Predictive and Efficient Modeling of Hot Carrier Degradation with Drift-Diffusion Based Carrier Transport Models

3.4 The Energy Driven Paradigm

Rauch and La Rosa suggested that in the case of scaled devices HCD is driven by the carrier energy deposited at the interface rather than by the electric field [23, 167]. They also investigated the importance of electron-electron scattering. Due to the low supply voltages in ultra-scaled MOSFETs, the single-carrier mechanism is not very prominent as the probability of finding carriers with very high energies is low. The energy exchange between carriers via carrier-carrier scattering populates the high energy tail of the carrier energy distribution function, thus increasing the probability of a single-carrier bond breakage process and of the multiple-carrier process as well [11]. The role of electron-electron scattering in scaled devices also explains the increase in HCD at elevated temperatures, which is contrary to the trend for long channel devices. At elevated temperatures, the scattering events are more intense which lead to a reduction of carrier energies in long channel devices and thus weakening of HCD. In short channel devices, however, an increase in temperature leads to more efficient scattering between the carriers causing an increase in carrier concentration in the high energy region. This suggests that the population of hot-carriers increases leading to a larger degradation [5, 148, 168, 149].

The Rauch and LaRosa approach introduce a shift of the HCD paradigm from being field driven to energy driven. The defect generation rate in the Rauch and La Rosa model has a similar form as Equation 3.1 given by: $\int f\left (\varepsilon \right )S\left (\varepsilon \right )\mathrm {d}\varepsilon$ , where $f\left (\varepsilon \right )$ represents the carrier distribution function and $S\left (\varepsilon \right )$ the reaction cross section. The balance of slopes of the DF and the reaction cross section curves ( $\mathrm {d}\ln f/\mathrm {d}\varepsilon =-\mathrm {d}\ln S/\mathrm {d}\varepsilon$ ) determines a knee energy. The Knee energy is the energy at which the defect generation rate attains a local maximum, see Figure 3.5. The knee energy was found to be weakly dependent on the drain voltage. The defect generation rate can then be calculated from the knee energy if the maximum of the product $f\left (\varepsilon \right )S\left (\varepsilon \right )$ is narrow enough to be approximated by a delta function. Thus, the integration over the entire energy range may be avoided.

This paradigm allows consideration of HCD without time consuming and computationally demanding transport simulations. However, there are also some shortcomings. In most cases the $f\left (\varepsilon \right )S\left (\varepsilon \right )$ peak is not narrow and, thus, integration over the entire energy range is required. Further, the authors used some empirical parameters based on the dominant knee energy to calculate the DF which does not capture the distribution and localization of $N_{\mathrm {it}}$ , a characteristic feature of HCD. Finally, the device lifetime was estimated based on the $N_{\mathrm {it}}$ generation rate instead of using the changes observed in the device characteristics.