Frequency-dependent interface capacitance of Al-Al₂O₃-Al tunnel junctions

Four-terminal ac impedance measurements have been used to characterize Al-Al₂O₃-Al tunnel-junction capacitors over the frequency range of 10 Hz-100 kHz. The insulating barriers are thin enough to assure that the response can be modeled by a frequency-dependent interface capacitance in parallel with a frequency-independent tunnel junction resistor R₀. The data reveal no sign of loss peaks down to 10 Hz and the impedance curves for a single junction, annealed to give different tunnel-junction resistance, collapse onto a single curve when R₀ is used as a scaling parameter. The loss mechanism is ascribed to interface traps and is found to give an unusual asymptotic phase angle response when the real and imaginary parts of the complex capacitance are plotted against each other.