Novel Ion-Lens Configurations: A Further Step to 2-nm Ion-Beam Lithography

Abstract

Composite axially symmetric immersion ion lenses are considered that consist of an electrostatic and a magnetic lens. For the first time, their performance is evaluated over the entire range of operating conditions: from the case of a zero magnetic field to the case of a zero ion energy on the target. Operating conditions are characterized in terms of τ = Wt/W0, where W0 is the energy of an ion at the boundary of the region in which the trajectories are parallel to the axis and Wt is that on the target. For the first time, simple analytical approximations are derived for Cc/r, Cs/r, f/r, and NI, where Cc is the chromatic-aberration coefficient, Cs is the third-order spherical-aberration coefficient, f is the focal distance, NI is the magnetomotive force of the coil, and r is the outer radius of the coil. The behavior of the four quantities is explored as a function of τ. The following conclusions are drawn: (i) The aberrations are maximum for a zero magnetic field. (ii) The aberration coefficients decrease monotonically with increasing NIand decreasing τ, the lens changing from an accelerating to a decelerating one. (iii) If τ → , then Cs/r – τ1/4, Cc/r – τ1/6, f/r– τ1/3, and NI – τ–1/2. (iv) The lenses are suitable for resistless heavy-ion projection lithography and can provide 20 × 1011 pixels of area 2 × 2 nm2 for an exposed area of 3 × 3 mm2. (v) Used in heavy-ion microprobe systems, the lenses could enable resistless lithography over much larger areas than existing equipment.