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RHEED intensity oscillations with extra maxima
Surface Science Letters 276 (1992) L15-L18 North-Holland
surface science letters
Surface Science Letters
RHEED
intensity oscillations with extra maxima
Z. Mitura I, M. Strbiak and M. Jalochowski Department of Experimental Physics, Institute of Physics, Marie-Curie Sklodowska University,pl. M. Curie-Sklodowskiej 1, 20-031 Lublin, Poland Received 18 March 1992; accepted for publication 7 July 1992
Ultrathin films of a lead-indium alloy are deposited on substrates of the same material at 110 K. The appearance of two maxima in a period of RHEED intensity oscillations for very low values of the glancing angle ( - 0.35” for incident electrons of the energy of 20 keV) is found experimentally. RHEED intensity oscillations are calculated to show that the results can be explained within the RHEED dynamical theory. The effect has important experimental consequences which are discussed.
Very recently, a new approach for interpreting RHEED intensity oscillations has been proposed by us [l-3]. In this approach only low values of the glancing angle of the incident electron beam are considered. The intensity of the specular electron beam is calculated by solving the Schrodinger equation with a one-dimensional model of a scattering potential of a growing film. For the low values of the glancing angle (less than 0.5” for the electron energy of 20 keV) such calculations may be expected to lead to results similar to those obtained assuming a three-dimensional model of the potential [2,3]. Taking the advantage of the simplicity of the above approach it is possible to foresee theoretically some effects [ 1,2] which may be looked for in experimental work. One of these is the appearance of double maxima of the RHEED intensity in a period of time corresponding to deposition of one monolayer [1,2]. The main aim of this Letter is to present results of experimental and theoretical investigations on this phenomenon. Figs. lb, 2b and 3b show experimental RHEED intensity oscillations observed during growth of a lead-indium alloy. Deposition of thin films was ’ Present address: Department University of Leicester, 7RH, UK.
of Physics and Astronomy, University Road, Leicester LEl
carried out in an UHV system with the basic pressure less than lo-” mbar. The energy of incident electrons was equal to 20 keV. The divergence of the specularly reflected electron beam could be estimated to be equal to about 0.1”. The values of the glancing angle f - 0.35”) presented in figs. lb, 2b and 3b were determined to +0.03”. Precisely aligned optical system with a phosphorus screen and a photodiode was used to observe RHEED specular beam intensity changes during growth of the thin films. The deposited alloy contained 35% of In atoms (in the further part of this Letter we use the abbreviation Pb-35%In). It was found earlier [41 that for this composition of the alloy at low temperatures thin films can be expected to grow epitaxially in a near monolayerby-monolayer mode if Si(lll)-(7 x 7) substrates are used. In our case thin films were deposited on buffers of the same alloy Pb-35%In. The temperature of the buffers during deposition of thin films was equal to about 110 K. The buffers were prepared by deposition of 20 ML-thick layers of the alloy on Si(lll)-(7 X 7) substrates. During the deposition of the buffers the temperature of the Si substrates was also equal to about 110 IS. However, the buffers were first annealed to room temperature and next before they were used to produce thin films they were cooled again to a temperature of about 110 K. Both the buffers and
0039~6028/92/$05.00 0 1992 - Elsevier Science Publishers B.V. All rights reserved
Z. Mitura et al. / RHEED
intensity oscillations with extra maxima
the thin films had a fee structure. They were grown in (111) planes. Figs. la, lc, 2a, 2c, 3a and 3c show numerically determined RHEED intensity oscillation shapes for the case of the ideal monolayer-by-monolayer growth of the alloy Pb-35%In. Calculations were carried out within a dynamical approach using a multislice method developed by one of the authors [3] and already applied earlier [2,5]. In this method a crystal is divided into slices parallel to a surface. For each slice a transfer matrix is calculated by directly solving (with a Runge-KuttaMerson method) a set of differential equations developed by Maksym and Beeby [6]. Next, for the top of each slice a reflectivity matrix is found using an algorithm from Ichimiya’s work [7]. The reflectivity matrix relates backward and forward traveling electron waves. Finding this matrix for of the last slice is enough for determina0
2
4
THICKNESS Fig. 2. As fig. 1 but for the incident
6
8
1’0
(ML) beam
direction
azimuth
(zii) + 150.
