Optimization of an anode membrane with a transmission-type target in a system of soft X-ray sources for X-ray nanolithography

In this paper, we propose a method for optimizing the design and composition of the anode membrane with a transmission-type target as part of a system of soft X-ray sources based on field-emission triodes for performing tasks in the field of X-ray nanolithography. It allows to prevent the degradation of the operating characteristics of the system when significant electrostatic deformation of the anode occurs under the influence of a control electric field in the inter-electrode space of the triodes. For this purpose, the inclusion of an additional control electrode in the system design is considered, which makes it possible to compensate for the deformation of the anode membrane to an acceptable level and thereby stabilize the operation of X-ray sources. A numerical model of the electrostatic deflection of the anode assembly in a modified design is developed, based on which the optimal composition and geometric parameters of the anode membrane with a compensating electrode are determined. In particular, the optimal distance between the anode membrane in the initial (undeformed) state and the compensating electrode was found (equal to 5 $\mu$m), at which a minimum voltage difference (about 1.15 kV) should be applied to these electrodes to prevent critical deflection of the membrane (0.72 $\mu$m with a membrane radius of 750 $\mu$m). It is also shown that, due to their extremely high hardness ($>$ 80 GPa), diamond-like films are the most promising material for the anode electrode. The results obtained can also be useful for the development of miniature X-ray generation devices for various applications.