Proximity Effect Correction 

Correction of E-beam and Optical Proximity Effects 

Correction of E-beam or Optical proximity effects has become a very hot topic in recent years. Those involved in direct-write-on-wafer applications have had the need to perform critical E-beam proximity effect corrections for several years.

Sceleton is a high-speed, high-precision Monte Carlo simulator. It performs high precision Monte Carlo simulation of electron trajectories in arbitrarily complex material stacks. The calculated radial energy density distribution (point spread) can be used directly as input for the proximity correction program PROXECCO, resist profile simulation tools or graphical data analysis.

Physics behind the scenes:
Monte Carlo simulation is carried out using a single scattering model, where the electron trajectory is followed through a series of scattering events in the resist / substrate stack. Elastic scattering events are described using the screened Rutherford formula. Energy dissipation due to inelastic scattering is modeled by Bethe's energy loss formula in the continuously slowing down approximation (CSDA).

Accuracy and speed:
Special emphasis has been put on ultrahigh simulation fidelity. Precise path integration in CSDA coding has been found to be of utmost importance for high simulation accuracy and has been implemented by high-precision algorithms without sacrificing simulation speed. Trajectory calculation in multilayer material stacks has to cope with frequently changing scattering cross sections due to interface crossing. sceleton makes use of tailored algorithms, giving supreme simulation fidelity even for complex material stacks and the full range of electron injection energies.

User extensible material database:
Description of materials is based on stoichiometry and mass density only. Derivation of dependent parameters is performed automatically at run-time, using an internal database of atomic elements. Therefore, an extension of the material database can be done by the user very easily, without the need for supplying complex atomic parameters.

Arbitrarily complex material stacks:
Electron scattering in complex multilayer material stacks can be simulated. Description of material stacks is based on a list, containing one 3-parameter entry per layer. Using a standard text-editor, the user can build even complex material stacks within minutes.

Automatic simulation mesh generation:
Sceleton allows for different methods of simulation mesh generation. In automatic mode, the selection of mesh parameters is left entirely to the program, which automatically adapts to the simulation parameters. Manual and semiautomatic modes give the user the opportunity to force the program to special simulation regimes.

Sceleton performs at a typical speed of ~ 40 traced electrons / s (20 keV injection energy) on a DIGITAL VAXstation 4000/90 running VMS. Typically between 10^5 and 10^6 electrons are traced in order to achieve good simulation statistics, giving total computation times between one and seven hours. Usually sceleton is run as a low priority background process. Simulation results are periodically written to disk.

CATS also supports PROXECCO. Available for all platforms supported by CATS and integrated into the fracture process of CATS, PROXECCO utilizes an N-gaussian analytical function or a point-wise proximity function determined by the Monte Carlo simulation package Sceleton. PROXECCO corrects for the e-beam proximity effect through dose modulation on systems which support shape-based dose modulation and through either a unique N-pass writing technique or geometric shape manipulation (see below) for systems which do not support shape-based dose modulation (MEBES, Varian).

E-beam proximity effect correction is an effective means of correcting for line-end shortening, critical dimension linearity, and the typical line-edge variations seen between nested and isolated lines.

In the examples shown here, the design data (top) is first "sleeved" by CATS (center) and then corrected by Proxecco (bottom). The enlargement shows the relative dose values assigned to each shape. Higher values indicate higher doses.