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Monte-Carlo simulations of 2-MeV α-particle channeling in Si1−xSnx alloy
Nuclear Instruments and Methods in Physics Research B 164±165 (2000) 103±107
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Monte-Carlo simulations of 2-MeV a-particle channeling in Si1ÿx Snx alloy E.V. Monakhov a
a,*
, M.F. Fyhn b, A. Nylandsted Larsen
b
Royal Institute of Technology, Solid State Electronics, Electrum 229, Kista-Stockholm, S-16440, Sweden b Institute of Physics and Astronomy, University of Aarhus, DK-8000, Aarhus C, Denmark
Abstract Monte-Carlo simulations of 2-MeV a-particle channeling in Si1ÿx Snx alloys with 0 6 x 6 1 have been performed. The simulations are compared with measured channeling-angular scans for strained Si0:95 Sn0:05 layers grown by molecular beam epitaxy (MBE). Agreement between simulated and measured angular scans can only be achieved if we assume a deviation of the crystal structure from the ideal one. This deviation can be attributed to a mosaic structure in the ®lms and to an atomic-scale distortion of the crystal lattice due to an expected dierence in the bond lengths between the Si± Si, Si±Sn and Sn±Sn atoms (such a dierence in bond lengths has been observed in the epitaxial Si1ÿx Gex system). The contributions from both of these imperfections are estimated and discussed. Ó 2000 Elsevier Science B.V. All rights reserved.
1. Introduction As a group-IV semiconductor alloy with variable biaxial strain, epitaxially grown Si1ÿx Snx alloy layers have attracted interest within the last few years [1±4]. Also the interest is due to theoretical predictions that, at a considerable content of Sn, this material might have a direct band gap [5]. Until now, however, the successful synthesis of epitaxial Si1ÿx Snx has only been reported for Sn concentrations smaller than about 5% grown on (0 0 1)-oriented Si [1]. Recently, we have reported on Monte-Carlo channeling simulations in relaxed Si1ÿx Gex ®lms [6]. It was found that the evolution of the chan*
Corresponding author. E-mail address: [email protected] (E.V. Monakhov).
neling parameters with varying Ge concentration could not be explained by a concentrational dependence only. Two possible deviations from the perfect crystallinity were suggested and tested: (a) a static displacement of atoms due to dierent lengths of the Si±Si, Si±Ge and Ge±Ge bonds [7] and (b) a mosaic structure which had previously been observed in relaxed Si1ÿx Gex ®lms [8]. Since Si1ÿx Gex and Si1ÿx Snx belong to the same family of group-IV semiconductor alloys, it is intriguing to test the Si1ÿx Snx alloy layers for crystalline imperfections similar to those in Si1ÿx Gex . In this paper we report on Monte-Carlo simulations of 2 MeV a-particle channeling in Si1ÿx Snx alloys with dierent Sn content from pure Si to pure a-Sn. The simulations are then compared with measured [9] channeling-angular scans on strained Si0:95 Sn0:05 layers grown by MBE.
0168-583X/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 1 0 4 8 - 4
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E.V. Monakhov et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 103±107
2. Experiment The strained Si0:95 Sn0:05 ®lms with the thickness were grown on (0 0 1) Si substrates by 1700 A MBE. The growth temperature and rate were respectively. 300°C and 0.4 A/s, The channeling measurements were carried out using 2 MeV He ions. The angular dependencies of the backscattered yield near a h1 0 0i axis were obtained by rotating the crystal around the axis with an increasing tilt angle. The depth window for the integration of the backscattered yield was set to the Sn and Si portions of the RBS spectra from 500 to 1500 A. 3. Monte-Carlo simulations 3.1. General considerations The Monte-Carlo simulations used in the present study is based on the approach pioneered by Barrett [10], in which the nuclear encounter probabilities are obtained as a function of depth, and further developed in [11,12]. In the simulation program, the crystal is divided into three-dimensional rectangular cells, each containing one atom in the center. Thus, each step of the simulation is performed in one cell, where the ion trajectory is calculated using a binary collision model in the impulse approximation. The detailed description of the division procedure can be found in [12]. The Lindhard standard potential [13] is chosen for the ion±atom interactions. The electronic energy loss, in the model, is considered to depend on the impact parameter. Thermal vibrations of the atoms are taken into account as atomic shifts from their equilibrium positions with the distribution approximated by a Gaussian. The azimuthally averaged axial scans are simulated in the way they have been measured in the experiment, e.g., when a certain dose of particles is simulated, the beam direction is changed to another azimuthal position with the same tilt angle, thus the beam direction makes a full circle with a constant tilt angle. The simulated yield at a tilt angle of 3° is used for normalization, and the simulations were performed for 2 MeV He ions.
