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Etching of DLC films using a low intensity oxygen plasma jet
Diamond and Related Materials 9 (2000) 685–688 www.elsevier.com/locate/diamond
Etching of DLC films using a low intensity oxygen plasma jet W.I. Urruchi a,b, *, M. Massi a, H.S. Maciel a, C. Otani a, L.N. Nishioka a a Departamento de Fı´sica, ITA, CTA, 12228-900 Sao Jose´ dos Campos SP, Brazil b Universidade Braz Cubas, 08773-380 Mogi das Cruzes SP, Brazil
Abstract This article describes the characteristics of the etching process of diamond-like carbon (DLC ) films using a new plasma system based on an oxygen plasma jet which comprises charged particles and activated neutral species in a range of energies and fluxes suitable for the etching process. This plasma source was used to etch DLC films which were grown on silicon substrates by magnetron sputtering technique. Prior to etching these films were characterized by different methods, namely Raman spectroscopy, Fourier transform infrared spectroscopy (FTIR), current×voltage curves and atomic force microscopy (AFM ). Etch rates in the range 7.0–25 nm/min were measured for substrates placed at different positions along the axis of the plasma jet. An attractive feature observed in this work was the influence of an axial magnetic field applied to improve the confinement of the plasma stream. An increase by a factor of 3.4 in the etch rate was verified when the magnetic field increased from 2.5 to 6.0 mT. Raman spectra features ( line shapes, frequencies and line width) of the etched films were compared with those obtained before etching. The results show that this plasma jet etching is a reliable technique for DLC film processing. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Diamond-like carbon; Oxygen plasma jet; Plasma etching
1. Introduction Diamond-like carbon (DLC ) films have been studied intensively in the last two decades, because of their attractive mechanical, optical, electrical, chemical and tribological properties [1,2]. The combination of these properties makes possible the use of DLC films as protective coatings for magnetic recordings [3], antireflective layers for silicon solar cells [4], and solid lubricant coatings for vacuum applications [5]. For microelectronics purposes they can be used as gate dielectrics, intermetal dielectrics and passivation layers [6 ]. These films are usually deposited by plasma enhanced chemical vapor deposition (PECVD) or physical vapor deposition techniques, using different carbon precursors [1,2]. In the present work the films were deposited on silicon substrate by magnetron sputtering using a high purity graphite target and argon as the discharge gas [7]. For some applications, such as microelectronic
* Corresponding author. Fax: +55-12-347-5934. E-mail addresses: [email protected] ( W.I. Urruchi), [email protected] (M. Massi)
devices, it is usually necessary to etch part of the film. This is commonly done by a reactive ion etching ( RIE) system [8], but sputtering of the electrode material can occur, with consequent undesirable production of micromasking on the film. For etching of DLC films we use a new plasma system that produces a stream of plasma (plasma jet) of low intensity. Recently a plasma system composed of a multi-plasma stream produced by a similar discharge constriction mechanism was built and evaluated for deposition processes [9]. The etching system we use consists basically of two chambers, namely a source chamber (or cathodic chamber) where the gas is fed at a range of pressure suitable for glow discharge formation and an expansion chamber (or anodic chamber) where the plasma beam is generated [10]. They are connected through an aperture which can be an intermediate electrode (capillary or channel ), as in the case of a duoplasmatron [11], or simply an opening (orifice or short channel ) made on the separating wall, as in the present case [12]. A strong pressure gradient is established, by differential pumping, in the passage between the chambers, the gas pressure on the anode side being at least three orders of magnitude lower than on the cathode side. A supersonic gas jet, driven by the pressure
0925-9635/00/$ - see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S0 9 25 - 9 63 5 ( 0 0 ) 00 2 0 8- 9
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W.I. Urruchi et al. / Diamond and Related Materials 9 (2000) 685–688
gradient, emerges from the exit of the orifice and expands in the vacuum chamber. An external magnetic field was applied to improve the confinement of the plasma jet. In this work, the influence of the axial magnetic field and the distance between the expansion orifice and the substrate on the etch characteristics of the films were studied. In general, it is desirable to have an etching process which does not modify the atom bonding configuration of the film. Raman scattering is a powerful characterization technique, able to detect the different types of carbon atom bond [13], and therefore it is used in this work. The first order Raman spectra of DLC thin films are normally characterized by two bands: the G band at 1550 cm−1, originating from crystalline graphite, and the D band at about 1370 cm−1, which is associated with a disordered graphite lattice. These bands can present different shapes, spectral positions and band widths depending on the structural characteristics of the film. Raman spectra of the films, before and after etching, were analyzed in this work.
