A computationally efficient model to quantify the microdefect distributions in Czochralski grown silicon crystals is proposed and numerically solved. All microdefects are approximated as spherical clusters. The novelty of the proposed model centers on a simplified treatment of the population of the clusters at any location; the average radius of the clusters in the population is approximated by the square root of the average of the squared radii of all clusters. The formation of the clusters is described by the classical nucleation theory. The growth of the clusters at any location is quantified by an auxiliary variable proportional to the total surface area of the clusters present at the location. A comparison between the predictions of the novel model with both a traditional model treating the size distribution of the clusters in the actual cluster population and the experimental observations validate the novel model. (c) 2005 The Electrochemical Society.