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

1.2 Hot-Carrier Degradation

Similar to BTI, HCD is also related to the build-up of defects at/near the $\mathrm {Si}\slash \mathrm {SiO_{2}}$ interface. However, during BTI stress, the electric field component along the channel is usually constant as the source and drain contacts are grounded. Thus, only the perpendicular component of the oxide field plays a role in defect creation. Hot carrier degradation, on the other hand, occurs when a voltage between source and drain is applied, leading to the

increase in the carrier flux along the channel. This makes HCD even more complex due to the simultaneous action of the two electric field components. Therefore, one can conclude that HCD has one more degree of freedom than BTI. For example, in a MOSFET, when the drain to source voltage becomes comparable or greater than the gate voltage, the inversion layer is no longer homogeneous along the channel and the carrier concentration is higher near the source. In the saturation region pinch-off occurs at the drain side. This results in a high field region near the drain leading to an increased energy of the carriers travelling from the source to the drain. These high energy carriers strike the interface breaking the Si-H bonds [72]. Additionally, the energetic carriers may lead to generation of electrons and holes by impact ionization which further facilitate Si-H bond breakage [1]. This leads to the creation of interface defects and/or charging of the already present defects, see Figure 1.4. Some of the carriers with sufficient energy to overcome the energy barrier might get injected in the oxide and create or charge oxide defects.

The high electric field near the drain region causes strong localization of the HCD near the drain or the pinch-off region as has been reported in

various studies [73, 1, 5, 7]. This localization of damage is another factor that distinguishes HCD from BTI. In modern scaled devices as well as in high voltage devices, the channel hot-carrier degradation is the main regime among the many regimes of HCD identified in literature. Other HCD mechanisms are drain avalanche, secondary generated hot-carrier, substrate hot-carrier, Fowler-Nordheim and direct tunneling [1, 74]. Drain avalanche and secondary generated hot-carrier mechanisms occur due to electron-hole pair generation from impact ionization, see Figure 1.5. Substrate hot-carrier degradation originates from injection from the channel-substrate p-n junction [75]. In Fowler-Nordheim emission, the carriers overcome the triangular potential barrier and are injected into the SiO (math image) conduction band, while in direct tunneling carriers tunnel to the channel overcoming the trapezoidal potential barrier. Both Fowler-Nordheim and direct tunneling are quantum mechanical effects and are observed in scaled devices. Note that direct tunneling is observed in very thin oxides while Fowler-Nordheim tunneling can occur in thicker oxides but requires a higher applied potential. Although HCD is a more general term, in this work it will be used to refer to the channel hot-carrier degradation mechanism.

The dominance of interface trap generation in hot-carrier degradation has been universally accepted for almost all technologies [76, 77, 1, 25]. Several stress and recovery measurements, see [78], show the absence of a recoverable component in HCD which leads to a controversy regarding the contribution of oxide traps as discussed in Section 1.1. The recovery in device degradation measurements is attributed to $N_{\mathrm {ot}}$ traps, whereas no recovery indicates pure $N_{\mathrm {it}}$ . Moreover, many studies suggest an absence of oxide trap contribution to HCD [79, 80, 81]. NBTI and HCD also differ in their response to elevated temperatures. While NBTI is found to worsen with a rise in temperature for all devices [68], HCD becomes less pronounced in long-channel/high-voltage devices with increase in temperature [82, 83, 84]. For scaled devices, on the other hand, HCD aggravates at high temperature as electron-electron scattering populates the high energy fraction of the ensemble [85, 86]. Alternatively, the importance of electron-electron scattering in HCD has been disputed by others [87] and the cause for the increase in HCD is attributed to a mixed-mode process [87]. Recently, HCD was found to decrease at elevated temperatures in MOSFETs with SiON gate dielectric [88]. At low stress voltages, the degradation was observed to be less severe with increasing temperature, while at higher voltages no change in degradation was observed with increase in temperature. This behavior was explained as being due to different thermal responses of the two bond breakage mechanisms. The rate of the multiple-carrier process was found to decrease and the rate of the single-carrier process increased with increasing temperature [88]. In a few other investigations, HCD accelerated by self-heating has been suggested to be an important reliability concern in modern devices [89, 90]. Thus, there are a number of complex factors that collectively contribute

to HCD and need to be considered in modeling. The situation becomes even more complex when BTI mixes with HCD [91].

A comprehensive summary of widely used HCD models is presented in Chapter 3. A majority of these models are empirical while a few are physics based. However, a common feature among all modeling attempts is the interface state creation process which is controlled by the manner how the carriers are distributed over energy. Thus, the carrier energy distribution is the most important ingredient in modeling of HCD.