This Is AuburnElectronic Theses and Dissertations

True Three-Dimensional Proximity Effect Correction in Electron-beam Lithography: Control of Critical Dimension and Sidewall Shape




Dai, Qing

Type of Degree



Electrical Engineering


One of the major limiting factors in electron-beam (e-beam) lithography is the geometric distortion of written features due to electron scattering, i.e., proximity effect, which puts a fundamental limit on the minimum feature size and maximum pattern density that can be realized. A conventional approach to proximity effect correction (PEC) is, through two-dimensional (2-D) simulation, to determine the dose distribution and/or shape modification for each feature in a circuit pattern such that the written pattern is as close to the target pattern as possible. For circuit patterns with nanoscale features, it is not unusual that the actual written pattern is substantially different from the written pattern estimated by a 2-D PEC method. One of the reasons for this deviation is that the 2-D model ignores the exposure variation along the resist depth dimension. Earlier, it was shown that three-dimensional (3-D) PEC which considers the variation of exposure along the resist depth dimension would be required for nanoscale features, especially for feature size well below 100 nm. In 3-D PEC, the resist profile estimated through simulation of resist development process was employed instead of the exposure distribution, in order to obtain more realistic results. However, It has been demonstrated that in order to minimize any deviation from a target resist profile, a 3-D PEC scheme must check the estimated resist profile during the dose optimization procedure. One practical issue of such an approach to 3-D PEC is that a time-consuming resist development simulation needs to be carried out in each iteration of the dose optimization for each feature. For the case of large-scale circuit patterns, such a feature-by-feature correction procedure would be too time-consuming to be practical. Also, it has been shown that the dose distribution of ``V-shape", which is used by most 2-D PEC schemes, is not optimal for realizing a vertical sidewall of the resist profile, especially when the total dose is to be minimized. In this dissertation, the characteristics of our 3-D exposure model are further analyzed and utilized for accurate estimation of resist profiles. Our true 3-D PEC method is also extended to applications for large-scale circuit patterns. A variety of optimizations are developed in order to improve the correction efficiency, such as path-based resist development simulation, critical-location-based dose control, etc. New types of dose distributions are derived under our 3-D exposure model and 3-D PEC method for achieving better sidewall shapes with total dose being minimized. For improving the correction efficiency without sacrificing the correction quality, a dose optimization scheme with a systematic type-based dose updating procedure is developed which is adaptable to different dose distribution types. A dose determination scheme is also developed which can adaptively determine the optimal dose distribution type and the minimum of required total dose based on a given circuit pattern and substrate system settings. The results from extensive simulation along with experiments are provided for performance analysis.