  We investigate electrode geometries required to produce periodic
2-dimensional ion-trap arrays with the ions placed between two planes of
electrodes. We present a generalization of previous methods for traps
containing a single electrode plane to this new geometry, and show that for a
given ion-electrode distance and applied voltages, the inter-ion distance can
be reduced by a factor of up to 3 relative to single-plane traps. This
represents an increase by a factor of 9 in the trap density and a factor of 27
in the exchange coupling between the oscillatory motion of neighboring ions.
The resulting traps are also considerably deeper for bi-layer structures than
for single-plane traps. These results could offer a useful path towards
2-dimensional ion arrays for quantum simulation. We also discuss issues with
the fabrication of such traps.
