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

Abstract

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 10') of similar volume had comparable noise. The power spectrum Sv(f) was proportional to V'/0 f~, where V is the mean voltage across the sample, 0 is the sample volume, and 1.0 & y & 1.4. SI,(f)/ V' was reduced as the temperature was lowered. Manganin, with a temperature coefficient of resistance (P) close to zero, had no discernible noise. These results suggest that the noise arises from equilibrium temperature fluctuations modulating the resistance to give Sv(f)~V 'p'k~T'/CI" where CV is the total heat capacity of the sample. The noise was spatially correlated over a length X(f) -(D/f)'", 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 obser red spectrum. However, the empirical inclusion of an explicit 1/f region and appropriate normalization lead to Sv(f)/ V'~P k~T '/ C&[3 + 21n(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 5and 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 jf 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.

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