Dimension Reduction of Multivariable Optical Emission Spectrometer Datasets for Industrial Plasma Processes

Abstract

A new data dimension-reduction method, called Internal Information Redundancy Reduction (IIRR), is proposed for application to Optical Emission Spectroscopy (OES) datasets obtained from industrial plasma processes. For example in a semiconductor manufacturing environment, real-time spectral emission data is potentially very useful for inferring information about critical process parameters such as wafer etch rates, however, the relationship between the spectral sensor data gathered over the duration of an etching process step and the target process output parameters is complex. OES sensor data has high dimensionality (fine wavelength resolution is required in spectral emission measurements in order to capture data on all chemical species involved in plasma reactions) and full spectrum samples are taken at frequent time points, so that dynamic process changes can be captured. To maximise the utility of the gathered dataset, it is essential that information redundancy is minimised, but with the important requirement that the resulting reduced dataset remains in a form that is amenable to direct interpretation of the physical process. To meet this requirement and to achieve a high reduction in dimension with little information loss, the IIRR method proposed in this paper operates directly in the original variable space, identifying peak wavelength emissions and the correlative relationships between them. A new statistic, Mean Determination Ratio (MDR), is proposed to quantify the information loss after dimension reduction and the effectiveness of IIRR is demonstrated using an actual semiconductor manufacturing dataset. As an example of the application of IIRR in process monitoring/control, we also show how etch rates can be accurately predicted from IIRR dimension-reduced spectral data.

Virtual metrology modeling of time-dependent spectroscopic signals by a fused lasso algorithm

“…However, previous studies have focused on reduced datasets summarized by their statistical measures such as mean, variance, maximum, and minimum [9,11,21]. Because plasma processing is a dynamic process, preserving time information is crucial [22]. In addition, utilization of the statistical measures causes problems related to model interpretability.…”

“…In some cases, there may be more observations than features in VM modeling problems. However, in spectroscopic signal used in this study, the number of features exceeds the number of observations in most cases [21,22,25]. To address this highdimensionality problem, dimension reduction is critical.…”

About the Data Analysis of Optical Emission Spectra of Reactive Ion Etching Processes—The Method of Spectral Redundancy Reduction

“…However, a small amount of scientific reports currently describe methods for extracting the emission lines of a plasma process that have particular significance for that process. For example, Yang et al [6] reported on a method that they named Internal Information Redundancy Reduction (IIRR). Their approach involves removing all wavelength variables that exhibit saturation at a given time point.…”

Development of a High-Linearity Voltage and Current Probe with a Floating Toroidal Coil: Principle, Demonstration, Design Optimization, and Evaluation

“…Recently, low-frequency modulation technology and non-invasive types have been proposed and are still under development [ 27 , 31 , 32 , 38 , 39 ]. Commonly implemented plasma process monitoring tools are the OES and VI probe; they are non-invasive and easy to install in the process equipment [ 40 , 41 , 42 , 43 , 44 ]. In general, an OES measures the optical emission from plasma via an optical window and is used for gas composition analysis and anomalous behavior detection.…”