Resistive states in strontium titanate thin films: Bias effects and mechanisms at high and low temperature

A schematic of the sample setup is shown in Fig. 1(a). The surface quality was investigated by AFM in tapping mode as shown in Fig. 1(b). A smooth surface with tiny islands but without any cracks, grain boundaries or larger surface particles was observed for the thin films. The surface roughness was r_a ~ 0.2 nm.

Thin films were investigated by high-resolution X-ray reciprocal space mapping (HRXR-RSM). The corresponding reciprocal space map measured close to the (002) diffraction is shown in Fig. 1(c). The substrate peak (higher intensity) is located slightly above the layer peak which emphasizes that the out-of plane lattice parameter for the thin film is slightly greater than the one for the substrate. These findings indicate a slight non-stoichiometry of the Fe:STO thin film and are in agreement with literature [36, 37]. Cation non-stoichiometry in STO can result from preparation at high temperature where a certain equilibrium non-stoichiometry is frozen-in at temperature where cations become immobile. For techniques working at low temperatures such as PLD in this work, A:B cation ratios in perovskites which are not perfectly 1 can occur and lead to a certain low amount of cation vacancies which act as acceptor dopand and increase the lattice parameter.

Transmission electron microscopy (TEM) lamellae were prepared by focused ion beam (FIB). TEM cross section images with two different magnifications of the entire 100 nm Fe:STO layer (Fig. 1(d)) and a close-up view of the Nb:STO|Fe:STO interface (Fig. 1(e)) are shown. From the TEM images, unobstructed homoepitaxial growth is clearly shown.

The thin films were investigated by impedance spectroscopy using (LSC) microelectrodes as top contacts according to the schematic in Fig. 1(a). Nyquist-plots of the impedance response of Fe:STO thin films of different thickness recorded at 600 °C are shown in Fig. 2. Two features are clearly visible: A large, partly distorted semicircle at intermediate frequencies and one small shoulder at low frequencies. A clear dependence of the resistance of the large semicircle on film thickness can be seen. Indeed, a direct scaling of the resistance with Fe:STO film thickness was observed in the investigated temperature range. This is also visible from Fig. 3 (graphs marked “e” and “f”), where the conductivity at a certain temperature is independent of the film thickness. This is a strong indication that the large semicircle is the resistive response of the entire Fe:STO layer, despite some distortions of the arc. Additional evidence comes from the capacitance calculated for undistorted large semicircles, which agrees well with the geometrical capacitance of the Fe:STO thin film expected for a permittivity ε = 160 at 300 °C [38]. The small low frequency feature (in the 10–100 Hz range for the 413 nm layer, Fig. 2) has a larger capacitance in the order of μF/cm². No evidence of significant resistive contributions of the p-n junction at the Fe:STO|Nb:STO interface or any space charge region at the LSC electrode were found; such resistive contributions would not scale with the thickness of the thin film. A metal-insulator transition in a thin zone at the surface of Nb:STO [39] could be a possible cause of the small low frequency arc, but can be excluded as dominating resistive contribution due to its observed scaling with thickness.

Upon varying the temperature, the Fe:STO impedance response remains one single arc in the investigated temperature range 350 °C–750 °C. However, plotting this resistance in an Arrhenius diagram (Fig. 3) a clear transition at about 390 °C is visible. At higher temperatures (“e”) the investigated Fe:STO thin films show an activation energy of the conductivity of about 1.6 eV, while at lower temperatures (f) the activation energy is only about 0.8 eV. For comparison, also a polycrystalline Fe:STO sample (i.e. a pellet used as PLD target) was investigated by impedance spectroscopy. Two semicircles were found and in agreement with literature interpreted as grain and grain boundary resistances. From a brick layer model analysis [40] we obtain the grain and grain boundary conductivities shown in Fig. 3(a), (b). The values are in acceptable agreement with literature data for polycrystals with a similar doping level see Fig. 3(c), (d) [41].

