Diamond substrates supporting an internal array of conductive graphitic wires inscribed by a femtosecond pulse laser, are useful for the detection of ionising radiation in a range of applications. Various parameters involved in the laser fabrication process were investigated in this paper to understand their impact on the electrical properties of the wires. The study revealed an effect, whereby the wires exhibit insulating behaviour until a barrier potential is overcome. When high enough voltages are applied, the wires display ohmic behaviour. The magnitude of the barrier potential, which in some cases exceeds 300 V, is shown to be strongly dependent on the laser fabrication parameters. Through process optimisation, the potential barrier may be minimised and effectively removed, coinciding with reduced values of the wire resistance.