## 3 Results and Discussion
### SET Operation  
Reversible switching in the PCM cell is achieved by recrystallization of the amorphous GST material in the phase change layer. In common, the PCM cell in the RESET state, in which a portion of GST material near the GST-BE interface is in the amorphous state after a RESET operation, is utilized for the SET operation. Simulations for the PCM cell with the phase distributions in Figure 3b is biased on a 1.9 mA, 150 ns positive pulse for the SET operation. At the end of pulse, the temperature of the central part of the initially amorphous region exceeds the melting temperature of the GST material, and the cell temperature decreases from this inner region in an outwards direction, as plotted in Figure 7a. When the current pulse is removed, the whole cell begins to cool down. The central molten region cools into an amorphous state due to the large cooling rate comparable to that of the RESET operation, and the GST material close to the GST-BE interface experiences crystallization, as shown in Figure 7b. The crystalline high-conductive current path between the top and bottom electrodes determines the low-resistive state of the cell, which means the implement of SET operation. Since the phase change dynamics in the case of the SET operation is rather complex as compared to the RESET operation, the temperature history within the PCM cell was simulated for further analysis. For example, in Figure 8a we compare the temporal evolution of the temperature at the position of the hot spot (A) and the center of the GST-BE interface (B), marked in Figure 7a. The temperature of whole cell increases rapidly at first and reaches the maximum at the end of the SET pulse. The heating/cooling rate is further calculated by the derivative of dT/dt from the temperature curve, as shown in Figure 8b. The heating rates of the two positions are both maximum at the beginning of the pulse, and drop quickly up to become flat, which always stay above 0.8 K/ns. The following cooling rate rapidly increases to its maximum value at the first several nanoseconds (3 ns), and subsequently drops down. Since the simulated crystallization kinetics in the PCM cell is quite different from that based on the isothermal annealing process, the heating rate in the SET process should be considered, and its effects on crystallization start temperature (\(T_{c}\)) were also studied by other groups [21; 22]. On the basis of these results, [PERSON] et al. [21] gave an empirical relation between \(T_{c}\) (\({}^{\circ}\)C) and heating rate (\(\alpha\), \({}^{\circ}\)C/min) as below  
\[T_{c}(\alpha)=-84.32+52.60\cdot\ln(\alpha+79.98). \tag{3}\]  
According to the heating rate above, the calculated crystallization start temperature exceeds 1600 K, far beyond the temperature reached in the GST layer, shown in Figure 8a. It indicates that crystallization is almost prohibited during the heating process because of the relatively high \(T_{c}\) caused by the excessive heating rate. That is contradictory to our simulation results in Figure 7b, where crystallization occurs at the GST material adjacent to the GST-BE interface. Therefore, we believe that crystallization most likely occurs during the cooling process. Figure 7: (**a**) Temperature profiles of the cells at the end of the current pulse (1.9 mA, 150 ns), point “A” represents the position of the hot spot while point “B” is located at the center of the GST-BE interface; (**b**) corresponding phase distribution within the GST layer. Blue and red regions represent the amorphous and crystalline phase, respectively. The cooling process in the GST layer was studied in detail, and the temperature variation between the A and B points is plotted in Figure 9. Because of the asymmetry of the cell structure, the central part can reach higher temperature, and then cools down more rapidly. It is well known that crystallization temperature and crystallization time determine the formation of small crystalline nuclei of critical size and their subsequent growth, respectively.