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Investigations of intrinsic strain and structural ordering in a-Si:H using synchrotron radiation diffraction
Thin Solid Films 501 (2006) 75 – 78 www.elsevier.com/locate/tsf
Investigations of intrinsic strain and structural ordering in a-Si:H using synchrotron radiation diffraction M. Ha¨rting a, D.T. Britton a,*, E. Minani a,b, T.P. Ntsoane a,c, M. Topic a, T. Thovhogi a, O.M. Osiele a,d, D. Knoesen e, S. Harindintwari e, F. Furlan f, C. Giles f,g a Department of Physics UCT, Rondebosch 7701, South Africa Department of Physics, Kigali Institute of Education, Kigali, Rwanda c iThemba LABS, PO Box 72, Faure, 7131, South Africa d Department of Physics, Federal University of Technology, Akure, Nigeria e Department of Physics, University of the Western Cape, Bellville 7530, South Africa f Laborato´rio Nacional de Luz Sı´ncrotron, Caixa Postal 6192, CEP 13084-971, Campinas-SP, Brazil g Instituto de Fı´sica Gleb Wataghin, Universidade Estadual de Campinas, C.P. 6165, CEP 13083-970 Campinas-SP, Brazil b
Available online 25 October 2005
Abstract The residual strain in a-Si:H layers has been determined directly using synchrotron radiation diffraction, at LNLS in Brazil, by two different methodologies. Using a method previously presented using laboratory X-ray sources, the height and length of side of the Si – Si4 tetrahedron are determined from variations in the diffraction angle of the first two amorphous peaks. In a more extensive calculation, the spatially dependent pair correlation function is calculated, allowing the separation of strain resulting from changes in the bond length and the bond angle. Two different layers, deposited by HW-CVD on glass substrates at growth temperatures of 300 and 500 -C, have been studied to investigate the effect of growth temperature on residual stress. D 2005 Elsevier B.V. All rights reserved. Keywords: Synchrotron radiation; Residual strain; a-Si:H; sin2W
1. Introduction Residual strains, which occur without any applied mechanical stress [1], in thin films are generally considered to consist of a superposition of thermal and intrinsic strains, e.g. [2]. The thermal contribution arises due to differences in thermal expansion coefficients of the layer and substrate materials, and can be calculated if the deposition temperature and the thermal expansivity data are known. If the appropriate elastic constants are known, this can then be expressed in terms of a thermal stress. In contrast, the formation of intrinsic stresses is more complex, depending on both the history of the sample and the deposition process itself. In the case of hot wire chemical vapour deposited (HWCVD) films, these intrinsic stresses are ascribed to the presence of structural * Corresponding author. Tel.: +27 21 650 3327; fax: +27 21 650 3343. E-mail address: [email protected] (D.T. Britton). 0040-6090/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2005.07.110
defects [3]. The reason for, in general, compressive intrinsic stresses in amorphous hydrogenated silicon (a-Si:H) films of ‘‘device-quality’’ is to date elusive. In [4], it is suggested that the processes of invasive incorporation of hydrogen, proposed in [5] for remote hydrogen plasma and rf glowdischarge deposition, are responsible. The most often employed methods for stress determination in a-Si:H films are based on the measurement of the curvature appearing due to the film deposition of substrate/ film couples. The measurement techniques vary from profilometry [4], to optical methods [6] and microscopy [7]. This curvature can easily be expressed as a uniform planar strain, and then related to the magnitude of the effective stress via Stoney’s equation. Although widely used for stress and strain determination in crystalline thin films [1], X-ray diffraction (XRD) is mainly applied to amorphous materials for investigation of the microstructure and local ordering [8]. In contrast to
76
M. Ha¨rting et al. / Thin Solid Films 501 (2006) 75 – 78
crystalline material, XRD from a-Si:H usually shows only two or three broad peaks. The first observable peak, at ˚ 1 (2h = 28- for Cu Ka scattering vector about 1.97 A radiation), corresponds to the (111) diffraction peak in crystalline silicon (c-Si) and has a relative full width at half maximum (fwhm) of about 50% of its position [9– 11]. The interatomic spacing d 1, corresponding to this scattering vector, is equivalent to the perpendicular height of the Si– Si4 tetrahedron, from which the amorphous network is constructed [11]. Similarly, the second diffuse peak, which is equivalent to the (220) reflection of c-Si, corresponds to a spacing d 2 equal to half of the length of side of the basic tetrahedron, which is also the second nearest neighbour distance. In liquids and amorphous solids, the structure is often described in terms of the radial distribution function (RDF) or radial density [12], which gives the relative probability of an atom being found at