Any exploration of the operation and potential of the annular-electrode-based PCM devices must be divided into two parts: the electrical characteristics and the underlying physical model. The latter requires an acceptance of what I will call my initiating molten hotspot (IMH) model that I will describe in the later sections of this paper.
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 r2/r3 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.
Click image to enlarge.
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.
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 . 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.
For illustrative and discussion purposes, we will use the Jc
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, Jc
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 center of the contact without changing Jc
at the contact. This behavior 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
) and the ratio ac
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.