Perspective: Entropy-stabilized oxide memristors

Energy consumption by computation has grown exponentially following the growth of artificial intelligence (AI) and machine learning (ML) technologies.¹ In AI/ML applications, hardware systems have been forced to store and process large quantities of data. In conventional computers based on the Von Neumann architecture, where memory and processing units are segregated, data move between the two segregated components via a data bus. This shuttling of data causes severe latency and energy consumption issues.^2–4 The problem is compounded as the amount and frequency of data shuttled back and forth increases, leading to a state where the system speed is bounded, not by computing capability (compute-bound), but by the data movement (memory-bound)—the so-called memory bottleneck.^2–5 

A recent approach for accelerated AI/ML tasks is achieving a reduced data path. Thus, recent computing fabrics have portioned some processing units near or into memory units.^6–17 For example, compute-in-memory (CIM) technologies have successfully achieved an acceleration with crossbar arrays of memory technologies, such as static random access memory (SRAM) and dynamic RAM (DRAM).¹⁸ In parallel, CIM technologies have expanded to include emerging memories such as resistive RAM (RRAM),¹⁹ phase change memory (PCM),²⁰ spin-transfer torque magnetic RAM (STT-MRAM),^12,21 and the ferroelectric field effect transistor (FeFET).²² In the memristor array, voltage inputs applied to rows of the array (vector) is natively multiplied with information stored in the conductance (matrix) of the array nodes by simple Ohm's law. The resultant currents are gathered at the columns of the array following Kirchhoff's current law [multiplicate-accumulate (MAC)]. The simple structure and the nature of memristors jointly execute vector-matrix multiplication (VMM) much faster and with far greater energy efficiency (∼pJ per MAC operation) than conventional computers (∼nJ) by bypassing retrieval of data from the segregated memory to the processing units. The performance enhancements can support intensive ML-based computing.^23–28 

Further acceleration has been explored in the analog domain utilizing multi-bit precision of analog memristors. The approach reduces the amount of data to be handled in a digitized manner, leading to shorter latency, bypassing bitwise processing.^38–40 Multiple memory technologies have been developed and adopted, depending on the application, in order to optimize the strengths and weaknesses of each (e.g., high programming power and lack of symmetric conductance for PCM, low on/off ratio, and lack of multi-bit storage for STT-MRAM).^41,42 A summary of the technologies is presented in Table I. The acceleration achieved in the analog domain, however, is degraded by arithmetic or logical operations other than MAC operations in computing systems.^43,44 Arithmetic logic units (ALUs) that were originally designed to work in the digital domain enforce intermediate analog outputs from the analog MAC operation to be converted into digital values by analog–digital converters (ADCs). The ADCs burden the system and diminish the benefits of analog MAC.^45–47 The performance degradation is compounded when analog acceleration techniques require analog inputs, as the digital values from the ALUs will be again converted back into analog by digital–analog converters (DACs).

RRAM can play a critical role in minimizing the conversion deficiencies by executing operations beyond MAC in the analog domain.⁴⁸ In conventional filament-based RRAM, atoms or vacancies are moved within these materials to create or terminate conductive filaments, resulting in the modulation of electrical conductance. The conductance characteristics can natively adapt a variety of analog functionalities in their natural response to analog inputs.^49–53 It can not only resolve the issue by eliminating the necessity of conversions, but also improve expressivity that may have been compromised by digital computers. For instance, non-linear activation functions have been developed and adopted by AI/ML models to infuse non-linear neuronal or synaptic behavior.^54–57 The conventional digital computer that is great at binary and linear mathematical operations, such as addition and multiplication, indirectly executes the non-linear functions utilizing approximation such as Taylor series and lookup tables (LUTs) due to the lack of non-linearity.^58,59 However, filamentary RRAM can naturally demonstrates non-linearity in a very power-efficient manner.^49–53 

