Monte Carlo Simulation Study Of Secondary Electron Emission From Bulk And Layered Solids

Theoretical investigations are imperative to facilitate the application of electron emission from solids in electron beam-related techniques,including scanning electron microscopy(SEM),transmission electron microscopy(TEM),scanning transmission electron microscopy(STEM),elastic peak electron spectroscopy(EPES),Auger electron spectroscopy(AES),electron energy loss spectroscopy(EELS)and reflection electron energy loss spectroscopy(REELS),etc.In addition,considering the fact that the electron emission yields of solids are essential parameters for photomultipliers,plasma thrusters,hall effect engines,satellite communication devices,etc,.and in various fields of physics,chemistry,and engineering,including catalysis,surface science,chemical analysis of thin films and much more,it is also important to carry out a systematic theoretical study of electron emission yields.The interaction of electrons with solids forms the physical basis of SEM imaging.Therefore,Monte Carlo(MC)simulation technique is able to be used for analyzing the imaging signal and contrast formation mechanism to explain various experimentally observed effects,which finally improves the imaging technology towards nano metrology based on SEM.The previous studies related to SEM image simulation dealt with mainly the geometrical structures with sharp edges.In this work,by constructing the geometric structure with the help of the Gmsh software,we have combined the arbitrary complex geometric structures with our MC simulator,CTMC3DSEM,which enables the SEM image simulation for the characterization of nanomaterials in complex 3D sample geometries.With such a MC simulation method,we have performed an SEM image characterization for a grating structure which was experimentally prepared with a laser-focused atomic deposition technique.This grating structure has a smoothly varying waveform cross-sectional profile,whose pitch is fixed at λ/2 as the period of the standing wave laser light field,where λ is the wavelength of the corresponding laser light,and is thus length traceable.This grating can be used as an ideal nanoscale metrological length tool in future.Therefore,it was important to characterize its structural features over a large area by SEM imaging to help the quality control,with the aim of mass reproduction.In the study,we have found a side effect in imaging of the waveform structure,which explains the sensitivity of the contrast the structure parameter.Intensive experimental studies have been carried out on several important aspects related to electron emission from the bulk since the 1950s,in particular the energy distribution,secondary electron yield(SEY)and backscattered electron coefficient(BSC).However,the SEY data measured by different researchers are rather scattered as most of these data were not measured in ultrahigh vacuum conditions and/or lacking of suitable surface cleaning processes.Consequently,surface contamination significantly affects SEY through the change of the work function or electron affinity.Surface cleaning with ion sputtering would increase the surface roughness and,hence,alter the SEY.Since the reliable data from accurate experimental measurements for clean surfaces is quite limited,the generation mechanism and transport process related to secondary electron emission from solids are still not yet fully understood.Therefore,given that computational technology and theoretical modelling of the electron-solid interaction have made significant advances in recent years,there is an urgent need to improve the MC simulation study for elemental solids to derive more reliable theoretical SEY data and establish database.1st Chapter gives a brief overview of the interaction between an electron beam and solids with its applications.The various electron signals generated during the interaction processes are discussed.The development and fundamental principle of the scanning electron microscope(SEM)and other various types of electron spectroscopies are concisely discussed.The uncertainty analysis techniques along with some basic terminologies and basic concepts are also introduced in this chapter;the factors that can cause uncertainty in the measurement of electron emission yields and an introduction to uncertainty quantification(UQ)for electron emission yields are also discussed.2nd Chapter presents a relevant explanation about the electron scattering theories related to the present MC physical model and MC simulation method.The complex transport process of electron-solid interaction produces secondary and backscattered electrons along with many other signals.Because these electron signals are generated via the elastic scattering and various inelastic scattering processes,therefore,Mott cross-section formulation with several potential models has been explained in this chapter.We have used dielectric functional theory for the description of inelastic electron scattering process with several dielectric function models.We have also introduced the related calculation models for electron inelastic