Feedback controlled electromigration for the fabrication of point contacts and noise measurement applications
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Lithographically fabricated point contacts serve as important examples of mesoscopic conductors, as electrodes for molecular electronics, and as ultra-sensitive transducers for mechanical motion. We have developed a reproducible technique for fabricating metallic point contacts through electromigration. We employ fast analog feedback in a four-wire configuration in combination with slower computer controlled feedback to avoid catastrophic instability even when there is significant series resistance. This hybrid system allows electromigration to proceed while dissipating approximately constant power in the wire. We are able to control the final resistance of the point contact precisely below 5 kOhm and to within a factor of three when the target resistance approaches 12 kOhm where only a single conducting channel remains. This system makes it possible to efficiently create point contacts through electromigration for fundamental studies of atomic-size conductors or applications such as displacement transducers. As an application of the hybrid feedback system for forming point contacts, we have developed a low-temperature, high-frequency noise measurement system. The system, which operates from 0.8 to 1.5 GHz at temperatures as low as 320 mK, takes advantage of impedance matching techniques to improve power transfer by up to 65%. This is accomplished by combining an inductor with unavoidable stray capacitance to form a resonant LC circuit. Noise measurement tests with a photodiode-LED pair at room temperature demonstrated the ability to resolve shot noise down to 5e-26 A^2/Hz. This corresponds to the shot noise of 155 nA through a single channel point contact. We designed and fabricated an aluminum superconducting planar inductor coupled to a gold point contact wire to test the noise measurement system at ultra-low temperatures. Finite element simulations suggested that the inductor may not be superconducting at the onset of electromigration but the study was not conclusive. Tests at 320 mK revealed that the inductor was not superconducting at the currents required for electromigration, preventing controlled electromigration and noise measurements. Future work should explore alternative inductor designs to allow for noise measurements in the 0.8-1.5 GHz range.