Virtual metrology for plasma etch processes.
PhD thesis, National University of Ireland Maynooth.
Plasma processes can present dicult control challenges due to time-varying dynamics
and a lack of relevant and/or regular measurements. Virtual metrology (VM) is the
use of mathematical models with accessible measurements from an operating process to
estimate variables of interest. This thesis addresses the challenge of virtual metrology
for plasma processes, with a particular focus on semiconductor plasma etch.
Introductory material covering the essentials of plasma physics, plasma etching, plasma
measurement techniques, and black-box modelling techniques is rst presented for readers
not familiar with these subjects. A comprehensive literature review is then completed
to detail the state of the art in modelling and VM research for plasma etch processes.
To demonstrate the versatility of VM, a temperature monitoring system utilising a
state-space model and Luenberger observer is designed for the variable specic impulse
magnetoplasma rocket (VASIMR) engine, a plasma-based space propulsion system. The
temperature monitoring system uses optical emission spectroscopy (OES) measurements
from the VASIMR engine plasma to correct temperature estimates in the presence of
modelling error and inaccurate initial conditions. Temperature estimates within 2% of
the real values are achieved using this scheme.
An extensive examination of the implementation of a wafer-to-wafer VM scheme to estimate
plasma etch rate for an industrial plasma etch process is presented. The VM
models estimate etch rate using measurements from the processing tool and a plasma
impedance monitor (PIM). A selection of modelling techniques are considered for VM
modelling, and Gaussian process regression (GPR) is applied for the rst time for VM
of plasma etch rate. Models with global and local scope are compared, and modelling
schemes that attempt to cater for the etch process dynamics are proposed. GPR-based
windowed models produce the most accurate estimates, achieving mean absolute percentage
errors (MAPEs) of approximately 1:15%. The consistency of the results presented
suggests that this level of accuracy represents the best accuracy achievable for
the plasma etch system at the current frequency of metrology.
Finally, a real-time VM and model predictive control (MPC) scheme for control of
plasma electron density in an industrial etch chamber is designed and tested. The VM
scheme uses PIM measurements to estimate electron density in real time. A predictive
functional control (PFC) scheme is implemented to cater for a time delay in the VM
system. The controller achieves time constants of less than one second, no overshoot,
and excellent disturbance rejection properties. The PFC scheme is further expanded by
adapting the internal model in the controller in real time in response to changes in the
process operating point.
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