Electrical resistivity of thin bismuth films

The thickness dependence of electrical resistivity of thin bismuth films deposited on to glass substrates has been studied in the temperature range 77 to 350 K. The structural studies show that films are polycrystalline with grain size increasing with thickness. The electrical resistivity decreases with increasing temperature. This type of temperature dependence of electrical resistivity arises due to the competition between the temperature dependences of carrier density and carrier mobility, the temperature coefficients of which are opposite in sign. The electrical properties of bismuth films are greatly affected by the presence of surface states. The size effect theory of Pichard and colleagues (PTT) has been modified to investigate the variation of charge carrier concentration with thickness. The experimental results on electrical resistivity are found to be consistent with the predictions of this modified three-dimensional model (PTT). The value of specularity parameter,p, is about 0.43 and it exhibits no temperature dependence. The experimental results on grain-boundary resistivity agree fairly well with the theoretical variations. The values of transmission coefficient,t, are determined from the experimental data.