Trap‐Assisted Memristive Switching in HfO2‐Based Devices Studied by In Situ Soft and Hard X‐Ray Photoelectron Spectroscopy

Memristive devices are under intense development as non‐volatile memory elements for extending the computing capabilities of traditional silicon technology by enabling novel computing primitives. In this respect, interface‐based memristive devices are promising candidates to emulate synaptic functionalities in neuromorphic circuits aiming to replicate the information processing of nervous systems. A device composed of Nb/NbOx/Al2O3/HfO2/Au that shows promising features like analog switching, no electro‐forming, and high current‐voltage non‐linearity is reported. Synchrotron‐based X‐ray photoelectron spectroscopy and depth‐dependent hard X‐ray photoelectron spectroscopy are used to probe in situ different resistance states and thus the origin of memristive switching. Spectroscopic evidence for memristive switching based on the charge state of electron traps within HfO2 is found. Electron energy loss spectroscopy and transmission electron microscopy support the analysis. A device model is proposed that considers a two‐terminal metal–insulator–semiconductor structure in which traps within the insulator (HfO2/Al2O3) modulate the space charge region within the semiconductor (NbOx) and, thereby, the overall resistance. The experimental findings are in line with impedance spectroscopy data reported in the companion paper (Marquardt et al). Both works complement one another to derive a detailed device model, which helps to engineer device performance and integrate devices into silicon technology.


Introduction
Today's digital computers are based on a separation of memory and computation. Thus, data has to be continually transferred from the memory location to the location of computing and vice versa in traditional computing architecture, leading to high latency and energy consumption. [1][2][3] One potential concept to overcome this so-called von Neumann bottleneck for certain applications is the development of neuromorphic computing architectures, which aim to emulate information processing in the human brain. [4][5][6][7] In biology, information processing takes place in huge networks of neurons and synapses, without physical separation between computation and memory, [8] leading to an impressive performance in tasks like sensory processing, motor control, and pattern recognition, [9] while at the same time consuming less energy, orders of magnitude lower than digital computers require to conduct similar tasks. [5,6,10,11] Memristive devices are under intense development as non-volatile memory elements for extending the computing capabilities of traditional silicon technology by enabling novel computing primitives. In this respect, interfacebased memristive devices are promising candidates to emulate synaptic functionalities in neuromorphic circuits aiming to replicate the information processing of nervous systems. A device composed of Nb/NbO x /Al 2 O 3 / HfO 2 /Au that shows promising features like analog switching, no electroforming, and high current-voltage non-linearity is reported. Synchrotronbased X-ray photoelectron spectroscopy and depth-dependent hard X-ray photoelectron spectroscopy are used to probe in situ different resistance states and thus the origin of memristive switching. Spectroscopic evidence for memristive switching based on the charge state of electron traps within HfO 2 is found. Electron energy loss spectroscopy and transmission electron microscopy support the analysis. A device model is proposed that considers a two-terminal metal-insulator-semiconductor structure in which traps within the insulator (HfO 2 /Al 2 O 3 ) modulate the space charge region within the semiconductor (NbO x ) and, thereby, the overall resistance. The experimental findings are in line with impedance spectroscopy data reported in the companion paper (Marquardt et al). Both works complement one another to derive a detailed device model, which helps to engineer device performance and integrate devices into silicon technology.
However, spectroscopic evidence for the proposed switching mechanism is often missing.
Among a multitude of different methods to probe memristive switching, [44] transmission electron microscopy (TEM) together with energy electron loss spectroscopy (EELS), [45] and photoelectron spectroscopy (PES) [46] are widely used techniques to study structural, chemical and electronic properties of the material systems. In particular, X-ray photoelectron spectroscopy (XPS) [46] and hard X-ray photoelectron spectroscopy (HAXPES) [47] allow to probe film compositions, chemical states, band alignment as well as band bending in buried layers and their dependence on depth. [46,48,49] Hard X-rays (>2 keV) from synchrotron sources with orders of magnitude higher photon flux compared to laboratory sources provide an information depth of up to a few 10 nm while simultaneously allowing for reasonable energy resolution. [47] Furthermore, non-destructive depth profiling is possible with XPS/HAXPES by collecting photoelectrons that are ejected with different angles of emission. [46,47] Thus, XPS and HAXPES allow in situ and in operando investigations of memristive switching processes [50][51][52][53][54][55] in functional devices, where switching takes place within a few 10 nm below the sample surface.
Memristive devices based on metal oxides are often composed of oxide bi-or multi-layers sandwiched between two metal electrodes. [22,33,42,43,[55][56][57][58][59][60][61][62] One oxide serves as an active switching material, while the other oxides act, for example, as diffusion barriers, [33,57,62] as oxygen ion reservoirs, [22,55,59] as rectification layers, [43,56,60,61,63] or affect the local heat distribution, [59] thus significantly improving the device characteristics. Within this work, an analog switching interface-type memristive device consisting of the layer sequence Nb/NbO x /Al 2 O 3 / HfO 2 /Au (see Figure 1) is investigated. HfO 2 is widely investigated and applied as an active switching layer in memristive devices [22,38,39,42,[50][51][52][53][54][55][56]62,63] due to its CMOS compatibility. [64] Among other applications, hafnia is used as a gate dielectric for metal-oxide-semiconductor field-effect transistors (MOS-FETs), [64,65] as charge trapping layer in charge trap flash (CTF) memory, [66] and as an active layer in CMOS-integrated filamentary-type resistive random access memory (RRAM) devices. [38,39] On the other hand, Al 2 O 3 is reported to serve as a diffusion barrier for oxygen ions [33,57,58,62] which can lead to an enhanced retention time of interface-type memristive devices, and simultaneously suppress an oxygen exchange with adjacent layers. [33] Alumina is also compatible with CMOS technology. [62] Furthermore, stoichiometric Nb 2 O 5 is known to be a good insulator, [67] but oxygen-deficient films are reported to show n-type semiconducting behavior. [67,68] Thus, a NbO x layer can in principle be used to fabricate rectifying metal-semiconductor (MS) or metal-insulator-semiconductor (MIS) devices. [69,70] The investigated Nb/NbO x /Al 2 O 3 /HfO 2 /Au device is based on similar devices with a NbO y layer instead of HfO 2 . [33] The Schottky barrier of the NbO y /Au interface was reported to be altered by the drift of negatively charged oxygen ions, while the probability for tunneling through the Al 2 O 3 is simultaneously affected, [33] as modeled by a kinetic Monte Carlo simulation, [71] and a cloudin-a-cell (CIC) scheme [72] that also covers the device variability. Furthermore, the charging and discharging of interface trap states are also reported as a possible mechanism responsible for memristive switching. [33] The integration into passive crossbar arrays [41] and the utilization as artificial synapses in neuromorphic networks for pattern recognition tasks have already been reported for the devices based on NbO y as the active layer. [19,41] Here, the origin of memristive switching in the HfO 2 -based devices is investigated by depth-dependent synchrotron-based HAXPES and synchrotron-based XPS with soft X-rays. Varying the recorded angle of emission ϑ allowed for non-destructive depth profiling of chemical and electronic properties. The measurement setup is schematically illustrated in Figure 1. In combination with structural data from TEM, chemical information from EELS, and current density versus voltage (J-V) characterizations, a model to qualitatively describe the physics of the interface-based memristive device is proposed in this manuscript: A two-terminal MIS structure, in which electron traps within the insulator modulate the space-charge region within the semiconductor and, thereby, the Schottky barrier height, is consistently used to explain the findings from all experiments. In particular, we identify a causal relationship between the charge-trapping state of HfO 2 and the overall device resistance. Spectroscopic evidence (by XPS/HAXPES) for such a switching mechanism has not been reported so far. Furthermore, impedance spectroscopy (ImpSpec) [73] is exploited by Marquardt et al. in a companion paper [74] to probe memristive switching in the same device. The findings presented in both papers indicate that the memristive switching can be attributed to a Schottky barrier modulation by a charge-trapping mechanism. The obtained device model is advantageous for both device integration into silicon technology to exploit the benefits of hybrid memristive-CMOS neuromorphic circuits and engineering of device characteristics for specific applications. In this respect, some design rules for CMOS integration are provided at the end of this work.

