Design of defect-chemical properties and device performance in memristive systems

Impurities and dopants in memristive devices determine their switching kinetics, performance, and neuromorphic functionalities.


S1.1. Target synthesis and thin films
Pure and doped silica sputtering targets prepared by Heraeus GmbH according to (29,30).

S1.2. Thin Film Deposition and Control
In Figure S1 the principle influences of the sputter parameters (substrate temperature and gas composition) in microstructure can be seen. The sputtering power was set to 150 W. The substrate temperature and the processing gas composition have a huge influence on the microstructure of the sputtered films. While the SiO2 films are relatively porous if prepared at low temperatures, high substrate temperature deposition leads to a densification and improved homogeneity. An even larger effect is observed after addition of 10 % oxygen to the processing gas as can be seen comparing Fig. S1 a) and d). The oxygen content leads not only to a tenfold reduction of the sputter rate (~15 nm/min down to 1,75 nm/min), but also for a significantly improved homogeneity and reduced roughness of the films. As a consequence we determined the optimum parameters for SiO2 deposition to be at ≥150°C and a processing gas mixture of 90% Ar and 10 % oxygen. The dense and pore-free deposition process of stoichiometric SiO2 allows to avoid/suppress external influences, such as the uptake and release of oxygen and/or moisture. The increase of the film density was also verified by XRR measurements (Supplementary Figure S2A) The homogeneity of the compositions of the sputtered films were verified using secondary ion mass spectrometry (SIMS) depth profiling. An exemplary SIMS measurement of a highly doped SiO2:(Al,Cu)1 film is shown in Supplementary Figure S2 B. The intensities of all elements are constant throughout the whole film thickness.

S1.3. Measurement Setup for Switching Kinetics.
The choice for the input impedances of 50 Ω and 1 MΩ was made because of the easy setup and low influence of parasitic capacities (short cables and pulling the shielding of the cables on same potential right after the device). To protect the cells from irreversible damages, 1 MΩ input impedance of the oscilloscope was used. However, the high input impedance can hinder the investigation of the underlying physical processes (high RC time), and therefore we performed in parallel measurements with 50 Ω shunt resistance. Using 50 Ω input impedance the setup allows for a small RC time, and the internal capacitance of the devices is quickly saturated (for example for εr = 6 the time is ~ 6.10 -12 s) and the electrochemical processes and filament formation can further proceed. Whereas, when measuring with 1 MΩ input impedance, the RC time is drastically increased, the capacitance is loaded much slower (130 ns for same device), meaning that there will be a much longer time shift (voltage dividerequation S2) before switching processes can start. Figure S3: Measurement setup for the SET kinetics determination. The pulse generator sends a rectangular pulse to the device simultaneously measured at a 50 Ω terminated channel (CH1) of the oscilloscope. The device response is measured at an either 50 Ω or 1 MΩ terminated second channel as converted voltage drop over the shunt resistor corresponding to the current flowing through the device. The SET time was determined to be the time difference between the rising edges at 50 % height.

S2. Effects of moisture and materials' density.
The sensitivity of determination of dopant concentration by permittivity measurements is high.
As it can be seen from the inset of Supplementary Figure   The permittivity increases linearly with increasing the non-volatile dopant concentration.
Incorporation of moisture and/or OH --ions increases drastically the permittivity as water itself has a large εr value of 78-80 at room temperature (OH-and immobilized water can have a permittivity between 4 to 80, corresponding to the degree of immobility (46)), whereas defect free SiO2 (e.g. Suprasil-W from Heraeus GmbH) has a εr value of 3.8073 at 300 K (26,27).
Because of the different electron affinities of the foreign dopants and/or defects, stronger or weaker (compared to silicon and oxygen) interatomic electrostatic interactions are induced.
These interactions lead to formation of dipoles, influencing the permittivity and capacitance of the electrolyte film.
The ε-values were determined at 100 kHz in air (≈ 35 % relative humidity (RH)), vacuum Moisture is not only changing dielectric properties but is also an essential factor for the electrode processes, as it can undergo the required counter electrode reactions at the counter electrode interface. This process is essential for the oxidation of the active electrode material in ECM (13,32) or the incorporation of oxygen in VCM (33) systems. The counter redox reaction can also influence the switching performance as rate-limiting step.
We identified nanoscale porosity as one of the crucial factors, influencing the uptake of Increasing the humidity levels results in the increase of the film permitivitty.

