Hybrid and data feed forward methodologies are well established for advanced optical process control solutions in highvolume semiconductor manufacturing. Appropriate information from previous measurements, transferred into advanced optical model(s) at following step(s), provides enhanced accuracy and exactness of the measured topographic (thicknesses, critical dimensions, etc.) and material parameters. In some cases, hybrid or feed-forward data are missed or invalid for dies or for a whole wafer. We focus on approaches of virtual metrology to re-create hybrid or feed-forward data inputs in high-volume manufacturing. We discuss missing data inputs reconstruction which is based on various interpolation and extrapolation schemes and uses information about wafer’s process history. Moreover, we demonstrate data reconstruction approach based on machine learning techniques utilizing optical model and measured spectra. And finally, we investigate metrics that allow one to assess error margin of virtual data input.
In this article, we investigate the penalized spline (P-spline) approach to restrict flexibility of dielectric function
parameterization by B-splines and prevent overfitting of the ellipsometric data. The penalty degree is easily controlled by
a certain smoothing parameter. The P-spline approach offers a number of advantages over well-established B-spline
parameterization. First of all, it typically uses an equidistant knot arrangement which simplifies the construction of the
roughness penalties and makes it computationally efficient. Since P-splines possess the “power of the penalty” property,
a selection of the number of knots is no longer crucial, as long as there is a minimum knot number to capture all
significant spatial variability of the data curves. We demonstrate the proposed approach by real-data application with
ellipsometric spectra from aluminum-coated sample.
Johs and Hale developed the Kramers–Kronig consistent B-spline formulation for the dielectric function modeling in
spectroscopic ellipsometry data analysis. In this article we use popular Akaike, corrected Akaike and Bayesian
Information Criteria (AIC, AICc and BIC, respectively) to determine an optimal number of knots for B-spline model.
These criteria allow finding a compromise between under- and overfitting of experimental data since they penalize for
increasing number of knots and select representation which achieves the best fit with minimal number of knots. Proposed
approach provides objective and practical guidance, as opposite to empirically driven or “gut feeling” decisions, for
selecting the right number of knots for B-spline models in spectroscopic ellipsometry. AIC, AICc and BIC selection
criteria work remarkably well as we demonstrated in several real-data applications. This approach formalizes selection of
the optimal knot number and may be useful in practical perspective of spectroscopic ellipsometry data analysis.
The majority of scatterometric production control models assume constant optical properties of the materials and only dimensional parameters are allowed to vary. However, this assumption, especially in case of thin-metal films, negatively impacts model precision and accuracy. In this work we focus on optical modeling of the TiN metal hardmask for scatterometry applications. Since the dielectric function of TiN exhibits thickness dependence, we had to take this fact into account. Moreover, presence of the highly absorbing films influences extracted thicknesses of dielectric layers underneath the metal films. The later phenomenon is often not reflected by goodness of fit. We show that accurate optical modeling of metal is essential to achieve desired scatterometric model quality for automatic process control in microelectronic production. Presented modeling methodology can be applied to other TiN applications such as diffusion barriers and metal gates as well as for other metals used in microelectronic manufacturing for all technology nodes.
Optical metrology techniques such as ellipsometry and reflectometry are very powerful for routine process monitoring and control in the modern semiconductor manufacturing industry. However, both methods rely on optical modeling therefore, the optical properties of all materials in the stack need to be characterized a priori or determined during characterization. Some processes such as ion implantation and subsequent annealing produce slight variations in material properties within wafer, wafer-to-wafer, and lot-to-lot; such variation can degrade the dimensional measurement accuracy for both unpatterned optical measurements as well as patterned (2D and 3D) scatterometry measurements. These variations can be accounted for if the optical model of the structure under investigation allows one to extract not just dimensional but also material information already residing within the optical spectra. This paper focuses on modeling of ion implanted and annealed poly Si stacks typically used in high-k technology. Monitoring of ion implantation is often a blind spot in mass production due to capability issues and other limitations of common methods. Typically, the ion implantation dose can be controlled by research-grade ellipsometers with extended infrared
range. We demonstrate that multi-channel spectroscopic reflectometry can also be used for ion implant monitoring in the mass-production environment. Our findings are applicable across all technology nodes.