One of the manifestations of Hot-Carrier Degradation (HCD) is the linear drain current (Idlin) change. This change is a consequence of a large number of microscopic contributions. These contributions are related to the dangling bonds produced due to the Si-H bond dissociation. A dangling bond can capture a carrier, thereby producing a charged defect, which perturbs the electrostatics of a device and degrades the mobility. The driving force of the bond-breakage process is the energy deposited by carriers and thus the distribution of the energy describes the intensity of the bond dissociation mechanism. At the same time, the carrier ensemble evolves as it moves through the device. Physically this means that the carrier distribution function, and the Acceleration Integral (AI), changes with the coordinate along the interface. Since the AI defines the characteristic time for trap creation, the interface states are distributed spatially and over the characteristic time. This time, in turn, describes the activation exponent and thus the dynamics of the defect creation process. Therefore, the acceleration integral is a macroscopic quantity that characterizes the cumulative ability of the carrier ensemble to rupture a Si-H bond.
Our analytical approach to HCD simulation is directly obtained from our physics-based Technology Computer-Aided Design (TCAD) model. The model relies on a thorough solution of the Boltzmann transport equation by means of the Monte Carlo approach. Since in our physics-based version of the model the quantity controlling the matter is the carrier acceleration integral, in the analytical approach we also deal with this value. Therefore, the AI profile is represented by a fitting formula, which also gives an analytical expression for the linear drain current change with time. Although the linear drain current change with time is expressed as a superposition of exponential integrals, the solution employing the asymptotics of this special function may be simplified. For instance, such a simplification is to be done for long times and short time/weak stresses. One of the main advantages of this analytical approach is that it is based on a physics-based TCAD model rather than on an empirical fit to experimental data. Thus, the model captures the superposition of the single-carrier and multiple- carrier for Si-H bond-breakage and the degradation saturation. This is very important while passing from accelerated stress to real operating conditions, which are usually characterized by lower voltages, i.e. one may expect a more pronounced contribution of the multiple-carrier component. The model also represents the saturation of HCD observed at relatively long stress times. The flexibility of the resulting expression allows us to employ this approach while considering the impact of fluctuating parameters of device topology on HCD. In this case, the time-consuming Monte Carlo method leads to extremely high computational costs.