A conceptual optical system. The half-space is under vacuum; the half-space is an infinite silicon slab. The center of a short pulse of soft x-ray radiation produced far away in the remote past reaches the surface at . Part of it penetrates the material medium, while part of it is reflected.
Reflectivity of a silicon ideal surface for glancing incidence at an angle of 30 mrad, as calculated by XOP2.0 (Refs. 4 and 7).
Temperature distribution at fixed moments inside the silicon slab after normal incidence of a Gaussian radiant energy pulse. The slab is supposed to be at before irradiation. Notice that as long as the heat front has time to advance just a distance z small compared to the Gaussian radius , the heat flow is essentially one dimensional. For longer times, the heat flow becomes three dimensional, the energy dissipates much more rapidly, and the maximum temperature tends to zero.
Temperature distribution at fixed points inside the silicon slab after normal incidence of a Gaussian radiant energy pulse. The slab is supposed to be at before irradiation.
Silicon surface normal displacement at the center of the silicon hot spot after normal incidence of a Gaussian radiant energy pulse. Notice that at very short times the surface displacement is very small, in agreement with the simple estimates discussed in Secs. II and IV. So, for single pulse operation, there is no optical aberration related to thermal effects. However, at , the surface bulges out by more than 1 nm, and the surface figure error can become significant, a question of concern for operation with pulse trains if the pulses are closely spaced.
Silicon surface normal displacement , after normal incidence of a Gaussian radiant energy pulse, as a function of the radial distance from the center of the silicon hot spot. This is shown for three different instants of time: 40, 200, and 1000 ns after pulse arrival at the silicon surface.
(Silicon surface normal displacement required to satisfy the boundary condition of “free surface” at and the resulting total displacement, at . From the figure, we see that for , the surface figure error is , which is larger than presently attainable surface quality and would therefore significantly degrade optical performance.
Silicon general properties.
Thermoelastic constants for silicon.
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