The next step is to link the current density for an annular device to the current density of the solid electrode device from which it is derived. Figure 3 is a simple PCM structure-independent plot from simple geometric consideration of the ratio of ac/Ab as a function of electrode diameter with the thickness of the annulus t as the curve parameter. This set of curves can then be used with equation 1 to obtain link between Jc and Jb.
For the moment, I rely on the assumption that at any diameter, Jc is the value for the solid electrode device. From figure 3, for a 35-nm-diameter bottom electrode with a 5-nm-thick annulus, the value of Jb would drop to 50% of the particular value of Jc, while for a 3-nm annulus, the 50% point would occur at a device diameter of approximately 20 nm. From geometric considerations alone, even with very narrow widths to the annular edge contact and with sub-20-nm-diameter apertures, it would appear the opportunity to take advantage of the current-density reductions of the Jb = Jc(ac/Ab) relationship are limited. We must also consider the feasibility of reproducing devices with very thin edge contacts in volume. Those proposing the annular electrode structure as the solution to sub-20-nm PCM scaling problems must address the questions that these simple geometric considerations expose.
Click image to enlarge
Figure 3: Plot of annular area ratio ac/Ab versus electrode diameter shows points at which electrode current density Jb falls to Jc/2.
The next step is to link the area related current density of figure 3 to device characteristics. The green and brown curves in figure 2 show the resulting device characteristics, i.e. Jb
for devices with annular contact thickness of 3 nm and 5 nm. Any damaging effects at the active material-electrode interface remain because Jc
has not changed. For a 50% reduction, the gains are not significant and for a 10-nm diameter device, they hardly appear to be worth the effort.
In the past, most of the annular devices reported have had diameters of the order 40 nm or greater. As will be discussed in a later section, thermal coupling may provide some cause for optimism to those wishing to pursue sub-20-nm PCM developments.