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Dielectric function of disorder in high-fluence helium-implanted silicon
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 253 (2006) 192–195 www.elsevier.com/locate/nimb
Dielectric function of disorder in high-fluence helium-implanted silicon P. Petrik
b
a,*
, M. Fried a, T. Lohner a, N.Q. Kha´nh a, P. Basa a, O. Polga´r a, C. Major a, J. Gyulai a, F. Cayrel b, D. Alquier b
a Research Institute for Technical Physics and Materials Science, H-1525 Budapest, P.O. Box 49, Hungary University of Tours, Laboratoire de Microe´lectronique de Puissance, 16, rue Pierre et Marie Curie, B.P. 7155, F37071 Tours Cedex, France
Available online 7 November 2006
Abstract Dielectric function of disorder in single-crystalline silicon (c-Si) implanted by He with energy of 40 keV and fluences from 1 · 1016 to 1 · 1017 cm2 were determined around the E1 and E2 critical points (CPs) by spectroscopic ellipsometry. The implanted material was modeled by an effective medium composition of c-Si and damaged Si. The dielectric function of damaged Si was calculated using the model dielectric function of Adachi to fit the E1 and E2 CP parameters of the MDF. The penetration depth of light in the photon energy range of 3–5 eV is less than 100 nm, which allows a simple layer structure of (surface oxide)/(surface amorphous layer)/(c-Si + damaged Si as a substrate). The oscillator energies and strengths decrease, while the broadening parameters increase with increasing fluence. Rutherford backscattering spectrometry was used for cross-checking of the surface disorder. 2006 Elsevier B.V. All rights reserved. PACS: 78.66.w; 78.66.Db; 78.66.Fd; 78.68.+m; 61.72.Vv; 77.22.Ch; 78.20.Ci
1. Introduction Ion implantation-caused disorder largely influences the critical point (CP) structure, and therefore also the complex dielectric function of semiconductors [1–3]. Since the E0, E1 and E2 direct interband transitions of Si are located in the visible–near UV photon energy range, structural changes can be sensitively measured by a standard spectroscopic ellipsometer setup [4]. Damage profiles can be measured routinely assuming that the damaged region is a composition of single-crystalline and ion implantationamorphized Si [5]. The damage profiles can be parametrized using a Gaussian function [6], an error function [7], or a modified Gaussian with dynamically changing sublayer thicknesses [8]. Ellipsometry can be used to measure damage profiles even in polycrystalline silicon, where Rutherford backscattering spectrometry (RBS) can not be used due to the lack of quasi-orientation of the grains [9]. The
*
Corresponding author. Tel.: +36 1 3922222; fax: +36 1 3922226. E-mail address: [email protected] (P. Petrik).
0168-583X/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.10.054
dielectric function can be parametrized to investigate changes of CP structure and long range order in the Si crystal [2,10]. In the present study the CP features consisting mainly of point defects were characterized using parametrization of the model dielectric function (MDF) of Adachi [11]. 2. Experimental details (1 1 1) p-type Czochralski c-Si samples were implanted with 40-keV He+ at room temperature using fluences of 1 · 1016 to 1 · 1017 cm2. The ellipsometric measurements were performed in the photon energy range of 1.3–5.0 eV at angles of incidences around the Brewster angle of 75. The depth distribution of disordered atoms were measured by Rutherford backscattering spectrometry and channeling techniques (RBS/C). The backscattered He+ ions were detected using an ORTEC surface barrier detector mounted in Cornell geometry at scattering angle of 165. To increase the depth resolution at the surface, a glancing detection angle of 97 was also used. The RBS/ C spectra were evaluated using the software RBX [13].
P. Petrik et al. / Nucl. Instr. and Meth. in Phys. Res. B 253 (2006) 192–195
193
Fig. 1. RBS/C profiles from 165 scattering angle (resolution of 15 nm) for different fluences showing the depth-distribution of disorder.
100 40 keV He+ <111 >Si (x1016 /cm2)
Damage (%)
80
10 8 4 2 1
60
40
Fig. 3. Pseudo-dielectric function for different fluences together with the cSi and ia-Si references.
20
0 0
100
200
300
Depth (nm)
Fig. 2. Surface-sensitive RBS/C spectra with a resolution of 5 nm, measured at a scattering angle of 97.
