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Annealing simulations of nano-sized amorphous structures in SiC
Nuclear Instruments and Methods in Physics Research B 228 (2005) 282–287 www.elsevier.com/locate/nimb
Annealing simulations of nano-sized amorphous structures in SiC F. Gao *, R. Devanathan, Y. Zhang, W.J. Weber Pacific Northwest National Laboratory, MS K8-93, P.O. Box 999, Richland, WA 99352, USA
Abstract A two-dimensional model of a nano-sized amorphous layer embedded in a perfect crystal has been developed, and the amorphous-to-crystalline (a–c) transition in 3C-SiC at 2000 K has been studied using molecular dynamics methods, with simulation times of up to 88 ns. Analysis of the a–c interfaces reveals that the recovery of the bond defects existing at the a–c interfaces plays an important role in recrystallization. During the recrystallization process, a second ordered phase, crystalline 2H-SiC, nucleates and grows, and this phase is stable for long simulation times. The crystallization mechanism is a two-step process that is separated by a longer period of second-phase stability. The kink sites formed at the interfaces between 2H- and 3C-SiC provide a low energy path for 2H-SiC atoms to transfer to 3C-SiC atoms, a process which can be defined as a solid-phase epitaxial transformation (SPET). It is observed that the nano-sized amorphous structure can be fully recrystallized at 2000 K in SiC, which is in agreement with experimental observations. Published by Elsevier B.V. PACS: 61.72.Vv; 61.43.Dq; 81.10.Jt; 07.05.Tp Keywords: Defects; Amorphous layer; Annealing simulations; Silicon carbide
1. Introduction Silicon carbide (SiC) is a potential material for applications in power devices, optoelectronic devices and high temperature electronics [1], as well as structural components in nuclear reactors [2,3]. A critical problem for SiC device technology
*
Corresponding author. Tel.: +1 509 376 6275; fax: +1 509 376 5106. E-mail address: [email protected] (F. Gao). 0168-583X/$ - see front matter Published by Elsevier B.V. doi:10.1016/j.nimb.2004.10.057
is the annealing of the irradiation damage introduced during ion implantation into SiC [4]. It is well known that ion-beam-amorphized SiC is very stable against thermal annealing, and temperatures higher than 1723 K are necessary for its recrystallization [4]. The epitaxial regrowth of implantation-induced amorphous layers due to thermal annealing [5,6] or ion-beam-induced epitaxial crystallization (IBIEC) [7] has been studied by Rutherford backscattering spectrometry (RBS) and by transmission electron microscopy (TEM). The amorphous-to-crystalline transformation has
F. Gao et al. / Nucl. Instr. and Meth. in Phys. Res. B 228 (2005) 282–287
been observed at lower temperatures by IBIEC [7] or by thermal annealing in (1 1 0 0)- and (1 1 2 0)oriented SiC [5,6] than thermal annealing in (0 0 0 1)-oriented SiC. Molecular dynamics (MD) simulations have also been carried out to study defect annealing in SiC [8], but no crystallization occurred due to the very short time scales. In the present work, a two-dimensional model of 3C-SiC is developed, and a nano-sized amorphous zone is created by melting the central part of the crystal and then quenching to 0 K. In order to develop an atomic-scale understanding of recrystallization mechanisms in SiC, the annealing simulations of the amorphous zone are performed using MD simulations, with a previously developed interatomic potential [9].
283
brated for 0.2 ns to allow full mixing in the central region of the crystal, and then quenched to 0 K at the rate 1013 K/s. The system was relaxed for another 50 ps under zero-external pressure condition. The crystal was rescaled to 2000 K, and the annealing simulation employed the constant NPT ensemble with zero-external pressure.
