Electrical resistivity of vacuum-deposited and vacuum-annealed β-${\mathrm{Ag}}_2$Se thin films of thicknesses between 600 and 2000 Å has been measured in vacuum. It is found that all the films exhibit semiconducting behavior and the energy band gap is a function of thickness increasing linearly with it. It is also found that the film resistivity and temperature coefficient of resistivity (TCR) are both functions of inverse thickness as expected from the thin-film size-effect theories. The linear dependence of the band gap on thickness is thought to be due to the large density of dislocations in thin films and its variation with thickness and the changing stoichiometry of the films. The reciprocal thickness dependence of resistivity and TCR is explained by the effective mean-free-path models. The mean free path $l_g$ estimated from this model turns out to be about 1300 Å and the value estimated from the ρ plot agrees well with that estimated from the β plot. Also, carrier concentration in the films is estimated to be about 6×${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$.

• Received 16 June 1988

DOI:https://doi.org/10.1103/PhysRevB.39.10872