Random doping fluctuations of small-signal parameters in nanoscale semiconductor devices

Random doping fluctuations affect negatively the functionality and yield of many analog and mixed signal circuits that are based on pairs of nearly identical elements and whose performance depends on the matching properties of their components (e.g. differential amplifiers, A/D converters, etc). Most of the existing approaches to the analysis of random doping fluctuations in semiconductor devices focus on the analysis of fluctuations of threshold voltages while fluctuations of small-signal parameters, such as transconductance, gate capacitance, and admittance matrix parameters have received very little attention. The only existing work on fluctuations of small-signal parameters is presented by Andrei and Mayergoyz (2003). This approach is based on the linearization of transport equations and has the advantage that it is computationally very efficient. It yields information on the sensitivity of fluctuations of small-signal parameters to the locations of doping fluctuations, and, as a result, it can be used in the design of fluctuation resistant structures of semiconductor devices. However, its numerical implementation is cumbersome because it requires the computation of the second-order derivatives of the discretized transport equations with respect to the state variables (electrostatic potential, electron and hole concentrations, quasi-Fermi potentials) and doping concentration. For this reason, the approach presented by Andrei and Mayergoyz (2003) is difficult to implement in commercial device simulators such as DESSIS, PISCES, etc. In this article we present a method that avoids the numerical implementation of second-order derivatives of transport equations by using only the Jacobian matrix of transport equations (that are first-order derivatives). The Jacobian matrix is usually readily available in device simulators, which makes our method easy to implement.