3. Results and discussions Fig. 1(a) illustrates the amorphous structure obtained by melt-quenching liquid SiC, where light spheres represent C atoms and dark spheres indicate Si atoms. The central part of the crystal lacks any degree of periodicity and shows no evidence for residual crystallinity. Two interfaces are created between the amorphous phase and crystalline
2. Computational method For the present annealing simulations, a modified version of the MOLDY computer code is employed with a variable time step algorithm, and a Brenner-type empirical many body potential [9] combined with Ziegler–Biersak–Littmak potential [10] at separation distance less than 0.1 nm. Also examined are some of the under- and over-coordinated structures of SiC, and the results are reasonable in comparison with available experimental data and theoretical calculations, which will be reported elsewhere [11]. The simulation cell consisted of a 2a0 · 8a0 · 40a0 rectangular cell containing 5120 movable atoms extended along the z axis, which is particularly convenient for simulating the interface between amorphous and crystalline materials, where a0 is the lattice constant of 3C-SiC. Periodic boundary conditions were applied to all three directions. To generate a nanosize amorphous zone, the MD block was divided along the longitudinal axis into layers of thickness a0, with each layer containing four atomic planes of 128 atoms each in the perfect crystal of 3CSiC. A heat spike with a Gaussian profile was initially generated by applying a suitable distribution of kinetic energy to the atoms of the central 20 layers, and the maximum temperature was 6000 K. The crystal containing a molten zone was equili-
Fig. 1. (a) Atomic plot showing the central part of the crystal, where the melt-quenched amorphous layer lacks any degree of periodicity and two a–c interfaces can be clearly seen. Dark spheres indicate Si atoms, while light grey spheres represent C atoms. (b) The C–C and Si–Si pair-correlation functions of SiC corresponding the melt-quenched amorphous layer.
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materials. An analysis of the pair-correlation function, bond angles and bond length indicates that the central disordered region is a liquid-like structure that is consistent with an amorphous state. The pair-correlation function shown in Fig. 1(b) demonstrates that the C–C and Si–Si homonuclear bond peaks are visible at about 0.17 and 0.25 nm, respectively, which is consistent with observed bond peaks at about 0.15 and 0.24 in 6H-SiC amorphized by electrons [12] as well as by ion irradiation [13]. The extent of short-range disorder can be quantified by the fraction of homonuclear bonds, as suggested by Yuan and Hobbs [14]. Due to the difficulty in defining Si–Si bonds in highly damaged SiC, it has been recommended to use the C homonuclear bond ratio, v, which is defined as the ratio of C–C bonds to C–Si bonds [14]. This ratio ranges from a value of 0 for a perfect crystal to 1 for a completely disordered structure of SiC, and is also sensitive to the choice of bond cutoff distance in amorphized SiC. The present work uses a cutoff distance of 0.2 nm to calculate C–C and C–Si bonds, at which the first peak of the C–C pair-correlation vanishes in the amorphous SiC, as shown in Fig. 1(b). The short-range disorder parameter for the melt-quenched region,
v, is 0.14, which is consistent with the value of 0.13 obtained in a melt-quenched bulk SiC [15]. Further simulations of the structure at 0 K allows the interfaces to relax to a reasonable structure of low energy before reheating the temperature to 2000 K. It should be noted that the present amorphous structure and amorphous–crystalline interfaces are obtained by a melt-quenched (MQ) approach. However, it has been demonstrated that in-cascade or direct-impact amorphization in SiC does not occur during the cascade lifetime, even with high-energy recoil [16], and the amorphization in SiC is mainly due to defect accumulation [16,17]. Furthermore, the amorphous structure for completely cascade-overlap-amorphized (CA) SiC is similar to that obtained by melt-quenched SiC [16,17]. These results suggest that the structures of a full amorphized SiC by defect accumulation can be well represented by the MQ-SiC samples, but the partial amorphized SiC, particularly in the formation of large disordered domains during cascade overlap, cannot be described by the MQ-SiC samples. The results of annealing simulations are shown in Fig. 2 as a function of time, and the atomic projections are viewed perpendicular to the interfaces
Fig. 2. Computer generated plots showing the recrystallization process at 2000 K, the nucleation of the second-ordered phase and its growth as a function of time, where atom representation is same as that in Fig. 1. Two circles in (b) indicate the nucleation sites, and a partial-ordered phase is emphasized by a circle in (d).
