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Optical properties of isostructural β-FeSi2,OsSi2,Fe0.5Os0.5Si2 and Os0.5Fe0.5Si2
Optical Materials 17 (2001) 335±338
www.elsevier.nl/locate/optmat
Optical properties of isostructural b-FeSi2; OsSi2; Fe0:5Os0:5Si2 and Os0:5Fe0:5Si2 D.B. Migas a,*, W. Henrion b, M. Rebien b, V.L. Shaposhnikov c, V.E. Borisenko c, Leo Miglio a a
INFM and Dipartimento di Scienza dei Materiali, Universit a di Milano-Bicocca, via Cozzi 53, Milano 20125, Italy b Hahn±Meitner-Institute, Kekul estr 5, Berlin D-12489, Germany c Belarusian State University of Informatics and Radioelectronics, P. Browka 6, Minsk 220027, Belarus
Abstract We have performed a comparative study of optical properties of isostructural b-FeSi2 ; OsSi2 , and two ternary con®gurations of (FeOs)Si2 by ®rst-principle calculations of band structure and the imaginary part of the dielectric function. The latter for b-FeSi2 and OsSi2 were compared to those deduced from ellipsometric measurements, indicating an excellent agreement. From theoretical calculations both binaries are found to be indirect gap semiconductors, whereas one ternary is characterised by a direct transition with high oscillator strength. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: b-FeSi2 ; OsSi2 ; Ternary compounds; Band structure; Ellipsometry; Optical properties
1. Introduction
2. Computational and experimental details
Both b-FeSi2 and OsSi2 belong to a base-centered orthorhombic structure having two inequivalent transition metal sites [1]. The former is still actively studied in relation to some optoelectronic applications [1,2]. There are only a few papers devoted to OsSi2 and only one theoretical prediction on FeOsSi2 ternaries [1]. In this paper we present a theoretical evidence that the ternary compound Os0:5 Fe0:5 Si2 possesses a direct bandgap nature and a big value of oscillator strength is predicted for the ®rst direct transition at 0.76 eV.
The electronic and optical properties are calculated by a full-potential linear augmented plane wave method [3]. We considered the experimental lattice constants for b-FeSi2 (a 9:863 A, b 7:7791 A, c 7:833 A) and OsSi2 (a 10:1496 b 8:1168 A, c 8:223 A) [1], and relaxed the A, atomic positions by keeping the Cmca symmetry. In case of ternaries we replaced all Fe-1 or Fe-2 sites by osmium atoms in the b-FeSi2 structure, obtaining the Os0:5 Fe0:5 Si2 and Fe0:5 Os0:5 Si2 con®gurations, respectively. Optimization of the lattice parameters by isotropic modi®cation of the volume and atomic position relaxation have been subsequently performed. The following lattice b 7:963 constants were obtained: a 10:081 A, c 8:006 A for Os0:5 Fe0:5 Si2 and a 10:044 A, A, c 7:977 A for Fe0:5 Os0:5 Si2 . b 7:934 A,
* Corresponding author. Tel.: +39-02-64485212; fax: +39-0264485403. E-mail address: [email protected] (D.B. Migas).
0925-3467/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 3 4 6 7 ( 0 1 ) 0 0 0 5 6 - 8
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D.B. Migas et al. / Optical Materials 17 (2001) 335±338
Spectroscopic ellipsometry measurements on polycrystalline OsSi2 were carried out using a Woollam VASE ellipsometer over the spectral range 0.75±4.5eV. To extract the dielectric function values a layer model was established taking into account a native SiO2 oxide layer and the presence of microscopic voids estimated from atomic force microscopy. The consistency of the modelling procedure was checked by comparison
(a)
with spectrophotometric measurements. Experimental values for the dielectric function of b-FeSi2 have been determined previously [4]. 3. Results and discussion The band structure of b-FeSi2 , shown in Fig. 1(a), is characterised by an indirect transition
(b)
(c)
(d)
(e)
(f)
Fig. 1. Band structure of (a) b-FeSi2 , (b) OsSi2 , (e) Fe0:5 Os0:5 Si2 and (f) Os0:5 Fe0:5 Si2 calculated along the high-symmetry directions of the base-centered orthorhombic Brillouin zone. Comparison between experimental (dashed line) and calculated (solid line) imaginary part of the dielectric function for (c) b-FeSi2 and (d) OsSi2 .
