Single crystal silicon thin films have been grown on Si(100) substrates using pulsed supersonic jets of a disilane (Si2H6)-hydrogen mixture. Digital epitaxy has been achieved at substrate temperatures of 400-500 degrees C, with a growth rate of 0.1 Angstrom/pulse at T-s=450 degrees C. Sticking coefficients of up to 0.3 are observed implying an order of magnitude increase over conventional gas source molecular beam epitaxy. A fundamental model, based on an approach proposed in the literature, has been developed to explain experimental results. Incorporating cyclic adsorption and regeneration steps, the resulting growth rate expression is fit to data to extract rate constants. An activation energy of 2.22 eV is obtained for the kinetic rate constant for hydrogen desorption, the limiting step in low temperature growth. A Monte Carlo approach has been used for the first time to study the atomic scale roughness variations in supersonic jet growth. Simulation studies show that the high energy jets only affect short-range diffusion, whereas long-range diffusion, responsible for improving surface roughness, is still thermally driven. A true atomic layer epitaxy (growth process, independent of substrate temperature), is predicted for incident jet energy exceeding the hydrogen desorption activation energy.