F. Gao et al. / Nucl. Instr. and Meth. in Phys. Res. B 228 (2005) 282–287
on the xz plane, which clearly illustrate the movement of the amorphous–crystalline interfaces with time. The interface positions may be followed from plots of the planar density of atoms as a function of distance along the h0 0 1i direction, and the images in Fig. 2 indicate that recrystallization takes place continuously, as the crystalline portion increases with increasing time. This growth process is consistent with a model of solid-phase epitaxial growth (SPEG), where the amorphous–crystal interface separates a disordered, uniform phase from a highly ordered phase. In SPEG, the mobility of atoms is very low, which may relate to atomic relaxations to overcome dangling bonds and bond defects at the interfaces, rather than longrange thermal or atomic transport. It can be seen that there are a large number of bond defects existing at the interfaces, and the recovery of these bond defects plays an important role in recrystallization. In the present study, annealing simulations were carried out only at 2000 K, which does not allow the activation energy for thermal recrystallization to be determined. However, it is possible to determine the interface velocity, t, from visual location of the interface between the crystalline and amorphous regions during the simulations, and the estimated value of t is about 0.25 m/s. A more accurate value may be obtained by calculating the fraction of ‘‘crystalline’’ atoms to ‘‘amorphous’’ atoms as a function of time, as suggested by Bernstein et al. [18], and the detailed analysis will be described elsewhere.
285
In addition to the SPGE process at the interfaces, one of the interesting observations from the present simulations is that a second ordered phase can grow inside the amorphous region, as shown in Fig. 2(c). During the annealing simulation, the nucleation of the second ordered phase can be clearly seen in Fig. 2(b), as indicated within the circles, and the increase in the size of the second ordered phase with increasing time suggests that the growth of this ordered phase plays an important role in the recrystallization kinetics of amorphous SiC. A completely recrystallized phase is reached at about 37 ns, as shown in Fig. 2(d), where the second ordered phase forms a continuous network and is embedded in the perfect 3C-SiC. However, the atoms at the interfaces between the second ordered phase and the 3C-SiC crystal are randomly distributed, and a large number of dangling bonds are formed. In fact, these dangling bonds lead to the formation of the kink sites on [1 0 1] ledges separating the (1 1 1) terraces, as indicated by the solid lines in Fig. 2(d). These kink sites are responsible for the phase transformation along the [1 0 1] ledges during subsequent annealing simulation. A partially ordered domain can be clearly seen, as indicated within the circle, which consists of a transition region. The transformation of this region to the 3C-SiC structure will occur in a very short time. In order to understand the structure of the second ordered phase, a local region at the central part of the crystal in Fig. 2(d) is shown in Fig. 3, where the representation of atoms is the same as
Fig. 3. (a) Atomic structure in a small region at the top of the crystal showing in Fig. 2(d), where Si and C atoms are distinguished by dark and light grey spheres, respectively. (b) The stick presentation showing same structure in (a), but the crystal is rotated by a small angle such that the second ordered phase (2H-SiC) can be clearly viewed, where the orientation relationship between 3C-SiC and 2HSiC is indicated.
