power. Before deposition, the target was presputtered to remove any contaminants and eliminate any differential sputtering effects. The presputtering time was 20 min and the deposition time of the CdTe film was 40 min. Films were deposited at substrate temperature of 250, 350 and 4008C, respectively. The composition of the films around the CdTerCdS interface was investigated by Auger electron spectroscopy ŽAES.. The AES analysis were performed in an system ESCArSAM Perkin-Elmer PHI-560 equipped with a double pass cylindrical mirror analyzer. The samples were chemically cleaning by immersion in methanol with 3% bromine for 1 min before this analysis. The atomic concentration were estimated analyzing a region of the films by an electron beam of 10 mm, and using sensitivity factor of SCd s 1, STe s 0.662 and SS s 0.8 w10,11x.
The results of Fig. 1a,b show that the films consisted of cadmium and tellurium at the 1.26, 1.1 and 0.9 mm depth, and of sulfur, cadmium, and tellurium at the 1.36, 1.2 and 1.0 mm for films deposited at substrate temperature of 250, 350 and 4008C, respectively. Fig. 2a–c show that the interface between the CdTe layer and CdS was not abrupt and alloys of sulfur and tellurium were formed at the CdTerCdS interface. This gradual interface due to interdiffusion represents reduced lattice mismatch and lower interface defect density, resulting in improved cell efficiency w12x. The thickness of the interfaces was about 0.09, 0.16 and 0.18 mm for films deposited at substrate temperature of 250, 350 and 4008C, respectively. The ratio of peak-to-peak intensities between the sulfur, cadmium and tellurium peaks of the films indicated that the interfa-
Fig. 1. AES data obtained from CdTerCdS interface grown at Ts s 2508C, Ts s 3508C and Ts s 4008C respectively. Ža. The curves obtained at the 1.26 mm, 1.1 mm and 0.9 mm depth, respectively. Žb. The curves obtained at the 1.36 mm, 1.2 mm and 1.0 mm depth, respectively.
R. Castro-Rodrıguez et al.r Materials Letters 37 (1998) 281–284 ´
283
and X j2 Ž t s constant. ; exp Ž yEarkT .
Ž 2.
where C0 is the concentration of diffusing atoms at the source surface ŽCdTerCdS interface., X j is the distance from the interface, D 1 is the coefficient of volume diffusion, C j is the concentration of the element at a distance from interface equal to X j and Ea is the activation energy of diffusion. The dependence of X j2 s f Ž1rT ., was determined on the basis of experimental Auger profiles for tgrown s 40 min, using the experimental S Auger profiles on the CdTerCdS interface. This allowed us to evaluate the coefficient of S volume diffusion into CdTe 2
D 1 s X j2 Ž erfc C jrC0 . r4 t
Fig. 2. Auger depth profiles of CdTe interface grown at substrate temperature of Ža. 2508C, Žb. 3508C and Žc. 4008C, respectively. The d 0 indicates the depth at t s 0.
Ž 3.
Žwhen Ts s 2508C, D 1 f 4.39 = 10y1 3 cm2 sy1 , for Ts s 3508C, D1 f 6.84 = 10y1 5 cm2 sy1 , and for Ts s 4008C, D 1 f 9.13 = 10y1 5 cm2 sy1 . and the activation energy of this process Ž Ea .. For the range of temperatures 250–4008C Ea had a value ; 0.142 eV. Knowing D 1 and Ea gives us the possibility of writing down the general equation of temperature
cial layer might be a CdS-rich ternary phase ŽCdS1y xTe x . as show in Fig. 1b. As one can see from the curves in Fig. 2a–c, the Cd and Te distribution profiles at the CdTerCdS interface practically does not chance during the formation of the CdTerCdS interface. This demonstrates that the component of S but not the components of CdTe, by penetration into the CdTe film promote the expansion of the CdTerCdS interface. For determination of the mechanism of penetration of S by diffusion into CdTe at the CdTerCdS interface we examined the profiles of the S distribution in CdTe film Žsee Fig. 2.. From Fig. 2a–c one can see that experimental Auger profiles look like typical diffusion profiles corresponding to classical diffusion correlation w13,14x C1 s C0 erfc X jr2 Ž D 1 t . X j Ž T s constant. ; t 1r2
1r2
Ž 1.
Fig. 3. Temperature dependence of the diffusion coefficient of interface expansion of CdTerCdS interface in slow diffusion for t s 40 min.
