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

5.4 Drift-Diffusion Based Model

To avoid the cumbersome SHE simulations, the approximate DD method described in Section 4.3 is used. As can be seen in Figures 5.3 and 5.4, the DD-based model for the carrier

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Figure 5.4: The hole DFs obtained with ViennaSHE and with the DD-based model for \( V_{\mathrm {ds}} \) = \( - \)50 \( \, \)V, \( V_{\mathrm {gs}} \) = \( - \)1.5 \( \, \)V, calculated for different positions near the drain and close to the STI region of the pLDMOS transistor.

DF represented by Equation 4.22 can predict the DF curves as accurately as the SHE method [147]. The high concentration of traps in low energy region suggests that also in the case of long-channel and/or high-voltage devices, the multiple-carrier process has a significant contribution and cannot be ignored [26, 13, 147].

It is important to note that the contribution of oxide traps was not considered. There are two reasons for this. First, bulk oxide traps are known to be responsible for the recoverable component of degradation [56]. However, in the devices used in this work, no recovery was observed under the stress conditions used here. Second, various studies on the intimately related phenomenon of bias temperature instability suggest that trapping in the oxide bulk starts to play a prominent role at oxide fields of 6 \( \, \)MV/cm and higher [115]. The maximum oxide field in the nLDMOS transistors used was \( \sim \)1.3 \( \, \)MV/cm for \( V_{\mathrm {ds}} \) = 22 \( \, \)V, \( V_{\mathrm {gs}} \) = 2 \( \, \)V which is significantly smaller than 6 \( \, \)MV/cm, see Figure 5.5. Therefore, the contribution of bulk oxide traps can be neglected.

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Figure 5.5: Electric field profiles simulated with Minimos-NT for an nLDMOS at \( V_{\mathrm {ds}} \) = 22 \( \, \)V, \( V_{\mathrm {gs}} \) = 2 \( \, \)V.

The effect of majority carriers is twofold: they can contribute to the interface trap generation and also be captured by existing amphoteric traps. The former mechanism was reported to be responsible for threshold voltage and drain current turn-around effects [201, 202]. In the measurements, however, no turn-around effects were observed implying that the majority carrier contribution to HCD is weak. Drift-diffusion simulations performed for the LDMOS devices, as discussed in next section, also showed that impact ionization leads to low or moderate majority carrier concentrations throughout the channel in the interface region.