Electrical Characterization
Typical semi-logarithmic current density versus voltage (|J|-V) characteristics of devices from the reference wafer (see Experimental Section for fabrication and characterization details) with a top electrode size of 625 µm 2 are presented in Figure 2a.
Here, the mean behavior of ten adjacent devices is depicted in black, while the characteristics of single devices are drawn in gray. The inset of Figure 2a shows the mean |J|-V characteristics for low applied voltages (±1.2 V). The hysteresis observed for small current densities arises from capacitive effects of the measurement setup since only noise is detected and no memristive switching takes place. As it is shown in Figure 2a, higher voltages (± 3.7 V) induce memristive switching. The diode-like electrical properties allow for integration into passive crossbar arrays without requiring additional selector devices. [41] Furthermore, no initial electro-forming or current compliance is needed to operate the devices and the observed smooth hysteresis reveals analog switching. Such analog interface-type memristive devices can be used for emulating synaptic functionalities, as reported for various devices. [15,17,19,22,42] In particular, devices with a similar material stack produced with the very same processes but containing a sputtered NbO y layer instead of HfO 2 [33] show similar electrical characteristics. The possibility of using these NbO y -based devices for the emulation of synaptic functionalities has been shown experimentally on both the device level [18,19] and the network level. [41] The area-dependent current transport is shown in Figure 2b. Here, the resistance mean value and standard deviation of ten neighboring devices per area for a bias voltage of 1.2 V are depicted. The resistance scales linearly with the area of the device in the high resistance state (HRS) and in a low resistance state (LRS). Thus, homogeneous current transport through the whole device area is indicated for both HRS and LRS.
The relaxation of the LRS toward higher resistances is shown in Figure 2c as red circles. The device is set to an LRS by applying a positive voltage sweep with V max = 3.7 V and the device resistance R is read out with 0.5 V voltage pulses of 4 s length after the set sweep, and with delay times of 300 (next 12 pulses), and 1800 s (all further pulses). R is further divided by the initial resistance R 0 , which is determined as the mean of ten consecutive read out pulses prior to switch the device. The resistance increases with time so that it approaches R 0 in ≈25.5 h and does not increase further in the next 13 h. The relaxation process can be fitted with a power law of the form ∝t α , as reported for other memristive devices, [22,30,33,34] as well as for describing charge trapping under bias in HfO 2 . [75] In Figure 1. Schematic illustration of the HAXPES measurement setup and the probed devices: An X-ray beam is directed onto the sample surface. The kinetic energies of electrons ejected at specific polar angles of emission ϑ are measured. During HAXPES measurements, the device electrodes are connected to common ground with the analyzer to ensure charge compensation and to obtain defined electrostatic conditions within the device. The memristive state can be read out and switched in the vacuum chamber by connecting a source measurement unit to the electrodes. When voltages were applied, the beam was never directed onto the sample.
www.advelectronicmat.de particular, a power law with α = 0.46 fits well the LRS retention characteristics. An α between 0.18 and 0.57 is reported for similar devices, [22,30,33,34] while filamentary devices based on HfO x show a much longer retention time with α = 0.02. [22] After measuring the relaxation process of the LRS resistance, the device is switched to an even higher resistance by applying a negative voltage sweep with V min = −3.7 V, and the resistance is read out with the same procedure as the LRS resistance. No distinct trend can be observed in the resistance evolution but a drift toward R 0 is expected on a longer time scale, since the resistance evolution of the LRS does not reveal a further drift toward the HRS resistance. The origin of the rather strong fluctuations in the HRS resistance evolution is unknown and needs to be further investigated in the future. It should be emphasized that the HRS resistance is rather close to the initial resistance (R HRS ≈ 3 × R 0 ) while most of the switching window can be attributed to the difference between the initial resistance and the LRS (R LRS ≈ 0.01 × R 0 ). A much longer retention time of typically more than 10 years is needed for memory applications, [76] but shorter retention times are expected to be beneficial for certain neuromorphic applications. [11] In particular, processing real-world data with spiking neural networks (SNNs) requires not only non-volatile memory elements but also volatile memristive devices with times-scales in the order of the time-scales of the data. [14] One example is reported by Park et al., who utilize volatile analog memristive devices as short-term memory in leaky-integrate-and-fire (LIF) neurons to process sequential data. [77] However, a long retention time is needed for inference in a pattern recognition task. [78,79] Thus, the retention time of the here reported devices has to be enhanced for this application. Nevertheless, the training of pattern recognition networks can be done with memristive devices with moderate retention times, [78,79] as already shown with interface-type memristive devices. [41] Table 1 further provides a comparison between the devices presented here and those previously reported in literature with similar metal-oxide-based interface-type devices. [30,32,33,42,77] We consider devices that comprise an area-dependent resistance in both HRS and LRS, and that require no external current compliance during switching. The first column of Table 1 shows the devices' material stacks. The electrical parameters extracted from the current-voltage hysteresis curves are the switching window ΔR = R LRS /R HRS measured with a typical read-out voltage V read , the highest positive and lowest negative voltage used to record the evaluated hysteresis curves (V sw, LRS and V sw, HRS ), the maximum absolute value of the current density flowing during switching |J sw, max | (i.e., during switching to LRS for all compared devices, thus |J sw, max | = J sw, LRS, max ), the ratios ΔJ sw of the maximum absolute value of the current densities flowing during switching to LRS |J sw, LRS, max | and HRS |J sw, HRS, max |, and the absolute value of the current density flowing during read-out the HRS |J read, HRS |. Furthermore, the retention characteristics at room temperature are compared in two ways. The next to last column provides ΔR, measured after a certain time has elapsed since switching. The last column contains the coefficient α of the ∝t α power law used for fitting the relaxation kinetics (if available). nm are determined, respectively. The NbO x /Al 2 O 3 interface is rough relative to the film size, leading to local Al 2 O 3 thickness variations between ≈2 and 7 nm. Such roughness is also observed in Nb/ Al-based tunnel junctions. [85,86] All other interfaces are smooth due to the planning effect of Al on Nb. [85,86] In a high-resolution (HR) STEM image (see Figure S1, Supporting Information), the HfO 2 appears to be polycrystalline, while Al 2 O 3 and NbO x are amorphous. It should be noted that HRTEM measurements of similar functional devices show amorphous HfO 2 (data not shown). Thus, it is expected that the crystalline state is not crucial for memristive switching.