0
2 THICKNESS
4
6
8
10
(ML)
Fig. 1. RHEED intensity oscillations for the incident beam direction azimuth (271): (a) calculated, (b) experimental, (c) calculated. The values of the glancing angle are shown in the figure. All curves are for 20 keV electrons for growth of thin films of the Pb-35%In(lll). Alloy on substrates of the same material.
tion of beam intensities of scattered electrons. We can use arbitrary thicknesses of the slices. Due to this we can eliminate problems associated with the numerical description of evanescent electron waves, which appear in the considered slices because of multiple scattering effects and a difference in the average scattering potential of the vacuum and the crystal. To determine the real part of the potential we used atomic coefficient tabulated by Doyle and Turner [8] assuming thermal vibrations of atoms typical for 155 K. The imaginary part of the potential we assumed to be equal to 0.2 of the real part. To determine the contribution of the partially filled topmost monolayer to the potential of a whole layer we used the following formula: V”‘(8, r) = f31/“‘(1, r),
(1) where V’“‘(1, r) means the potential after fulfilling the monolayer, Vm’(B, r> means the potential of the growing monolayer and 19means the cover-
Z. Mitura et al. / RHEED intensity oscillations with extra maxima
CALC.
EXP.
@)
CALC .
(c)
THICKNESS
(ML)
Fig. 3. As fig. 1 but for the incident beam direction azimuth (00).
age (within the range O-1) of the monolayer. Formula (1) (in a slightly different form) was developed by Kawamura and Maksym [9] for the case of the perpendicular stacking of atom island edges in relation to the azimuth of the incident beam direction. Also those authors suggested using formula (1) in more general cases 191. In the approximation given by formula (1) we omit some effects connected with island shapes on the surface: random scattering by island edges and interference between waves scattered by terraces of different heights. From simple geometrical considerations it follows that this approximation should be valid for very small glancing angles. Probably, it is possible to improve the approximation using perturbation methods. We have applied formula (1) because of its simplicity. The achieved agreement between theoretical and experimental results presented in this Letter confirms the usefulness of the approximation given by formula (1). Nevertheless, it seems interesting
to do further theoretical work to investigate in more detail different possible approximations. In the calculations we took into account only a few electron beams. This requires a short explanation. In the general case finding the proper number of electron beams included in the calculations seems to be a serious problem. It was pointed out by Zhao et al. [lo] that in principle a large number of beams should be considered to obtain convergent results. However, in our case selecting the important beams is not especially difficult. As was discussed in ref. [23, for low glancing angles dynamical effects connected with lateral arrangement of atoms become small. To obtain a rough qualitative approximation it is even enough to consider only one, principal beam. Including further beams gives only small corrections [2]. For the azimuths (211) (figs. la and lc) and (liO> (figs. 3a and 3c) we used in the computations five and seven beams, respectively. Including many beams (more than one) means that calculations are based on the three-dimensional model of the scattering potential. The results of one-beam calculations (the one-dimensional model of the potential) we present in figs. 2a, and 2c and they are shown together with the experimental results (fig. 2b) obtained for a “random” azimuth, that is an azimuth far from a symmetry azimuth. In all calculations we considered a crystal slab of thickness of at least 12 monolayers. In order to take into account the divergence of an actual specular electron beam we calculated RHEED intensity oscillations for two values of the glancing angle for each experimental curve. For the experimental oscillations (figs. lb, 2b and 3bl we can observe very clearly two maxima in a period. The additional maximum is especially strong for the azimuth (110) (fig. 3b). The weak but also noticeable second maximum exists for the “random” azimuth (fig. 2b). So, we can conclude that multiple scattering of electrons connected with lateral distributions of atoms in monolayers (as for the azimuths (110) and (2ii)) enhances the appearance of the effect. In all cases the second maximum disappears after deposition of several monolayers. Probably, it is caused by a gradual increase of disorder in a settling of atoms at surfaces of growing films.
