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Si superlattices
Solid State Communications 151 (2011) 846–849
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Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Raman spectroscopy of pseudomorphic Si0.989 C0.011 /Si superlattices E. Silveira ∗ Departamento de Fisica - UFPR, Caixa Postal 19044, 81531-990 Curitiba-PR, Brazil
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Article history: Received 8 January 2011 Received in revised form 14 March 2011 Accepted 16 March 2011 by L. Brey Available online 2 April 2011 Keywords: A. Semiconductors D. Optical properties D. Raman scattering
abstract Raman spectroscopy is used here to study pseudomorphic Si0.989 C0.011 /Si superlattices grown by molecular beam epitaxy. The high crystalline quality of the samples was tested by a high resolution X-ray diffraction experiment. The lineshape of the LO Si–Si peak shows an asymmetry, which correlates with the increase of the alloy layer width. The Raman spectra show three additional peaks in the high energy side above the LO mode of Si. One of them is due to the local vibration of the C substitutional atoms, and the other two can be attributed to the formation of short range order with C atoms occupying second and third nearest-neighbor places. On the low energy side of the LO Si–Si mode, we have observed two other peaks associated with the relaxation of the Si atoms around the substitutional C. Although the X-ray experiments show clear evidence of superperiodicity, no indication of the superlattice formation could be observed in the parallel polarized Raman spectra, where the folded acoustic modes are allowed. © 2011 Elsevier Ltd. All rights reserved.
1. Introduction The new possibilities and potential applications of materials involving binary Si1−x Cx and ternary Si1−x−y Gex Cy alloys in band gap and strain engineering have attracted a lot of interest since the 1990s [1–4], with regard to their growth and the characterization of physical properties. Due to a large mismatch of about 50% between Si and diamond, the extremely low C solubility in Si (10−6 at 1420 °C) [5] and the thermodynamically favored silicon carbide phases, the pseudomorphic growth of Si1−x Cx alloy layers on Si is normally limited to a few percent of C content. Using alternate evaporation of Si and C, it was possible to grow pseudomorphic layers and superlattices of ordered Si–C alloys with higher C contents of up to 50% [3,6]. Vegard’s law states that one can find the lattice constant of any alloy by interpolating between the lattice parameters of the constituents [7]. Contrary to this, Pauling’s model asserts that there is a characteristic length for each chemical bond. There is still a controversy about these two limits for the microscopic arrangement of atoms in these structures, with extended X-ray absorption fine structure measurements [8] confirming the predictions of Pauling’s model and Raman measurements with a modified valence force model, which shows some deviations from this picture [9]. Also, other theoretical models show some relaxations of the bond lengths towards Vegard’s law. It is very important to know the exact atomic arrangement in these structures, since small deviations mean large effects on the electronic properties [10]. Low temperature
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photoluminescence measurements of Si1−x Cx /Si multiquantum wells and superlattices have demonstrated a linear decrease of these luminescence lines with increasing carbon content [1]. These results are consistent with theoretical calculations, that take into account the microscopic properties of these new materials [11]. This model contradicts prediction of the virtual crystal approximation, which predicted an increased gap for Si1−x Cx alloys compared to Si [12]. Raman scattering together with theoretical modeling has been used to understand and develop a detailed picture of the peculiar atomic and strain arrangement of Si1−x−y Gex Cy and Si1−x Cx alloy layers [13–16]. We present here results of polarized Raman spectra of Si0.989 C0.011 /Si superlattices grown by MBE pseudomorphically on two types of Si substrates. These results will be discussed in terms of previous Raman studies in Si1−x Cx and Si1−x−y Gex Cy [13,14], and recent calculations using a modified Keating valence force model [15]. 2. Materials and methods Two series of nominally Si0.989 C0.011 /Si superlattice samples were grown by solid source MBE at temperatures about 475 °C. A detailed description of the growth parameters can be found elsewhere [17]. The first series of five superlattices was grown on n(P) doped Si(001) substrates with a resistivity greater than 2 k cm. The widths of the alloy layer and the Si layer were varied from 4 nm to 12 nm and from 12 nm to 4 nm, respectively, maintaining the overall period as 16 nm. The other series, composed of three samples, was grown on p(B) doped Si(001) substrates. As for the first series, the period was kept constant at 14 nm, and the alloy layer and the Si layer were varied from 3.5 nm to 10.5 nm and from 10.5 nm to 3.5 nm, respectively. All samples
E. Silveira / Solid State Communications 151 (2011) 846–849
Fig. 1. Rocking curve around the 004 reflection of a Si0.989 C0.01 1/Si superlattice with 20 periods of 12 nm alloy layer and 4 nm Si layer thicknesses. The dashed line shows a dynamical simulation.
