Spatiotemporal lithium concentration profile for case 1A. The homogeneous lithium concentration initially changes only at the interfaces, eventually approaching a linear profile.
Spatiotemporal lithium concentration profile for case 1B. The lower initial lithium concentration compared to case 1A leads to decreased steady-state lithium concentrations.
Spatiotemporal electric field profile evolution for case 1A. The complex electric field evolution arises from the creation/destruction of acceptors at the anode/cathode.
Spatiotemporal case 1B electric field profile. The electric field is dominated by the creation and destruction of acceptors as lithium is drifted in the device.
Resistance transient response for the case 1A and 1B simulated memristors. The increased initial lithium concentration of case 1A leads to a faster and larger resistance change.
Spatiotemporal lithium concentration profile for mobility as a function of acceptor concentration, case 2. Case 1B and case 2 have similar lithium concentration profiles due to minimal hole mobility differences.
Spatiotemporal electric field profile for case 2. The anodic and cathodic regions of the case 2 simulated memristor are less and more conductive than the case 1B memristor, respectively, due to slight increases in cathodic hole mobility and decreases in anodic hole mobility.
Spatiotemporal hole mobility profile for case 2. As lithium is drifted in the analog memristor, the hole mobility is increased (decreased) at the cathode (anode). The average hole mobility in the analog memristor increases as time increases.
Transient resistance response for the case 2 simulated memristor. The steady-state resistance change has slightly increased from case 1B due to the local anode mobility reduction in spite of the overall spatially integrated increase in hole mobility as shown in Fig. 8 .
Transient resistance response for the case 3 memristors with varied constrictive flow geometries. The resistance response for case 1B is included for comparison. Greater resistance changes are achieved as the top to bottom contact width ratio is increased.
Spatiotemporal lithium concentration for the 2× geometry memristor. The constrictive flow geometry facilitates higher local cathodic steady-state lithium concentrations than the Case 1B simulated memristor.
2× geometry memristor spatiotemporal electric field. The inhomogeneous initial electric field profile resulting from current crowding at the cathode magnifies in time as the concentration of lithium vacancies at the cathode decreases.
Lithium concentration spatiotemporal response for the 5× geometry case. As the contact width ratio is increased to 5×, higher amounts of lithium accumulate at the cathode and deplete from the anode, thus facilitating a greater change in resistance.
Spatiotemporal electric field progression for the 5× geometry case. Compared to the 2× case, higher electric fields are facilitated as the contact width ratio increases due to greater current crowding and lower concentrations of lithium vacancies (acceptors) at the cathode.
Spatiotemporal lithium concentration for the 10× geometry case. As the contact width ratio is increased to 10×, the maximum steady-state cathodic lithium concentration and thus resistance change begins to saturate due to volumetric constraints as stoichiometric lithium levels are approached.
Spatiotemporal electric field for the 10× geometry case. As the contact width ratio is increased to 10×, the maximum electric fields in the device increase due to higher lithium concentrations and magnified current crowding facilitated by the constrictive flow geometry.
Spatiotemporal lithium concentration profile for constant ion flux, case 4. A non-volatile analog memristive device is simulated by incorporating lithium extraction at the cathode.
Spatiotemporal electric field profile for case 4. As lithium is extracted from nearly stoichiometric levels, the electric field rapidly changes due to the highly non-linear relationship between lithium concentration and resistivity, Eq. (11) .
Transient resistance response for the case 4 biased memristor. Ion extraction facilitates over two orders of magnitude resistance change and is the preferred mechanism for analog ionic memristor operation provided the ionic extraction and replacement is repeatable without crystalline damage.
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