X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fupb-ua-xc.tex;h=78b1ef52853e8a7d4e4c74621057bb611e31e2f9;hb=a9b873c00599fbcfa38cbaf058f9846732a4f773;hp=906a0027f35a3f8b00ac31fe799dc6cd3180ee05;hpb=792f53fd52b825dc48ced04fa6de8d08365ec03f;p=lectures%2Flatex.git

diff --git a/posic/talks/upb-ua-xc.tex b/posic/talks/upb-ua-xc.tex
index 906a002..78b1ef5 100644
--- a/posic/talks/upb-ua-xc.tex
+++ b/posic/talks/upb-ua-xc.tex
@@ -1969,6 +1969,7 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$
  }
 
  \includegraphics[width=6cm]{c_00-1_0-10_mig_vasp.ps}
+ \includegraphics[width=6cm]{c_00-1_0-10_mig_dis_vasp.ps}
 
 \end{slide}
 
@@ -1999,10 +2000,9 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$
  \includegraphics[width=3cm]{si_pd_vasp/vac_2333.eps}\\
  \underline{\hkl<1 1 0> interstitial}
  \begin{itemize}
-  \item $E_{\text{f}}=3.63\text{ eV}$
+  \item $E_{\text{f}}=3.39\text{ eV}$
  \end{itemize}
- %\includegraphics[width=3cm]{si_pd_vasp/vac_2333.eps}
- in progress
+ \includegraphics[width=3cm]{si_pd_vasp/110_2333.eps}
  \end{minipage}
  \begin{minipage}{4.5cm}
  \begin{center}
@@ -2012,14 +2012,65 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$
  \end{minipage}
  \begin{minipage}{4.5cm}
  \begin{center}
- %\includegraphics[height=8cm]{si_pd_vasp/vac_2333_ksl.ps}
- in progress
+ \includegraphics[height=8cm]{si_pd_vasp/110_2333_ksl.ps}
  {\scriptsize \hkl<1 1 0> interstitial}
  \end{center}
  \end{minipage}
 
 \end{slide}
 
+\begin{slide}
+
+ {\large\bf\boldmath
+  Silicon point defects
+ }
+
+ \begin{minipage}{3.1cm}
+ \underline{Hexagonal}
+ \begin{itemize}
+  \item $E_{\text{f}}=3.42\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{si_pd_vasp/hex_2333.eps}\\
+ \underline{Tetrahedral}
+ \begin{itemize}
+  \item $E_{\text{f}}=3.77\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{si_pd_vasp/tet_2333.eps}
+ \end{minipage}
+ \begin{minipage}{3.7cm}
+ \begin{center}
+ \includegraphics[height=8cm]{si_pd_vasp/hex_2333_ksl.ps}\\
+ {\scriptsize Hexagonal}
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{3.7cm}
+ \begin{center}
+ \includegraphics[height=8cm]{si_pd_vasp/tet_2333_ksl.ps}
+ {\scriptsize Tetrahedral}
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[c]{0.1cm}
+ \hfill
+ \end{minipage}
+ \begin{minipage}[c]{1.9cm}
+{\tiny
+\underline{Energy - Occup.}\\
+5.5063 - 0.32840\\
+5.5064 - 0.32793\\
+5.5064 - 0.32764\\
+5.5777 - 0.00691\\
+5.5777 - 0.00691\\
+5.6031 - 0.00074\\
+5.6031 - 0.00074\\
+5.6035 - 0.00071\\
+5.6357 - 0.00002\\
+5.6453 - 0.00001\\
+5.6453 - 0.00001
+}
+ \end{minipage}
+
+\end{slide}
+
 \begin{slide}
 
  {\large\bf\boldmath
@@ -2053,6 +2104,32 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$
  
 \end{slide}
 
+\begin{slide}
+
+ {\large\bf\boldmath
+  Carbon point defects in silicon
+ }
+ 
+ \begin{minipage}{3.2cm}
+ \underline{C tetrahedral}\\
+ Relaxes into \hkl<0 0 1> configuration\\[0.2cm]
+ \underline{C hexagonal}\\
+ Relaxes into \hkl<0 0 1> configuration\\[0.4cm]
+ \underline{\hkl<1 1 0> interstitial}
+ \begin{itemize}
+  \item $E_{\text{f}}=3.60\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{c_pd_vasp/110_2333.eps}
+ \end{minipage}
+ \begin{minipage}{9cm}
+ \begin{center}
+ \includegraphics[height=8cm]{c_pd_vasp/110_2333_ksl.ps}
+ {\scriptsize \hkl<1 1 0> interstitial}
+ \end{center}
+ \end{minipage}
+ 
+\end{slide}
+
 \begin{slide}
 