any given distance r from a particular atom. The use of the term ‘‘radial’’ in the nomenclature implies that the local structure is assumed to be isotropic. Experimentally, the RDF is obtained, as the Si –Si pair correlation function, by Fourier transformation of the scattered intensity (as a function of scattering vector) after correction for the atomic scattering factor [13]. The first two peaks in the pair correlation function correspond directly to the first and second nearest neighbour separations, r 1 and r 2, in the direction perpendicular to the scattering vector. High-resolution RDF investigation [14] related the structural relaxation of ion-implanted a-Si films on thermal annealing to the removal of point self-defects. In other studies [8], relaxation of the bond length and angle has been shown to accompany annealing of the free volume defect structure. Diffraction-based strain measurement relies on the use of the interatomic spacing in the material as an internal strain gauge [1]. Under a uniaxial or biaxial stress, Poisson contraction will lead to an angular asymmetry in the observed strain. Basically, if the material is stretched in the plane of the layer, it will be compressed in the direction perpendicular to it. At an intermediate tilt angle W, the observed strain will vary continuously between the two extreme values. For a biaxial strain, the observed dependence on the orientation is given by [15] eðU;WÞ ¼
1þm r11 cos2 U þ r12 sin2U þ r22 sin2 U sin2 W E m ð1Þ ½r11 þ r22 E
where U is the azimuthal angle, which for a single orientation may conveniently be defined as zero. In this case, r 11 is then the stress in plane of the layer. Young’s modulus, E, and the Poisson ratio, m, are generally replaced by experimentally determined X-ray elastic constants. When the elastic constants are not well known, it is more
appropriate to eliminate them and work directly in terms of strain. Combining with eij ¼
1þm m rij ½r11 þ r22 dij ; E E
ð2Þ
Eq. (1) yields (for U K 0) eðWÞ ¼ ðe11 e33 Þsin2 w þ e33 ;
ð3Þ
where ( 11 and ( 33 are the principle strains in the plane of the layer and in the normal direction respectively.
2. Experimental details Hydrogenated amorphous silicon layers were deposited on barium borosilicate glass substrates (Corning 7059) at different substrate temperatures using a commercial hot wire CVD system from MV Systems. Additional substrate material was treated to identical thermal conditions, with the exception that the silane was replaced by hydrogen in the deposition system. For the actual deposition, pure silane without hydrogen dilution was used. In all cases, a tantalum filament at 1600 -C was used with gas flow rate of 60 sccm and pressure of 40 Abar. The thickness of the deposited layers was estimated by UV absorption spectroscopy to be in the range of 1.3– 1.7 Am for both samples. The synchrotron radiation diffraction experiments were performed using the 3 axis XPD diffractometer on beamline 10B at the Laborato´rio Nacional de Luz Sı´ncrotron (LNLS) using 11 keV radiation, corresponding to a wavelength of ˚ . A full diffraction pattern, over a 2h range of 4– 1.125 A 129- in steps of 0.025-, was recorded for both the deposited layers and the treated substrates for tilt angles w of 0, 20, 40, 60, 80, and 85-. Under these conditions, the maximum ˚ 1. scattering vector is 10 A The diffraction pattern for the deposited layer was extracted by subtraction of the pattern for the equivalent substrate, measured at the same tilt, after weighting with the absorption in silicon. The mass absorption coefficient was calculated from parameters given in the International Tables for X-ray crystallography [16], but the effective layer thickness was allowed to vary between samples to account for slight variations in density. For each set of data, however, the thickness was held constant and was comparable to that obtained from UV absorption. These data have been analysed in two ways. Firstly, a direct determination of the positions of the first diffraction peaks, using a Gaussian fit to the data, without smoothing or any other manipulation, was used to determine the interatomic separations d 1 and d 2. These were then converted to strain, using the expected values for perfect crystalline silicon as reference values. Secondly, Si –Si pair correlation functions, for each tilt, were calculated using a simple numerical sine transform [13] directly from the substrate subtracted data. Correction for the atomic scattering factor has been applied using
M. Ha¨rting et al. / Thin Solid Films 501 (2006) 75 – 78
standard data for silicon [16]. Again no smoothing or other data manipulation has been applied, but a lower limit on the diffraction angle of 11- had to be imposed because of the interference of scattered radiation from the primary beam. The first two interatomic separations, r 1 and r 2, were then determined from the positions of the maxima and converted to strains, again referred to crystalline silicon.
