Proximity effect in e-beam lithography is mainly due to the “nonideal” distribution of exposure (energy deposited in the resist). The proximity effect correction schemes developed so far employ a two-dimensional (2D) model, i.e., exposure variation along the resist depth dimension is not considered. The exposure distribution estimated by the 2D model can be significantly different from the actual exposure distribution, especially for the nanoscale patterns. In this article, a three-dimensional (3D) correction method which uses a 3D point spread function in controlling e-beam dose distribution within each circuit feature in order to achieve a certain desired 3D remaining resist profile after development is described. The dose to be given to each region of a feature is determined based on the estimated remaining resist profile (with the emphasis on the sidewall shape) through iterations. Simulation results demonstrating the potential improvements by the 3D correction are provided.

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True three-dimensional proximity effect correction in electron-beam lithography

Electron beam lithography simulation is presented. A line pattern edge roughness of a resist after development process is discussed based on simulations of electron scattering in the resist film and the resist development process. Fixed threshold energy model is applied for the simulation and variations of linewidth and the line edge roughness are obtained as functions of the incident electron energy, resist thickness, and electron doses. The energy range calculated is from 1to5keV, the resist thickness ranges from 20to70nm, and the electron dose ranges from 1to100μC∕cm2. The resist assumed is poly(methylmethacrylate) and the film is on a Si substrate. In the present study, the threshold energy density is determined as 1.44×1021(eV∕cm3) to draw a given linewidth of 100nm, then the value of the line edge roughness is obtained. The minimum line edge roughness is obtained when the dose is more than that to produce the designed linewidth. As the dose is increased more than that to obtain the minimum edge roug...

Dependence of linewidth and its edge roughness on electron beam exposure dose

I review the work of proximity effect correction (PEC) in electron-beam (e-beam) lithography with emphasis on dose modification and shape modification PEC techniques.

A Review of Proximity Effect Correction in Electron-beam Lithography

Positive and negative lithographic patterns have been produced in epitaxial layers of GaAs, achieved by electron beam writing and subsequent etching by Cl2 gas at elevated temperatures. A latent image is formed in the native oxide which is either less resistant to thermal Cl2 etching (positive pattern) or more resistant to thermal Cl2 etching (negative pattern), depending on the electron beam dose. The pattern is stable in air for at least several weeks. The tone of the pattern also depends on the electron beam accelerating voltage, the etching conditions, and the thickness and initial state of the native oxide. Significant changes in the resulting lithography are due to changes in an oxide only a few monolayers thick. Both positive and negative patterns can be produced in adjacent areas with high contrast by variation of the electron‐beam does. Initial Auger analysis suggests that chemical rearrangement of the native oxide occurs with electron beam exposure. The discovery that the native oxide on GaAs ac...

Positive and negative ‘‘resistless’’ lithography of GaAs by electron beam exposure and thermal Cl2 etching

Thermally modulated Nanophotonic Phased Arrays (NPAs) can be used as phase-only holographic displays. Compared to the holographic displays based on Liquid Crystal on Silicon Spatial Light Modulators (LCoS SLMs), NPAs have the advantage of integrated light source and high refresh rate. However, the formation of the desired wavefront requires accurate modulation of the phase which is distorted by the thermal proximity effect. This problem has been largely overlooked and existing approaches to similar problems are either slow or do not provide a good result in the setting of NPAs. We propose two new algorithms based on the iterative phase retrieval algorithm and the proximal algorithm to address this challenge. We have carried out computational simulations to compare and contrast various algorithms in terms of image quality and computational efficiency. This work is going to benefit the research on NPAs and enable the use of large-scale NPAs as holographic displays.

Correcting the Proximity Effect in Nanophotonic Phased Arrays

A limitation on the quality of electron beam lithography is the proximity effect. This produces exposure of the resist at locations remote from the point of incidence of the electron beam. One of the techniques used to mitigate this problem is to precompensate the applied beam dose. Traditional approaches to this problem have required extensive calculations which occasionally fail to produce satisfactory results. However, the proximity correction problem is quite similar to the edge enhancement problem which arises in pattern recognition. Furthermore, the issue of data base compaction for the precompensated lithography is quite similar to bandwidth compression in image transmission. In this paper, we examine the application of image processing methods to the proximity correction problem. We find that, while the match between these disciplines is not perfect, the idea appears quite promising.

K. Molnar

Papers

An image processing approach to fast, efficient proximity correction for electron beam lithography