Suppression of Shot Noise During the Soft Reset by Cascaded Transitions on a Potential Ladder With Single-Carrier Charging Steps

A shot noise suppression process of the emission-limited or the "soft" reset in an image sensor is investigated by analytically solving a master (Kolmogorov-Bateman) equation for a continuous-time Markov chain with correlated carrier emission rates. An explicit form of the probability distribution function, the hypoexponential type, is derived. An analytical form of the soft-reset (SR) noise is derived as the second-order moment, that is, variance, of the distribution function. It describes all the main characteristics of the SR noise previously reported; time-dependent shot noise suppression approaching an asymptotic limit of the half amount of noise charges as those of the fast or "hard" reset. The noise suppression mechanism is attributed to cascaded transitions of the storage node potential on a potential ladder giving the variance composed of a uniformly decreasing convergent series. The noise reduction factor is shown to be determined by the ladder spacing of a single-carrier charging potential. From the first-order moment analysis, an average time or lifetime dependence identical to that of the deterministic diode-decay equation is derived. Thus, the SR noise can be characterized by the governing probability law and its moments.