From 40806113920d686245243a06844fb4976baf736f Mon Sep 17 00:00:00 2001 From: hackbard Date: Tue, 28 Sep 2010 17:12:40 +0200 Subject: [PATCH] typos --- posic/publications/sic_prec.tex | 82 ++++++++++++++++----------------- 1 file changed, 41 insertions(+), 41 deletions(-) diff --git a/posic/publications/sic_prec.tex b/posic/publications/sic_prec.tex index 33e0708..f993bce 100644 --- a/posic/publications/sic_prec.tex +++ b/posic/publications/sic_prec.tex @@ -14,7 +14,7 @@ \begin{document} % ref mod: no capital letters (by editors) -\title{Combined ab initio and classical potential simulation study on the silicon carbide precipitation in silcon} +\title{Combined ab initio and classical potential simulation study on the silicon carbide precipitation in silicon} \author{F. Zirkelbach} \author{B. Stritzker} \affiliation{Experimentalphysik IV, Universit\"at Augsburg, 86135 Augsburg, Germany} @@ -28,7 +28,7 @@ \begin{abstract} Atomistic simulations on the silicon carbide precipitation in bulk silicon employing both, classical potential and first-principles methods are presented. For the quantum-mechanical treatment basic processes assumed in the precipitation process are mapped to feasible systems of small size. -Results of the accurate first-principles calculations on the carbon diffusion in silicon are compared to results of calssical potential simulations revealing significant limitations of the latter method. +Results of the accurate first-principles calculations on the carbon diffusion in silicon are compared to results of classical potential simulations revealing significant limitations of the latter method. An approach to work around this problem is proposed. Finally results of the classical potential molecular dynamics simulations of large systems are discussed. \end{abstract} @@ -47,7 +47,7 @@ The high breakdown field, saturated electron drift velocity and thermal conducti Different modifications of SiC exist, which solely differ in the one-dimensional stacking sequence of identical, close-packed SiC bilayers\cite{fischer90}. Different polytypes exhibit different properties, in which the cubic phase of SiC (3C-SiC) shows increased values for the thermal conductivity and breakdown field compared to other polytypes\cite{wesch96}, which is, thus, most effective for high-performance electronic devices. Much progress has been made in 3C-SiC thin film growth by chemical vapor deposition (CVD) and molecular beam epitaxy (MBE) on hexagonal SiC\cite{powell90,fissel95,fissel95_apl} and Si\cite{nishino83,nishino87,kitabatake93,fissel95_apl} substrates. -Howeve, the frequent occurrence of defects such as twins, dislocations and double position boundaries remains a challenging problem. +However, the frequent occurrence of defects such as twins, dislocations and double position boundaries remains a challenging problem. Next to these methods, high-dose carbon implantation into crystalline silicon (c-Si) with subsequent or in situ annealing was found to result in SiC microcrystallites in Si\cite{borders71}. Utilized and enhanced, ion beam synthesis (IBS) has become a promising method to form thin SiC layers of high quality and exclusively of the 3C polytype embedded in and epitactically aligned to the Si host featuring a sharp interface\cite{lindner99,lindner01,lindner02}. @@ -69,16 +69,16 @@ It will likewise offer perspectives for processes that rely upon prevention of p Atomistic simulations offer a powerful tool to study materials on a microscopic level providing detailed insight not accessible by experiment. In particular, molecular dynamics (MD) constitutes a suitable technique to investigate the dynamical and structural properties of some material. Modelling the processes mentioned above requires the simulation of a large amount of atoms ($\approx 10^5-10^6$), which inevitably dictates the atomic interaction to be described by computationally efficient classical potentials. -These are, however, less accurate compared to quantum-mechnical methods and theire applicability for the description of the physical problem has to be verified first. +These are, however, less accurate compared to quantum-mechanical methods and their applicability for the description of the physical problem has to be verified first. The most common empirical potentials for covalent systems are the Stillinger-Weber\cite{stillinger85} (SW), Brenner\cite{brenner90}, Tersoff\cite{tersoff_si3} and