2. Experimental Non-hydrogenated carbon (a-C ) films of approximately 1.5 mm thick were deposited on p-type, (100), 10 V cm silicon substrates, by a d.c. planar magnetron sputtering discharge, at a deposition rate of 15 nm/min. The target was a 4.00◊ diameter disk of graphite with 99.999% carbon content, placed at 45 mm from the substrate. The gas used during the depositions was argon (flow=5.0 sccm) at a pressure of 0.32 Pa. The electrical power input of the discharge was 200 W and the substrate temperature was 200°C. Details of the deposition system and processes can be found in Ref. [7]. The films obtained under these experimental conditions have the following characteristics: electrical resistivity 5×106 V cm; relative dielectric constant 2.9; compressive stress 9.5 GPa; rms roughness 0.25 nm. The etching processes were performed in a home-
built reactor ( Fig. 1). The cathodic chamber is a cylindrical Pyrex tube of 27 mm internal diameter and 200 mm length. The anode chamber, also made of Pyrex, with a metallic flange at each end, has a length of 350 mm and a diameter of 140 mm. The chambers are joined together, passage between them being made through a channel (1.0 mm diameter and 2.0 mm long) opened in the center of the wall at the end of the cathodic chamber. A turbomolecular pump backed by a rotary pump is attached to the anodic chamber through a connection on the side of the end flange. Both metallic flanges serve as an anode. The source is pumped down to about 1.3×10−4 Pa and then oxygen gas is fed into the tube at a flow rate of 2.0 sccm, corresponding to a pressure range of 66.5 Pa in the discharge tube and 5.9×10−3 Pa in the vacuum chamber. The expansion chamber was partly surrounded by a magnetic coil. An axial magnetic field in the range 2.5– 6.0 mT was obtained in the region of the substrate by varying the coil current. Characterization of this plasma source operating with argon was reported in Ref. [10]. The results indicate that the typical kinetic energy of the charged particles in the plasma jet is in the range 10–140 eV. During the etching processes, a part of the samples was covered with a mechanical mask to produce a step between the etched and non-etched regions. This step was measured by an Alpha-Step 500 profile meter, and the etch rates were determined. The Raman spectra of the films, in the range 1060–1930 cm−1, were obtained by a Renishaw Raman Imaging Microscope System using 50 mW of 514.5 nm laser light. The spectra were decomposed into two Gaussian line shapes in order to analyze the shape, frequency position, width and integrated area of the D and G bands.
3. Results and discussion Table 1 shows the etch rate of the DLC films for different distances between the expansion orifice and the substrate. The work conditions were: oxygen flow 2.0 sccm; discharge current 100 mA; axial magnetic field 2.5 mT. A reduction of about 70% in the etch rate is observed when the distance increases from 20 to 50 mm. The influence of the axial magnetic field on the etch Table 1 Etch rate of the DLC films as a function of the distance between the expansion orifice and the substrate
Fig. 1. Experimental setup of the etching system.
Distance (mm)
Etch rate (nm/min)
20 35 50
24.9 10.6 6.8
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W.I. Urruchi et al. / Diamond and Related Materials 9 (2000) 685–688 Table 2 Results of the Raman spectra of the DLC films Etch depth (nm)
0 136 211 456
D band
I /I D G
G band
Position (cm−1)
Width (cm−1)
Position (cm−1)
Width (cm−1)
1387 1391 1378 1387
277 270 275 291
1580 1574 1575 1575
116 112 113 110
rate is shown in Fig. 2. The curve shows a significant increase in the etch rate, from 6.8 to 23.3 nm/min, when the magnetic field is increased from 2.5 to 6.0 mT. This is interesting behavior, because by the control of an external parameter (coil current) it is possible to obtain good control of the etch rate. As shown in Ref. [7] under reactive ion etching it is possible to obtain etch rates approximately four times (100 nm/min) higher than those obtained in this work. It is probably possible to attain such etch rate levels in our system using a multi-channel plasma jet or by increasing the axial magnetic field, with the advantage of having a much lower pressure in the processing chamber and an absence of electrodes that could create impurities, micromasking and other undesirable effects. Besides, with RIE etching there is no possibility of etch rate control by an independent operational parameter, as we have here with an almost linear increase of the etch rate with field B. An analysis of the influence of the etching process on the atom bonding configuration of the films was done by Raman spectroscopy. These films were gradually etched, with a typical etch rate of 6.8 nm/min. Raman spectra of the film before etching and after etching steps of 136, 216 and 456.2 nm were recorded. These spectra were decomposed into D and G bands. The results shown in Table 2 indicate that the atom
3.3 3.4 3.6 3.6
bonding configuration of the film was only slightly modified by the etching.
