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rate. Here, the activation energy was found to fall from 2.34 eV for 190 nm diameter devices to 1.9 eV for 20 nm diameter devices, indicating a deterioration of data re- tention as the Ge$_{2}$Sb$_{2}$Te$_{5}$ nanowire diameter is reduced. However, Yu and co-workers did not observe a depen- dence of the crystallization temperature on the device diameter for PCM devices fabricated by contacting GeTe and Sb$_{2}$Te$_{3}$ nanowires using Cr/Au contacts[69]. 

Figure 6 shows phase change nanoparticles fabri- cated by a variety of techniques including electron beam lithography, solution-based chemistry, self-assembly- based lithography combined with sputter deposition, and self-assembly-based lithography combined with spin-on deposition of the phase change material. When the crystallization temperature of amorphous-as-fabricated nanoparticles was studied, it was found that larger phase change nanoparticles have a very similar crystallization temperature compared to bulk material[62, 70], whereas the smallest nanoparticles in the 10 nm range can show either decreased[71] or increased[72] crystallization tem- perature. 

In terms of size effects, ultra-thin films still can show crystallization down to thicknesses of only 1.3 nm[66], and nanoparticles as small as 2-5 nm synthe- sized by solution-based chemistry have been found to be crystalline[73]. This is very promising for the scalability of PCM technology to future device generations. 

Beyond crystallization temperature, the melting tem- perature is a parameter which can vary with composition and, at small dimensions, with size. In fact, reduction in the melting temperature of phase change materials has been observed for very thin films[74], nanowires[75] and nanoparticles[76]. This is advantageous for device per- formance, because a lower melting point implies a re- duction in the power (and current) required to RESET such a PCM cell. The electrical resistivity for thin films increases slightly for both phases when film thickness is reduced[65]. This is also beneficial for scaling because higher resistivities lead to higher voltage drop across the material and can thus reduce switching currents. 

The threshold voltage is a phenomenological parame- ter of PCM devices that describes the applied voltage (typically around 1V) required to induce an electrical 

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breakdown effect. Such a sudden increase in electrical conductivity allows the PCM device to rapidly and ef- ficiently attain a significantly lower dynamic resistance (typically 3–10 × lower than the room-temperature SET resistance), allowing efficient heating with moderate ap- plied voltages. Thus the presence of this electrical switch- ing effect is an important component of PCM technology. 

However, a more accurate description of the underly- ing physical process calls for a threshold electric field, rather than a threshold voltage, that must be surpassed for the amorphous material to become highly conductive. Studies of phase change bridge devices (described in Sec- tion II D) have shown that the threshold voltage scales 

