Using a Monte Carlo simulation, the growth and roughness characteristics of
polymer surfaces are studied in 2+1 dimensions. Kink-jump and reptation dy
namics are used to move polymer chains under a driving field where they dep
osit onto an impenetrable attractive wall. Effects of field (E), chain leng
th (L-c), and the substrate size (L) on the growing surfaces are studied. I
n low field, the interface width (W) shows a crossover from one power-law g
rowth in time (W similar to t(beta 1)) to another (W similar to t(beta 2)),
before reaching its asymptotic value (W-s), with beta(1)(similar to 0.5+/-
0.1)< beta(2)(similar to 0.6-1.0). For short chain lengths (L-c=4), the sat
urated width (W-s) is independent of the substrate length (L), while for lo
ng chain lengths, W-s, decays with L, before becoming independent at large
L. W-s depends strongly on the magnitude of the field: for short chains, W(
s)similar to E-delta with delta similar or equal to 0.4, while for long cha
ins, it varies nonmonotonically with E.