(635f) Experimental Design Approach to Optimizing Thin Film Deposition

When finding the best settings for a process to create the desired amount and quality of product, one rarely has a perfect model of the process to ensure the correct settings are chosen. As a result, one performs experiments to relate process settings to final performance and properties. The experimental data is then combined with a model to estimate model parameters and to determine which model is best [1,2]. This model is then used to select additional experiments needed. In many cases, an empirical model such as a polynomial fit is used on the data. In other cases, mechanistic models based on physical principles are used [3]. Unfortunately there is very little crossover between these two schools of thought.

With the ever-changing product industry (particularly microelectronics and pharmaceuticals), one will have to modify and re-optimize a process many times over the equipment's lifetime. Not only could the process be used for different products, but the specifications for products could change frequently due to new technology or tighter government regulation. The advantage of a mechanistic model compared to an empirical fit is that it can be adapted and reused for such modified situations. Due to better understanding of the process, the time needed to perform subsequent optimizations is reduced. However, empirical models are typically easier to generate and have fewer parameters to identify. If limited experimental data is available, they may be more useful for beginning process optimization than a multiscale model with a large number of parameters.

In the new methodology presented here, the two distinct approaches used by Box and by Buzzi-Ferraris [4] are combined using the framework of model discrimination. An objective function is proposed that accounts for system performance, based on the probabilities of the candidate models. Both empirical and mechanistic models are included. The case study for this method is from thin film deposition (a process used for microelectronics). Chemical vapor deposition (CVD) is a process where the properties of the thin film (microns) are determined by the microstructure (nm) which in turn is determined by the processing conditions.

The goal of the case study presented in this paper is to compare the usefulness of a mechanistic and an empirical model in the early ?nucleation? phase of the multiscale deposition process [5]. Both models have a number of parameters that must be estimated from measurements. Computer simulations are then run to estimate parameters for this nucleation model, as well as the empirical fitted model. Once the initial set of experiments has been run, a sequential experimental design approach is followed which uses an objective function that chooses the next set of experiments to distinguish between the models while also minimizing nucleation density. Simulations are useful to explore the properties of the methodology before running expensive experiments. Different forms of the discrimination function are studied as well as the effect of noise and initial information on convergence of the discrimination function. The results of the simulation study are used to guide an experimental study into the microstructure of thin films. By combining empirical and mechanistic modeling techniques, the resulting models will be more reliable than models developed without this method.

1. Stewart, W. E.; Shon, Y.; Box, G. E. P. ?Discrimination and goodness of fit of multiresponse mechanistic models?; AIChE Journal; 1998, 44, 1404?1412

2. Montgomery, Douglas C. ?Design and Analysis of Experiments? 6th ed. 2005

3. Fujiwara, M; Nagy, Z. K.; Chew, J. W.; Braatz, R. D. Journal Of Process Control; 2005, 15, 493?504

4. Buzzi-Ferraris, G. and Forzatti, P. ?A new sequential experimental design procedure for discriminating among rival models? Chemical Engineering Science,1983, 38, 225-232.

5. Evans, Thiel, and Bartelt; ?Morphological evolution during epitaxial thin film growth: Formation of 2D islands and 3D mounds?, Surface Science Reports, 2006, 61, 1-128.