3. Results and discussion Fig. 1 shows the variation in strain with sin2w, as determined from the positions of the first two diffraction peaks. For the layer grown at 300 -C, the negative slopes in both Fig. 1(a) and (b) indicate a compressive stress in the plane of the layer (according to Eq. (1)). However, neither curve exhibits a true linear dependence, indicating a nonbiaxial stress state and hence a gradient in the stress [17].
0.02
Table 1 Strain difference (( 11 – ( 33) determined for different interatomic spacings in a-Si:H for two different growth temperatures Spacing
Growth temperature
d 1 (tetrahedron height) d 2 (tetrahedron edge) r 1 (bond length)
300 -C
500 -C
1.34 T 0.10% 4.16 T 0.04% 1.08 T 0.48%
1.10 T 0.24% +2.88 T 0.34%
d 1 and d 2 are determined from the positions of the first and second amorphous diffraction peaks, and correspond to the height and edge of the Si – Si4 tetrahedron respectively. r 1 is the nearest neighbour separation obtained from the Si – Si pair correlation (orientation-dependent RDF).
Further work is being carried out with a more complete data set to investigate this in detail. In addition, the absolute values of (, and therefore of the intercept, which should give a direct measure of the normal strain ( 33, are very sensitive to systematic errors, including both alignment and the choice of reference value for the strain [1,15]. The following discussion will therefore focus primarily on the difference between the in-plane and normal strains (( 11 – ( 33) which is the slope of the curve with respect to sin 2W. For
(a)
0.01
bond strain [relative to c-Si]
strain [relative to c-Si]
(a)
77
0.00
o
300 C o
-0.01
500 C
0.0
0.2
0.4
0.6
0.8
0.005
0.000
-0.005
-0.010
1.0 -0.015
sin2Ψ
0.0
0.2
0.4
0.6
0.8
1.0
sin2Ψ -0.06
(b)
0.01
o
300 C
t
o
(b) s
f
2
0
-0.07
-0.08
-0.09
1
2
7
strain in r 2 (RDF) strain in r 2 (diffraction peak)
0.00
strain [relative to c-Si]
strain [relative to c-Si]
500 C
-0.01 -0.02 -0.06 -0.07 -0.08 -0.09
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
sin Ψ 2
Fig. 1. Variation of strain with sin w for a-Si:H deposited at 300 -C and 500 -C, determined from the diffraction patterns: (a) first diffraction peak, equivalent to the (111) reflection in c-Si and corresponding to the height of the Si – Si4 tetrahedron; (b) second diffraction peak, equivalent to the (220) reflection in c-Si and corresponding to the length of side of the Si – Si4 tetrahedron.
0.6
0.8
1.0
sin Ψ
2
2
2
Fig. 2. Variation of strain with sin w for a-Si:H deposited at 300 -C and 500 -C, determined from the pair correlation functions: (a) nearest neighbour separation, corresponding to the Si – Si bond length; (b) second nearest neighbour separation, corresponding to the length of side of the Si – Si4 tetrahedron, compared with the equivalent strain determined from the diffraction pattern. The solid lines are guides to the eye with the same slope.