have 20 periods. High resolution X-ray diffraction (HRXRD) was used to verify the crystalline quality of the superlattices. Fig. 1 shows a typical result of a HRXRD coupled scan around the (004) reciprocal lattice point of a twenty times 16 nm period superlattice with 12 nm thick Si0.989 C0.011 layers inside each period. This rocking curve shows clearly resolved finite thickness fringes and the superlattice satellite peaks. Shown also in Fig. 1 is a simulation of the diffraction pattern. With good correspondence between the simulation and the measurements and the appearance of the finite thickness fringes, it is possible to conclude that the samples have proper periodicity and are of very good crystalline quality [3]. By monitoring the average C concentration inside one period, which can be done by evaluating the angle difference between the Si(004) substrate and the central superlattice peak SL0, it can be shown that the C content of Si0.989 C0.011 layers is constant over the whole series. The Raman measurements were performed in backscattering geometry from the growth surface using the 514.5 nm line of an Ar+ laser as the exciting radiation at a constant power level of 40 mW for a focused spot with a diameter of about 30 µm. The scattered light was analyzed in a DILOR XY triple monochromator and detected in a charge coupled device multichannel system. The spectral resolution was kept below 2 cm−1 . The samples were maintained in a cryostat at a temperature of 77 K. No signal of SiC phase formation was found in the range of about 800 cm−1 . We use z as the growth direction. 3. Results and discussion Fig. 2 shows the Raman spectra for the depolarized z (xy)z configuration in the frequency range of the LO Si mode of a series of superlattices of the type Si0.989 C0.011 /Si with common period length of 16 nm. The relations of Si0.989 C0.011 –Si layer thicknesses for the samples are given in the legend of Fig. 2. In this figure, a spectrum of the Si substrate used in the growth of these samples is also displayed. The Raman spectra were normalized to a constant LO Si intensity. In the depolarized z (xy)z configuration, the longitudinal optical (LO) modes are allowed exclusively. Besides the small energy shift of the LO Si modes for the superlattices in comparison to that of the substrate, there is an asymmetric broadening of these lines to the lower energy side. This effect is summarized in Fig. 3. In this figure the half width at the half maximum (HWHM) for both energy sides of the LO Si mode of the samples is represented as a function of the Si0.989 C0.011 layer width inside one period. We started by finding the frequency, in wavenumbers, of the peaks, maximum for each normalized spectra shown in Fig. 2, using derivative methods. The half widths at the half maximum (HWHM) for each spectra have been then
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Fig. 2. The Raman spectra for z (xy)z configuration of a series of Si0.989 C0.011 /Si on Si(100). The spectra were normalized to a constant LO Si intensity.
evaluated by taking the difference between the interpolated values of the measurements and the maximum position of the peaks for each side, always at half of the peak intensity, neglecting the background level. The lines connecting the experimental points are only guides to the eye. We can observe a monotonical increase of the HWHM for the lower energy side (squares) of the LO Si mode, while the HWHM for the higher energy side (dots) is almost the same for all the alloy layer widths as it is for the substrate. This broadening, together with a broadening of the C local mode for concentrations as low as 0.76%, was assigned to disorder effects due to the introduction of C atoms in the Si lattice [13]. In our case, we did not observe a broadening in the C local mode, as will be shown later. This effect is attributed to the alloy potential fluctuations, which destroy the translational invariance, breaking the Raman selection rules for the Γ point of the Brillouin zone. Using a spatial correlation model, as described in Ref. [18], with a Gaussian spatial correlation function, it is possible to explain the asymmetry and broadening of the Raman line. In order to obtain the dispersion of the LO phonon mode, needed in the model, we have used a bond charge plane model described in Ref. [19] with the same parameters calculated therein. Fitting the spectra of Fig. 2 with this model, we have obtained correlation lengths of about 180 Å, for the superlattice with 12 nm alloy thickness in one period, up to 260 Å, for the sample with 4 nm. For an ideal crystal, the spatial correlation function of the phonon is infinite in extent. We have applied the same model to fit the spectrum of a sample constituted of a 140 nm Si0.989 C0.011 alloy layer on Si substrate, grown at the same conditions as the superlattice samples. The correlation length then obtained for this sample is about 250 Å. The agreement between this value and that for the superlattice samples is quite good. It should be mentioned here that the values for the correlation lengths of the superlattices indicate a mean value inside a period. An interpretation of the result is less evident than that for microcrystalline effects. The variation of the correlation lengths with the variation of the alloy layer thickness for the superlattice samples can be understood, inside this model, as a variation of the carbon concentration, leading to a mean value inside one period. Fig. 4 shows the Raman spectra of the series of superlattices with a period of 16 nm, in the z (xy)z geometry and low energy side of the LO Si mode. In order to enhance the modifications caused by the introduction of the C atoms, the Raman spectra were normalized to a constant LO Si intensity and a Raman spectrum of the Si substrate was subtracted from each of them. This procedure was used in the past in other Raman studies for Si1−x Cx [13,15]. The spectra were vertically shifted in order to permit a better comparison. Normally, C atoms in Si1−x Cx alloys for low C concentration occupy substitutional lattice sites, giving
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Fig. 3. Half width at half maximum of the LO Si mode as a function of the alloy width inside one period. The lines are only guides to the eye.