EELS data of the entire layer sequence are shown in Figure 3b, Supporting Information. Here, a line scan of the O-K edge with a vertical step size of 1.75 nm is depicted. The whole HfO 2 and Al 2 O 3 appear fully oxidized, and the Nb bottom electrode is also oxidized at the interface to Al 2 O 3 , as previously reported for similar devices. [80] The spectra of the O-K edges indicate stoichiometric HfO 2 and Al 2 O 3 , as shown when compared to reference spectra. [81,82] Moreover, an excess of oxygen may be indicated in the center of the Al 2 O 3 layer by the pre-peak of the Al 2 O 3 -related O-K spectra in Figure 3b, Supporting Information. The O 2 seems to be molecular [82,87] or incorporated as peroxide groups, [88] that is, O-O bonds since both can produce the observed pre-peak. We, therefore, interpret this pre-peak as an excess of oxygen. It should be noted that the pre-peak is not stable within the electron beam, as shown in Figure S2, Supporting Information. Moreover, at the same position in the alumina layer, incorporated Ar is found by EELS (see Figure S3, Supporting Information) and energydispersive X-ray spectroscopy (data not shown). Since devices without an Al 2 O 3 layer show similar memristive switching, as shown in Section 3.1, the elements incorporated into alumina are expected to be not crucial for memristive switching. However, these defects could potentially decrease the overall electrical resistance of the Al 2 O 3 layer. The electron energy-loss near-edge structure (ELNES) of NbO x close to the Al 2 O 3 interface can be attributed to a mixture of Nb 2 O 5 and NbO 2 since fingerprints of both reference spectra can be found. [67] Moreover, the intensity of the O-K edge decreases with an increasing distance to Al 2 O 3 , suggesting a continuously decreasing oxygen content in the NbO x . Note that the ELNES of the NbO x after the O-K pre-peak has vanished (due to electron irradiation) and now resembles more Nb 2 O 5 , which could suggest an in situ oxidation of the Nb electrode induced by the electron beam. The low-loss region of the hafnia layer is further analyzed. The corresponding spectra are shown in Figure 3c, together with reference spectra. [83] Despite the broad peak at 34 eV, due to a collective excitation, [89] the HfO 2 spectra show distinct peaks characteristic for the monoclinic structure. The intense plasmon peak at 23 eV, which is sensitive to the oxygen concentration, [83,90] indicates stoichiometric rather than substoichiometric hafnia. Figure S3, Supporting Information shows the evolution of the low-loss regime within the HfO 2 layer. The intensity differences of the plasmon peaks might be due to an oxygen gradient [91] or result from the overlapping low-loss regime of Au and Al 2 O 3 . These cases cannot be distinguished due to the very small dimensions and the roughness of the films. Figure 3d depicts the Al L 23 edge measured from the Al 2 O 3 , which matches well the ELNES of stoichiometric Al 2 O 3 . [84] For comparison, the L 23 edge of metallic aluminum is shown, depicting an onset at 4 eV lower energies and a different ELNES than Al 2 O 3 .

X-Ray Photoelectron Spectroscopy
XPS and HAXPES measurements were performed at the synchrotron radiation facility PETRA III of DESY (Hamburg,

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Germany) by employing the experimental photoemission endstation ASPHERE III (beamline P04 [92] ) and the HAXPES endstation at beamline P22, [93] respectively. Details on energy referencing, peak fitting, and in situ electrical characterization can be found in Experimental Section, together with the sample design enabling PES on functional memristive devices (see also Figure S4, Supporting Information). The fabrication of the devices is also described in detail in Experimental Section.

Soft X-Ray Photoelectron Spectroscopy
A memristive device with a 6 nm thin Au top electrode is switched in situ from a high resistance state (HRS1) to a low resistance state (LRS) and back to a high resistance state (HRS2). Au 4f and Hf 4f core-level spectra for all resistance states are measured. A typical Au 4f spectrum is shown in Figure S5, Supporting Information together with a |J|-V curve measured in situ, which indicates memristive switching. The Hf 4f spectra mainly stem from the Au/HfO 2 interface due to an inelastic mean free path λ of the Hf 4f electrons in Au of 1.8 nm estimated using the TPP-2M formula with the parameters provided in ref. [94]. Since ≈95% of the signal intensity originates within 3λ, [95] only the HfO 2 near the Au interface can be probed. The Hf 4f spectra are shown in Figure 4. Here, a linear function models most accurately the background (gray solid lines   [81] amorphous Al 2 O 3 , [82] Nb 2 O 5 , [67] and NbO 2 . [67] c) EELS low loss region of HfO 2 (black solid line: mean value of 36 measurements on adjacent positions, which are shown as gray solid lines) together with reference spectra. [83] d) EELS Al L 23 of Al 2 O 3 (black solid line: mean value of 36 measurements on adjacent positions, which are shown as gray solid lines) together with reference spectra for alumina and metallic aluminum. [84] www.advelectronicmat.de back again leads to BE shifts of 110 ± 10 meV, with a higher BE for LRS. The difference between HRS1 and HRS2 being within the error margins shows that the core-level switches back to its initial BE. All peaks can be attributed to Hf 4 + species in HfO 2 with reported BEs between 16.3 and 18.5 eV [48,[51][52][53][54][55][96][97][98][99][100] dependent on, for example, the band alignment with adjacent layers or the amount of charges within HfO 2 or adjacent layers. No additional spectral features attributed to sub-stoichiometric HfO x can be seen, which appear at lower BEs corresponding to metallic Hf with a shift of 2.6-3.8 eV, [51][52][53]96,97] and to hafnium sub-oxide with smaller shifts. [52][53][54]96,97,101] As such a signal is linked to filamentary-switching [51][52][53][54] with an oxygen vacancy concentration of typically 10 21 cm −3 , [102] this shows that the oxygen vacancy concentration in our devices is lower than in filamentary-based devices. This is in agreement with the EELS data indicating stoichiometric HfO 2 . Also, additional spectral shape changes commonly observed in the case of chemical changes [55,101] are absent from our spectra. Note that quantitative analyses of the material composition using XPS can lead to an error of less than 5% under best experimental conditions, while relative changes in the composition of less than 1% can be detected, [103] which defines the resolution of XPS. Moreover, while BEs shift of the order of +100 meV, similar to these observed here between HRS and LRS, can be attributed to an additional amount of oxygen vacancies, [101] the hypothesis of such a chemical change can be excluded for the devices studied here (even though the signal-to-noise ratio of the presented Hf 4f peaks is low) as the positive bias applied to the Au top electrode cannot lead to an accumulation of (positively charged) oxygen vacancies near the Au interface. Hence, the BE shift toward higher energies in LRS can be attributed to an increased electrostatic potential near the Au interface, the origin of which is discussed in Section 3.2.
Finally, no defects caused by the X-ray radiation during XPS measurement are observed since no radiation-time dependent spectral shifts or additional spectral features, similar to those reported for in operando measurements on ferroelectric Pb(Mg 1/3 Nb 2/3 ) 0.72 Ti 0.28 O 3 (PMN-PT), [104] are detected here.

