Isothermal Switching and Detailed Filament Evolution in Memristive Systems

Abstract

The steady-state solution of filamentary memristive switching may be derived directly from the heat equation, modelling vertical and radial heat flow. This solution is shown to provide a continuous and accurate description of the evolution of the filament radius, composition, heat flow, and temperature during switching, and is shown to apply to a large range of switching materials and experimental time-scales.

Detection and characterization of multi-filament evolution during resistive switching

“…(3), are compared to the steady-state solution for filamentary switching. 10 The quantitative agreement provides strong evidence that the switching profiles of multiple filaments has been resolved. The physical fitting parameters were found to be T crit ¼ 1225 K, r ¼ 2:66e5 S, and k E ¼ 120 W=mK.…”

“…Figure 1 shows a typical bipolar current-voltage hysteresis loop, composed of four distinct regimes, measured on TaO x devices using an Agilent 4156C parameter analyzer (sample preparation has been previously described [14][15][16] ). The device begins in the OFF state (regime 1) and remains there until sufficient positive voltage (or power) is applied to the device to thermally activate the motion of ionic dopants, 10 activating ON switching (regime 2). Once the resistance state of the device begins to evolve, the operation mode can result in substantially different switching events.…”

“…Due to an upper limit in the oxygen vacancy concentration, to continue ON switching (decreasing resistance) the activated filament must increase its radius. 10 To do so requires that T ¼ T crit at the outer edge of the filament, which requires an increase in applied voltage as radius increases according to Eq. (1).…”

“…3(c)). Therefore, the resistance of each filament is defined by the equation (2)) includes the filament radius at all switching points (determined by knowing the filament resistance and conductivity at each point, and R ¼ d O r pr 2 F ), 10 and because the filaments were shown to switch in isolated regimes, the resistance-power values of each filament may be consecutively determined (A OFF is first assumed to be approximately three times A 1 which is determined from a fit to the initial switching data, then A OFF may be re-approximated after each A i is determined). Figure 4 shows that the extracted resistance-power switching profiles for all three filaments agree well with a common fit to Eq.…”

Reconfigurable Memristive Device Technologies

“…The static I-V behavior of TaO x and HfO devices (with I RESET in the range of $0.5-5 mA) can be accurately described by assuming that switching occurs at a critical temperature at which the vacancies are able to migrate [38], [40]. SET and RESET switching can be accurately modeled analytically by solving the Fourier heat equation for a cylindrical filament, suggesting a significant contribution by Joule heating to the operation of these devices [38].…”