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that in Fig. 1(a). Fig. 3(b) is obtained by rotating a certain angle relative to Fig. 3(a), which shows much clearer configurations of the second ordered phase and the orientation relationship. It can be seen that the second ordered phase forms a layered structure along the [1 1 1] direction, similar to a hexagonal stacking along the c-axis, with the stacking periodicity of two. The atomic rows are formed on the basal planes along the [ 1 1 2] direction, as indicated in Fig. 3(b). The atomic structure in the second ordered region is identified as a 2H-SiC polytype. Reduction of sticking sequences from 6H-SiC to 3C has been observed experimentally by thermal annealing [5,6] or IBIEC of amorphous layers [7]. The formation of polytype crystals was suggested to be originated from the random rearrangement of atoms at the interface between regrown and residual amorphous layers where the atomic stacking sequence of the original polytype disappears. The growth of 3C polytype phase results in the formation of polycrystalline 3C-SiC. In general, polycrystalline 3C-SiC can stop the regrowth process, which requires much higher temperatures to completely anneal out the damage structure. The nucleation of the second polycrystalline phase in amorphous SiC and its growth during recrystallization in the current MD simulations are in agreement with the experimental observations. It is found that the polycrystalline 2H-SiC is very stable, and demands significant time to be annealed or transformed to the 3C-SiC structure. Detailed analysis of the atomic configurations will be reported elsewhere [11]. However, it is of interest to note that the transformation behavior from 2H-SiC to 3C-SiC is different from the traditional phase transformation, and is very similar to the recrystallization process at the amorphous–crystal interface, which may be defined as a solid-phase epitaxial transformation (SPET) [11]. The kink sites formed by dangling bonds and atomic rearrangements at the kink sites represent the dynamic process associated with SPET. Once the kink sites are formed, the solid-phase epitaxial transformation of atoms will occur in very short times. The complete transformation of 2H-SiC to 3C-SiC is attained in about 88 ns, which suggest that the nano-sized amorphous structure in SiC can be fully recrystallized at 2000 K. RBS in conjunction
with channeling, positron annihilation spectroscopy and cross-sectional transmission electron microscopy techniques (XTEM) have been employed to study annealing behavior of amorphous SiC layers [19], and the results suggest that the recrystallization strongly depends on annealing temperatures. The annealing of amorphous SiC layers performed by Wendler at al. [20] shows that perfect recrystallization seems to be attained at the annealing temperature of 1773 K. The present simulation results are generally in agreement with these experimental observations.
4. Summary The recrystallization of nano-sized amorphous layer has been investigated by a classical MD study in 3C-SiC at 2000 K. In general, the recrystallization process is consistent with a solid-phase epitaxial growth model. There exist a large number of bond defects at the amorphous–crystalline interfaces, and the recovery of bond defects and rearrangement of atoms at the interfaces play an important in recrystallization. One of the interesting results is that a second ordered phase can nucleate and grow inside the amorphous layer, and the detail analysis of atomic structure reveals that this second ordered phase is the 2H-SiC polytype. The kink sites formed at the interfaces between 2H- and 3C-SiC provide a low energy path for 2H-SiC atoms to transfer to 3C-SiC atoms, which can be defined as a solid-phase epitaxial transformation. Further simulation at 2000 K will lead to a polytype transformation from 2H-SiC to 3C-SiC, and a complete transformation is reached in about 88 ns. The simulation results are generally in good agreement with the previous experimental annealing behavior in SiC, and thus, provide atomic-level insights into the interpretation of experimental observed phenomena.
Acknowledgements This research is supported by the Division of Materials Sciences and Engineering, Office of
F. Gao et al. / Nucl. Instr. and Meth. in Phys. Res. B 228 (2005) 282–287
Basic Energy Sciences, US Department of Energy under Contract DE-AC06-76RLO 1830.
References [1] W. Bolse, Nucl. Instr. and Meth. B 148 (1999) 83. [2] K. Minato, K. Sawa, K. Koya, T. Tomita, A. Ishikawa, C.A. Baldwin, W.A. Gabbard, C.M. Malone, Nucl. Technol. 131 (2000) 36. [3] J.A. Lake, R.G. Bennett, J.F. Kotek, Sci. Am. 286 (2002) 73. [4] J.A. Edmond, S.P. Withrow, H.S. Kong, R.F. Davies, Mater. Res. Soc. Symp. Proc. 51 (1986) 395. [5] M. Satoh, Y. Nakaike, T. Nakamura, J. Appl. Phys. 89 (2001) 1986. [6] M. Satoh, K. Okamoto, Y. Nakaike, K. Kuriyama, M. Kanaya, N. Ohitani, Nucl. Instr. and Meth. B 148 (1999) 567. [7] V. Heera, J. Stoemenos, R. Kogler, W. Skorupa, J. Appl. Phys. 77 (1995) 2999. [8] L. Malerba, J.M. Perlado, J. Nucl. Mater. 289 (2001) 571.
