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Structural characterization of a-SiC:H by thermal desorption spectroscopy
Applied Surface Science 70/71 (1993) 768-771 North-Holland
applied surface s c i e n c e
Structural characterization of a-SiC" H by thermal desorption spectroscopy F. M a a s s
1 j.
B e r t o m e u , J.M. Asensi, J. P u i g d o l l e r s , J. A n d r e u , J.C. D e l g a d o a n d J. E s t e v e
Universitat de Barcelona, Departament de F{sica Aplicada i Electrbnica, Av. Diagonal 647, E-08028 Barcelona, Spain
Received 24 August 1992; accepted for publication 11 October 1992
The structure of a-Si1 xCx : H thin films prepared from different mixtures of S i l l 4 a n d CH 4 was studied by thermal desorption spectroscopy. The influence of the gas phase composition and the thickness on the hydrogen evolution spectra is presented and discussed. A third hydrogen evolution was observed in a-Sil_xCx films with higher carbon content. The results show that the surface controlled desorption processes become dominant when increasing the carbon content.
1. Introduction Considerable effort to understand the structural characteristics of hydrogenated amorphous silicon (a-Si:H) has been undertaken in the last few years. The complete understanding of its structural characteristics and its relationship with its interesting optoelectronic properties is still an open question. In addition, the research on hydrogenated amorphous silicon has led to a family of related alloys. Hydrogenated amorphous silic o n - c a r b o n (a-Si l_xCx : H) is one of these alloys, with important practical applications as p-layer in p - i - n solar cells [1], active i-layer in tandem solar cells [2] and electroluminescent devices [3]. This material has been prepared by different techniques, but the best properties for optoelectronic applications have been obtained in R F glow discharge films. But a - S i l _ x C x : H alloys present a wide range of structures and stoichiometries, depending on the preparation conditions, that hinders the exploration of the technological preparation conditions. In the present paper, we report an extensive thermal desorption spectroscopy (TDS) study of Permanent address: Universidad de Antofagasta, Departamento de Fisica, Av. Angamos 601, Antofagasta, Chile.
samples grown with a conventional plasma-CVD radiofrequency reactor in a low power regime and for a wide range of gas phase compositions. New features of the TDS spectra are put in evidence for the samples with higher carbon content.
2. Experimental The samples were obtained by R F (13.56 MHz) glow discharge decomposition of pure silane and methane in a reactor described elsewhere [4]. The use of a rotating substrate holder enables us to deposit under exactly the same conditions four samples with different thicknesses. The films were deposited onto crystalline silicon polished on both faces. The RF power, the substrate temperature, the pressure and the total flow rate were kept at 5 W, 300°C, 30 Pa and 20 sccm. These conditions gave a device quality a - S i : H in our reactor, with a low density of defects and good properties [5]. The methane ratio in the gas phase (Y) was varied from 0 to 0.95. For Y = 0.5 and 0.95, four different thicknesses were deposited. Composition of the samples was estimated from XPS measurements (table 1). The TDS system consists of a quartz tube, a quadrupolar mass spectrometer (Dataquad, Spec-
0169-4332/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
769
F. Maass et al. / Structural characterization of a-SiC: H by TDS
Table 1 Carbon contents (x) obtained from XPS measurements and thicknesses (d) for several a-SiI xCx :H alloys deposited from different methane ratios in gas phase (Y) Y
x
d (/~m)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95
0 0.03 0.07 0.08 0.09 0.15 0.21 0.24 0.31 0.37 0.41
0.63 0.53 0.47 0.51 0.45 0.21, 0.41, 0.91, 1.82 0.38 0.47 0.44 0.33 0.11, 0.21, 0.48, 0.93
tramass), an oil diffusion pump, a temperature controller (Phillips KS 4580), and a personal computer which collects the data from the spectrometer and controls the temperature ramp. Before each experiment the system was pumped down to 10 -4 Pa, and the quartz tube was heated up to 1000°C. When the tube reached room temperature again, the furnace was shifted to an extreme of the tube and the sample was dropped into it. Thus possible outgassing from the tube walls due to heating is avoided. The temperature ramp was 0.33°C s a and the temperature was raised until all the hydrogen was removed (typically 900°C).
v
13
z 0"~ 0
I
I
200
I
400
I
I
I
600
I
800
Temperature (°C) Fig. 1. Hydrogen effusion spectra of a-Sil_xC x :H alloys deposited from different gas phase compositions.