In amorphous switching medium-based memristors, however, the resistive switching (RS) and the non-linear dynamics rely on the stochastic movement of oxygen vacancies, causing intrinsic limits on reliability and controllability of device properties. Further, today's AI models demand different hardware requirements depending on their operation. Thus, large AI models whose size is too big to be mapped at once are more vulnerable to reliability errors and require memories that consume less energy for write operations due to inevitable repetition of mapping a partial model (matrices) on crossbar arrays.^60–63 On the other hand, a longer retention and less energy for read operations are more desirable for models that can be mapped on a computing hardware at once, because the computing systems can keep reusing the full model parameters once they are mapped. However, those properties are fundamentally coupled in the memristors in that the higher energy barrier for oxygen vacancy migration enhances the memory retention while increasing energy consumption for programming, and vice versa. Furthermore, analog computing systems demands higher reliability, high ON-OFF ratio, and multiple conductance states to ensure that a sufficient number of bits can be mapped onto a single device.^64–66 In the case of non-linear functions that are usually adopted on all hierarchies in neural networks and executed per inference, much higher criteria for cycle-to-cycle variation (C2C, reliability) are required to execute tasks as desired. In addition to reliability, the performance of neural networks largely depends on the optimized non-linear functions.⁶⁷ Thus, the ability to tune the various tradeoffs is critical to properly design hardware for neural networks.

These requirements are difficult to achieve in the amorphous filamentary-based memristors that are characterized by abrupt changes in resistance upon switching. A fundamental approach is required to engineer the physical dynamics of the switching medium to mitigate variability in devices (Fig. 1).

Entropy-stabilized oxides (ESOs) are emerging materials in ceramics. ESOs are a solid solution of more than five different cations, differentiated by high-entropy oxides (HEOs) in that they are stabilized in a single phase by a configuration entropy that overcomes an enthalpy penalty (Fig. 2).^68,69 The initial report of a rock salt (MgNiCoCuZn)O ESO in 2019 by Rost and colleagues⁶⁸ has since spurred a wide range of research in the broader area of high (configurational) entropy oxides.^70–73 

Regarding material properties that may be harnessed for memristor phenomena, the homogeneous dispersion of cations suggests uniform properties (as long as the measurement length scale is longer than any correlation or coherence length—note that about the second nearest neighbor distance is where bond lengths begin to appear uniform)⁷⁴ reducing the expected device to device variation. Further, the cation composition can be continuously tuned over a large range and facilitates the continuous control of macroscopic physical properties. In cases, the properties can be dominated by local configurations where cation size differences and coordination preferences lead to local structural disorder and stereochemical configurations. While these features are exciting for materials design, it is the latter that may provide a pathway to new or rare phenomena (Fig. 2). It is in these features that we will discuss recent findings on the interplay between composition, local disorder and strain, intrinsic point defect formation, and the associated electronic structure. Building upon these leads to exciting opportunities for memristor behavior that can be harnessed for efficient computing.

As a homogeneous solid solution, the homogeneous multicationic sublattice leads to local structural disorder due to differing cation size and stereochemistry.^70,74–76 While a rock salt binary oxide is characterized by a single type of bond length and bond angle, rock salt (MgNiCoCuZn)O accommodates a broad range of local configurations even when only considering site occupancy on an ideal rock salt structure (Fig. 2). Naturally, the true local structure that has local structural distortions broadens this histogram. The probability of a local configuration and associated structural distortion can be tuned by the cationic composition (Fig. 2). For example, Cu-rich ESOs have the most structural distortion due to the Jahn–Teller distortion, and the opposite is for Mg-rich composition as MgO is the most stable in rock salt with the lattice parameter closest to the ESO among the other constituent elements.^74,76–78 As the local stress induced by Cu²⁺ ions can be accommodated by the formation of vacancies in the nearby lattice, single-phase ESO can be commensurate with the formation of a high density native vacancies; otherwise, multi-phases form via phase segregation.⁷⁹ 

On the other sublattice, the structural distortion at an oxygen site is dependent upon the local nearest neighbor cation configuration, as the different combination of cations in the nearest neighbor leads to different local bond configurations [Fig. 3(c)]. As Cu (Mg) causes the most (least) structural distortion, oxygen vacancies are the most (least) likely to form in Cu (Mg)-rich local sites within the ESO. This allows control of vacancy concentration via the alloy composition [Fig. 3(d)]. One strategy to building the defect formation energy from an element-by-element contribution involves a linear regression analysis of DFT computed formation energies over the number of each cation in the nearest neighbor coordination shell.⁸¹ Using the linear regression model, the formation energies of V_Os for the 210 possible combinations of the 1NN shell are calculated, notated by $ELRfVO$⁠. The distribution of $ELRf(VO)$ is plotted in Fig. 3(e), showing a large variation of vacancy formation energies (from −0.8 to 2.4 eV) resulting from the local configuration. The presence of negative vacancy formation energies indicates the spontaneous formation of V_O in Cu-rich local configurations [the inset in Fig. 3(e)]. This not only explains that ESO natively have a large density of V_Os (∼10²¹ cm⁻³ in bulk, equimolar composition) but is a clear example of a case where a physical phenomenon is dominated by the rare local configurations located at the tail of the local microstructure histogram (e.g., N_Cu > 3).

