Calculation of the Absorbed Electron Energy 3D Distribution by the Monte Carlo Method, Presentation of the Proximity Function by Three Parameters α, β, η and Comparison with the Experiment

Abstract

The paper presents a program for simulating electron scattering in layered materials ProxyFn. Calculations show that the absorbed energy density is three-dimensional, while the contribution of the forward-scattered electrons is better described by a power function rather than the commonly used Gaussian. It is shown that for the practical correction of the proximity effect, it is possible, nevertheless, to use the classical two-dimensional proximity function containing three parameters: α, β, η. A method for determining the parameters α, β, η from three-dimensional calculations based on MC simulation and development consideration is proposed. A good agreement of the obtained parameters and experimental data for various substrates and electron energies is shown. Thus, a method for calculating the parameters of the classical proximity function for arbitrary layered substrates based on the Monte Carlo simulation has been developed.

Keywords

• electron-beam lithography
• Monte Carlo method
• proximity function
• electrons scattering