Z. Mitura et al. / RHEED
intensity oscillations with extra maxima
All experimental results are in a rather good agreement with theoretical ones. This means that the effects described are caused only by multiple scattering of electron waves. The appearance of a sudden intensity drop after the second maximum can be seen both for calculated and experimental oscillations. Especially interesting drops appear for the experimental results presented in fig. lb. On the basis of the results of the calculations presented in figs. la and lc, we can say that in this case decreases of the intensities begin when new monolayers start to grow. The above finding may be helpful for researchers dealing with the preparation of thin films as it may be useful in the precise determination of coverages of growing films. In fig. 3 there is some difference between the experimental curve and the theoretical ones, which should be discussed. All even minima in fig. 3b (counting from the starting point of growth) are weak, while on the basis of the calculations, these minima (figs. 3a and 3c) are expected to be very deep. At present, we can suppose two shortcomings of the assumed theoretical description which imply this difference: using formula (a) oversimplifies scattering processes and/or the assumed perfect monolayer-by-monolayer growth mode is too rough an approximation. The results presented in this Letter seem to be important because of two reasons. First, earlier
theoretical predictions of RHEED intensity oscillation shapes [1,2] were confirmed experimentally. The successful predictions were carried out using the dynamical RHEED theory introduced by Maksym and Beeby. Second, RHEED oscillations with two maxima in a period provide new and promising possibilities for monitoring growth. The authors would like to thank Dr. P.A. Maksym and Dr. J.M. McCoy for helpful discussions. This work was supported by the Polish Scientific Research Committee Grant No. 2 03 82 91 01.
References 111Z. Mitura,
A. Daniluk, M. Stroiak, M. JaJochowski, A. Smal and M. Subotowicz, Acta Phys. Pol. A 80 (1991) 365. 121Z. Mitura and A. Daniluk, Surf. Sci., in press. [31 Z. Mitura, PhD Thesis, MCS Univ., Lublin (1991) [in Polish]. I41 M. Jalochowski, H. Knoppe, G. Lilienkamp and E. Bauer, Phys. Rev. B, submitted for publication. and M. Subotowicz, Phys. [51 Z. Mitura, M. Jalochowski Lett. A 150 (1990) 51. [61 P.A. Maksym and J.L. Beeby, Surf. Sci. 110 (1981) 423. [71 A. Ichimiya, Jpn. J. Appl. Phys. 22 (1983) 176. [Sl P.A. Doyle and P.S. Turner, Acta Cryst. A 24 (1968) 390. and P.A. Maksym, Surf. Sci. 161 (1985) 12. 191 T. Kawamura I101 T.C. Zhao, H.C. Poon and S.Y. Tong, Phys. Rev. B 38 (1988) 1172.
surface science letters
Surface Science Letters
RHEED
intensity oscillations with extra maxima
Z. Mitura I, M. Strbiak and M. Jalochowski Department of Experimental Physics, Institute of Physics, Marie-Curie Sklodowska University,pl. M. Curie-Sklodowskiej 1, 20-031 Lublin, Poland Received 18 March 1992; accepted for publication 7 July 1992
Ultrathin films of a lead-indium alloy are deposited on substrates of the same material at 110 K. The appearance of two maxima in a period of RHEED intensity oscillations for very low values of the glancing angle ( - 0.35” for incident electrons of the energy of 20 keV) is found experimentally. RHEED intensity oscillations are calculated to show that the results can be explained within the RHEED dynamical theory. The effect has important experimental consequences which are discussed.
Very recently, a new approach for interpreting RHEED intensity oscillations has been proposed by us [l-3]. In this approach only low values of the glancing angle of the incident electron beam are considered. The intensity of the specular electron beam is calculated by solving the Schrodinger equation with a one-dimensional model of a scattering potential of a growing film. For the low values of the glancing angle (less than 0.5” for the electron energy of 20 keV) such calculations may be expected to lead to results similar to those obtained assuming a three-dimensional model of the potential [2,3]. Taking the advantage of the simplicity of the above approach it is possible to foresee theoretically some effects [ 1,2] which may be looked for in experimental work. One of these is the appearance of double maxima of the RHEED intensity in a period of time corresponding to deposition of one monolayer [1,2]. The main aim of this Letter is to present results of experimental and theoretical investigations on this phenomenon. Figs. lb, 2b and 3b show experimental RHEED intensity oscillations observed during growth of a lead-indium alloy. Deposition of thin films was ’ Present address: Department University of Leicester, 7RH, UK.
