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Multi-linear silicon drift detectors (MLSDD) are silicon detectors in which signal electrons are confined within parallel drifting columns at few micrometers from the anodes' surface and transported towards point-like anodes by an electrostatic field. During the initial motion across the thickness the signal electrons spread in all directions to a given width - we call this phenomenon pre-diffusion - until the signal electrons are focused in the drift channels which suppress any further spread into adjacent channels. This work is devoted to the study of the initial motion of the electron cloud when the electrons are being focused toward the minimum of the potential energy. We developed an analytical model to predict the initial charge spread and carried out a detailed measurement campaign to evaluate the impact of the detector operating conditions and of the charge injection level on the initial charge spread. The design of the electron spread during pre-diffusion allows optimization of MLSDD for different applications.