  We numerically investigate a hybrid trapping architecture for 2D ion crystals
using static electrode voltages and optical cavity fields for in-plane and
out-of-plane confinements, respectively. By studying the stability of 2D
crystals against 2D-3D structural phase transitions, we identify the necessary
trapping parameters for ytterbium ions. Multiple equilibrium configurations for
2D crystals are possible, and we analyze their stability by estimating
potential barriers between them. We find that scattering to anti-trapping
states limits the trapping lifetime, which is consistent with recent
experiments employing other optical trapping architectures. These 2D ion
crystals offer an excellent platform for quantum simulation of frustrated spin
systems, benefiting from their 2D triangular lattice structure and
phonon-mediated spin-spin interactions. Quantum information processing with
tens of ions is feasible in this scheme with current technologies.