3. Results and discussion T h e results of the effusion spectra are repres e n t e d in s e m i - l o g a r i t h m i c plots in figs. 1, 2 a n d 3. Fig. 1 p r e s e n t s the spectra for s a m p l e s n e a r 0.5 /xm d e p o s i t e d u n d e r gas p h a s e c o m p o s i t i o n s r a n g i n g from Y = 0 to 0.95. Fig. 2 p r e s e n t s the effusion spectra for s a m p l e s d e p o s i t e d u n d e r gas p h a s e c o m p o s i t i o n of Y = 0.5 a n d different thicknesses b e t w e e n 0.2 a n d 1.8 /xm. Fig. 3 p r e s e n t s the effusion spectra of s a m p l e s grown u n d e r gas p h a s e c o m p o s i t i o n of Y = 0.95 a n d thicknesses r a n g i n g b e t w e e n 0.1 a n d 0 . 9 / ~ m . T h e p r e s e n t results show the g e n e r a l t r e n d s previously r e p o r t e d for a-Sia_xC x : H [6,7], two peaks in the h y d r o g e n e v o l u t i o n spectra a p p e a r e d
~m ~2 v
o I
200
400
600
800
Temperature (°C) Fig. 2. Hydrogen effusion spectra of four a-Si0.ssC0as:H samples (Y= 0.5) with different thicknesses obtained in the same run.
F. Maass et al. / Structural characterization of a-SiC: H by TDS
770
0.93 /zm
0.48 /~m
O~ 0.11
I
200
l
l
400
l
I
600
I
Temperafure (°C)
I
800
Fig. 3. Hydrogen effusion spectra of four a-Sio.59Co.41:H samples (Y = 0.95) with different thicknesses obtained in the same run.
for the samples with moderate carbon concentration (fig. 1), the low t e m p e r a t u r e (LT) peak being attributed to the surface controlled desorption process in voids surface and diffusion of the H 2 molecule through the percolated voids [6]. For optoelectronic grade amorphous silicon samples, the LT p e a k was not observed because the voids were not percolated. But for the alloy with increasing carbon content, the porosity increased [8] and the L T p e a k appeared. This p e a k appeared at a t e m p e r a t u r e independent of the thickness of the sample (fig. 2), indicating the presence of a surface controlled effusion. The other p e a k present in the samples with moderate carbon content is the high t e m p e r a t u r e (HT) peak, being attributed to diffusion of atomic hydrogen through the dense material [9]. The diffusion origin of the peak was evidenced in fig. 2, which shows a displacement to higher temperatures of the p e a k when the thickness of the samples increases. Whereas the LT peak a p p e a r e d at the same t e m p e r a t u r e independently of the carbon content, the H T p e a k shifted to higher temperatures when increasing the carbon content of samples with similar thicknesses (fig. 1). Another feature of the presented effusion spectra was the presence of regions where the signal of hydrogen flux seemed to be affected by noise, these zones can be observed in the zone of
400°C in the samples of fig. 1 with low carbon content and was attributed to the rupture of the voids. This behaviour is also present in the spectra of fig. 2, where the thinner samples presented the rupture at higher temperatures (dashed line A of the figure), possibly due to structural differences caused by the tensions induced by the substrate. One of the more remarkable features of the present results was the presence of a third peak in the TDS spectra, labeled B in the figures, which was not previously reported, and appeared in the samples with higher carbon content. The peak began to be present for carbon concentrations of 0.24 (measured by XPS) and became dominant for the sample with carbon concentration of 0.37 and 0.41. The temperature of the maximum of the peak did not significantly change with the thickness of the sample, indicating a surface controlled effusion process, as can be seen in fig. 3. But unlike the LT peak, this peak changed its position towards higher temperatures when carbon content was increased. The origin of this peak requires a more exhaustive study, but it is possible to advance a possible base for its interpretation. The surface effusion of hydrogen from a Si surface requires the presence of two neighbouring hydrogen atoms that are combined to form the H 2 molecule, the energy involved in the process is the difference between the rupture of the two Sill bonds and the energy of the recombination of the two H atoms to form the H 2 molecule [9]. When the carbon content in the sample is low, this process is likely responsible for the hydrogen effusion assuming that the hydrogen eventually bonded to a C atom can change its position to a neighbouring Si atom at the surface. But when the carbon concentration increases, the probability of finding two Si neighbouring atoms in the surface decreases and the surface effusion can be then controlled by a process involving the breaking of a Sill bond, a C H bond, and the H 2 reconstruction. The dominant presence of this third evolution in samples deposited from Y = 0.95 is interpreted as a consequence of a highly percolated structure which enhances the surface controlled desorption processes with respect to the diffusion through dense matrix.