D.B. Migas et al. / Optical Materials 17 (2001) 335±338
of 0.68 eV between the valence band maximum (VBM) at the Y point and the conduction band minimum (CBM) situated along the C Z direction (approximately 0:6 C Z, conventionally named K ). The ®rst direct transition at Y has a value of 0.73 eV. OsSi2 possesses an indirect band gap of 1.01 eV (see Fig. 1(b)) between the VBM and the CBM located at K and at C, respectively, and the direct transition at Y has been estimated to be 1.13 eV. The results of the ellipsometry measurements e2 in comparison with the calculated data for b-FeSi2 and OsSi2 are presented in Fig. 1(c,d). In case of iron disilicide epitaxial ®lms with mainly a orientation [4] we have found an excellent agreement with our E ? a polarisation. Since only polycrystalline material with no predominant orientation has been investigated in case of osmium disilicide, we assumed an average of the optical spectra computed for Eka; Ekb and Ekc. For both disilicides excellent agreement has been found between experimental and theoretical data. The
(a)
(c)
337
discrepancy at low energies is attributed to defect absorption due to 0.5 at% of Al in the OsSi2 sample. In contrast to the binaries and another theoretical prediction [1], the ternaries show a direct band gap nature (see Fig. 1(e,f)), where the transitions at Y have been found of about 0.70 and 0.76 eV for Fe0:5 Os0:5 Si2 and Os0:5 Fe0:5 Si2 , respectively. The energy dependence of the imaginary part of the dielectric function, shown in Fig. 2, can be interpreted in terms of interband transitions indicating for binaries a low value of oscillator strength of the ®rst direct transition at Y (0.73 and 1.01 eV, respectively), as the rapid increase in e2 starts at 0.97 eV for b-FeSi2 and 1.85 eV for OsSi2 . The start of rapid e2 increase is traced at about 0.77 eV for Fe0:5 Os0:5 Si2 and Os0:5 Fe0:5 Si2 manifesting a higher optical eciency of the ®rst direct transition especially in the second case. The reason why large anisotropy eects are present for all compounds and why the Ekb contribution is so ecient in Os0:5 Fe0:5 Si2 will be investigated in a
(b)
(d)
Fig. 2. The imaginary part of the dielectric function of (a) b-FeSi2 , (b) OsSi2 , (c) Fe0:5 Os0:5 Si2 , and (d) Os0:5 Fe0:5 Si2 calculated for dierent light polarisations in the energy range from 0 to 5 eV.
338
D.B. Migas et al. / Optical Materials 17 (2001) 335±338
forthcoming paper with an estimation of the total energies corresponding to the dierent ternary con®gurations. Here we just point out that FeOsSi2 compounds should be studied experimentally. Acknowledgements We would like to thank Dr. Bruce Cook for the sample preparation and Glen Birdwell for performing of the AFM measurements. One of us (D.B.M.) acknowledges partial support from UNESCO-ROSTE.
References [1] V.E. Borisenko (Ed.), Semiconducting Silicides, Springer, Berlin, 2000. [2] C. Spinella, S. Coa, C. Bongiorno, S. Pannitteri, M.G. Grimaldi, Appl. Phys. Lett. 76 (2000) 173. [3] P. Blaha, K. Schwarz, J. Luitz, WIEN97, Vienna University of Technology 1997. (Improved and updated Unix version of the original copyrighted WIEN-code, which was published by P. Blaha, K. Schwarz, P. Sorantin, S.B. Trickey, in Comput. Phys. Commun. 59, 399, 1990). [4] V.N. Antonov, O. Jepsen, W. Henrion, M. Rebien, P. Stauss, H. Lange, Phys. Rev. B 57 (1998) 8934.
