Comparison of analytic distribution function models for hot-carrier degradation modeling in nLDMOSFETs

a r t i c l e i n f o Keywords: Distribution function Hot-carrier degradation nLDMOS transistor Spherical harmonics expansion Drift–diffusion scheme Interface states Modeling We analyze the applicability of different analytic models for the carrier distribution function (DF), namely the heated Maxwellian, the Cassi model, the Hasnat approach, the Reggiani model, and our own concept, to describe hot-carrier degradation (HCD) in nLDMOS devices. As a reference, we also obtain the carrier distribution function as a direct solution of the Boltzmann transport equation using the spherical harmonics expansion method. The DFs evaluated with these models are used to simulate the interface state generation rates, the interface state density profiles, and changes of the linear and saturation drain currents as well as the threshold voltage shift. We show that the heated Maxwellian approach leads to an underestimated HCD at long stress times. This trend is also typical for the Cassi and Hasnat models but in these models HCD is underestimated in the entire stress time window. While the Reggiani model gives good results in the channel and drift regions, it cannot properly represent the high-energy tails of the DF near the drain, and thus leads to a weaker curvature of the degradation traces. We show finally that our model is capable of capturing DFs with very good accuracy and, as a result, the change of the device characteristics with stress time. A physics-based model for hot-carrier degradation (HCD) needs to be based on a microscopic description of Si–H bond-breakage mechanisms [1–4]. As has been already established, both the single-and multiple carrier processes contribute to defect generation [1,5,6]. A solitary hot carrier can induce a bond-breakage event in a single collision, which is called a single-carrier process. If the carrier flux is substantial but carriers have low energies, several cold carriers subsequently interacting with the bond can heat and eventually rupture it. Such a scenario corresponds to the multiple-carrier process. The rates of these processes are determined by the carrier energy distribution function (DF) which determines the probability density to find a carrier in a certain elementary energy range. A rigorous way to obtain the carrier distribution functions is to solve the Boltzmann transport equation (BTE). There are two different strategies to achieve this goal: the stochastic Monte-Carlo method [7,8] and the deterministic approach based on the spherical harmonics expansion (SHE). In the former method one needs to consider the trajectories …