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[9] F. Gao, W.J. Weber, Nucl. Instr. and Meth. B 191 (2002) 504. [10] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Matter, Pergamon, New York, 1985. [11] F. Gao, Y. Zhang, R. Devanathan, W.J. Weber, in press. [12] M. Ishimaru, I.-T. Bae, Y. Hurotsu, Phys. Rev. B 68 (2003) 144102. [13] M. Ishimaru, I.-T. Bae, Y. Hirotsu, S. Matsumura, K.E. Sickafus, Phys. Rev. Lett. 89 (2002) 055502. [14] X. Yuan, L.W. Hobbs, Nucl. Instr. and Meth. B 191 (2002) 74. [15] R. Devanathan, F. Gao, W.J. Weber, Appl. Phys. Lett. 84 (2004) 3909. [16] F. Gao, W.J. Weber, Phys. Rev. B 66 (2002) 024106. [17] L. Malerba, J.M. Perlado, J. Nucl. Mater. 289 (2001) 57. [18] N. Bernstein, M.J. Aziz, E. Kaxiras, Phys. Rev. B 61 (2000) 6696. [19] Y. Pacaud, J. Stoemenos, G. Brauer, R.A. Yankov, V. Heera, M. Voelskow, R. Kogler, W. Skotupa, Nucl. Instr. and Meth. B 120 (1996) 177. [20] E. Wendler, A. Heft, W. Wesch, Nucl. Instr. and Meth. B 141 (1998) 105.
Annealing simulations of nano-sized amorphous structures in SiC F. Gao *, R. Devanathan, Y. Zhang, W.J. Weber Pacific Northwest National Laboratory, MS K8-93, P.O. Box 999, Richland, WA 99352, USA
Abstract A two-dimensional model of a nano-sized amorphous layer embedded in a perfect crystal has been developed, and the amorphous-to-crystalline (a–c) transition in 3C-SiC at 2000 K has been studied using molecular dynamics methods, with simulation times of up to 88 ns. Analysis of the a–c interfaces reveals that the recovery of the bond defects existing at the a–c interfaces plays an important role in recrystallization. During the recrystallization process, a second ordered phase, crystalline 2H-SiC, nucleates and grows, and this phase is stable for long simulation times. The crystallization mechanism is a two-step process that is separated by a longer period of second-phase stability. The kink sites formed at the interfaces between 2H- and 3C-SiC provide a low energy path for 2H-SiC atoms to transfer to 3C-SiC atoms, a process which can be defined as a solid-phase epitaxial transformation (SPET). It is observed that the nano-sized amorphous structure can be fully recrystallized at 2000 K in SiC, which is in agreement with experimental observations. Published by Elsevier B.V. PACS: 61.72.Vv; 61.43.Dq; 81.10.Jt; 07.05.Tp Keywords: Defects; Amorphous layer; Annealing simulations; Silicon carbide
1. Introduction Silicon carbide (SiC) is a potential material for applications in power devices, optoelectronic devices and high temperature electronics [1], as well as structural components in nuclear reactors [2,3]. A critical problem for SiC device technology
*
Corresponding author. Tel.: +1 509 376 6275; fax: +1 509 376 5106. E-mail address: [email protected] (F. Gao). 0168-583X/$ - see front matter Published by Elsevier B.V. doi:10.1016/j.nimb.2004.10.057
is the annealing of the irradiation damage introduced during ion implantation into SiC [4]. It is well known that ion-beam-amorphized SiC is very stable against thermal annealing, and temperatures higher than 1723 K are necessary for its recrystallization [4]. The epitaxial regrowth of implantation-induced amorphous layers due to thermal annealing [5,6] or ion-beam-induced epitaxial crystallization (IBIEC) [7] has been studied by Rutherford backscattering spectrometry (RBS) and by transmission electron microscopy (TEM). The amorphous-to-crystalline transformation has
F. Gao et al. / Nucl. Instr. and Meth. in Phys. Res. B 228 (2005) 282–287
been observed at lower temperatures by IBIEC [7] or by thermal annealing in (1 1 0 0)- and (1 1 2 0)oriented SiC [5,6] than thermal annealing in (0 0 0 1)-oriented SiC. Molecular dynamics (MD) simulations have also been carried out to study defect annealing in SiC [8], but no crystallization occurred due to the very short time scales. In the present work, a two-dimensional model of 3C-SiC is developed, and a nano-sized amorphous zone is created by melting the central part of the crystal and then quenching to 0 K. In order to develop an atomic-scale understanding of recrystallization mechanisms in SiC, the annealing simulations of the amorphous zone are performed using MD simulations, with a previously developed interatomic potential [9].