Depth-Dependent Hard X-Ray Photoelectron Spectroscopy
Non-destructive depth profiling was done via HAXPES on a memristive device with a 13 nm thin Au top electrode. The measured angle of emission ϑ was varied (see Figure 1), leading to the highest information depth for small angles. All HAXPES spectra of Au 4f , Hf 3d 5/2 , and Al 1s were recorded for three different ϑ and two different resistance states (HRS and LRS) switched in situ. The depth-dependent measurements are called "surface sensitive" (ϑ = 15°), "sub-surface sensitive" (ϑ = 41.4°), and "bulk sensitive" (ϑ = 60°) throughout this work. Since the Au top electrode is relatively thick (13 nm), the signalto-noise ratio of Hf 3d 5/2 and Al 1s decreases significantly with increasing surface sensitivity (i.e., increasing detection angles). The HAXPES recording of spectra with a good signal-to-noise ratio required approximately between 1 and 3 h. Since the LRS significantly relaxes toward the HRS within several hours (see. Figure 2c), the measurement time had to be constant (≈1 h) to ensure that all measurements reflect the same memristive state. Hence, spectra for 41.4° (sub-surface sensitive) and 60° (surface sensitive) were measured two and three times, respectively, and were merged afterward to enhance the signal-to-noise ratio, while the memristive state was refreshed in between (see Experimental Section and Figure S6a, Supporting Information). No Al spectra were evaluated for 60°, and no NbO x spectra were measured for any ϑ due to the limited information depth of HAXPES. Furthermore, no radiation-induced defects were observed in the HAXPES spectra.
A typical Au 4f spectrum is shown in Figure S6b, Supporting Information. Figures S7 and S8, Supporting Information show the raw spectra and the determined backgrounds for Hf 3d 5/2 in HRS and LRS, respectively. The raw Al 1s spectra for HRS and LRS are shown in Figures S9 and S10, Supporting Information, respectively. The merged Hf 3d 5/2 and Al 1s spectra, together with the peak fits, can be found in Figures 5a and 5b for Hf 3d 5/2 and Al 1s, respectively, for both HRS and LRS. All spectra show single peaks. The BE and FWHM of the resulting fits are shown in Figure 5c for merged Hf 3d 5/2 and Al 1s, respectively, in both HRS and LRS. Error bars denote standard deviations, which are determined by the fitting algorithm. All fitting parameters can be found in Table S11, Supporting Information.
The Hf 3d 5/2 core-level is first investigated in HRS as a function of the angle of emission, revealing BEs between 1662.08 and 1662.28 eV, which can be attributed to Hf 4 + . [51,100,105] Again, no indication of metallic Hf, and therefore no indication for www.advelectronicmat.de a significant amount of vacancies is detectable. In contrast, filamentary-type Hf x Al 1−x O y memristive devices show a peak feature at 1660.6 eV. [51] Furthermore, the BE increases at larger angles of emission, that is, closer to the Au interface. At the same time, the FWHM does not vary significantly between the sub-surface sensitive and the bulk sensitive measurement. The spectral shape also does not vary, and a chemical difference being responsible for the BE gradient can be excluded. [55,101] Hence, a variation in the electrostatic potential is deduced to be accountable for the BE variation. [48,49] Since the bulk sensitive spectrum is very noisy, the higher FWHM should not be attributed to a chemical change (see Table S11, Supporting Information).
For Al 1s in HRS, BEs of 1561.77 and 1561.95 eV are extracted for the bulk sensitive and the sub-surface sensitive measurement, respectively, indicative of Al 2 O 3 since BEs for alumina (Al 3+ ) are reported between 1562.6 and 1563 eV. [106,107] No features of metallic Al are present, which are reported between 1559.6 and 1559.8 eV. [107,108] A similar BE gradient as detected in HfO 2 is visible, suggesting a decreasing electrostatic potential with increasing distance to hafnia. It should again be noted that the noise significantly impacts the peak form of the sub-surface sensitive Al 1s spectrum at 41.4° (see Table S11, Supporting Information).
Next, Hf 3d 5/2 peaks are evaluated in the LRS. Again, no metallic Hf feature is present (see Figure 5a). BEs shift to higher energies by ≈120 and 70 meV for bulk sensitive and sub-surface sensitive measurements, respectively, as shown in Figure 5c. No significant BE shift can be measured for the surface sensitive spectrum. However, the standard deviations for both HRS and LRS are larger than 70 meV for the surface sensitive measurements so that any BE shift below this value cannot be reliably resolved. Nevertheless, an obvious trend is visible toward higher BE in LRS, with the most pronounced shift near Al 2 O 3 . The FWHM for bulk sensitive and subsurface sensitive measurements do not change, and no additional peak features appear ( Figure S12a, Supporting Information). Thus, no electrical bias-induced chemical change can be detected. [55,101] The shifted BE is hence attributed to a change in the electrostatic potential within hafnia toward a higher potential in LRS. No additional peak features are present for Al 1s as well (see Figures 5b and S12b, Supporting Information). Here, www.advelectronicmat.de for 15° (bulk sensitive) and 41.4° (sub-surface sensitive), the BEs shift in opposite directions (see Figure 5c). Near HfO 2 , the BE shifts by −40 meV (41.4°), and deeper in Al 2 O 3 , the BE shifts by +40 meV (15°). However, the BE difference between HRS and LRS for 41.4° (near HfO 2 ) is within one standard deviation of the uncertainty of the fit. The peak width is getting smaller in LRS (≈0.1 eV) for the bulk sensitive spectrum. The peak shape of the sub-surface sensitive measurement is not evaluated as explained above. Altogether, the BE variation in alumina can be ascribed to a variation in the electrostatic potential. In particular, the potential decreases at the HfO 2 interface and increases further inside in LRS.

Current Transport Mechanism
The |J|-V curves (Figure 2a) show a high non-linearity and a rectification of several orders of magnitude. This can be attributed to a Schottky-like contact which can form due to a direct metal/semiconductor contact but can also be established with a thin oxide layer between metal and semiconductor. [69,70] In particular, a Pt/HfO 2 (5 nm)/n-GaAs Schottky diode has already been reported. [109] According to literature, current transport in the devices under study can thus be attributed to thermionic emission [69,70,109] for low applied voltages (but above a memristive state-dependent threshold) in combination with an intrinsic current compliance dominant for high voltages (see Section S13, Supporting Information for a more detailed explanation), as also reported for similar devices. [33] A positively charged space charge region (SCR) within an n-type semiconductor is consistent with the positive forward bias on the high work function Au top electrode. Thus, the electrostatic potential in the semiconductor increases with the distance to Au. In contrast, the potential within HfO 2 and Al 2 O 3 decreases with distance to the gold electrode for both memristive states, as revealed by HAXPES non-destructive depth profiling. Therefore, the NbO x at the interface to Al 2 O 3 is most probably responsible for the rectifying properties leading to a two-terminal MIS structure with a bilayer HfO 2 /Al 2 O 3 insulator. While stoichiometric Nb 2 O 5 is known to be a good insulator, [67] it is reported that even a small reduction leads to an n-type semiconducting behavior. [67,68] Since EELS data indicate a mixture of Nb 2 O 5 and NbO 2 with an oxygen gradient, semiconducting NbO x can be expected.
