Heat transport in masks for deep X-ray lithography during the irradiation process

The problem of heat generation and heat transport due to the absorption of the synchrotron beam energy in the X-ray mask and the resist during the lithographic process has been examined. For this purpose a numerical simulation with the finite element method has been performed coupled with experimental measurements of the temperature rise on the mask during the synchrotron irradiation at the electron stretcher accelerator (ELSA) of Bonn University. Our results show that the temperature rise on the mask is localized to the immediate vicinity of the synchrotron beam position with an absolute value of about 12°C while it remains at ambient temperature apart from beam profile. Within the resist the temperature rise is up to 15°C depending on the material and the thickness of the ground plate used. Due to the low thermal conductivity of the resist a temperature gradient exists across its thickness. The influence of the parameters which can affect the amplitude and the distribution of the temperature on the mask and within the resist like the beam current, scanning velocity of the beam, the beam width, the thickness of the resist and the material selection of the ground plate has been studied using the finite element model. The results of this model have been verified experimentally by measurements with a specific mask which has been designed to measure the temperature during the irradiation process.