# Reliability of NAND Flash Memories: Planar Cells and Emerging Issues in 3D Devices
## 3 NAND Flash Memory Reliability
### Charge Detrapping
#### 3.4.1 Main Experimental Data  
Figure 19 shows experimental data from a retention experiment at room temperature on a 16 nm NAND vehicle after \(10^{4}\) P/E cycles [226]. Note the difference with respect to Figure 16 (right): no specific tail is detected here, but rather the entire distribution is affected, although different charge loss rates can be detected between the main part and the lower extreme of the distribution (see right-hand side of Figure 19). Note also the logarithmic dependence on time of \(\Delta V_{T}\), which can be fully characterized by its slope \(\alpha\).  
The dependence of charge detrapping on the cycling conditions is reported in Figure 20: its left-hand side shows that \(\Delta V_{T}\) increases with \(N_{C}\), as more electrons are trapped during P/E operations and emitted afterwards. The right-hand side reports the dependence of \(\alpha\) on \(N_{C}\): a square-root law was found as soon as the cycling-induced damage overcomes the native detrapping, in agreement with observations on RTN-related defects [138]. This dependence is also independent of the programmed level and temperature (note that the curves for different programmed levels have been vertically shifted to highlight the square-root law and avoid excessive overlap). Figure 21 shows instead the dependence on the bake conditions: note that the detrapping dynamics depend on the time \(t_{0}\) elapsing between the last program and the first read operation (left-hand side), resulting in a shift of the detrapping curve along the log-time axis by a quantity exactly equal to \(t_{0}\). Also, \(\Delta V_{T}\) depends upon the bake temperature \(T_{B}\) (right-hand side of Figure 21), demonstrating that detrapping is thermally activated: the \(\Delta V_{T}\) curves at different \(T_{B}\) are shifted according to an Arrhenius law with activation energy \(E_{A}\approx 1.1\) eV [221; 222; 228; 229], a single detrapping curve can be obtained for an equivalent \(T_{B}\). This value of activation energy had been also observed in earlier retention experiments [51]. Careful account of additional effects which may compromise a reliable extraction of \(E_{A}\), such as interface-state and mobility recovery [230; 231] or disturbs [232], is required.  
Figure 19: (**Left**) \(V_{T}\) cdf over time for 60 nm NAND Flash cell arrays after cycling; (**Right**) \(V_{T}\) shift vs. time extracted from the cdfs at fixed probability levels [226], © 2011 IEEE.  
The last data to be discussed relate to the cycling conditions dependence. Figure 22 shows \(\Delta V_{T}\) for different values of the cycling time \(t_{C}\) (left) and temperature \(T_{C}\) (right). Note that a smaller \(\Delta V_{T}\) is detected if cycling is distributed over a longer period of time or performed at higher temperatures. This is consistent with a picture that assumes electron detrapping between one cycle and the next one, reducing the number of trapped electrons at the end of the last cycle that are then lost during the bake phase. Coherently with this interpretation, the activation energy for cycling was found to be the same as for bake. These findings have important implications for the device reliability, that will be discussed after reviewing the quantitative understanding of the phenomenon together with other experimental data.  
Figure 21: Dependence of \(\Delta V_{T}\) on bake conditions, namely time \(t_{0}\)[226], © 2011 IEEE (**left**) and bake temperature \(T_{B}\) (**right**). Data are referred to 60 and 16 nm NAND Flash vehicles. Data on the right-hand side show a) experimental data for different \(T_{B}\) and b) the same data when \(t_{B}\) is shifted on log scale according to \(E_{A}\).  
Figure 20: (**Left**) average \(\Delta V_{T}\) transients measured on 16 nm NAND Flash arrays for increasing number of P/E cycles [227], © 2016 IEEE; (**Right**) dependence of the slope \(\alpha\) on \(N_{C}\) for different programmed levels (colors) and temperatures (symbols). Curves for different programmed levels have been vertically shifted for better clarity.