Figure 1

(Color online) SEM images of (a) an EM junction and (b) a suspended bridge device used in the MCBJ setup. Panel (c) shows a characteristic EM induced evolution of the junction resistance $R_J$ as a function of applied junction voltage $U_J$. Electromigration narrows the junction cross section in regime II (Ref. 52). Panel (d) shows schematics of the electric circuit used to measure the noise. $R_L$ denotes the resistance of each lead in the four-terminal setup and $C$ summarizes the total capacitance of the preamplifier and the connecting cables. The inductor $L_S$ is used to separate the ac-noise measurement on the right from the dc biasing on the left.Reuse & Permissions

Figure 2

(Color online) (a) Calibration of the setup by measuring the thermal noise of eight standard metal-film resistors with values $R$ ranging from $10\Omega$ to $10\text{k}\Omega$. The dashed curves are calculated, taking the frequency dependence of the circuit and gain of the amplifiers into account. In (b) the measured thermal noise is corrected for the known frequency dependence of the circuit and amplifier gains. The horizontal lines mark the theoretical thermal noise of $4kTR$. In the shaded region the corrected noise is frequency independent and coincide with the expected thermal noise values. This frequency interval is used to measure the $1/f$ noise in nanojunctions.Reuse & Permissions

Figure 3

(Color online) Noise spectra of a single EM junction, measured at $U_J=50\text{mV}$ and for relatively low junction resistances $R_J$ ranging from 10 to $65\Omega$ (from bottom to top). For comparison we also show $S_V\left(f\right)$ for $R_J=1\text{k}\Omega$. Inset (a): the exponent $\nu$ of the frequency dependence deduced from the noise spectrum of many junctions with a large range of junction resistances $R_J$ and bias voltages $U_J$. The open symbols correspond to devices with small $R_J$ and measurements at small bias voltage $U_J$, displaying only white noise originating from the lead resistances. The average value of $\nu$ for the filled symbols is equal to 1.1 and therefore close to the expected value for $1/f$ noise. The inset (b) shows the bias voltage dependence of $S_V$ at a frequency $f$ of $f_0=100\text{kHz}$ and for three different $R_J$ values.Reuse & Permissions

Figure 4

(Color online) Magnitude of the $1/f$ noise, shown as a log-log scatter plot of $S_V\left(f_0\right)/V^2$ with $f_0=100\text{kHz}$ of four MCBJ samples and one EM sample (open squares) as a function of junction resistance $R_J$. The inset (a) shows the data from two MCBJs separately where the upper set is vertically shifted by 2 orders of magnitude for clarity. Dashed lines are guides for the eyes for the expected power-law dependencies $S_V\left(f_0\right)/V^2\propto R_J^p$ in the diffusive $\left(p=3\right)$ and ballistic $\left(p=1.5\right)$ regimes. The dashed-dotted line has a slope of $p=0.5$ (see text). The inset (b) shows a histogram of $\alpha$ values deduced from $S_V$ for the single-atom contact when $R_J=h/2e^2$.Reuse & Permissions