of Physics and Astronomy, University Road, Leicester LEl
carried out in an UHV system with the basic pressure less than lo-” mbar. The energy of incident electrons was equal to 20 keV. The divergence of the specularly reflected electron beam could be estimated to be equal to about 0.1”. The values of the glancing angle f - 0.35”) presented in figs. lb, 2b and 3b were determined to +0.03”. Precisely aligned optical system with a phosphorus screen and a photodiode was used to observe RHEED specular beam intensity changes during growth of the thin films. The deposited alloy contained 35% of In atoms (in the further part of this Letter we use the abbreviation Pb-35%In). It was found earlier [41 that for this composition of the alloy at low temperatures thin films can be expected to grow epitaxially in a near monolayerby-monolayer mode if Si(lll)-(7 x 7) substrates are used. In our case thin films were deposited on buffers of the same alloy Pb-35%In. The temperature of the buffers during deposition of thin films was equal to about 110 K. The buffers were prepared by deposition of 20 ML-thick layers of the alloy on Si(lll)-(7 X 7) substrates. During the deposition of the buffers the temperature of the Si substrates was also equal to about 110 IS. However, the buffers were first annealed to room temperature and next before they were used to produce thin films they were cooled again to a temperature of about 110 K. Both the buffers and
0039~6028/92/$05.00 0 1992 - Elsevier Science Publishers B.V. All rights reserved
Z. Mitura et al. / RHEED
intensity oscillations with extra maxima
the thin films had a fee structure. They were grown in (111) planes. Figs. la, lc, 2a, 2c, 3a and 3c show numerically determined RHEED intensity oscillation shapes for the case of the ideal monolayer-by-monolayer growth of the alloy Pb-35%In. Calculations were carried out within a dynamical approach using a multislice method developed by one of the authors [3] and already applied earlier [2,5]. In this method a crystal is divided into slices parallel to a surface. For each slice a transfer matrix is calculated by directly solving (with a Runge-KuttaMerson method) a set of differential equations developed by Maksym and Beeby [6]. Next, for the top of each slice a reflectivity matrix is found using an algorithm from Ichimiya’s work [7]. The reflectivity matrix relates backward and forward traveling electron waves. Finding this matrix for of the last slice is enough for determina0
2
4
THICKNESS Fig. 2. As fig. 1 but for the incident
6
8
1’0
(ML) beam
direction
azimuth
(zii) + 150.
0
2 THICKNESS
4
6
8
10
(ML)
Fig. 1. RHEED intensity oscillations for the incident beam direction azimuth (271): (a) calculated, (b) experimental, (c) calculated. The values of the glancing angle are shown in the figure. All curves are for 20 keV electrons for growth of thin films of the Pb-35%In(lll). Alloy on substrates of the same material.
tion of beam intensities of scattered electrons. We can use arbitrary thicknesses of the slices. Due to this we can eliminate problems associated with the numerical description of evanescent electron waves, which appear in the considered slices because of multiple scattering effects and a difference in the average scattering potential of the vacuum and the crystal. To determine the real part of the potential we used atomic coefficient tabulated by Doyle and Turner [8] assuming thermal vibrations of atoms typical for 155 K. The imaginary part of the potential we assumed to be equal to 0.2 of the real part. To determine the contribution of the partially filled topmost monolayer to the potential of a whole layer we used the following formula: V”‘(8, r) = f31/“‘(1, r),
(1) where V’“‘(1, r) means the potential after fulfilling the monolayer, Vm’(B, r> means the potential of the growing monolayer and 19means the cover-
Z. Mitura et al. / RHEED intensity oscillations with extra maxima
CALC.
EXP.
@)
CALC .
(c)
THICKNESS
(ML)
Fig. 3. As fig. 1 but for the incident beam direction azimuth (00).