The spectra at the scattering angle of 165 are shown in Fig. 1. The damage peak is located at a depth of about 300 nm. The relative damage reaches 1 for fluences above 4 · 1016 cm2. The relative damage increases towards the surface for depths lower than 50 nm caused by diffusion of point defects to the surface. High resolution spectra (Fig. 2) at scattering angle of 97 reveal surface amorphous layers [14,15] with thicknesses of 0.0, 0.0, 1.2, 2.8 and 3.2 nm (error of 0.3 nm) for fluences of 1 · 1016, 2 · 1016, 4 · 1016, 8 · 1016 and 10 · 1016 cm2, respectively. The thickness of the surface amorphous layer was calculated by subtracting the surface peak of the non-implanted sample, and assuming an amorphous layer with density of c-Si (5 · 1022 cm3). 3. Optical models In Fig. 3 the pseudo-dielectric function is plotted for the different fluences compared with c-Si and implantation-
amorphized (ia-Si) references. The E2 critical point (4.2 eV) feature vanishes almost completely for high fluences, while the strength of the E1 critical point changes only in a small extent, with an increasing broadening. The change of the E2 feature is similar to that found for ion implantation-amorphized and annealed silicon [10]. The penetration depth is less than 100 nm for photon energies above 2.5 eV (see bottom graph of Fig. 3). Compared with Fig. 1 it is obvious that the E1 and E2 features of Fig. 3 are influenced only by point defects near to the surface (below 100 nm). The buried damage (depth from 150 to 450 nm, see Fig. 1) is visible only for photon energies below 2.5 eV (see the small oscillations at the red end of the e1 and e2 spectra). Above photon energies of 2.5 eV the buried damage can be disregarded in the optical model, because of the limited penetration depth (<100 nm) of the light. In this range, an optical model of (surface oxide)/(surface amorphous layer)/(substrate of disordered c-Si) was used. For the dielectric function of the surface amorphous layer, the reference data for ion implantation-amorphized Si (ia-Si) were taken from [6]. The disordered region consisting mainly of point defects was assumed to be a mixture of ordered (c-Si) and disordered (MDF) regions. The effective dielectric function of the composite material was calculated by the Bruggeman effective medium approximation using the dielectric functions of the components.
194
P. Petrik et al. / Nucl. Instr. and Meth. in Phys. Res. B 253 (2006) 192–195
ðEÞ ¼ F v2 2m ln
1 v2cl ; 1 v22m
ð4Þ
with E þ iC ; E2 E þ iC vcl ¼ ; Ecl v2m ¼
Fig. 4. CP contributions of the MDF model fitted to c-Si.
The dielectric function of the disordered component was described by the MDF [10,11]. The two-dimensional CP at 3.4 eV (E1, curve 1 in Fig. 4) is described by 2 ðEÞ ¼ Bv2 1 lnð1 v1 Þ;
ð1Þ
with v1 ¼
where F and C are the strength and broadening parameters, Ecl is a low-energy cutoff assumed to occur at E1. The E 0 0 (curve 5 in Fig. 4) and E 0 1 (curve 6 in Fig. 4) CPs are not strong compared to the previous ones, and they are simply characterized by the DHO. The measured and the fitted spectra, as well as the fitted values of the strongest CP contributions are shown in Figs. 5 and 6, respectively. The thickness of the surface amorphous layer increases from 0 to 4.3 nm with increasing fluence, in good agreement with the RBS/C results of 0 to 3.2 nm, as written in Section 2. The volume fraction of disordered regions decreases from 0.97 to 0.76 with increasing fluence. This is because the MDF model can describe the other EMA component, c-Si. For low fluences the layer consists solely of c-Si, for which the MDF component is preferred by the fit. The oscillator energies and strengths decrease, while the broadening parameters increase with increasing fluence, in agreement with results of [10].