F. Maass et al. / Structural characterization o f a-SiC : H by TDS
4. Conclusions T D S has t u r n e d o u t to b e a very s u i t a b l e t e c h n i q u e to c h a r a c t e r i z e t h e s t r u c t u r e o f aSi 1_xCx : H thin films. U s e f u l i n f o r m a t i o n can b e o b t a i n e d w h e n a p p l y i n g T D S to i d e n t i c a l s a m p l e s o f d i f f e r e n t thicknesses. Three different hydrogen evolutions were det e c t e d in s a m p l e s p r e p a r e d u n d e r d i f f e r e n t gas p h a s e c o m p o s i t i o n . A n L T evolution, which app e a r e d at low c a r b o n c o n t e n t s a n d w h o s e position did n o t d e p e n d on t h e c a r b o n c o n c e n t r a t i o n n o r thickness, was a t t r i b u t e d to surface cont r o l l e d d e s o r p t i o n p r o c e s s e s in i n t e r n a l voids. A n H T evolution, which shifted to h i g h e r t e m p e r a t u r e s w h e n i n c r e a s i n g c a r b o n c o n t e n t o r thickness, was a t t r i b u t e d to diffusion t h r o u g h d e n s e m a t e r i a l . A third e v o l u t i o n a p p e a r e d for h i g h e r carbon concentrations, becoming dominant when Y = 0.95 a n d b e i n g a t t r i b u t e d to a s u r f a c e cont r o l l e d d e s o r p t i o n o f H2 f r o m a S i l l b o n d a n d a C H b o n d . This was i n t e r p r e t e d in t e r m s o f struct u r a l c h a n g e s o f the films w h e n c a r b o n c o n t e n t is high. O t h e r p e a k s which shift to lower t e m p e r a t u r e s w h e n i n c r e a s i n g the t h i c k n e s s w e r e a t t r i b u t e d to r u p t u r e o f voids, which can b e r e l a t e d to t h e t e n s i o n s i n d u c e d by t h e s u b s t r a t e .
771
Acknowledgements W e a c k n o w l e d g e t h e c o l l a b o r a t i o n of t h e S c i e n t i f i c - T e c h n i c a l Services o f t h e U n i v e r s i t y o f Barcelona, where XPS measurements were perf o r m e d . T h i s w o r k was s u p p o r t e d by t h e D G I CYT of the Spanish Government under program PB8-0236.
References [1] Y. Tawada, K. Tsuge, M. Kondo, H. Okamoto and Y. Hamakawa, J. Appl. Phys. 53 (1982) 5273. [2] A. Catalano, R.R. Ayra, M. Bennett, L. Yang, J. Morris, B. Goldstein, B. Fieselmann, J. Newton and S. Wiedeman, Sol. Cells 27 (1989) 25. [3] D. Kruangam, T. Endo, W. Guang-Pu, H. Okamoto and Y. Hamakawa, Jpn. J. Appl. Phys. 24 (1985) L806. [4] J. Bertomeu, J.M. Asensi, J. Puigdollers, J. Andreu and J.L. Morenza, Vacuum 44 (1993) 129. [5] J. Serra, J. Andreu, G. Sardin, C. Roch, J.M. Asensi, J. Bertomeu and J. Esteve, Physica B 170 (1991) 269. [6] W. Beyer, H. Wagner and F. Finger, J. Non-Cryst. Solids 77&78 (1985) 857. [7] W. Beyer, J. Non-Cryst. Solids 97&98 (1987) 1027. [8] R. Arce, R.R. Koropecki, R.H. Buitrago, F. Alvarez and I. Chambuleyron, J. Appl. Phys. 66 (1989) 4544. [9] W. Beyer, Physica B 170 (1991) 105.
applied surface s c i e n c e
Structural characterization of a-SiC" H by thermal desorption spectroscopy F. M a a s s
1 j.
