A new approach to increase the downsize scalability of perpendicular STT-MRAM is presented. It consists in significantly increasing the thickness of the storage layer in out-of-plane magnetized tunnel junctions (pMTJ) as compared to conventional pMTJ in order to induce a perpendicular shape anisotropy (PSA) in this layer. This PSA is obtained by depositing a thick ferromagnetic (FM) layer on top of an MgO/FeCoB based magnetic tunnel junction (MTJ) so that the thickness of the storage layer becomes of the order or larger than the diameter of the MTJ pillar. In contrast to conventional spin transfer torque magnetic random access memory (STT-MRAM) wherein the demagnetizing energy opposes the interfacial perpendicular magnetic anisotropy (iPMA), in these novel memory cells, both PSA and iPMA contributions favor out-of-plane orientation of the storage layer magnetization. Using thicker storage layers in these PSA-STT-MRAM has several advantages. Thanks to the PSA, very high and easily tunable thermal stability factors can be achieved, even down to sub-10 nm diameters. Moreover, low damping material can be used for the thick FM material thus leading to a reduction of the write current. The paper describes this new PSA-STT-MRAM concept, practical realization of such memory arrays, magnetic characterization demonstrating thermal stability factor above 200 for MTJs as small as 8nm in diameter and possibility to maintain thermal stability factor above 60 down to 4nm diameter.