From: hackbard <hackbard@sage.physik.uni-augsburg.de>
Date: Thu, 18 Mar 2010 17:28:44 +0000 (+0100)
Subject: started mig in combined defect system
X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=886e55594bdd8a1a17ba824f3c1371e5b9709088;p=lectures%2Flatex.git

started mig in combined defect system
---

diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex
index 509c753..756c45b 100644
--- a/posic/thesis/defects.tex
+++ b/posic/thesis/defects.tex
@@ -655,6 +655,7 @@ The focus is on combinations of the \hkl<0 0 -1> dumbbell interstitial with a se
 The second defect is either another \hkl<1 0 0>-type interstitial occupying different orientations, a vacany or a substitutional carbon atom.
 Several distances of the two defects are examined.
 Investigations are restricted to quantum-mechanical calculations.
+
 \begin{figure}[th]
 \begin{center}
 \begin{minipage}{7.5cm}
@@ -722,7 +723,7 @@ For defects far away from each other the formation energy of the defect combinat
 Thus, $E_{\text{b}}$ can be best thought of a binding energy, which is required to bring the defects to infinite separation.
 In fact, a \hkl<0 0 -1> dumbbell interstitial created at position R with a distance of $\frac{a_{\text{Si}}}{2}\hkl<3 2 3>$ ($\approx 12.8$ \AA) from the initial one results in an energy as low as -0.19 eV.
 There is still a low interaction which is due to the equal orientation of the defects.
-By changing the orientation of the second dumbbell interstitial to the \hkl<0 -1 0>-type the interaction is even mor reduced resulting in an energy of $E_{\text{b}}=-0.05\text{ eV}$ for a distance, which is the maximum that can be realized due to periodic boundary conditions.
+By changing the orientation of the second dumbbell interstitial to the \hkl<0 -1 0>-type the interaction is even more reduced resulting in an energy of $E_{\text{b}}=-0.05\text{ eV}$ for a distance, which is the maximum that can be realized due to periodic boundary conditions.
 The energies obtained in the R column of table \ref{eq:defects:e_of_comb} are used as a reference to identify, whether less distanced defects of the same type are favorable or unfavorable compared to the far-off located defect.
 Configurations wih energies greater than zero or the reference value are energetically unfavorable and expose a repulsive interaction.
 These configurations are unlikely to arise or to persist for non-zero temperatures.
@@ -801,7 +802,7 @@ Figure \ref{fig:defects:comb_db_02} c) displays the results of another \hkl<0 0
 The binding energy is -2.05 eV.
 Both dumbbells are tilted along the same direction remaining parallely aligned and the second dumbbell is pushed downwards in such a way, that the four dumbbell atoms form a rhomboid.
 Both carbon atoms form tetrahedral bonds to four silicon atoms.
-However, silicon atom 1 and 3, which are bond to the second carbon dumbbell interstitial are also bond to the initial carbon atom.
+However, silicon atom 1 and 3, which are bound to the second carbon dumbbell interstitial are also bound to the initial carbon atom.
 These four atoms of the rhomboid reside in a plane and, thus, do not match the situation in silicon carbide.
 The carbon atoms have a distance of 2.75 \AA.
 In figure \ref{fig:defects:comb_db_02} b) a second \hkl<0 1 0> dumbbell is constructed at position 2.
@@ -899,7 +900,6 @@ Figure \ref{fig:defects:comb_db110} shows the corresponding plot of the data inc
 The funtion found most suitable for curve fitting is $f(x)=a/x^3$ comprising the single fit parameter $a$.
 Thus, far-off located dumbbells show an interaction proportional to the reciprocal cube of the distance and the amount of bonds along \hkl<1 1 0> respectively.
 This behavior is no longer valid for the immediate vicinity revealed by the saturating binding energy of a second dumbbell at position 1, which is ignored in the fitting procedure.
-{\color{red}Todo: DB mig along 110?}
 