E þ iC ; E1
where B1 and C are the strength and broadening parameters, respectively. The contribution of the 2D-M0 excitonic transition is described by a Lorentzian lineshape (curve 2 in Fig. 4): ðEÞ ¼
1 X
1
B1x 3
n¼1
2
ð2n 1Þ E1 ½G=ð2n 1Þ E iC
;
ð2Þ
where B1x is the exciton strength parameter and G is the 2D exciton Rydberg energy. Since the strength of the excited states (n P 2) are much weaker than that of the ground state (n = 1), we take into account only the n = 1 state. The value of G is also assumed to be zero. The E2 CP at 4.3 eV is described by a combination of a damped harmonic oscillator (DHO) and a two-dimensional CP. The DHO (curve 3 in Fig. 4) can be written as ðEÞ ¼
C ð1
v22 Þ
iv2 c
;
ð3Þ
with v2 ¼
E ; E2
where C and c are the nondimensional strength and broadening parameters, respectively. The contribution of the two-dimensional CP (curve 4 in Fig. 4) can be written as
Fig. 5. Measured and fitted pseudo-dielectric functions.
P. Petrik et al. / Nucl. Instr. and Meth. in Phys. Res. B 253 (2006) 192–195
195
parameters and the small changes in the pseudo-dielectric function under photon energies of 2.5 eV (see Fig. 3). 4. Conclusions Near-surface disorder caused mainly by point defects was described by the MDF. The oscillator energies and strengths decrease, while the broadening parameters increase with increasing fluence, similarly to that found for heavier ions [10]. The surface amorphous layer measured by SE increases from 0 to 4.3 nm, in good agreement with RBS/C results. Acknowledgements Support from the Hungarian Scientific Research Fund (OTKA Grant Nos. K61725 and T047011) and from the European Commission in the frame of FP6 project SEMINANO, No. 505285, is greatly appreciated. References
Fig. 6. Fitted values of the surface oxide (dox), the surface amorphous layer (dia-Si), the volume fraction of disordered Si described by MDF (fMDF), and the strongest CP parameters.
An attempt was made to model the buried disorder with a Gaussian distribution [12] using sublayers with components of either c-Si + ia-Si or c-Si + MDF. No reasonable fit was found, mainly because of the large number of
[1] D.E. Aspnes, S.M. Kelso, C.G. Olson, D.W. Lynch, Phys. Rev. Lett. 48 (1982) 1863. [2] G.F. Feng, R. Zallen, Phys. Rev. B 40 (1989) 1064. [3] P.J. McMarr, K. Vedam, J. Narayan, J. Appl. Phys. 59 (1986) 694. [4] M. Fried, T. Lohner, P. Petrik, in: H.S. Nalwa (Ed.), Handbook of Surfaces and Interfaces of Materials, Solid Thin Films and Layers, Vol. 4, Academic, San Diego, CA, 2001, p. 335 (Chapter 6). [5] J. Vanhellemont, Ph. Roussel, H.E. Maes, Nucl. Instr. and Meth. B 55 (1991) 183. [6] M. Fried, T. Lohner, W.A.M. Aarnink, L.J. Hanekamp, A. van Silfhout, J. Appl. Phys. 71 (1992) 5260. [7] W. Fukarek, J.R. Kaschny, J. Appl. Phys. 86 (1999) 4160. [8] P. Petrik, O. Polga´r, M. Fried, T. Lohner, N.Q. Kha´nh, J. Gyulai, J. Appl. Phys. 93 (2003) 1987. [9] P. Petrik, T. Lohner, M. Fried, N.Q. Kha´nh, O. Polga´r, J. Gyulai, Nucl. Instr. and Meth. B 147 (1999) 84. [10] S. Adachi, H. Mori, J. Appl. Phys. 93 (2003) 115. [11] S. Adachi, Phys. Rev. B 38 (1988) 12966. [12] M. Fried, T. Lohner, W.A.M. Aarnink, L.J. Hanekamp, A. van Silfhout, J. Appl. Phys. 71 (1992) 2835. [13] E. Ko´tai, Nucl. Instr. and Meth. B 85 (1994) 588. [14] W. Fukarek, W. Mo¨ller, N. Hatzopoulos, D.G. Armour, J.A. van den Berg, Nucl. Instr. and Meth. B 127/128 (1997) 879. [15] T. Lohner, M. Fried, N.Q. Kha´nh, P. Petrik, H. Wormeester, M.A. El-Sherbiny, Nucl. Instr. and Meth. B 147 (1999) 90.
