29 mushroom PCM cells, Pirovano et. al.[147] showed a retention activation energy of 2.6eV, adequate for more than 300 years of data retention at 85 $^{◦}$C. Later Redaelli et. al.[200–202] proposed a percolation model for retention on 180 nm µ -trench PCM cells and analyzed this model using a temperature dependent per- colation effect. This is the most widely accepted model for PCM retention. By showing that repeated reten- tion measurements on the same device resulted in widely varying retention times, they demonstrated the stochas- tic component to GST crystallization discussed earlier. They proposed that this variation has its origin in the random spatial configuration of the as-nucleated grains in the amorphous region. As nucleation proceeds with time, the cell resistance decreases significantly when a percolation path finally appears through the amorphous layer. Since the crystalline state is so much more conduc- tive, the occurrence of even a partial path through the amorphous plug can strongly reduce the overall device resistance. Due to these percolation effects, the measured reten- tion times of an ensemble of cells tend to obey Weibull statistics, where the cumulative distribution of retention times represent a line of constant slope β on a Weibull plot (which plots the logarithm of the fraction of failed cells against the logarithm of elapsed time). It was also experimentally observed that β increases (e.g., distribu- tions become tighter) at lower measurement tempera- tures. This temperature dependency was explained using a Monte Carlo model which randomly generated crys- talline nuclei and let them grow in the thin amorphous re- gion (note that heterogeneous nucleation was neglected). By comparing this model to experimental data, they also showed that the effective grain size r at most tempera- tures is higher than the as-nucleated grain radius, with the difference being attributed to grain growth. By as- suming a temperature-activated Arrhenius model for fail- ure times, retention exceeding 10 years at 105 $^{◦}$C was pre- dicted using this model. Below 120 $^{◦}$C, the model postu- lated that grain growth is negligible, so that the size r of each grain is no larger than nucleation-limited FCC GST-crystal monomer radius. Thus nucleation becomes solely responsible for retention failures, and this causes the Weibull slope β to increase significantly. This also implies that the distributions of retention times could become very tight in the temperature regime of interest for retention (around 85 $^{◦}$C) which led them to conclude that PPB retention failures should still exceed 10 years at 103 $^{◦}$C. Modeling and simulations done on different PCM cell structures also showed that the retention properties are identical when the effective amorphous layer thick- ness is the same. The previous papers also assumed that failure times have an Arrhenius temperature dependency and that de- fect mechanisms played no role in tail-bit (PPB) fail- ures. Russo et. al.[203] showed that a pure Arrhenius extrapolation[201, 202] would be pessimistic in its esti- mation of retention and concluded that GST-based PCM Early work[40] used the activation energy of blanket GST (3.5 eV) to estimate that a 10 year lifetime at 120 $^{◦}$C should be possible for PCM cells. Using data on On the other hand, thermally activated crystallization of the amorphous material eventually leads to significant reduction in the resistance of the active layer, causing eventual retention failures for both binary and MLC stor- age. Data retention measurements typically involve mon- itoring the resistance of the cell that has been put in the RESET state, as shown in Figure 26. When the resis- tance of the cell falls below a threshold resistance (be- tween the SET and RESET resistance values), the cell is said to have suffered a retention failure. Similar to accelerated tests used on other nonvolatile memory can- didates, PCM retention measurements are done at higher temperatures to speed up this crystallization process and the subsequent resistance change. Using measurements done at a number of high temperatures (typically near 160 $^{◦}$C) and a reasonable activation model, the reten- tion properties of PCM at 85 $^{◦}$C can be predicted fairly well. Of course, the validity of the activation model and of the extrapolation from higher temperature measure- ments is also strongly dependent on the nucleation and grain-growth properties of the specific phase change ma- terial being used in the memory cell. Since the crystalline SET state is a stable low-resistance state, it is the stability of the quenched high-resistance RESET phase which dominates retention issues. Not sur- prisingly. the stability of this phase has been investigated widely. As discussed earlier, the amorphous phase suffers from two independent resistance-altering processes: re- sistance drift and spontaneous crystallization. The drift process is a steady increase in the resistivity of the amor- phous phase, related to structural rearrangement of the amorphous chalcogenide and the dynamics of intrinsic traps. Since this process increases the ON/OFF ratio, it does not cause any data-loss for binary PCM devices. FIG. 26: Accelerated failure of a µ -trench PCM cell, showing decrease in RESET resistance as a function of time at 210 $^{◦}$C. Reprinted with permission from Reference [200] ( c ○ 2006 IEEE).