A theoretical model is presented to describe the effect of ion beam bombardment rate on the formation of tetrahedral amorphous carbon (ta-C) films. The critical ion energy, E(c), corresponding to a 50% sp(3) content in the films, is found to be dependent on both the effective thermal resistance and the ion beam bombardment rate. In the model, the ’window’ width in the ion energy scale for the formation of ta-C material increases with decreasing deposition rate and with a reduction in the effective thermal resistance, until limited by lower and upper boundary thresholds. Experimental data are reproduced by the model. The plasmon energy, which correlates with sp(3) fraction, is found experimentally to be higher for lower deposition rate and smaller effective thermal resistance. Data points for high sp(3) content ta-C films deposited on silicon substrates at room temperature occupy a region in the ion energy-deposition rate (E-r) diagram similar to that predicated from the theory.