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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 

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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. 

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. 

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 

