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%%%%%%%%%%%%%%%%%%%% SUPPLEMENTAL MATERIAL %%%%%%%%%%%%%%%%%%%%%%%%%
\section{Supplemental Material}

The calculated self-limited width for several angles between the basal and lateral facets has been calculated, keeping all the other parameters constant in (8) fixed.  A pronounced decrease of the profile is seen for increasing angle values, due to an increased growth rate on the lateral (111)A with respect to the (111)B bottom facets. 

\begin{figure}[h!]
\includegraphics[width=6cm]{FigSM.eps}
\caption{Calculated self-limiting width as a function of Al concentration obtained from (8) for different values of the basal angle $\theta$ [see Fig.2 (c)]. As the profile becomes sharper (greater angles), the width decreases.}
\label{figSM}
\end{figure}


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