Analysis of the proximity function in electron-beam lithography on high- superconducting thin-films

Abstract

In this paper we approximate by the combination of double Gaussian and exponential functions the radial distributions of the absorbed electron energy density in a 125 nm PMMA resist layer on YBa 2 Cu 3 O 7 thin-film/substrate targets obtained by means of Monte Carlo simulation for a zero-width δ-function and the following variables (i) the substrate material (SrTiO 3 and MgO), (ii) the electron beam energy E 0 (25, 50 and 75 keV) and (iii) the YBa 2 Cu 3 O 7 film thickness d (0, 100, 200 and 300 nm). The values of the parameters of the analytical function are calculated using an original Monte Carlo technique. These values are presented in the form of 3D diagrams which show their dependences on beam energy and on high-temperature superconducting film thickness and can also be used for approximate determination of the parameters at different initial conditions.

Electron beam lithography simulation for sub-quarter-micron patterns on superconducting substrates

“…In the case of YBCO films over STO or MgO substrates the addition of an exponential function in equation ( 1) is found to be adequate [13]. Thus EDF(r ) could be approximated as…”

“…The specific HTS film considered is YBa 2 Cu 3 O 7−δ (YBCO) on MgO and SrTiO 3 substrates. The first module is based on the Monte Carlo (MC) algorithm [12,13,18] and the second is based on an analytical solution of the Boltzmann transport equation (AS) [15,23,25]. These modules have been successfully applied in the past, for the prediction of EDF(r, z) in the case of Si substrates and various beam energies.…”

“…Thus the application of an appropriate simulation tool would significantly decrease the time and cost required for the development of a suitable high resolution patterning technology. Nevertheless, limited attention has been paid so far to the EBL simulation in the case of HTS substrates [12,13]. It should be noted that the simulation algorithms are valid for both EBDW and EBPL methods.…”

Computer Simulation of Processes at Electron and Ion Beam Lithography, Part 1: Exposure Modeling at Electron and Ion Beam Lithography

“…The values of the proximity effect parameters are evaluated from the fitting of EDF(r) with a sum of suitable functions (Eq.29) and their dependence on all investigated variables are discussed (Gueorguiev et al, 1995;Gueorguiev et al, 1996;Gueorguiev et al, 1998;Olziersky et al, 2004). The absorbed energy distributions obtained and the calculated parameters of the proximity function can be used in a proper proximity effect correction algorithm as well as in a resist profile development model.…”

“…The proximity effect in the case of patterning the thin films of the most widely used HTS material, namely YBCO, deposited on two typical substrates (STO and MgO) is investigated (Gueorguiev et al, 1995;Gueorguiev et al, 1996;Gueorguiev et al, 1998;Olziersky et al, 2004;. HTS samples represent a more difficult case study since the substrate consists of bulk substrate STO or MgO and a very thin YBCO layer on top (multilayer substrate).…”