Electrical characteristics of interfacial barriers at metal—TiO₂ contacts

The studied metal-TiO₂-metal devices are presented in figure 2(a). In order to obtain quantitative results the tested devices were modelled by the equivalent circuit presented in figure 2(b). This consists of two series resistances accounting for the top (R_TE) and the bottom (R_BE) access electrodes and the device under test (DUT). As TiO₂ exhibits an intrinsic n-type character [23], the DUT can be considered as two inverse polarised Schottky diodes, both emulating the TE and BE contacts, connected through a resistance that corresponds to the TiO₂ core. This equivalent circuit was further used for calculating the effective applied bias (V_eff)/electric field across the DUT, with respect to the bias applied through the voltage source (V_S) and as a function of the measured current (I), summarised by equation (1):

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{V}_{eff}}=V_{\rm S}-I\left( {{R}_{{\rm TE}}}+{{R}_{{\rm BE}}} \right).\nonumber \end{align} \tag{ 1 }$$

Zoom In Zoom Out Reset image size

In the absence of an interface barrier, the Schottky diodes (TE and BE) can be considered as short-circuit. In this case the I–V characteristic should be symmetric with respect to the applied bias polarity and the dominant transport mechanism is determined purely by the properties of the active layer film. For the wide band gap materials, various mechanisms may dominate the transport. Most of them are critically affected by the density and the energy distribution of the band gap states, and spatially by the film microstructure, e.g. conduction paths across the grain boundaries commonly exist in nanocrystalline films [45]. Depending on the applied electric field intensity and the operation temperature, transport may be dominated by hopping, space charge limited currents, the Frenkel–Poole effect, or even by free carriers in the bands [46]. The contribution of internal point defect-related ionic motions [47, 48] and/or those originating from the electrodes should also be taken into consideration. In particular for TiO₂ films, the Ti/TiO₂/Ti stack appears to be very useful for these studies as it allowed for a detailed assessment of the core material controlled conduction mechanism [49, 50]. The latter is supported by our results, as Ti was found to form ohmic or non-rectifying contact when used both as a TE and as a BE.

Interface-controlled transport is typically identified by an asymmetric I–V characteristic with respect to the applied bias polarity. The transport is then dominated by either tunnelling through the barrier formed at the interface or by thermionic emission over it. The two mechanisms can be distinguished via the temperature dependence of the I–V [46].

Tunnelling currents obey the following equation (2):

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle I\propto V^{2}\exp \left( -\frac{b}{{{V}}} \right)\nonumber \end{align} \tag{ 2 }$$

with b being just a constant. Consequently, an asymmetric, temperature-independent I–V supporting also a linear relation on a ln($I/V_{eff}^{2}$) versus 1/V_eff signature plot serves as a strong indication of tunneling-dominated transport.

Conversely, thermionic emission over the interface barrier is the most common thermally-activated mechanism for interface-controlled transport. For those Schottky-type contacts the current flow depends on whether the contact is forward or reverse biased. The forward current–voltage characteristic is given by equation (3):

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{I}_{for}}=A{{T}^{2}}\exp \left( -\frac{q{{\Phi }_{{ B}0}}}{KT} \right)\left\{\exp \left( -\frac{q\left( V-{{I}_{for}}R \right)}{nKT} \right)-1 \right\}~\nonumber \end{align} \tag{ 3 }$$

while the reverse biased case can be described by equation (4):

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{I}_{rev}}=A{{T}^{2}}\exp \left( -\frac{q({{\Phi }_{{ B}0}}-a\sqrt{{{V}}})}{KT} \right)~\nonumber \end{align} \tag{ 4 }$$

where K is the Boltzmann constant, T is the absolute temperature, Φ_B0 is the zero bias potential barrier height at the metal/MO interface, A  =  (area × A^*), with A^* being the Richardson constant, n is the ideality factor, 'α' is the barrier lowering factor, q is the electron charge, and R stands for any series resistance.

For the cases where an interface barrier is formed, which is the main focus of this work, any positive bias applied to the TE will result in a forward biased TE/TiO₂ contact and reverse biased TiO₂/BE contact. This is the system of two back-to-back Schottky contacts that is described in detail in [51]. In our case, we emphasize our analysis in the regime where the current flow is determined by the reverse biased BE, given that this constitutes the most resistive element in this series configuration, and thus as a first approximation we may assume that V_eff ≈ V. The situation is the opposite when a negative bias is applied to the TE; then the TE will determine the current flow.