Fig. 1. The experimental and simulated h1 0 0i-axial angular dips for Si.
The program was ®rst tested on a h1 0 0i-axial scan for Si. A value of the one-dimensional vib [14] was used for rational amplitude of u1 0:08 A the simulations. The beam divergence was taken to be 0.03° as estimated for the experimental channeling setup. The results of the test are presented in Fig. 1. The screening radius in the Lindhard standard potential can be chosen in the form given by Lindhard [13] or Firsov [15,16]. As is seen from Fig. 1, the screening radius given by Firsov gives a better agreement between the simulations and the experimental data for Si, particularly near the critical angle. As a consequence of this result, in the following simulations the screening radius given by Firsov will be used. 3.2. Simulation model In order to simulate a two-component alloy, the following assumptions are made: (a) the atoms of both components are randomly distributed over the lattice sites, thus the probability for the ion to encounter a Sn atom in each ion±atom interaction is equal to the Sn concentration; (b) the lattice constant depends on the Sn concentration according to a linear interpolation between the val and a-Sn (6.49 A); (c) the ues for Si (5.43 A) thermal vibration of the atoms of both components are of the same amplitude. A perfect Si1ÿx Snx crystal is considered to have the atomic thermal vibrations of an amplitude of u1 0:08 A.
E.V. Monakhov et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 103±107
It was previously established for the Si1ÿx Gex alloy that the Ge±Ge and Ge±Si bond lengths dier from the prediction of both the Vegard's approach where the bond length are equal and the Bragg±Pauling limit where the bonds keep their natural length independent of composition [7], the value of the dierence between Ge±Si and Ge±Ge for x 0:36. bond lengths was found as 0:03 A Thus, the dierence in Si±Si, Si±Ge and Ge±Ge bond lengths causes distortions of the atomic con®guration in the crystal and results in a displacement of the atoms from their lattice sites. Due to the fact that the valent radius of a Sn atom is larger than that of a Ge atom, the eect of different bond lengths is expected to be more pronounced in the Si1ÿx Snx alloy. Assuming that the atoms are statically shifted with a Gaussian distribution, which is a reasonable approximation for the bond length distribution calculated ab inito in [17], and remembering that the thermal vibrations of the atoms are taken into account as atomic shifts from their lattice sites also with a Gaussian distribution, one can model the eect of the displacement by increasing the amplitude of atomic vibrations in the simulations u21 u210 d 2 ; where u10 is the real amplitude of the thermal vibrations and d is the standard deviation in the Gaussian distribution of the static displacements. It has been previously reported [18] that the grown ®lms have a developed surface morphology that consists of rectangular features, mounds, which have a pyramid-like shape. The sides of the pyramidal mounds are parallel to the h1 1 0i direction in the surface plane. Transmission electron microscopy studies [18] have revealed a columnar structure in the cross-section of the ®lms with the same periodicity as that of the surface roughness. It has been suggested that the observed columnar structure is due to Sn concentration ¯uctuations. No other extended imperfections such as precipitates, voids or dislocations, however, have been observed in the ®lms. Thus, a possible mosaic structure due to the columnar structure in the ®lms must be taken into account. Similar to the case of atomic shifts, a mosaic structure can be simulated by introducing an eective beam divergence,
105
r2 r20 h2 ; where r0 is the real beam divergence in the experiment and h is the mosaic spread. As reported in [9], the angular dependencies of the backscattered yield from Si and Sn atoms in strained Si1ÿx Snx ®lms are identical for the asgrown ®lms and for the ®lms annealed at temperatures 6 600°C, which indicates the absence of phase separation or preferential shifts of either Si or Sn atoms from the lattice sites. The identity of the angular dependencies of the Si and Sn backscattered yields also indicates that the thermal vibrational amplitudes of the Si and Sn atoms are almost the same. In further simulations, the backscattered yield from Si1ÿx Snx is a sum of the backscattered yields from Si and Sn atoms. Fig. 2 demonstrates the azimuthally averaged angular scans of a h1 0 0i axis for a Si1ÿx Snx ideal crystal with dierent Sn content from pure Si to pure a-Sn. The critical angle, w1=2 , increases from 0.45° for Si to 0.65° for a-Sn. The minimum backscattered yield, vmin , decreases from 3.3% for Si to 2.7% for a-Sn. It should be mentioned that the simulated scans for dierent Sn content are obtained with the same thermal vibrational amplitude of Si and Sn atoms as for pure Si, Although this assumption may cause u1 0:08 A. some inaccuracy in the simulations for high Sn
Fig. 2. The simulated h1 0 0i-axial angular dips for an ideal Si1ÿx Snx crystal with dierent Sn content from pure Si to pure a-Sn.
