The physical model I propose to account for the “flat” part of the current density characteristics is based on the concept that during the early part of the reset pulse, an initial minimum-size molten hot spot forms at some defect on the surface or within the matrix of the crystal (see figure 4). The model suggests that this hot spot is on the order 3 nm to 5 nm in diameter.
Figure 4: During the early part of the reset pulse, a molten hot spot (red dot) on the order 3 to 5 nm forms within a region of the crystalline material that has risen to near-melting temperature (orange); this effect may account for the quasi-constant current density shown in figure 2. The dotted lines illustrate the effects of an aperture that defines the reset volume of the device.
My model suggests that the magnitude of the reset current is determined by the thermal conditions required to form the initiating molten hot spot in the crystallized active material. These thermal conditions are necessary to preheat a substantial volume of the crystallized active material to a near-melting temperature Tpre
Tpre = Tm - δT 
is the material’s melting temperature; then to raise the hot spot to Tm
. Figure 4(a) illustrates the equi-potentials and current-flow contours from a PCM electrode structure, showing the region at Tpre
and the hot spot at Tm
. This model assumes a PCM device with a hemisphere-like reset volume. It is important to note that the hemisphere structure is losing popularity in favor of designs in which an aperture or pore (dotted lines in figure 4) limits the volume. The latter structure serves the need for more closely packed PCM arrays.
Once the IMH forms, there is a discontinuity between the electrical conductivity of the crystalline material and the higher electrical conductivity of the molten material. This discontinuity acts to localize the current. At this point, one of two things can occur: the hot spot can increase in temperature for constant size, or the hotspot can increase in size for constant temperature. If it is energetically more efficient to raise the temperature of a thin surface layer around the hot spot by some amount δT
, up to Tm
, the hot spot will expand at a constant temperature close to the melting temperature. As long as the volume of the surface layer is less than the volume of the expanding molten hotspot, the rate of expansion will be determined by the reset current. For this to succeed, the localized reset current must supply sufficient energy to raise the temperature of the thin surface layer by δT
and provide for the latent heat of melting.
As the total volume of molten material increases, the growth rate will decrease. For a large-diameter electrode, the reset current density required to form an IMH in the central region of the electrode must compensate for heat loss from the edges of the electrode. In the case of a smaller-diameter device such as that shown in figure 4(b), the same current density will be able to offset the edge losses. In that situation, if sufficient additional surface area is available to allow for the formation of a 3-nm- to 5-nm-diameter molten hotspot, the electrode contact current density Jc
will remain approximately the same, resulting in a reduction in the reset current.
If the IMH model correctly describes the situation, then it would appear that an annulus thickness t
of about 6 to 7 nm represents a limit. As figure 3 shows, we have to limit our device to about 40 nm in order to obtain a 50% reduction in Jc
; once the edges become significant, we need to make an increase in the value of Jc
. Figure 4(c) shows an annular electrode device where Jc
will remain the same as for figure 4 (a) and (b), assuming t
is sufficient to provide the area for the hot spot to form.
Both solid and annular electrodes will be operating in the quasi-constant current region illustrated in figure 2. In the case of solid electrode devices, once the diameter of the device is reduced to the point at which the edge losses become significant, the current density must be increased to allow the creation of the molten hot spot; this is demonstrated by the steep part of the current density curve in figure 2 for sub 20-nm diameter solid-electrode surface devices. For annular devices, depending on the diameter, the Jb
) relationship may no longer hold. The value of Jc
may be much higher than used to obtain the representative characteristics of Jb
in figure 2.