For this regime, a straight line on a ln(I/T²) versus 1000/T plot for any applied electric field serves as strong evidence of thermionic emission. The slope of this line corresponds to the apparent interface barrier (Φ_App) and should decrease by increasing the applied electric field/bias, as:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{\Phi }_{App}}={{\Phi }_{{ B}0}}-\alpha \sqrt{{{V}_{eff}}}.\nonumber \end{align} \tag{ 5 }$$

If this Φ_App versus $V_{eff}^{1/2}$ signature plot is also supported by the extracted results, then the intercept extrapolated to V_eff  =  0 V provides an experimental determination of Φ_B0, while the slope corresponds to α. By following the aforementioned methodology we can obtain clear signature plots that allow the deciphering of the transport mechanism and provide quantitative measures of interfaces in metal-TiO₂-metal structures. Moreover, this analysis does not require an accurate knowledge of the Richardson constant for the amorphous MO as this might differ by orders of magnitude with respect to its commonly adopted value for silicon. This further highlights the necessity for implementing a temperature-dependent characterization.

The TE/TiO₂ contacts have been assessed to date mainly through evaluating the DUT's resistance at a specific read-out voltage, typically of 1 V. Here we aim to present an approach focusing more on a quantitative extraction of parameters with physical meaning, i.e. the zero bias potential barrier at the interface, Φ_Β0. To do this, several configurations having different TEs were fabricated on the same wafer, with the TiO₂ active layer films deposited on top of the Au BE during the same process step. Therefore, with the exception of the TE interface, identical characteristics are expected. To the contrary, the results depicted in figure 3 provide evidence that the TE deposition plays a major role in the characteristics of the device. For the I–Vs, the discrepancy appearing at V  =  0 V, as earlier mentioned, arises from our data acquisition system. However, I–Vs not crossing the zero voltage point are also expected in our case, due to the change in the dominant Schottky contact at the point where the bias polarity changes [51]. Moreover, it is worth mentioning, particularly for the metal/electrolyte systems, that this behaviour has also been correlated with the nanobattery effect [30]. A more detailed study of this aspect will require precise measurements around zero.

Zoom In Zoom Out Reset image size

Using Ti and Al as a TE result in no rectifying barrier formation, and thus core material controlled conductivity, depicted by the symmetric I–V curves (figure 3(a)). Despite the identical (by fabrication) core films, differences in conductivity are obtained. A possible mechanism for the role of metal electrodes on the device resistivity is proposed in [39], based on the Ellingham diagram, where the argument is that electrode metals interact with TiO₂ generating oxygen vacancies. Oxygen vacancies act as n-type dopants, providing free electrons in the MO conduction band and thus determining the device resistance. The relation is not necessary straightforward, however, as in wide band gap materials the conductivity is also determined by the properties of the gap states through mechanisms such as hopping and Poole–Frenkel. Nevertheless, a thorough investigation of the conduction mechanism through the film was not our main intent in this work.

When Au, Pt and Ni (figure 3(b)) are used as the TE, interface barriers are formed, as denoted by the asymmetric I–V curves (figure 3(b)). For these materials, a detailed temperature characterization (figure 4) was performed and clear signature plots were extracted (figure 5). This led to the calculation of the zero bias potential barrier Φ_Β0 and the barrier lowering factor α (figure 6(a)) that are summarized in table 1. For these TE materials the conductivity is controlled by thermionic emission over the interface barriers, as confirmed by the clear signature plots (figures 5 and 6(a)).

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Considering our pristine (not electroformed) and almost stoichiometric TiO_2−x films, a low concentration of mobile ions is expected and the interface barrier should in principle be proportional to the metal work function [46] (W_f [52]). But in cases where a large amount of defect states are present at the interface, the total trapped charge also has an important role [46]. Fermi level pinning resulting in barrier heights independent of or weakly dependent on the metal work function are commonly obtained, as for example in the case of III–V materials [53]. This does not apply to our work, as although the barrier formed is not proportional to the metal work function, significant variations exist for distinct electrode materials. In order to better understand the formation of the interfacial barrier we also have to bear in mind that intermediate thin oxide layers of a few nanometres may be formed at metal/oxide interfaces [37], especially on samples exposed to environmental conditions [36]. Further to this, electrode/electrolyte interfaces may be degraded due to electrode reactions [34], while some induction of oxygen vacancies, acting as equivalent to doping, is also expected [38]. These processes result in the formation of an effective barrier with a height that deviates from the expected theoretical predictions. For ionic materials, the formed barriers have been correlated to the metal electronegativity [46] (X_m [54]). The strength of the correlation is typically assessed by the index S:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle S=\frac{d{{\Phi }_{{ B}0}}}{d{{X}_{m}}}{\rm .}\nonumber \end{align} \tag{ 6 }$$

