Symmetric and asymmetric capacitively coupled radio-frequency plasmas in oxygen at 40 Pa, 300 V voltage amplitude and a discharge gap of 40 mm are investigated by means of one-dimensional numerical semi-kinetic fluid modeling on the basis of a simplified reaction scheme including the dominant positive and negative ions, background gas, and electrons. An improved treatment, by accounting for the dependence of ion mobilities on E/N, is compared to the standard approach, based on using zero-field mobility values only. The charged particle dynamics as a result of direct electron impact ionization of oxygen, secondary electron release from the electrodes, the spatial distribution of all involved particles as well as impact of geometry and model modification on ion energies is analyzed and compared to independent simulations and experiments.

Abstract-Virtual metrology (VM) is the estimation of metrology variables that may be expensive or difficult to measure using readily available process information. This paper investigates the application of global and local VM schemes to a data set recorded from an industrial plasma etch chamber. Windowed VM models are shown to be the most accurate local VM scheme, capable of producing useful estimates of plasma etch rates over multiple chamber maintenance events and many thousands of wafers. Partial least-squares regression, artificial neural networks, and Gaussian process regression are investigated as candidate modeling techniques, with windowed Gaussian process regression models providing the most accurate results for the data set investigated.Index Terms-Gaussian process regression, local modeling, neural network applications, plasma etch, virtual metrology (VM).

a b s t r a c tPlasma etch is a semiconductor manufacturing process during which material is removed from the surface of semiconducting wafers, typically made of silicon, using gases in plasma form. A host of chemical and electrical complexities make the etch process notoriously difficult to model and troublesome to control. This work demonstrates the use of a real-time model predictive control scheme to control plasma electron density and plasma etch rate in the presence of disturbances to the ground path of the chamber. Virtual metrology (VM) models, using plasma impedance measurements, are used to estimate the plasma electron density and plasma etch rate in real time for control, eliminating the requirement for invasive measurements. The virtual metrology and control schemes exhibit fast set-point tracking and disturbance rejection capabilities. Etch rate can be controlled to within 1% of the desired value. Such control represents a significant improvement over open-loop operation of etch tools, where variances in etch rate of up to 5% can be observed during production processes due to disturbances in tool state and material properties.

-In semiconductor manufacturing advanced process control (APC) refers to a range of techniques that can be used to improve process capability. As the dimensions of electronic devices have decreased, the application of APC has become more and more important for the critical stages of production processes. However, the economic disadvantage of employing APC is that it requires feedback information in the form of downstream metrology data, which is both time consuming and costly to obtain.

-Plasma etch is a complex semiconductor manufacturing process in which material is removed from the surface of a silicon wafer using a gas in plasma form. As the process etch rate cannot be measured easily during or after processing, virtual metrology is employed to predict the etch rate instantly using ancillary process variables. Virtual metrology is the prediction of metrology variables using other easily accessible variables and mathematical models. This paper investigates the use of Gaussian process regression as a virtual metrology modelling technique for plasma etch data.