Three-dimensional finite element model was developed to simulate the X-ray lithography mask distortion during electron-beam writing (EBW). Equivalent heat flux density method was proposed and the transient thermal stress simulation was done. The results show that the in-plane distortion (IPD) of the mask fluctuates with the time. The
maximum value is 8.24 nm, and the direction is deviated from the electron beam center. The maximum out-of-plane distortion (OPD) is 9.75μm. The direction is normal to the pattern window, and occurred in the center of the beam center.
A distributed RC transmission-line approximation is used to analyze the transient response characteristic of
one-dimensional (1D) position sensitive detectors (PSDs). A generalized mathematical model has been developed for a
moving light source illuminated on the PSD. The relative error curve has been given between the computed and true
incident positions of light under different moving speeds, and the impact of different starting positions has been analyzed
on the position detection error of light. It is shown that when the moving speed is less than the tenth characteristic speed,
the output photocurrents can be rather linearly detected as long as the measuring time is longer than the delayed time
maximum. It is also found that the distance between the original point and starting position should be as short as possible
in order to obtain the correct incident position of light. The computed photocurrents have been compared with data
simulated using the ANSYS software, and qualitative agreement is found.
For the problem of the impact of slanting installation of PSD used as photoelectric detector on spot position, a
mathematical model of this distortion error of the spot position is established and the simulation is done. Some
conclusions show that the distortion error of the spot position increases with the increasing of slanting angle of PSD
surface, beam waist radius and distance between PSD and beam waist position. The effect on spot positioning precision
of foregoing two can be ignored in a little range, and the last one has great effect. The distortion error model of spot
position and simulative results provide an available theoretical reference for the actually engineering applications of
Three-dimensional finite element short-pulsed models of X-ray mask have been developed and the energy absorption
function along the mask thickness direction has been considered. The results show that the absorber's temperature is
higher than the substrate's because the absorber has higher absorption coefficient. In addition, the lower the absorber
coverage of the mask, the lower the mask temperature is. The transient simulation results show that the mask temperature
reached the maximum at the end of the short-pulsed exposure. It occurs at the interface between the substrate and the
absorber, and the maximum is 52.7°C.
Heat source method was adopted to build a generalized mathematical model for the dynamic position detection of
position sensitive detector. The impact of different scanning speeds on the position detection was analyzed. It is shown
that the satisfaction of the linear relation between the detected positions and the true incident positions needs two
conditions. The relative position detection error decreases with the decrease of the scanning speed or the increase of the
angle intersected by the direction of speed and x-axis. The photocurrents for the analytical solution are compared with
data simulated by the ANSYS software. Qualitative agreement is found.