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E.V. Monakhov et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 103±107
concentration in Si1ÿx Snx , this is believed to be a reasonable estimation for a Sn content x 6 0:05, at which the simulations are compared with the experimental data.
4. Results and discussion 4.1. The eect of composition on channeling parameters Fig. 3 displays the measured azimuthally averaged angular dependencies of the backscattered yield near a h1 0 0i axis for three samples grown at the same conditions: Si on Si and strained Si1ÿx Snx with x 0:025 and 0.05. The angular dips obtained for a bulk Si crystal is identical to that for Si on Si for both h1 0 0i and h1 1 0i directions indicating a high crystalline quality of the Si ®lm grown on Si at a relatively low temperature (295°C). Fig. 3 shows that the channeling dip narrows and the minimum yield increases for larger Sn concentrations, which is in clear contradiction with the expected compositional dependence of the channeling parameters in Si1ÿx Snx (Fig. 2). A similar change of the angular dips for Si1ÿx Snx ®lms compared to Si on Si is found for a h1 1 0i channeling direction. As mentioned above, there is no observable dierence
Fig. 3. The experimental h1 0 0i-axial angular dips for the Si1ÿx Snx samples grown at the same conditions.
Fig. 4. The experimental and the simulated h1 0 0i-axial angular dips for the Si0:95 Sn0:05 layer with assumptions of the perfect crystallinity (a), increased either the beam divergence or the thermal vibrational amplitude (b) and increased both the beam divergence and the thermal vibrational amplitude.
E.V. Monakhov et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 103±107
between the backscattered yields from Si and Sn atoms. The angular dependencies of the backscattered yield from the Si1ÿx Snx ®lms suggest the presence of some imperfections in the crystal structure of the ®lms. 4.2. Comparison of the simulations with the experiment Since the deviation of the angular dip for the ®lm with x 0:05 from the expected one for an ideal crystal is more pronounced, the experimental results for x 0:05 have been chosen for the comparison with the channeling simulations. The dierence between the simulations with the parameters for a perfect Si0:95 Sn0:05 crystal and the experimental az(r 0:03°, u1 0:08 A) imuthally averaged h1 0 0i-axial scan for the strained Si0:95 Sn0:05 ®lm can be seen in Fig. 4(a). An increase in the beam divergence to r 0:12° corresponding to a mosaic spread of 0.11°, to obtain the value of vmin observed in the experimental axial dip, leads to a poor agreement in the critical angle (Fig. 4(b)). A thermal vibration (static displacement 0.08 A), amplitude of 0.11 A chosen to ®t the experimental value of vmin , results in a slightly better agreement of the simulations with the experiment. A good agreement of the simulations with the experimental axial dip can be reached if one suggests the simultaneous presence of both a mosaic structure and a static displacement of the atoms. Fig. 4(c) demonstrates the experimental angular dip and the simulations with a beam divergence r 0:09° and a thermal vib that corresponds rational amplitude u1 0:10 A, to a mosaic spread of 0.08° and a static atomic displacement of 0.05 A. 5. Conclusions Monte-Carlo simulations of h1 0 0i-axial channeling of 2 MeV He ions in Si1ÿx Snx alloy with 0 6 x 6 1 have been performed. The channeling simulations for pure Si are found to be in good agreement with the experimental results for single-
107
crystalline Si(1 0 0). A comparison between the experimentally measured h1 0 0i-axial scans for epitaxial strained Si0:96 Sn0:05 ®lms and the simulated angular dips reveals the presence of a deviation from perfect crystallinity in the ®lms. Two types of the deviations are suggested and tested in order to ®t the experimental data: (a) a static displacement of atoms from their lattice sites and (b) a mosaic structure. It has been found that neither of the deviations can alone describe the experimental results. The agreement between the simulations and the experiment can be reached by assuming the presence of both a mosaic spread of 0.08° and a static atomic displacement of 0.05 A.
