In this work, the ⁹Be(d,n)¹⁰B reaction has been studied since it presents promising characteristics to be considered for Accelerator-Based Boron Neutron Capture Therapy (AB-BNCT). At low bombarding energies (less than about 1.3 MeV) the ⁹Be(d,n)¹⁰B reaction produces a neutron spectrum which can be moderated in order to obtain a thermal flux at the patient position. Such flux is useful for superficial tumor treatment (e.g. skin melanoma). A computational model of a neutron source has been built by means of interpolating the incomplete data available in the literature. Subsequently, an exhaustive Monte Carlo simulation study (using the code MCNP) was carried out to optimize a set of parameters involved in such a treatment. In the simulated geometry, a head phantom and the treatment room have been included and the constraint of keeping the normal tissue dose below its maximum allowed value of 12.5 Gy-Eq was considered. In order to reach a high Tumor Control Probability (TCP) of 98% in the skin melanoma (loaded with 40 ppm ¹⁰B), the TESQ (Tandem Electrostatic Quadrupole Accelerator) design, based on a deuteron current of 30 mA and 1.0 and 1.1 MeV beam energies were considered. Among the Beam Shaping Assembly (BSA) configurations studied, the one using D₂O as a moderator material showed a good performance. In particular, the best performance among the investigated cases corresponds to the 1.0 MeV deuteron beam on a thick Be target. In this case, a 98% TCP (for 38 Gy-Eq in the tumor position) can be reached in less than 45 minutes with a 25-30 cm thick D₂O moderator.