Two Point Correlation Function and Monte Carlo Simulations of Clustering Properties of Manganese Populated Areas In Scandium Nitride System

Author:  Philip N. Hess 1, Kangkang Wang 2, Abhijit Chinchore 2, Arthur R. Smith 2, Kai Sun 3
Institution:  George Mason University 1, Ohio University 2, University of Michigan 3
Date:  October 2010

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Dilute magnetic semiconductors are materials that couple useful magnetic and semiconductor properties. However, making them useful for electronic application requires them to have reliable ferromagnetism sustained all the way to room temperature and above. Understanding the clustering behavior of magnetic dopants in dilute magnetic semiconductors is very important since it can reveal the source of the magnetism. In a previous work, we experimentally observed that manganese scandium nitride with 3%, and 5% manganese incorporation exhibit weak magnetic signal above room temperature, making it a good candidate as a dilute magnetic semiconductor. In this paper we present a map of manganese populated areas into a manganese scandium nitride film with 5% manganese incorporation. The experimentally obtained map was done using scanning transmission electron microscopy and energy dispersive spectroscopy, and the resolution of the experiment is limited to a possible range of 20-4400 manganese atoms per observed data point. In addition, we statistically characterized the clustering properties of manganese populated areas showed in the map by two point correlation function, Monte Carlo, and chi-squared methods. A java program that was created to carry out these methods is also presented and thoroughly explained. Within the limit of the experimental resolution, our statistical tests indicate that manganese populated areas are randomly distributed within the crystal lattice of scandium nitride.