4. Conclusions A low intensity oxygen plasma jet was used to etch diamond-like carbon (DLC ) films. Etch rates in the range 5–25 nm/min were obtained for operational conditions of discharge current (100 mA), O flow rate 2 (2.0 sccm), pressure in the processing chamber (5.9×10−3 Pa) and magnetic field in the substrate region (2.5–6.0 mT ). The analysis of the Raman spectra indicates that this etching process does not affect the atom bonding (sp2, sp3) configuration of the film, as desirable, for example, in microelectronic materials processing. Control of the etch rate could be made by variation of the magnetic field or by the distance between the substrate and the output of the plasma stream. It is also possible to make this control by the variation of the gas flow rate and discharge current. The etching of materials in a processing chamber at very low pressure is always an advantage of this system in comparison with RIE systems. It prevents contamination with sputtered electrode materials, which eventually produces undesirable micromasks. Other practical advantages are: robust operation over a wide range of gas pressure of the glow discharge (cathodic chamber); low cost; and independent control of the etch rate by different operational parameters, especially by a weak external variable magnetic field. The performance of the plasma jet etching has already been shown to be suitable for microelectronic material processing, but it can be further improved regarding the increase of the etch rate and etching uniformity by making a plasma source with various channels, it being necessary, in this case, to have a vacuum system of higher pumping speed to assure the supersonic regime of the plasma stream.
Acknowledgements
Fig. 2. Influence of the axial magnetic field (B) on the etch rate.
The authors thank Drs. Ne´lia, Corat and Sena of LAS-INPE for the use of the Raman system, the step
688
W.I. Urruchi et al. / Diamond and Related Materials 9 (2000) 685–688
height meter and helpful discussions. The financial support of FINEP is acknowledged.
References [1] H.O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, Noyes Publications, Piscataway, NJ, 1993. [2] A. Grill, Diamond Relat. Mater. 8 (1999) 428–434. [3] S.T. Patton, B. Bhushan, IEEE Trans. Magn. 34 (1998) 575–587. [4] M. Alaluf, J. Appelbaum, L. Klibanov, D. Brinker, D. Scheiman, N. Crotoru, Thin Solid Films 256 (1995) 1–2. [5] R. Maboudian, Surf. Sci. Rep. 30 (1998) 207–269.
[6 ] A. Grill, V. Patel, C. Jahnes, J. Electrochem. Soc. 145 (5) (1998) 1649–1653. [7] M. Massi, H.S. Maciel, L.N. Nishioka, C. Otani, R.D. Mansano, P. Verdonck, in: Proc. XIII Conf. of the Brazilian Microelectronics Society, Curitiba, Brazil (1998) 35–40. [8] M. Massi, R.D. Mansano, H.S. Maciel, C. Otani, P. Verdonck, L.N. Nishioka, Thin Solid Films 343/344 (1998) 378–380. [9] A. Anders, R.A. MacGill, M. Rubin, IEEE Trans. Plasma Sci. 27 (1999) 82–83. [10] W.I. Urruchi, H.S. Maciel, G. Petraconi, C. Otani, J. Tech. Phys. 40 (1) (1999) 419–422. [11] J.W. Bradley, D.A. Forder, M.G. Rusbridge, Plasma Sources Sci. Technol. 4 (1995) 516–526. [12] A. Anders, S. Anders, Plasma Sources Sci. Technol. 4 (1995) 571–575. [13] D. Beeman, J. Silverman, R. Lynds, M.R. Anderson, Phys. Rev. B 30 (1984) 870–875.
