Statistical properties and scaling of 1/f noise in disordered nicr thin-film resistors

Abstract

This work investigates the statistical properties and scaling behaviour of 1/f noise in resistive elements based on disordered nickel–chromium films. Thin Ni₈₀Cr₂₀ layers with thicknesses of 20, 40 and 80 nanometres were sputtered onto oxidized silicon substrates, patterned into micron-scale devices, and structurally characterized by atomic force microscopy and transmission electron microscopy. Low-frequency voltage noise was measured in a closed-cycle cryostat between 90 and 300 kelvin under strictly ohmic bias conditions, and converted into resistance noise spectra and time-domain fluctuation series for statistical analysis. All devices exhibit near-ideal 1/f noise, with spectral exponents between about 0.9 and 1.1 over roughly two decades in frequency. The normalized noise level at 1 hertz decreases strongly with thickness, from approximately 3.2 × 10⁻¹⁰ hertz⁻¹ for 20 nanometres to 0.7 × 10⁻¹⁰ hertz⁻¹ for 80 nanometres, while cooling modestly increases the noise and slightly steepens the spectra. Normalized resistance fluctuations are nearly Gaussian for thicker films and higher temperatures, but develop heavier tails in thinner films at low temperature, consistent with a reduced effective number of active fluctuators. Rescaling the spectra by a characteristic amplitude and correlation time produces an approximate collapse onto a common curve, indicating a nearly universal scaling function within the studied NiCr films rather than a strictly material-independent universality. Estimates of the Hooge parameter place the NiCr resistors in the low-noise range typical for precision thin-film technologies. These results show that 1/f noise in disordered nickel–chromium resistors is governed by a robust ensemble of relaxation processes whose collective behaviour is largely independent of microscopic details within this material class, providing guidance for designing low-noise resistive elements and for testing models of noise in disordered conductors.