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Time required to program virgin Ag/GeS2/W cells (Ref. 4) under constant voltage for three different thicknesses of GeS2. Dots and error bars are data from Jameson et al. (Ref. 3). The 400 Å cells exhibit the exponential voltage dependence commonly observed in CBRAM cells at high Va , whereas a progressive flattening is observed in thinner cells. Solid lines are medians of five kinetic Monte Carlo simulations at each Va . Dashed lines are the previous analytical treatment of the model (Ref. 3), which ignores transport and therefore misses the cooperative effects captured here by the Monte Carlo simulations.
Time required to program virgin Ag/GeS2/W cells (Ref. 4) with 400 Å of GeS2 using pulses of height Va , width ton , and spacing toff . Symbols (connected by thin lines) are experimental data. Thick lines (labeled by ton ) are the corresponding Monte Carlo simulations (median of five simulations at each Va ). tp was calculated as ton times the number of pulses (or fraction thereof) required to program the cell. The curve for ton = 4 μs is nearly indistinguishable from the curve for constant-Va programming (not shown), whereas curves for ton < 4 μs show a dramatic upturn at low Va .
Model proposed to describe the programming kinetics of Ag/GeS2/W CBRAM cells, after Jameson et al. (Ref. 3). The potential V (x) has Nw total wells. Well 0 represents the anode surface (always occupied) and well Nw the cathode surface. The illustration depicts the potential with a net voltage Vac between the anode and cathode, yielding an electric field between the anode surface and the tip of a filament of length l(t).
Qualitative descriptions of the cooperative effects giving rise to: (a) and (b), the flattening at high Va in Fig. 1 and (c)–(f) the upturn at low Va in Fig. 2. For clarity, the potentials are drawn with zero electric field.
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