environment-dependent interatomic potential (EDIP)\cite{bazant96,bazant97,justo98}. These potentials are assumed to be reliable for large-scale simulations\cite{balamane92,huang95,godet03} on specific problems under investigation providing insight into phenomena that are otherwise not accessible by experimental or first-principles methods. Until recently\cite{lucas10}, a parametrization to describe the C-Si multicomponent system within the mentioned interaction models did only exist for the Tersoff\cite{tersoff_m} and related potentials, e.g. the one by Gao and Weber\cite{gao02} as well as the one by Erhart and Albe\cite{albe_sic_pot}. -All these potentials are short range potentials employing a cut-off function, which drops the atomic interaction to zero inbetween the first and second next neighbor distance. +All these potentials are short range potentials employing a cut-off function, which drops the atomic interaction to zero in between the first and second next neighbor distance. In a combined ab initio and empirical potential study it was shown that the Tersoff potential properly describes binding energies of combinations of C defects in Si\cite{mattoni2002}. However, investigations of brittleness in covalent materials\cite{mattoni2007} identified the short range character of these potentials to be responsible for overestimated forces necessary to snap the bond of two next neighbored atoms. In a previous study\cite{zirkelbach10a} we approved explicitly the influence on the migration barrier for C diffusion in Si. Using the Erhart/Albe (EA) potential\cite{albe_sic_pot} an overestimated barrier height compared to ab initio calculations and experiment is obtained. -A proper edscription of C diffusion, however, is crucial for the problem under study. +A proper description of C diffusion, however, is crucial for the problem under study. In this work, a combined ab initio and empirical potential simulation study on the initially mentioned SiC precipitation mechanism has been performed. High accurate quantum-mechanical results have been used to identify shortcomings of the classical potentials, which are then taken into account in these type of simulations. @@ -99,16 +99,16 @@ Spin polarization has been fully accounted for. For the classical potential calculations, defect structures were modeled in a supercell of nine Si lattice constants in each direction consisting of 5832 Si atoms. Reproducing the SiC precipitation was attempted by the successive insertion of 6000 C atoms (the number necessary to form a 3C-SiC precipitate with a radius of $\approx 3.1$ nm) into the Si host, which has a size of 31 Si unit cells in each direction consisting of 238328 Si atoms. At constant temperature 10 atoms were inserted at a time. -Three different regions within the total simulation volume were considered for a statistically distributed insertion of the C atoms: $V_1$ corresponding to the total simulation volume, $V_2$ corresponding to the size of the precipitate and $V_3$, whih holds the necessary amount of Si atoms of the precipitate. +Three different regions within the total simulation volume were considered for a statistically distributed insertion of the C atoms: $V_1$ corresponding to the total simulation volume, $V_2$ corresponding to the size of the precipitate and $V_3$, which holds the necessary amount of Si atoms of the precipitate. After C insertion the simulation has been continued for \unit[100]{ps} and cooled down to \unit[20]{$^{\circ}$C} afterwards. A Tersoff-like bond order potential by Erhart and Albe (EA)\cite{albe_sic_pot} has been utilized, which accounts for nearest neighbor interactions only realized by a cut-off function dropping the interaction to zero in between the first and second next neighbor distance. The potential was used as is, i.e. without any repulsive potential extension at short interatomic distances. Constant pressure simulations are realized by the Berendsen barostat\cite{berendsen84} using a time constant of \unit[100]{fs} and a bulk modulus of \unit[100]{GPa} for Si. The temperature is kept constant by the Berendsen thermostat\cite{berendsen84} with a time constant of \unit[100]{fs}. Integration of equations of motion is realized by the velocity Verlet algorithm\cite{verlet67} and a fixed time step of \unit[1]{fs}. -For structural relaxation of defect structures the same algorith is used with the temperature