Annular electrodes as PCM solution (Part 1)
Keywords:phase change memory? annular electrode? lithography?
First, let's review the electrical characteristics. The current density as a function of electrode diameter for an average PCM device with a solid electrode surface is very similar to the curve that traces the ratio of surface area to volume of a cylinder. This is an illustration of what is often referred to as the r^{2}/r^{3} problem, which for a sphere is the ratio of surface area to volume or, more simply, how by Joule heating, the ability to lose energy (area) is related to the ability to generate it (volume). This relationship has a dramatic effect on scaling predictions for PCM devices.
In earlier work, this writer plotted the results of current density as a function of lithographic nodes for both cylindrical and link PCM structures; collected from across the published literature [5]. Those curves were in general agreement with the purple curve in figure 2. Clearly changes in materials that make up the PCM structure can move this curve; but not, to date, in such a way that has solved the PCM contact current density problems.
Figure 2: Plot of current density as a function of electrode diameter for a solid electrode (purple) shows that current density remains quasi-constant for electrode diameters beyond 50 nm. The remaining two parametric curves show electrode current density for annular thicknesses t=3 nm and t=5 nm; the orange lines indicate regime within which the annular electrode essentially acts as a solid electrode. |
For illustrative and discussion purposes, we will use the J_{c} curve from figure 2 for solid electrode surfaces as a baseline throughout this paper. The key feature is at device diameters greater than 50 nm, J_{c} enters a regime within which, to a first approximation, it remains relatively constant with increases in diameter. In this flat region, it appears possible to remove large parts of the electrode by reducing its diameter or removing the centre of the contact without changing J_{c} at the contact. This behaviour is the basis of equation 1.
Simple device-independent geometric considerations allow us to explore what might be scaling problems or limitations with respect to annular electrode PCM structures. The first occurs when the electrode diameter d is twice the thickness of the annulus (d = 2t) and the ratio a_{c}/A_{b} is unity. At that scaling limit, the annulus electrode has reverted to a solid surface electrode and the device will have the same current density characteristics as the solid electrode device. In figure 2, the vertical solid orange lines highlight the scaling end points or limits for devices with 3-nm-and 5-nm-thick annular electrodes at device diameters of 6 and 10 nm respectively.
Exploring the effect of annular thickness
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 a_{c}/A_{b} 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 J_{c} and J_{b}.
For the moment, I rely on the assumption that at any diameter, J_{c} 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 J_{b} would drop to 50% of the particular value of J_{c}, 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 J_{b} = J_{c}(a_{c}/A_{b}) 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.
Figure 3: Plot of annular area ratio a_{c}/_{}A_{b} versus electrode diameter shows points at which electrode current density _{}J_{b} falls to _{}J_{c}/2. |
Related Articles | Editor's Choice |
Visit Asia Webinars to learn about the latest in technology and get practical design tips.