13 FIG. 8: Crystal growth velocity (red line) for GeSb as inferred by matching between simulation and empirical measurements. Low tem- perature crystal growth speed was measured by monitoring the slow growth of crystalline nuclei for growth-dominated (AIST) material[93]; high-temperature crystal growth speeds represent the best match be- tween the measured optically-induced recrystallization of amorphous marks on thin-film GeSb and simulations of this process[93, 105]. crystal growth speed can vary by more than 15 orders of magnitude between room temperature (which is off- scale in Figure 8) and the melting point. The sym- bols in Figure 8 correspond to growth speeds of less than 10 nanometers per second, measured by exhaus- tive atomic force microscopy (AFM) at temperatures below 180 $^{◦}$C[93]. (This data was taken for AIST, a growth-dominated material similar to GeSb, although both Ge$_{2}$Sb$_{2}$Te$_{5}$ and Ge$_{4}$Sb$_{1}$Te$_{5}$ were measured to have very similar low-temperature growth velocities[93]). The solid curve in Figure 8 represents a simulation model built to match both this low-temperature experimental data as well as extensive recrystallization data for GeSb measured on a static laser tester. This experimental data included both reflectivity measurements similar to Fig- ure 7 as well as AFM measurements of the size of melt- quenched spots before and after laser pulses[105]. The sharp increase in crystal growth speed above the glass transition temperature at 205 $^{◦}$C is associated with a sharp drop in viscosity at these temperatures, character- istic of “fragile glass-forming” materials[106, 107]. This wide range of crystal growth speeds between mod- erate and high temperatures is one of the most important features of phase change materials. It allows the amor- phous phase to remain unchanged for several years at temperatures near room temperature, while at program- ming temperatures crystallization can proceed in < 100 ns. The kinetic response of phase change materials to temperature has been described by nucleation theory in great detail[107–109]. Perhaps the most influential pa- rameters from nucleation theory involve the relation be- tween the interfacial energy (energetic cost of adding ma- terial to a crystalline-amorphous interface) and the free energy of crystallization (thermodynamic driving force for crystallization). This interplay controls the size of the critical or smallest stable nucleus, which in turn influ- ences the nucleation rate at which such nuclei can be in- cubated at lower temperatures (typically reaching a max- imum rate near the glass transition temperature), and the growth rate at which large nuclei expand into the sur- rounding undercooled liquid (typically peaking at higher temperatures closer to the melting point). The presence of these sub-critical nuclei can be detected by Fluctu- ation Transmission Electron Microscopy (FTEM)[110], which can explore medium-range spatial correlations be- yond the nearest atomic neighbor. Using FTEM, it was observed that an increase in the population of sub-critical nuclei led to a decrease in the incubation time before crystallization[110], as predicted by classical nucleation theory[107]. As discussed earlier, scaling is beneficial for PCM device speed. For example, it was observed that the SET time (crystallization time) and RESET times (melt- quenching) were reduced for Ge$_{2}$Sb$_{2}$Te$_{5}$ material when device dimensions were reduced from 90/1.5 ns for SET/RESET operation for 470 nm diameter “pore” cell devices to 2.5/0.4 ns for 19 nm diameter devices[33]. Such results help move towards one important goal of However, pulse duration is often confused with ma- terial switching speed. This is an oversimplifica- tion: crystallization and growth are thermally activated processes[115, 116] and removal of stimulation is followed by a cooling period where additional crystal growth can contribute to observed phenomenon. Nevertheless, from a large aggregate of reports we can expect first gen- eration devices to attain switching speeds of 20-200ns. These phase change materials have the significant ad- vantage of being highly nonvolatile at temperatures near room temperature, while retaining fast switching speeds There are certainly phase change materials which crystallize at much higher speed than the widely used Ge$_{2}$Sb$_{2}$Te$_{5}$ alloy. For example, GeSb and Sb$_{2}$Te$_{3}$ are two high speed materials which have been demonstrated to crystallize in tenths of nanoseconds, comparable to the performance of consumer SRAMs. Phase-change mem- ory devices fabricated from Ge-Te were shown to switch in resistance by nearly 3 orders of magnitude with SET pulses of one nanosecond[36]. Femtosecond laser pulses have been demonstrated to induce disorder-to-order tran- sition in amorphous GeSb films[42, 113, 114], indicating very high speed potential. phase change materials research: the quest for materials that can reliably switch at speeds comparable to RAM (approximately 10-50 ns) without sacrificing retention, endurance, or any other critical performance specifica- tion. Due to the large number of experimental variables that can contribute to switching kinetics (thermal envi- ronment, deposition conditions, changes or damage in- duced during processing, etc.), extrapolating from sim- ple thin-film recrystallization experiments to PCM de- vices remains difficult. Crystallization from electrical pulses has been reported to range from 2.5 ns[111] to 1 microsecond[112] for similar materials Ge$_{2}$Sb$_{2}$Te$_{2}$ and Ge$_{2}$Sb$_{2}$Te$_{5}$, respectively.