Optimum dose for shot noise limited CD uniformity in electron-beam lithography

To maximize the performance of an electron-beam lithography system the resist sensitivity must be chosen carefully. Very sensitive resists require only a low illumination dose, thus increasing the throughput. However, shot noise effects may give rise to unacceptable line edge roughness and variations in critical dimension (CD). In this study, the physical parameters which influence the effect of shot noise statistics on CD uniformity (CD-u) and linewidth roughness (LWR) are determined and an analytical model for CD-u and LWR is derived. It is found that the CD-u and LWR depend on the dose, the Gaussian beam probe size, the diffusion length d(r) of secondary electrons and acids in resist. The influence of background dose and non-shot-noise dose variations must also be taken into account. Monte Carlo simulations are performed to obtain the statistical variation of the two-dimensional solubility distribution of illuminated resist in a developer. The results of this simulation are used to validate the model. For the CD-u and the LWR, different expressions were found for describing the effect of the shot noise because, to describe the LWR, an extra factor must be incorporated to include the effect that spatial frequencies lower than 2 CDs do not have a contribution. Also, the area over which the dose must be integrated for the shot noise 2 calculation is different for CD-u and LWR. For CD-u this area depends on d(r) - CD, for LWR on d(r)(2). From the model it can be concluded that shot noise has a significant effect on both the CD uniformity and the LWR and cannot be neglected in the optimization of the dose for high-throughput electron-beam lithography. With the specific relation between the current and the resolution of an e-beam tool, an expression for CD uniformity is found from which the throughput can be maximized for the required CD-u by optimizing the dose, probe size, and diffusion parameter. The background dose and the other dose variations are input parameters for such an optimization. For electron-beam systems with a typical resolution of 30 nm and a required CD uniformity contribution of 3.5 nm (3sigma) due to all dose variations, a dose of 30 muC/cm(2) is needed if 20% background and 3% (3sigma) non-shot-noise dose variations are taken into account. 0 2004 American Vacuum Society