1/fNoise as a Nonequilibrium Temperature Fluctuation

Abstract

1=f resistance noise has long been studied but the details of its generation mechanism are still unknown. Hooge et al. derived the empirical formula from the observed data on resistance fluctuations. Kleinpenning and de Kuijper measured the 1=f fluctuation which persisted to 10 6 Hz. Voss and Clarke observed 1=f resistance fluctuation in a sample at thermal equilibrium and they asserted that the origin of 1=f resistance fluctuation was the current fluctuation caused by the conductance fluctuation. Kogan and Nagaev reported that the origin of 1=f conductance fluctuation is the mobility fluctuation in metals. On the other hand, Vandamme et al. reported that the origin of 1=f conductance fluctuation is the carrier number fluctuation in n-type metal-oxide-semiconductor (n-MOS) devices and it is the mobility fluctuation in p-MOS devices. Jensen has also proposed a lattice gas model, in an example of broad physical relevance, in which 1=f fluctuation can arise due to self-organized criticality. Musha et al. measured the fluctuation of Brillouin scattering from quartz and they reported that the origin of 1=f mobility fluctuation is the number fluctuation of thermally excited phonons. We have also shown, using the higher order correlation function, that the 1=f resistance fluctuation had the same statistical property as that of the 1/2-order integration of white noise, which is equivalent to one-dimensional diffusion with a white noise source. The time inversion asymmetry of the time series of the resistance fluctuation was the same as that of the 1/2-order integration of white noise. Taking the above finding into account, we propose, in the present paper, a physical model of 1=f noise which is explained as the temperature fluctuation of a nonequilibrium heat source accompanied by heat flows. Let us consider one-dimensional thermal conduction along a wire of a medium. A heat source is assumed to be located at the end of the wire, whose temperature T0ðtÞ is also assumed to vary with time t under the influence of an external heat supply Q0ðtÞ and the heat flux qðtÞ emitted into the wire (see Fig. 1). The temperature distribution Tðz; tÞ on the wire along the z-axis in contact with the heat source is well known to be given by