Nuclear Instruments and Methods in Physics Research B 253 (2006) 192–195 www.elsevier.com/locate/nimb
Dielectric function of disorder in high-fluence helium-implanted silicon P. Petrik
b
a,*
, M. Fried a, T. Lohner a, N.Q. Kha´nh a, P. Basa a, O. Polga´r a, C. Major a, J. Gyulai a, F. Cayrel b, D. Alquier b
a Research Institute for Technical Physics and Materials Science, H-1525 Budapest, P.O. Box 49, Hungary University of Tours, Laboratoire de Microe´lectronique de Puissance, 16, rue Pierre et Marie Curie, B.P. 7155, F37071 Tours Cedex, France
Available online 7 November 2006
Abstract Dielectric function of disorder in single-crystalline silicon (c-Si) implanted by He with energy of 40 keV and fluences from 1 · 1016 to 1 · 1017 cm2 were determined around the E1 and E2 critical points (CPs) by spectroscopic ellipsometry. The implanted material was modeled by an effective medium composition of c-Si and damaged Si. The dielectric function of damaged Si was calculated using the model dielectric function of Adachi to fit the E1 and E2 CP parameters of the MDF. The penetration depth of light in the photon energy range of 3–5 eV is less than 100 nm, which allows a simple layer structure of (surface oxide)/(surface amorphous layer)/(c-Si + damaged Si as a substrate). The oscillator energies and strengths decrease, while the broadening parameters increase with increasing fluence. Rutherford backscattering spectrometry was used for cross-checking of the surface disorder. 2006 Elsevier B.V. All rights reserved. PACS: 78.66.w; 78.66.Db; 78.66.Fd; 78.68.+m; 61.72.Vv; 77.22.Ch; 78.20.Ci
1. Introduction Ion implantation-caused disorder largely influences the critical point (CP) structure, and therefore also the complex dielectric function of semiconductors [1–3]. Since the E0, E1 and E2 direct interband transitions of Si are located in the visible–near UV photon energy range, structural changes can be sensitively measured by a standard spectroscopic ellipsometer setup [4]. Damage profiles can be measured routinely assuming that the damaged region is a composition of single-crystalline and ion implantationamorphized Si [5]. The damage profiles can be parametrized using a Gaussian function [6], an error function [7], or a modified Gaussian with dynamically changing sublayer thicknesses [8]. Ellipsometry can be used to measure damage profiles even in polycrystalline silicon, where Rutherford backscattering spectrometry (RBS) can not be used due to the lack of quasi-orientation of the grains [9]. The
*
Corresponding author. Tel.: +36 1 3922222; fax: +36 1 3922226. E-mail address: [email protected] (P. Petrik).
0168-583X/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.10.054
dielectric function can be parametrized to investigate changes of CP structure and long range order in the Si crystal [2,10]. In the present study the CP features consisting mainly of point defects were characterized using parametrization of the model dielectric function (MDF) of Adachi [11]. 2. Experimental details (1 1 1) p-type Czochralski c-Si samples were implanted with 40-keV He+ at room temperature using fluences of 1 · 1016 to 1 · 1017 cm2. The ellipsometric measurements were performed in the photon energy range of 1.3–5.0 eV at angles of incidences around the Brewster angle of 75. The depth distribution of disordered atoms were measured by Rutherford backscattering spectrometry and channeling techniques (RBS/C). The backscattered He+ ions were detected using an ORTEC surface barrier detector mounted in Cornell geometry at scattering angle of 165. To increase the depth resolution at the surface, a glancing detection angle of 97 was also used. The RBS/ C spectra were evaluated using the software RBX [13].
P. Petrik et al. / Nucl. Instr. and Meth. in Phys. Res. B 253 (2006) 192–195
193
Fig. 1. RBS/C profiles from 165 scattering angle (resolution of 15 nm) for different fluences showing the depth-distribution of disorder.
100 40 keV He+ <111 >Si (x1016 /cm2)
Damage (%)
80
10 8 4 2 1
60
40
Fig. 3. Pseudo-dielectric function for different fluences together with the cSi and ia-Si references.
20
0 0
100
200
300
Depth (nm)
Fig. 2. Surface-sensitive RBS/C spectra with a resolution of 5 nm, measured at a scattering angle of 97.
