Refinement of Monte Carlo simulations of electron–specimen interaction in low-voltage SEM

A Monte Carlo tool is presented for the simulation of secondary electron (SE) emission in a scanning electron microscope (SEM). The tool is based on the Geant4 platform of CERN. The modularity of this platform makes it comparatively easy to add and test individual physical models. Our aim has been to develop a flexible and generally applicable tool, while at the same time including a good description of low-energy (<50 eV) interactions of electrons with matter. To this end we have combined Mott cross-sections with phonon-scattering based cross-sections for the elastic scattering of electrons, and we have adopted a dielectric function theory approach for inelastic scattering and generation of SEs. A detailed model of the electromagnetic fields from an actual SEM column has been included in the tool for ray tracing of secondary and backscattered electrons. Our models have been validated against experimental results through comparison of the simulation results with experimental yields, SE spectra and SEM images. It is demonstrated that the resulting simulation package is capable of quantitatively predicting experimental SEM images and is an important tool in building a deeper understanding of SEM imaging.

[1]  Z. J. Ding,et al.  A Monte Carlo modeling of electron interaction with solids including cascade secondary electron production , 2006 .

[2]  Xiangdong Liu,et al.  Monte-Carlo simulation of low-energy electron scattering in PMMA - using stopping powers from dielectric formalism , 2005 .

[3]  Z. Ding,et al.  Application of Monte Carlo simulation to SEM image contrast of complex structures , 2005 .

[4]  C. Powell Attenuation lengths of low-energy electrons in solids , 1974 .

[5]  J. Sempau,et al.  PENELOPE-2006: A Code System for Monte Carlo Simulation of Electron and Photon Transport , 2009 .

[6]  R. Gauvin,et al.  CASINO: A new monte carlo code in C language for electron beam interaction —part I: Description of the program , 2006 .

[7]  J. C. Ashley Interaction of low-energy electrons with condensed matter: stopping powers and inelastic mean free paths from optical data , 1988 .

[8]  Z. Ding,et al.  Inelastic collisions of kV electrons in solids , 1989 .

[9]  Ding Ze-jun,et al.  A comparison of Monte Carlo simulations of electron scattering and X-ray production in solids , 1993 .

[10]  Nicholas W. M. Ritchie,et al.  A new Monte Carlo application for complex sample geometries , 2005 .

[11]  A. Pasciak,et al.  An accurate approximation for the highly efficient sampling of polar scattering angle of electron elastic single-scattering events. , 2007, Scanning.

[12]  R. Gauvin,et al.  CASINO: A new monte carlo code in C language for electron beam interactions—part II: Tabulated values of the mott cross section , 1997 .

[13]  D. Joy,et al.  Experimental secondary electron spectra under SEM conditions , 2004, Journal of microscopy.

[14]  E. Napchan MONTE CARLO SIMULATION OF ELECTRON TRAJECTORIES , 1992 .

[15]  R. H. Ritchie,et al.  Electron inelastic mean free paths and energy losses in solids: I. Aluminum metal , 1979 .

[16]  B. L. Henke,et al.  X-Ray Interactions: Photoabsorption, Scattering, Transmission, and Reflection at E = 50-30,000 eV, Z = 1-92 , 1993 .

[17]  R. H. Ritchie,et al.  Electron inelastic mean free paths and energy losses in solids II: Electron gas statistical model☆☆☆ , 1979 .

[18]  D. R. Penn,et al.  Electron mean-free-path calculations using a model dielectric function. , 1987, Physical review. B, Condensed matter.

[19]  J.-Ch. Kuhr,et al.  Attenuation and escape depths of low-energy electron emission , 2001 .

[20]  E. Palik Handbook of Optical Constants of Solids , 1997 .

[21]  C. Powell,et al.  Monte Carlo strategies for simulations of electron backscattering from surfaces , 2005 .

[22]  David C. Joy,et al.  Calculations of Mott scattering cross section , 1990 .

[23]  Dominique Drouin,et al.  CASINO: A new monte Carlo code in C language for electron beam interactions—part III: Stopping power at low energies , 1997 .

[24]  J. Zemek,et al.  Surface excitations in electron backscattering from silicon surfaces , 2004 .

[25]  L. Kövér,et al.  Measurement of the surface excitation probability of medium energy electrons reflected from Si, Ni, Ge and Ag surfaces , 2005 .

[26]  David C. Joy,et al.  A model for calculating secondary and backscattered electron yields , 1987 .

[27]  D. Joy A database on electron‐solid interactions , 2006 .

[28]  O. Heavens Handbook of Optical Constants of Solids II , 1992 .

[29]  Z. Ding,et al.  Monte Carlo simulation of secondary electron and backscattered electron images for a nanoparticle–matrix system , 2005 .

[30]  Z. Ding,et al.  Monte Carlo modelling of electron-solid interactions , 1992 .

[31]  J. L. Olsen,et al.  Electron States and Fermi Surfaces of Elements , 1984 .

[32]  H. Fitting,et al.  Monte Carlo simulation of secondary electron emission from the insulator SiO2 , 2002 .