78
M. Ha¨rting et al. / Thin Solid Films 501 (2006) 75 – 78
convenience, these are tabulated in Table 1 for all results presented here. The shape of the curve shown in Fig. 1(a) is similar to that previously determined in a similar sample using a laboratory X-ray source and a much more restricted range of scattering vector [18]. Neglecting the slight curvature, a fit to Eq. (3) yields a compressive strain difference of 1.34 T 0.10%. At the higher growth temperature, the nonlinearity of the curve increases, but there is an overall reduction in the gradient. Neglecting the initial apparently tensile behaviour at low tilts, the compressive strain difference is slightly relaxed to 1.10 T 0.24% by increasing the growth temperature to 500 -C. If, instead, the whole curve shown in Fig. 1(a) is assumed to be linear, the resulting average strain difference is almost fully relaxed for the higher temperature growth. In contrast, the orientational strain dependence for the edge of the Si– Si4 tetrahedron, 2d 2, changes dramatically from compressive to tensile on changing the deposition temperature from 300 to 500 -C. However, both curves have a high degree of nonlinearity, approaching similar negative constant values for high tilts, and indicate very high strains, ( 33, in the growth direction. As this interatomic spacing is mainly determined by the bond angle, this is indicative of a very high distortion in the bond angles compared to c-Si, which is intrinsic to the amorphous network. Beyond this, the strain differences calculated for this interatomic spacing, included in Table 1, only describe the strong orientational dependence at low W shown in Fig. 1(b). It is, however, readily apparent from a comparison of the values, that most of the strain in a-Si:H is carried by a scissor-like distortion of the bond angles, rather than uniaxial strain along Si– Si bond. Fig. 2 shows the strain calculated from the nearest and second neighbour separations for the material deposited at 300 -C. Also included in Fig. 2(b) is the strain derived from the second diffraction peak, which should give the same information as the second nearest neighbour distance. It can be seen that, although the absolute values are different, the form of the curve is similar. Furthermore, within uncertainties, the strain difference, given by the gradient, is the same, as can be seen by the two parallel lines drawn as guides to the eye in the figure. Similar results were also obtained for the sample grown at 500 -C. The bond strain, shown in Fig. 2(a), is clearly tensile and uniform. The magnitude of the strain difference 1.08 T 0.48% is significant, with most of the uncertainty arising from the outlying data point at W = 20-. The discrepancy with this point results from noise in the data affecting the Fourier transform, which has also prevented the consistent analysis (using the raw data) of the nearest neighbour separation in the sample grown t 500 -C.
4. Conclusions In this paper, it has been shown that diffraction-based methods can be successfully applied to the study of strain in amorphous materials, yielding information which cannot be gained by other methods. Using information on interatomic spacings obtained from both the direct diffraction pattern and the atomic pair correlations, a consistent picture of the strain state can be built up. If the appropriate elastic constants of the material are known, the relevant values of the residual stress can be determined. In the case of a-Si:H grown by HWCVD, we find that generally, the layer is under a compressive strain difference (( 11 –( 33) of the order of 1%. Most of this strain appears to be carried by distortion of the bond angles, as seen by comparison of nearest and second nearest neighbour strains. For a-Si:H grown at 300 -C, which is under a compressive residual stress, the bond strain is however under tension. This is consistent with the above supposition of strain in the bond angles dominating the overall strain.