B e r t o m e u , J.M. Asensi, J. P u i g d o l l e r s , J. A n d r e u , J.C. D e l g a d o a n d J. E s t e v e
Universitat de Barcelona, Departament de F{sica Aplicada i Electrbnica, Av. Diagonal 647, E-08028 Barcelona, Spain
Received 24 August 1992; accepted for publication 11 October 1992
The structure of a-Si1 xCx : H thin films prepared from different mixtures of S i l l 4 a n d CH 4 was studied by thermal desorption spectroscopy. The influence of the gas phase composition and the thickness on the hydrogen evolution spectra is presented and discussed. A third hydrogen evolution was observed in a-Sil_xCx films with higher carbon content. The results show that the surface controlled desorption processes become dominant when increasing the carbon content.
1. Introduction Considerable effort to understand the structural characteristics of hydrogenated amorphous silicon (a-Si:H) has been undertaken in the last few years. The complete understanding of its structural characteristics and its relationship with its interesting optoelectronic properties is still an open question. In addition, the research on hydrogenated amorphous silicon has led to a family of related alloys. Hydrogenated amorphous silic o n - c a r b o n (a-Si l_xCx : H) is one of these alloys, with important practical applications as p-layer in p - i - n solar cells [1], active i-layer in tandem solar cells [2] and electroluminescent devices [3]. This material has been prepared by different techniques, but the best properties for optoelectronic applications have been obtained in R F glow discharge films. But a - S i l _ x C x : H alloys present a wide range of structures and stoichiometries, depending on the preparation conditions, that hinders the exploration of the technological preparation conditions. In the present paper, we report an extensive thermal desorption spectroscopy (TDS) study of Permanent address: Universidad de Antofagasta, Departamento de Fisica, Av. Angamos 601, Antofagasta, Chile.
samples grown with a conventional plasma-CVD radiofrequency reactor in a low power regime and for a wide range of gas phase compositions. New features of the TDS spectra are put in evidence for the samples with higher carbon content.
2. Experimental The samples were obtained by R F (13.56 MHz) glow discharge decomposition of pure silane and methane in a reactor described elsewhere [4]. The use of a rotating substrate holder enables us to deposit under exactly the same conditions four samples with different thicknesses. The films were deposited onto crystalline silicon polished on both faces. The RF power, the substrate temperature, the pressure and the total flow rate were kept at 5 W, 300°C, 30 Pa and 20 sccm. These conditions gave a device quality a - S i : H in our reactor, with a low density of defects and good properties [5]. The methane ratio in the gas phase (Y) was varied from 0 to 0.95. For Y = 0.5 and 0.95, four different thicknesses were deposited. Composition of the samples was estimated from XPS measurements (table 1). The TDS system consists of a quartz tube, a quadrupolar mass spectrometer (Dataquad, Spec-
0169-4332/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
769
F. Maass et al. / Structural characterization of a-SiC: H by TDS
Table 1 Carbon contents (x) obtained from XPS measurements and thicknesses (d) for several a-SiI xCx :H alloys deposited from different methane ratios in gas phase (Y) Y
x
d (/~m)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95
0 0.03 0.07 0.08 0.09 0.15 0.21 0.24 0.31 0.37 0.41
0.63 0.53 0.47 0.51 0.45 0.21, 0.41, 0.91, 1.82 0.38 0.47 0.44 0.33 0.11, 0.21, 0.48, 0.93
tramass), an oil diffusion pump, a temperature controller (Phillips KS 4580), and a personal computer which collects the data from the spectrometer and controls the temperature ramp. Before each experiment the system was pumped down to 10 -4 Pa, and the quartz tube was heated up to 1000°C. When the tube reached room temperature again, the furnace was shifted to an extreme of the tube and the sample was dropped into it. Thus possible outgassing from the tube walls due to heating is avoided. The temperature ramp was 0.33°C s a and the temperature was raised until all the hydrogen was removed (typically 900°C).
v
13
z 0"~ 0
I
I
200
I
400
I
I
I
600
I
800
Temperature (°C) Fig. 1. Hydrogen effusion spectra of a-Sil_xC x :H alloys deposited from different gas phase compositions.
