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03-01-diamond.tex
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03-01-diamond.tex
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\chapter{Diamond}
To start with I investigated regular $3D$ diamond crystal (fig. \ref{fig:diamond_lattice}). I considered here the case where we have only one set of $s$, $p_z$, $p_y$, and $p_z$ orbitals at each
atomic site (used parameters are placed at the table \ref{tab:diamond_params}). Calculated band structure is placed on the fig. \ref{fig:tb_diamond}. Agreement with experimental results \cite{diamond} (fig. \ref{fig:theory_diamond}) is quite good. However actual band structure of diamond has indirect band gap. And band structure calculated with TB is characterized by direct band gap at $\Gamma$ point.
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.3\linewidth]{img/diamond_crystall}
\caption{Diamond crystal structure. \label{fig:diamond_lattice}}
\end{center}
\end{figure}
\begin{table}[h]
\begin{center}
\begin{tabular}{|c|c|}
\hline
Parameter&Value, [eV]\\ \hline
$\epsilon_s$ & $0.0$ \\ \hline
$\epsilon_p$ & $7.4$ \\ \hline
$V_{ss \sigma}$ & $-3.8$ \\ \hline
$V_{sp \sigma}$ & $4.44$\\ \hline
$V_{pp \sigma}$ & $-1.325$ \\ \hline
$V_{pp \pi}$ & $4.9$\\ \hline
\end{tabular}
\end{center}
\caption{TB parameters for diamond. \label{tab:diamond_params}}
\end{table}
\begin{figure}
\includegraphics[width=\linewidth]{img/diamond_sp}
\caption{Calculated band structure of diamond. \label{fig:tb_diamond}}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width=0.5\linewidth]{img/diamond_exp_band_struct}
\caption{Band structure of diamond (experiment). \label{fig:theory_diamond}}
\end{center}
\end{figure}