Excitations of MHz acoustic modes are studied numerically in 10-µm-thick silicon disk membranes with a radius of 100 and 500 µm actuated by an attached 1-µm-thick (AlSc)N thin-film transducer. It is shown how higher-harmonic membrane modes can be excited selectively and efficiently by appropriate patterning of the transducer electrodes. When filling the half-space above the membrane with a liquid, the higher-harmonic modes induce acoustic pressure fields in the liquid with interference patterns that result in the formation of a single, strong trapping region located 50 -100 µm above the membrane, where a single suspended cell can be trapped in all three spatial directions. The trapping strength depends on the acoustic contrast between the cell and the liquid, and as a specific example it is shown by numerical simulation that by using a 60% iodixanol solution, a cancer cell can be held in the trap.