283
brated for 0.2 ns to allow full mixing in the central region of the crystal, and then quenched to 0 K at the rate 1013 K/s. The system was relaxed for another 50 ps under zero-external pressure condition. The crystal was rescaled to 2000 K, and the annealing simulation employed the constant NPT ensemble with zero-external pressure.
3. Results and discussions Fig. 1(a) illustrates the amorphous structure obtained by melt-quenching liquid SiC, where light spheres represent C atoms and dark spheres indicate Si atoms. The central part of the crystal lacks any degree of periodicity and shows no evidence for residual crystallinity. Two interfaces are created between the amorphous phase and crystalline
2. Computational method For the present annealing simulations, a modified version of the MOLDY computer code is employed with a variable time step algorithm, and a Brenner-type empirical many body potential [9] combined with Ziegler–Biersak–Littmak potential [10] at separation distance less than 0.1 nm. Also examined are some of the under- and over-coordinated structures of SiC, and the results are reasonable in comparison with available experimental data and theoretical calculations, which will be reported elsewhere [11]. The simulation cell consisted of a 2a0 · 8a0 · 40a0 rectangular cell containing 5120 movable atoms extended along the z axis, which is particularly convenient for simulating the interface between amorphous and crystalline materials, where a0 is the lattice constant of 3C-SiC. Periodic boundary conditions were applied to all three directions. To generate a nanosize amorphous zone, the MD block was divided along the longitudinal axis into layers of thickness a0, with each layer containing four atomic planes of 128 atoms each in the perfect crystal of 3CSiC. A heat spike with a Gaussian profile was initially generated by applying a suitable distribution of kinetic energy to the atoms of the central 20 layers, and the maximum temperature was 6000 K. The crystal containing a molten zone was equili-
Fig. 1. (a) Atomic plot showing the central part of the crystal, where the melt-quenched amorphous layer lacks any degree of periodicity and two a–c interfaces can be clearly seen. Dark spheres indicate Si atoms, while light grey spheres represent C atoms. (b) The C–C and Si–Si pair-correlation functions of SiC corresponding the melt-quenched amorphous layer.
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materials. An analysis of the pair-correlation function, bond angles and bond length indicates that the central disordered region is a liquid-like structure that is consistent with an amorphous state. The pair-correlation function shown in Fig. 1(b) demonstrates that the C–C and Si–Si homonuclear bond peaks are visible at about 0.17 and 0.25 nm, respectively, which is consistent with observed bond peaks at about 0.15 and 0.24 in 6H-SiC amorphized by electrons [12] as well as by ion irradiation [13]. The extent of short-range disorder can be quantified by the fraction of homonuclear bonds, as suggested by Yuan and Hobbs [14]. Due to the difficulty in defining Si–Si bonds in highly damaged SiC, it has been recommended to use the C homonuclear bond ratio, v, which is defined as the ratio of C–C bonds to C–Si bonds [14]. This ratio ranges from a value of 0 for a perfect crystal to 1 for a completely disordered structure of SiC, and is also sensitive to the choice of bond cutoff distance in amorphized SiC. The present work uses a cutoff distance of 0.2 nm to calculate C–C and C–Si bonds, at which the first peak of the C–C pair-correlation vanishes in the amorphous SiC, as shown in Fig. 1(b). The short-range disorder parameter for the melt-quenched region,
v, is 0.14, which is consistent with the value of 0.13 obtained in a melt-quenched bulk SiC [15]. Further simulations of the structure at 0 K allows the interfaces to relax to a reasonable structure of low energy before reheating the temperature to 2000 K. It should be noted that the present amorphous structure and amorphous–crystalline interfaces are obtained by a melt-quenched (MQ) approach. However, it has been demonstrated that in-cascade or direct-impact amorphization in SiC does not occur during the cascade lifetime, even with high-energy recoil [16], and the amorphization in SiC is mainly due to defect accumulation [16,17]. Furthermore, the amorphous structure for completely cascade-overlap-amorphized (CA) SiC is similar to that obtained by melt-quenched SiC [16,17]. These results suggest that the structures of a full amorphized SiC by defect accumulation can be well represented by the MQ-SiC samples, but the partial amorphized SiC, particularly in the formation of large disordered domains during cascade overlap, cannot be described by the MQ-SiC samples. The results of annealing simulations are shown in Fig. 2 as a function of time, and the atomic projections are viewed perpendicular to the interfaces
Fig. 2. Computer generated plots showing the recrystallization process at 2000 K, the nucleation of the second-ordered phase and its growth as a function of time, where atom representation is same as that in Fig. 1. Two circles in (b) indicate the nucleation sites, and a partial-ordered phase is emphasized by a circle in (d).
