KEYWORDS: Monte Carlo methods, Electron beams, Scanning electron microscopy, Beam shaping, Silicon, Line scan image sensors, Scattering, Optical simulations, Solids, Image processing
Based on a Monte Carlo simulation method we have analyzed the influence of electron beam focusing to linewidth measurement for Si trapezoid lines by scanning electron microscopy (SEM) image. The electron probe focusing with finite probe width due to aberration is considered by two different models for simulating incident electron trajectories. The simulation result shows that on the specimen surface the electron beam profile is deviated from the Gaussian probe shape because of the surface topography; the measured linewidth then depends on the focus position and aperture angle.
Monte Carlo simulated SEM images for realistic instrumental conditions are used to evaluate measurement methods for SEM image sharpness. The Monte Carlo simulation of the SEM image is based on a well-developed physical model of electron-solid interaction, which employs Mott’s cross section for elastic electron scattering and dielectric functional approach to electron inelastic scattering with cascade secondary electron production included, a finite element mesh modeling of complex sample topography and a modeling of SEM instrumental conditions (i.e. focus, astigmatism, drift and vibration). A series of simulated SEM images of a realistic sample, gold particles on a carbon substrate, for different instrumental parameters are generated to represent practical images where all instrumental conditions are precisely known and controlled. An estimation of three measurement methods of SEM image sharpness, i.e. FT, CG and DR methods, has then been performed with these simulated images. The responses of image sharpness measurement methods to various instrumental conditions are studied. The calculation shows that all the three methods present similar and reasonable response to focus parameter; their dependences of the measured sharpness on astigmatism coefficient are complicated and CG method presents reasonable sharpness value. For drift and vibration, the situation is more complex because CG/DR methods can be less or more sensitive to vibration coefficient than FT method. Because of the different response behaviors of the three sharpness measurement methods to experimental parameters, we propose to use a mean, simple average or weighted average, of three sharpness values as a proper measure of sharpness.
A new Monte Carlo method is built to describe the generation and transport processes of photoelectrons excited by incident X-ray. XPEEM images for Ag- and Au-dot array on substrate Si are simulated at different incident conditions by the Monte Carlo method. The trajectories of electrons scattered near dot sides and substrate surface were given to visualize the photoelectron penetrating processes. The simulated XPEEM images in TEY mode are found very close to the experimental observations.
Differential surface excitation probability for medium energy electrons traveling in Cu is extracted from reflection electron energy loss spectra using various theoretical models and the Werner’s elimination-retrieved algorithm. While the reflection electron energy loss spectra of Cu thin film were measured by the hemispherical analyzer, the bulk spectra of Cu were recorded by a cylindrical mirror analyzer. Surface Kramers-Kronig dispersion relationship is employed to analyze the surface energy loss function and to derive the complex dielectric constant. We found that the obtained surface optical data approximate reasonably well the optical properties of surface layer.
KEYWORDS: Monte Carlo methods, Scattering, Scanning electron microscopy, Silicon, Data modeling, Copper, Electron microscopes, Dielectrics, Model-based design, Binary data
The most accurate width measurements in a scanning electron microscope (SEM) require raw images to be corrected for instrumental artifacts. Corrections are based on a physical model that describes the sample-instrument interaction. Models differ in their approaches or approximations in the treatment of scattering cross sections, secondary electron generation, material properties, scattering at the surface potential barrier, etc. Corrections that use different models produce different width estimates. We have implemented eight models in the Java Monte Carlo simulator for secondary electrons (JMONSEL) SEM simulator. Two are phenomenological models based on fitting measured yield versus energy curves. Two are based on a binary scattering model. Four are variants of a dielectric function approach. These models are compared to each other in pairwise simulations in which the output of one model is fit to the other by using adjustable parameters similar to those used to fit measured data. The differences in their edge position parameters is then a measure of how much these models differ with respect to a width measurement. With electron landing energy, beam width, and other parameters typical of those used in industrial critical dimension measurements, the models agreed to within ±2.0 nm on silicon and ±2.6 nm on copper in 95% of comparisons.
KEYWORDS: Scattering, Monte Carlo methods, Scanning electron microscopy, Silicon, Copper, Data modeling, Binary data, Dielectrics, Model-based design, Physics
The most accurate width measurements in a scanning electron microscope (SEM) require raw images to be corrected for
instrumental artifacts. Corrections are based upon a physical model that describes the sample-instrument interaction.
Models differ in their approaches or approximations in the treatment of scattering cross sections, secondary electron (SE)
generation, material properties, scattering at the surface potential barrier, etc. Corrections that use different models
produce different width estimates. We have implemented eight models in the JMONSEL SEM simulator. Two are
phenomenological models based upon fitting measured yield vs. energy curves. Two are based upon a binary scattering
model. Four are variants of a dielectric function approach. These models are compared to each other in pairwise
simulations in which the output of one model is fit to the other by using adjustable parameters similar to those used to fit
measured data. The differences in their edge position parameters is then a measure of how much these models differ with
respect to a width measurement. With electron landing energy, beam width, and other parameters typical of those used in
industrial critical dimension measurements, the models agreed to within ±2.0 nm on silicon and ±2.6 nm on copper in
95% of comparisons.
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