References [1] S.Y. Shiryaev, J.L. Hansen, P. Kringhùj, A. Nylandsted Larsen, Appl. Phys. Lett. 67 (1995) 2287. [2] M.F. Fyhn, J. Lundsgaard Hansen, J. Chevallier, A. Nylandsted Larsen, Appl. Phys. A 68 (1999) 259. [3] K. Sung Min, H.A. Atwater, Appl. Phys. Lett. 72 (1998) 1884. [4] F.J. Guarin, S.S. Iyer, A.R. Powell, B.A. Ek, Appl. Phys. Lett. 68 (1996) 3608. [5] R.A. Soref, C.H. Perry, J. Appl. Phys. 69 (1991) 539. [6] E.V. Monakhov, A. Nylandsted Larsen, Nucl. Instr. and Meth. B 117 (1996) 71. [7] D.B. Aldrich, R.J. Nemanich, D.E. Sayers, Phys. Rev. B 50 (1994) 15026. [8] P.M. Mooney, F.K. LeGoues, J.O. Chu, S.F. Nelson, Appl. Phys. Lett. 62 (1993) 3464. [9] M.F. Fyhn, J. Chevallier, A. Nylandsted Larsen, J. Vac. Sci. Technol. B 16 (1998) 1777. [10] J.H. Barrett, Phys. Rev. B 3 (1971) 1527. [11] K.K. Bourdelle, V.A. Khodyrev, A. Johansen, E. Johansen, L. Sarholt-Kristensen, Phys. Rev. B 50 (1994) 523. [12] V.A. Khodyrev, V.Ya. Chumanov, K.K. Bourdelle, G.P. Pokhil, Nucl. Instr. and Meth. B 94 (1994) 523. [13] J. Lindhard, K. Dan, Vidensk. Selsk. Mat. Fys. Medd. 34 (14) (1965). [14] A. Dygo, W.N. Lennard, I.V. Mitchell, Nucl. Instr. and Meth. B 90 (1994) 161. [15] O.B. Firsov, Soviet Phys. JETP 6 (1957) 534. [16] L.C. Feldman, J.W. Mayer, S.T. Picraux, Material Analysis by Ion Channeling, Academic Press, New York, 1982. [17] S. de Gironcoli, P. Gianozzi, S. Baroni, Phys. Rev. Lett. 66 (1991) 2116. [18] M.F. Fyhn, S.Y Shiryaev, J.L. Hansen, A. Nylandsted Larsen, Appl. Phys. Lett. 69 (1996) 394.
www.elsevier.nl/locate/nimb
Monte-Carlo simulations of 2-MeV a-particle channeling in Si1ÿx Snx alloy E.V. Monakhov a
a,*
, M.F. Fyhn b, A. Nylandsted Larsen
b
Royal Institute of Technology, Solid State Electronics, Electrum 229, Kista-Stockholm, S-16440, Sweden b Institute of Physics and Astronomy, University of Aarhus, DK-8000, Aarhus C, Denmark
Abstract Monte-Carlo simulations of 2-MeV a-particle channeling in Si1ÿx Snx alloys with 0 6 x 6 1 have been performed. The simulations are compared with measured channeling-angular scans for strained Si0:95 Sn0:05 layers grown by molecular beam epitaxy (MBE). Agreement between simulated and measured angular scans can only be achieved if we assume a deviation of the crystal structure from the ideal one. This deviation can be attributed to a mosaic structure in the ®lms and to an atomic-scale distortion of the crystal lattice due to an expected dierence in the bond lengths between the Si± Si, Si±Sn and Sn±Sn atoms (such a dierence in bond lengths has been observed in the epitaxial Si1ÿx Gex system). The contributions from both of these imperfections are estimated and discussed. Ó 2000 Elsevier Science B.V. All rights reserved.