Fig. 5. The Raman spectra in the region of the local modes of the substitutional C atom. One spectrum from the substrate was subtracted from each curve in this figure, using the same procedure as before.
Fig. 4. The Raman spectra of the Si0.989 C0.011 /Si superlattices for the z (xy)z geometry in the low energy side of the LO Si line. The spectra were normalized and a Si substrate spectrum was subtracted from each of them.
rise to a local mode near 609 cm−1 . Despite the controversy about the validity of the Pauling’s model in this case, it is clear that even when we take into account some relaxation as in complex models, the substitution of a Si atom in a Si lattice by a C atom generates an extended defect involving at least its next nearestneighbors, that means 16 atoms [13]. In Fig. 4, we observe two other peaks at approximately 475 and 497 cm−1 . These peaks are related to vibrations of the Si atoms next to the substitutional C atom [13]. The changes of the force constants and the bond lengths due to relaxation of the Si atoms around the substitutional C atom are responsible for this effect. The assignment of this peak to the motion of neighboring Si atoms to the C atom was possible in the past due to the observation of an analogous structure in Ge1−x Cx alloys [13] and comparison with theoretical valence force model calculations [15]. Rücker et al. [15] have also observed shoulders at 470 and 495 cm−1 in Raman spectra of a Si1−x Cx epilayer on a Si substrate. The complex structure around the substitutional C atom and its interaction with other neighboring C atoms produces
diverse modes in the frequency region of the C–Si local mode at about 609 cm−1 , as can be seen in Fig. 5. We would like to point out that despite the use of B doped Si substrates, it was not possible to observe any vibrational mode in the Raman spectra of this substrate at 623 cm−1 , where a peak due to substitutional B atoms should appear. Apart from this, the Raman scattering cross section of substitutional B in Si has a strong dependence on its concentration [13]. Possibly in our case the boron concentration is too low to observe this vibrational mode. The only structure in this region appears at about 610 cm−1 and is due to two-phonon processes associated with a combination of optic and acoustic phonons in the Σ direction [20]. No difference could be noted between the Raman spectra of the two types of Si substrates, P doped and B doped. Fig. 5 shows the Raman spectra of the same superlattice series with a 16 nm period width in the region of the local C–Si mode. We have used the same procedure of normalization and subtraction of a substrate spectrum as for the spectra in Fig. 4. In the spectra we can observe two other structures at about 555 cm−1 and about 628 cm−1 , besides the main peak at 609 cm−1 , which is attributed to the local vibration of the carbon atom. By comparison with calculations of the Raman spectra based on an anharmonic Keating model and Raman and infrared absorption measurements on Si1−x Cx alloy layers [15], it is possible to assign the peak at about 628 cm−1 as being vibrations due to C–C pairs arranged as third nearest-neighbors. This structure was also observed in the simple Si1−x Cx alloy layers cited before. Following the same path, the observation of another satellite peak at about 555 cm−1 may be due to the formation of C atom pairs arranged as second nearest-neighbors, although energetically unfavorable. According to the calculations, the second nearest-neighbors arrangement also produces a peak, not resolved in the spectra, between the peak due to the local vibration of C and the peak due to C–C pairs arranged
E. Silveira / Solid State Communications 151 (2011) 846–849
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4. Conclusions
Fig. 6. The Raman spectra in the region of the local mode of the substitutional C atom. The peak at about 628 cm−1 is attributed to third nearest-neighbor C pairs.
as third nearest-neighbors. On the contrary, the Raman spectra of the group of samples grown on p(B) doped substrates in Fig. 6 show the same aspect as for the Si1−x Cx alloy layers, with a more pronounced and better resolved peak at about 628 cm−1 , due to the formation of a short range order with C–C pairs preferably as third nearest-neighbors. We have used for this figure the same normalization and subtraction of a substrate spectrum procedure mentioned earlier for Figs. 4 and 5. These features at about 630 cm−1 were attributed to interstitial C, instead of C ordering [16]. In comparison to the spectra of Fig. 5, the lower amount of substitutional C atoms in a second nearestneighbor configuration shows that the C atoms are more randomly distributed in the first series, grown on n-type substrates. The absence of the peaks arising from second nearest-neighbor pairs around 555 cm−1 for the samples grown on p-type substrates reinforces the argument of C ordering. Also, as pointed out in Ref. [16], differences in the microscopic structure of this kind of sample are mostly due to different growth techniques and rates. As an example, for samples of Ref. [21] grown by reducedpressure chemical vapor deposition using certain parameters, as mass flow ratios, all the carbon atoms have been incorporated into substitutional sites. In the scattering geometry where the folded acoustic phonons are allowed, i.e. parallel polarized z (xx)z Raman spectra (not shown here), no indication of these modes could be observed for the same integration times used to measure the perpendicular polarized Raman spectra. Disorder activated acoustic phonons were also not observed. The only observed structures are related to multiphonon Raman processes, such as the 2TA phonon band at about 300 cm−1 , and a forbidden low intensity Si optical mode at 520 cm−1 , probably due to small imperfections in the polarization of the light and the sample orientation.
