Statistical modeling for the optimal deposition of sputtered piezoelectric films

The quality of sputtered-deposited piezoelectric films used for integrating bulk acoustic wave (BAW) and surface acoustic wave (SAW) devices with semiconductor circuitry depends on several deposition parameters including substrate temperature, background pressure, gas composition, gas flow rate, and deposition rate. It is desirable to establish the fabrication process based on a a selection of the controllable parameter values that optimizes the film quality. It is common practice to perform a number of deposition experiments by varying the controllable parameters to determine the optimal film growth conditions. The films are grown under a number of different conditions within this space and a response parameter related to film performance is measured. Then a multiple linear regression model is fit to the data. By optimizing the fitted response the best growth conditions can be obtained. This approach is illustrated with data from recent work on the development of very high quality magnetron sputtered aluminum nitride (AlN) films whose acoustic characteristics are like those of epitaxial films grown at considerably higher substrate temperatures. Because the resource cost involved can be high depending upon the number of deposition runs made, it is desirable to minimize the number of experiments and maximize the amount of information gained from them. A discussion is given on how the statistical theory of experimental design can be used to obtain this goal.