# Reliability of NAND Flash Memories: Planar Cells and Emerging Issues in 3D Devices
## 3 NAND Flash Memory Reliability
### Random Telegraph Noise (RTN)
#### 3.2.2 Main Experimental Data  
The first experimental data on the statistical distribution of RTN amplitude in Flash memory arrays were published in 2006 [95]. For each cell in the array, the authors applied a staircase control-gate bias, recording the \(V_{T}\) value at which the cell switched from on to off state. Because of RTN, different \(V_{T}\)s are recorded every time the experiment is repeated, and their maximum and minimum values will give the amplitude of the RTN fluctuation (two staircases are actually employed, with increasing and decreasing control-gate bias, but the working principle does not change). Results for the fluctuation amplitude on a 90 nm cell are reported in Figure 7: note that the majority of cells exhibit negligible \(V_{T}\) fluctuations, but a small number of them can reach \(V_{T}\) shifts of a few hundred mV. Moreover, the number of cells exhibiting this behavior increases with P/E cycling. Figure 6: Probability density function (**left**) and cumulative distribution (**right**) for the threshold voltage shift determined by the charging of a single interfacial trap, \(\Delta V_{T}^{1}\), in a decananometer NAND Flash cell [112], © 2008 IEEE. A simpler characterization technique for RTN is reported in Figure 8[96], where the \(V_{T}\) values at two different times are recorded for each cell. The RTN amplitude is now defined as the \(V_{T}\) difference between the two values. Note that this technique does not measure the _maximum_ RTN fluctuation amplitude, as accomplished by [90; 95; 97; 99], because a noisy cell can give either positive, negative or zero fluctuation, depending upon the sampling time (see the different cases Figure 8). However, this technique will return the actual RTN amplitude distribution that matters under real operating conditions, when a cell is read after being programmed. Typical results obtained with this technique are shown in Figure 9 for NOR (left) and NAND (right) Flash arrays [96; 122; 123]. Figures show the cumulative density function (cdf) and its complement, highlighting clear exponential tails down to very low probability values [124] for both high and low \(\Delta V_{T}\) values. The region around \(\Delta V_{T}=0\) is affected by Gaussian noise, and the exponential tails depart from such region at different probabilities. Note also that when \(\Delta V_{T}\) is evaluated between the \(n\)th and the first read operation, the tails slightly increase with \(n\). Differences between NOR and NAND RTN levels and amplitude are determined by cell design parameters (see Equation (3)) as well as by the cycling conditions. Figure 8: Time dependence of \(V_{T}\) for three Flash cells affected by RTN. \(V_{T}\) is sampled at times \(t_{1}\) and \(t_{2}\) and the RTN amplitude is defined as the \(V_{T}\) difference. Note that **(a)** null, **(b)** negative and **(c)** positive \(\Delta V_{T}\) can result. Figure 7: Experimental cumulative distribution function for the \(V_{T}\) shift induced by RTN in a Flash array [95], © 2007 IEEE. Figure 7 shows that RTN depends on P/E cycling. An increase in the tail height was also reported in [98; 123; 125], where different technologies were compared. Figure 10 (left) shows experimental data for RTN in a NAND array for different cycling conditions: note that the exponential tails grow while their slope is hardly affected. This is reported in the right-hand side of Figure 10 where the slope \(\lambda\) of the exponential tails and the probability at a fixed \(|\Delta V_{T}|\) value are shown as a function of \(N_{\text{C}}\), for the same technology. Note the negligible dependence of \(\lambda\) on \(N_{\text{C}}\), confirming that cycling results in a parallel shift of the RTN tails. The increase in tail height follows a power-law dependence with exponent 0.29 for this technology [123]. Different values were found in NOR arrays, owing once more to differences in cell design and cycling conditions.