R. Castro-Rodrıguez et al.r Materials Letters 37 (1998) 281–284 ´
284
dependence of the effective coefficient of S volume diffusion at the CdTerCdS interface. When Ts s 250–4008C, this formula is D 1 s D 0 exp Ž yEarkT .
Ž 4.
fur diffusion at temperatures and coefficients of Ts s 2508C, D 1 f 4.39 = 10y1 3 cm2 sy1 , Ts s 3508C, D 1 f 6.84 = 10y1 5 cm2 sy1 , and Ts s 4008C, D1 f 9.13 = 10y1 5 cm2 sy1 , makes the dominant contribution to this process.
where D 0 ; 1.02 = 10y1 3 cm2 sy1 .
Ž 5.
as we can see in Fig. 3. The Ea value is approximated equal to the migration energy of Cd vacancies into CdTe Ž D MmŽ VS . s 155 meV.. This value of D Mm has been calculated by Khalal et al. w15x for several II–VI semiconductor multilayers. This suggest that in the case the S diffusion at the CdTerCdS interface is limited by VCd migration into the CdTe lattice. We do not observe in the diffusion profiles any behavior that corresponds to a diffusion along the grain boundaries ŽGB.. This is based on the following points: Ži.
Žii.
Atomic force microscopy data demonstrate that the grain structure does not change. The grain diameter and the grain size distribution are very similar in all samples. In the Auger profiles we did not noticed a display typical of the GB diffusion effect, such as sulfide accumulated at the grain surface Žsurface of CdTe..
4. Conclusions We can conclude that the CdTerCdS interfaces are not abrupt. A gradually changing hetero-interface structure decreases the lattice mismatch, mismatchinduced interface states and tunneling current, and optical loss due to the gradual change in index. AES measurements also indicated that the interfacial layers within the CdTerCdS interface could be CdS-rich ternary phase ŽCdS1y xTe x ., and the broadening of the CdTerCdS interface is caused by diffusion. Sul-
Acknowledgements The authors would like to thank Mr. Roberto Sanchez, Wilian Cauich, Oswaldo Gomez, Victor Rejon ´ and Mario Herrera for the technical support. This work was supported by CONACYT-SEP ŽMexico. under project number 2367P-E. References w1x A.A. Brikman, CdTe-based solar cells, in: Capper ŽEd.., Properties of narrow gap cadmium-based compounds, INSPEC, England, 1994. w2x S.P. Albright, B. Ackerman, J.F. Jordan, IEEE Transaction on Electron Devices 37 Ž1990. 434. w3x A. Fischer, Z. Feng, E. Bykov, G. Contreras-Puentes, A. Compaan, F. de Landa Castillo-Alvarado, J. Avedano, ˜ A. Mason, Appl. Phys. Lett. 70 Ž24. Ž1997. 3239. w4x T.L. Chu, S.S. Chu, Prog. Photovolt. Rest. Appl. 1 Ž1993. 31. w5x T.L. Chu, S.S. Chu, J. Britt, C. Ferekides, Q.C. Wu, J. Appl. Phys. 70 Ž1991. 2688. w6x J. Britt, C. Ferekides, Appl. Phys. Lett. 62 Ž22. Ž1993. 2851. w7x T. Chu, S. Chu, Final letter report to the National Renewable Energy Laboratory, EAT-3-13159-01-104149, Oct. 1993. w8x M. Hsu, R. Jih, P. Lin, H. Ueng, Y. Hsu, H. Hwang, J. Appl. Phys. 59 Ž1986. 6307. w9x Y.S. Tyan, Solar Cells 23 Ž1988. 19. w10x M. Zapata Torres, Physics Doctoral Thesis 1995, Department of Applied Physics, Cinvestav IPN-Merida. ´ w11x L.E. Davis, N.C. MacDonald, P.W. Palmberg, G.E. Riach, R.E. Weber, Handbook of Auger Electron Spectroscopy, Perkin-Elmer, Eden Prairie, 1978. w12x Z.C. Feng, H.C. Chou, A. Rohatgi, G.K. Lim, A.T.S. Wee, K.L. Tan, J. Appl. Phys. 79 Ž4. Ž1996. 2152. w13x J.P. Stark, Diffusion in Solid State, Energia, Moscow, 1980. w14x J.C. Fisher, J. Appl. Phys. 22 Ž1951. 74. w15x K. Khalal, A.C. Chami, E. Ligeon, J. Fontanille, A. Hamoundi, G. Berard, J. Cibert, J. Appl. Phys. 76 Ž6. Ž1995. 3706.