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

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 = W _t/W ₀, where W ₀ is the energy of an ion at the boundary of the region in which the trajectories are parallel to the axis and W _t is that on the target. For the first time, simple analytical approximations are derived for C _c/r, C _s/r, f/r, and NI, where C _c is the chromatic-aberration coefficient, C _s 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 . 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 , the lens changing from an accelerating to a decelerating one. (iii) If , then C _s/r – ^1/4, C _c/r – ^1/6, f/r– ^1/3, and NI – ^–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.