Full Penn Research Articles

Determination of the maximum energy loss for electron stopping power calculations and its effect on backscattering electron yield in Monte-Carlo simulations applying continuous slowing-down approximation

The maximum energy loss for electron stopping power calculations by the full Penn algorithm within the dielectric formalism is determined with taking into account the contribution of electron and plasmon excitations. Use of these calculated electron stopping powers in Monte Carlo simulations applying continuous slowing down approximation gives the backscattering electron yields in much better agreement with experimental data than previous other theoretical results. The muffin-tin model is used to describe the electron elastic scattering by atom bound in solids with taking into account the exchange correlation and polarization effect.

Calculations of mean escape depths of photoelectrons in elemental solids excited by linearly polarized X-rays for high-energy photoelectron spectroscopy

We have calculated mean escape depths (MEDs, D) of photoelectrons from Si, Cu, and Au excited by linearly polarized X-rays over the 50–10,000eV energy range for high-energy photoelectron spectroscopy. These calculations were done with Monte Carlo methods using the values of electron inelastic mean free paths λ that were calculated by the relativistic full Penn algorithm and the Dirac–Hartree–Fock atomic potential for elastic scattering of electrons. In order to know the dependence of MED on the asymmetry parameter β and the emission angle θ, we calculated MEDs for β=−1 to β=2 (by 0.5 steps) and θ=0° to θ=80° (with respect to the surface normal). The resulting MED values increase as the β values decrease over the 50–10,000eV energy range. We also found that the values of D/λcosθ are approximately constant to within 10% for a given value of θ and for energies over 1000eV (except for the condition of β=−1) over a range of emission angles (typically 0–40° or 60°). We also found that the energy dependence of the ratios D/λcosθ at emission angle θ=0° can be expressed by the Jablonski–Powell predictive equation over the 50–10,000eV energy range.Finally, we have obtained a predictive MED equation that could be applied to the wide range of experimental conditions that are used in high-energy XPS with synchrotron radiation.

Monte Carlo Simulation of CD‐SEM Images for Linewidth and Critical Dimension Metrology

In semiconductor industry, strict critical dimension control by using a critical dimension scanning electron microscope (CD-SEM) is an extremely urgent task in near-term years. A Monte Carlo simulation model for study of CD-SEM image has been established, which is based on using Mott's cross section for electron elastic scattering and the full Penn dielectric function formalism for electron inelastic scattering and the associated secondary electron (SE) production. In this work, a systematic calculation of CD-SEM line-scan profiles and 2D images of trapezoidal Si lines has been performed by taking into account different experimental factors including electron beam condition (primary energy, probe size), line geometry (width, height, foot/corner rounding, sidewall angle, and roughness), material properties, and SE signal detection. The influences of these factors to the critical dimension metrology are investigated, leading to build a future comprehensive model-based library.

Calculations of electron stopping powers for 41 elemental solids over the 50 eV to 30 keV range with the full Penn algorithm

We present mass collision electron stopping powers (SPs) for 41 elemental solids (Li, Be, graphite, diamond, glassy C, Na, Mg, Al, Si, K, Sc, Ti, V, Cr, Fe, Co, Ni, Cu, Ge, Y, Nb, Mo, Ru, Rh, Pd, Ag, In, Sn, Cs, Gd, Tb, Dy, Hf, Ta, W, Re, Os, Ir, Pt, Au, and Bi) that were calculated from experimental energy-loss-function data with the full Penn algorithm for electron energies between 50 eV and 30 keV. Improved sets of energy-loss functions were used for 19 solids. Comparisons were made of these SPs with SPs calculated with the single-pole approximation, previous SP calculations, and experimental SPs. Generally satisfactory agreement was found with SPs from the single-pole approximation for energies above 100 eV, with other calculated SPs, and with measured SPs.