In the present paper we have investigated the polarized Raman spectra of two series of Si0.989 C0.011 /Si superlattices with different period widths and thicknesses of the alloy layers grown epitaxially on two different types of Si substrates. No differences between the Raman spectra of the two substrates were found. In the Raman spectra of the superlattice samples we have observed a monotonous increase of the HWHM of the LO Si line for its low energy side, with the increase of the alloy layer thickness inside one period, while the HWHM for the high energy side stays almost constant. Two other peaks due to the relaxation of the Si atoms around the substitutional C atom were observed at 475 and 497 cm−1 . In the frequency range of the C local mode (∼ =609 cm−1 ) it was possible to notice differences between the two series of superlattices. The series grown on n-type Si substrate shows two other peaks, at 555 and 628 cm−1 , besides that of the local vibration of the C atom. By comparison with theoretical calculations for Si1−x Cx alloys, it was possible to assign these peaks to C–C atoms arranged as second and third nearest-neighbors, respectively, although the formation of C–C pairs as second nearest-neighbor is energetically unfavorable in the picture of this theoretical model. The experimental Raman spectra show some similarities with the Raman spectrum calculated for a random alloy. Conversely, the series of superlattices grown on p-type substrates shows in their Raman spectra only the structure due to the local C mode and that due to the formation of C–C pairs as third nearest-neighbors. No sign of superlattice formation was observed for the parallel polarized Raman spectra, where the folded acoustic modes are allowed. Acknowledgments The author is grateful to T. Gutheit for the samples. Helpful discussions with Prof. G. Abstreiter are gratefully acknowledged. Financial support from CAPES e CNPq (Brazilian agencies) are acknowledged. References [1] K. Brunner, K. Eberl, W. Winter, Phys. Rev. Lett. 76 (1996) 303. [2] W. Faschinger, S. Zerlauth, G. Bauer, L. Palmesthofer, Appl. Phys. Lett. 67 (1995) 3933. [3] W. Faschinger, S. Zerlauth, J. Stangl, G. Bauer, Appl. Phys. Lett. 67 (1995) 2630. [4] P. Boucaud, C. Francis, A. Larré, F.H. Julien, J.-M. Lourtioz, D. Bouchier, S. Bodnar, J.L. Regolini, Appl. Phys. Lett. 66 (1995) 70. [5] S.S. Iyer, K. Eberl, M.S. Goorsky, F.K. LeGoues, J.C. Tsang, Appl. Phys. Lett. 60 (1992) 356. [6] H. Rücker, M. Methfessel, E. Bugiel, H.J. Osten, Phys. Rev. Lett. 72 (1994) 3578. [7] J.L. Martins, A. Zunger, Phys. Rev. B 30 (1984) 6217. [8] H. Kajiyama, S. Muramatsu, T. Shimada, Y. Nishino, Phys. Rev. B 45 (1992) 14005. [9] B. Dietrich, H.J. Osten, H. Rücker, M. Methfessel, P. Zaumseil, Phys. Rev. B 49 (1994) 17185. [10] S.T. Chang, C.Y. Lin, C.W. Liu, J. Appl. Phys. 92 (2002) 3717. [11] A.A. Demkov, O.F. Sankey, Phys. Rev. B 48 (1993) 2207. [12] R.A. Soref, J. Appl. Phys. 70 (1991) 2470. [13] J.C. Tsang, K. Eberl, S. Zollner, S.S. Iyer, Appl. Phys. Lett. 61 (1992) 961. [14] J. Menéndez, P. Gopalan, G.S. Spencer, N. Cave, J.W. Strane, Appl. Phys. Lett. 66 (1995) 1160. [15] H. Rücker, M. Methfessel, B. Dietrich, K. Pressel, H.J. Osten, Phys. Rev. B 53 (1996) 1302. [16] D.J. Lockwood, H.X. Xu, J.-M. Baribeau, Phys. Rev. B 68 (2003) 115308. [17] T. Gutheit, M. Heinau, H.-J. Füsser, C. Wild, P. Koidl, G. Abstreiter, J. Cryst. Growth 157 (1995) 426. [18] P. Parayanthal, F. Pollak, Phys. Rev. Lett. 52 (1983) 1822. [19] P. Molinàs-Mata, M. Cardona, Phys. Rev. B 43 (1991) 9799. [20] P.A. Temple, C.E. Hathaway, Phys. Rev. B 7 (1973) 3685. [21] V. Loup, J.M. Hartmann, G. Rolland, P. Holliger, F. Laugier, M.N. Séméria, J. Vac. Sci. Technol. B 21 (2003) 246.