Further information on the effect of the single material layers on the device functionality can be obtained by exchanging or omitting some of the layers and comparing the |J|-V characteristics with those of the reference devices. To this end, three additional device compositions were investigated (see Experimental Section for fabrication details). The corresponding |J|-V curves measured on devices with a top electrode size of 625 µm 2 are shown in Figure 6, where the insets show the respective material stack. Figure 6a displays the same data as shown in Figure 2a for a better comparison to the characteristics of the other devices. The |J|-V switching characteristics of ten individual devices and the corresponding mean curve is shown, together with the mean read-out characteristics. Figure 6b depicts the |J|-V characteristics of ten devices having a Hf bottom electrode instead of Nb. The Hf should be oxidized at the interface to Al 2 O 3 , similar to the Nb electrode. A significantly different performance is revealed compared to the reference devices in Figure 6a. For instance, a significant current can only be measured for positive voltages higher than 4.5 V when applying voltage sweeps with ±5 V amplitude. Moreover, Figure 6. a) |J|-V characteristic of reference devices and b-d) devices with different material stacks. The respective material stacks are shown as insets. Each black and red solid line shows the mean |J|-V data of ten individual devices.

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no analog memristive switching is observed even at higher voltages. However, a few devices show a threshold switching behavior [110] when the positive bias is increased up to 6 V (see green solid line and blue dashed line). Note that this behavior differs strongly for different adjacent devices and is not well reproducible. Thus, replacing the Nb bottom electrode with Hf drastically changes the devices' |J|-V characteristics and the memristive switching process. This demonstrates the relevance of the bottom electrode on the device characteristics. Figure 6c shows |J|-V characteristics of ten devices without any Al 2 O 3 . Here, the qualitative behavior is the same as for the reference devices, that is, diode-like current transport and analog memristive switching for voltages above a certain threshold. However, the devices do not allow to apply voltages with an absolute value as high as the other device types, especially for negative bias. Therefore, V max = 3.3 V and V min = −1.5 V are used to induce memristive switching. This clearly shows that memristive switching in the reported devices does not rely on the Al 2 O 3 layer. However, the Al 2 O 3 leads to less degradation of device performance over time (not shown) and significantly increases the retention time in similar devices. [33] The |J|-V curves of ten device with an additional 2.5 nm thin Al 2 O 3 layer between HfO 2 and Au can be found in Figure 6d. The lower Al 2 O 3 and the HfO 2 layer are thinner so that the overall oxide thickness increases by ≈1 nm. The Nb bottom electrode is most probably oxidized again. These devices show qualitatively the same behavior as the other devices with Nb bottom electrodes. Thus, a device with an Au/Al 2 O 3 interface leads to similar performance as a device with an Au/HfO 2 interface. The overall resistance, however, is increased compared to the reference devices and the device variability for positive and negative bias is significantly larger. For switching sweeps, voltage amplitudes of V max = 3.7 V and V min = −4 V are used.
We can conclude that current transport is dominated by the SCR within NbO x while the HfO 2 /Al 2 O 3 double oxide layer acts as intrinsic current compliance. This is found by the tremendous change in the electrical characteristics when replacing the Nb bottom electrode with a Hf bottom electrode. It further agrees with the missing positively charged SCR in hafnia and alumina, as revealed by the depth-dependent HAXPES measurements, and with the composition of the NbO x , as determined by EELS.

Memristive Switching Mechanism
The XPS and HAXPES spectra reflect the memristive switching mechanism in the following way. A net potential increase in HfO 2 is shown by a combination of the Hf 3d 5/2 data (see Figure 5c) and the Hf 4f spectra (see Figure 4). In particular, Hf 3d 5/2 spectra reveal a higher potential increase at ϑ = 15° and thus near the Al 2 O 3 interface than at the sub-surface sensitive measurements (ϑ = 41.4°). The measured signals are too noisy to distinguish a potential peak shift for surface sensitive measurements (near the Au interface). The Hf 4f spectra, which stem from the Au/HfO 2 interface, indicate a potential increase near the Au interface as well. Movement of negatively charged oxygen ions or positively charged oxygen vacancies within hafnia would lead to an increased potential at one interface together with a decreased potential at the opposite interface. Moreover, the exchange of negatively charged oxygen ions between HfO 2 and Al 2 O 3 can also be excluded since the positive voltage applied to Au to switch to LRS would attract these ions, and the hafnia would charge negatively. Furthermore, positively charged oxygen vacancies cannot enter HfO 2 from Al 2 O 3 when switching to LRS since the electric field under positive bias repels them. Thus, ion movement can be excluded with high probability.
Here, we suggest charging and discharging of localized traps within the HfO 2 layer or at the HfO 2 /Al 2 O 3 interface as an alternative switching mechanism. Probable candidates for these traps are oxygen vacancies. Simulations using a hybrid density functional suggest that these vacancies are singly positively charged (i.e., one electron is trapped) or neutrally charged (i.e., two electrons are trapped) if the Fermi level is located between 3.7 and 4 eV or 4 and 5.5 eV above the HfO 2 valence band maximum (VBM), respectively. [111] The theoretical barrier height [69,70] between HfO 2 and Au is 3.1 eV with an Au work function of 5.3 eV [112] and a HfO 2 electron affinity of 2.2 eV [99] leading to a Fermi level position of 2.6 eV above the VBM when considering a band gap of 5.7 eV. [99] However, the actual barrier can deviate strongly (toward lower effective barriers) from these theoretical values, [48,69,70] and this can be expected for the multi-layer device structure here. Thus, neutral or singly positively charged vacancies in thermodynamic equilibrium are reasonable since a lower effective barrier leads to an increased Fermi level with respect to the VBM. Applying a positive potential to Au can lead to a positive charging of the vacancies since electrons can be ejected. [28,30,43] This agrees with the BE shifts toward higher energies in LRS. Moreover, additional positive charges within the HfO 2 layer influence the potential drop across the Al 2 O 3 layer as well. Here, negative image charges may lead to the decreased potential at the HfO 2 /Al 2 O 3 in LRS and thus to the decreased potential drop across alumina as indicated by the depth-and state-dependent BEs of the Al 1s spectra (see Figure 5c). The decreasing FWHM of Al 1s spectra are consistent with a decreasing voltage drop across this layer (see Figure 5c) since the width of photoelectron spectra can increase due to an increased voltage drop across the probed layer. [100,105] No significant changes in the FWHM of Hf 3d 5/2 and Hf 4f are found. However, a potential of 0.9 V across HfO 2 is estimated to lead to a Hf 3d 5/2 spectral broadening of 0.1 eV in ref. [100]. Thus, the smaller change in the potential in the HfO 2 layer cannot be detected through a change in FWHM within the standard deviation of the determined peak width.