It is clearly visible that the thin films investigated in this study show much lower conductivity values than macroscopic polycrystalline samples [41‐43]. Also the activation energies do not agree. Two possible causes for the observed difference between epitaxial thin films and single crystals are: (i) strain effects from thin film growth or (ii) a high dislocation density in the thin films so that the resulting space charges in the vicinity of each dislocation overlap and affect the whole film. It is beyond the scope of this paper to further clarify this point (e.g. by isotope tracer experiments over the whole temperature regime, but we assume that the high and low temperature conductivities of the thin films can be attributed to electronic (high T) and ionic (low T) conduction. Arguments in favor of the first point (electronic at high T) are earlier measurements on the bias dependence of the spectra and I-V curves [29]. There, a model based on electron conduction and redistribution of ions upon bias was able to consistently explain very unusual impedance spectra. Some aspects of this model are described below and used to further confirm consistency of our interpretation in terms of electron or ion conduction. A second argument fitting to the interpretation of electrons, as the conducting species at higher temperatures is the high activation energy (ca. 1.6 eV) which is about half the band gap. This, however, would suggest that the thin films are electronically close to the intrinsic state. The interpretation of the low temperature conductivity as ionic is supported by the activation energy, which fits to the migration barrier assumed for SrTiO₃ [41]. Two further arguments result from the additional measurements described below.

Ionic conductivity in strontium titanate is possible via oxygen vacancies, represented by δ in the stoichiometry SrTiO_3-δ. These can be created or filled via the oxygen exchange reaction.

Furthermore, the concentration of oxygen vacancies can be increased by acceptor doping.

Ionic conductivities can be calculated from oxygen tracer diffusion coefficients measured via isotope exchange depth profiling using time-of-flight secondary ion mass spectrometry (ToF-SIMS). Fig. 4 displays an isotope exchange depth profile (IEDP) found after thermal isotope exchange at 440 °C for 1080 min. The profile reveals that a LSC|Fe:STO interfacial diffusion barrier leads to an isotope concentration step between LSC and Fe:STO. However, the nature of this highly resistive interface is not clear. Analysis of the entire profile requires numerical calculation (finite elements method) to obtain the tracer surface exchange coefficient k* and the tracer diffusion coefficient D* in LSC and SrTiO₃ simultaneously in one fit. In these numerical calculations, also a thin zone at the LSC|Fe:STO interface with reduced diffusivity and a finite diffusion coefficient in Nb:STO was used. The reason for the latter is still under debate. For the comparison of tracer diffusion coefficient D ^* and bulk electrical conductivity due to oxygen diffusion, it is necessary to calculate the electrical diffusion coefficient D ^q . D ^q relates to D ^* via the Haven ratio according to Eq. 3.

The Haven ratio can be assumed to be similar to the correlation factor f_s which is 0.69 for perovskites, which was used for this study [44, 45]. Via the Nernst-Einstein equation

it is then possible to convert the diffusion coefficient into ionic conductivity values. The resulting value is plotted as star shaped data point in Fig. 3 and is close to the extrapolation of the low temperature (ionic) conductivity and thereby support the given interpretation.

As described before, oxygen vacancy formation is driven by the exchange of oxygen as well as by acceptor doping. The corresponding set of defect chemical equations for acceptor doped bulk SrTiO₃ are well established in literature [41]. Therefore, it is possible to calculate the electronic and ionic charge carrier mobilities and concentrations for a defined situation (oxygen partial pressure, temperature and doping level). The investigated parameter regime of ambient air, a temperature range from 350 to 750 °C and a doping concentration of 0.37 mol% results in a defect chemical situation where oxygen vacancies are the majority charge carriers in the bulk [7]. For our films we expect in accordance that oxygen vacancy concentrations are larger than electronic charge carrier concentrations in the whole temperature range. However, they determine the overall conductivity only at low temperatures, where only very few electronic charge carriers exist, while the high temperature regime reflects electronic conduction due to the much larger mobilities compared to ions. In such a situation, a novel electrochemical method for determining the ionic conductivities can be applied. This method was introduced in Ref. [29] and is based on potentiodynamic electrical impedance spectroscopy, which means that different DC biases are applied during the AC measurement. Both bias directions lead to non-trivial impedance spectra as indicated in Fig. 5.