References [1] I.C. Noyan, J.B. Cohen, Residual Stress Measurements by Diffraction and Interpretation, Springer, New York, 1987. [2] Y.C. Tsui, T.W. Clyne, Thin Solid Films 306 (1997) 23. [3] X.L. Peng, Y.C. Tsui, T.W. Clyne, Diamond Relat. Mater. 6 (1997) 1612. [4] B. Stannowski, R.E.I. Schropp, R.B. Wehrspohn, M.J. Powell, J. NonCryst. Solids 299 – 302 (2002) 1340. [5] K.S. Stevens, N.M. Johnson, J. Appl. Phys. 71 (1992) 2628. [6] M.M. de Lima Jr., R.G. Lacerda, J. Vilcarromero, F.C. Marques, J. Appl. Phys. 86 (1999) 4936. [7] E. Spanakis, E. Stratakis, P. Tzanetakis, H. Fritsche, S. Guha, J. Yang, J. Non-Cryst. Solids 299 – 302 (2002) 512. [8] M. Ha¨rting, D.T. Britton, R. Bucher, E. Minani, A. Hempel, M. Hempel, T.P. Ntsoane, C. Arendse, D. Knoesen, J. Non-Cryst. Solids 299 – 302 (2002) 103. [9] A.H. Mahan, J. Yang, S. Guha, D.L. Williamson, Phys. Rev., B 61 (2000) 1677. [10] A.H. Mahan, D.L. Williamson, T.E. Furtak, MRS Symp. Proc. 467 (1997) 657. [11] D.T. Britton, A. Hempel, M. Ha¨rting, G. Ko¨gel, P. Sperr, W. Triftsha¨user, C. Arendse, D. Knoesen, Phys. Rev., B 64 (2001) 075403. [12] A. Madan, M.P. Shaw, The Physics and Application of Amorphous Semiconductors, Academic Press, Inc., London, 1988. [13] R.W. James, Optical Principles of the Diffraction of X-rays, G. Bell & Sons, London, 1948, p. 477, (Ch. 9). [14] K. Laaziri, S. Kycia, S. Roorda, M. Chicione, J.L. Robertson, J. Wang, S.C. Moss, Phys. Rev., B 60 (1999) 1352. [15] A.D. Krawitz, Introduction to Diffraction in Materials Science and Engineering, John Wiley & Sons Inc, New York, 2001. [16] International Tables for X-ray Crystallography, Kluwer Academic Publishers, Dordrecht, 1989. [17] M. Ha¨rting, Acta Mater. 46 (1998) 1427. [18] M. Ha¨rting, S. Woodford, D. Knoesen, R. Bucher, D.T. Britton, Thin Solid Films 430 (2003) 153.
Investigations of intrinsic strain and structural ordering in a-Si:H using synchrotron radiation diffraction M. Ha¨rting a, D.T. Britton a,*, E. Minani a,b, T.P. Ntsoane a,c, M. Topic a, T. Thovhogi a, O.M. Osiele a,d, D. Knoesen e, S. Harindintwari e, F. Furlan f, C. Giles f,g a Department of Physics UCT, Rondebosch 7701, South Africa Department of Physics, Kigali Institute of Education, Kigali, Rwanda c iThemba LABS, PO Box 72, Faure, 7131, South Africa d Department of Physics, Federal University of Technology, Akure, Nigeria e Department of Physics, University of the Western Cape, Bellville 7530, South Africa f Laborato´rio Nacional de Luz Sı´ncrotron, Caixa Postal 6192, CEP 13084-971, Campinas-SP, Brazil g Instituto de Fı´sica Gleb Wataghin, Universidade Estadual de Campinas, C.P. 6165, CEP 13083-970 Campinas-SP, Brazil b
Available online 25 October 2005
Abstract The residual strain in a-Si:H layers has been determined directly using synchrotron radiation diffraction, at LNLS in Brazil, by two different methodologies. Using a method previously presented using laboratory X-ray sources, the height and length of side of the Si – Si4 tetrahedron are determined from variations in the diffraction angle of the first two amorphous peaks. In a more extensive calculation, the spatially dependent pair correlation function is calculated, allowing the separation of strain resulting from changes in the bond length and the bond angle. Two different layers, deposited by HW-CVD on glass substrates at growth temperatures of 300 and 500 -C, have been studied to investigate the effect of growth temperature on residual stress. D 2005 Elsevier B.V. All rights reserved. Keywords: Synchrotron radiation; Residual strain; a-Si:H; sin2W
1. Introduction Residual strains, which occur without any applied mechanical stress [1], in thin films are generally considered to consist of a superposition of thermal and intrinsic strains, e.g. [2]. The thermal contribution arises due to differences in thermal expansion coefficients of the layer and substrate materials, and can be calculated if the deposition temperature and the thermal expansivity data are known. If the appropriate elastic constants are known, this can then be expressed in terms of a thermal stress. In contrast, the formation of intrinsic stresses is more complex, depending on both the history of the sample and the deposition process itself. In the case of hot wire chemical vapour deposited (HWCVD) films, these intrinsic stresses are ascribed to the presence of structural * Corresponding author. Tel.: +27 21 650 3327; fax: +27 21 650 3343. E-mail address: [email protected] (D.T. Britton). 0040-6090/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2005.07.110