1. Introduction As a group-IV semiconductor alloy with variable biaxial strain, epitaxially grown Si1ÿx Snx alloy layers have attracted interest within the last few years [1±4]. Also the interest is due to theoretical predictions that, at a considerable content of Sn, this material might have a direct band gap [5]. Until now, however, the successful synthesis of epitaxial Si1ÿx Snx has only been reported for Sn concentrations smaller than about 5% grown on (0 0 1)-oriented Si [1]. Recently, we have reported on Monte-Carlo channeling simulations in relaxed Si1ÿx Gex ®lms [6]. It was found that the evolution of the chan*
Corresponding author. E-mail address: [email protected] (E.V. Monakhov).
neling parameters with varying Ge concentration could not be explained by a concentrational dependence only. Two possible deviations from the perfect crystallinity were suggested and tested: (a) a static displacement of atoms due to dierent lengths of the Si±Si, Si±Ge and Ge±Ge bonds [7] and (b) a mosaic structure which had previously been observed in relaxed Si1ÿx Gex ®lms [8]. Since Si1ÿx Gex and Si1ÿx Snx belong to the same family of group-IV semiconductor alloys, it is intriguing to test the Si1ÿx Snx alloy layers for crystalline imperfections similar to those in Si1ÿx Gex . In this paper we report on Monte-Carlo simulations of 2 MeV a-particle channeling in Si1ÿx Snx alloys with dierent Sn content from pure Si to pure a-Sn. The simulations are then compared with measured [9] channeling-angular scans on strained Si0:95 Sn0:05 layers grown by MBE.
0168-583X/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 1 0 4 8 - 4
104
E.V. Monakhov et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 103±107
2. Experiment The strained Si0:95 Sn0:05 ®lms with the thickness were grown on (0 0 1) Si substrates by 1700 A MBE. The growth temperature and rate were respectively. 300°C and 0.4 A/s, The channeling measurements were carried out using 2 MeV He ions. The angular dependencies of the backscattered yield near a h1 0 0i axis were obtained by rotating the crystal around the axis with an increasing tilt angle. The depth window for the integration of the backscattered yield was set to the Sn and Si portions of the RBS spectra from 500 to 1500 A. 3. Monte-Carlo simulations 3.1. General considerations The Monte-Carlo simulations used in the present study is based on the approach pioneered by Barrett [10], in which the nuclear encounter probabilities are obtained as a function of depth, and further developed in [11,12]. In the simulation program, the crystal is divided into three-dimensional rectangular cells, each containing one atom in the center. Thus, each step of the simulation is performed in one cell, where the ion trajectory is calculated using a binary collision model in the impulse approximation. The detailed description of the division procedure can be found in [12]. The Lindhard standard potential [13] is chosen for the ion±atom interactions. The electronic energy loss, in the model, is considered to depend on the impact parameter. Thermal vibrations of the atoms are taken into account as atomic shifts from their equilibrium positions with the distribution approximated by a Gaussian. The azimuthally averaged axial scans are simulated in the way they have been measured in the experiment, e.g., when a certain dose of particles is simulated, the beam direction is changed to another azimuthal position with the same tilt angle, thus the beam direction makes a full circle with a constant tilt angle. The simulated yield at a tilt angle of 3° is used for normalization, and the simulations were performed for 2 MeV He ions.
Fig. 1. The experimental and simulated h1 0 0i-axial angular dips for Si.