A positive bias applied to the top electrode (LSC) leads to a feature at low frequencies (Fig. 5(a)) which resembles an “inductive” loop sometimes found as measurement artifact. However, this additional feature is not an artifact and can be parameterized using a negative resistance ΔR _slow and a negative capacitance C _slow , here represented by a constant phase element CPE _slow . A negative bias often leads to a semicircle-like feature at low frequencies (Fig. 5(b)). As can be seen from Fig. 2 as well as Fig. 5(a), (b), the low frequency features do not occur in impedance measurements without bias. The equivalent circuits which were used for fitting the bias dependent impedance data are shown in Fig. 5(a), (b). The additional R _HF CPE _HF element used for negative bias takes account of the more pronounced high frequency shoulder found in such cases. A detailed derivation of these circuits and of the defect chemical reasons behind the different bias features is given in Ref [29]. The features appearing under bias are caused by the different response times of electronic and ionic charge carriers adapting to the bias non-equilibrium. At high frequencies, the current response from electrons or holes is probed for a given distribution of ionic defects. Ionic charge carriers are not able to move substantial distances within a single half wave of the AC sine function. At low frequencies, long range movement of oxygen vacancies takes places also within a single AC half wave. That means, at low frequencies the redistribution of oxygen vacancies over the entire film thickness leads to a change in the local stoichiometry and resistivity of the material. This is sketched in Fig. 5(c), (d). These changes of the electronic currents cause the additional loops or semicircles at low frequencies. Hence, the appearance of the low frequency feature in impedance measurements can give information on the ionic resistance, although no ionic contribution to the current is directly probed. Following the model in Ref. [29], this ionic resistance R_ion determines the low frequency capacitance according to:

ΔR _slow and C _slow are fit parameters describing the additional low frequency loop or arc and were evaluated for the entire range of bias voltages. When assuming an ion blocking interfacial capacitance C _el , the ionic resistance becomes accessible via Eq. 5. The peak frequency of the low frequency loop or arc depends on R_ion and C_el according to:

As it can be seen from Fig. 6 the deduced ionic conductivity has only a minor dependence on the bias. This is in good agreement with the assumption that oxygen vacancies are the majority charge carriers. In other words, the redistribution of ionic charge carriers as a reaction to the applied bias, is small in comparison to the total concentration of oxygen vacancies within the thin film. The distinct response of electronic charge carriers on the bias and thus on the ionic redistribution can be explained by the small concentration of these charge carriers. To get information on the non-biased ionic conductivity, the ionic conductivity values in Fig. 6 are extrapolated to 0 V resulting in an ionic conductivity of 1.7 × 10⁻⁹ S/cm for 450 °C. When applying this procedure to the different film thicknesses at varying temperature, we obtain the ionic conductivities shown in Fig. 3(h). An ion blocking interface capacitance of ~20 μF/cm² was assumed according to a relative permittivity of ε ~ 100 and a typical ionic space charge thickness of ~4 nm. Despite some scatter, the data are in excellent agreement with the extrapolation of the low temperature zero bias conductivities. This agreement further supports the interpretation of low temperature conductivities as ionic conductivities. Electronic conductivities can still be evaluated from the high temperature arc and are strongly bias dependent in agreement with our model.

At elevated temperatures only a constant applied bias voltage can sustain the redistributed state of oxygen vacancies. Changing or removing the voltage immediately leads to an adaption of the charge carrier distribution to the new situation. This makes probing of a certain resistive state difficult. “Slow” I-V curves conducted at these temperatures probe a different vacancy distribution and thus a different resistive state in each voltage point. The continuous change of the voltage during such DC measurement results in a continuous charge carrier redistribution within the layer. In addition to the electrically driven movement of the ionic charge carrier, their increased mobility due to thermal activation is responsible for the fast changes of the charge carrier distribution. At high temperature, there is a maximum time allowed for probing a given resistive state by a “fast” I-V curve without changing the state. This time was estimated from the impedance spectra: a frequency higher than the onset of the low frequency feature (loop or arc) has to be taken to avoid redistribution of ions. Thus times <ms result above 700 °C. Consequently, in the higher temperature regime we could not access particular resistive states via I-V measurements.

