  The low-lying structure of $^{13}$Be has remained an enigma for decades.
Despite numerous experimental and theoretical studies, large inconsistencies
remain. Being both unbound, and one neutron away from $^{14}$Be, the heaviest
bound beryllium nucleus, $^{13}$Be is difficult to study through simple
reactions with weak radioactive ion beams or more complex reactions with
stable-ion beams. Here, we present the results of a study using the
$^{12}$Be(d,p)$^{13}$Be reaction in inverse kinematics using a 9.5~MeV per
nucleon $^{12}$Be beam from the ISAC-II facility. The solid deuteron target of
IRIS was used to achieve an increased areal thickness compared to conventional
deuterated polyethylene targets. The Q-value spectrum below -4.4~MeV was
analyzed using a Bayesian method with GEANT4 simulations. A three-point angular
distribution with the same Q-value gate was fit with a mixture of $s$- and
$p$-wave, $s$- and $d$-wave, or pure $p$-wave transfer. The Q-value spectrum
was also compared with GEANT simulations obtained using the energies and widths
of states reported in four previous works. It was found that our results are
incompatible with works that revealed a wide $5/2^+$ resonance but shows better
agreement with ones that reported a narrower width.
