Modeling and Validation of Sensor and Actuator Dynamics for, And Real-Time Feedback Control of Thermal Chlorine Etching
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and the system outputs are chlorine pressure and etch depth. We treat substrate temperature as a modeling parameter. In this study we use spectroscopic ellipsometry (SE) [1,2] to sense etch depth. Ellipsometry measures the change in the polarization state of light reflected from a surface and then uses it to estimate sample properties (i.e. film thickness, temperature, etc.). This is done by fitting a model to the ellipsometry data. In the second section we describe the thermal chlorine etching process, our etching system and the data. In the third section we construct the mathematical model and discuss the identification of unknown parameters. In the fourth section the model is validated, while the fifth section is concerned with real time feedback control. A sixth section contains concluding remarks.
EXPERIMENTAL SETUP We used a spectroscopic ellipsometer to provide real-time sensing of film thickness. The pressure is measured by a manometer. The inflow rate of high purity Cl 2 is controlled by a high accuracy mass flow controller. A throttle valve installed at the pumping port enables the effective pumping speed to be varied. The throttle valve can be commanded to take on 1001 discrete positions (Closed: 0, Open: 1000). The substrate is heated by a radiative heater which is controlled by a thermocouple. Both the substrate temperature and the thickness of the GaAs layer were determined 159 Mat. Res. Soc. Symp. Proc. Vol. 569 c 1999 Materials Research Society
by spectroscopic ellipsometry, though different working wavelength ranges were exploited for each purpose. The SE measurements in the wavelength regime of 300 nm to 500 nm are sensitive to the GaAs temperature, while the SE measurements in the longer wavelength regime of 600 nm to 760 nm are sensitive to changes in the GaAs layer thickness. The basis for our simulation and control model is a dynamic relationship between etch rate and substrate temperature and chlorine pressure. The form of our model and the values of the physical parameters which appear in the model are determined using experimental data. We designed and carried out etching experiments to provide data from which the rate of change of etch depth could be characterized as a function of substrate temperature and the chlorine pressure. The details of these experiments are discussed in [3]. MODELING AND IDENTIFICATION The log-log plot on the left in Figure 1 shows the dependence of etch rate on chlorine pressure for different values of T,, the substrate temperature. The semi-log plot on the right in Figure 1 shows the dependence of our etch rate data on the inverse of substrate temperature for fixed chlorine pressure. This linear dependence suggests an Arrhenius relationship. Based on the features of the plots in Figure 1, we chose to fit an empirical relationship 1epe.tue(. 1i6 A 62 a 91 o 52e a
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