Modeling of plasma etch systems using ordinary least squares, recurrent neural network, and projection to latent structure models

In microelectronics manufacturing, control strategies for plasma etch systems have been limited to traditional statistical process control and recipe control techniques. The lack of in situ real-time measurements of process performance and appropriate models has hindered the introduction of feedback control systems. This paper focuses on empirical model building for advanced process control using two real-time diagnostic sensors for measurement of the reactor state. Laser interferometry for measurement of etch rate and voltage and current probes for measurement of effective radio-frequency power and sheath voltage, coupled with data acquisition hardware and software, provided the foundation for steady-state and dynamic model development of the plasma etch process. Several linear and nonlinear steady-state techniques including ordinary least squares, neural networks, and projection to latent structures were used in empirical model building. Both linear regression and recurrent neural network model structures provided a satisfactory fit of the data for the operating space investigated. Projection to latent structures techniques indicated that the most relevant variables were power, pressure, and chamber impedance. The addition of the impedance measurement significantly improved the predictive capability of the model.