Electron-beam (e-beam) lithography is widely employed in pattern transfer thanks to its ability to write fine features on a substrate system. However, the main drawback is the proximity effect due to electron scattering in the resist, which causes the blurring of written features imposing the fundamental limit on the minimum feature size and therefore the feature density that are realizable by e-beam lithography. With a computational model of the e-beam exposure process, we started to work on developing efficient methods to correct for the proximity effect to minimize the critical dimension (CD) error, resulting in PYRAMID - a hierarchical rule-based scheme for the proximity effect correction (PEC). The first version of PYRAMID modifies the feature shape only with a uniform dose for the entire pattern to enable fast and accurate correction. Subsequently, for a more flexible and optimal correction, both dose and shape-dose modifications were also incorporated into the PYRAMID correction hierarchy. During this early phase of research, various techniques were implemented to enhance the accuracy and applicability of PYRAMID.

As the feature size continued to decrease, the conventional two-dimensional model revealed the fundamental limitation on the correction accuracy due to the fact that the exposure variation along the resist-depth dimension is not taken into account. The correction hierarchy of PYRAMID was augmented in implementing the true three-dimensional PEC. Meanwhile, another effort was made to demonstrate the applicability of PYRAMID to grayscale lithography, leading to the fabrication of nanostructures such as staircase and sawtooth structures. The typical dose distribution for PEC of a feature is of V-shape which is not optimal especially when a vertical sidewall is to be achieved for a small feature. New types of dose distributions were introduced and demonstrated to be more effective in realizing the vertical sidewall while minimizing the CD error.

An unavoidable issue in any lithography is the roughness in the boundaries of written feature. In the case of e-beam lithography, the roughness stems from the stochastic nature of electron scattering in the resist, leading to stochastic exposure. A stochastic model of exposure was adopted in developing a realistic method which employs both shape and dose modifications to effectively minimize CD error and LER. Also, in an analytic study, the mathematical expression of LER was derived and employed in minimizing the LER in a single feature and a large-scale uniform pattern, avoiding the repetitive and costly simulation or experiment. In another study, a practical method of modeling the e-beam lithographic process directly from SEM (scanning electron microscope) images was developed. Since the modeling is based on the SEM images, the minimization of CD error and LER is likely to obtain realistic results.

The conventional e-beam system suffers from a limited writing speed since a single beam exposes each individual feature one at a time. Recently, a massively-parallel e-beam system (MPES) with a large number of beams, e.g., 512 x 512 beams, was introduced to overcome this drawback. The optimal use of such MPES was one of our recent research topics. In the beginning, the effects of faulty or abnormal beams were analyzed, and a new writing method (multirow writing) was developed and compared to the existing writing method (multipass writing). Subsequently, the writing method was refined and optimized to reduce the exposing time further. An effective scheme utilizing both shape and dose modifications under the constraints of MPES was developed for minimizing the CD error and LER, and generalized such that a cost function including the exposing time can be specified for the optimization.

The current research is focused on analytic study on some of the fundamental issues in e-beam lithography. The outcomes in the form of closed-form expressions from this analytic study allow one to investigate such issues without simulation or experiment.