16 imposes the restriction that, to first order, the applied electric pulse width should be such that the thermal dif- fusion length should not exceed the half-pitch distance, F , in order to avoid cross-talk during programming, where D is the diffusion constant defined as ( κ/dC$_{p}$ ) and τ is the time duration of the applied electric pulse. This approximation is only good to first order, however, be- cause thermal diffusion through a 1–D geometry is not identical to a 1–D slice of diffusion through a 3–D geom- etry. We address this issue again in Section IV B where we discuss cell-to-cell thermal crosstalk. However, this computation allows us to set a lower bound for the required current density to achieve melt- ing. We can use the expected pulse duration τ from Equation 4 to satisfy the minimum condition that the supplied energy should be large enough to raise the tem- perature of the critical volume above the melting point, F > √ 2 Dτ, (4) J $^{2}$ρ > dC$_{p}$ Δ T τ , (5) where Δ T is the difference between the melting point of the phase change material and ambient temperature. Note that the energy spent to heat neighboring material, as well as any inhomogeneous heating of the center of the critical volume beyond the melting point, is not included. Figure 11 shows a plot of pulse duration τ and, more importantly, the lower bound on current density required to heat the minimum volume. Here typical material pa- rameters for phase change materials have been used. This analysis thus suggests that we will need to supply a cur- rent density of at least 10 $^{6}$A/cm2 (10 4 µ A/ µ m $^{2}$) to be able to melt the critical volume within the cell for RE- SET. In contrast, the measurements and simulations shown in Figure 10 would seem to indicate that the current density required is actually much larger, possibly as high as 300 µ A for a 300nm 2 aperture, or 10 $^{8}$A/cm2 (10 6 µ A/ µ m $^{2}$). However, the large expanse of metal- lic electrodes in close proximity to these tiny proto- type devices actually makes this number more pessimistic than is warranted. Other demonstrations, such as the 160 µ A RESET current shown for a 7.5nm × 65nm dash- type cells[134], seem to suggest a number like J$_{PCM}$ ∼ 3 × 10 $^{7}$A/cm2 = 3 × 10 $^{5}$µ A/ µ m $^{2}$. Because the estimated numbers plotted in Figure 11 represent a lower bound, we will instead use this higher empirical value in the re- mainder of this discussion. In a full memory array, an access device such as a diode or transistor must be included at each memory cell to ensure that the read and write currents on each bitline are interacting with one and only one memory device at a time. The amount of current that this access de- vice can supply must comfortably exceed the required RESET current of the worst-case PCM element. Unfor- tunately, the CMOS FETs often considered for use as Over the next few technology generations, the most se- rious consideration for PCM is the large current needed to switch PCM cells. We can roughly estimate this re- quired current using “back-of-the-envelope” calculations. The operation of the PCM cell relies on Joule heating, so the cell structure and operating conditions are dictated by the electro-thermal diffusion equation shown earlier (Equation 2). We can assume that the critical volume undergoing phase change within the cell in a closely packed mem- ory array is laid out at a pitch of 2 F . This immediately A. Cell structures III. DESIGN AND FABRICATION OF PCM In this section, we discuss issues relevant to the design of PCM cells, such as cell structures and access circuitry, as well as those related to fabrication, such as the effects of variability and the deleterious effects of semiconductor processing on PCM materials and devices. current (dots) and the predictions of numerical simula- tions (lines)[42] decrease linearly with the cross-sectional area of the bridge device. This indicates a favorable scal- ing behavior because the required RESET current deter- mines the size of the access device which in turn deter- mines the effective density of the PCM array. It was possible to repeatedly cycle bridge devices fabri- cated from fast-switching Ge-Sb material with SET and RESET pulses of 10ns[34, 35], confirming the observa- tions of fast crystallization for this material seen in op- tical testing (Figure 7). Very short switching times and reduced switching times with reduced device dimensions have also been observed for ultra-scaled pore devices by Wang and co-workers[33]. FIG. 10: RESET current of doped-GeSb phase change bridge devices vs. cross-sectional area defined by the lithographic bridge width W and the ultra-thin film thickness H . Reprinted with permission from Reference [42] ( c ○ 2006 IEEE).