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Current-voltage characteristic during EM for a wire with resistance . The voltage V is increased until the wire reaches a critical temperature . If the lead resistance , the IV relation is double-valued and the process is unstable. The instability is removed if . The inset shows power dissipated in the wire during the process. As V is initially increased, the power increases until a critical power is attained. When EM is controlled, is constant (red dashed line). If EM is not controlled and the applied voltage is held constant, the power dissipated in the wire exceeds the critical power (black dotted line). (Parts of figure adapted from Ref. 15 .)
Schematic of the hybrid feedback system in a four-wire configuration. The PID controller (SRS-SIM960) monitors the voltage across the point contact junction as measured with a differential amplifier (Signal Recovery 5113 pre-amp) and adjusts its output to keep this voltage at a given setpoint. The voltage across the junction as well as the current through it are monitored (Agilent 34970, HP 34401) by a computer, which then controls the PID setpoint according to the feedback algorithm. The scale bar is 500 nm.
EM results for (a)–(c) a 108 nm wide wire in ambient conditions and (d)–(f) a 77 nm wide wire at 77 K. (a), (d) IV characteristic during EM. The solid and dashed curves show constant power dissipated in the wire. (b), (e) The average wire temperature T calculated from the temperature coefficient of resistance and the average temperature and maximum temperature of the wire determined from the temperature–resistance relationship of a finite element simulation. (c), (f) Wire conductance at the end of the EM process.
Temperature contours for a finite element model of (a) a 100 nm wide wire and (b) a 2 nm notch in the wire. Half of the model is shown as the forward facing plane is a symmetry plane. (c) IV characteristics for a finite element simulation of a 30 × 100 × 200 nm (t × w × l) Au wire in Coventor. 21 The cross section of the center of the Au wire was decreased from 100 × 30 nm to 2 × 2 nm over a 10 nm length. Curves of constant power in the Au wire, maximum temperature T, and maximum current density j were calculated beginning where . The inset shows the temperature and current density along the curve of constant dissipated power.
(a) Final device resistance for various target resistances for EM in ambient conditions as well as at 77 K. The sourced voltage began at 50 mV and the feedback condition was . (b)–(c) Evolution of wire resistance after completion of the EM process for devices at room temperature.
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