  {\large\bf\boldmath
@@ -2062,34 +2139,37 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$
  \begin{itemize}
   \item Supercell: $3\times 3\times 3$ Type 2
   \item Starting configuration: \hkl<0 0 -1> C-Si interstitial
+        ($E_{\text{f}}=3.15\text{ eV}$)
   \item Energies: $E_{\text{f}}$ of the interstitial combinations in eV
  \end{itemize}
 
  \underline{Along \hkl<1 1 0>:}
 
- \begin{tabular}{|l|p{1.8cm}|p{1.8cm}|p{1.8cm}|p{1.8cm}|}
+ \begin{tabular}{|l|p{2.0cm}|p{1.8cm}|p{1.8cm}|p{1.8cm}|}
  \hline
   {\scriptsize
   \backslashbox{2nd interstitial}{Distance $[\frac{a}{4}]$}
   }
   & \hkl<1 1 -1> & \hkl<2 2 0> & \hkl<3 3 -1> & \hkl<4 4 0>\\
  \hline
- \hkl<0 0 -1> & 6.23514\newline {\color{blue}6.23514} 
-              & 4.65214\newline {\color{blue}4.65014} 
-              & 5.97314\newline {\color{blue}5.97314}
-              & 6.45514\newline {\color{blue}6.45714} \\
+ \hkl<0 0 -1> & 6.23\newline {\color{blue}6.23514} 
+              & 4.65\newline {\color{blue}4.65014} 
+              & 5.97\newline {\color{blue}5.97314}
+              & 6.45\newline {\color{blue}6.45714} \\
+ \hline
+ \hkl<0 0 1> & 6.64\newline {\color{blue}6.65114} 
+             & 4.78\newline {\color{blue}4.78314} 
+             & 6.53\newline {\color{blue}6.53614}
+             & 6.18\newline {\color{blue}6.18914} \\
  \hline
- \hkl<0 0 1> & 6.65114\newline {\color{blue}6.65114} 
-             & 4.78514\newline {\color{blue}4.78314} 
-             & 6.53614\newline {\color{blue}6.53614}
-             & 6.18914\newline {\color{blue}6.18914} \\
+ \hkl<1 0 0>, \hkl<0 1 0> & 4.06\newline alkmene
+                          & 4.93
+                          & 5.72
+                          & 6.00\\
  \hline
- \hkl<1 0 0>, \hkl<0 1 0> & 4.07014\newline alkmene
-                          & 4.93814
-                          & 5.72914
-                          & 6.00214\\
+ \hkl<-1 0 0>, \hkl<0 -1 0> & 3.92 & 4.43 & 6.02 & 6.02 \\
  \hline
- \hkl<-1 0 0>, \hkl<0 -1 0> & 3.93014 & 4.43414 & 6.02814 & 6.02414 \\
+ Vacancy & 1.39 ($\rightarrow\text{ C}_{\text{S}}$)& 5.81 & 5.47 & 6.50 \\
  \hline
  \end{tabular}
 
@@ -2152,26 +2232,103 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$
   Combination of defects
  }
 
- \begin{tabular}{|l|l|l|l|}
+ \begin{tabular}{|l|l|l|l|l|l|}
  \hline
- & 2 & 3 & 4 \\
+ & 2 & 3 & 4 & 5 & 6 \\
  \hline
-\hkl<0 0 -1> & 6.23 & 5.16 & \\
+\hkl<0 0 -1> & 6.23 & 5.16 & 6.23 & 6.35 & 4.65\\
  \hline
-\hkl<0 0 1> & 6.64 & 6.31 & \\
+\hkl<0 0 1> & 6.64 & 6.31 & 4.26 & 6.57 & 4.78 \\
  \hline
-\hkl<1 0 0> & 4.06 & 6.13 & \\
+\hkl<1 0 0> & 4.06 & 6.13 & 6.21 & 6.03 & 4.93 \\
  \hline
-\hkl<-1 0 0> & - & 4.41 & \\
+\hkl<-1 0 0> & \hkl<0 -1 0> & 4.41 & 4.06 & 6.19 & 4.43 \\
  \hline
-\hkl<0 1 0> & -  & 5.95 & \\
+\hkl<0 1 0> & \hkl<1 0 0> & 5.95 & \hkl<-1 0 0> & \hkl<-1 0 0> & \hkl<1 0 0> \\
  \hline
-\hkl<0 -1 0> & 3.92 & ... & \\
+\hkl<0 -1 0> & 3.92 & 4.15 & \hkl<1 0 0> & \hkl<1 0 0> & \hkl <-1 0 0> \\
+ \hline
+Vacancy & 1.39 & 6.19 & 3.65 & 6.24 & 6.50 \\
  \hline
  \end{tabular}
 
