Using a Monte Carlo simulation, the growth and roughness characteristics of polymer surfaces are studied in 2 + 1 dimensions. Kink-jump and reptation dynamics are used to move polymer chains under a driving field where they deposit onto an impenetrable attractive wall. Effects of field (E) chain length (Lc) and the substrate size (L) on the growing surfaces are studied. In low field, the interface width (W) shows a crossover from one power-law growth in time (W∼tβ1) to another (W∼tβ2 before reaching its asymptotic value (Ws), with β1(∼0.5±0.1)\u3cβ2(∼0.6-1.0). For short chain lengths (Lc=4), the saturated width (Ws) is independent of the substrate length (L), while for long chain lengths, Ws decays with L before becoming independent at large L. Ws depends strongly on the magnitude of the field: for short chains, Ws∼E-δ with δ≃0.4, while for long chains, it varies nonmonotonically with E