F. Gao et al. / Nucl. Instr. and Meth. in Phys. Res. B 228 (2005) 282–287
on the xz plane, which clearly illustrate the movement of the amorphous–crystalline interfaces with time. The interface positions may be followed from plots of the planar density of atoms as a function of distance along the h0 0 1i direction, and the images in Fig. 2 indicate that recrystallization takes place continuously, as the crystalline portion increases with increasing time. This growth process is consistent with a model of solid-phase epitaxial growth (SPEG), where the amorphous–crystal interface separates a disordered, uniform phase from a highly ordered phase. In SPEG, the mobility of atoms is very low, which may relate to atomic relaxations to overcome dangling bonds and bond defects at the interfaces, rather than longrange thermal or atomic transport. It can be seen that there are a large number of bond defects existing at the interfaces, and the recovery of these bond defects plays an important role in recrystallization. In the present study, annealing simulations were carried out only at 2000 K, which does not allow the activation energy for thermal recrystallization to be determined. However, it is possible to determine the interface velocity, t, from visual location of the interface between the crystalline and amorphous regions during the simulations, and the estimated value of t is about 0.25 m/s. A more accurate value may be obtained by calculating the fraction of ‘‘crystalline’’ atoms to ‘‘amorphous’’ atoms as a function of time, as suggested by Bernstein et al. [18], and the detailed analysis will be described elsewhere.
285
In addition to the SPGE process at the interfaces, one of the interesting observations from the present simulations is that a second ordered phase can grow inside the amorphous region, as shown in Fig. 2(c). During the annealing simulation, the nucleation of the second ordered phase can be clearly seen in Fig. 2(b), as indicated within the circles, and the increase in the size of the second ordered phase with increasing time suggests that the growth of this ordered phase plays an important role in the recrystallization kinetics of amorphous SiC. A completely recrystallized phase is reached at about 37 ns, as shown in Fig. 2(d), where the second ordered phase forms a continuous network and is embedded in the perfect 3C-SiC. However, the atoms at the interfaces between the second ordered phase and the 3C-SiC crystal are randomly distributed, and a large number of dangling bonds are formed. In fact, these dangling bonds lead to the formation of the kink sites on [1 0 1] ledges separating the (1 1 1) terraces, as indicated by the solid lines in Fig. 2(d). These kink sites are responsible for the phase transformation along the [1 0 1] ledges during subsequent annealing simulation. A partially ordered domain can be clearly seen, as indicated within the circle, which consists of a transition region. The transformation of this region to the 3C-SiC structure will occur in a very short time. In order to understand the structure of the second ordered phase, a local region at the central part of the crystal in Fig. 2(d) is shown in Fig. 3, where the representation of atoms is the same as
Fig. 3. (a) Atomic structure in a small region at the top of the crystal showing in Fig. 2(d), where Si and C atoms are distinguished by dark and light grey spheres, respectively. (b) The stick presentation showing same structure in (a), but the crystal is rotated by a small angle such that the second ordered phase (2H-SiC) can be clearly viewed, where the orientation relationship between 3C-SiC and 2HSiC is indicated.
