Set and Reset Voltage Interdependence in Resistive Switching Memory Cells

Resistive switching (RS) devices are a primary candidate to supplant current NVM memory based on floating gate MOSFET. However, RS devices suffer from broad distributions of set and reset threshold voltages.  The state transition from the initial high resistance state (HRS) to a low resistance state (HRS) is called SET process characterized by a critical voltage V_set.  A high current passing through the filament can rupture the bridge and restore the HRS state, in a so-called RESET process of the device and characterized by a critical voltage V_reset. Cu/TaO_x/Pt memory cells have been fabricated with 16 nm thick oxygen-deficient TaO_x formed by e-beam evaporation. The bottom Pt electrode has been deposited by evaporation and patterned by lift-off on a thermally oxidized Si wafer. The top Cu electrode lines were processed in the same way but patterned perpendicularly to the bottom Pt lines. The width of the metal lines varies between 1μm and 35μm. When a positive voltage is applied to the active electrode, Cu cations dissolve in the solid electrolyte and migrate through it. Cu cations are electrochemically reduced on the Pt cathode. As more Cu atoms accumulate, a nanoscale metalic filament (CF) forms at V_set a conductive path between two electrodes. Here, we report a statistical dependence of set voltage, V_set, on the preceding reset voltage, V_reset, for the same device. Such (V_set, V_reset) pairs have been collected for a multitude of devices in resistive RRAM Cu/TaO_x/Pt memory arrays. This dependence appears to be linear and is explained in terms of two interlocking mechanisms responsible for the formation and dissolution of the filaments. The V_set~V_reset dependence on a multitude of memory cells can be replicated also on a single device by intentionally varying V_reset values by the application of different linear voltage ramp rates (rr). The latter mechanism is well modeled under the assumption that a critical heat Q_crit deposited locally in the filament triggers the rupturing of the Cu conductive filament.  Q_crit can be obtained as a time integral over the instantaneous power p(t)=(rr·t)²/R_on from t=0 till the reset time t_reset=V_reset/rr. The experimental V_reset data shows a cubic root dependence on the voltage ramp rate in close agreement with the model, i.e. |V_reset|=V_reset,min +γ(rr)^1/3. The model predicts also that γ=(3·Q_crit·R_on)^1/3, with R_on being the resistance of the on-state and is fully borne out by experiment on several different Ron values. R_on can be controlled by the compliance current I_cc during the set operation according to R_on=0.17/I_cc.  Moreover, from experimental data and model assumptions, we can extract Q_crit to amount to 6μJ per erase operation. A separate mechanism is proposed to explain the impact of V_reset value on the subsequent V_set value, in terms of increased Cu⁺ ion mobility at high local temperatures just after the reset and the time τ_diss needed to dissipate the Q_crit heat. A higher |V_reset| translates then into larger rupturing gap Δ than a low |V_reset| according to Δ=(|V_reset|/Δ_o)·μ_Cu+·τ_diss where Δ_o is the initial ruptured gap due to high temperature at the most resistive segment of CF caused by Joules heating. Larger rupturing gate translates then to larger V_set~Δ.  The V_reset~V_set relation can be used to tighten V_set and V_reset distributions. RRAM suffers from broad natural distributions of Vset and Vreset obtained at fixed ramp rates. In our method, an array of memory cells with large spread of initial V_set values, has been subjected to three different ramp rates:  the devices with high V_set have been reset at a lower ramp rate than devices with low V_set values. The moderate Vset values have been subjected to intermediate ramp rate. The effect of such pre-conditioning results in much tighter distribution of Vreset. The subsequent set operation at constant ramp rate leads to a very tight distribution of Vset. Repeated set and reset operations converge on a very tight V_set and V_reset distributions. This means that the conditioning step has to be applied only once. A natural broad distribution has been selected with experimental data consisting essentially of three clusters of V_set values: (i) centered on V_set=1.0V, (ii) centered on V_set=3.8V, and (iii) data lying in-between. For the natural distribution, the mean value and standard deviation are V_set,m=2.5V and σ=1.35V, respectively. The devices of cluster (i) underwent a reset operation at ramp rate 1V/s, the devices of cluster (ii) at a ramp rate of 1mV/s, while devices with natural V_set in-between have been reset at 10mV/s. After this very simple and not further optimized procedure, a very tight (10x tighter) distribution has been obtained with V_set,m=2.13V and σ=0.14V.