A thin-film inductance using thermal filaments

A particular thin-film structure is analyzed to determine the conditions for thermal filament formation. Assuming that these conditions are satisfied and that the structure is electrically biased so that a thermal filament exists, the current-voltage characteristic and small-signal equivalent circuit for a general conductivity-temperature characteristic in the thin film are determined. It is shown that an abrupt or discontinuous change in conductivity with temperature of the type observed in materials exhibiting semiconductor-metal transitions is not necessary to obtain thermal filaments. It is also shown that if there is no thermal hysteresis in the conductivity -temperature characteristic of the thin film, the filament equivalent circuit for the particular structure analyzed is closely approximated by a resistance in parallel with an inductance. The thin-film prop. erties required for this inductance to be independent of both the ambient temperature and the bias current are defined. If thermal hysteresis exists, the analysis shows that small-signal distortions occur, the inductance will become frequency dependent at low frequencies, and a nonlinear resistance must be added to the equivalent circuit in series with the inductance. Measurements on this structure using VO
2
as the thin-film material are presented and discussed, and are shown to verify the conclusions based on the analysis.