Anomalous variation of resistance in bismuth thin films and the effect of substrate temperature

Bismuth thin films of thickness 720 Å have been vacuum deposited at various substrate temperatures on glass substrates and their resistances are recorded as a function of temperature after annealing the films at 200°C. The resistance (R) versus temperature (t) curves show anomalous behaviour, in that the resistance first decreases as the temperature increases and then increases as the temperature increases, thus showing a minimum in resistance, R_min at a temperature t_min. The position of R_min (i.e. t_min) and the magnitude of R_min vary with substrate temperature. However, no such anomalous behaviour is observed for the film deposited at room temperature and its resistance monotonically decreases with increase in temperature. These observations have been explained by considering that the bismuth films behave as narrow band gap semiconductors because of the quantum size effect and by the facts that in polycrystalline films the electronic mean free path will be limited by the grain size and also that the average grain size of the film increases as the substrate temperature during deposition increases.