www.elsevier.nl/locate/optmat
Optical properties of isostructural b-FeSi2; OsSi2; Fe0:5Os0:5Si2 and Os0:5Fe0:5Si2 D.B. Migas a,*, W. Henrion b, M. Rebien b, V.L. Shaposhnikov c, V.E. Borisenko c, Leo Miglio a a
INFM and Dipartimento di Scienza dei Materiali, Universit a di Milano-Bicocca, via Cozzi 53, Milano 20125, Italy b Hahn±Meitner-Institute, Kekul estr 5, Berlin D-12489, Germany c Belarusian State University of Informatics and Radioelectronics, P. Browka 6, Minsk 220027, Belarus
Abstract We have performed a comparative study of optical properties of isostructural b-FeSi2 ; OsSi2 , and two ternary con®gurations of (FeOs)Si2 by ®rst-principle calculations of band structure and the imaginary part of the dielectric function. The latter for b-FeSi2 and OsSi2 were compared to those deduced from ellipsometric measurements, indicating an excellent agreement. From theoretical calculations both binaries are found to be indirect gap semiconductors, whereas one ternary is characterised by a direct transition with high oscillator strength. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: b-FeSi2 ; OsSi2 ; Ternary compounds; Band structure; Ellipsometry; Optical properties
1. Introduction
2. Computational and experimental details
Both b-FeSi2 and OsSi2 belong to a base-centered orthorhombic structure having two inequivalent transition metal sites [1]. The former is still actively studied in relation to some optoelectronic applications [1,2]. There are only a few papers devoted to OsSi2 and only one theoretical prediction on FeOsSi2 ternaries [1]. In this paper we present a theoretical evidence that the ternary compound Os0:5 Fe0:5 Si2 possesses a direct bandgap nature and a big value of oscillator strength is predicted for the ®rst direct transition at 0.76 eV.
The electronic and optical properties are calculated by a full-potential linear augmented plane wave method [3]. We considered the experimental lattice constants for b-FeSi2 (a 9:863 A, b 7:7791 A, c 7:833 A) and OsSi2 (a 10:1496 b 8:1168 A, c 8:223 A) [1], and relaxed the A, atomic positions by keeping the Cmca symmetry. In case of ternaries we replaced all Fe-1 or Fe-2 sites by osmium atoms in the b-FeSi2 structure, obtaining the Os0:5 Fe0:5 Si2 and Fe0:5 Os0:5 Si2 con®gurations, respectively. Optimization of the lattice parameters by isotropic modi®cation of the volume and atomic position relaxation have been subsequently performed. The following lattice b 7:963 constants were obtained: a 10:081 A, c 8:006 A for Os0:5 Fe0:5 Si2 and a 10:044 A, A, c 7:977 A for Fe0:5 Os0:5 Si2 . b 7:934 A,
* Corresponding author. Tel.: +39-02-64485212; fax: +39-0264485403. E-mail address: [email protected] (D.B. Migas).
0925-3467/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 3 4 6 7 ( 0 1 ) 0 0 0 5 6 - 8
336
D.B. Migas et al. / Optical Materials 17 (2001) 335±338
Spectroscopic ellipsometry measurements on polycrystalline OsSi2 were carried out using a Woollam VASE ellipsometer over the spectral range 0.75±4.5eV. To extract the dielectric function values a layer model was established taking into account a native SiO2 oxide layer and the presence of microscopic voids estimated from atomic force microscopy. The consistency of the modelling procedure was checked by comparison
(a)
with spectrophotometric measurements. Experimental values for the dielectric function of b-FeSi2 have been determined previously [4]. 3. Results and discussion The band structure of b-FeSi2 , shown in Fig. 1(a), is characterised by an indirect transition
(b)
(c)
(d)
(e)
(f)
Fig. 1. Band structure of (a) b-FeSi2 , (b) OsSi2 , (e) Fe0:5 Os0:5 Si2 and (f) Os0:5 Fe0:5 Si2 calculated along the high-symmetry directions of the base-centered orthorhombic Brillouin zone. Comparison between experimental (dashed line) and calculated (solid line) imaginary part of the dielectric function for (c) b-FeSi2 and (d) OsSi2 .
