This first article in a series on simulation of growth of thin films by the ALD (=atomic layer deposition) technique deals with the theoretical background for growth and preparation of amorphous films. The growth dynamics of amorphous thin films have been simulated on the basis of growth on randomly positioned hemisphere-shaped seed objects. The objects were positioned in the simulation space according to rules which intend to create entirely random or guided random patterns. The simulations are able to reproduce the non-linear growth in the initial stages of ALD growth according to type-2 substrate-inhibited growth, and provide a mechanism for this based on purely geometrical concepts; also a self-driving mechanism toward flat surfaces is demonstrated. An initial stage of roughening of the films occurs before smoothening takes over. (c) 2006 Elsevier B.V. All rights reserved.