Modeling and Simulation Issues in Monte Carlo Calculation of Electron Interaction with Solid Targets

Vladimir V. Ivin1 ( ivin-AT-soft-tec-DOT-ru.gif ), Mihail V. Silakov1, George A. Babushkin1, Bing Lu2, Pawitter Mangat2, Kevin Nordquist3, Douglas J. Resnick3
1SOFT-TEC, Nakhimovsky Prst. 34, Moscow 117218, Russia ( http://www.soft-tec.ru ).
2Motorola, Adv. Process Dev. & Ext. Research, DigitalDNA(TM) Laboratories, 7700 S. River Parkway, Tempe, AZ 85284, USA
3Motorola Labs, 7700 S. River Parkway, Tempe, AZ 85284, USA

An accurate simulation of electron interaction with solid films and substrates is essential for e-beam lithography process development and optimization. The electron movement through a solid matter is commonly modeled via multiple electron scattering at the substance atoms; in actual calculation the Monte Carlo technique is typically used for simulating random electron scattering acts. This approach assumes that the differential cross-sections (DCS) for the processes of elastic and inelastic electron scatter at the atoms are known. The accuracy of calculated electron-target interaction characteristics, such as electron backscatter coefficient (BSC) or absorbed energy, is then determined by the accuracy of the DCS used in simulation. However, it is known that using more accurate DCS increases the total simulation runtime so a balanced tradeoff between the accuracy and the speed of calculation should be made in practical model applications. In this work we compare simulation accuracy and efficiency of different Monte Carlo models for initial beam energy 10-100 keV. The models in question include Rutherford versus Mott elastic scatter DCS, Moller versus Gryzinski inelastic scatter DCS for generation of secondary electrons, and continuous versus discrete electron energy loss treatment in-between scattering acts. In all cases, the simulation results are compared with published experimental data on electron BSC for a variety of substrate stacks and beam energies.