We investigate the addition spectra of arrays of quantum dots (QDs) under different geometrical distributions. We use a Hubbard Hamiltonian where we include intra- and inter-dot interactions. These parameters, which determine the correlation between the electrons, are varied on different QD array spatial distributions and the effects on the Coulomb staircase and conductance of the system are analysed. Exact diagonalization is used to calculate the eigenstates of arrays containing several QDs and the conductance addition spectrum is calculated using the Beenakker approach for a single dot generalized to an array of QDs. The charging/discharging process of the QDs is theoretically studied when a bias is applied to a metallic gate on top of the structure. The occupancy and conductance as functions of the gate bias are obtained, a crucial feature to the understanding of the memory charging process for non-volatile memories that are based on MOS devices with embedded semiconductor nanocrystals. A memory-device proposal application is given, where the storage of information is based on the charge present on the QDs, readable by means of the threshold voltage necessary to observe a current flowing in a narrow channel underneath the QD array structure.