Johnson noise in one- and two-dimensional distributed resistor-capacitor systems

Abstract

Johnson noise is often the dominant noise source in microelectronic devices. While the magnitude and frequency dependence of noise within a network of discrete resistors and capacitors is well documented, there appears to be a lack of analogous results for distributed resistor-capacitor systems. This latter model is quite relevant to microelectronic devices since one finds that long resistive conductors are capacitively coupled with varying strength to other elements along the entire conductor length. We solve both the one-and two-dimensional distributed resistor-capacitor systems and find both the autocorrelation function of the potential at any point and the frequency spectrum of the associated mean-square potential fluctuations. We note that the one-dimensional result exhibits an extended ‘‘1/f’’ region in the power spectrum at high frequencies and speculate that all systems with macroscopic behavior governed by a diffusion equation may share this frequency dependence if the diffusivity depends appropriately on spatial frequency. The two-dimensional system solution shows us that Johnson noise within the epitaxial layer of a two-dimensional image sensor will not dominate other imager noise sources.