set to 0 K. +For structural relaxation of defect structures the same algorithm is used with the temperature set to 0 K. -The formation energy $E-N_{\text{Si}}\mu_{\text{Si}}-N_{\text{C}}\mu_{\text{C}}$ of a defect configuration is defined by chosing SiC as a particle reservoir for the C impurity, i.e. the chemical potentials are determined by the cohesive energies of a perfect Si and SiC supercell after ionic relaxation. +The formation energy $E-N_{\text{Si}}\mu_{\text{Si}}-N_{\text{C}}\mu_{\text{C}}$ of a defect configuration is defined by choosing SiC as a particle reservoir for the C impurity, i.e. the chemical potentials are determined by the cohesive energies of a perfect Si and SiC supercell after ionic relaxation. Migration and recombination pathways have been investigated utilizing the constraint conjugate gradient relaxation technique\cite{kaukonen98}. \section{Results} @@ -142,12 +142,12 @@ The second most favorable configuration is the C$_{\text{i}}$ \hkl<1 1 0> DB fol For both configurations EA overestimates the energy of formation by approximately \unit[1]{eV} compared to DFT. Thus, nearly the same difference in energy has been observed for these configurations in both methods. However, we have found the BC configuration to constitute a saddle point within the EA description relaxing into the \hkl<1 1 0> configuration. -Due to the high formation energy of the BC defect resulting in a low probability of occurence of this defect, the wrong description is not posing a serious limitation of the EA potential. +Due to the high formation energy of the BC defect resulting in a low probability of occurrence of this defect, the wrong description is not posing a serious limitation of the EA potential. A more detailed discussion of C defects in Si modeled by EA and DFT including further defect configurations are presented in a previous study\cite{zirkelbach10a}. Regarding intrinsic defects in Si, both methods predict energies of formation that are within the same order of magnitude. However discrepancies exist. -Quantum-mechanical results reveal the Si$_{\text{i}}$ \hkl<1 1 0> DB to compose the energetically most favorabe configuration, which is the consensus view for Si$_{\text{i}}$\cite{leung99,al-mushadani03}. +Quantum-mechanical results reveal the Si$_{\text{i}}$ \hkl<1 1 0> DB to compose the energetically most favorable configuration, which is the consensus view for Si$_{\text{i}}$\cite{leung99,al-mushadani03}. The EA potential does not reproduce the correct ground state. Instead the tetrahedral defect configuration is favored. This limitation is assumed to arise due to the cut-off. @@ -165,7 +165,7 @@ However the energy of formation is slightly higher than that of the C$_{\text{i} For a possible clarification of the controversial views on the participation of C$_{\text{s}}$ in the precipitation mechanism by classical potential simulations, test calculations need to ensure the proper description of the relative formation energies of combined structures of C$_{\text{s}}$ and Si$_{\text{i}}$ compared to C$_{\text{i}}$. This is particularly important since the energy of formation of C$_{\text{s}}$ is drastically underestimated by the EA potential. -A possible occurence of C$_{\text{s}}$ could then be attributed to a lower energy of formation of the C$_{\text{s}}$-Si$_{\text{i}}$ combination due to the low formation energy of C$_{\text{s}}$, which obviously is wrong. +A possible occurrence of C$_{\text{s}}$ could then be attributed to a lower energy of formation of the C$_{\text{s}}$-Si$_{\text{i}}$ combination due to the low formation energy of C$_{\text{s}}$, which obviously is wrong. Since quantum-mechanical calculation reveal the Si$_{\text{i}}$ \hkl<1 1 0> DB as the ground state configuration of Si$_{\text{i}}$ in Si it is assumed to provide the energetically most favorable configuration in combination with C$_{\text{s}}$. Empirical potentials, however, predict Si$_{\text{i}}$ T to be the energetically most favorable configuration. @@ -185,9 +185,9 @@ Results of VASP and EA calculations are summarized in Table~\ref{tab:defect_comb \end{table} Obviously the EA potential properly describes the relative energies of formation. Combined structures of C$_{\text{s}}$ and Si$_{\text{i}}$ T are energetically less favorable than the ground state C$_{\text{i}}$ \hkl<1 0 0> DB configuration. -With increasing separation distance the enrgies of formation