defects [3]. The reason for, in general, compressive intrinsic stresses in amorphous hydrogenated silicon (a-Si:H) films of ‘‘device-quality’’ is to date elusive. In [4], it is suggested that the processes of invasive incorporation of hydrogen, proposed in [5] for remote hydrogen plasma and rf glowdischarge deposition, are responsible. The most often employed methods for stress determination in a-Si:H films are based on the measurement of the curvature appearing due to the film deposition of substrate/ film couples. The measurement techniques vary from profilometry [4], to optical methods [6] and microscopy [7]. This curvature can easily be expressed as a uniform planar strain, and then related to the magnitude of the effective stress via Stoney’s equation. Although widely used for stress and strain determination in crystalline thin films [1], X-ray diffraction (XRD) is mainly applied to amorphous materials for investigation of the microstructure and local ordering [8]. In contrast to
76
M. Ha¨rting et al. / Thin Solid Films 501 (2006) 75 – 78
crystalline material, XRD from a-Si:H usually shows only two or three broad peaks. The first observable peak, at ˚ 1 (2h = 28- for Cu Ka scattering vector about 1.97 A radiation), corresponds to the (111) diffraction peak in crystalline silicon (c-Si) and has a relative full width at half maximum (fwhm) of about 50% of its position [9– 11]. The interatomic spacing d 1, corresponding to this scattering vector, is equivalent to the perpendicular height of the Si– Si4 tetrahedron, from which the amorphous network is constructed [11]. Similarly, the second diffuse peak, which is equivalent to the (220) reflection of c-Si, corresponds to a spacing d 2 equal to half of the length of side of the basic tetrahedron, which is also the second nearest neighbour distance. In liquids and amorphous solids, the structure is often described in terms of the radial distribution function (RDF) or radial density [12], which gives the relative probability of an atom being found at any given distance r from a particular atom. The use of the term ‘‘radial’’ in the nomenclature implies that the local structure is assumed to be isotropic. Experimentally, the RDF is obtained, as the Si –Si pair correlation function, by Fourier transformation of the scattered intensity (as a function of scattering vector) after correction for the atomic scattering factor [13]. The first two peaks in the pair correlation function correspond directly to the first and second nearest neighbour separations, r 1 and r 2, in the direction perpendicular to the scattering vector. High-resolution RDF investigation [14] related the structural relaxation of ion-implanted a-Si films on thermal annealing to the removal of point self-defects. In other studies [8], relaxation of the bond length and angle has been shown to accompany annealing of the free volume defect structure. Diffraction-based strain measurement relies on the use of the interatomic spacing in the material as an internal strain gauge [1]. Under a uniaxial or biaxial stress, Poisson contraction will lead to an angular asymmetry in the observed strain. Basically, if the material is stretched in the plane of the layer, it will be compressed in the direction perpendicular to it. At an intermediate tilt angle W, the observed strain will vary continuously between the two extreme values. For a biaxial strain, the observed dependence on the orientation is given by [15] eðU;WÞ ¼
1þm r11 cos2 U þ r12 sin2U þ r22 sin2 U sin2 W E m ð1Þ ½r11 þ r22 E
where U is the azimuthal angle, which for a single orientation may conveniently be defined as zero. In this case, r 11 is then the stress in plane of the layer. Young’s modulus, E, and the Poisson ratio, m, are generally replaced by experimentally determined X-ray elastic constants. When the elastic constants are not well known, it is more
appropriate to eliminate them and work directly in terms of strain. Combining with eij ¼
1þm m rij ½r11 þ r22 dij ; E E
ð2Þ
Eq. (1) yields (for U K 0) eðWÞ ¼ ðe11 e33 Þsin2 w þ e33 ;
ð3Þ
where ( 11 and ( 33 are the principle strains in the plane of the layer and in the normal direction respectively.
