Simulation of electron beam lithography of nanostructures

Abstract

The authors report a numeric simulation tool that they developed for the modeling and analysis of electron beam lithography (EBL) of nanostructures employing a popular positive tone resist polymethylmethacrylate (PMMA). Modeling and process design for EBL fabrication of 5–50 nm PMMA structures on solid substrates is the target purpose of the simulator. The simulator is functional for exposure energies from 1 to 50 keV with arbitrary writing geometries. The authors employ a suite of kinetic models for the traveling of primary, secondary, and backscattered electrons in the resist, compute three-dimensional (3D) distributions of the yield of main-chain scission in PMMA, and convert these into the local volume fractions of fragments of various sizes. The kinetic process of development is described by the movement of the resist-developer interface with the rate derived from the mean-field theory of polymer diffusion. The EBL simulator allows the computation of detailed 3D distributions of the yield of main-chain scission in PMMA for various conditions of exposure, the corresponding volume fractions of small fragments, and the clearance profiles as functions of the development in time and temperature. This article describes the models employed to simulate the EBL exposure and development, reports examples of the computations, and presents comparisons of the predicted development profiles with experimental cross-sectional resist profiles in dense gratings.

Nanomachining and clamping point optimization of silicon carbon nitride resonators using low voltage electron beam lithography and cold development

“…A detailed description of the approach employed in the EBL simulator is presented elsewhere. 10,11 In brief, the EBL simulator allows the user to visualize electron beam exposure, fragmentation, and development of exposed positive tone EBL resist, PMMA, on conductive substrates. The EBL simulator accepts two-dimensional graphical inputs along with substrate and exposure conditions to generate three-dimensional ͑3D͒ spatial maps of yield of main chain resist polymer scission and distributions of resist fragments of various sizes ͑expo-sure plots͒.…”

“…In this work, we co-optimize the EBL exposure and development conditions with the help of an original EBL simulator 10,11 to achieve uniform sub-20-nm doubly clamped resonators with lengths ranging from 1 to 20 m. We demonstrate the capacity to precisely control the width of these resonators by selecting the appropriate process conditions. In addition, we have investigated the resonant behavior of these nanostructures.…”

Molecular Dynamics Study of Line Edge Roughness and the Proximity Effect in Electron Beam Lithography

“…Numerical simulations are indispensable for evaluating and predicting the pattern profiles in lithography techniques [1][2][3][4][5][6][7][8][9]. With the progress of pattern formation techniques, the feature size of the resist pattern has decreased.…”

Multiphysics Simulation of Nanopatterning in Electron Beam Lithography

“…Numerical simulations have become a powerful approach to evaluate and predict the pattern profiles in lithography techniques [1][2][3][4][5][6][7][8][9]. With the progress of pattern formation techniques, the feature size of the resist pattern has decreased.…”