  While diproton decay was first theorized in 1960 and first measured in 2002,
it was first observed only in 2012. The measurement of $^{14}$Be in coincidence
with two neutrons suggests that $^{16}$Be does decay through the simultaneous
emission of two strongly correlated neutrons. In this work, we construct a full
three-body model of $^{16}$Be (as $^{14}$Be + n + n) in order to investigate
its configuration in the continuum and in particular the structure of its
ground state. In order to describe the three-body system, effective n-$^{14}$Be
potentials were constructed, constrained by the experimental information on
$^{15}$Be. The hyperspherical R-matrix method was used to solve the three-body
scattering problem, and the resonance energy of $^{16}$Be was extracted from a
phase shift analysis. In order to reproduce the experimental resonance energy
of $^{16}$Be within this three-body model, a three-body interaction was needed.
For extracting the width of the ground state of $^{16}$Be, we use the full
width at half maximum of the derivative of the three-body phase shifts and the
width of the three-body elastic scattering cross section. Our results confirm a
dineutron structure for $^{16}$Be, dependent on the internal structure of the
subsystem $^{15}$Be.