The potential variation is used to estimate the amount of charges involved in switching, as shown in detail in Section S14, Supporting Information. Two scenarios are considered, that is, uniformly distributed bulk charges and charges located at the HfO 2 /Al 2 O 3 interface, in agreement with ref. [30]. A bulk charge density of N B = 1.6 × 10 19 cm −3 , and an interface charge density of N I = 4.7 × 10 12 cm −2 are estimated. It should be noted that the estimated charges are not the maximum amount of charges involved in switching for two reasons. First, recording a single Hf 3d 5/2 spectrum takes about 19 min, during which the respective energy range is scanned six times, and the single sweeps are then combined into a single spectrum. In this time span, a relaxation toward HRS takes place www.advelectronicmat.de (see Figure 2c). Thus, the determined BE shift between HRS and LRS reflects the mean potential difference within this time frame. Second, the BE shift at the bulk sensitive measurements (15°) is used to estimate the potential increase at the hafnia/alumina interface. Yet, the real potential increase is higher since the photoelectron spectra for 15° angle of emission include contributions from all parts of the HfO 2 layer. The potential only linearly contributes to the estimated charge densities (see Equations (S14.2) and (S14.4), Supporting Information). Thus, the order of magnitude calculated for both densities does only change if the actual potential increase deviates from the estimated increase by one order of magnitude, which is not to be expected. Since the oxygen vacancy density in physical vapor deposition (PVD) processed HfO 2 is reported to be in the order of 10 19 cm −3 , [113] the estimated value of N B is reasonable. Moreover, this vacancy density is too small to be detected by photoelectron spectroscopy, which allows for finding differences in the material composition down to ≈ 1% . [103] This explains why no fingerprints of oxygen vacancies can be found in the spectra. The estimated value of N I is also reasonable since charge densities of up to 7.8 × 10 12 cm −2 at a HfO 2 /GaN interface are reported. [114] Thus, bulk charges in HfO 2 , interface charges at the alumina interface, or a combination of both can explain the potential variation.
In addition, filamentary switching is likely to be suppressed in the reported devices due to the low amount of vacancies compared to other devices showing filamentary switching together with spectral fingerprints of oxygen vacancies. [50,51,54] In this respect, first principles-based simulations reveal that for efficient nucleation and growth of oxygen-deficient filaments in HfO x an x in the range of 1.50-1.75 is optimal. [115] This is experimentally supported by Park et al., [22] who show a filamentary-type switching for x = 1.80 and an area-type switching process for x = 1.98. HfO 2 films, which are stoichiometric after deposition, can also lead to filamentary switching if an initial electro-forming step reduces the HfO 2 locally. [59] This is avoided in our devices by using a noble metal top electrode and an Al 2 O 3 film acting as a diffusion barrier for oxygen ions [33,57] as adjacent layers.
In summary, the memristive switching in the devices under study can be directly correlated with the electrostatic potential within HfO 2 and, thus, with the charge state of electron traps which are most probably oxygen vacancies. Indeed, HfO 2 is widely investigated as charge trapping layer in CTF memory. [66] Here, trapped charges are assumed to modulate the conduction channel in MOSFETs. Moreover, memristive devices based on charging and discharging of traps within HfO 2 have already been reported [42,56,63] without spectroscopic evidence. The influence of the potential variation on the device resistance is explained in the next section.

Device Model
A schematic band diagram of the qualitative device model can be found in Figure 7. A band diagram is used to visualize the involved potential profiles and barriers. The widths of the layers are drawn to scale, while the band alignment and the amount of band bending are drawn qualitatively. The current transport is dominated by the SCR within NbO x while hafnia and alumina act as intrinsic current compliance. The current through the dielectrics can be assumed to be assisted by defects so that a significantly high current can flow even for ≈6.5 nm insulators. In particular, the current through Al 2 O 3 can be assumed to be dominated by the thinnest parts (≈2 nm) of the layer (see the width of alumina relative to hafnia in Figure 7). The total charge distribution within the multi-layer stack is unknown. The HfO 2 and Al 2 O 3 bands are drawn linearly in HRS in Figure7a for simplicity but can have a more complex shape. The upward band bending in the dielectrics is indicated by the HAXPES data, while the downward band bending in the semiconducting NbO x is extracted from the forward bias of the diode-like characteristics. A significant amount of negative charges at the Al 2 O 3 /NbO x interface is deduced to account for the band profile. Additional positive charges in the hafnia layer and at the HfO 2 /Al 2 O 3 interface in LRS, as qualitatively indicated in Figure 7b, are attributed to electron de-trapping from neutral or singly positively charged oxygen vacancies. Bulk traps, interface traps, or a combination of both can explain the switching.
The additional positive charges in the HfO 2 layer in LRS influence the charge distribution within the buried NbO x such that the built-in potential decreases. This is similar to HfO 2 / SiO 2 /Si gate stacks, in which positive charges within HfO 2 lead to a decreased upward band bending within silicon. [116] Furthermore, positive charges within interfacial oxide layers in metal/semiconductor Schottky contacts are also reported to decrease the upward band bending. [70] Thus, the effective barrier height and, thereby, the overall device resistance decrease due to positive charging of electron traps in HfO 2 . Switching the device back to HRS results in the initial charge distribution and, thereby, in the initial resistance. The proposed model can also explain the different current fluctuations for positive and negative bias (see Figure 2a and 6a). The devices are initially in the HRS, and the voltage is swept in positive direction first. For low voltages, the current transport is dominated by thermionic emission, and no memristive switching takes place. An intrinsic current compliance becomes dominant for voltages high enough to induce memristive switching (see Section S13, Supporting Information). The current density shows low fluctuations for both low and high positive voltages. When the voltage is swept back to 0 V, the device resistance relaxes toward HRS, www.advelectronicmat.de even without applied bias (see Figure 2c). Thus, switching toward HRS takes place for all negative biases. The electron trapping can be expected to cause the observed noise for negative bias. [117] This effect is probably only visible for switching to HRS because the current density during switching to LRS is orders of magnitude higher. Besides, an additional higher variability for negative bias can potentially be explained by the inhomogeneous Al 2 O 3 layer (see Section 2.2) if the current transport for negative bias is restricted by the alumina. Moreover, the proposed model does also explain why the device with Hf bottom electrode does not show interface-type memristive switching (see Figure 6b). In contrast to the NbO x , no SCR exists in the HfO x below alumina. Thus, a variation in the charge distribution in HfO 2 does not impact the current transport as significantly as for the reference device since no SCR is modulated.
It is further estimated that the NbO x cannot completely screen the built-in potential due to its thickness of d x ≈ 5 nm NbO . For an estimate, the standard formula for the Debye length λ D is used [69,118] (see Equation (S15.1) and Section S15, Supporting Information). The relative permittivity of NbO x is assumed to be between 10 (NbO 2 ) and 41 (Nb 2 O 5 ). [68] Thus, 63% of the built-in potential can be screened in NbO x (i.e., d x λ = D N bO ) if the doping concentration is between 2.9 × 10 17 and 1.2 × 10 18 cm −3 . These are reasonable doping concentrations since concentrations of up to 6 × 10 19 cm −3 for Nb 2 O 5-x are reported. [68,119] However, a complete screening can be expected for d x λ ≈ = 10 D N bO , as is the case for GaAs. [69] This requires a doping concentration between 2.9 × 10 19 and 1.2 × 10 20 cm −3 . Since an increase in charge density in the order of 10 19 ) is estimated to have a significant impact on the charge distribution within NbO x , such a doping concentration is unlikely in the reported devices, and part of the built-in potential should drop in the Nb bottom electrode. Moreover, in the latter case, ≈95% of the built-in potential would be screened within 1.5 nm, and thus direct tunneling is expected to have a significant impact on current transport so that no diode-like behavior would occur. More details about these calculated results can be found in Section S15, Supporting Information.