age (within the range O-1) of the monolayer. Formula (1) (in a slightly different form) was developed by Kawamura and Maksym [9] for the case of the perpendicular stacking of atom island edges in relation to the azimuth of the incident beam direction. Also those authors suggested using formula (1) in more general cases 191. In the approximation given by formula (1) we omit some effects connected with island shapes on the surface: random scattering by island edges and interference between waves scattered by terraces of different heights. From simple geometrical considerations it follows that this approximation should be valid for very small glancing angles. Probably, it is possible to improve the approximation using perturbation methods. We have applied formula (1) because of its simplicity. The achieved agreement between theoretical and experimental results presented in this Letter confirms the usefulness of the approximation given by formula (1). Nevertheless, it seems interesting
to do further theoretical work to investigate in more detail different possible approximations. In the calculations we took into account only a few electron beams. This requires a short explanation. In the general case finding the proper number of electron beams included in the calculations seems to be a serious problem. It was pointed out by Zhao et al. [lo] that in principle a large number of beams should be considered to obtain convergent results. However, in our case selecting the important beams is not especially difficult. As was discussed in ref. [23, for low glancing angles dynamical effects connected with lateral arrangement of atoms become small. To obtain a rough qualitative approximation it is even enough to consider only one, principal beam. Including further beams gives only small corrections [2]. For the azimuths (211) (figs. la and lc) and (liO> (figs. 3a and 3c) we used in the computations five and seven beams, respectively. Including many beams (more than one) means that calculations are based on the three-dimensional model of the scattering potential. The results of one-beam calculations (the one-dimensional model of the potential) we present in figs. 2a, and 2c and they are shown together with the experimental results (fig. 2b) obtained for a “random” azimuth, that is an azimuth far from a symmetry azimuth. In all calculations we considered a crystal slab of thickness of at least 12 monolayers. In order to take into account the divergence of an actual specular electron beam we calculated RHEED intensity oscillations for two values of the glancing angle for each experimental curve. For the experimental oscillations (figs. lb, 2b and 3bl we can observe very clearly two maxima in a period. The additional maximum is especially strong for the azimuth (110) (fig. 3b). The weak but also noticeable second maximum exists for the “random” azimuth (fig. 2b). So, we can conclude that multiple scattering of electrons connected with lateral distributions of atoms in monolayers (as for the azimuths (110) and (2ii)) enhances the appearance of the effect. In all cases the second maximum disappears after deposition of several monolayers. Probably, it is caused by a gradual increase of disorder in a settling of atoms at surfaces of growing films.
Z. Mitura et al. / RHEED
intensity oscillations with extra maxima
All experimental results are in a rather good agreement with theoretical ones. This means that the effects described are caused only by multiple scattering of electron waves. The appearance of a sudden intensity drop after the second maximum can be seen both for calculated and experimental oscillations. Especially interesting drops appear for the experimental results presented in fig. lb. On the basis of the results of the calculations presented in figs. la and lc, we can say that in this case decreases of the intensities begin when new monolayers start to grow. The above finding may be helpful for researchers dealing with the preparation of thin films as it may be useful in the precise determination of coverages of growing films. In fig. 3 there is some difference between the experimental curve and the theoretical ones, which should be discussed. All even minima in fig. 3b (counting from the starting point of growth) are weak, while on the basis of the calculations, these minima (figs. 3a and 3c) are expected to be very deep. At present, we can suppose two shortcomings of the assumed theoretical description which imply this difference: using formula (a) oversimplifies scattering processes and/or the assumed perfect monolayer-by-monolayer growth mode is too rough an approximation. The results presented in this Letter seem to be important because of two reasons. First, earlier
theoretical predictions of RHEED intensity oscillation shapes [1,2] were confirmed experimentally. The successful predictions were carried out using the dynamical RHEED theory introduced by Maksym and Beeby. Second, RHEED oscillations with two maxima in a period provide new and promising possibilities for monitoring growth. The authors would like to thank Dr. P.A. Maksym and Dr. J.M. McCoy for helpful discussions. This work was supported by the Polish Scientific Research Committee Grant No. 2 03 82 91 01.
References 111Z. Mitura,
A. Daniluk, M. Stroiak, M. JaJochowski, A. Smal and M. Subotowicz, Acta Phys. Pol. A 80 (1991) 365. 121Z. Mitura and A. Daniluk, Surf. Sci., in press. [31 Z. Mitura, PhD Thesis, MCS Univ., Lublin (1991) [in Polish]. I41 M. Jalochowski, H. Knoppe, G. Lilienkamp and E. Bauer, Phys. Rev. B, submitted for publication. and M. Subotowicz, Phys. [51 Z. Mitura, M. Jalochowski Lett. A 150 (1990) 51. [61 P.A. Maksym and J.L. Beeby, Surf. Sci. 110 (1981) 423. [71 A. Ichimiya, Jpn. J. Appl. Phys. 22 (1983) 176. [Sl P.A. Doyle and P.S. Turner, Acta Cryst. A 24 (1968) 390. and P.A. Maksym, Surf. Sci. 161 (1985) 12. 191 T. Kawamura I101 T.C. Zhao, H.C. Poon and S.Y. Tong, Phys. Rev. B 38 (1988) 1172.