Another unique physical feature of defect formation in ESOs is that the charges from V_O can be accommodated by the shift of cation valence. Kotsonis et al.⁸¹ observed that the valence control of Co upon deposition temperature is attributed to the formation of cation vacancies, showing that Co is tolerant to multivalency (+2 and +3) in the ESO. The valence control of Co further allows tunability of magnetic disorder as Co²⁺/Co³⁺ has high/low spin state.⁷⁶ 

Defect formation in ESO accompanies a charge transition where the charge state of defects depends on the Fermi energy and the equilibrium Fermi energy is determined by the interplay of charged defects. In rock salt (MgNiCoCuZn)O, V_O is a deep donor with ionization energy of 1.24 eV, while V_Cu (a dominant cation vacancy) is a deep acceptor with ionization energy of 0.658 eV. The interplay between V_O and V_cations pins the Fermi energy at a deep energy level within the bandgap, which explains electrically insulating behavior of ESOs.⁸⁰ Instead, the conduction of ESO is dominated by the hopping conduction of trapped electrons through randomly distributed localized electronic trap states created by vacancy defects.^82,83 Jacobson et al. related the conductivity of the ESO to the oxygen stoichiometry, which shifts the oxidation state of Co and suggests the hopping conduction of ESO is mediated by the charge transfer of Co.⁸² 

Combining these observations with prior theory results would imply that hopping barrier and hopping distance can be systematically tuned with the composition of the ESO. However, the transport studies have been focused on bulk samples (polycrystals) and thin films with top-electrodes only as single-crystalline ESO thin films had only been grown on insulating MgO substrates (for the case of the parent composition [(MgNiCoCuZn)O]). To fabricate single-crystalline ESO thin films in metal-insulator-metal (MIM) structure, an epitaxial bottom layer of conducting materials needs to be inserted. Candidate materials are pure metals that can be epitaxially grown on MgO substrates such as Fe or Ge; however, challenges arise from their oxidation during the integration process. Other candidates are conducting oxides, and among them, YBa₂Cu₃O_7–x (YBCO) is identified to work as a bottom electrode for the ESO. Yoo et al. employed YBCO bottom electrodes and fabricated single-crystalline ESO memristors. Despite the large lattice misfit between in-plane lattice parameters of ESO and YBCO (10.7% and 8.86% along the a and b directions, respectively), x-ray diffraction shows a strong 002 peak in the symmetric scan as well as ESO 022 and YBCO 026 peaks in the asymmetric scan, verifying in-plane epitaxial relationship of [100]_ESOǁ[100]_YBCO.

Frequency-dependent conductivity measurements of Mg-varied single crystalline ESO thin films show agreement with the correlated barrier hopping (CBH) model where the hopping barrier of the ESO can be obtained from the slope of measured ac conductivity as a function of frequency. The hopping barrier decreases for Mg-poor (vacancy-rich) samples, which can be explained by the shift of vacancy level as a function of local cation configurations. The tunable defect formation and energy level enables design of properties of devices that comprise ESOs.