Calculations of electron inelastic mean free paths. IX. Data for 41 elemental solids over the 50 eV to 30 keV range

AbstractWe have calculated inelastic mean free paths (IMFPs) for 41 elemental solids (Li, Be, graphite, diamond, glassy C, Na, Mg, Al, Si, K, Sc, Ti, V, Cr, Fe, Co, Ni, Cu, Ge, Y, Nb, Mo, Ru, Rh, Pd, Ag, In, Sn, Cs, Gd, Tb, Dy, Hf, Ta, W, Re, Os, Ir, Pt, Au and Bi) for electron energies from 50 eV to 30 keV. The IMFPs were calculated from experimental optical data using the full Penn algorithm for energies up to 300 eV and the simpler single‐pole approximation for higher energies. The calculated IMFPs could be fitted to a modified form of the Bethe equation for inelastic scattering of electrons in matter for energies from 50 eV to 30 keV. The average root‐mean‐square (RMS) deviation in these fits was 0.48%. The new IMFPs were also compared with IMFPs from the predictive TPP‐2M equation; in these comparisons, the average RMS deviation was 12.3% for energies between 50 eV and 30 keV. This RMS deviation is almost the same as that found previously in a similar comparison for the 50 eV–2 keV range. Relatively large RMS deviations were found for diamond, graphite and cesium. If these three elements were excluded in the comparison, the average RMS deviation was 9.2% between 50 eV and 30 keV. We found satisfactory agreement of our calculated IMFPs with IMFPs from recent calculations and from elastic‐peak electron‐spectroscopy experiments. Copyright © 2010 John Wiley & Sons, Ltd.

A Monte Carlo simulation study on the image resolution in scanning electron microscopy

AbstractThe resolution of the scanning electron microscope limited by the beam–sample interaction is studied by Monte Carlo simulation. The simulation model is based on the full Penn algorithm for electron inelastic scattering and the associated secondary electron generation as well as on a constructive solid geometry modeling of a complex sample structure. The line‐scan profiles for gold nanoparticles of different diameters on a carbon substrate are obtained in the simulation. The gap method and contrast‐to‐gradient (C–G) method performed for two separated particles of the same size and different sizes are considered to determine the resolution. Both methods are applied to the simulated images. A comparison on the obtained resolutions performed for the different sample topographies shows that the gap resolution depends excessively on the topography by the shading effect and gap method underestimates the influence of probe size, while C–G method overestimates this influence. Copyright © 2010 John Wiley & Sons, Ltd.

Electron inelastic scattering and secondary electron emission calculated without the single pole approximation

In this work, aimed primarily at providing more accurate electron inelastic mean free paths (IMFPs) and stopping powers (SPs) at low energies than are provided by the single pole approximation, the “full Penn” algorithm has been employed to derive the electron inelastic scattering energy loss function in solids. IMFPs and SPs have thus been calculated in the energy range from 1 eV to 10 keV and are in good agreement with the experimental data. This treatment of electron inelastic scattering combined with a consistent model for the cascade secondary electron generation has enabled more elaborate Monte Carlo simulations of secondary electron emission from metals. The calculated results of the energy distributions and the secondary electron emission yields for Al and Cu agree reasonably with experimental results.

Monte Carlo simulation study of scanning electron microscopy images of rough surfaces

In this paper, we have developed a Monte Carlo (MC) simulation method for calculation of scanning electron microscopy (SEM) images of rough surfaces. The roughness structure is constructed in a finite element triangulated mesh by using a Gaussian function to describe the distribution of amplitude of the random rough peaks. Further spatial subdividing can accelerate the calculation and improves MC simulation efficiency. The MC model is based on the using of the Mott cross section for description of the electron elastic scattering and the using of the full Penn algorithm in a dielectric functional approach to the electron inelastic scattering. This simulation relates directly a defined rough surface structure modeling described by exact values of roughness parameters to the contrast observed in a SEM image, enabling the investigation of the influence of line edge roughness to the critical dimension (CD) metrology of a metal-oxide-semiconductor device by SEM. Example calculation of line images with sidewall roughness demonstrates that the present MC simulation method is useful for CD metrology of nanostructures by CD-SEM and, especially, for the linewidth measurement in the integrated circuit industry.