There is considered to be a strong correlation to electronegativity when the S index approaches 1. For example, for silicon S  =  0.05, while for SiO₂, S  =  1 [46]. A clear linear relation is supported by our results depicted in figure 6(b). The calculated index is S  =  0.32. A similar trend, extracted in a completely different way, is presented in [38] that resulted in S  =  0.55, including materials such as Al and Ti, which in our case appear not to form an interface barrier. This is referred to as partial Fermi pinning that showcases the important role of interface states.

At this point it is worth noting an issue that has not been pointed out to date. This is the obtained inter-relationship between the two interfaces. Throughout this study, we employ this term to highlight that the TE material also results in modifications to the BE interfaces (positive biases in the I–V). Considering that the BE and the TiO₂ should be identical, due to common fabrication, we consider this an interesting finding and therefore it is discussed in more detail in the following section.

The TE material is found to affect the bottom Au/TiO₂ contacts (figure 3, positive biases) that are nominally identical for all employed prototype devices. In the cases of Al and Ti, no barrier is formed and therefore the conductivity is mainly determined by the film properties. In contrast, depositing Ni, Pt or Au as the TE appears also to instigate the formation of a barrier at the bottom interface, offering the opportunity to perform a quantitative study regarding the role of the TE to the BE interface.

Before proceeding to this analysis, however, it is essential to confirm that the differences obtained in the postitive part of the I–Vs are not the effect of the forward biased TE Schottky contact. For this we initially assumed that the BE is indeed ohmic, and the current flow is then described by equation (3), resulting in a forward biased Schottky contact. In this case, by differentiating (and for V  >  3 KT q^–1), we obtain

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \frac{dV}{d(LnI)}=RI+n\frac{{\rm KT}}{{\rm q}}.\nonumber \end{align} \tag{ 7 }$$

Therefore, a plot of dV/d(LnI) versus I should give a straight line with a slope corresponding to series resistance R and the intercept to the ideality factor n [55]. The plots for Ni, Pt and Au TEs are shown in figure 7 where clearly no linearity was observed.

Zoom In Zoom Out Reset image size

Another potential conduction mechanism, in the case of an ohmic BE, is space charge limited currents (SCLCs). SCLCs are commonly obtained in wide band gap materials and insulators when electrons are injected from the electrodes and no compensation charge exists. Typically, SCLCs present an ohmic dependence for low biases, followed by a regime where the traps dominate the process and I ~ V^m with m  >  2 [56]. For higher biases and injection conditions, the SCLC density J is given by equation (8) [46]:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle J=\frac{8}{9}\epsilon \mu \frac{{{V}^{2}}}{{{d}^{3}}} ~ \nonumber \end{align} \tag{ 8 }$$

where ε is the dielectric permittivity, µ the electron mobility and d the film thickness.

In this case, where the series resistance is not constant, we can then write from equation (8):

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle R\left( I \right)=\frac{V}{I}\sim {{I}^{-1/2}}.\nonumber \end{align} \tag{ 9 }$$

By subtracting R in equation (3) with equation (9) and by differentiating, equation (7) modifies to equation (10):

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \frac{dV}{d(LnI)}={\rm cons}{{{\rm t}}^{*}}{{I}^{1/2}}+n\frac{{\rm KT}}{{\rm q}}.\nonumber \end{align} \tag{ 10 }$$

Thus a linear relation in a plot of dV/d(LnI) versus I^1/2 is expected. The results for the TE metals are presented in figure 8.

Zoom In Zoom Out Reset image size

In addition to this, for high biases where any interface barrier (forward or reverse biased, equation (4)) is diminished, the SCLC should obey equation (8) by showing V² dependence and very weak (or negligible, for a narrow temperature range) temperature variation possibly due to changes in the electron mobility.

Although the results presented in figure 8 may be considered as supportive to equation (10) in the case of Pt (figure 8(b)) (fitting the linear regimes for Ni (figure 8(a)) and Au (figure 8(c)) TE results in ideality factor n  <  1), the current–voltage dependence does not obey equation (8) as presented in figure 9, while a strong temperature effect is also presented in figure 4. Such a bias dependence (m  >  2) obtained above V  =  2 V along with the temperature variation may be attributed to traps-controlled SCLC. This indicates that the devices have not reached the high injection regime (equation (8)), and thus for lower biases (V  <  2 V) an ohmic dependence is expected rather than the one indicated by equation (8). However, the latter is supported neither by figure 7 (equation (7)) nor by figure 9.