decrease. +With increasing separation distance the energies of formation decrease. However, even for non-interacting defects, the energy of formation, which is then given by the sum of the formation energies of the separated defects (\unit[4.15]{eV}) is still higher than that of the C$_{\text{i}}$ \hkl<1 0 0> DB. -Unexpectedly, the structure of a Si$_{\text{i}}$ \hkl<1 1 0> DB and a next neighbored C$_{\text{s}}$, which is the most favored configuration of C$_{\text{s}}$ and Si$_{\text{i}}$ according to quantum-mechanical caluclations\cite{zirkelbach10b} likewise constitutes an energetically favorable configuration within the EA description, which is even preferred over the two least separated configurations of C$_{\text{s}}$ and Si$_{\text{i}}$ T. +Unexpectedly, the structure of a Si$_{\text{i}}$ \hkl<1 1 0> DB and a next neighbored C$_{\text{s}}$, which is the most favored configuration of C$_{\text{s}}$ and Si$_{\text{i}}$ according to quantum-mechanical calculations\cite{zirkelbach10b} likewise constitutes an energetically favorable configuration within the EA description, which is even preferred over the two least separated configurations of C$_{\text{s}}$ and Si$_{\text{i}}$ T. This is attributed to an effective reduction in strain enabled by the respective combination. Thus, a proper description with respect to the relative energies of formation is assumed for the EA potential. @@ -243,21 +243,21 @@ Additionally the Si-Si radial distribution shows non-zero values at distances ar This is accompanied by a reduction of the number of bonds at regular Si distances of c-Si. A more detailed description of the resulting C-Si distances in the C$_{\text{i}}$ \hkl<1 0 0> DB configuration and the influence of the defect on the structure is available in a previous study\cite{zirkelbach09}. -For high C concentrations the defect concentration is likewise increased and a considerable amount of damamge is introduced in the insertion volume. +For high C concentrations the defect concentration is likewise increased and a considerable amount of damage is introduced in the insertion volume. A subsequent superposition of defects generates new displacement arrangements for the C-C as well as Si-C pair distances, which become hard to categorize and trace and obviously lead to a broader distribution. Short range order indeed is observed, i.e. the large amount of strong next neighbored C-C bonds at \unit[0.15]{nm} as expected in graphite or diamond and Si-C bonds at \unit[0.19]{nm} as expected in SiC, but only hardly visible is the long range order. This indicates the formation of an amorphous SiC-like phase. -In fact resulting Si-C and C-C radial distribution functions compare quite well with these obtained by cascade amorphized and melt-quenched amorphous SiC using a modifed Tersoff potential\cite{gao02}. +In fact resulting Si-C and C-C radial distribution functions compare quite well with these obtained by cascade amorphized and melt-quenched amorphous SiC using a modified Tersoff potential\cite{gao02}. In both cases, i.e. low and high C concentrations, the formation of 3C-SiC fails to appear. With respect to the precipitation model the formation of C$_{\text{i}}$ \hkl<1 0 0> DBs indeed occurs for low C concentrations. However, sufficient defect agglomeration is not observed. -For high C concentrations a rearrangment of the amorphous SiC structure, which is not expected at prevailing temperatures, and a transition into 3C-SiC is not observed either. +For high C concentrations a rearrangement of the amorphous SiC structure, which is not expected at prevailing temperatures, and a transition into 3C-SiC is not observed either. On closer inspection two reasons for describing this obstacle become evident. First of all there is the time scale problem inherent to MD in general. To minimize the integration error the discretized time step must be chosen smaller than the reciprocal of the fastest vibrational mode resulting in a time step of \unit[1]{fs} for the current problem under study. -Limitations in computer power result in a slow propgation in phase space. +Limitations in computer power result in a slow propagation in phase space. Several local minima exist, which are separated by large energy barriers. Due to the low probability of escaping such a local minimum a single transition event corresponds to a multiple of vibrational periods. Long-term evolution