Local Heating During Electron Beam Patterning of Lithography Masks

Abstract

The semiconductor industry is constantly seeking to improve the performance of integrated circuits by drastically increasing the density and reducing the pattern feature size. Accurate patterning of advanced lithography masks is a key issue in the production of integrated circuits with sub-0.13 ?m feature size. Predicting and subsequently correcting for the errors produced in writing the pattern is essential.

One source of pattern error is the heating of the lithography mask during the electron beam patterning process. Mask heating during writing causes pattern errors through the resist stress relief, local over- or under-development of the resist due to the temperature dependent resist sensitivity, and by thermal distortions. These pattern errors depend upon the transient temperature distribution in the mask during the electron-beam-writing process.

In this thesis local mask temperature profiles are predicted for various writing conditions. The local mask heating of an optical reticle during writing of a single electron beam flash is analyzed. The contribution of multiple electron beam flashes on an X-ray mask to global mask heating during writing is determined by calculating the transient mask temperature profile during the patterning process using a finite element software package.

Two levels of model are compared. A very detailed small-scale model of pattern writing is developed with the element size that of a pattern shape. An averaging large-scale model in which the electron beam energy is distributed over many elements is also developed. The averaging technique is often used in thermal analyses to reduce computation time. The average temperature rise and local maximum of the two methods are compared. It is found that the averaging technique predicts the average temperature rise accurately, but significantly under-predicts the maximum local temperatures.

A procedure for developing thermal models with high accuracy, minimal number of elements, and reasonable calculation time is described. Design rules for finite element models used for the simulation of local mask heating are presented.