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Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Raman spectroscopy of pseudomorphic Si0.989 C0.011 /Si superlattices E. Silveira ∗ Departamento de Fisica - UFPR, Caixa Postal 19044, 81531-990 Curitiba-PR, Brazil
article
info
Article history: Received 8 January 2011 Received in revised form 14 March 2011 Accepted 16 March 2011 by L. Brey Available online 2 April 2011 Keywords: A. Semiconductors D. Optical properties D. Raman scattering
abstract Raman spectroscopy is used here to study pseudomorphic Si0.989 C0.011 /Si superlattices grown by molecular beam epitaxy. The high crystalline quality of the samples was tested by a high resolution X-ray diffraction experiment. The lineshape of the LO Si–Si peak shows an asymmetry, which correlates with the increase of the alloy layer width. The Raman spectra show three additional peaks in the high energy side above the LO mode of Si. One of them is due to the local vibration of the C substitutional atoms, and the other two can be attributed to the formation of short range order with C atoms occupying second and third nearest-neighbor places. On the low energy side of the LO Si–Si mode, we have observed two other peaks associated with the relaxation of the Si atoms around the substitutional C. Although the X-ray experiments show clear evidence of superperiodicity, no indication of the superlattice formation could be observed in the parallel polarized Raman spectra, where the folded acoustic modes are allowed. © 2011 Elsevier Ltd. All rights reserved.
1. Introduction The new possibilities and potential applications of materials involving binary Si1−x Cx and ternary Si1−x−y Gex Cy alloys in band gap and strain engineering have attracted a lot of interest since the 1990s [1–4], with regard to their growth and the characterization of physical properties. Due to a large mismatch of about 50% between Si and diamond, the extremely low C solubility in Si (10−6 at 1420 °C) [5] and the thermodynamically favored silicon carbide phases, the pseudomorphic growth of Si1−x Cx alloy layers on Si is normally limited to a few percent of C content. Using alternate evaporation of Si and C, it was possible to grow pseudomorphic layers and superlattices of ordered Si–C alloys with higher C contents of up to 50% [3,6]. Vegard’s law states that one can find the lattice constant of any alloy by interpolating between the lattice parameters of the constituents [7]. Contrary to this, Pauling’s model asserts that there is a characteristic length for each chemical bond. There is still a controversy about these two limits for the microscopic arrangement of atoms in these structures, with extended X-ray absorption fine structure measurements [8] confirming the predictions of Pauling’s model and Raman measurements with a modified valence force model, which shows some deviations from this picture [9]. Also, other theoretical models show some relaxations of the bond lengths towards Vegard’s law. It is very important to know the exact atomic arrangement in these structures, since small deviations mean large effects on the electronic properties [10]. Low temperature
∗
Tel.: +55 41 33613092; fax: +55 41 33613418. E-mail addresses: [email protected], [email protected].
0038-1098/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2011.03.016
photoluminescence measurements of Si1−x Cx /Si multiquantum wells and superlattices have demonstrated a linear decrease of these luminescence lines with increasing carbon content [1]. These results are consistent with theoretical calculations, that take into account the microscopic properties of these new materials [11]. This model contradicts prediction of the virtual crystal approximation, which predicted an increased gap for Si1−x Cx alloys compared to Si [12]. Raman scattering together with theoretical modeling has been used to understand and develop a detailed picture of the peculiar atomic and strain arrangement of Si1−x−y Gex Cy and Si1−x Cx alloy layers [13–16]. We present here results of polarized Raman spectra of Si0.989 C0.011 /Si superlattices grown by MBE pseudomorphically on two types of Si substrates. These results will be discussed in terms of previous Raman studies in Si1−x Cx and Si1−x−y Gex Cy [13,14], and recent calculations using a modified Keating valence force model [15]. 2. Materials and methods Two series of nominally Si0.989 C0.011 /Si superlattice samples were grown by solid source MBE at temperatures about 475 °C. A detailed description of the growth parameters can be found elsewhere [17]. The first series of five superlattices was grown on n(P) doped Si(001) substrates with a resistivity greater than 2 k cm. The widths of the alloy layer and the Si layer were varied from 4 nm to 12 nm and from 12 nm to 4 nm, respectively, maintaining the overall period as 16 nm. The other series, composed of three samples, was grown on p(B) doped Si(001) substrates. As for the first series, the period was kept constant at 14 nm, and the alloy layer and the Si layer were varied from 3.5 nm to 10.5 nm and from 10.5 nm to 3.5 nm, respectively. All samples
E. Silveira / Solid State Communications 151 (2011) 846–849
Fig. 1. Rocking curve around the 004 reflection of a Si0.989 C0.01 1/Si superlattice with 20 periods of 12 nm alloy layer and 4 nm Si layer thicknesses. The dashed line shows a dynamical simulation.