In summary, the experimental findings consistently indicate that our devices consist of a two-terminal MIS-like structure in which electron traps within the insulator modulate the spacecharge region of the semiconductor and, thereby, the overall device resistance. This is consistent with the results of ImpSpec conducted on the reference devices, performed by Marquardt et al. and reported in the companion paper. [74] Here, the kinetics of the set process and of the retention imply charging of traps rather than ion movement. Furthermore, quantitative model parameters describing current transport in HRS and LRS and switching dynamics are given. In particular, current transport is described by thermionic emission with an effective barrier height of 0.84 and 0.675 eV, as well as an ideality factor of 3.71 and 4.9 in HRS and LRS, respectively. A series resistance of 12 kΩ and a reach-through [120] complete the current transport model. The results from Marquardt et al. are in agreement with the qualitative model proposed here, which could be applied to explain memristive switching phenomena in other devices as well.
Similar device models have already been reported by other groups without spectroscopic evidence. In this respect, Mikheev et al. [30] explained memristive switching in Pt/Nb:SrTiO 3 (NSTO) by a modulation of the Schottky barrier height by a variation in trapped charges within an inter-layer consisting of carbon contamination between metal and semiconductor and a potentially damaged single crystalline NSTO interface. Kim et al. investigated TiN/NbO z /TiO 2 /NbO z /Pt memristive devices. [43] Here, electrons are reported to be ejected from traps ascribed to Ti-sites in the upper NbO z layer (adjacent to Pt) by applying a positive voltage to the Pt electrode. This modulates the Schottky barrier of the NbO z /Pt interface. The NbO z is a mixture of ≈60% Nb 2 O 5 and 40% NbO 2 . Gao et al. report on an optoelectronic indium tin oxide (ITO)/NSTO junction in which memristive switching is induced by Schottky barrier modulation due to electron de-trapping while illuminated with light. [36] Furthermore, charge trapping at an HfO 2 /Ti interface is reported as a memristive switching mechanism. [42] In addition, devices are reported in which resistance switching is based on electron trapping in HfO 2 which changes the bulk conductivity of hafnia and, thereby, the overall resistance, while a rectifying barrier is unaffected. [56,63] Moreover, an MIS model that explains memristive switching in Au/NSTO and Au/ BaTiO 3 /NSTO devices through electron trapping and de-trapping in an interfacial layer is given by Fan et al. [34] Their model is supported by scanning Kelvin probe microscopy (SKPM) and piezoresponse force microscopy (PFM) studies on both the NSTO substrate and the BaTiO 3 layer, respectively. Thus, we show spectroscopic evidence on functional devices for Schottky barrier modulation by electron trapping/de-trapping in general and for electron trapping/de-trapping in HfO 2 in particular, in agreement with the other models.
The device model allows to propose methods for engineering the device characteristics for specific applications. In this respect, the defect density in the HfO 2 could be tuned by adjusting the sputter deposition parameters which affects the switching window. [22,121] A strong impact of the top electrode's work function and metal-insulator interface quality on the read-out and switching parameters is further expected, since these properties crucially affect the current transport in interface-type devices. Reducing the roughness between the NbO x and the Al 2 O 3 might lead to less device variability. Finally, the device model can be exploited to deduce design rules for the integration of the devices into CMOS technology. First, the amount of charge traps involved in switching should be larger than the amount of charges in the SCR so that the traps can have a significant impact on the depletion region. Second, the insulator should guarantee an intrinsic current compliance to protect the device from dielectric breakdown while simultaneously allowing a significant current flow. Third, the density of oxygen vacancies in the insulator must be low enough to prevent filament formation. Fourth, for a back-end-of-line (BEOL) compatible process and, thereby, for a potential 3D integration and a more flexible chip design, CMOS-compatible semiconductors such as amorphous or poly-crystalline Si could be explored. Fifth, a fab-friendly metal that forms a rectifying barrier with the semiconductor should be used. Sixth, the overall current density should be orders of magnitude higher than in the reported devices to enable a geometrical scaling to the nanometer regime while obtaining a measurable read-out current (see inset of Figure 2a). www.advelectronicmat.de

Conclusion
In summary, a comprehensive characterization of analog memristive switching devices composed of Nb/NbO x /Al 2 O 3 / HfO 2 /Au showing diode-like |J|-V characteristics is reported. The stoichiometry of HfO 2 and Al 2 O 3 is confirmed by EELS and HAXPES, while an excess of oxygen and argon in the center of the Al 2 O 3 is indicated by EELS. The oxidation state of the NbO x is determined by EELS to be a mixture of Nb 2 O 5 and NbO 2 with decreasing oxygen content toward the Nb bottom electrode. Non-destructive depth-dependent HAXPES and XPS measurements show that the space-charge region that accounts for the diode-like behavior is neither located in the HfO 2 nor in the Al 2 O 3 layer. Memristive state-dependent core-level shifts indicate that the charging of vacancies within HfO 2 is responsible for switching. The experimental results suggest a purely electronic origin of memristive switching in the investigated devices. We could not find any hints of ionic drift as a source for the observed switching behavior. Devices with adjusted layer stacks reveal that the diode-like behavior is caused by the NbO x layer, while Al 2 O 3 is not crucial for the memristive switching. The proposed memristive device model consists of a two-terminal MIS-like structure in which electron traps within the insulator modulate the space-charge region within the semiconductor and, thereby, the overall device resistance. While similar memristive device models have been reported before, we present here spectroscopic evidence on functional devices for the charging and discharging of electron traps as the origin of memristive switching in such devices.
The worked-out model is in agreement with the companion paper Marquardt et al. that exploits ImpSpec to probe the current transport and switching kinetics of the same devices. [74] Based on two different experimental approaches (XPS/HAXPES and ImpSpec), our findings strongly indicate an electronic charging and discharging of traps as the fundamental origin of resistive switching in our devices, instead of ionic drift.

Experimental Section
Device Fabrication: In the standard process, all layers were deposited using DC magnetron sputtering without breaking the vacuum with a base pressure of less than 5 × 10 −7 mbar. The devices were fabricated on 100 mm Si wafers passivated by 400 nm thermally oxidized SiO 2 . Metallic Nb and Al were first deposited in Ar atmosphere. The following deposition of HfO 2 in a reactive Ar/O 2 gas mixture using a metallic Hf target leads to the oxidation of the Al layer and, to some degree, of the Nb layer. [80,121] The Au top electrode was deposited in an Ar atmosphere. The device patterning was performed by standard optical lithography, lift-off processes, and Au etching in potassium iodide to get different electrode areas. The fabrication process was developed by Hansen et al. for similar devices (with NbO y instead of HfO 2 ) [33] and is described in more detail in refs. [33,121]. The HfO 2 layers investigated here were produced in exactly the same process as the NbO x in refs. [33,80,121], that is, with a total process pressure of 1.21 × 10 -2 mbar in poisoned mode (7 sccm Ar, 23 sccm O 2 ), a discharge power of 100 W and with a target to substrate distance of ≈53 mm. The Hf bottom electrode for the device shown in Figure 6b was deposited with the same sputter parameters as the Nb bottom electrode. The upper 2.5 nm thin Al 2 O 3 layer for the device in Figure 6c was deposited with the same process pressure, gas composition, and power as the HfO 2 . Here, the HfO 2 and Al layers were deposited slightly thinner than for the reference device so that the overall Al 2 O 3 /HfO 2 /Al 2 O 3 tri-layer is ≈1 nm thicker than the insulator bi-layer of the reference devices.
