Real-time generation of circular patterns in electron beam lithography

Electron beam lithography (EBL) involves the transfer of a pattern onto the surface of a substrate by first scanning a thin layer of organic film (called resist) on the surface by a tightly focused and precisely controlled electron beam (exposure) and then selectively removing the exposed or nonexposed regions of the resist in a solvent (developing). It is widely used for fabrication of integrated circuits, mask manufacturing, photoelectric device processing, and other fields. The key to drawing circular patterns by EBL is the graphics production and control. In an EBL system, an embedded processor calculates and generates the trajectory coordinates for movement of the electron beam, and outputs the corresponding voltage signal through a digital-to-analog converter (DAC) to control a deflector that changes the position of the electron beam. Through this procedure, it is possible to guarantee the accuracy and real-time control of electron beam scanning deflection. Existing EBL systems mostly use the method of polygonal approximation to expose circles. A circle is divided into several polygons, and the smaller the segmentation, the higher is the precision of the splicing circle. However, owing to the need to generate and scan each polygon separately, an increase in the number of segments will lead to a decrease in the overall lithography speed. In this paper, based on Bresenham’s circle algorithm and exploiting the capabilities of a field-programmable gate array and DAC, an improved real-time circle-producing algorithm is designed for EBL. The algorithm can directly generate circular graphics coordinates such as those for a single circle, solid circle, solid ring, or concentric ring, and is able to effectively realizes deflection and scanning of the electron beam for circular graphics lithography. Compared with the polygonal approximation method, the improved algorithm exhibits improved precision and speed. At the same time, the point generation strategy is optimized to solve the blank pixel and pseudo-pixel problems that arise with Bresenham’s circle algorithm. A complete electron beam deflection system is established to carry out lithography experiments, the results of which show that the error between the exposure results and the preset patterns is at the nanometer level, indicating that the improved algorithm meets the requirements for real-time control and high precision of EBL.