Etching of DLC films using a low intensity oxygen plasma jet W.I. Urruchi a,b, *, M. Massi a, H.S. Maciel a, C. Otani a, L.N. Nishioka a a Departamento de Fı´sica, ITA, CTA, 12228-900 Sao Jose´ dos Campos SP, Brazil b Universidade Braz Cubas, 08773-380 Mogi das Cruzes SP, Brazil
Abstract This article describes the characteristics of the etching process of diamond-like carbon (DLC ) films using a new plasma system based on an oxygen plasma jet which comprises charged particles and activated neutral species in a range of energies and fluxes suitable for the etching process. This plasma source was used to etch DLC films which were grown on silicon substrates by magnetron sputtering technique. Prior to etching these films were characterized by different methods, namely Raman spectroscopy, Fourier transform infrared spectroscopy (FTIR), current×voltage curves and atomic force microscopy (AFM ). Etch rates in the range 7.0–25 nm/min were measured for substrates placed at different positions along the axis of the plasma jet. An attractive feature observed in this work was the influence of an axial magnetic field applied to improve the confinement of the plasma stream. An increase by a factor of 3.4 in the etch rate was verified when the magnetic field increased from 2.5 to 6.0 mT. Raman spectra features ( line shapes, frequencies and line width) of the etched films were compared with those obtained before etching. The results show that this plasma jet etching is a reliable technique for DLC film processing. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Diamond-like carbon; Oxygen plasma jet; Plasma etching
1. Introduction Diamond-like carbon (DLC ) films have been studied intensively in the last two decades, because of their attractive mechanical, optical, electrical, chemical and tribological properties [1,2]. The combination of these properties makes possible the use of DLC films as protective coatings for magnetic recordings [3], antireflective layers for silicon solar cells [4], and solid lubricant coatings for vacuum applications [5]. For microelectronics purposes they can be used as gate dielectrics, intermetal dielectrics and passivation layers [6 ]. These films are usually deposited by plasma enhanced chemical vapor deposition (PECVD) or physical vapor deposition techniques, using different carbon precursors [1,2]. In the present work the films were deposited on silicon substrate by magnetron sputtering using a high purity graphite target and argon as the discharge gas [7]. For some applications, such as microelectronic
* Corresponding author. Fax: +55-12-347-5934. E-mail addresses: [email protected] ( W.I. Urruchi), [email protected] (M. Massi)
devices, it is usually necessary to etch part of the film. This is commonly done by a reactive ion etching ( RIE) system [8], but sputtering of the electrode material can occur, with consequent undesirable production of micromasking on the film. For etching of DLC films we use a new plasma system that produces a stream of plasma (plasma jet) of low intensity. Recently a plasma system composed of a multi-plasma stream produced by a similar discharge constriction mechanism was built and evaluated for deposition processes [9]. The etching system we use consists basically of two chambers, namely a source chamber (or cathodic chamber) where the gas is fed at a range of pressure suitable for glow discharge formation and an expansion chamber (or anodic chamber) where the plasma beam is generated [10]. They are connected through an aperture which can be an intermediate electrode (capillary or channel ), as in the case of a duoplasmatron [11], or simply an opening (orifice or short channel ) made on the separating wall, as in the present case [12]. A strong pressure gradient is established, by differential pumping, in the passage between the chambers, the gas pressure on the anode side being at least three orders of magnitude lower than on the cathode side. A supersonic gas jet, driven by the pressure
0925-9635/00/$ - see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S0 9 25 - 9 63 5 ( 0 0 ) 00 2 0 8- 9
686
W.I. Urruchi et al. / Diamond and Related Materials 9 (2000) 685–688
gradient, emerges from the exit of the orifice and expands in the vacuum chamber. An external magnetic field was applied to improve the confinement of the plasma jet. In this work, the influence of the axial magnetic field and the distance between the expansion orifice and the substrate on the etch characteristics of the films were studied. In general, it is desirable to have an etching process which does not modify the atom bonding configuration of the film. Raman scattering is a powerful characterization technique, able to detect the different types of carbon atom bond [13], and therefore it is used in this work. The first order Raman spectra of DLC thin films are normally characterized by two bands: the G band at 1550 cm−1, originating from crystalline graphite, and the D band at about 1370 cm−1, which is associated with a disordered graphite lattice. These bands can present different shapes, spectral positions and band widths depending on the structural characteristics of the film. Raman spectra of the films, before and after etching, were analyzed in this work.