such as a phase transformation and defect diffusion, in turn, are made up of a multiple of these infrequent transition events. @@ -267,16 +267,16 @@ New accelerated methods have been developed to bypass the time scale problem ret However, the applied potential comes up with an additional limitation already mentioned in the introductory part. The cut-off function of the short range potential limits the interaction to next neighbors, which results in overestimated and unphysical high forces between next neighbor atoms. This behavior, as observed and discussed for the Tersoff potential\cite{tang95,mattoni2007}, is supported by the overestimated activation energies necessary for C diffusion as investigated in section \ref{subsection:cmob}. -Indeed it is not only the strong C-C bond which is hard to break inhibiting C diffusion and further rearrengements in the case of the high C concentration simulations. +Indeed it is not only the strong C-C bond which is hard to break inhibiting C diffusion and further rearrangements in the case of the high C concentration simulations. This is also true for the low concentration simulations dominated by the occurrence of C$_{\text{i}}$ \hkl<1 1 0> DBs spread over the whole simulation volume, which are unable to agglomerate due to the high migration barrier. \subsection{Increased temperature simulations} -Due to the potential enhanced problem of slow phase space propagation, pushing the time scale to the limits of computational ressources or applying one of the above mentioned accelerated dynamics methods exclusively might not be sufficient. +Due to the potential enhanced problem of slow phase space propagation, pushing the time scale to the limits of computational resources or applying one of the above mentioned accelerated dynamics methods exclusively might not be sufficient. Instead higher temperatures are utilized to compensate overestimated diffusion barriers. These are overestimated by a factor of 2.4 to 3.5. Scaling the absolute temperatures accordingly results in maximum temperatures of \unit[1460-2260]{$^{\circ}$C}. -Since melting already occurs shortly below the melting point of the potetnial (2450 K)\cite{albe_sic_pot} due to the presence of defects, a maximum temperature of \unit[2050]{$^{\circ}$C} is used. +Since melting already occurs shortly below the melting point of the potential (2450 K)\cite{albe_sic_pot} due to the presence of defects, a maximum temperature of \unit[2050]{$^{\circ}$C} is used. Fig.~\ref{fig:tot} shows the resulting radial distribution functions for various temperatures. \begin{figure} @@ -285,7 +285,7 @@ Fig.~\ref{fig:tot} shows the resulting radial distribution functions for various \includegraphics[width=\columnwidth]{../img/tot_pc3_thesis.ps}\\ \includegraphics[width=\columnwidth]{../img/tot_pc2_thesis.ps} \end{center} -\caption{Radial distribution function for Si-C (top), Si-Si (center) and C-C (bottom) pairs for the C insertion into $V_1$ at elevated temperatures. For the Si-C distribution resulting Si-C distances of a C$_{\text{s}}$ configuration are plotted. In the C-C distribution dashed arrows mark C-C distances occuring from C$_{\text{i}}$ \hkl<1 0 0> DB combinations, solid arrows mark C-C distances of pure C$_{\text{s}}$ combinations and the dashed line marks C-C distances of a C$_{\text{i}}$ and C$_{\text{s}}$ combination.} +\caption{Radial distribution function for Si-C (top), Si-Si (center) and C-C (bottom) pairs for the C insertion into $V_1$ at elevated temperatures. For the Si-C distribution resulting Si-C distances of a C$_{\text{s}}$ configuration are plotted. In the C-C distribution dashed arrows mark C-C distances occurring from C$_{\text{i}}$ \hkl<1 0 0> DB combinations, solid arrows mark C-C distances of pure C$_{\text{s}}$ combinations and the dashed line marks C-C distances of a C$_{\text{i}}$ and C$_{\text{s}}$ combination.