The tunability leads to controllable resistive switching (RS) of the ESO-based memristors. The tunable RS dynamics was demonstrated by Yoo et al.⁶⁷ This work reported (MgNiCoCuZn)O ESO memristors where the RS mechanism is based on trapping/detrapping electrons in defects [Fig. 4(a)]. The major defects in the ESO are oxygen vacancies, which have mid-gap energy levels. Those defects are normally filled, resulting in a high resistive state (HRS). At high applied voltage, electrons trapped in the defect levels escape from the traps, and these empty traps can facilitate hopping conduction of injected electrons, leading to low resistance state (LRS). After the bias is removed, it takes finite time (τ) to refill the traps.⁶⁷ As the traps are being filled, the number of hopping sites reduces, increasing the average hopping distances (⁠ $R¯nm$⁠) and exponential decay of hopping conductivity [ $σ∼exp(−R¯nm)$].⁸⁴ 

The conductance dependence on the number of hopping sites is illustrated by an experiment where four consecutive pulses are applied to a memristor and the corresponding conductance modulation range is derived [Fig. 4(b)]. It displays that the smaller range of hopping sites (proportional to the number of oxygen vacancy) leads to the narrower conductance range. Despite the ability to modulate intrinsic device parameters, electron-based RS mechanism leads to a short-term memory effect. The volatility makes the (MgNiCoCuZn)O ESO-based memristor inappropriate as a nonvolatile memory (NVM) for CIM architecture-based hardware. However, the volatility presents a different opportunity for neural network hardware.

Leveraging the compositionally tunable τ and conductance modulation range, ESO memristors with different cation compositions can uniquely respond to the various combinations of pulses (1/0 represents the existence/absence of a pulse) [Fig. 4(d)]. It indicates that the ESO enables systematic design of devices that can process information in a way harnessing the compositional tuning of the dynamical conductance. In addition to the dynamics (characterized by τ and β), the experiment demonstrates tunability of a range of device parameters in ESO memristors, such as leakage current, conductance at the low resistance states, or impedance.⁶⁷ In addition to the controllability, the high endurance of the ESO memristor (>10⁶ cycles) makes the memristor more eligible for neural network applications.⁶⁷ 

The ability to fine tune the non-linear response is crucial for the applicability of memristors. One example is presented in Ref. 88. As an algorithmic framework, RRAM with the exponential conductance decay in time can efficiently work with an event-based camera with neuromorphic vision sensors.⁸⁸ It produces an event (spike) whenever the intensity of pixels in the frame changes above a threshold.⁸⁹ 

In the work, each RRAM is proposed to be dedicated to a pixel and receive spikes as produced [Fig. 5(a)]. The RRAMs encode the temporal information hidden in the spikes following their native exponential decay [Fig. 5(b)]. The behavior upon temporal inputs gives neural networks temporal information that can easily be dismissed by conventional encoding methods, such as a simple accumulation of spikes.⁹⁰ The proper controllability of the characteristics is essential for the optimal performance of the network, because different hierarchies in the network leveraging the RRAM demand different relaxation time constants to process temporal information at different timescales. Figure 5(c) presents the performance-cost comparison of the network to others on a neuromorphic vision task, indicating the RRAM realizes a better and lighter network.

The fine tunability of device dynamics discussed in Secs. II C–IV makes ESO an excellent candidate for task-specific neural networks, such as the aforementioned example,⁸⁸ which has remained challenging in traditional amorphous oxides-based memristors. As a physical demonstration of a dynamic-based neural network, the reservoir computing (RC) network was implemented with ESOs and performed spoken-digit recognition task [Fig. 5(d)].⁶⁷ 

RC systems process data that are not easily separable in its original feature space and instead use non-linear functions to map them into a high-dimensional computational space (i.e., the reservoir state) where they become easily separable.^91,92 The demonstration showed that the ESO can offer optimal non-linear functions depending on the timescale of tasks (all identical except for the time resolution—100, 250, and 450 ns, respectively) [Fig. 5(e)]. It confirms that the fine tunability of non-linear function is of high significance for task-specific AI hardware.

The ESO memristor also demonstrates excellent energy efficiency where the energy dissipated per spike is 3.39 pJ for ESO memristors, while 54.8  $μ$ J for a CPU-based system, 143 nJ for a FPGA-based system, and 20 pJ for the most power-efficient memristor in the literature (HfO₂).^92,93

(MgNiCoCuZn)O-based ESO memristors show excellent tunability of device parameters; however, the tunable internal time constant was only tuned in the ns range (159 < τ < 279 ns).⁶⁷ To make ESO memristors more competitive for a wider range of applications, it is desirable to expand the accessible time constant range so that the optimal time constant for each application can be selected. While the conduction of (MgNiCoCuZn)O occurs via electron excitation from trap states, other physical mechanisms, such as ion diffusion or a thermodynamic phase change, can give a longer time constant (up to ms range) or retention period (longer than a year).⁹⁴ 

