Finite element modeling of ion-beam lithography masks for pattern transfer distortions

Abstract

ABSTRACT As one ofthe Next Generation Lithographies, Ion-beam Projection Lithography (IPL) will be subject to strict error budgetsfor the sub-130 nm regime and will require high pattern placement accuracy. Meeting these stringent conditions in a timelyand cost-effective manner will depend upon accurate predictions of the mechanical distortions induced in IPL stencil masksduring fabrication and pattern transfer. To simulate pattern transfer, finite element (FE) structural models of the stencil maskshave been developed to predict distortions due to the fabrication of voids in stressed mask membranes. In this paper, anapplication of FE modeling for stencil masks has been demonstrated using both the IBM Falcon pattern and more uniformpatterns (to simulate the advantages ofcomplementary masks).Keywords: Ion-beam lithography, stencil masks, finite element analysis, equivalent modeling techniques. 1. INTRODUCTION With Ion-beam Projection Lithography (IPL) as a candidate for the Next Generation Lithography,'2 the development of ahigh resolution, low distortion stencil mask becomes a key issue. One of the primary sources of distortion is the fabricationof the perforations in the stressed mask membrane, also known as pattern transfer. The ability to simulate pattern transfer,and thus predict image placement accuracy is the first step in the design process. Subsequent procedures can then beperformed to correct or minimize these in-plane distortions (IPD).Previously, finite element (FE) modeling has been used to predict both fabrication and pattern transfer distortions.38 Becauseof the number and size of the perforations in IPL masks, equivalent models are needed to increase computational efficiency.Such modeling facilitates global distortion analysis which can subsequently be used with refined local models to predictpattern specific distortions. Fisher et al.3'4'6 were the first to develop equivalent modeling techniques for simulating thedistortions in perforated IPL masks. These techniques were based upon the determination of equivalent stiffness parametersfor uniform patterns of square holes in a square array, leading to the approximation and use of isotropic elastic properties.The focus of this paper is to refine the previous modeling by assessing the orthotropic characteristics of patterns of squareholes in a square array. In addition, a more general orthotropic pattern is considered to illustrate the modeling procedures;the IBM Falcon pattern9 is used as an example for this case.