  We present a detailed analysis of two chip-based superconducting trap
architectures capable of levitating micrometer-sized superconducting particles
in the Meissner state. These architectures are suitable for performing novel
quantum experiments with more massive particles or for force and acceleration
sensors of unprecedented sensitivity. We focus in our work on a chip-based
anti-Helmholtz coil-type trap (AHC) and a planar double-loop (DLP) trap. We
demonstrate their fabrication from superconducting Nb films and the fabrication
of superconducting particles from Nb or Pb. We apply finite element modeling
(FEM) to analyze these two trap architectures in detail with respect to trap
stability and frequency. Crucially, in FEM we account for the complete
three-dimensional geometry of the traps, finite magnetic field penetration into
the levitated superconducting particle, demagnetizing effects, and flux
quantization. We can, thus, analyze trap properties beyond assumptions made in
analytical models. We find that realistic AHC traps yield trap frequencies well
above 10kHz for levitation of micrometer-sized particles and can be fabricated
with a three-layer process, while DL traps enable trap frequencies below 1kHz
and are simpler to fabricate in a single-layer process. Our numerical results
guide future experiments aiming at levitating micrometer-sized particles in the
Meissner state with chip-based superconducting traps. The modeling we use is
also applicable in other scenarios using superconductors in the Meissner state,
such as for designing superconducting magnetic shields or for calculating
filling factors in superconducting resonators.