A long-term memristor based on the high entropy system was first reported using (ZrHfNbTaMoW)O in 2021⁹⁵ where the strategy of compositional tuning was employed to obtain better resistive switching (RS) properties. For example, WO₃ memristors show gradual conductance changes; however, it is challenged by poor retention. HfO₂ memristors show good retention but abrupt conduction changes. (ZrHfNbTaMoW)O memristors demonstrated the strengths of the component binary oxides [Figs. 6(a) and 6(b)]: a gradual conductance modulation, 6-bit operation, and long retention (10³ s).⁹⁵ The RS mechanism here is the migration of V_Os and the large amount of V_Os that can be accommodated as the charges from V_O can be compensated by the valence change of the cations (mainly Mo and W). However, the RS properties still suffer from stochasticity, and compositionally tunable device properties were not demonstrated.

Recently, Tsai et al. reported spinel (CrMnFeCoNi)₃O₄ memristors epitaxially grown on a Nb-doped SrTiO₃ conducting substrate⁹⁶ [Fig. 6(c)]. The switching mechanism is attributed to the spinel-to-rock salt structure transition that accompanies both a valence change of the cations and the formation of oxygen vacancies, resulting in a change of electrical conductivity.⁹⁶ The electrical measurement shows a high ON/OFF ratio (∼10⁵), endurance (>4550 cycles), long retention time (>10⁴ s), and increased stability.⁹⁶ Although the control of the valence state in high-entropy materials facilitates the memristive switching properties, the associated phase transition involves coordination changes, reduction of entropy, and the migration of oxygen vacancies toward the electrode. Ultimately, the effects alter the thermodynamic ground state, which is likely to limit the endurance. To achieve endurance sufficient for extensive AI training, it will be required to control phase stability and vacancy movement/pinning.

(MgNiCoCuZn)O-based ESOs have shown superionic conductivity when doped with mobile cations, such as Li⁺ or Na⁺, showing the promise for long-term memristors based on ionic transport. Improved ionic mobility and reliability is demonstrated when applied as solid-state electrolytes.^97,98 This is because the local lattice distortions in ESOs give rise to an overlapping distribution of site energies for alkali ions and provides a diffusion pathway with a reduced activation energy.⁹⁹ Design of the ESOs ionic conduction via composition and disorder can be a promising direction for future work and has the potential to allow broader range of internal dynamics for various applications.

The extension of relaxation time into the millisecond timescale opens the possibility for memristors to interplay with biological systems.¹⁰⁰ Relaxation timescales in the nanosecond or sub-nanosecond timescales enable memristors to work with signals arising within the conventional digital computer. For example, ESO memristors with nanosecond time constants can be used for a RC-based branch predictor (BP), which predicts the execution of branches in advance and enables pipeline parallelism in modern computers.^2,101 To comply with the BP's motivation (enabling pipeline parallelism seamlessly), the branch predictor should make a prediction in one or two cycles using execution history.^2,101,102 The cycle limitation has hindered BPs from being complicated (deeper), even though several efforts have been made to utilize the neural network fashion.^103,104 In that RC networks have demonstrated outstanding performance over relatively deeper neural networks even with a single readout layer,^91,92 a RC-based BP can push the boundaries of BP performance in the dynamic execution circumstance by letting ESO memristors encode execution histories, which are delivered in pulses at low cost and high speed.

Modern algorithms and architectures require non-linear mathematics beyond a simple exponential function.^54–57,105 Sigmoid, tanh, GLU, and SoftMax are the most frequently and commonly adopted.^54–57,105 In conventional computers, the non-linear calculation relies on an approximation such as Taylor series or the lookup tables (LUT) that hold input-dependent outputs and provide the pre-calculated output according to the nearest inputs, which makes the precision of the function compromised by the power and area efficiency.^58,59 On the other hand, a memristor's RS behavior can be described by non-linear equations, therefore, can perform the calculation natively at much lower cost.