I-V curves were also measured for the intermediate temperature regime (<500 °C), see Fig.3. For “slow” I-V curves the scan rate corresponds to a frequency smaller than the frequency points for which in impedance spectra the real axis is reached for low frequencies. Only then, a new steady state can be ensured in each voltage point. The most important defect species to form the new steady state are oxygen vacancies, however, for a more complete picture complex defect associates and negative frozen-in metal vacancies need to be considered [30, 46]. By taking into account that the mobility of all ionic charge carriers is reduced at lower temperatures, it becomes obvious that the required time for “slow” I-V curves increases with decreasing temperature and may reach the range of days. On the other hand, the reduced mobility of oxygen vacancies now offers the opportunity to probe the charge carrier distribution in a “frozen-in” situation and thus particular resistive states. Such states can be realized by applying a bias voltage for a finite time. Within this time a constant current is reached which is associated to a distinct charge carrier distribution. Other than at high temperature, this embossed state can now be probed by “fast” I-V measurements: The appropriate time for “fast” I-V curves is again evaluated from impedance spectra conducted at a given bias voltage, see above. At lower temperatures, the required sweep rate shifts into the range of seconds and is therefore experimentally accessible.

Such fast conducted I-V measurements reflect the properties of dedicated resistive states. Different resistive states were adjusted by different voltages and probed for a 200 nm sample at 425 °C (T_set), which is shown for the anodic case in Fig. 7(a) and for the cathodic case in Fig. 7(b). For comparison, the slow I-V curve for the same temperature is also given. The slight voltage off-set for the open circuit condition (slow I-V curve) can be attributed to the asymmetric heating /thermovoltage within the experimental set-up. The off-sets of the fast I-V curves are predominantly due to hysteretic effects.

It becomes obvious from Fig. 7 that the established resistive state can be probed by fast I-V curves but does not sustain more than one cycle, which is in contrast to non-volatile resistive switching at room temperature. Already conducting a cycle after an anodic bias, i.e. sweeping from positive to negative and back to positive voltage results in a small change of the measured current. In other words, the charge carriers still slightly adapt to the changing voltage, which results in a small redistribution accompanied with a changed current. Subsequently applied constant voltage and repeating the measurement after reestablishing steady state yields again the same I-V curves. Irreversible effects could therefore be excluded as cause for the observed resistance changes. This behavior was found despite the fact that the appropriate sweep rate for a “fast” I-V curve is easily accessible in the anodic case, due to the fact that impedance data points cross the real axis. Therefore, the frequency point without phase shift can be exactly determined and transferred into a sweep rate. The slight change in the current probably originates from the fact that this appropriate sweep rate depends on bias voltage which changes during the measurement.

We could further monitor that fast conducted I-V curves starting in the cathodic regime strongly depend on the sweep rate. This can be attributed to the fact that there is no intercept with the real axis in the corresponding impedance spectrum, see Fig. 8. The two recorded semicircles overlap, which makes it hard to evaluate the appropriate frequency, as there is no frequency without phase shift in that range. Therefore a sweep rate without additional effects does not exist. Also for the most appropriate frequency, the recorded fast I-V curve in Fig. 8(b) does not reflect a true frozen-in defect chemical situation. It rather contains contributions either of the charging of the geometrical capacitance, more pronounced for higher sweep rate, see Fig. 8(a), or the redistributing of oxygen vacancies due to the AC signal for lower sweep rates shown in Fig. 8(c).

Regardless of the observed differences between the anodic and cathodic regime, bias induced motion of oxygen vacancies plays an important role in the establishment of resistive states at these temperatures.

In most oxygen ionic devices, temperatures above 300 °C or higher are typically necessary for devices to function. The reason for that is the relatively high migration barrier that oxygen ions have to overcome in most materials. All alterations of the resistive states at high temperatures are enabled by the substantial mobility of ionic charge carriers. At room temperature it is also possible to alter resistive states by redistributing ions, however, a large driving force in the form of a strong electric field is necessary to overcome the very low ionic mobilities. Via such an effect of large electric fields, non-volatile resistive switching of SrTiO₃ is possible at room temperature in ambient conditions [23, 47]. For surpassing today’s transistor-based memory technology, this requires long retention of more than 10 years of the resistive states at low bias and fast switching within nanoseconds at large electric bias. This “voltage-time dilemma” [23] is one of the central challenges for using resistive switching as novel memory technology.

