The concept of $perpendicular\ shape\ anisotropy\ spin-transfer-torque\ magnetic\ random-access\ memory$ (PSA-STT-MRAM) consists of the increase of the storage layer thickness to values comparable to the cell diameter, to induce a perpendicular shape anisotropy in the layer. Making use of that contribution, the downsize scalability of the STT-MRAM can be extended towards sub-10 nm technological nodes, thanks to a reinforcement of the thermal stability factor $\Delta$. Although the larger storage layer thickness improves $\Delta$, it negatively impacts the writing current. Hence, optimization of the cell dimensions (diameter, thickness) is of utmost importance for attaining a sufficiently high $\Delta$ while keeping a moderate writing current. Micromagnetic simulations were thus carried out for different pillar thicknesses, with a square cross-section of fixed size 20 nm. The dependence of the switching time and the reversal behavior was analyzed as a function of the applied voltage. Below a thickness threshold of 50 nm, the magnetization reversal occurs by a collective buckling-like mechanism. Above that threshold, a transverse domain wall is nucleated at the surface near the insulator and propagates along the vertical axis of the pillar. It was further observed that the inverse of the switching time follows a linear relation with the applied bias voltage. This dependency remains linear when considering thermal fluctuations.