A new theory of chemical vapor deposition (CVD) with variable diffusion coefficient describes the time evolution of the free surface of a film to closure on trench walls. The diffusion coefficient decreases with the distance from the mouth and with time as the trench is closed by film formation, and it reduces to the conventional continuum value at high pressure. However, we predict higher rates of transport than by Knudsen diffusion at low pressure in small features as do ballistic transport calculations. The shape of the film and its uniformity depend on the Damkohler number (Da), the aspect ratio (A), and the Knudsen number (lambda(1)) for a first order surface reaction. Free boundary solutions were obtained to closure for various values of these parameters, and the step coverage at closure is correlated well by two dimensionless numbers, DaA(2) and lambda(1), over a wide range of reactor pressures (10(-2)-760 Torr). The generalized correlation of the figure of merit for step coverage in the tetraethyl orthosilicate-ozone agrees well with the experimental results. Our feature scale model, coupled with commercial reactor models through the diffusive flux of reactant at the wafer surface, enables gap filling/step coverage to be determined as a function of process conditions.