} \label{fig:tot} \end{figure} The first noticeable and promising change observed for the Si-C bonds is the successive decline of the artificial peak at the cut-off distance with increasing temperature. @@ -294,18 +294,18 @@ Additionally a more important structural change was observed, which is illustrat Obviously the structure obtained at \unit[450]{$^{\circ}$C}, which was found to be dominated by C$_{\text{i}}$, transforms into a C$_{\text{s}}$ dominated structure with increasing temperature. Comparing the radial distribution at \unit[2050]{$^{\circ}$C} to the resulting bonds of C$_{\text{s}}$ in c-Si excludes all possibility of doubt. -The phase transformation is accompanied by an arising Si-Si peak at \unit[0.325]{nm}, which corresponds to the distance of second next neighbored Si atoms alonga \hkl<1 1 0> boind chain with C$_{\text{s}}$ inbetween. +The phase transformation is accompanied by an arising Si-Si peak at \unit[0.325]{nm}, which corresponds to the distance of second next neighbored Si atoms along \hkl<1 1 0> bond chain with C$_{\text{s}}$ in between. Since the expected distance of these Si pairs in 3C-SiC is \unit[0.308]{nm} the existing SiC structures embedded in the c-Si host are stretched. -According to the C-C radial distribution agglomeration of C fails to appear even for elevated temperatures as can be seen on the total amount of C pairs within the investigated separation range, wich does not change significantly. -However, a small decrease in the amount of next neighboured C pairs can be observed with increasing temperature. -This high temperature behavior is promising since breaking of these diomand- and graphite-like bonds is mandatory for the formation of 3C-SiC. -Obviously acceleration of the dynamics occured by supplying additional kinetic energy. +According to the C-C radial distribution agglomeration of C fails to appear even for elevated temperatures as can be seen on the total amount of C pairs within the investigated separation range, which does not change significantly. +However, a small decrease in the amount of next neighbored C pairs can be observed with increasing temperature. +This high temperature behavior is promising since breaking of these diamond- and graphite-like bonds is mandatory for the formation of 3C-SiC. +Obviously acceleration of the dynamics occurred by supplying additional kinetic energy. A slight shift towards higher distances can be observed for the maximum located shortly above \unit[0.3]{nm}. Arrows with dashed lines mark C-C distances resulting from C$_{\text{i}}$ \hkl<1 0 0> DB combinations while arrows with solid lines mark distances arising from combinations of C$_{\text{s}}$. -The continuous dashed line corresponds to the distance of C$_{\text{s}}$ and a next neighboured C$_{\text{i}}$ DB. +The continuous dashed line corresponds to the distance of C$_{\text{s}}$ and a next neighbored C$_{\text{i}}$ DB. Obviously the shift of the peak is caused by the advancing transformation of the C$_{\text{i}}$ DB into the C$_{\text{s}}$ defect. -Quite high g(r) values are obtained for distances inbetween the continuous dashed line and the first arrow with a solid line. +Quite high g(r) values are obtained for distances in between the continuous dashed line and the first arrow with a solid line. For the most part these structures can be identified as configurations of C$_{\text{s}}$ with either another C atom that basically occupies a Si lattice site but is displaced by a Si interstitial residing in the very next surrounding or a C atom that nearly occupies a Si lattice site forming a defect other than the \hkl<1 0 0>-type with the Si atom. Again, this is a quite promising result since the C atoms are taking the appropriate coordination as expected in 3C-SiC. @@ -324,24 +324,24 @@ However, the decrease of the cut-off artifact and slightly sharper peaks observe However, it is not sufficient to enable the amorphous to crystalline transition. In contrast, even though next neighbored C bonds could be partially dissolved in the system exhibiting low C concentrations the amount of next neighbored C pairs even increased in the latter case. Moreover the C-C peak at \unit[0.252]{nm}, which gets slightly more distinct, equals the second next neighbor distance in diamond and indeed is made up by a structure of two C atoms interconnected by a third C atom. -Obviously processes that appear to be non-conducive are likewise accelerated in a system, in which high amounts of C are incoorporated within a short period of time, which is accompanied by a concurrent introduction of accumulating, for the reason of time non-degradable, damage. +Obviously processes that appear to be non-conducive are likewise accelerated in a system, in which high amounts of C are incorporated within a short period of time, which is accompanied by a concurrent introduction of accumulating, for the reason of time non-degradable, damage. % non-degradable, non-regenerative, non-recoverable