The spectra at the scattering angle of 165 are shown in Fig. 1. The damage peak is located at a depth of about 300 nm. The relative damage reaches 1 for fluences above 4 · 1016 cm2. The relative damage increases towards the surface for depths lower than 50 nm caused by diffusion of point defects to the surface. High resolution spectra (Fig. 2) at scattering angle of 97 reveal surface amorphous layers [14,15] with thicknesses of 0.0, 0.0, 1.2, 2.8 and 3.2 nm (error of 0.3 nm) for fluences of 1 · 1016, 2 · 1016, 4 · 1016, 8 · 1016 and 10 · 1016 cm2, respectively. The thickness of the surface amorphous layer was calculated by subtracting the surface peak of the non-implanted sample, and assuming an amorphous layer with density of c-Si (5 · 1022 cm3). 3. Optical models In Fig. 3 the pseudo-dielectric function is plotted for the different fluences compared with c-Si and implantation-
amorphized (ia-Si) references. The E2 critical point (4.2 eV) feature vanishes almost completely for high fluences, while the strength of the E1 critical point changes only in a small extent, with an increasing broadening. The change of the E2 feature is similar to that found for ion implantation-amorphized and annealed silicon [10]. The penetration depth is less than 100 nm for photon energies above 2.5 eV (see bottom graph of Fig. 3). Compared with Fig. 1 it is obvious that the E1 and E2 features of Fig. 3 are influenced only by point defects near to the surface (below 100 nm). The buried damage (depth from 150 to 450 nm, see Fig. 1) is visible only for photon energies below 2.5 eV (see the small oscillations at the red end of the e1 and e2 spectra). Above photon energies of 2.5 eV the buried damage can be disregarded in the optical model, because of the limited penetration depth (<100 nm) of the light. In this range, an optical model of (surface oxide)/(surface amorphous layer)/(substrate of disordered c-Si) was used. For the dielectric function of the surface amorphous layer, the reference data for ion implantation-amorphized Si (ia-Si) were taken from [6]. The disordered region consisting mainly of point defects was assumed to be a mixture of ordered (c-Si) and disordered (MDF) regions. The effective dielectric function of the composite material was calculated by the Bruggeman effective medium approximation using the dielectric functions of the components.
194
P. Petrik et al. / Nucl. Instr. and Meth. in Phys. Res. B 253 (2006) 192–195
ðEÞ ¼ F v2 2m ln
1 v2cl ; 1 v22m
ð4Þ
with E þ iC ; E2 E þ iC vcl ¼ ; Ecl v2m ¼
Fig. 4. CP contributions of the MDF model fitted to c-Si.
The dielectric function of the disordered component was described by the MDF [10,11]. The two-dimensional CP at 3.4 eV (E1, curve 1 in Fig. 4) is described by 2 ðEÞ ¼ Bv2 1 lnð1 v1 Þ;
ð1Þ
with v1 ¼
where F and C are the strength and broadening parameters, Ecl is a low-energy cutoff assumed to occur at E1. The E 0 0 (curve 5 in Fig. 4) and E 0 1 (curve 6 in Fig. 4) CPs are not strong compared to the previous ones, and they are simply characterized by the DHO. The measured and the fitted spectra, as well as the fitted values of the strongest CP contributions are shown in Figs. 5 and 6, respectively. The thickness of the surface amorphous layer increases from 0 to 4.3 nm with increasing fluence, in good agreement with the RBS/C results of 0 to 3.2 nm, as written in Section 2. The volume fraction of disordered regions decreases from 0.97 to 0.76 with increasing fluence. This is because the MDF model can describe the other EMA component, c-Si. For low fluences the layer consists solely of c-Si, for which the MDF component is preferred by the fit. The oscillator energies and strengths decrease, while the broadening parameters increase with increasing fluence, in agreement with results of [10].
