In modern semiconductor devices degradation due to high energetic carriers leads to different degradation mechanisms. This typically includes the Negative and Positive Bias Temperature Instability (NBTI and PBTI), Time-dependent Dielectric Breakdown (TDDB), and Hot-Carrier Degradation (HCD). Among other groups, the Institute of Microelectronics works on detailed modeling approaches considering microscopic and macroscopic models. The object of this work is to model and simulate the HCD mechanism using efficient methods making them suitable for industry use.
HCD mechanisms, in particular, greatly depend on the energy distribution of electrons and holes. With knowledge of the complete distribution function interface degradation models can be used that reproduce the drain current degradation as observed in measurements. However, the distribution function is found by solving the Boltzmann Transport Equation (BTE), which is commonly accomplished using the statistical Monte Carlo method, however, this is a very time consuming process. Among others, the Spherical Harmonics method can also be used, which obtains solutions of the BTE in reasonable time.
The main macroscopic transport equations used today include the Drift-Diffusion (DD) and the Energy-Transport (ET) models. DD delivers no information on the distribution function, as per definition, the "cold" Maxwellian distribution is assumed. In ET the average carrier energy is evaluated and the "heated" Maxwellian distribution is assumed. Both transport models give no extra information on the distribution function in the high energy range and the hot-carrier population remains unknown. Despite this shortcoming, the advantages of DD and ET, i.e. high availability, robustness, simplicity, as well as its relative short simulation times, suggest utilizing methods to estimate the HCD phenomenons. To accomplish this, it is necessary to estimate the distribution function using the electric field, the current density, the carrier density, and, for ET, the average carrier temperature. Different methods have been suggested to accomplish this task. The usability of the different estimations is not directly evaluated by comparing the shape of the distribution functions with references from the Monte Carlo method. Instead, the resulting acceleration integral along the Metal-Oxide-Semiconductor (MOS) transistor channel, which is relevant for the damage rate, is considered as important. The strong peak near the drain end of the transistor is of particular importance, highlighting the strong localization of the degradation mechanism. As expected, the shapes found using the different approximations do not perfectly fit the Monte Carlo data, but they are still useful to evaluate the resulting interface damage that lead to reduced drain currents.