Thus, for these systems even larger time scales, which are not accessible within traditional MD, must be assumed for an amorphous to crystalline transition or structural evolution in general. % maybe put description of bonds in here ... -Nevertheless, some results likewiese indicate the acceleration of other processes that, again, involve C$_{\text{s}}$. +Nevertheless, some results likewise indicate the acceleration of other processes that, again, involve C$_{\text{s}}$. The increasingly pronounced Si-C peak at \unit[0.35]{nm} corresponds to the distance of a C and a Si atom interconnected by another Si atom. Additionally the C-C peak at \unit[0.31]{nm} corresponds to the distance of two C atoms bound to a central Si atom. For both structures the C atom appears to reside on a substitutional rather than an interstitial lattice site. However, huge amount of damage hampers identification. -The alignment of the investigated structures to the c-Si host is lost in many cases, which suggests the necissity of much more time for structural evolution to maintain the topotaptic orientation of the precipitate. +The alignment of the investigated structures to the c-Si host is lost in many cases, which suggests the necessity of much more time for structural evolution to maintain the topotactic orientation of the precipitate. \section{Summary and discussion} -Investigations are targeted on the initially stated controversy of SiC precipitation, i.e. whether precipitation occurs abrubtly after ehough C$_{\text{i}}$ agglomerated or a successive agglomeration of C$_{\text{s}}$ on usual Si lattice sites (and Si$_{\text{i}}$) followed by a contraction into incoherent SiC. -Results of a previous ab initio study on defects and defect combinations in C implanted Si\cite{zirkelbach10b} sugeest C$_{\text{s}}$ to play a decisive role in the precipitation of SiC in Si. +Investigations are targeted on the initially stated controversy of SiC precipitation, i.e. whether precipitation occurs abruptly after enough C$_{\text{i}}$ agglomerated or a successive agglomeration of C$_{\text{s}}$ on usual Si lattice sites (and Si$_{\text{i}}$) followed by a contraction into incoherent SiC. +Results of a previous ab initio study on defects and defect combinations in C implanted Si\cite{zirkelbach10b} suggest C$_{\text{s}}$ to play a decisive role in the precipitation of SiC in Si. To support previous assumptions MD simulations, which are capable of modeling the necessary amount of atoms, i.e. the precipitate and the surrounding c-Si structure, have been employed in the current study. -In a previous comparative study\cite{zirkelbach10a} we have schown that the utilized empirical potential fails to describe some selected processes. +In a previous comparative study\cite{zirkelbach10a} we have shown that the utilized empirical potential fails to describe some selected processes. Thus, limitations of the employed potential have been further investigated and taken into account in the present study. We focussed on two major shortcomings: the overestimated activation energy and the improper description of intrinsic and C point defects in Si. Overestimated forces between next neighbor atoms that are expected for short range potentials\cite{mattoni2007} have been confirmed to influence the C$_{\text{i}}$ diffusion. @@ -350,15 +350,15 @@ Concerning point defects the drastically underestimated formation energy of C$_{ It turned out that the EA potential still favors a C$_{\text{i}}$ \hkl<1 0 0> DB over a C$_{\text{s}}$-Si$_{\text{i}}$ configuration, which, thus, does not constitute any limitation for the simulations aiming to resolve the present controversy of the proposed SiC precipitation models. MD simulations at temperatures used in IBS resulted in structures that were dominated by the C$_{\text{i}}$ \hkl<1 0 0> DB and its combinations if C is inserted into the total volume. -Incoorporation into volmes $V_2$ and $V_3$ led to an amorphous SiC-like structure within the respective volume. +Incorporation into volumes $V_2$ and $V_3$ led to an amorphous SiC-like structure within the respective volume. To compensate overestimated diffusion barriers we performed simulations at accordingly increased temperatures. No significant change was observed for high C concentrations. The amorphous phase is maintained. -Due to the incoorparation of a huge amount of C into a small volume within a