Different device structures were built for this work: (i) Reference devices with structures described in ref. [33] were fabricated. Here, six different contact areas ranging from 100 to 2500 µm 2 are arranged across the wafer. Furthermore, a 720 nm thick Ti wiring layer covers the top electrodes and connects them to Ti contact pads. A SiO x layer is needed as insulation between the wiring layer and the mesa structures. The devices shown in Figure 6 were also fabricated with the same design. (ii) Functional devices for the XPS and HAXPES measurements were fabricated with a different design. Here, the top electrode has to be much thinner and must not be covered with a wiring layer because the information depth of HAXPES is in the order of a few ten nm, while it is even less for lower energetic X-rays also used in this work. [47,51] The device structure is shown in Figure S4, Supporting Information which is inspired by ref. [105]. The Au top electrodes are electrically connected to Ti contact pads by Ti wiring lines, which only cover a small percentage of the device area. The total top electrode areas of the investigated devices are 13650 µm 2 . 9000 µm 2 are not covered by insulation or wiring layers allowing to probe the devices with PES. To obtain functional devices, the top electrode has to form a continuous film. Since thin gold films are known to grow in an island-like structure on ceramics, [122] an optimization of the top electrode deposition process has been performed. In the sputter deposition process, the thinnest continuous film produced has a thickness of 13 nm. A device produced that way was probed by HAXPES. The Au was thermally evaporated to get even thinner continuous films of 6 nm. Therefore, the respective wafer had to be transferred from the sputter deposition chamber to the evaporation chamber being exposed to normal atmosphere for less than 5 min. The wafers with structures (ii) not only contain devices with the described structures but also test structures as described in (i). These devices only work if the Ti wiring layer has no direct contact with HfO 2 . Thus, measuring the electrical characteristics of these test structures verified that the deposited Au formed continuous layers.

Electrical Measurements and Memristive Switching:
The bias voltage was applied to the Au top electrode while the bottom electrode was grounded. Trapezoid-shaped voltage sweeps were applied, where the voltage was increased from 0 V to the positive maximum bias V max , then decreased to the negative bias V min and increased again to 0 V. In total, 100 voltage steps with a total bias time of 220 s were used. The read-out characteristics of the devices with Nb/NbO x /HfO 2 /Au material stack were recorded with a total bias time of 16 s, which leads to the higher noise level in Figure 6(c) (red line). In situ switching to HRS or LRS in XPS/HAXPES experimental chambers was done with trapezoidalshaped voltage sweeps of one polarity only (50 steps, 110 s). All data from the reference wafer ( Figure 2) and the devices with alternative layer stacks ( Figure 6) were measured with an HP4156A semiconductor parameter analyzer. Electrical characterization and memristive switching at the synchrotron beamlines were done with an Agilent E5260 source measurement unit (SMU) at beamline P04, and an Agilent B2912A SMU at beamline P22, respectively. The X-ray beam was never directed to the sample while applying bias to the devices.
The spectra for emission angles of 41.4° (sub-surface sensitive) and 60° (surface sensitive) were measured two and three times for each memristive state, respectively, and the state was refreshed in between. First, the spectra were recorded for HRS for all three angles. Afterward, the device was switched to an LRS with a unipolar voltage sweep with V max = 4 V. To guarantee that all spectra for all detection angles were recorded for the same resistance state, a current compliance of 30 µA was utilized. Refreshing the resistance state to one and the same level was possible, and the device's retention was long enough to record data www.advelectronicmat.de for two distinct resistance states, as shown in Section S6, Supporting Information. The higher read-out voltage of 1.8 V was necessary because the noise level of the |J|-V measurement within the vacuum chamber did not allow to use lower voltages. However, the device state was not significantly affected by the higher read-out voltage (see Section S6, Supporting Information).
TEM and EELS: TEM characterization was performed using an FEI Titan 3 at an acceleration voltage of 300 kV with spherical aberration (C s ) probe correction and monochromator. The EEL spectra were acquired with a GIF Quantum Dual EELS detector. To probe the whole material stack, a focused ion beam lamella was extracted from a functional device in HRS of structure (ii) with a 13 nm Au top electrode. The line scan in Figure 3b is constructed from a spectral image by summing all spectra horizontally and binning two of these lines to obtain a vertical step size of 1.75 nm.
XPS and HAXPES: The Au top electrode was electrically connected to a common ground with the analyzer during photoelectron spectroscopy. During HAXPES measurements, also the bottom electrode was connected to the common ground leading to defined electrical boundary conditions when evaluating potential profiles. All recorded Hf and Al spectra were aligned with the Au 4f 7/2 peak of the top electrode at 84.0 eV BE. It should be emphasized that this provides an energy reference relative to the Fermi level of the Au rather than an exact alignment of the energy with E F = 0 eV. All corelevel spectra were fitted with the XPST add-on for IGOR Pro software (WaveMetrics), which utilized the Pseudo-Voigt function described in ref. [123]. Here, the Voigt profile was approximated by a Lorentzian-Gaussian sum function. Shirley-type backgrounds [124] were used for spectra with a sufficient signal-to-noise ratio. Otherwise, linear backgrounds were used. The XPS measurements with soft X-rays were measured with an X-ray energy of 1550 eV, a beam spot diameter of <15 µm, and an energy resolution of ≈200 meV. The HAXPES spectra were obtained with an energy of 7000 eV, a beam spot of 20 × 20 µm 2 , and a total experimental energy resolution of ≈300 meV. Depthdependent information was obtained by measuring HAXPES spectra from different angles of emission. This was achieved by rotating the sample relative to the analyzer and also to the X-ray beam so that the footprint of the beam was elongated in one direction with a factor of 1/sin (ϑ) (i.e., a maximum footprint of 20 × 80 µm 2 for the bulk sensitive measurements at 15°). All PES measurements were conducted at 300 K.
Au 4f spectra were fitted with a fixed spin-orbit splitting of 3.7 eV, an intensity ratio of 0.75 for f-orbitals and the same FWHM for both components. [125] For XPS measurements with the 6 nm top electrode, two doublet features assigned to surface states and bulk Au [126] were detected (see Section S5, Supporting Information). For HAXPES measurements with a 13 nm Au top electrode, a single asymmetric doublet peak (see Section S6, Supporting Information) with additional features at higher BE was detected as it was usually observed for XPS spectra of gold and other metals. [123] This asymmetry was incorporated into the fit by using an asymmetric Pseudo-Voigt function. [123] No resistance state-dependent peak shift was observed for the Au 4f spectra, and no gold oxides [127] were formed in both samples.
Hf 4f spectra were fitted with a fixed spin-orbit splitting of 1.67 eV, an intensity ratio of 0.75 for f-orbitals and the same FWHM for both components. [96] The spectra were aligned to the respective bulk Au 4f 7/2 peaks at 84.0 eV recorded for all resistive states.
Hf 3d 5/2 and Al 1s spectra for an angle of emission of 41.4° (subsurface sensitive) and 60° (surface sensitive) were measured two and three times, respectively. The spectra corresponding to the same angle and the same memristive state were combined afterward. To this end, the single spectra were aligned to the corresponding Au 4f 7/2 peak at 84.0 eV, and the backgrounds of the single spectra were subtracted before the spectra taken at one and the same angle and resistive state were summed up. Raw spectra and fitted backgrounds can be found in Section S7-S10, Supporting Information. The merged Hf 3d 5/2 and Al 1s spectra could be fitted best with single Pseudo-Voigt functions.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.