  In this communication we report studies of d.c current-voltage (I-V)
characteristics of ultra thin films of Bi, quench condensed on single crystal
sapphire substrates at T = 15K. The hysteretic I-V characteristics are
explained using a resistively and capacitively shunted junction (RCSJ) model of
Josephson junction arrays. The Josephson coupling energy($E_J$) and the
charging energy($E_c$) are calculated for different thickness($d$) values. A
low resistance state is found in the low current regime below the critical
current, $I_c$. This resistance $R_0$ is found to have a minimum at a
particular thickness ($d_c$) value. Reflection High Energy Electron Diffraction
(RHEED) studies are done on these films. A distinct appearance of a diffuse
ring near $d_c$ is observed in the diffraction images, consistent with the
recent STM studies(Ekinci and Valles, PRL {\bf 82}(1999) 1518). These films
show an irreversible annealing when temperature is increased. The annealing
temperature ($T_a$) also has a maximum at the same thickness. Althoguh the
R$_s$ vs T of quench condensed Bi films suggest that the films are uniform, our
results indicate that even in thick films, the order parameter is not fully
developed over the complete area of the film. These results are discussed
qualitatively.