short period of time damage is produced, which obviously decelerates strcutural evolution. +Due to the incorporation of a huge amount of C into a small volume within a short period of time damage is produced, which obviously decelerates structural evolution. For the low C concentrations, time scales are still too low to observe C agglomeration sufficient for SiC precipitation, which is attributed to the slow phase space propagation inherent to MD in general. -However, we observed a phase tranisiton of the C$_{\text{i}}$-dominated into a clearly C$_{\text{s}}$-dominated structure. +However, we observed a phase transition of the C$_{\text{i}}$-dominated into a clearly C$_{\text{s}}$-dominated structure. The amount of substitutionally occupied C atoms increases with increasing temperature. -Entropic contributions are assumed to be responsible for these structures at eleveated temperatures that deviate from the ground state at 0 K. +Entropic contributions are assumed to be responsible for these structures at elevated temperatures that deviate from the ground state at 0 K. Indeed, in a previous ab initio MD simulation\cite{zirkelbach10b} performed at \unit[900]{$^{\circ}$C} we observed the departing of a Si$_{\text{i}}$ \hkl<1 1 0> DB located next to a C$_{\text{s}}$ atom instead of a recombination into the ground state configuration, i.e. a C$_{\text{i}}$ \hkl<1 0 0> DB. % postannealing less efficient than hot implantation @@ -370,7 +370,7 @@ Implantations of an understoichiometric dose at room temperature followed by the Since, however, the implantation temperature is considered more efficient than the postannealing temperature, SiC precipitates are expected -- and indeed are observed for as-implanted samples\cite{lindner99,lindner01} -- in implantations performed at \unit[450]{$^{\circ}$C}. Implanted C is therefor expected to occupy substitutionally usual Si lattice sites right from the start. -Thus, we propose an increased participation of C$_{\text{s}}$ already in the initial stages of the implantation process at temperatures above \unit[450]{$^{\circ}$C}, the temperature most aplicable for the formation of SiC layers of high crystalline quality and topotactical alignment\cite{lindner99}. +Thus, we propose an increased participation of C$_{\text{s}}$ already in the initial stages of the implantation process at temperatures above \unit[450]{$^{\circ}$C}, the temperature most applicable for the formation of SiC layers of high crystalline quality and topotactical alignment\cite{lindner99}. Thermally activated, C$_{\text{i}}$ is enabled to turn into C$_{\text{s}}$ accompanied by Si$_{\text{i}}$. The associated emission of Si$_{\text{i}}$ is needed for several reasons. For the agglomeration and rearrangement of C Si$_{\text{i}}$ is needed to turn C$_{\text{s}}$ into highly mobile C$_{\text{i}}$ again. @@ -379,7 +379,7 @@ Si$_{\text{i}}$ serves either as supply of Si atoms needed in the surrounding of The latter has been directly identified in the present simulation study, i.e. structures of two C$_{\text{s}}$ atoms with one being slightly displaced by a next neighbored Si$_{\text{i}}$ atom. It is, thus, concluded that precipitation occurs by successive agglomeration of C$_{\text{s}}$ as already proposed by Nejim et~al.\cite{nejim95}. -This agrees well with a previous ab inito study on defects in C implanted Si\cite{zirkelbach10b}, which showed C$_{\text{s}}$ to occur in all probability. +This agrees well with a previous ab initio study on defects in C implanted Si\cite{zirkelbach10b}, which showed C$_{\text{s}}$ to occur in all probability. However, agglomeration and rearrangement is enabled by mobile C$_{\text{i}}$, which has to be present at the same time and is formed by recombination of C$_{\text{s}}$ and Si$_{\text{i}}$. In contrast to assumptions of an abrupt precipitation of an agglomerate of C$_{\text{i}}$\cite{werner96,werner97,eichhorn99,lindner99_2,koegler03}, however, structural evolution is believed to occur by a successive occupation of usual Si lattice sites with substitutional C. This mechanism satisfies the experimentally observed alignment of the \hkl(h k l) planes of the precipitate and the substrate, whereas there is no obvious reason for the topotactic orientation of an agglomerate consisting exclusively of C-Si dimers, which would necessarily involve a much more profound change in structure for the transition into SiC. -- 2.39.2