The program was ®rst tested on a h1 0 0i-axial scan for Si. A value of the one-dimensional vib [14] was used for rational amplitude of u1 0:08 A the simulations. The beam divergence was taken to be 0.03° as estimated for the experimental channeling setup. The results of the test are presented in Fig. 1. The screening radius in the Lindhard standard potential can be chosen in the form given by Lindhard [13] or Firsov [15,16]. As is seen from Fig. 1, the screening radius given by Firsov gives a better agreement between the simulations and the experimental data for Si, particularly near the critical angle. As a consequence of this result, in the following simulations the screening radius given by Firsov will be used. 3.2. Simulation model In order to simulate a two-component alloy, the following assumptions are made: (a) the atoms of both components are randomly distributed over the lattice sites, thus the probability for the ion to encounter a Sn atom in each ion±atom interaction is equal to the Sn concentration; (b) the lattice constant depends on the Sn concentration according to a linear interpolation between the val and a-Sn (6.49 A); (c) the ues for Si (5.43 A) thermal vibration of the atoms of both components are of the same amplitude. A perfect Si1ÿx Snx crystal is considered to have the atomic thermal vibrations of an amplitude of u1 0:08 A.
E.V. Monakhov et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 103±107
It was previously established for the Si1ÿx Gex alloy that the Ge±Ge and Ge±Si bond lengths dier from the prediction of both the Vegard's approach where the bond length are equal and the Bragg±Pauling limit where the bonds keep their natural length independent of composition [7], the value of the dierence between Ge±Si and Ge±Ge for x 0:36. bond lengths was found as 0:03 A Thus, the dierence in Si±Si, Si±Ge and Ge±Ge bond lengths causes distortions of the atomic con®guration in the crystal and results in a displacement of the atoms from their lattice sites. Due to the fact that the valent radius of a Sn atom is larger than that of a Ge atom, the eect of different bond lengths is expected to be more pronounced in the Si1ÿx Snx alloy. Assuming that the atoms are statically shifted with a Gaussian distribution, which is a reasonable approximation for the bond length distribution calculated ab inito in [17], and remembering that the thermal vibrations of the atoms are taken into account as atomic shifts from their lattice sites also with a Gaussian distribution, one can model the eect of the displacement by increasing the amplitude of atomic vibrations in the simulations u21 u210 d 2 ; where u10 is the real amplitude of the thermal vibrations and d is the standard deviation in the Gaussian distribution of the static displacements. It has been previously reported [18] that the grown ®lms have a developed surface morphology that consists of rectangular features, mounds, which have a pyramid-like shape. The sides of the pyramidal mounds are parallel to the h1 1 0i direction in the surface plane. Transmission electron microscopy studies [18] have revealed a columnar structure in the cross-section of the ®lms with the same periodicity as that of the surface roughness. It has been suggested that the observed columnar structure is due to Sn concentration ¯uctuations. No other extended imperfections such as precipitates, voids or dislocations, however, have been observed in the ®lms. Thus, a possible mosaic structure due to the columnar structure in the ®lms must be taken into account. Similar to the case of atomic shifts, a mosaic structure can be simulated by introducing an eective beam divergence,
105
r2 r20 h2 ; where r0 is the real beam divergence in the experiment and h is the mosaic spread. As reported in [9], the angular dependencies of the backscattered yield from Si and Sn atoms in strained Si1ÿx Snx ®lms are identical for the asgrown ®lms and for the ®lms annealed at temperatures 6 600°C, which indicates the absence of phase separation or preferential shifts of either Si or Sn atoms from the lattice sites. The identity of the angular dependencies of the Si and Sn backscattered yields also indicates that the thermal vibrational amplitudes of the Si and Sn atoms are almost the same. In further simulations, the backscattered yield from Si1ÿx Snx is a sum of the backscattered yields from Si and Sn atoms. Fig. 2 demonstrates the azimuthally averaged angular scans of a h1 0 0i axis for a Si1ÿx Snx ideal crystal with dierent Sn content from pure Si to pure a-Sn. The critical angle, w1=2 , increases from 0.45° for Si to 0.65° for a-Sn. The minimum backscattered yield, vmin , decreases from 3.3% for Si to 2.7% for a-Sn. It should be mentioned that the simulated scans for dierent Sn content are obtained with the same thermal vibrational amplitude of Si and Sn atoms as for pure Si, Although this assumption may cause u1 0:08 A. some inaccuracy in the simulations for high Sn
Fig. 2. The simulated h1 0 0i-axial angular dips for an ideal Si1ÿx Snx crystal with dierent Sn content from pure Si to pure a-Sn.
