Method for determining an edge profile of a volume of a photoresist after a development process

Abstract

The present invention relates to a method for determining an edge profile of a volume of a photoresist after a development process. At first, the volume of the photoresist is divided into cells. A chemical master equation is set up which reflects the stochastic kinetics of chemical reactions proceeding in cells of the volume of the photoresist during the development process. The chemical master equation is solved for a given development time on the basis of a Gillespie algorithm in order to determine developed and non-developed cells of the volume of the photoresist at the end of the development process. Finally, the edge profile of the volume of the photoresist after the development process is determined on the basis of a cluster of non-developed cells.

Description

TECHNICAL FIELD OF THE INVENTION [0001] The present invention relates to a method for simulating the complex kinetics of chemical reactions, and in particular, to a method for determining an edge profile of a volume of a photoresist after a development process. BACKGROUND OF THE INVENTION [0002] The fabrication of highly integrated electrical circuits with small structural dimensions requires special structuring procedures. One of the most common procedures is the so-called lithographic structuring method. This method comprises depositing a thin layer of a radiation sensitive photoresist on the surface of a semiconductor substrate disk, also referred to as wafer, applying a so-called soft bake step during which the solvent content of the photoresist is reduced and exposing the photoresist to radiation transmitted through a lithographic mask. In the so-called photolithography, electromagnetic radiation is used. During the exposure step, lithographic structures located on the mask are...

AI Technical Summary

Benefits of technology

[0014] One advantage of an embodiment of the present invention is to provide a fast and efficient method for determining an edge profile of a volume of a photoresist after a development process.

[0033] In a similar manner this method makes it possible to model the complex kinetics of chemical reactions proceeding in a volume of a photoresist during a development process with a high accuracy, in particular on a molecular level. As a consequence fluctuations which result in a surface or profile roughness of the photoresist can be incorporated. In addition, the method is relatively fast and efficient so that determining a developed profile of the volume of the photoresist can be carried out within a reasonable computation time.

Problems solved by technology

However, conventional simulation methods generally require a high computing time.

As a consequence the practical application of such methods in order to predict an edge profile of a volume of a photoresist after a development process is limited.

Moreover the existing methods do not model on a molecular level so that fluctuations like e.g. polymer density variations, fluctuations induced by reaction mechanisms and variations in polymer length and developer penetration depth, which have an impact on roughness of a photoresist like the line edge roughness are taken into account only to some degree.

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