2. Experimental Non-hydrogenated carbon (a-C ) films of approximately 1.5 mm thick were deposited on p-type, (100), 10 V cm silicon substrates, by a d.c. planar magnetron sputtering discharge, at a deposition rate of 15 nm/min. The target was a 4.00◊ diameter disk of graphite with 99.999% carbon content, placed at 45 mm from the substrate. The gas used during the depositions was argon (flow=5.0 sccm) at a pressure of 0.32 Pa. The electrical power input of the discharge was 200 W and the substrate temperature was 200°C. Details of the deposition system and processes can be found in Ref. [7]. The films obtained under these experimental conditions have the following characteristics: electrical resistivity 5×106 V cm; relative dielectric constant 2.9; compressive stress 9.5 GPa; rms roughness 0.25 nm. The etching processes were performed in a home-
built reactor ( Fig. 1). The cathodic chamber is a cylindrical Pyrex tube of 27 mm internal diameter and 200 mm length. The anode chamber, also made of Pyrex, with a metallic flange at each end, has a length of 350 mm and a diameter of 140 mm. The chambers are joined together, passage between them being made through a channel (1.0 mm diameter and 2.0 mm long) opened in the center of the wall at the end of the cathodic chamber. A turbomolecular pump backed by a rotary pump is attached to the anodic chamber through a connection on the side of the end flange. Both metallic flanges serve as an anode. The source is pumped down to about 1.3×10−4 Pa and then oxygen gas is fed into the tube at a flow rate of 2.0 sccm, corresponding to a pressure range of 66.5 Pa in the discharge tube and 5.9×10−3 Pa in the vacuum chamber. The expansion chamber was partly surrounded by a magnetic coil. An axial magnetic field in the range 2.5– 6.0 mT was obtained in the region of the substrate by varying the coil current. Characterization of this plasma source operating with argon was reported in Ref. [10]. The results indicate that the typical kinetic energy of the charged particles in the plasma jet is in the range 10–140 eV. During the etching processes, a part of the samples was covered with a mechanical mask to produce a step between the etched and non-etched regions. This step was measured by an Alpha-Step 500 profile meter, and the etch rates were determined. The Raman spectra of the films, in the range 1060–1930 cm−1, were obtained by a Renishaw Raman Imaging Microscope System using 50 mW of 514.5 nm laser light. The spectra were decomposed into two Gaussian line shapes in order to analyze the shape, frequency position, width and integrated area of the D and G bands.
3. Results and discussion Table 1 shows the etch rate of the DLC films for different distances between the expansion orifice and the substrate. The work conditions were: oxygen flow 2.0 sccm; discharge current 100 mA; axial magnetic field 2.5 mT. A reduction of about 70% in the etch rate is observed when the distance increases from 20 to 50 mm. The influence of the axial magnetic field on the etch Table 1 Etch rate of the DLC films as a function of the distance between the expansion orifice and the substrate
Fig. 1. Experimental setup of the etching system.
Distance (mm)
Etch rate (nm/min)
20 35 50
24.9 10.6 6.8
687
W.I. Urruchi et al. / Diamond and Related Materials 9 (2000) 685–688 Table 2 Results of the Raman spectra of the DLC films Etch depth (nm)
0 136 211 456
D band
I /I D G
G band
Position (cm−1)
Width (cm−1)
Position (cm−1)
Width (cm−1)
1387 1391 1378 1387
277 270 275 291
1580 1574 1575 1575
116 112 113 110
rate is shown in Fig. 2. The curve shows a significant increase in the etch rate, from 6.8 to 23.3 nm/min, when the magnetic field is increased from 2.5 to 6.0 mT. This is interesting behavior, because by the control of an external parameter (coil current) it is possible to obtain good control of the etch rate. As shown in Ref. [7] under reactive ion etching it is possible to obtain etch rates approximately four times (100 nm/min) higher than those obtained in this work. It is probably possible to attain such etch rate levels in our system using a multi-channel plasma jet or by increasing the axial magnetic field, with the advantage of having a much lower pressure in the processing chamber and an absence of electrodes that could create impurities, micromasking and other undesirable effects. Besides, with RIE etching there is no possibility of etch rate control by an independent operational parameter, as we have here with an almost linear increase of the etch rate with field B. An analysis of the influence of the etching process on the atom bonding configuration of the films was done by Raman spectroscopy. These films were gradually etched, with a typical etch rate of 6.8 nm/min. Raman spectra of the film before etching and after etching steps of 136, 216 and 456.2 nm were recorded. These spectra were decomposed into D and G bands. The results shown in Table 2 indicate that the atom
3.3 3.4 3.6 3.6
bonding configuration of the film was only slightly modified by the etching.
