Proximity Effect Correction for 1:1 X-Ray Mask Fabrication

Abstract

The kinetic energy density t G (r), where G denotes the gradient form (∇ψ) 2 , is known to be a functional of the ground-state density ρ(r), but the functional remains unknown. For an arbitrary number of closed shells in a bare Coulomb field, an exact first-order differential equation is derived giving t G (r) solely in terms of s-state information. Numerical illustrations are given of the main analytical results. PACS numbers: 21.10.Sf, 31.15.Ew Some time ago, one of us [1] obtained a spatial generalization of Kato's theorem