(427b) Run-to-Run Control of PECVD of Thin Film Solar Cells

Thin film solar cells are receiving a growing amount of attention because of lower prices for solar equipment, higher efficiency, as well as tax and rebate incentives from the government, and provide a promising alternative to conventional energy sources. Among many solar cell systems, amorphous silicon (a-Si:H) thin film solar cells is one of the most widely used solar cell systems and plasma enhanced chemical vapor deposition (PECVD) plays a key role for the manufacturing of thin film solar cells. However, handling the varying nature of the operation of the PECVD process which persists from run-to-run remains a challenging problem due to the lack of appropriate in situ measurements for the product quality [1]. For example, a batch-to-batch change in the operating conditions or impurities in the feedstock container may significantly alter the quality of the thin film product. This is because the process model employed for in-batch control may significantly deviate from the actual process behavior, and thus, control actions derived using a nominal model are more likely to increase the variability of a process.

Motivated by this, a run-to-run (R2R) control scheme is developed and applied to a PECVD process using post-batch measurements. The major benefit of using R2R control is in its unique ability to compensate for process drift through correlations developed to describe process model parameter variations as a function of changes in the process environment [2,3]. Specifically, the present work initially focuses on the development of a multiscale modeling and operation framework for PECVD of thin film silicon solar cells with uniform thickness and desired film surface microstructure that improves light trapping efficiency. While the modeling of chemical reactions and transport phenomena in the gas-phase is based on two-dimensional in space partial differential equations, a novel microscopic model is developed for the a-Si:H thin film surface evolution, which directly accounts for four microscopic processes: physisorption, surface migration, hydrogen abstraction, and chemisorption. Then, a hybrid kinetic Monte Carlo (kMC) model is used to improve the computational efficiency without compromising the accuracy of the model [4], which is then calibrated with experimentally obtained growth rates and surface morphology data from the literature. After the wafer surface is separated into four concentric zones, the dependence of film growth rate on substrate temperature is modeled where the substrate temperature of each zone is adjusted with an independent heating element to compensate for a radially non-uniform deposition rate caused by depletion in the radical concentration in the gas-phase along the wafer [5]. Then, to deal with batch-to-batch variability, after each batch is over, the post-batch measurements including surface roughness and height-height correlation length are used to estimate off-line the process model (used in the feedback controller) parameters drifted from nominal values via a multivariable optimization problem. Additionally, the exponentially-weighted-moving-average scheme is used to deal with the remaining offset in the desired product qualities and thereby to compute a set of optimal jacket temperatures for each concentric substrate region [6]. Extensive simulations demonstrate that the use of appropriate sinusoidal wafer grating and the regulation of substrate temperature via the proposed R2R-based feedback control scheme provide a viable and effective way for the PECVD of thin film silicon solar cells with uniform thickness and film surface microstructure that optimizes light trapping.

[1] Campbell WJ, Firth SK, Toprac AJ, Edgar TF. A comparison of run-to-run control algorithms. In Proceedings of the American Control Conference, Anchorage, AK, 2002:2150-2155.

[2] Sachs E, Guo RS, Ha A. On-line process optimization and control using the sequential design of experiments. Symposium on VLSI Technology, Honolulu, HI, 1990:99-100.

[3] Wang Y, Gao F, Doyle FJ. Survey on iterative learning control, repetitive control, and run-to-run control. J. of Process Control. 2009;19:1589-1600.

[4] Tsalikis D, Baig C, Mavrantzas V, Amanatides E, Mataras D. A hybrid kinetic Monte Carlo method for simulating silicon films growth by plasma-enhanced chemical vapor deposition. J.  Chem. Phys. 2013;139:204706.

[5] Crose M, Kwon JS, Nayhouse M, Ni D, Christofides PD. Multiscale modeling and operation of PECVD of thin film solar cells. Chem. Eng. Sci. 2015, in press. 

[6] Kwon JS, Nayhouse M, Orkoulas G, Ni D, Christofides PD. Run-to-Run-based model predictive control of protein crystal shape in batch crystallization. Ind. & Eng. Chem. Res. 2015;54:4293-4302.