In Ref. 67, RS dynamics of (MgNiCoCuZn)O-based ESO memristors are fitted by the stretched exponential function (SEF), which is employed for data processing in a reservoir computing network. For future work, richer RS dynamics can be studied by using various analog state variables such as pulse sequence, time interval (t_interval), amplitude (A), frequency (f), or their combinations. The devices can potentially offer internal dynamics-governed responses whose mathematical description maps to (non-linear) activation functions beyond the SEF, a key part of analog neural network hardware design (Fig. 7). The short time constant, τ, eliminates the need to refresh memristors (reset the state) to guarantee reliable output from the same initial states, leading to better energy efficiency. Collective use of the activation functions with VMM operations accelerated by analog memristor crossbar arrays can offer further improvement by performing various machine learning tasks such as natural language process, computer vision, transformer, and deep learning with the least involvement of ADCs or DACs. Also, the analog crossbar arrays can be implemented by ESO memristors if important requirements, such as retention, endurance, and others, are improved in the future. This will realize ESO memristor-based AI accelerators with transformative energy efficient computing performance compared to CMOS-based computing.

For the use of ESO devices in IC chips, ESO devices must be integrated with Si—the platform for modern electronic technology. Integration of high-quality single-crystalline materials on a Si wafer has remained challenging because the growth of single-crystalline thin films requires (1) a stringent substrate condition such as crystalline state and geometry to support epitaxial growth and/or (2) a high temperature for crystallization that might exceed the thermal budget of IC technology.

ESOs have shown promising pathways toward Si integration. First, it can be directly grown on Si/SiO₂ substrates by employing integration techniques such as ion beam assisted deposition (IBAD).¹⁰⁶ While films grow in random alignment on a substrate that does not induce epitaxy, the IBAD technique employs ion bombardment during deposition to help align grains of the film azimuthally [Fig. 8(a)]. It is also possible to grow epitaxial ESO thin films on a Si wafer using rock salt template layers such as SrO and CaO or using perovskite template such as SrTiO₃¹⁰⁷ [Fig. 8(b)]. For example, SrTiO₃ has epitaxial relationship with Si, which allows the growth of fully crystalline SrTiO₃ thin film at growth temperature < 550 °C.¹⁰⁷ Owing to the cubic geometry and relatively small lattice mismatch, ESO thin films can be epitaxially grown on SrTiO₃ or MgO/SrTiO₃ buffered Si substrate [Fig. 8(c)].

Another benefit of ESOs is the low crystallization temperature (<400  $°C$⁠) that facilitates back-end-of-line (BEOL) compatibility; therefore, dense integration via vertical stacking is possible. 3D vertical RRAM (VRRAM) array can also provide higher parallelism, capacity, and density for VMM operation.¹⁹ Monolithic 3D integration is the most cost-effective route for VRRAM; however, it is challenged by the synthesis of high-quality materials within BEOL constraints (all processing must remain below 450  $°C$⁠).¹⁰⁸ While typical oxide compounds require high deposition temperature to crystallize, the ESO uses configurational entropy and a rapid quench to stabilize the crystalline structure. Physical vapor deposition naturally provides this condition as the plasma/vapor temperature is very high leading to a high entropy and kinetic energy of the species, while the quench is facilitated by the condensation of the species onto the substrate surface that is at much lower temperature.¹⁰⁸ Combined with the integration techniques above, further work on BEOL compatibility and 3D integration of ESO devices on Si will be interesting and important future work.

Single-crystalline ESO memristors show the ability to delicately tune the internal transport dynamics via composition control of point defects. This allows implementation of neural network systems for task-specific ML applications with transformative low electricity consumption. Future works, such as tuning broader range of internal dynamics, demonstration of higher functionality, and integration in Si, will make ESO memristors even more promising for sustainable AI computing.

This work was supported by the National Science Foundation through NSF MRSEC DMR-2011839. The authors would also like to acknowledge the many that have contributed to their understanding of entropy stabilized oxides through collaboration and discussion, such as Susan Trolier-McKinstry, Jon-Paul Maria, Christina Rost, and Ismailia Dabo.

The authors have no conflicts to disclose.

Sieun Chae and Sangmin Yoo contributed equally to this work.

Sieun Chae: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Sangmin Yoo: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). Emmanouil Kioupakis: Conceptualization (equal); Investigation (equal); Methodology (equal); Resources (equal); Writing – review & editing (equal). Wei D. Lu: Conceptualization (equal); Investigation (equal); Methodology (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). John Heron: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.