Tetra, a modeling system for the generation of the atomic configurations of branched wurtzite/zincblende nanostructures*

The first step in simulating properties of nanostructures is generation of accurate atomic configurations. For complex objects such as the multiply branched heterostructures synthesized by Alivisatos et al.$^{1}$, this is nontrivial. We report here on our code, ``tetra,'' that accomplishes this task. Borrowing from techniques of computer graphics, we represent the complex structure as a tree, each node of which is a shape with fixed crystal structure, and use concatenation of 4 by 4 homogeneous transformation matrices to arrange these fixed building blocks into the final object. A simple text based input ``language'' describes the connectivity and dimensions of the structure. The ultimate purpose of this code is use within a package that will explore and optimize electronic properties of such structures with respect to their geometry$^{2}$. We will present examples of both structures and subsequent semi-empirical pseudopotential-based$^{3}$ electronic structure calculations. [1] A. P. Alivisatos, et al., \textit{Nature,} \textbf{430}, 190 (2004). [2] J. Li and L. W. Wang, \textit{NanoLetters}, \textbf{3}, 10, 1357-1363 (2003). [3] L. W. Wang and A. Zunger, \textit{Phys. Rev. B} \textbf{51}, 17398 (1995).