6.5  Results on Trap-Assisted Tunneling

   

DTTAT DTTAT

Figure 6.23:

Left: Gate Ig and drain current Id simultanously recorded on a n-channel MOSFET with an EOT of 2.3nm  [159]. It is clear that gate and drain current are strongly correlated. Whenever a trap becomes occupied (low drain current) the gate current is decreased as well. In total the gate current is reduced by nearly 80%. Right: A schematic of the two tunneling processes to explain the experimental data (left). The total tunneling gate current is composed of direct tunneling (DT) and trap-assisted tunneling (TAT). On the far right, the assumption of a purely electrostatic interaction between the direct tunneling current and the trap occupancy is depicted.

In 2012 Toledano et al.  [159] showed that there is a correlation between gate and drain current fluctuations in MOSFETs. Figure 6.23 shows a portion of the experimental data. Interestingly the difference between high and low gate current is 80% of the gate current maximum and temperature independent. Due to the correlation with the drain current it is concluded that the charged trap significantly changes the tunneling current. A possible explanation is that the charged trap changes the local potential such that the number of charge carriers, which tunnel through the oxide, is reduced by 80%. This would also explain the temperature independence of the reduction, inherent in direct tunneling. Another explanation is that the tunneling current is a trap assisted NMP process. In  [160] we explored whether the experimental data could be reproduced by assuming that an occupied trap reduces the direct tunneling current by purely electrostatic interaction. To assess whether or not this is correct, we first simulated the electrostatics of the n-channel MOSFET. For this we used the 3D density gradient and drift diffusion simulator MinimosNT and additionally considered random dopants. The simulations were done per device, once without and once with a single discrete trapped charge in the oxide (cf. Chapter 5). Our sample size consisted of 201 microscopically different devices, i.e. different dopant positions. Then 1D potential profiles (normal to the semiconductor-oxide interface) were extracted in 1nm increments. These profiles were then loaded into our NEGF (cf. Chapter 2) simulator, VSP  [51], in order to calculate the relative change in the gate current (direct tunneling) ΔIg∕Ig. The relative tunneling current change ΔIg∕Ig was obtained by comparing the tunneling currents for the devices without trap to the devices with trap. In Figure 6.24 (left) a normalized map of the local ΔIg∕Ig over the whole gate area is shown. The map shows high local changes in the vicinity of the trap. However, as the histogram in Figure 6.24 (right) shows, we could hardly find a dopant-trap configuration for which the total change in tunneling current exceeded 1%. This is in stark contrast with the experimentally reproducibly found decrease of 80% in Ig.

   

Figure 6.24:

Left: Map of local ΔIg∕Ig (1nm increments) due to the charging of a single trap for a particular random discrete doping. High changes in the direct tunneling current in the vicinity of the trap are visible. The contour line corresponds to a one percent change in the local gate current. Nevertheless, the total gate current does not change by more than two percent  [160]. Right: Histogram of ΔIg∕Ig for active and inactive traps exhibiting a log-normal distribution (solid line). From this data it is clear that the reduction of the direct tunneling current due to active traps is unlikely to be decreased by more than 2%  [160].

Thus trap-assisted tunneling in the context of the presented four-state NMP model has been (successfully) explored  [161]. Extending the four-state NMP model (cf. Figure 6.25) by taking interactions with the poly-gate into account, the experimental data could be reproduced (cf. Figure 6.26). In this extended model one has to differentiate whether the charge carrier to be trapped originated from the poly-gate or the substrate. Nevertheless, the basic rate equations do not change. However, the source of the quantities and the tunneling distances are different. In order to correctly evaluate the capture τ_c and emission times τ_e for the trap-assisted tunneling current the charge state (whether or not the defect is charged) in the modified model had to be taken into account. In the course of the evaluation of the five-state NMP model it was found that the weak temperature dependence of the time constants is due to the weak electron-phonon coupling (small NMP transition barriers) needed to reproduce the measurement data (cf. Figure 6.26 right top). For details on the model, the reader is referred to  [161].

 

Figure 6.26:

Left: A fit of the five-state NMP model for trap-assisted tunneling (cf. Figure 6.25) to the experimental data from  [159]. The top figure illustrates the weak temperature dependence of the trap-assisted tunneling process, due to weak electron-phonon coupling. The lower figure shows the exponential dependence of the tunneling current on the gate voltage. Right: A fit of the model to the characteristic time constants of the tunneling process (cf. Figure 6.23). The capture and emission time constants can be reproduced quite well. The model can thus represent the temperature and oxide field dependence of the tunneling current as well as the experimentally observed characteristic time constants.