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F. Gao et al. / Nucl. Instr. and Meth. in Phys. Res. B 228 (2005) 282–287
that in Fig. 1(a). Fig. 3(b) is obtained by rotating a certain angle relative to Fig. 3(a), which shows much clearer configurations of the second ordered phase and the orientation relationship. It can be seen that the second ordered phase forms a layered structure along the [1 1 1] direction, similar to a hexagonal stacking along the c-axis, with the stacking periodicity of two. The atomic rows are formed on the basal planes along the [ 1 1 2] direction, as indicated in Fig. 3(b). The atomic structure in the second ordered region is identified as a 2H-SiC polytype. Reduction of sticking sequences from 6H-SiC to 3C has been observed experimentally by thermal annealing [5,6] or IBIEC of amorphous layers [7]. The formation of polytype crystals was suggested to be originated from the random rearrangement of atoms at the interface between regrown and residual amorphous layers where the atomic stacking sequence of the original polytype disappears. The growth of 3C polytype phase results in the formation of polycrystalline 3C-SiC. In general, polycrystalline 3C-SiC can stop the regrowth process, which requires much higher temperatures to completely anneal out the damage structure. The nucleation of the second polycrystalline phase in amorphous SiC and its growth during recrystallization in the current MD simulations are in agreement with the experimental observations. It is found that the polycrystalline 2H-SiC is very stable, and demands significant time to be annealed or transformed to the 3C-SiC structure. Detailed analysis of the atomic configurations will be reported elsewhere [11]. However, it is of interest to note that the transformation behavior from 2H-SiC to 3C-SiC is different from the traditional phase transformation, and is very similar to the recrystallization process at the amorphous–crystal interface, which may be defined as a solid-phase epitaxial transformation (SPET) [11]. The kink sites formed by dangling bonds and atomic rearrangements at the kink sites represent the dynamic process associated with SPET. Once the kink sites are formed, the solid-phase epitaxial transformation of atoms will occur in very short times. The complete transformation of 2H-SiC to 3C-SiC is attained in about 88 ns, which suggest that the nano-sized amorphous structure in SiC can be fully recrystallized at 2000 K. RBS in conjunction
with channeling, positron annihilation spectroscopy and cross-sectional transmission electron microscopy techniques (XTEM) have been employed to study annealing behavior of amorphous SiC layers [19], and the results suggest that the recrystallization strongly depends on annealing temperatures. The annealing of amorphous SiC layers performed by Wendler at al. [20] shows that perfect recrystallization seems to be attained at the annealing temperature of 1773 K. The present simulation results are generally in agreement with these experimental observations.
4. Summary The recrystallization of nano-sized amorphous layer has been investigated by a classical MD study in 3C-SiC at 2000 K. In general, the recrystallization process is consistent with a solid-phase epitaxial growth model. There exist a large number of bond defects at the amorphous–crystalline interfaces, and the recovery of bond defects and rearrangement of atoms at the interfaces play an important in recrystallization. One of the interesting results is that a second ordered phase can nucleate and grow inside the amorphous layer, and the detail analysis of atomic structure reveals that this second ordered phase is the 2H-SiC polytype. The kink sites formed at the interfaces between 2H- and 3C-SiC provide a low energy path for 2H-SiC atoms to transfer to 3C-SiC atoms, which can be defined as a solid-phase epitaxial transformation. Further simulation at 2000 K will lead to a polytype transformation from 2H-SiC to 3C-SiC, and a complete transformation is reached in about 88 ns. The simulation results are generally in good agreement with the previous experimental annealing behavior in SiC, and thus, provide atomic-level insights into the interpretation of experimental observed phenomena.
Acknowledgements This research is supported by the Division of Materials Sciences and Engineering, Office of
F. Gao et al. / Nucl. Instr. and Meth. in Phys. Res. B 228 (2005) 282–287
Basic Energy Sciences, US Department of Energy under Contract DE-AC06-76RLO 1830.
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