\affiliation{Department Physik, Universit\"at Paderborn, 33095 Paderborn, Germany}\r
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\begin{abstract}\r
-We present a first principles investigation of the mobility of carbon interstitials in silicon. \r
-The migration mechanism of carbon \hkl<1 0 0> dumbbell interstitials in otherwise defect-free silicon has been investigated using density functional theory calculations.\r
-Furthermore, the influence of near-by vacancies, carbon interstitial and substitutional defects and silicon self-interstitials has been investigated systematically.\r
-A long range capture radius for vacancies has been found....\r
+A first principles investigation of the mobility of carbon interstitials in silicon is presented.\r
+The migration mechanism of a carbon \hkl<1 0 0> interstitial and a silicon \hkl<1 1 0> self-interstitial in otherwise defect-free silicon has been investigated using density functional theory calculations.\r
+Furthermore, the influence of nearby vacancies, another carbon interstitial and substitutional defects as well as silicon self-interstitials has been investigated systematically.\r
+Interactions of various combinations of defects have been characterized including a couple of selected migration pathways within these configurations.\r
+Almost all of the investigated pairs of defects tend to agglomerate allowing for a reduction in strain.\r
+The formation of structures involving strong carbon-carbon bonds was found to occur very unlikely.\r
+In contrast substitutional carbon was found to occur in all probability.\r
+A long range capture radius has been found for pairs of interstitial carbon as well as interstitial carbon and vacancies.\r
+A rather small capture radius has been identified for substitutional carbon and silicon self-interstitials.\r
+Based on these results conclusions regarding the precipitation mechanism of silicon carbide in bulk silicon are derived and its conformability to experimental findings is discussed.\r
\end{abstract}\r
\r
\keywords{point defects, migration, interstitials, first principles calculations }\r
Silicon carbide (SiC) is a promising material for high-temperature, high-power and high-frequency electronic and optoelectronic devices employable under extreme conditions\cite{edgar92,morkoc94,wesch96,capano97,park98}.\r
Ion beam synthesis (IBS) consisting of high-dose carbon implantation into crystalline silicon (c-Si) and subsequent or in situ annealing constitutes a promising technique to fabricate nano-sized precipitates and thin films of cubic SiC (3C-SiC) topotactically aligned to and embedded in the silicon host\cite{borders71,lindner99,lindner01,lindner02}.\r
However, the process of the formation of SiC precipitates in Si during C implantation is not yet fully understood.\r
-Based on experimental studies\cite{werner96,werner97,eichhorn99,lindner99_2,koegler03} it is assumed that incorporated C atoms form C-Si dimers (dumbbells) on regular Si lattice sites.\r
+Based on experimental high resolution transmission electron microscopy (HREM) studies\cite{werner96,werner97,eichhorn99,lindner99_2,koegler03} it is assumed that incorporated C atoms form C-Si dimers (dumbbells) on regular Si lattice sites.\r
The highly mobile C interstitials agglomerate into large clusters followed by the formation of incoherent 3C-SiC nanocrystallites once a critical size of the cluster is reached.\r
In contrast, investigations of the precipitation in strained Si$_{1-y}$C$_y$/Si heterostructures formed by molecular beam epitaxy (MBE)\cite{strane94,guedj98} suggest an initial coherent clustering of substitutional instead of interstitial C followed by a loss of coherency once the increasing strain energy surpasses the interfacial energy of an incoherent 3C-SiC precipitate in c-Si.\r
-These two different mechanisms of precipitation might be attributed to the respective method of fabrication.\r
+These two different mechanisms of precipitation might be attributed to the respective method of fabrication, i.e. whether it occurs inside the Si bulk or on a Si surface.\r
However, in another IBS study Nejim et al. propose a topotactic transformation remaining structure and orientation likewise based on the formation of substitutional C and a concurrent reaction of the excess Si self-interstitials with further implanted C atoms in the initial state\cite{nejim95}.\r
Solving this controversy and understanding the effective underlying processes will enable significant technological progress in 3C-SiC thin film formation driving the superior polytype for potential applications in high-performance electronic device production\cite{wesch96}.\r
\r
This finding is in good agreement with a combined ab initio and experimental study of Liu et~al.\cite{liu02}, who first proposed this structure as the ground state identifying an energy difference compared to configuration B of \unit[0.2]{eV}.\r
% mattoni: A favored by 0.2 eV - NO! (again, missing spin polarization?)\r
A net magnetization of two spin up electrons, which are euqally localized as in the Si$_{\text{i}}$ \hkl<1 0 0> DB structure is observed.\r
+In fact, these two configurations are very similar and are qualitatively different from the C$_{\text{i}}$ \hkl<1 0 0> DB that does not show magnetization but a nearly collinear bond of the C DB atom to its two next neighbored Si atoms while the Si DB atom approximates \unit[120]{$^{\circ}$} angles inbetween its bonds.\r
Configurations a, A and B are not affected by spin polarization and show zero magnetization.\r
Mattoni et~al.\cite{mattoni2002}, in contrast, find configuration b less favorable than configuration A by \unit[0.2]{eV}.\r
Next to differences in the XC-functional and plane-wave energy cut-off this discrepancy might be attributed to the missing accounting for spin polarization in their calculations, which -- as has been shown for the C$_{\text{i}}$ BC configuration -- results in an increase of configurational energy.\r
