24 FIG. 23: Cycling performance of the SET and RESET state of a single PCM cell. Reprinted with permission from Reference [141] ( c ○ 2001 IEEE). FIG. 22: RESET tail modulation by the quenching time t$_{Q}$ . A long quench time results in a partial SET of a small fraction of devices within a large array. Reprinted from Reference [168] ( c ○ 2008 Elsevier). creases the already high resistance of the RESET state, it is not an issue for binary PCM devices. However, drift can be particularly problematic in the context of multiple bits per cell, as discussed in Section V A. crease of RESET resistance, which accelerates at elevated temperature[169, 170]. It has been shown that a small fraction of cells in the RESET state will tend to show these effects more rapidly than the average cell, but that the location of these cells is random from cycle to cy- cle. A cell may participate in this tail of the resistance distribution on one cycle, yet show much improved re- sistance to the anneal upon the next, consistent with random nucleation of crystalline grains within the amor- phous plug[170]. Thus we can expect that this random formation of crystalline grains is present throughout the portion of the cell that reaches elevated temperatures. Upon the application of a subsequent programming pulse, the temperature distribution of the cell may not be exactly identical to the previous cycle, leading to variations in resistance. This intra-device programming variability can be readily observed in any single-cell en- durance plot, as illustrated in Figure 23. Drift would be bad enough if all cells changed in re- sistance along the same trajectory. However, variability introduces different drift coefficients, so that cells with similar resistances immediately after programming tend to separate in resistance over time. In addition, some variability in crystallization speed has been observed over large arrays of PCM devices, so that some cells tend to SET more easily (both at elevated temperature and after low-temperature anneals) than the average cell[168]. Fig- ure 22 illustrates the signature of this effect, with RESET tail bits emerging when a RESET programming pulse with an insufficiently short quench time is used for pro- gramming. Although such anomalous devices can be RE- SET to high resistance by using pulses with rapid quench, such tail-bit devices will still be associated with increased long-term retention loss and resistance distributions that broaden more rapidly over time. In general, combining the effects of drift and recrystallization, variable drift ef- fects tend to broaden the resistance distribution of a large collection of cells over time: some cells increase in resis- tance due to structural relaxation, some cells decrease due to partial recrystallization. While some may first increase and then only later decrease, the random walk nature of these effects typically leads to broader distri- butions over time. Variability also forces the use of iterative write schemes for programming of multi-level resistance states, as il- lustrated in Figure 24[60]. Here, a collection of cells is programmed with single current pulses, with the trailing edges controlled to produce intermediate resistance val- ues. The highest and lowest resistance levels have the smallest variation in resistance — for these states the RESET and SET resistances tend to saturate, as overly large voltages produce little additional increase in RE- SET resistance and overly long pulses produce little ad- ditional decrease in SET resistance. The intermediate resistance levels, which represent hybrid states where a smaller portion of the cell is amorphous than in the full RESET state[171], are much more sensitive to variability. Even so, since each given cell does respond in a some- what reproducible and hence predictable manner, the de- sired resistance value can be produced by an iterative write scheme. As illustrated in Figure 25, the same cells 5. Variability and MLC 4. Intra-device variability The act of programming a PCM cell involves the re- arrangement and movement of atoms within the cell. When a given cell, starting from the polycrystalline SET state, is melt-quenched and then crystallized back to the SET state, the distribution of crystal grains within the cell is not identical. The nucleation of these crys- talline grains within the amorphous plug leads to a de-