Zoom In Zoom Out Reset image size

Considering all these aspects, the Au(BE)/TiO₂ interfaces have been further assessed in detail following the previously employed temperature-dependent methodology. The obtained results for the Au/TiO₂ BE with respect to the TE material are summarized in table 2, while the corresponding signature plots are presented in figure 10. The fitting results (signatures) strongly support this analysis. A linear relation to the electronegativity of the TE material was also obtained for the BE interface barriers. In this case, the barriers formed are lower than those for the TEs but the same trend is followed. The data presented in figure 11 lead to S  =  0.48. This clearly depicts the influence of the TE material throughout the TiO₂ all the way to the BE, but also signifies the major role of the interface states.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

It is worth noting that while this feature was identified for the TE, it is not the case for the BE, highlighting the differences in the formation mechanisms of the two interfaces.

It is quite possible for the BE–TiO₂ interface to show a distinct behaviour to an identical interface, in terms of electrode material, lying at the top of a device, due to processing-induced effects. The up-to-date published works have typically used non-rectifying junctions for the BE, solely targeting the influence on the top interface characteristics and assuming similar signatures for both interfaces due to symmetry. Nonetheless, we recently demonstrated that even symmetric structures may overall render an asymmetric performance [57].

The I–V characteristics of structures having Au, Ti, Ni and Pt as the BE are presented in figure 12(a). The study was performed on a separate wafer target fabricated for this study (figure 1(b)). In all cases the TE is TiN deposited by sputtering. By observation of the acquired symmetric I–Vs, it follows that no interface barrier is formed in the cases where Au and Ti were used as BEs, denoting that the overall conductivity is controlled by the TiO₂ thin-film. Besides, the two structures exhibit different conductivities, suggesting that the BE material also plays a major role on the electrical properties of the deposited film. In cases where Pt and Ni were used as the BE, strongly asymmetric I–V characteristics were obtained, denoting an interface-controlled transport. In these cases, the I–V characteristics have been further assessed in the temperature range of 300 K–350 K in order to obtain the corresponding signature plots. The applied biases have been limited to 1.5 V and 1 V respectively, so as to avoid the devices undergoing either a soft or irreversible (hard) breakdown. For the sample with a Pt BE (figure 12(b)), the part of I–V plot corresponding to the BE (positive biases) presents a temperature-independent behaviour (highlighted in the red square). This, along with the signature plot presented in figure 12(c), supports the conclusion that tunnelling is the major mechanism responsible for the conductivity, indicating the presence of quite a high barrier at this interface, but which cannot be measured via equation (2).

Zoom In Zoom Out Reset image size

Conversely, for the device formed atop the Ni BE (figure 12(d)), signature plots have been obtained that confirm thermionic emission over the interface barrier as the dominant transport mechanism. The data analysis led to the estimation of the zero bias potential barrier at the interface (figures 12(e) and (f)). The results for the BE study are summarized in table 3 along with the metal work function and electronegativity, as those parameters may determine the interface barrier.

The differences obtained when the same metals were used as TE or BE could be assigned both to differences in the two interfaces as well as the core area of the film. It has been reported that BE materials may affect the concentration of the ions in the film [58], while local imperfections, e.g. roughness, could play a major role on the film microstructures [59], and thus both parameters can in turn modify the electrical response of the device. These two parameters are also heavily involved in the formation of the interface barrier. However, this is a much more complicated issue. The BE is the first layer that is deposited and thus this interface is more exposed during the sequential fabrication steps and the environmental influences than the top one, which is typically the last step before the characterization [58]. Moreover, during the oxide film deposition highly energetic particles are coming into contact with the BE material, making the local formation of the interfacial layer sensitive to this process step [34]. Conversely, for the upper layers of the film, the new deposited particles are hosted on a well-formed oxide film, rendering the formation of the top interface completely different to that of the BE. Therefore, identical metals form quite different barriers when used as TEs or BEs [57]. We note, however, that no straightforward quantitative correlation can be obtained at this stage for the BE, nor for its influence on the top interface. Therefore our results should raise attention to the necessity for more thorough and targeted studies towards understanding and control of the BE/TiO₂ interface. Ni as a BE results in Schottky behaviour for the TiN TE, whilst in the case of Pt, the important hysteresis presented in figure 10(b) denotes the notable contribution of ions that do not allow for the accurate extraction of parameters for the TiN TE (in the presence of a sufficient number of mobile ions, the conventional Schottky analysis is not valid), although its rectifying character is revealed.