Resistive switching was already shown in literature for SrTiO₃-based devices [25, 26, 48‐50]. Therefore, the resistive response of our Fe:SrTiO₃ thin films was also investigated under ambient conditions at room temperature and higher electric field strengths using differently sized microelectrodes of Pt and LSC. In Fig. 9, ten current voltage cycles (±3 V, 100 mV/s) of a 200 nm Fe:STO thin film with 200 μm diameter Pt top electrode are exemplarily shown. Resistive switching is reproducibly observed over all 10 cycles, however, a slight drift of the currents in the ON- and OFF-state to lower values is found over the 10 cycles. The average resistance values of the two resistive states at low voltages were R _ON  = 28 kΩ, R _OFF  = 150 kΩ and the R_OFF/R_ON ratio is consequently about 5.

In a following screening study, different circular Pt or LSC microelectrodes with 50–200 μm diameter were investigated. A large number of microelectrodes (> 60) was measured, each by 3 cyclic voltammetry cycles of ±4 V with 200 mV/s sweep rate, starting with positive bias applied to the top electrode. All investigations were done without pretreatment or a forming step as often described in literature. Several results were obtained from this screening study: (i) No hysteretic resistive switching curves were observable with LSC as top electrode. (ii) 16 out of 40 (40%) Pt top electrodes showed reproducible resistive switching curves in all cycles (cf. Fig. 9), while the remaining film regions with Pt top electrodes typically remained in a high resistive state. (iii) No dependence of the low resistive (ON) state on the electrode diameter was found. ON currents were about −2 to −3 mA at −4 V bias for the different electrode sizes as shown in Fig. 10 for all electrodes exhibiting resistive switching. (iv) A higher fraction of samples showing resistive switching was found for larger top electrode diameters (3/10, 30% for 50 μm; 6/15, 40% for 100 μm, 7/15, 47% for 200 μm).

(i) The reasons why resistive switching does not occur in the LSC|Fe:STO|Nb:STO devices is not immediately clear. The fact that the current-voltage curves with LSC are similar to those in the ON-state with Pt-electrodes leads to the conclusion that switching from ON to OFF state is not possible with LSC. Two main differences exist between Pt and LSC top electrodes: the band energies and therefore the resulting space charge in Fe:STO close to the interface and the fact that LSC is a better oxygen ion conductor than Pt. Either of those properties seems to prevent interrupting the low resistive ON state to form the OFF state at large positive biases with LSC.

(ii),(iv) The typical resistive switching mechanism in SrTiO₃ is via conductive filaments as described in literature. Characteristic features of this mechanism such as current fluctuations at switching from ON to OFF (+1.5 V to +2.5 V in Fig. 9) and from OFF to ON (−0.9 V to −1.5 V in Fig. 9) are also directly observable from our current-voltage curves. The fact that the ON state is independent of the electrode size as shown in Fig. 10 is another strong indication that switching is filament-type: Independent of the electrode size, just one conductive filament enables a current of about 2–3 mA at 4 V in the ON state.

(iii) The rather low total success rate for resistive switching in Pt|Fe:STO|Nb:STO and the dependence of this rate on the electrode size are connected. Resistive switching without a forming step typically requires some critical defects or proto-filaments which can form a conductive filament upon switching. In the measured samples we expect very few of such critical defects due to the homoepitaxial growth. Indeed, more often such critical defects seem to be present in SrTiO₃ regions beneath electrodes with larger size, which explains their higher rate of resistive switching. The majority (60%) of investigated microelectrodes remained in a high resistive state and didn’t show switching. We interpret those film regions to be free of such critical defects. This, however, does not mean that they cannot be utilized for resistive switching. Forming procedures (high applied currents or voltages over an extended time period) are often used to create proto-filaments in thin films that would otherwise not show resistive switching. We expect that by such a forming step the number of microelectrodes that show switching would increase significantly.