3. Results and discussion T h e results of the effusion spectra are repres e n t e d in s e m i - l o g a r i t h m i c plots in figs. 1, 2 a n d 3. Fig. 1 p r e s e n t s the spectra for s a m p l e s n e a r 0.5 /xm d e p o s i t e d u n d e r gas p h a s e c o m p o s i t i o n s r a n g i n g from Y = 0 to 0.95. Fig. 2 p r e s e n t s the effusion spectra for s a m p l e s d e p o s i t e d u n d e r gas p h a s e c o m p o s i t i o n of Y = 0.5 a n d different thicknesses b e t w e e n 0.2 a n d 1.8 /xm. Fig. 3 p r e s e n t s the effusion spectra of s a m p l e s grown u n d e r gas p h a s e c o m p o s i t i o n of Y = 0.95 a n d thicknesses r a n g i n g b e t w e e n 0.1 a n d 0 . 9 / ~ m . T h e p r e s e n t results show the g e n e r a l t r e n d s previously r e p o r t e d for a-Sia_xC x : H [6,7], two peaks in the h y d r o g e n e v o l u t i o n spectra a p p e a r e d
~m ~2 v
o I
200
400
600
800
Temperature (°C) Fig. 2. Hydrogen effusion spectra of four a-Si0.ssC0as:H samples (Y= 0.5) with different thicknesses obtained in the same run.
F. Maass et al. / Structural characterization of a-SiC: H by TDS
770
0.93 /zm
0.48 /~m
O~ 0.11
I
200
l
l
400
l
I
600
I
Temperafure (°C)
I
800
Fig. 3. Hydrogen effusion spectra of four a-Sio.59Co.41:H samples (Y = 0.95) with different thicknesses obtained in the same run.
for the samples with moderate carbon concentration (fig. 1), the low t e m p e r a t u r e (LT) peak being attributed to the surface controlled desorption process in voids surface and diffusion of the H 2 molecule through the percolated voids [6]. For optoelectronic grade amorphous silicon samples, the LT p e a k was not observed because the voids were not percolated. But for the alloy with increasing carbon content, the porosity increased [8] and the L T p e a k appeared. This p e a k appeared at a t e m p e r a t u r e independent of the thickness of the sample (fig. 2), indicating the presence of a surface controlled effusion. The other p e a k present in the samples with moderate carbon content is the high t e m p e r a t u r e (HT) peak, being attributed to diffusion of atomic hydrogen through the dense material [9]. The diffusion origin of the peak was evidenced in fig. 2, which shows a displacement to higher temperatures of the p e a k when the thickness of the samples increases. Whereas the LT peak a p p e a r e d at the same t e m p e r a t u r e independently of the carbon content, the H T p e a k shifted to higher temperatures when increasing the carbon content of samples with similar thicknesses (fig. 1). Another feature of the presented effusion spectra was the presence of regions where the signal of hydrogen flux seemed to be affected by noise, these zones can be observed in the zone of
400°C in the samples of fig. 1 with low carbon content and was attributed to the rupture of the voids. This behaviour is also present in the spectra of fig. 2, where the thinner samples presented the rupture at higher temperatures (dashed line A of the figure), possibly due to structural differences caused by the tensions induced by the substrate. One of the more remarkable features of the present results was the presence of a third peak in the TDS spectra, labeled B in the figures, which was not previously reported, and appeared in the samples with higher carbon content. The peak began to be present for carbon concentrations of 0.24 (measured by XPS) and became dominant for the sample with carbon concentration of 0.37 and 0.41. The temperature of the maximum of the peak did not significantly change with the thickness of the sample, indicating a surface controlled effusion process, as can be seen in fig. 3. But unlike the LT peak, this peak changed its position towards higher temperatures when carbon content was increased. The origin of this peak requires a more exhaustive study, but it is possible to advance a possible base for its interpretation. The surface effusion of hydrogen from a Si surface requires the presence of two neighbouring hydrogen atoms that are combined to form the H 2 molecule, the energy involved in the process is the difference between the rupture of the two Sill bonds and the energy of the recombination of the two H atoms to form the H 2 molecule [9]. When the carbon content in the sample is low, this process is likely responsible for the hydrogen effusion assuming that the hydrogen eventually bonded to a C atom can change its position to a neighbouring Si atom at the surface. But when the carbon concentration increases, the probability of finding two Si neighbouring atoms in the surface decreases and the surface effusion can be then controlled by a process involving the breaking of a Sill bond, a C H bond, and the H 2 reconstruction. The dominant presence of this third evolution in samples deposited from Y = 0.95 is interpreted as a consequence of a highly percolated structure which enhances the surface controlled desorption processes with respect to the diffusion through dense matrix.