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E.V. Monakhov et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 103±107
concentration in Si1ÿx Snx , this is believed to be a reasonable estimation for a Sn content x 6 0:05, at which the simulations are compared with the experimental data.
4. Results and discussion 4.1. The eect of composition on channeling parameters Fig. 3 displays the measured azimuthally averaged angular dependencies of the backscattered yield near a h1 0 0i axis for three samples grown at the same conditions: Si on Si and strained Si1ÿx Snx with x 0:025 and 0.05. The angular dips obtained for a bulk Si crystal is identical to that for Si on Si for both h1 0 0i and h1 1 0i directions indicating a high crystalline quality of the Si ®lm grown on Si at a relatively low temperature (295°C). Fig. 3 shows that the channeling dip narrows and the minimum yield increases for larger Sn concentrations, which is in clear contradiction with the expected compositional dependence of the channeling parameters in Si1ÿx Snx (Fig. 2). A similar change of the angular dips for Si1ÿx Snx ®lms compared to Si on Si is found for a h1 1 0i channeling direction. As mentioned above, there is no observable dierence
Fig. 3. The experimental h1 0 0i-axial angular dips for the Si1ÿx Snx samples grown at the same conditions.
Fig. 4. The experimental and the simulated h1 0 0i-axial angular dips for the Si0:95 Sn0:05 layer with assumptions of the perfect crystallinity (a), increased either the beam divergence or the thermal vibrational amplitude (b) and increased both the beam divergence and the thermal vibrational amplitude.
E.V. Monakhov et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 103±107
between the backscattered yields from Si and Sn atoms. The angular dependencies of the backscattered yield from the Si1ÿx Snx ®lms suggest the presence of some imperfections in the crystal structure of the ®lms. 4.2. Comparison of the simulations with the experiment Since the deviation of the angular dip for the ®lm with x 0:05 from the expected one for an ideal crystal is more pronounced, the experimental results for x 0:05 have been chosen for the comparison with the channeling simulations. The dierence between the simulations with the parameters for a perfect Si0:95 Sn0:05 crystal and the experimental az(r 0:03°, u1 0:08 A) imuthally averaged h1 0 0i-axial scan for the strained Si0:95 Sn0:05 ®lm can be seen in Fig. 4(a). An increase in the beam divergence to r 0:12° corresponding to a mosaic spread of 0.11°, to obtain the value of vmin observed in the experimental axial dip, leads to a poor agreement in the critical angle (Fig. 4(b)). A thermal vibration (static displacement 0.08 A), amplitude of 0.11 A chosen to ®t the experimental value of vmin , results in a slightly better agreement of the simulations with the experiment. A good agreement of the simulations with the experimental axial dip can be reached if one suggests the simultaneous presence of both a mosaic structure and a static displacement of the atoms. Fig. 4(c) demonstrates the experimental angular dip and the simulations with a beam divergence r 0:09° and a thermal vib that corresponds rational amplitude u1 0:10 A, to a mosaic spread of 0.08° and a static atomic displacement of 0.05 A. 5. Conclusions Monte-Carlo simulations of h1 0 0i-axial channeling of 2 MeV He ions in Si1ÿx Snx alloy with 0 6 x 6 1 have been performed. The channeling simulations for pure Si are found to be in good agreement with the experimental results for single-
107
crystalline Si(1 0 0). A comparison between the experimentally measured h1 0 0i-axial scans for epitaxial strained Si0:96 Sn0:05 ®lms and the simulated angular dips reveals the presence of a deviation from perfect crystallinity in the ®lms. Two types of the deviations are suggested and tested in order to ®t the experimental data: (a) a static displacement of atoms from their lattice sites and (b) a mosaic structure. It has been found that neither of the deviations can alone describe the experimental results. The agreement between the simulations and the experiment can be reached by assuming the presence of both a mosaic spread of 0.08° and a static atomic displacement of 0.05 A.
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