D.B. Migas et al. / Optical Materials 17 (2001) 335±338
of 0.68 eV between the valence band maximum (VBM) at the Y point and the conduction band minimum (CBM) situated along the C Z direction (approximately 0:6 C Z, conventionally named K ). The ®rst direct transition at Y has a value of 0.73 eV. OsSi2 possesses an indirect band gap of 1.01 eV (see Fig. 1(b)) between the VBM and the CBM located at K and at C, respectively, and the direct transition at Y has been estimated to be 1.13 eV. The results of the ellipsometry measurements e2 in comparison with the calculated data for b-FeSi2 and OsSi2 are presented in Fig. 1(c,d). In case of iron disilicide epitaxial ®lms with mainly a orientation [4] we have found an excellent agreement with our E ? a polarisation. Since only polycrystalline material with no predominant orientation has been investigated in case of osmium disilicide, we assumed an average of the optical spectra computed for Eka; Ekb and Ekc. For both disilicides excellent agreement has been found between experimental and theoretical data. The
(a)
(c)
337
discrepancy at low energies is attributed to defect absorption due to 0.5 at% of Al in the OsSi2 sample. In contrast to the binaries and another theoretical prediction [1], the ternaries show a direct band gap nature (see Fig. 1(e,f)), where the transitions at Y have been found of about 0.70 and 0.76 eV for Fe0:5 Os0:5 Si2 and Os0:5 Fe0:5 Si2 , respectively. The energy dependence of the imaginary part of the dielectric function, shown in Fig. 2, can be interpreted in terms of interband transitions indicating for binaries a low value of oscillator strength of the ®rst direct transition at Y (0.73 and 1.01 eV, respectively), as the rapid increase in e2 starts at 0.97 eV for b-FeSi2 and 1.85 eV for OsSi2 . The start of rapid e2 increase is traced at about 0.77 eV for Fe0:5 Os0:5 Si2 and Os0:5 Fe0:5 Si2 manifesting a higher optical eciency of the ®rst direct transition especially in the second case. The reason why large anisotropy eects are present for all compounds and why the Ekb contribution is so ecient in Os0:5 Fe0:5 Si2 will be investigated in a
(b)
(d)
Fig. 2. The imaginary part of the dielectric function of (a) b-FeSi2 , (b) OsSi2 , (c) Fe0:5 Os0:5 Si2 , and (d) Os0:5 Fe0:5 Si2 calculated for dierent light polarisations in the energy range from 0 to 5 eV.
338
D.B. Migas et al. / Optical Materials 17 (2001) 335±338
forthcoming paper with an estimation of the total energies corresponding to the dierent ternary con®gurations. Here we just point out that FeOsSi2 compounds should be studied experimentally. Acknowledgements We would like to thank Dr. Bruce Cook for the sample preparation and Glen Birdwell for performing of the AFM measurements. One of us (D.B.M.) acknowledges partial support from UNESCO-ROSTE.
References [1] V.E. Borisenko (Ed.), Semiconducting Silicides, Springer, Berlin, 2000. [2] C. Spinella, S. Coa, C. Bongiorno, S. Pannitteri, M.G. Grimaldi, Appl. Phys. Lett. 76 (2000) 173. [3] P. Blaha, K. Schwarz, J. Luitz, WIEN97, Vienna University of Technology 1997. (Improved and updated Unix version of the original copyrighted WIEN-code, which was published by P. Blaha, K. Schwarz, P. Sorantin, S.B. Trickey, in Comput. Phys. Commun. 59, 399, 1990). [4] V.N. Antonov, O. Jepsen, W. Henrion, M. Rebien, P. Stauss, H. Lange, Phys. Rev. B 57 (1998) 8934.