  This work reports on the first-time study of the temperature-dependent
behavior of the Lorenz number of bio-supported average 3.2 nm-thin Ir film down
to 10 K. Due to the strong imperfection-electron scattering, a very large
residual resistivity is observed for the film that dominates the overall
electron transport. The Debye temperature (221 K)of the film is found much
smaller than that of bulk (308 K). This phonon softening strongly confirms the
extensive surface and grain boundary electron scatterings. More than one order
of magnitude reduction is observed for the thermal conductivity of the film. We
find the Wiedemann-Franz Law still applies to our film even at low
temperatures. The overall Lorenz number and that of imperfection structure are
close to the Sommerfeld value and shows little temperature dependence. This is
contrast to other studied low dimensional metallic structures that have a much
larger Lorenz number. Electron tunneling and hopping in the biomaterial
substrate are speculated responsible for the observed Lorenz number.