have 20 periods. High resolution X-ray diffraction (HRXRD) was used to verify the crystalline quality of the superlattices. Fig. 1 shows a typical result of a HRXRD coupled scan around the (004) reciprocal lattice point of a twenty times 16 nm period superlattice with 12 nm thick Si0.989 C0.011 layers inside each period. This rocking curve shows clearly resolved finite thickness fringes and the superlattice satellite peaks. Shown also in Fig. 1 is a simulation of the diffraction pattern. With good correspondence between the simulation and the measurements and the appearance of the finite thickness fringes, it is possible to conclude that the samples have proper periodicity and are of very good crystalline quality [3]. By monitoring the average C concentration inside one period, which can be done by evaluating the angle difference between the Si(004) substrate and the central superlattice peak SL0, it can be shown that the C content of Si0.989 C0.011 layers is constant over the whole series. The Raman measurements were performed in backscattering geometry from the growth surface using the 514.5 nm line of an Ar+ laser as the exciting radiation at a constant power level of 40 mW for a focused spot with a diameter of about 30 µm. The scattered light was analyzed in a DILOR XY triple monochromator and detected in a charge coupled device multichannel system. The spectral resolution was kept below 2 cm−1 . The samples were maintained in a cryostat at a temperature of 77 K. No signal of SiC phase formation was found in the range of about 800 cm−1 . We use z as the growth direction. 3. Results and discussion Fig. 2 shows the Raman spectra for the depolarized z (xy)z configuration in the frequency range of the LO Si mode of a series of superlattices of the type Si0.989 C0.011 /Si with common period length of 16 nm. The relations of Si0.989 C0.011 –Si layer thicknesses for the samples are given in the legend of Fig. 2. In this figure, a spectrum of the Si substrate used in the growth of these samples is also displayed. The Raman spectra were normalized to a constant LO Si intensity. In the depolarized z (xy)z configuration, the longitudinal optical (LO) modes are allowed exclusively. Besides the small energy shift of the LO Si modes for the superlattices in comparison to that of the substrate, there is an asymmetric broadening of these lines to the lower energy side. This effect is summarized in Fig. 3. In this figure the half width at the half maximum (HWHM) for both energy sides of the LO Si mode of the samples is represented as a function of the Si0.989 C0.011 layer width inside one period. We started by finding the frequency, in wavenumbers, of the peaks, maximum for each normalized spectra shown in Fig. 2, using derivative methods. The half widths at the half maximum (HWHM) for each spectra have been then
847
Fig. 2. The Raman spectra for z (xy)z configuration of a series of Si0.989 C0.011 /Si on Si(100). The spectra were normalized to a constant LO Si intensity.
evaluated by taking the difference between the interpolated values of the measurements and the maximum position of the peaks for each side, always at half of the peak intensity, neglecting the background level. The lines connecting the experimental points are only guides to the eye. We can observe a monotonical increase of the HWHM for the lower energy side (squares) of the LO Si mode, while the HWHM for the higher energy side (dots) is almost the same for all the alloy layer widths as it is for the substrate. This broadening, together with a broadening of the C local mode for concentrations as low as 0.76%, was assigned to disorder effects due to the introduction of C atoms in the Si lattice [13]. In our case, we did not observe a broadening in the C local mode, as will be shown later. This effect is attributed to the alloy potential fluctuations, which destroy the translational invariance, breaking the Raman selection rules for the Γ point of the Brillouin zone. Using a spatial correlation model, as described in Ref. [18], with a Gaussian spatial correlation function, it is possible to explain the asymmetry and broadening of the Raman line. In order to obtain the dispersion of the LO phonon mode, needed in the model, we have used a bond charge plane model described in Ref. [19] with the same parameters calculated therein. Fitting the spectra of Fig. 2 with this model, we have obtained correlation lengths of about 180 Å, for the superlattice with 12 nm alloy thickness in one period, up to 260 Å, for the sample with 4 nm. For an ideal crystal, the spatial correlation function of the phonon is infinite in extent. We have applied the same model to fit the spectrum of a sample constituted of a 140 nm Si0.989 C0.011 alloy layer on Si substrate, grown at the same conditions as the superlattice samples. The correlation length then obtained for this sample is about 250 Å. The agreement between this value and that for the superlattice samples is quite good. It should be mentioned here that the values for the correlation lengths of the superlattices indicate a mean value inside a period. An interpretation of the result is less evident than that for microcrystalline effects. The variation of the correlation lengths with the variation of the alloy layer thickness for the superlattice samples can be understood, inside this model, as a variation of the carbon concentration, leading to a mean value inside one period. Fig. 4 shows the Raman spectra of the series of superlattices with a period of 16 nm, in the z (xy)z geometry and low energy side of the LO Si mode. In order to enhance the modifications caused by the introduction of the C atoms, the Raman spectra were normalized to a constant LO Si intensity and a Raman spectrum of the Si substrate was subtracted from each of them. This procedure was used in the past in other Raman studies for Si1−x Cx [13,15]. The spectra were vertically shifted in order to permit a better comparison. Normally, C atoms in Si1−x Cx alloys for low C concentration occupy substitutional lattice sites, giving
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Fig. 3. Half width at half maximum of the LO Si mode as a function of the alloy width inside one period. The lines are only guides to the eye.