 \begin{figure}[t!h!]
 \begin{center}
@@ -1000,36 +1000,75 @@ The creation of a vacancy at position 1 results in a configuration of substituti
 The carbon dumbbell atom moves to position 1 where the vacancy is created and the silicon dumbbell atom recaptures the dumbbell lattice site.
 With a binding energy of -5.39 eV, this is the energetically most favorable configuration observed.
 A great amount of strain energy is reduced by removing the silicon atom at position 3, which is illustrated in figure \ref{fig:defects:comb_db_06} b).
-The dumbbell structure shifts towards the position of the vacancy which replaces the silicon atom usually bond to and at the same time strained by the silicon dumbbell atom.
+The dumbbell structure shifts towards the position of the vacancy which replaces the silicon atom usually bound to and at the same time strained by the silicon dumbbell atom.
 Due to the displacement into the \hkl<1 -1 0> direction the bond of the dumbbell silicon atom to the silicon atom on the top left breaks and instead forms a bond to the silicon atom located in \hkl<1 -1 1> direction which is not shown in the figure.
 A binding energy of -3.14 eV is obtained for this structure composing another energetically favorable configuration.
+A vacancy ctreated at position 2 enables a relaxation of the silicon atom number 1 mainly in \hkl<0 0 -1> direction.
+The bond to silicon atom number 5 breaks.
+Hence, the silicon dumbbell atom is not only displaced along \hkl<0 0 -1> but also and to a greater extent in \hkl<1 1 0> direction.
+The carbon atom is slightly displaced in \hkl<0 1 -1> direction.
+A binding energy of -0.59 eV indicates the occurrence of much less strain reduction compared to that in the latter configuration.
+Evidently this is due to a smaller displacement of silicon atom number 1, which would be directly bound to the replaced silicon atom at position 2.
+In the case of a vacancy created at position 4, even a slightly higher binding energy of -0.54 eV is observed, while the silicon atom at the bottom left, which is bound to the carbon dumbbell atom, is vastly displaced along \hkl<1 0 -1>.
+However the displacement of the carbon atom along \hkl<0 0 -1> is less than it is in the preceding configuration.
+Although expected due to the symmetric initial configuration silicon atom number 1 is not displaced correspondingly and also the silicon dumbbell atom is displaced to a greater extent in \hkl<-1 0 0> than in \hkl<0 -1 0> direction.
+The symmetric configuration is, thus, assumed to constitute a local maximum, which is driven into the present state by the conjugate gradient method used for relaxation.
+Figure \ref{fig:defects:comb_db_06} d) shows the relaxed structure of a vacancy created at position 5.
+The silicon dumbbell atom is largely displaced along \hkl<1 1 0> and somewaht less along \hkl<0 0 -1>, which corresponds to the direction towards the vacancy.
+The silicon dumbbell atom approaches silicon number 1.
+Indeed a non-zero charge density is observed inbetween these two atoms exhibiting a cylinder-like shape superposed with the charge density known from the dumbbell itself.
+Strain reduced by this huge displacement is partially absorbed by tensile strain on silicon atom number 1 originating from attractive forces of the carbon atom and the vacancy.
+A binding energy of -0.50 eV is observed.
+{\color{red}Todo: Jahn-Teller distortion (vacancy) $\rightarrow$ actually three possibilities. Due to the initial defect, symmetries are broken. The system should have relaxed into the minumum energy configuration!?}
 