2. Experimental details Hydrogenated amorphous silicon layers were deposited on barium borosilicate glass substrates (Corning 7059) at different substrate temperatures using a commercial hot wire CVD system from MV Systems. Additional substrate material was treated to identical thermal conditions, with the exception that the silane was replaced by hydrogen in the deposition system. For the actual deposition, pure silane without hydrogen dilution was used. In all cases, a tantalum filament at 1600 -C was used with gas flow rate of 60 sccm and pressure of 40 Abar. The thickness of the deposited layers was estimated by UV absorption spectroscopy to be in the range of 1.3– 1.7 Am for both samples. The synchrotron radiation diffraction experiments were performed using the 3 axis XPD diffractometer on beamline 10B at the Laborato´rio Nacional de Luz Sı´ncrotron (LNLS) using 11 keV radiation, corresponding to a wavelength of ˚ . A full diffraction pattern, over a 2h range of 4– 1.125 A 129- in steps of 0.025-, was recorded for both the deposited layers and the treated substrates for tilt angles w of 0, 20, 40, 60, 80, and 85-. Under these conditions, the maximum ˚ 1. scattering vector is 10 A The diffraction pattern for the deposited layer was extracted by subtraction of the pattern for the equivalent substrate, measured at the same tilt, after weighting with the absorption in silicon. The mass absorption coefficient was calculated from parameters given in the International Tables for X-ray crystallography [16], but the effective layer thickness was allowed to vary between samples to account for slight variations in density. For each set of data, however, the thickness was held constant and was comparable to that obtained from UV absorption. These data have been analysed in two ways. Firstly, a direct determination of the positions of the first diffraction peaks, using a Gaussian fit to the data, without smoothing or any other manipulation, was used to determine the interatomic separations d 1 and d 2. These were then converted to strain, using the expected values for perfect crystalline silicon as reference values. Secondly, Si –Si pair correlation functions, for each tilt, were calculated using a simple numerical sine transform [13] directly from the substrate subtracted data. Correction for the atomic scattering factor has been applied using
M. Ha¨rting et al. / Thin Solid Films 501 (2006) 75 – 78
standard data for silicon [16]. Again no smoothing or other data manipulation has been applied, but a lower limit on the diffraction angle of 11- had to be imposed because of the interference of scattered radiation from the primary beam. The first two interatomic separations, r 1 and r 2, were then determined from the positions of the maxima and converted to strains, again referred to crystalline silicon.
3. Results and discussion Fig. 1 shows the variation in strain with sin2w, as determined from the positions of the first two diffraction peaks. For the layer grown at 300 -C, the negative slopes in both Fig. 1(a) and (b) indicate a compressive stress in the plane of the layer (according to Eq. (1)). However, neither curve exhibits a true linear dependence, indicating a nonbiaxial stress state and hence a gradient in the stress [17].
0.02
Table 1 Strain difference (( 11 – ( 33) determined for different interatomic spacings in a-Si:H for two different growth temperatures Spacing
Growth temperature
d 1 (tetrahedron height) d 2 (tetrahedron edge) r 1 (bond length)
300 -C
500 -C
1.34 T 0.10% 4.16 T 0.04% 1.08 T 0.48%
1.10 T 0.24% +2.88 T 0.34%
d 1 and d 2 are determined from the positions of the first and second amorphous diffraction peaks, and correspond to the height and edge of the Si – Si4 tetrahedron respectively. r 1 is the nearest neighbour separation obtained from the Si – Si pair correlation (orientation-dependent RDF).
Further work is being carried out with a more complete data set to investigate this in detail. In addition, the absolute values of (, and therefore of the intercept, which should give a direct measure of the normal strain ( 33, are very sensitive to systematic errors, including both alignment and the choice of reference value for the strain [1,15]. The following discussion will therefore focus primarily on the difference between the in-plane and normal strains (( 11 – ( 33) which is the slope of the curve with respect to sin 2W. For
(a)
0.01
bond strain [relative to c-Si]
strain [relative to c-Si]
(a)
77
0.00
o
300 C o
-0.01
500 C
0.0
0.2
0.4
0.6
0.8
0.005
0.000
-0.005
-0.010
1.0 -0.015
sin2Ψ
0.0
0.2
0.4
0.6
0.8
1.0
sin2Ψ -0.06
(b)
0.01
o
300 C
t
o
(b) s
f
2
0
-0.07
-0.08
-0.09
1
2
7
strain in r 2 (RDF) strain in r 2 (diffraction peak)
0.00
strain [relative to c-Si]
strain [relative to c-Si]
500 C
-0.01 -0.02 -0.06 -0.07 -0.08 -0.09
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
sin Ψ 2
Fig. 1. Variation of strain with sin w for a-Si:H deposited at 300 -C and 500 -C, determined from the diffraction patterns: (a) first diffraction peak, equivalent to the (111) reflection in c-Si and corresponding to the height of the Si – Si4 tetrahedron; (b) second diffraction peak, equivalent to the (220) reflection in c-Si and corresponding to the length of side of the Si – Si4 tetrahedron.
