Spectroscopic ellipsometry has been widely used as one of the metrology methods of choice in various industries: microelectronics, photovoltaic, optoelectronics, flat panel display, etc. We present an example of the characterization of dielectric multilayer structures on the substrates with unintended surface modifications involving macroscopic roughness. We assume that under our inspection conditions, the effect of macrorough surfaces can be treated as the presence of a specially designed overlayer on top of the ordinary substrate. A systematic procedure was then proposed to simulate the dielectric response of the overlayer. This approach is quite useful in a practical sense and provides more accurate process monitoring and control in a production environment.
All indirect optical metrology techniques, such as spectroscopic ellipsometry, reflectometry or scatterometry, for characterization of surfaces, thin films and complex 2D/3D multilayer structures require an appropriate modeling. Parametric sensitivity analysis (SA) is as an essential prerequisite step in optical metrology data modeling to quantify the relative importance of optical model parameters and to identify those with little influence in order to simplify a model. In our previous studies, we have detailed the use of the Morris or Elementary Effect (EE) method, a screening type SA procedure, applied it to the spectroscopic ellipsometry data processing and investigated different types of its convergence. The present study is a continuation of these investigations, extending the application of the EE method for ellipsometric modeling. The method is a global SA technique and uses a stepping of m parameters along certain so-called “trajectories”, or sequences of points in parameter space, randomly constructed in order to maximally fill the volume of the m-dimensional parameter space. However, it is reputed that the EE method relies heavily on a sampling strategy, or a way of selecting “optimized trajectories” in parameter space, i.e., the selection of a necessary number of trajectories chosen to be well spread over the space to properly cover the entire realistic ranges of all input factors. Here, we test some sampling methods for selecting trajectories with possibly different distributions and investigate their effects on the estimation of various sensitivity measures in spectroscopic ellipsometry data modeling. The results indicate that the performance of the sampling strategy should not be judged only by maximization of the trajectory spread but also by certain convergence criteria for the sensitivity index μ*.
KEYWORDS: Metrology, Semiconducting wafers, Data modeling, Machine learning, Data processing, Etching, Optics manufacturing, Wafer-level optics, Manufacturing, Process control
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.
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.
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.
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.
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