New theory of flicker noise

Abstract

It is shown that the flicker noise arises in islands, of any size (from a few nm to several \ensuremath{\mu}m), which are enclosed by a potential-energy barrier or which, especially for the smallest volumes, present an energy well for the carriers. The essential feature of such islands, which may be originated by many types of structural defects of the conducting medium, is that the current entering them, due to the thermionic and tunnel emissions in the first case and to generation-recombination processes in the second one, is an exponential function of a random variable energy $\ensuremath{\varphi}$. In fact, from that and from the Maxwell and Poisson equations, it follows that the fluctuations of the island charge obey a stochastic relaxation equation whose relaxation time $\ensuremath{\tau}$, according to the value range of $\ensuremath{\varphi}$, has a huge dispersion, even from ${10}^{\ensuremath{-}12}$ to ${10}^{8}$ sec. Moreover, it is shown that the random driving source of the equation is the shot noise across the island surface and that its spectrum, according the Schottky and Nyquist theorems, is inversely proportional to $\ensuremath{\tau}$ itself. The charge fluctuation in its turn induces a fluctuating current dipole vector whose effects on the voltage noise at the device terminals are computed by means of the impedance field method. Finally, by summing the independent contributions of the islands, a voltage noise spectrum of the type $\frac{\ensuremath{\Gamma}}{{f}^{\ensuremath{\gamma}}}$ is achieved, down to however low a frequency $f$, and its parameters $\ensuremath{\Gamma}$ and $\ensuremath{\gamma}$, with $0.7l\ensuremath{\gamma}l1.3$, are computed as functions of the $\ensuremath{\varphi}$ distribution and of other system quantities, such as volume, carrier number, temperature, current, and frequency itself.