S3. Calculation of the Debye length.
The Debye length was calculated using the equation: However, during uptake of moisture and/or doping the permittivity also changes. Expression that is more adequate is substituting equation S1 to obtain:

S4. Space charge layer and potential/filed distribution in ReRAM cells
Electrochemical double layer (EDL) has crucial importance for the reaction kinetics in electrochemical systems. The metal/electrolyte contact and resulting changes at the interface (EDL) are shown in Figure S5.    Figure 3D represents the case of high field reaction and transport where current depends exponentially on the electric field. Further details are provided in S6.
For valence change memory devices (VCM) the general picture is not changing compared to ECM cells. More specifically, in Supplementary Figure S6 is presented the situation for only one mobile ionic specie i.e. oxygen vacancies (in terms of Kroeger-Vink notation). In this case the vacancy accumulation will occur only at one of the electrodes (in this case Ta). The other part of the oxide is depleted of oxygen vacancies. Of course, considering moisture or Ta 5+ ions as additional ionic species, the profiles will take the form similar to that one shown in Figure 3. As seen from the field/potential profiles the existence of enriched and depleted zones will have significant impact on the switching kinetics in terms of both thermodynamic and kinetics. In highly pure samples the ions experience the filed effect across the entire film thickness, whereas in samples with high concentration of charges the field drops only within the enriched part, leading to a slower kinetics.

S5. Effects of the parameters a and
a G   at applied external voltage. Figure S7. Energy barriers and distances during redox reaction (red) and ion transport (blue) in nanoscale systems subject to field acceleration. ΔG is the activation energy for the reaction (red) and transport (blue), and a is the distance between two positions (planes). For simplicity it is assumed that in the amorphous oxide there is only one (averaged) jumping distance for the transport. Equation 3 (main manuscript) is formally representing field dependent redox reaction and transport, having own activation barrier and jump distance. The electrode redox reaction can be also regarded as a jump of an ion from the outset metal layer and first oxide layer ( Figure S7).
The jump distance and activation energy for redox reaction and transport in the general case is expected to deviate from each other, whereas these parameters should remain the same for the ion jumps related to transport within the film, for the case of pure material. Incorporation of doping elements within the solid electrolyte can add a second jump distance/activation energy, particularly in the case that these are rate limiting.
In case of symmetric cells e.g. Pt/Cu:SiO2/Pt int   is expected to be 0 and therefore at open circuit conditions less complex charge separation is expected. However, after external voltage appl   is applied, mobile charge carriers of opposite sign (and different mobility) will be attracted to the oppositely biased electrodes and charge separation will be induced. Considering the whole cell, the electroneutrality will be kept, but locally there will be regions enriched or depleted, respectively of mobile charges, resulting in different local electric field distribution.
In addition, variations in a and a G   can also lead to inhomogeneity in the electric field distribution. The jump distance a will or can be different within the same systems for the following cases: i) a (redox) and a (transport). a (redox) is the jump distance for the redox reaction i.e. this will be the distance from the metal electrode to the first layer of the oxide. This length is usually expected to differ from the jump distance for the ion during the transport in the oxide matrix a (transport). ii) In case of chemical or structural inhomogeneity of the oxide matrix there may be more than one jumping distance. For example, if we incorporate Al-ions that attract stronger the Cu-ions (compared to intrinsic defects). In such a case Cu slower transport/jump and longer jump distance a (transport) can be defined as from Al-to-Al ion.
Structural defects such as dislocations, voids etc as well as nanocrystalline nuclei within amorphous matrix and/or agglomerations of different stoichiometry and/or composition will lead to same effect. In all these cases the activation energy is also expected not to be equal.
Thus, upon application of external voltage charges can pile up at the defect locations and locally change the electric filed distribution.

