Simulation of electron beam lithography of nanostructures

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-cha...

[1]  Adolphe Chapiro,et al.  Radiation Chemistry of Polymeric Systems , 1962 .

[2]  M. Hatzakis,et al.  Analytical evaluation of the energy deposition function in electron‐beam lithography in the case of a composite substrate , 1993 .

[3]  David C. Joy,et al.  An empirical stopping power relationship for low‐energy electrons , 1989 .

[4]  D. F. Kyser,et al.  Monte Carlo simulation of spatially distributed beams in electron-beam lithography , 1975 .

[5]  E. Montroll,et al.  Theory of Depolymerization of Long Chain Molecules , 1940 .

[6]  D. Hess,et al.  Transport models for swelling and dissolution of thin polymer films , 1989 .

[7]  P. Staub.  Bulk target backscattering coefficient and energy distribution of 0.5-100 keV electrons : an empirical and synthetic study , 1994 .

[8]  New three dimensional simulator for low energy (∼1 keV) electron beam systems , 1999 .

[9]  An exposure model for electron-sensitive resists , 1974 .

[10]  Mihir Parikh,et al.  Energy deposition functions in electron resist films on substrates , 1979 .

[11]  Vlasis G. Mavrantzas,et al.  Crossover from the Rouse to the Entangled Polymer Melt Regime: Signals from Long, Detailed Atomistic Molecular Dynamics Simulations, Supported by Rheological Experiments , 2003 .

[12]  D. F. Kyser,et al.  Computer Simulation of Electron-Beam Resist Profiles , 1980, IBM J. Res. Dev..

[13]  Franco Cerrina,et al.  Stochastic modeling of high energy lithographies , 2003 .

[14]  W. Kuhn,et al.  Über die Kinetik des Abbaues hochmolekularer Ketten , 1930 .

[15]  P. G. de Gennes,et al.  Dynamics of Entangled Polymer Solutions. I. The Rouse Model , 1976 .

[16]  Kukjin Chun,et al.  New Approach of Monte Carlo Simulation for Low Energy Electron Beam Lithography , 1997 .

[17]  Kenji Murata,et al.  Studies of energy dissipation in resist films by a Monte Carlo simulation based on the Mott cross section , 1987 .

[18]  Kenji Murata,et al.  Monte Carlo simulation of fast secondary electron production in electron beam resists , 1981 .

[19]  X. Zhu,et al.  Physical models of diffusion for polymer solutions, gels and solids , 1999 .

[20]  M. Reisser,et al.  Spatial energy deposition distribution by a keV-electron beam in resist layers for electron-beam lithography , 1995 .

[21]  B. Paul.  An analytical model of the diffusive scattering of low-energy electrons in electron-beam resists , 1999 .

[22]  Balaji Narasimhan,et al.  The physics of polymer dissolution: Modeling approaches and experimental behavior , 1997 .

[23]  P. Gennes.  Reptation of a Polymer Chain in the Presence of Fixed Obstacles , 1971 .

[24]  I. Adesida,et al.  A study of electron penetration in solids using a direct Monte Carlo approach , 1980 .

[25]  Jack L. Koenig,et al.  A review of polymer dissolution , 2003 .

[26]  Xiaoming Yang,et al.  Monte Carlo simulation of process parameters in electron beam lithography for thick resist patterning , 2006 .

[27]  Xiangdong Liu,et al.  Monte-Carlo simulation of low-energy electron scattering in PMMA - using stopping powers from dielectric formalism , 2005 .

[28]  M. Hatzakis,et al.  Application of a new analytical technique of electron distribution calculations to the profile simulation of a high sensitivity negative electron‐beam resist , 1992 .

[29]  M. A. Mohammad,et al.  Interdependence of optimum exposure dose regimes and the kinetics of resist dissolution for electron beam nanolithography of polymethylmethacrylate , 2010 .

[30]  Jabłoński,et al.  Elastic electron backscattering from surfaces. , 1989, Physical review. B, Condensed matter.

[31]  A. Neureuther,et al.  Energy deposition and transfer in electron-beam lithography , 2001 .

[32]  A. Mumtaz,et al.  Influence of developer and development conditions on the behavior of high molecular weight electron beam resists , 2000 .

[33]  Ioannis Raptis,et al.  Electron beam lithography simulation for high resolution and high-density patterns , 2001 .

[34]  D. Achilias,et al.  A Review of Modeling of Diffusion Controlled Polymerization Reactions , 2007 .

[35]  M. A. Mohammad,et al.  Systematic study of the interdependence of exposure and development conditions and kinetic modelling for optimizing low-energy electron beam nanolithography , 2010 .

[36]  S. Dew,et al.  Simulation of the spatial distribution and molecular weight of polymethylmethacrylate fragments in electron beam lithography exposures , 2006 .

[37]  Norihiko Samoto,et al.  Theoretical study of the ultimate resolution in electron beam lithography by Monte Carlo simulation, including secondary electron generation: Energy dissipation profile in polymethylmethacrylate , 1983 .

[38]  T. Everhart,et al.  A semiempirical stopping‐power formula for use in microprobe analysis , 1978 .

[39]  Martin C. Peckerar,et al.  Modeling of electron elastic and inelastic scattering , 1996 .

[40]  F. Brochard,et al.  Polymer-Polymer Interdiffusion , 1986 .

[41]  P. Rez,et al.  Energy deposition in thin films calculated using electron transport theory , 1994 .

[42]  Ioannis Raptis,et al.  A fast electron beam lithography simulator based on the Boltzmann transport equation , 1996, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..