0.6
0.8
1.0
sin Ψ
2
2
2
Fig. 2. Variation of strain with sin w for a-Si:H deposited at 300 -C and 500 -C, determined from the pair correlation functions: (a) nearest neighbour separation, corresponding to the Si – Si bond length; (b) second nearest neighbour separation, corresponding to the length of side of the Si – Si4 tetrahedron, compared with the equivalent strain determined from the diffraction pattern. The solid lines are guides to the eye with the same slope.
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M. Ha¨rting et al. / Thin Solid Films 501 (2006) 75 – 78
convenience, these are tabulated in Table 1 for all results presented here. The shape of the curve shown in Fig. 1(a) is similar to that previously determined in a similar sample using a laboratory X-ray source and a much more restricted range of scattering vector [18]. Neglecting the slight curvature, a fit to Eq. (3) yields a compressive strain difference of 1.34 T 0.10%. At the higher growth temperature, the nonlinearity of the curve increases, but there is an overall reduction in the gradient. Neglecting the initial apparently tensile behaviour at low tilts, the compressive strain difference is slightly relaxed to 1.10 T 0.24% by increasing the growth temperature to 500 -C. If, instead, the whole curve shown in Fig. 1(a) is assumed to be linear, the resulting average strain difference is almost fully relaxed for the higher temperature growth. In contrast, the orientational strain dependence for the edge of the Si– Si4 tetrahedron, 2d 2, changes dramatically from compressive to tensile on changing the deposition temperature from 300 to 500 -C. However, both curves have a high degree of nonlinearity, approaching similar negative constant values for high tilts, and indicate very high strains, ( 33, in the growth direction. As this interatomic spacing is mainly determined by the bond angle, this is indicative of a very high distortion in the bond angles compared to c-Si, which is intrinsic to the amorphous network. Beyond this, the strain differences calculated for this interatomic spacing, included in Table 1, only describe the strong orientational dependence at low W shown in Fig. 1(b). It is, however, readily apparent from a comparison of the values, that most of the strain in a-Si:H is carried by a scissor-like distortion of the bond angles, rather than uniaxial strain along Si– Si bond. Fig. 2 shows the strain calculated from the nearest and second neighbour separations for the material deposited at 300 -C. Also included in Fig. 2(b) is the strain derived from the second diffraction peak, which should give the same information as the second nearest neighbour distance. It can be seen that, although the absolute values are different, the form of the curve is similar. Furthermore, within uncertainties, the strain difference, given by the gradient, is the same, as can be seen by the two parallel lines drawn as guides to the eye in the figure. Similar results were also obtained for the sample grown at 500 -C. The bond strain, shown in Fig. 2(a), is clearly tensile and uniform. The magnitude of the strain difference 1.08 T 0.48% is significant, with most of the uncertainty arising from the outlying data point at W = 20-. The discrepancy with this point results from noise in the data affecting the Fourier transform, which has also prevented the consistent analysis (using the raw data) of the nearest neighbour separation in the sample grown t 500 -C.
4. Conclusions In this paper, it has been shown that diffraction-based methods can be successfully applied to the study of strain in amorphous materials, yielding information which cannot be gained by other methods. Using information on interatomic spacings obtained from both the direct diffraction pattern and the atomic pair correlations, a consistent picture of the strain state can be built up. If the appropriate elastic constants of the material are known, the relevant values of the residual stress can be determined. In the case of a-Si:H grown by HWCVD, we find that generally, the layer is under a compressive strain difference (( 11 –( 33) of the order of 1%. Most of this strain appears to be carried by distortion of the bond angles, as seen by comparison of nearest and second nearest neighbour strains. For a-Si:H grown at 300 -C, which is under a compressive residual stress, the bond strain is however under tension. This is consistent with the above supposition of strain in the bond angles dominating the overall strain.
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