This is the first article of a series concerning the theoretical description of the current-potential and current-time profiles verified during electrochemical deposition of metals on n-silicon. Our goal is to derive an analytical expression that relates the deposition current to temperature, potential, concentration and potential scan rate - the macroscopic parameters, commonly used to control deposition experiments. In this paper we introduce a model that assumes the existence of two mechanisms to describe the nucleation and growth of the material deposited: the diffusion of ions and the catalytic reaction on the electrode. Analyzing the diffusion of ions into a finite electrochemical system and introducing the reaction kinetics through a time-dependent boundary condition, the model avoids the need for the depletion zone concept. A theoretical expression for current transients under diffusion-con trolled growth, I(c,k,t), is obtained as a function of the ion concentration c, the parameter that regulates the surface activity and the time t. An analytical expression for the current is particularly convenient to investigate the connection between k, the theoretical parameter that regulates the reaction kinetics, and the potential, which plays the same role in real experiments. This relationship is obtained through a comparison between theoretical and experimental results. (C) 2004 Elsevier B.V. All rights reserved.