On the use of response surface methodology to predict and interpret the preferred c-axis orientation of sputtered AlN thin films

This paper deals with experimental design applied to response surface methodology (RSM) in order to determine the influence of the discharge conditions on preferred c-axis orientation of sputtered AlN thin films. The thin films have been deposited by DC reactive magnetron sputtering on Si (1 0 0) substrates. The preferred orientation was evaluated using a conventional Bragg-Brentano X-ray diffractometer (θ-2θ) with the CuKα radiation. We have first determined the experimental domain for 3 parameters: sputtering pressure (2-6 mTorr), discharge current (312-438 mA) and nitrogen percentage (17-33%). For the setup of the experimental design we have used a three factors Doehlert matrix which allows the use of the statistical response surface methodology (RSM) in a spherical domain. A four dimensional surface response, which represents the (0 0 0 2) peak height as a function of sputtering pressure, discharge current and nitrogen percentage, was obtained. It has been found that the main interaction affecting the preferential c-axis orientation was the pressure-nitrogen percentage interaction. It has been proved that a Box-Cox transformation is a very useful method to interpret and discuss the experimental results and leads to predictions in good agreement with experiments.