E þ iC ; E1
where B1 and C are the strength and broadening parameters, respectively. The contribution of the 2D-M0 excitonic transition is described by a Lorentzian lineshape (curve 2 in Fig. 4): ðEÞ ¼
1 X
1
B1x 3
n¼1
2
ð2n 1Þ E1 ½G=ð2n 1Þ E iC
;
ð2Þ
where B1x is the exciton strength parameter and G is the 2D exciton Rydberg energy. Since the strength of the excited states (n P 2) are much weaker than that of the ground state (n = 1), we take into account only the n = 1 state. The value of G is also assumed to be zero. The E2 CP at 4.3 eV is described by a combination of a damped harmonic oscillator (DHO) and a two-dimensional CP. The DHO (curve 3 in Fig. 4) can be written as ðEÞ ¼
C ð1
v22 Þ
iv2 c
;
ð3Þ
with v2 ¼
E ; E2
where C and c are the nondimensional strength and broadening parameters, respectively. The contribution of the two-dimensional CP (curve 4 in Fig. 4) can be written as
Fig. 5. Measured and fitted pseudo-dielectric functions.
P. Petrik et al. / Nucl. Instr. and Meth. in Phys. Res. B 253 (2006) 192–195
195
parameters and the small changes in the pseudo-dielectric function under photon energies of 2.5 eV (see Fig. 3). 4. Conclusions Near-surface disorder caused mainly by point defects was described by the MDF. The oscillator energies and strengths decrease, while the broadening parameters increase with increasing fluence, similarly to that found for heavier ions [10]. The surface amorphous layer measured by SE increases from 0 to 4.3 nm, in good agreement with RBS/C results. Acknowledgements Support from the Hungarian Scientific Research Fund (OTKA Grant Nos. K61725 and T047011) and from the European Commission in the frame of FP6 project SEMINANO, No. 505285, is greatly appreciated. References
Fig. 6. Fitted values of the surface oxide (dox), the surface amorphous layer (dia-Si), the volume fraction of disordered Si described by MDF (fMDF), and the strongest CP parameters.
An attempt was made to model the buried disorder with a Gaussian distribution [12] using sublayers with components of either c-Si + ia-Si or c-Si + MDF. No reasonable fit was found, mainly because of the large number of
[1] D.E. Aspnes, S.M. Kelso, C.G. Olson, D.W. Lynch, Phys. Rev. Lett. 48 (1982) 1863. [2] G.F. Feng, R. Zallen, Phys. Rev. B 40 (1989) 1064. [3] P.J. McMarr, K. Vedam, J. Narayan, J. Appl. Phys. 59 (1986) 694. [4] M. Fried, T. Lohner, P. Petrik, in: H.S. Nalwa (Ed.), Handbook of Surfaces and Interfaces of Materials, Solid Thin Films and Layers, Vol. 4, Academic, San Diego, CA, 2001, p. 335 (Chapter 6). [5] J. Vanhellemont, Ph. Roussel, H.E. Maes, Nucl. Instr. and Meth. B 55 (1991) 183. [6] M. Fried, T. Lohner, W.A.M. Aarnink, L.J. Hanekamp, A. van Silfhout, J. Appl. Phys. 71 (1992) 5260. [7] W. Fukarek, J.R. Kaschny, J. Appl. Phys. 86 (1999) 4160. [8] P. Petrik, O. Polga´r, M. Fried, T. Lohner, N.Q. Kha´nh, J. Gyulai, J. Appl. Phys. 93 (2003) 1987. [9] P. Petrik, T. Lohner, M. Fried, N.Q. Kha´nh, O. Polga´r, J. Gyulai, Nucl. Instr. and Meth. B 147 (1999) 84. [10] S. Adachi, H. Mori, J. Appl. Phys. 93 (2003) 115. [11] S. Adachi, Phys. Rev. B 38 (1988) 12966. [12] M. Fried, T. Lohner, W.A.M. Aarnink, L.J. Hanekamp, A. van Silfhout, J. Appl. Phys. 71 (1992) 2835. [13] E. Ko´tai, Nucl. Instr. and Meth. B 85 (1994) 588. [14] W. Fukarek, W. Mo¨ller, N. Hatzopoulos, D.G. Armour, J.A. van den Berg, Nucl. Instr. and Meth. B 127/128 (1997) 879. [15] T. Lohner, M. Fried, N.Q. Kha´nh, P. Petrik, H. Wormeester, M.A. El-Sherbiny, Nucl. Instr. and Meth. B 147 (1999) 90.