4. Conclusions A low intensity oxygen plasma jet was used to etch diamond-like carbon (DLC ) films. Etch rates in the range 5–25 nm/min were obtained for operational conditions of discharge current (100 mA), O flow rate 2 (2.0 sccm), pressure in the processing chamber (5.9×10−3 Pa) and magnetic field in the substrate region (2.5–6.0 mT ). The analysis of the Raman spectra indicates that this etching process does not affect the atom bonding (sp2, sp3) configuration of the film, as desirable, for example, in microelectronic materials processing. Control of the etch rate could be made by variation of the magnetic field or by the distance between the substrate and the output of the plasma stream. It is also possible to make this control by the variation of the gas flow rate and discharge current. The etching of materials in a processing chamber at very low pressure is always an advantage of this system in comparison with RIE systems. It prevents contamination with sputtered electrode materials, which eventually produces undesirable micromasks. Other practical advantages are: robust operation over a wide range of gas pressure of the glow discharge (cathodic chamber); low cost; and independent control of the etch rate by different operational parameters, especially by a weak external variable magnetic field. The performance of the plasma jet etching has already been shown to be suitable for microelectronic material processing, but it can be further improved regarding the increase of the etch rate and etching uniformity by making a plasma source with various channels, it being necessary, in this case, to have a vacuum system of higher pumping speed to assure the supersonic regime of the plasma stream.
Acknowledgements
Fig. 2. Influence of the axial magnetic field (B) on the etch rate.
The authors thank Drs. Ne´lia, Corat and Sena of LAS-INPE for the use of the Raman system, the step
688
W.I. Urruchi et al. / Diamond and Related Materials 9 (2000) 685–688
height meter and helpful discussions. The financial support of FINEP is acknowledged.
References [1] H.O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, Noyes Publications, Piscataway, NJ, 1993. [2] A. Grill, Diamond Relat. Mater. 8 (1999) 428–434. [3] S.T. Patton, B. Bhushan, IEEE Trans. Magn. 34 (1998) 575–587. [4] M. Alaluf, J. Appelbaum, L. Klibanov, D. Brinker, D. Scheiman, N. Crotoru, Thin Solid Films 256 (1995) 1–2. [5] R. Maboudian, Surf. Sci. Rep. 30 (1998) 207–269.
[6 ] A. Grill, V. Patel, C. Jahnes, J. Electrochem. Soc. 145 (5) (1998) 1649–1653. [7] M. Massi, H.S. Maciel, L.N. Nishioka, C. Otani, R.D. Mansano, P. Verdonck, in: Proc. XIII Conf. of the Brazilian Microelectronics Society, Curitiba, Brazil (1998) 35–40. [8] M. Massi, R.D. Mansano, H.S. Maciel, C. Otani, P. Verdonck, L.N. Nishioka, Thin Solid Films 343/344 (1998) 378–380. [9] A. Anders, R.A. MacGill, M. Rubin, IEEE Trans. Plasma Sci. 27 (1999) 82–83. [10] W.I. Urruchi, H.S. Maciel, G. Petraconi, C. Otani, J. Tech. Phys. 40 (1) (1999) 419–422. [11] J.W. Bradley, D.A. Forder, M.G. Rusbridge, Plasma Sources Sci. Technol. 4 (1995) 516–526. [12] A. Anders, S. Anders, Plasma Sources Sci. Technol. 4 (1995) 571–575. [13] D. Beeman, J. Silverman, R. Lynds, M.R. Anderson, Phys. Rev. B 30 (1984) 870–875.