As the semiconductor industry continues to shrink the size microelectronic components, sources of critical dimension error that were unimportant in the past have surfaced, and must be resolved. Among these errors is the proximity heating effect. As an optical mask is patterned using an e-beam, there is heat diffusion away from the area being patterned. Due to the increase in temperature, the resist surrounding the patterned area increases in sensitivity and becomes more prone to development from scattered electrons. The unexpected development of resist and distortions due to thermal gradients can cause the final pattern to differ from the intended pattern.Unfortunately, there is no method to predict the magnitude of these errors.Guess and check methods are not feasible in the production environment due to the limited number of chip manufacturing tools, and the need to produce saleable products on these tools. Consequently, a method is needed to predict the magnitude and location of these errors. The topic of this thesis is to investigate the thermal response of the optical mask due to direct patterning using a finite element program, ANSYS. The results from this thesis, resist temperature as a function of position and time, can then be combined with experimental data relating the temperature history of the resist with its sensitivity, and Monte Carlo simulations that predict the scattering of electrons as they penetrate an optical substrate to yield the percentage of resist development at every point on the mask. The results of this analysis can then be iii compared with the desired pattern. Any regions containing unacceptable errors can then be redesigned.