  Current-voltage ($I-V$) characteristics and the increase of superconducting
transition temperature $T_c$ as a function of the number of half-unit-cell
layers $n$ are studied on Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta}$ thin films
grown by molecular beam epitaxy. These observations are interpreted in terms of
Kosterlitz-Thouless (KT) transition associated with vortex string threading the
film. Considering the change in the types of the lowest free-energy excitations
as a function of the size of vortex pair, we have formulated KT
renormalization-group (RG) equations. Using experimental data obtained with
Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta}$ thin films, we have solved the RG
equations. It is shown that the KT transition occurs in the vortex-string
region with interstring $\ln r$ interaction only. Our calculation successfully
explains KT scaling in $I-V$ characteristics and the relation between $T_c$ and
$n$. These results indicate that the interlayer interaction plays an important
role in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta}$ thin films.