In addition, a rather small activation energy of \unit[0.77]{eV} allows for the formation of a C$_{\text{s}}$-Si$_{\text{i}}$ pair originating from the C$_{\text{i}}$ \hkl<1 0 0> DB structure by thermally activated processes.\r
Thus, elevated temperatures might lead to configurations of C$_{\text{s}}$ and a remaining Si atom in the near interstitial lattice, which is supported by the result of the molecular dynamics run.\r
\r
+% add somewhere: nearly same energies of C_i -> Si_i + C_s, Si_i mig and C_i mig\r
+\r
These findings allow to draw conclusions on the mechanisms involved in the process of SiC conversion in Si.\r
Agglomeration of C$_{\text{i}}$ is energetically favored and enabled by a low activation energy for migration.\r
Although ion implantation is a process far from thermodynamic equlibrium, which might result in phases not described by the Si/C phase diagram, i.e. a C phase in Si, high activation energies are believed to be responsible for a low probability of the formation of C clusters.\r
\r
Unrolling these findings on the initially stated controversy present in the precipitation model, an increased participation of C$_{\text{s}}$ already in the initial stage must be assumed.\r
Thermally activated C$_{\text{i}}$ might turn into C$_{\text{s}}$.\r
-The associated emission of Si$_{\text{i}}$ serves two needs, as a vehicle for other C$_{\text{s}}$ and as a supply of Si atoms needed elsewhere to form the SiC structure.\r
+The associated emission of Si$_{\text{i}}$ serves two needs: as a vehicle for other C$_{\text{s}}$ and as a supply of Si atoms needed elsewhere to form the SiC structure.\r
As for the vehicle, Si$_{\text{i}}$ is believed to react with C$_{\text{s}}$ turning it into a highly mobile C$_{\text{i}}$ again, allowing for the rearrangement of the C atom.\r
The rearrangement is crucial to end up in a configuration of C atoms only occupying substitutionally the lattice sites of one of the fcc lattices that build up the diamond lattice as expected in 3C-SiC.\r
On the other hand the conversion of some region of Si into SiC by substitutional C is accompanied by a reduction of the volume since SiC exhibits a \unit[20]{\%} smaller lattice constant than Si.\r
The reduction in volume is compensated by excess Si$_{\text{i}}$ serving as building blocks for the surrounding Si host or a further formation of SiC.\r
\r
It is, thus, concluded that precipitation occurs by successive agglomeration of C$_{\text{s}}$.\r
-However, the process is governed by both, C$_{\text{s}}$ accompanied by Si$_{\text{i}}$ as well as C$_{\text{i}}$.\r
-... HIER WEITER ...\r
-By this, explains the alignment of the \hkl(h k l) lattice planes of the precipitate and the substrate.\r
-No contradiction to ... has Si int ... nice to explain cloudy TEM images indicating atoms in interstitial lattice.\r
-\r
-Our calculations show that point defects which unavoidably are present after ion implantation significantly influence the mobility of implanted carbon \r
-in the silicon crystal.\r
-A large capture radius has been found for... \r
-Especially vacancies.... \r
-\r
-\r
-C$_{\text{s}}$ must be attributed an important role in SiC formation ...\r
-\r
-Spin polarized ... Si or C-C show qualitatively other defect structure than C-Si , in which the C forms almot colinear bond and Si remains 120 ... COOL!\r
+However, the agglomeration and rearrangement of C$_{\text{s}}$ is only possible by mobile C$_{\text{i}}$, which has to be present at the same time.\r
+Thus, the process is governed by both, C$_{\text{s}}$ accompanied by Si$_{\text{i}}$ as well as C$_{\text{i}}$.\r
+It is worth to mention that there is no contradiction to results of the HREM studies\cite{werner96,werner97,eichhorn99,lindner99_2,koegler03}.\r
+Regions showing dark contrasts in an otherwise undisturbed Si lattice are attributed to C atoms in the interstitial lattice.\r
+However, there is no particular reason for the C species to reside in the interstitial lattice.\r
+Contrasts are also assumed for Si$_{\text{i}}$.\r
+Once precipitation occurs regions of dark contrasts disappear in favor of Moir\'e patterns indicating 3C-SiC in c-Si due to the mismatch in the lattice constant.\r
+Until then, however, these regions are either composed of stretched coherent SiC and interstitials or of yet contracted incoherent SiC surrounded by Si and interstitials too small to be detected in HREM.\r
+In both cases Si$_{\text{i}}$ might be attributed a third role, which is the partial compensation of tensile strain either in the stretched SiC or at the interface of the contracted SiC and the Si host.\r
+\r
+In addition, the experimentally observed alignment of the \hkl(h k l) planes of the precipitate and the substrate is statisfied by the mechanism of successive positioning of C$_{\text{s}}$.\r
+In contrast, 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.\r
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\section{Summary}\r
-In summary, we have shown that ...\r
-\r
-Interactions ... improved by migration paths and acivation energies ... probability ...\r
\r
+In summary, C and Si point defects in Si, combinations of these defects and diffusion processes within such configurations have been investigated.\r
+It is shown that C interstitials in Si tend to agglomerate, which is mainly driven by a reduction of strain.\r
+Investigations of migration pathways, however, allow to conclude that C clustering fails to appear by thermally activated processes due to high activation energies of the the respective diffusion processes.\r
+A highly attractive interaction and a large capture radius has been identified for the C$_{\text{i}}$ \hkl<1 0 0> DB and the vacancy indicating a high probability for the formation of C$_{\text{s}}$\r
+In contrast, a rapidly decreasing interaction with respect to the separation distance has been identified for C$_{\text{s}}$ and a Si$_{\text{i}}$ \hkl<1 1 0> DB resulting in a low probability of defects exhibiting respective separations ...\r
+These findings suggest an increased ... in prec model ....\r
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\section*{Acknowledgment}\r
projects / lectures / latex.git / commitdiff