F. Maass et al. / Structural characterization o f a-SiC : H by TDS
4. Conclusions T D S has t u r n e d o u t to b e a very s u i t a b l e t e c h n i q u e to c h a r a c t e r i z e t h e s t r u c t u r e o f aSi 1_xCx : H thin films. U s e f u l i n f o r m a t i o n can b e o b t a i n e d w h e n a p p l y i n g T D S to i d e n t i c a l s a m p l e s o f d i f f e r e n t thicknesses. Three different hydrogen evolutions were det e c t e d in s a m p l e s p r e p a r e d u n d e r d i f f e r e n t gas p h a s e c o m p o s i t i o n . A n L T evolution, which app e a r e d at low c a r b o n c o n t e n t s a n d w h o s e position did n o t d e p e n d on t h e c a r b o n c o n c e n t r a t i o n n o r thickness, was a t t r i b u t e d to surface cont r o l l e d d e s o r p t i o n p r o c e s s e s in i n t e r n a l voids. A n H T evolution, which shifted to h i g h e r t e m p e r a t u r e s w h e n i n c r e a s i n g c a r b o n c o n t e n t o r thickness, was a t t r i b u t e d to diffusion t h r o u g h d e n s e m a t e r i a l . A third e v o l u t i o n a p p e a r e d for h i g h e r carbon concentrations, becoming dominant when Y = 0.95 a n d b e i n g a t t r i b u t e d to a s u r f a c e cont r o l l e d d e s o r p t i o n o f H2 f r o m a S i l l b o n d a n d a C H b o n d . This was i n t e r p r e t e d in t e r m s o f struct u r a l c h a n g e s o f the films w h e n c a r b o n c o n t e n t is high. O t h e r p e a k s which shift to lower t e m p e r a t u r e s w h e n i n c r e a s i n g the t h i c k n e s s w e r e a t t r i b u t e d to r u p t u r e o f voids, which can b e r e l a t e d to t h e t e n s i o n s i n d u c e d by t h e s u b s t r a t e .
771
Acknowledgements W e a c k n o w l e d g e t h e c o l l a b o r a t i o n of t h e S c i e n t i f i c - T e c h n i c a l Services o f t h e U n i v e r s i t y o f Barcelona, where XPS measurements were perf o r m e d . T h i s w o r k was s u p p o r t e d by t h e D G I CYT of the Spanish Government under program PB8-0236.
References [1] Y. Tawada, K. Tsuge, M. Kondo, H. Okamoto and Y. Hamakawa, J. Appl. Phys. 53 (1982) 5273. [2] A. Catalano, R.R. Ayra, M. Bennett, L. Yang, J. Morris, B. Goldstein, B. Fieselmann, J. Newton and S. Wiedeman, Sol. Cells 27 (1989) 25. [3] D. Kruangam, T. Endo, W. Guang-Pu, H. Okamoto and Y. Hamakawa, Jpn. J. Appl. Phys. 24 (1985) L806. [4] J. Bertomeu, J.M. Asensi, J. Puigdollers, J. Andreu and J.L. Morenza, Vacuum 44 (1993) 129. [5] J. Serra, J. Andreu, G. Sardin, C. Roch, J.M. Asensi, J. Bertomeu and J. Esteve, Physica B 170 (1991) 269. [6] W. Beyer, H. Wagner and F. Finger, J. Non-Cryst. Solids 77&78 (1985) 857. [7] W. Beyer, J. Non-Cryst. Solids 97&98 (1987) 1027. [8] R. Arce, R.R. Koropecki, R.H. Buitrago, F. Alvarez and I. Chambuleyron, J. Appl. Phys. 66 (1989) 4544. [9] W. Beyer, Physica B 170 (1991) 105.