S6. Influence of the protective resistance on the recorded SET time.
Analyzing and discussing the SET kinetics we have to consider one important external factor, i.e. the input resistance used to protect the devices from overshooting and damages. Using higher resistances (more reliable in protecting the device) on samples with high permittivity may result in SET time determined entirely from the time of charging the device capacitance. This effect was observed for highly doped SiO2:(Al,Cu)1 devices. As it can be seen in Figure 4 the SET time after exceeding voltage pulses of 2 V remained constant (blue region), limited be the RC time. The higher doping concentration and induced charge separation is leading to a formation of electrochemical capacitor (see Figure 3C). This additional capacitance (~ 15 µF/cm 2 ) increases the switching time in the saturation region to about 1 ms. To avoid this effect we used for these samples 50 Ω input impedance, lowering the estimated RC time to ~6.10 -12 s, allowing to probe the actual SET kinetics of the devices.

S7. Approaching ultra-fast switching
To investigate the switching speed of the devices further below 10 ns timescale we also applied 10 ns pulses with a Picosecond PSPL2600C pulse generator and measured the current response with a Tektronix DPO73304D real time oscilloscope. The setup is similar to the one used in (47). To provide prober impedance matching at the contact pads the device was integrated into a coplanar waveguide structure. The applied voltage was set to 2 V. As the device has a high initial resistance the voltage of the applied pulse doubles over the devices stack resulting in 4V at the device. In Supplementary Figure S8   The following read pulse have confirmed the stability (non-volatility) of the ON state. It is also evidenced in Figure S8 B from the high ON state current (low resistance).

S8. Dopant concentration dependent kinetics.
The All experiments were performed on the same device within the same setup, without breaking the experiment. The complete removal of moisture has been confirmed by SIMS measurements using D2O saturated atmosphere to introduce Deuterium within Ta2O5 as a marker.
As it can be seen from Figure S9 B the switching performance of Ta/Ta2O5/Pt VCM device changes significantly when moisture is removed from the sample. Both ON and OFF resistances A .
C .
change (OFF resistance more pronounced) and also the SET voltage is significantly increased.
After introducing again air (Rh = 35%) in the chamber the I-V sweeps returned to their previous (initial) shape. This experiment clearly verifies that impurities/dopants have same influence on the switching kinetics in VCM as in ECM systems. (The influence of volatile dopants on the forming process and electrochemical behavior has been already demonstrated by us in series of papers for both ECM and VCM systems).
The effects of different impurities presented in the matrix are superimposed.
It is important to distinguish the experiment is this manuscript compared to those in Ag/SiO2 system reported in ref. 41. In the Nanotechnology paper the different concentrations that appear at the interfaces are solely result from different catalytic activity of the counter electrodes towards the counter electrode reaction. Therefore, higher catalytic activity results in higher reaction rate and lower switching time. The concentration in the SiO2 is constant (initially zero).
The formation of increased Ag-concentration at the Ag/SiO2 interface begins after the voltage is applied and depends on the catalytic activity of the counter electrode. The thickness of the oxide film plays no direct role in this process. The proposed model cannot distinguish between surface and "bulk" concentration. Butler-Volmer equation is formulated for macroscopic systems where the concertation of ionic species in the bulk and at the surface is the same (charge transfer limited process). The level of development of the model is not allowing to incorporate the counter electrode reaction (coupled to the active electrode reaction) and making the distinction.
In the present manuscript the situation is principally different. The concentration of Cu in SiO2 is different (systematically varied). An increased concentration of Cu ions at the interface as in Fig. 3C (and related charge separation) occurs only for the case of overlapping EDLs (low initial concentration of Cu in SiO2 and/or lower thicknesses of SiO2 film). This charge separation occurs before any voltage is applied. We do not change the counter electrode and therefore no difference in the catalytic activity of the electrode is present. Here, (in contrast to Nanotechnology paper) the determining factor is the initial concentration of Cu in SiO2 (we kept the thickness of SiO2 constant).