  The High Luminosity LHC (HL-LHC) upgrade requires the planned Inner Tracker
(ITk) of the ATLAS detector to tolerate extremely high radiation doses.
Specifically, the innermost parts of the pixel system will have to withstand
radiation fluences above $1\times10^{16}$ $n_{eq}cm^{-2}$. Novel 3D silicon
pixel sensors offer a superior radiation tolerance compared to conventional
planar pixel sensors, and are thus excellent candidates for the innermost parts
of the ITk. This paper presents studies of 3D pixel sensors with pixel size $50
\times 50$ $\mu m^2$ mounted on the RD53A prototype readout chip. Following a
description of the design and fabrication steps, Test Beam results are
presented for unirradiated as well as heavily irradiated sensors. For particles
passing at perpendicular incidence, it is shown that average efficiencies above
96% are reached for sensors exposed to fluences of $1\times10^{16}$
$n_{eq}cm^{-2}$ when biased to 80 $V$.
