Flicker (1/f) noise: Equilibrium temperature and resistance fluctuations

We have measured the 1/f voltage noise in continuous metal films. At room temperature, samples of pure metals and bismuth (with a carrier density smaller by 10⁵) of similar volume had comparable noise. The power spectrum S_V(f) was proportional to V̅ ²/Ωf^γ, where V̅ is the mean voltage across the sample, Ω is the sample volume, and 1.0≲γ≲1.4. S_V(f)/V̅ ² was reduced as the temperature was lowered. Manganin, with a temperature coefficient of resistance (β) close to zero, had no discernible noise. These results suggest that the noise arises from equilibrium temperature fluctuations modulating the resistance to give S_V(f)∝V̅ ²β²k_BT²/C_V, where C_V is the total heat capacity of the sample. The noise was spatially correlated over a length λ(f)≈(D/f)^1/2, where D is the thermal diffusivity, implying that the fluctuations obey a diffusion equation. The usual theoretical treatment of spatially uncorrelated temperature fluctuations gives a spectrum that flattens at low frequencies in contradiction to the observed spectrum. However, the empirical inclusion of an explicit 1/f region and appropriate normalization lead to S_V(f)/V̅ ²∝β²k_BT²/C_V[3+2ln(l/w)]f, where l is the length and w is the width of the film, in excellent agreement with the measured noise. If the fluctuations are assumed to be spatially correlated, the diffusion equation can yield an extended 1/f region in the power spectrum. We show that the temperature response of a sample to δ- and step-function power inputs has the same shape as the autocorrelation function for uncorrelated and correlated temperature fluctuations, respectively. The spectrum obtained from the cosine transform of the measured step-function response is in excellent agreement with the measured 1/f voltage noise spectrum. Spatially correlated equilibrium temperature fluctuations are not the dominant source of 1/f noise in semiconductors and discontinuous metal films. However, the agreement between the low-frequency spectrum of fluctuations in the mean-square Johnson-noise voltage and the resistance fluctuation spectrum measured in the presence of a current demonstrates that in these systems the 1/f noise is also due to equilibrium resistance fluctuations.