11 growth[94]. The latter two steps are the slowest, and re- alistically combine to determine the speed of the device. Not all of the steps will be encountered, however. Step 1 is relevant only if the device started in the high-resistance RESET state, so that a large portion of the applied volt- age dropped across material in the amorphous phase. widespread use of phase change materials in optical re- writable technology (DVDs, CDs and now Blu-Ray), and fostered renewed interest in PCM. In phase change devices, there are three steps that could determine the overall operating speed: read, RE- SET (to high resistance), and SET (to low resistance). The read operation depends on the speed with which two (or more) resistance states can be reliably distin- guished, and thus is dominated by the circuit considera- tions (capacitance of the bit-line being charged up, leak- age from unselected devices). Although the resistance contrast and absolute resistance of the PCM cell do play a role, the read operation can generally be performed in 1-10ns[53]. The SET and RESET steps, however, involve the physical “brute force” transformations between dis- tinct structural states. The energetically less-favorable amorphous phase — which gives a PCM cell in the RESET state its high resistance — is attained by melting and then rapidly cooling the material. As the temperature falls below the glass transition temperature and molecular motion of the under–cooled liquid is halted, a “kinetically trapped” phase results. This process can be separated into three steps: 1) current-induced heating above the melting tem- perature, 2) kinetics of melting[86], and 3) kinetics of solidifying the molten material[87]. Steps 1 and 2 in- volve the rapid injection of energy to first heat and then melt the material; Step 3 involves the rapid cooling to temperatures below those favorable to recrystallization (see below). Thus the most practical method to engi- neer Step 3 is through design of the PCM cell’s thermal environment[88]. If all of the contiguous PCM material being heated is in the amorphous phase, then step 3 must take place before step 4 can begin. An example is the first crystal- lization of materials (or devices) containing amorphous- as-deposited material, where no crystalline-amorphous interfaces are present. This nucleation step can be ex- tremely slow in so–called growth–dominated materials, where nucleation is a highly unlikely event compared to the fast speed of crystal growth. In fact, frequently the crystallization of microns of surrounding material in such materials can be traced to the creation of a single nanoscopic critical nucleus[95]. In contrast, nucleation– dominated materials tend to have a lower barrier to nucle- ation, so that a large region of crystalline material stems from the growth of numerous supercritical nuclei[96]. In a typical PCM cell, only a portion of the phase change material is quenched into the amorphous state, meaning that for both types of materials, step 4 above mainly depends on the crystal growth speed at high tem- perature. The main difference between the two classes of phase change materials is that the recrystallization of amorphous nucleation-dominated material will occur both within the interior (nucleation) as well as from the edge (growth), while for a growth-dominated mate- rial only the propagation of the crystalline–amorphous boundaries matters. This can either be an advantage or disadvantage, depending on whether this added nu- cleation is desirable (having seeded nuclei that can help speed up the SET operation), or undesirable (by causing data to be lost faster at low to intermediate tempera- tures). Examples of growth–dominated materials, where the rate of crystal nucleation < growth rate, include Ge- doped SbTe, GeSb, GeSnSb, and Ge$_{3}$Sb$_{6}$Te$_{5}$. In con- trast, Ge$_{2}$Sb$_{2}$Te$_{2}$, Ge$_{2}$Sb$_{2}$Te$_{5}$, and Ge$_{4}$Sb$_{1}$Te$_{5}$ are con- sidered nucleation-dominated materials, with a rate of crystal nucleation > growth rate. It should be noted that nucleation and growth kinetics have unique responses to temperature, so under certain conditions a mate- rial typically considered growth-dominated may appear nucleation-dominated, e.g. AIST[97]. The crystallization time of phase change materials, even those intended for use in electrical devices, can be measured relatively easily using optical techniques. This is because most phase change materials of inter- est to PCM also have the same large optical contrast between the two phases that originally motivated the rewritable optical storage application. Somewhat like an optical storage device with a stationary disk, a static laser tester uses a low-power continuous-wave laser to con- stantly monitor the reflectivity while a high-power pulsed laser induces the desired phase changes. The pulsed laser Formation of the crystalline phase involves as many as four steps: 1) threshold switching[46], 2) current- induced heating to elevated temperatures (but below the melting point), 3) crystal nucleation[93], and 4) crystal While the crystalline form is thermodynamically favor- able, its kinetics are much slower than the formation of the high resistance state[92], by typically at least one or- der of magnitude. Thus the step that dictates the achiev- able data rate for PCM technology is the crystallization process associated with the SET operation. These steps are each quite fast: electrical pulses as short as 400 picoseconds have been used to switch Ge$_{2}$Sb$_{2}$Te$_{5}$ into the amorphous state[33]. While the ki- netics of phase change devices are strongly material de- pendant, the generation of the amorphous phase in any practical phase change material is necessarily faster than the speed of crystallization — because otherwise, the amorphous phase would simply never be observed[87]. Note that after a RESET operation, the amorphous phase can continue to evolve extremely slowly at low temperature, undergoing both continued relaxation of the amorphous phase as well as electronic redistribution of the trapped charge that participates in the electrical breakdown phenomenon[49, 51, 89–91]. This drift can be an issue for MLC in PCM devices, as discussed in Section V A.