  Depleted Monolithic Active Pixel Sensor (DMAPS) prototypes developed in the
TowerJazz 180 nm CMOS imaging process have been designed in the context of the
ATLAS upgrade Phase-II at the HL-LHC. The pixel sensors are characterized by a
small collection electrode (3 $\mu$m) to minimize capacitance, a small pixel
size ($36.4\times 36.4$ $\mu$m), and are produced on high resistivity epitaxial
p-type silicon. The design targets a radiation hardness of $1\times10^{15}$ 1
MeV n$_{eq}$/cm$^{2}$, compatible with the outermost layer of the ATLAS ITK
Pixel detector. This paper presents the results from characterization in
particle beam tests of the Mini-MALTA prototype that implements a mask change
or an additional implant to address the inefficiencies on the pixel edges.
Results show full efficiency after a dose of $1\times10^{15}$ 1 MeV
n$_{eq}$/cm$^{2}$.