This study has provided several new insights into the electrical properties of metal-TiO₂ interfaces. Evidently, these cannot be considered as conventional metal–semiconductor contacts, where the formation of the interface barrier is determined by the metal work function. Our quantitative results suggest that there are many parameters involved in the formation of these barriers, not in a straightforward manner, and therefore the drawing of concluding remarks should be based on carefully selected experimental comparisons and observations. Considering these, and for the devices fabricated on the same wafer having nominally identical Au BE and TiO₂ active layers deposited during the same process, we can reliably demonstrate the following.

Regarding the top contacts, two major regimes obtained. Al and Ti TEs do not form a rectifying barrier. In these cases the conductivity of the structure is determined by the TiO₂ film. This is found to be affected by the TE material, possibly due to interactions leading to an increase in oxygen vacancies. Conversely, in the cases of Ni, Pt and Au TEs, an interface barrier is formed and we can present some clear conclusions. The barrier height at the top interface is found to be proportional to the metal electrode electronegativity, highlighting the important role of the interface reactions in the formation of these barriers. The proportionality factor (S index) is far from 1, thus denoting the major contribution of the interface states (partial pinning). This study also came across an unexpected observation (interface inter-relationship), where the common Au BE interface barrier is not identical but was found to be determined by the TE material. Non-rectifying and electronegativity dependent barriers obtained, respectively. This requires that the metal electrodes are selected in pairs, as the TE defines the properties of the bottom interface as well. Considering this interesting finding, which has not been reported before, a thickness dependence study will be a natural progression to further verify our results. Therefore, comparisons performed on different stacks should be carefully considered as they may lead to serious misinterpretations.

Regarding the BE, the same trend does not apply, i.e. the BE barrier is not determined by the electronegativity. It is therefore concluded that different mechanisms are responsible for the formation of the interfaces in the BE cases, where the TiO₂ film is deposited on the metal, in contrast to the TE interfaces where the metal is deposited atop the TiO₂ film. This is consistent with our previous study, where an asymmetric barrier obtained on purely symmetric contacts [57]. However, the BE also seems to affect the top interfaces, as presented by our results on devices having identical films and TiN TEs, but not with a straightforward quantitative relationship, however. This further supports our argument that electrode materials should always be selected in pairs. Moreover, each material should be carefully considered with respect to its use as a TE or BE; although in some cases, such as Ti, no rectifying barrier is formed for either configuration, rendering the Ti/TiO₂/Ti system as the most suitable with which to study the film-controlled transport [50].

Considering the growth of and the prospects [15, 16] for oxide-based applications, including the Internet of Things, wearable electronics, reconfigurable and/or bio-inspired systems, the major role of TiO₂-based electronic devices, as well as the necessity for metal electrodes on top of or below their active area, we proceed by sharing some thoughts on the usefulness of our results across diverse MO applications. In the field of RRAM, where typically the devices are used after an electroforming step, Schottky barriers are considered essential for supporting resistive switching [60]. It was also reported that high barriers support both unipolar and bipolar resistive switching, in contrast to lower barriers that typically favour bipolar operation [61]. Moreover, metal-oxide interfaces are critical in determining the operation of both valence change memories (VCMs) and electrochemical metallization cells through the formation of barriers and electrochemical reactions [34]. The proper selection of metal electrodes can be used to engineer the electroforming process, in terms of polarity and applied field intensity, and perhaps even in developing forming-free RRAM technologies. The electrodes' characteristics are also of major importance to semiconductor devices. For example, when considering TiO₂-based bipolar devices it is essential to avoid any rectification stemming from the metal electrodes. Moreover, in the case of TFTs, different configurations may require source and drain electrodes atop or below the deposited MO films defining the TFTs' active area, and thus should be selected accordingly. Finally, several applications require the monolithic integration of such technologies. A prominent example is the use of diodes or transistors as selecting elements [62] for RRAM, rendering 1D1R and/or 1T1R configurations. Such cases typically exploit common metal electrodes acting both as BE and TE for different devices and thus should be accordingly considered, also bearing in mind the TE and BE inter-relationship issues.