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

Quantum-size effects in n-type bismuth thin films

Abstract: Oscillatory thickness dependences of the electrical conductivity, Hall coefficient, charge carrier mobility, and Seebeck coefficient were obtained at room temperature for n-type thin Bi films (d=3–300 nm) fabricated by the thermal evaporation of a bismuth crystal in a vacuum and deposition on mica substrates at 380 K. We attribute this oscillatory behavior to quantum-size effects, which are observable when the electron mean-free path and Fermi wave length exceed the film thickness d.

Semiconducting behavior of Ag2Te thin films and the dependence of band gap on thickness

Abstract: Thin films of Ag2Te of various thicknesses in the range 500–1500 A have been prepared by thermal evaporation of the compound under vacuum on clean glass substrates held at room temperature. The electrical resistance of the films has been measured as a function of temperature during heating, which was carried out immediately after the film formation. The observed exponential decrease of resistance with temperature up to the transition point points to the semiconducting nature of the low temperature polymorph of Ag2Te. The band gap of the low temperature phase is calculated for various thicknesses of the films and it is found that the band gap is a function of film thickness, increasing with decreasing thickness. The increase in the band gap, which was found to be inversely proportional to the square of the film thickness, is attributed to quantization of electron momentum component normal to film plane.

Band gap and intergrain barrier activation energies in Bi90Sb10 thin films

Abstract: The electrical resistivity and Hall effect measurements have been made on vacuum evaporated Bi 90 Sb 10 alloy films of various thickness (350 A to 4500 A), in the temperature range of 77 to 510 K. As observed earlier, the alloy system behaves like a semiconductor, but with a band gap quite higher than previously reported for bulk single crystals. Also a kind of intergrain barrier is found in these films. The activation energy of these barriers is found to decrease with increasing film thickness and substrate temperature. This trend agrees with the earlier observations in other materials and also in the same alloy system. The higher band gaps in these films are attributed to quantum size effect and high dislocation density in these films. The decrease in the inter-grain barrier activation energy with increasing thickness and substrate temperature has been attributed to increased grain size of the films.

Lattice distortion energy spectra of as-grown bismuth thin films and their thickness dependence

Abstract: Bismuth thin films of various thicknesses between 15 nm and 350 nm were vacuum deposited at room temperature on to glass substrates, immediately after which they were twice heat treated at a uniform rate. During the heat treatment, the resistance changes were monitored and, using these data, the initial lattice distortion energy spectra of as-grown bismuth thin films have been evaluated. It is found that the defects have preferential activation energy values around 1.06 eV, 1.14 eV and 1.32 ev. It is also found that ∫F0 (E) dE oscillates with thickness, which is attributed to the quantum size effect.

Oscillatory behaviour of resistivity with thickness in bismuth thin films

Abstract: Bismuth thin films of various thicknesses in the range 150–3500 A have been vacuum deposited on clean glass substrates held at room temperature. Resistances were measured both before and after heat treatment in situ, which was carried out immediately after film formation. It is found that the resistivity oscillates with thickness both for unannealed and annealed films. The same kind of oscillatory behaviour with thickness is also observed in the case of defect resistivity. It is argued that the above oscillatory behaviour is due to the oscillatory behaviour of mobility with thickness. It has also been pointed out that the mobility due to scattering by point defect clusters also oscillates with thickness, if the range of the scattering potential is taken to be of the order of the linear dimensions of the clusters.

Temperature Dependence of the Electrical Properties of Bismuth-Antimony Alloys

Abstract: The electrical resistivity $\ensuremath{\rho}$ and Hall effect $R$ of zone-levelled single crystals of Bi-Sb alloys have been measured in the temperature range from 4.2\ifmmode^\circ\else\textdegree\fi{}K to 300\ifmmode^\circ\else\textdegree\fi{}K. $\mathrm{Log}(\frac{\ensuremath{\rho}}{{\ensuremath{\rho}}_{300}})$ vs $\frac{1}{T}$ curves suggest thermal activation of carriers in the concentration range from 5% to 40% Sb in the temperature range from 25\ifmmode^\circ\else\textdegree\fi{}K to 100\ifmmode^\circ\else\textdegree\fi{}K; approximate activation energies have been inferred from their slopes. The activation energy appears to have a maximum at a concentration near 12%. Some anomalies have been observed in the behavior of $\ensuremath{\rho}$ and $R$ on both sides of this concentration at low temperatures. Lattice parameters for these alloys have also been measured for the entire range of solid solubility. Both a maximum and minimum in the $c$-axis lattice parameter vs concentration occur near the concentration at which anomalies appear in transport properties. These phenomena are discussed in terms of a simple band model proposed by Blount and Cohen.

Size effect in the electrical properties of thin epitaxial bismuth films

Abstract: The thickness dependence of the electrical properties of thin epitaxial bismuth films (of thickness 02–3 μm) was studied at 42 and 77 K The size effect theory developed by Mayadas and Shatzkes was modified so that it could be applied to a system with two carriers (electrons and holes) The thickness dependence of the carrier densities was also taken into account The specularity parameter P at the surface and the reflection coefficient R at the grain boundaries were determined to be 07 and 02–03 respectively It should be noted that the effect of scattering of the carriers at the grain boundary planes parallel to the electric field could not be neglected

Quantum and classical size effects in the thermoelectric power of thin bismuth films

Abstract: Anomalous behaviour of the thermoelectric power of thin Bi films has been observed and the results are consistent with those anticipated, based on both quantum and classical size effects in scattering. Mayer's theory relating thermoelectric power to film thickness can be applied to the present results provided that the bulk conduction electron mean free path is used for calculations of the thermoelectric power of thick specimens and that the conduction electron de Broglie wavelength is used for thin specimens.

Kinetic properties of electrons in bismuth thin films

Abstract: The resistivity ϱ of bismuth films in the absence of a magnetic field exhibits the following features: it decreases with increasing temperature T ; the temperature dependence of the resistance has a maximum at low temperatures for very thin films and a minimum at higher temperatures for films of larger thickness; below 1000 A the conductivity increases with decreasing film thickness L (anomalous size effect); the classical size effect appears as the film thickness increases. For very thin films the magnetoresistance coefficient (in the region ωτ T : at a certain temperature determined by the film thickness a minimum appears and then an anomalous rise in magnetoresistance. From an analysis of the magnetic field dependence of σ xx and σ yx , calculated from our data on ϱ, Δϱ/ϱ and the Hall e.m.f., and using the formula of the two-band model for strong and weak magnetic fields, we obtained the change in concentration ( n,p ) and mobility (μ, ν) of the charge carriers with varying T and L , and hence we were able to explain the observed features of their kinetic properties. The appearance of anomalies results both from the resonance scattering of carriers under size quantization and from the non-uniformity of the distribution through the film thickness of carriers of different sign due to potential bending near the surface. This leads to a shift in the electron spectrum characteristics with decreasing Bi film thickness.