mean free path(IMFP).For the geometric representation of the sample structure,we have used a finite element triangular mesh throughout our simulation process.A detailed procedure for creating any complex structure by using Gmsh has also been discussed in this chapter.Finally,we have summarized the detailed MC simulation procedure of electron interaction with solids in a few steps.3rd Chapter investigates SEM characterization of wave nanostructure.We have described how to use the MC simulation technique to perform quantitative SEM characterization for the structure parameters of a smoothly varying grating structure(Pt coated Cr grid on Si substrate)in sinusoidal waveform.Previous studies on critical dimension(CD)by SEM have been mostly concerned about the line structures having sharp edges so that there is a noticeable edge bloom in the line-scan profile of secondary electrons.In contrast,the present grating structures prepared by a laser focused atomic deposition technique have smoothly varying waveforms in cross-sectional profiles,which present a difficulty for quantitative structural characterization by SEM.We have performed simulations of SEM imaging over a sizeable area.Taking into account different experimental factors,i.e.,primary electron beam parameters,geometrical parameters and material properties,the unknown geometrical parameters(i.e.,base height,peak height,linewidth shrinkage and tilt angle)of the grating lines have been successfully extracted from the experimental line-scan profiles of SEM images.Our results have indicated that,although there is a certain difference on line-scan profiles between far apart grating lines,however,their geometrical parameters retrieved from characterization are very similar.In the study we have found the side effect for the wave type structure,which explains the sensitivity of the image contrast to structure parameters.This work has successfully for the first time to realize the theoretical characterization for a complex 3D structure of a multilayer material,and thus laid down the foundation for characterization method for future length metrological appliance in nanometer scale.4th Chapter studies the simulation of the electron emission yield from solids and the uncertainty quantification(UQ)for the calculation results.We have explained the procedure of UQ for the MC simulation method and important input factors influencing the electron emission,including work function,density,optical energy loss function,dielectric function models and the potential models for elastic scattering.With the use of our CTMC-SEM simulator,we have performed a systematic and comprehensive computation for Si.The calculation results show that the density of silicon does not affect SEY significantly but does affect BSC.Work function mainly influences SEY.Elastic scattering cross section and energy loss function affect both SEY and BSC to a certain extent.At 75%level of confidence,experimentally measured electron emission data for relatively clean silicon surfaces(e.g.,Bronstein et al.and Goto et al.)lie within the uncertainty range of our simulated data.This implies that the existence of surface contamination causes other experimentally measured data to no longer be reliable.Therefore,it is highly necessary to carry out experiments using modern equipment with surface treatment techniques in ultra-high vacuum conditions.This work has for the first time done a theoretical uncertainty analysis for MC simulation results,and has provided a sufficient ground on the necessity of building a theoretical database of electron emission yields.5th Chapter investigates the theoretical uncertainty in critical dimension(CD)characterization.We have introduced the critical dimension scanning electron microscopy(CD-SEM)technique,which is widely used in the semiconductor industry.In recent years,not only precision but also accuracy for more precise CD control has been required in CD measurement technology.CD distortion between CD-SEM and a reference tool is the most important factor for more accurate CD measurement.CD bias varies by CD-SEM and pattern condition.Therefore,it is an urgent need that we identify,characterize and quantify those parameters that may or may not affect the CD measurement.The sensitivity of simulated CD-SEM images with multiple physical model components has been studied.In this work we have demonstrated that the work function and elastic cross-section models are the factors which although have the most significant impact on secondary electron emission,but do not influence the CD measurement,let alone density,optical energy loss function and dielectric function models.We have calculated the uncertainty in the line-scan profiles of a Si line structure due to different factors and found out that they have no effect on the CD measurement.Therefore,we conclude that the CD value and the uncertainty have no relation with computation modelling but relies only on the structure parameters and electron beam parameters.This work has provided a reference for semiconductor linewidth characterization.6th Chapter summarizes the work of this thesis.