-Vacancies created at positions 2 and 4 have similar
+{\color{blue}Todo: Si int + vac and C sub ...?
+Investigation of vacancy, Si and C interstitital.
+As for the ground state of the single Si self-int, a 110 is also assumed as the lowest possibility in combination with other defects (which is a cruel assumption)!
+}
+
+\section{Migration in systems of combined defects}
+
+During carbon implantation into crystalline silicon the energetic carbon atoms may kick out silicon atoms from their lattice sites.
+A vacancy accompanied by a silicon self-interstitial is generated.
+The silicon self-interstitial may migrate to the surface or recombine with other vacancies.
+Once a vacancy and a carbon interstitial defect exist the energetically most favorable configuration is the configuration of a substitutional carbon atom, that is the carbon atom occupying the vacant site.
+In addition, it is a conceivable configuration the system might experience during the silicon carbide precipitation process.
+Energies needed to overcome the migration barrier of the transformation into this configuration enable predictions concerning the feasibility of a silicon carbide conversion mechanism derived from these microscopic processes.
+This is especially important for the case, in which the vacancy is created at position 3, as discussed in the last section and figure \ref{fig:defects:comb_db_06} b).
+Due to the low binding energy this configuration might constitute a trap, which it is hard to escape from.
+However, migration simulations show that only a low amount of energy is necessary to transform the system into the energetically most favorable configuration.
+\begin{figure}[!t!h]
+\begin{center}
+\includegraphics[width=13cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[2.0cm]
+\begin{picture}(0,0)(170,0)
+\includegraphics[width=3.5cm]{vasp_mig/comb_2-1_init.eps}
+\end{picture}
+\begin{picture}(0,0)(60,0)
+\includegraphics[width=3.5cm]{vasp_mig/comb_2-1_seq.eps}
+\end{picture}
+\begin{picture}(0,0)(-120,0)
+\includegraphics[width=3.5cm]{vasp_mig/comb_2-1_final.eps}
+\end{picture}
+\begin{picture}(0,0)(25,20)
+\includegraphics[width=2.5cm]{100_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(230,0)
+\includegraphics[height=2.2cm]{001_arrow.eps}
+\end{picture}
+\end{center}
+\caption{Transition vacancy-interstitial combinations into the configuration of substitutional carbon.}
+\label{fig:defects:comb_mig_01}
+\end{figure}
+Figure \ref{fig:defects:comb_mig_01} shows the migration barriers and structures for transitions of the vacancy-interstitial configurations examined in figure \ref{fig:defects:comb_db_06} a) and b) into the configuration of substitutional carbon.
 
-Vac at position 2 and 4 have similar results.
-Less strain is reduced, since the displacement of the bottom silicon atom, whcih would be directly bond to the silicon atom replaced by the vacancy, is less.
-In the second case, there is even less strain reduction since the second next neighbour is replaced by the vacancy.
-A symmetric configuration is expected, but it is not!
-jahn-Teller distortion ... check this!
-In both cases the db is tilted in such a way, that the carbon atom moves towards the vacancy.
-At position 5 the silicon dumbbell atom moves in \hkl<1 1 0> direction, the same direction where the vacancy is located.
-Strain reducde by this is partialy absorbed by strain originating from the fact that si atom bound to and pulled by the carbon atom is also pulled by the vacancy.
 
-CHECK C-C DIST AND SI-C DIST !!! of all!!!
 
-{\color{red}Todo: Jahn-Teller distortion (vacancy) $\rightarrow$ actually three possibilities? Due to the initial defect symmetries are broken. It should have relaxed into the minumum energy configuration!?}
-Once a vacancy exists the minimal e conf is the c sub conf and ofcourse necessary for formation of SiC.
-The question is whether the migration into this conf is possible.
-Due to low e of conf at pos 3, this might constitute a trap.
-Thats why we havt to look at migration barriers into the configurations beneficial for SiC prec.
-Fig shows the migration of the 2 and 3 conf into the c sub conf.
 Low migration barriers, which means that SiC will modt probably form ... and so on ...
 
-{\color{red}Todo: Si int and C sub ...}
-The existance of a vacancy is most often accompanied by an interstitial.
-The silicon interstitital might diffuse to the surface or recombine with other vacancy defects and tus is out of the interested simulation region.
-However, investigation of near by vacancy, Si and C interstititla is necessary, too.
-As for the ground state of the single Si self-int a 110 this is also assumed as the lowest possibility in combination with other defects, which is a cruel assumption!!!
+
+{\color{red}Todo: DB mig along 110 (at the starting of this section)?}
+
+{\color{red}Todo: Migration of Si int + vac and C sub ...?}
 
 {\color{red}Todo: Model of kick-out and kick-in mechnism?}