Analysis of Charging Phenomena of Polymer Films on Silicon Substrates under Electron Beam Irradiation

Abstract

Charging phenomena of polymer films on silicon substrates under electron beam irradiation are studied by numerical simulation. The initial distribution of the charge deposited in the sample is calculated by a Monte Carlo simulation of electron scattering, and charge drift is simulated by taking into account the Poisson equation, the charge continuity equation, Ohm's law, and electron beam induced conductivity. The dependences of charging on electron energy and polymer thickness are explained by the secondary yield and the relationship between the electron range and polymer film thickness.

Comparison between Energy Straggling Strategy and Continuous Slowing Down Approximation in Monte Carlo Simulation of Secondary Electron Emission of Insulating Materials

“…[1][2][3]9,11,12,18,19) The mentioned alternative MC scheme to calculate the secondary electron yield, based on a continuous slowing down approximation, uses as input the electron stopping power of the material being considered. [6][7][8] The secondary electron yields calculated using the two approaches are very close. What is more, the two MC schemes give results in satisfactory agreement with the experiment.…”

“…The secondary electron yield is calculated, according to Dionne,4) Lin and Joy, 5) Yasuda et al, 6) and Walker et al, 7) assuming that (i) the number dn of secondary electrons generated along each step length ds, corresponding to the energy loss dE, is given by where ε s is the effective energy necessary to generate a single secondary electron and (ii) the probability P(z) that a secondary electron generated at depth z will reach the surface and will emerge from it follows the exponential decay law , ) ( …”

“…[4][5][6][7][8] The use of the first approach has stronger physical basis but, due to the detailed description of all the collisions in the secondary electron cascade, it corresponds to a scheme very time consuming. The continuous slowing down approximation represents instead an approach which saves a lot of CPU time.…”

Multiphysics Simulation of Nanopatterning in Electron Beam Lithography

“…A positive charge was deposited at the position where a secondary electron was generated, and a negative charge was deposited at the position where an electron stops in the sample. The charge drift in the sample was simulated by taking into account the Poisson equation, the charge continuity equation, Ohm's law, and the radiation-induced conductivity [13,17,18]. Figure 7 shows the surface potential distribution of the PMMA resist on a Si substrate during electron exposure at 0.…”

Nano-Pattern Recognition and Correlation Technique for Sub-Nanometer In-Plane Displacement Measurement

“…for nano-structure fabrication [33][34][35][36][37][38][39]. It has been extended successfully to fabricate regularly oriented structures [37,38].…”