A comprehensive model for sub-10 nm electron-beam patterning through the short-time and cold development

In this study, we propose a set of single-spot experiment to construct a comprehensive model of electron-beam lithography to describe the relation among the incident electrons, resist, and the development conditions such as durations and temperatures. Through the experiments, small feature can be achieved by performing a short-time development due to the high acceleration voltage and large depth of focus of electron-beam system. The singular point in the beginning of the development is also observed in our model and supported by the experimental data. In addition, we verify the characteristic region of each incident spot induced by the point spread function of the electron-beam system. We further fabricate the single line with narrow groove width by utilizing the results from single-spot experiment at low developing temperatures. The line is formed by arranging a series of incident points with a distance close to the characteristic radius. This method can eliminate the proximity effect effectively and thus the groove width is scaled down to 8 nm. By adopting the successful experience in the single line formation, dense array with narrow linewidth is also demonstrated under well suppression of the proximity effect. The minimum groove width of 9 nm with 30 nm pitch is achieved with 5 s development time at -10 °C. Finally, the exceptional capability of pattern transfer is presented due to the high aspect ratio of the resist.