Amorphous versus crystalline GeTe films. III. Electrical properties and band structure

Various transport studies have been carried out on amorphous and crystalline GeTe films of 80 Å to 10 μ thickness. Crystalline GeTe has a low resistivity (∼10-4 Ω-cm at 300°K) which increases with temperature slowly and nearly linearly at low temperatures (below ∼300°K) and rapidly at higher temperatures. The hole concentration (N∼1010-1021 cm-3) increases only slightly with temperature. Mobility varies as N-4/3. These results in conjunction with the tunnel-spectroscopy and optical data show that crystalline GeTe is a degenerate (and thus metallic conduction), ρ-type narrow band gap (∼0.1-0.2 eV) semiconductor with Fermi level ∼0.3-0.5 eV inside the valence band. The linear increase of the susceptibility mass with hole concentration, the constancy of the Hall coefficient up to ωLT=0.35 (ωL=Larmor frequency, T=collision relaxation time), and the monotonic increase of thermopower with temperature indicate that conduction takes place only in a single valence band. Amorphous GeTe films exhibit activated conduction. The dc resistivity varies from 410° to 77°K as ρ0 exp (Eg/2kT), where Eg is about 0.8 eV and ρ0 is the resistivity of crystalline GeTe films. Ac resistivity decreases with frequency (ω) as ω-n, where n lies between 0.5 and 1.0, depending on the temperature. The activation energy for ac conduction decreases rapidly from the dc value to zero with decreasing temperature as well as increasing frequency. The capacitance of amorphous GeTe at 77°K varies as ω-0.2 while the loss factor is independent of the frequency. With increasing dc field, the linear dependence of current on voltage changes to a power relation Vn, where n varies rapidly from ∼3 to 6 or more in a small range of the applied field. At very high fields, I ∞expβF1/2 (β=constant) is observed. These results, together with the tunnel-spectroscopy, and optical data suggest that amorphous GeTe may be represented as a ρ-type semiconductor with band gap ∼0.8 eV with exponential tailing of the bands and a continum of localized states in the vicinity (both sides) of the band edges. Conduction takes place by two parallel processes of intrinsic excitation across the band gap, and thermally and/or field-assisted hopping from one localized (trapping) state to another. Dc conduction by hopping at low fields is negligible. At higher fields, trap modified space-charge-limited current flow and Poole-Frenkel effect determine the nonlinear field dependence of current