Fig. 5. The Raman spectra in the region of the local modes of the substitutional C atom. One spectrum from the substrate was subtracted from each curve in this figure, using the same procedure as before.
Fig. 4. The Raman spectra of the Si0.989 C0.011 /Si superlattices for the z (xy)z geometry in the low energy side of the LO Si line. The spectra were normalized and a Si substrate spectrum was subtracted from each of them.
rise to a local mode near 609 cm−1 . Despite the controversy about the validity of the Pauling’s model in this case, it is clear that even when we take into account some relaxation as in complex models, the substitution of a Si atom in a Si lattice by a C atom generates an extended defect involving at least its next nearestneighbors, that means 16 atoms [13]. In Fig. 4, we observe two other peaks at approximately 475 and 497 cm−1 . These peaks are related to vibrations of the Si atoms next to the substitutional C atom [13]. The changes of the force constants and the bond lengths due to relaxation of the Si atoms around the substitutional C atom are responsible for this effect. The assignment of this peak to the motion of neighboring Si atoms to the C atom was possible in the past due to the observation of an analogous structure in Ge1−x Cx alloys [13] and comparison with theoretical valence force model calculations [15]. Rücker et al. [15] have also observed shoulders at 470 and 495 cm−1 in Raman spectra of a Si1−x Cx epilayer on a Si substrate. The complex structure around the substitutional C atom and its interaction with other neighboring C atoms produces
diverse modes in the frequency region of the C–Si local mode at about 609 cm−1 , as can be seen in Fig. 5. We would like to point out that despite the use of B doped Si substrates, it was not possible to observe any vibrational mode in the Raman spectra of this substrate at 623 cm−1 , where a peak due to substitutional B atoms should appear. Apart from this, the Raman scattering cross section of substitutional B in Si has a strong dependence on its concentration [13]. Possibly in our case the boron concentration is too low to observe this vibrational mode. The only structure in this region appears at about 610 cm−1 and is due to two-phonon processes associated with a combination of optic and acoustic phonons in the Σ direction [20]. No difference could be noted between the Raman spectra of the two types of Si substrates, P doped and B doped. Fig. 5 shows the Raman spectra of the same superlattice series with a 16 nm period width in the region of the local C–Si mode. We have used the same procedure of normalization and subtraction of a substrate spectrum as for the spectra in Fig. 4. In the spectra we can observe two other structures at about 555 cm−1 and about 628 cm−1 , besides the main peak at 609 cm−1 , which is attributed to the local vibration of the carbon atom. By comparison with calculations of the Raman spectra based on an anharmonic Keating model and Raman and infrared absorption measurements on Si1−x Cx alloy layers [15], it is possible to assign the peak at about 628 cm−1 as being vibrations due to C–C pairs arranged as third nearest-neighbors. This structure was also observed in the simple Si1−x Cx alloy layers cited before. Following the same path, the observation of another satellite peak at about 555 cm−1 may be due to the formation of C atom pairs arranged as second nearest-neighbors, although energetically unfavorable. According to the calculations, the second nearest-neighbors arrangement also produces a peak, not resolved in the spectra, between the peak due to the local vibration of C and the peak due to C–C pairs arranged
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Fig. 6. The Raman spectra in the region of the local mode of the substitutional C atom. The peak at about 628 cm−1 is attributed to third nearest-neighbor C pairs.
as third nearest-neighbors. On the contrary, the Raman spectra of the group of samples grown on p(B) doped substrates in Fig. 6 show the same aspect as for the Si1−x Cx alloy layers, with a more pronounced and better resolved peak at about 628 cm−1 , due to the formation of a short range order with C–C pairs preferably as third nearest-neighbors. We have used for this figure the same normalization and subtraction of a substrate spectrum procedure mentioned earlier for Figs. 4 and 5. These features at about 630 cm−1 were attributed to interstitial C, instead of C ordering [16]. In comparison to the spectra of Fig. 5, the lower amount of substitutional C atoms in a second nearestneighbor configuration shows that the C atoms are more randomly distributed in the first series, grown on n-type substrates. The absence of the peaks arising from second nearest-neighbor pairs around 555 cm−1 for the samples grown on p-type substrates reinforces the argument of C ordering. Also, as pointed out in Ref. [16], differences in the microscopic structure of this kind of sample are mostly due to different growth techniques and rates. As an example, for samples of Ref. [21] grown by reducedpressure chemical vapor deposition using certain parameters, as mass flow ratios, all the carbon atoms have been incorporated into substitutional sites. In the scattering geometry where the folded acoustic phonons are allowed, i.e. parallel polarized z (xx)z Raman spectra (not shown here), no indication of these modes could be observed for the same integration times used to measure the perpendicular polarized Raman spectra. Disorder activated acoustic phonons were also not observed. The only observed structures are related to multiphonon Raman processes, such as the 2TA phonon band at about 300 cm−1 , and a forbidden low intensity Si optical mode at 520 cm−1 , probably due to small imperfections in the polarization of the light and the sample orientation.
