linearly as a function of the length of the bridge along the applied voltage direction, confirming the role of an underlying material-dependent threshold field[77, 78]. 

No deviation from this linear behavior was observed for bridge devices as short as 20nm. The value of the threshold field varied considerably, from 8 V/ µ m for Ge(15 at.%)-Sb devices to 94 V/ µ m for thin Sb devices. For nanowire devices with even smaller amorphous ar- eas, however, Yu and co-workers observed a deviation from this linear behavior[69]. Once the amorphous vol- ume spanned less than approximately 10nm along the nanowire, the threshold voltage saturated, at 0.8 V and 0.6 V for GeTe and Sb$_{2}$Te$_{3}$ devices, respectively. This scaling behavior was explained with the impact ioniza- tion model previously developed to explain the threshold switching phenomenon[79]. 

Such a saturation in the effective threshold voltage is actually desirable, because for practical device perfor- mance a threshold voltage around 1 V is optimum. This places the switching point well above the typical reading voltage of about 50-100 mV, yet not so far that a transis- tor or diode access device would fail to easily deliver the required switching pulses with moderate supply voltages. (Note that exceeding the threshold voltage to produce breakdown is not the same as delivering sufficient power to heat the cell to achieve the RESET condition). If the threshold voltage were to continue as a linear function of device size for sub-10-nm devices, then reading the cells without accidentally switching them out of the RESET state could become problematic. 

The thermal conductivity of phase change materials is important because it strongly influences the thermal re- sponse of a PCM device to an electrical current pulse. However, so far the materials that have been studied (Ge$_{2}$Sb$_{2}$Te$_{5}$, nitrogen-doped Ge$_{2}$Sb$_{2}$Te$_{5}$, Sb$_{2}$Te and Ag- and In-doped Sb$_{2}$Te) show only a slight variation in the values for the thermal conductivities between 0.14 and 0.17 W/m · K for the as-deposited amorphous phase, and values between 0.25 and 2.47 W/m · K for the crystalline phase[80]. Reifenberg and co-workers[81] studied the thermal conductivity of Ge$_{2}$Sb$_{2}$Te$_{5}$ with thicknesses be- tween 60 and 350 nm using nanosecond laser heating and thermal reflectance measurements. They found about a factor of two decrease in the thermal conductivity as film thickness is reduced — from 0.29, 0.42, 1.76 W/m · K in the amorphous, fcc, and hexagonal phases, respectively for 350 nm thick films, to 0.17, 0.28, 0.83 W/m · K for 60 nm thick films. As with earlier results, such a trend leads to advantageous scaling behavior for PCM appli- cations, by helping reduce the energy required for the power-intensive RESET operation. 

In addition to these changes in effective material prop- erties as device sizes scale down, there are also simple yet powerful geometric effects which are associated with scaling. As we will discuss extensively in Section III A, scaling decreases the size of the limiting cross-sectional aperture within each PCM cell, thus driving down the RESET current. However, at constant material resis- 

tivity, geometric considerations cause both the SET and dynamic resistances to increase. As a result, the effec- tive applied voltage across the device during the RESET operation remains unchanged by scaling, at least to first order. These effects can be expected to eventually have adverse effects, as the decreasing read current (from the higher SET resistance) makes it difficult to accurately read the cell state rapidly, and as the non-scaling volt- ages exceed the breakdown limits of nearby scaled-down access transistors. 

To summarize scaling properties of phase change ma- terials, it has been observed that the crystallization tem- perature is in most cases increased as dimensions are reduced (beneficial to retention), and melting temper- atures are reduced as dimensions are reduced (beneficial to RESET power scaling). Similarly, resistivities in both phases tend to increase (beneficial for RESET power), threshold voltages are first reduced as dimensions are re- duced but then level out around 0.6-0.8 V for dimensions smaller than 10 nm (beneficial for voltage scaling), and thermal conductivity seems to decrease as film thickness is reduced (beneficial for RESET current scaling). As will be seen in more detail in the next section, the raw crystallization speed can either decrease (detrimental to write performance) or increase (beneficial), and seems to depend strongly on the materials and their environment. Crystallization has been observed to reliably occur for films as thin as 1.3 nm, and crystalline nanoparticles as small as 2-3 nm in diameter have been synthesized. Over- all, phase change materials show very favorable scaling behavior — from the materials perspective, this tech- nology can be expected to be viable for several future technology nodes. 

Of all the materials parameters mentioned so far, crys- tallization speed is probably the most critically impor- tant for PCM, because it sets an upper bound on the potential data rate. And as discussed in Section I C, data rate and endurance are the two device character- istics that dictate what possible application spaces could potentially be considered for PCM. (Of course, cost and reliability are then critically important to succeed in that space, but without the required speed and endurance for that market segment, such considerations would be moot anyway.) 

As mentioned in Section I B, the early discov- ery of electronic-induced phase change behavior by Ovshinsky[37] did not immediately develop into the cur- rent PCM field. Early phase change materials simply crystallized too slowly to be technologically competitive, with switching times in the microsecond to millisecond time regimes[82, 83]. Phase change technology began to gain traction in the late eighties with new phase change materials capable of recrystallization in the nanosecond time regime[84, 85]. These discoveries both led to the 

## B. Speed of PCM 