 \end{slide}
 
+\begin{slide}
+
+ {\large\bf
+  Brainstorming: Point defects in Si (as grown and as implanted)
+ }
+
+ \small
+
+ Supercell size: $2$ - $2000 \cdot 10^{-21}\text{ cm}^3$
+
+ \underline{After crystal growth}
+ \begin{itemize}
+  \item Si point defects at $450\, ^{\circ}\text{C}$
+        \begin{itemize}
+         \item Interstitials:
+         \item Vacancies: 
+        \end{itemize}
+  \item C impurities: $10^{17}\text{ cm}^{-3}$\\
+        $\Rightarrow$ $10^{-4}$ -- $10^{-1}$ per sc
+        $\rightarrow$ neglected in simulations
+ \end{itemize}
+
+ \underline{After/during implantation}
+ \begin{itemize}
+  \item Si point defects\\
+        $E_{\text{d}}^{\text{av}}=35\text{ eV}$,
+        $D_{\text{imp}}=1\text{ -- }4 \cdot 10^{17}\text{ cm }^{-2}$,
+        $d_{\text{sc}}=3\text{ -- }30\cdot 4.38\text { \AA}$,
+        $A=(3\text{ -- }30\text{ \AA})^2$,\\
+        Amount of collisions with $\Delta E > E_{\text{d}}$
+        in depth region $[h,h+d_{\text{sc}}]$: $n=$ .. (SRIM)\\
+        $\Rightarrow N_{\text{FP}}=nAD$
+  \item C point defects
+        \begin{itemize}
+         \item Substitutional C: ...
+         \item Intesrtitial C: ...
+        \end{itemize}
+ \end{itemize}
+ 
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Reminder (just for me to keep in mind ...)
+ }
+
+ \small
+
+ \underline{Volume of the MD cell}
+ \begin{itemize}
+  \item $T=450, 900, 1400\text{ K}$ - (no melting, N\underline{V}T!)
+  \item $\alpha=2.0 \cdot 10^{-6}\text{ K}^{-1}$
+  \item $a = a_0(1+\alpha \Delta T)$
+  \item Plain Si$(T=0)$: $a_0=5.4575\text{ \AA}$
+        $\rightarrow a(900\text{ K})=5.4674\text{ \AA}$
+  \item C \hkl<1 0 0> in Si$(T=0)$: $a_0^{\text{avg}}=
+        \frac{1}{3}(a_0^x+a_0^y+a_0^z)=5.4605\text{ \AA}$
+        $\rightarrow a(900\text{ K})=5.4704{ \AA}$
+ \end{itemize}
+ Used in first 900 K simulations: 5.4705 \AA\\
+ BUT: Better use plain Si lattice constant! (only local distortions)\\
+ $\Rightarrow a(1400\text{ K})=5.4728\text{ \AA}$
+
+ \underline{Zero total momentum simulations}
+ \begin{itemize}
+  \item If C is randomly inserted there is a net total momentum
+  \item No correction in the temperature control routine of VASP?
+  \item Relax a Si:C configuration first
+        (at T=0, no volume relaxation, scaled volume)
+  \item Use this configuration as the MD initial configuration
+ \end{itemize}
+
+\end{slide}
+
 \begin{slide}
 
  {\large\bf
@@ -2249,6 +2406,10 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$
  \item C \hkl<0 0 1> configuration persists
  \end{itemize}
 
+ Problem: Thermostat doesn't do momentum correction
+
+ TODO: Start MD using relaxed (at zero temperature) initial configuration
+
 \end{slide}
 
 \begin{slide}