In the present paper we have investigated the polarized Raman spectra of two series of Si0.989 C0.011 /Si superlattices with different period widths and thicknesses of the alloy layers grown epitaxially on two different types of Si substrates. No differences between the Raman spectra of the two substrates were found. In the Raman spectra of the superlattice samples we have observed a monotonous increase of the HWHM of the LO Si line for its low energy side, with the increase of the alloy layer thickness inside one period, while the HWHM for the high energy side stays almost constant. Two other peaks due to the relaxation of the Si atoms around the substitutional C atom were observed at 475 and 497 cm−1 . In the frequency range of the C local mode (∼ =609 cm−1 ) it was possible to notice differences between the two series of superlattices. The series grown on n-type Si substrate shows two other peaks, at 555 and 628 cm−1 , besides that of the local vibration of the C atom. By comparison with theoretical calculations for Si1−x Cx alloys, it was possible to assign these peaks to C–C atoms arranged as second and third nearest-neighbors, respectively, although the formation of C–C pairs as second nearest-neighbor is energetically unfavorable in the picture of this theoretical model. The experimental Raman spectra show some similarities with the Raman spectrum calculated for a random alloy. Conversely, the series of superlattices grown on p-type substrates shows in their Raman spectra only the structure due to the local C mode and that due to the formation of C–C pairs as third nearest-neighbors. No sign of superlattice formation was observed for the parallel polarized Raman spectra, where the folded acoustic modes are allowed. Acknowledgments The author is grateful to T. Gutheit for the samples. Helpful discussions with Prof. G. Abstreiter are gratefully acknowledged. Financial support from CAPES e CNPq (Brazilian agencies) are acknowledged. References [1] K. Brunner, K. Eberl, W. Winter, Phys. Rev. Lett. 76 (1996) 303. [2] W. Faschinger, S. Zerlauth, G. Bauer, L. Palmesthofer, Appl. Phys. Lett. 67 (1995) 3933. [3] W. Faschinger, S. Zerlauth, J. Stangl, G. Bauer, Appl. Phys. Lett. 67 (1995) 2630. [4] P. Boucaud, C. Francis, A. Larré, F.H. Julien, J.-M. Lourtioz, D. Bouchier, S. Bodnar, J.L. Regolini, Appl. Phys. Lett. 66 (1995) 70. [5] S.S. Iyer, K. Eberl, M.S. Goorsky, F.K. LeGoues, J.C. Tsang, Appl. Phys. Lett. 60 (1992) 356. [6] H. Rücker, M. Methfessel, E. Bugiel, H.J. Osten, Phys. Rev. Lett. 72 (1994) 3578. [7] J.L. Martins, A. Zunger, Phys. Rev. B 30 (1984) 6217. [8] H. Kajiyama, S. Muramatsu, T. Shimada, Y. Nishino, Phys. Rev. B 45 (1992) 14005. [9] B. Dietrich, H.J. Osten, H. Rücker, M. Methfessel, P. Zaumseil, Phys. Rev. B 49 (1994) 17185. [10] S.T. Chang, C.Y. Lin, C.W. Liu, J. Appl. Phys. 92 (2002) 3717. [11] A.A. Demkov, O.F. Sankey, Phys. Rev. B 48 (1993) 2207. [12] R.A. Soref, J. Appl. Phys. 70 (1991) 2470. [13] J.C. Tsang, K. Eberl, S. Zollner, S.S. Iyer, Appl. Phys. Lett. 61 (1992) 961. [14] J. Menéndez, P. Gopalan, G.S. Spencer, N. Cave, J.W. Strane, Appl. Phys. Lett. 66 (1995) 1160. [15] H. Rücker, M. Methfessel, B. Dietrich, K. Pressel, H.J. Osten, Phys. Rev. B 53 (1996) 1302. [16] D.J. Lockwood, H.X. Xu, J.-M. Baribeau, Phys. Rev. B 68 (2003) 115308. [17] T. Gutheit, M. Heinau, H.-J. Füsser, C. Wild, P. Koidl, G. Abstreiter, J. Cryst. Growth 157 (1995) 426. [18] P. Parayanthal, F. Pollak, Phys. Rev. Lett. 52 (1983) 1822. [19] P. Molinàs-Mata, M. Cardona, Phys. Rev. B 43 (1991) 9799. [20] P.A. Temple, C.E. Hathaway, Phys. Rev. B 7 (1973) 3685. [21] V. Loup, J.M. Hartmann, G. Rolland, P. Holliger, F. Laugier, M.N. Séméria, J. Vac. Sci. Technol. B 21 (2003) 246.