Space-charge limited conduction in epitaxial chromia films grown on elemental and oxide-based metallic substrates

The magnetoelectric (ME)¹ chromia (Cr₂O₃)² is an antiferromagnetic oxide, whose bulk order parameter may be manipulated by the application of an electric field. At the same time, this dielectric is known to exhibit a robust boundary magnetization (at its (0001) crystalline surface), the direction of which may be controlled by the application of a suitable electric field.^3–5 Recently, this boundary magnetization has been exploited to implement an all electrical scheme for the exchange biasing of a nearby magnetic multilayer,⁶ a result that represents a critical step for attempts to develop electrical control of magnetism for spintronics. This approach of voltage control of magnetism (VCM) has the potential to replace existing approaches to spintronics (such as spin transfer torque), which typically rely on the use of energetically-costly electrical currents for magnetic switching. In contrast, the use of even large electric fields to switch the boundary magnetization of chromia should (ideally) arise without any associated current, allowing VCM to be achieved at low power levels (the reader is referred to Ref. 7 for a recent benchmarking of chromia-based spintronics.)

Chromia is a linear ME that exhibits a transition from the paramagnetic to the antiferromagnetic phase at a Néel temperature of T_N = 307 K,^2,8 making it one of the few materials to exhibit magnetoelectricity at room temperature. Its boundary magnetization onsets with the appearance of the antiferromagnetic order, and is found to be insensitive to the presence of roughness.³ Dependent upon the oxygen partial pressure utilized during the growth process, and on the impurities present within the material, chromia can be either a p-type or an n-type semiconductor.^9,10 In bulk form, at least, its large bandgap of ∼3 eV¹¹ results in high intrinsic resistivity (ρ ∼10¹⁴ Ωcm at 300 K),¹² a key requirement for the implementation of low-power schemes for VCM. For practical devices, however, it is necessary to realize chromia in thin-film form, and a key challenge here is to meet this objective while maintaining the dielectric character of the material. Previously, thin-film growth has been implemented by a number of methods,^10,13–21 with significant variations being reported in the resistivity of the resulting films. Published values vary from 10² − 10⁹ Ωcm, with resistivities at the lower end of this range being obtained by sputter deposition,¹⁴ while those at the upper end are synthesized via pulsed-laser deposition.¹⁶ Most importantly, there have recently been successful reports^20,21 of VCM for Cr₂O₃ films with resistivity values as low as 10⁶ Ωcm. This places a useful lower constraint for the purpose of future device development.

While the discussion above makes clear the motivation for utilizing chromia in future spintronics, this field nonetheless remains at a nascent stage, with a strong need to optimize the electrical properties of this material. This is particularly true for the thin-film form of chromia, whose properties (as noted already) are already known to be strongly sensitive to the details of preparation. Motivated by this, we have undertaken a detailed electrical characterization of thin chromia films, deposited on various substrate materials (Pd, Pt and V₂O₃). These substrates were chosen due to their wide use in oxide-film synthesis, and exhibit different lattice mismatch (3.9% for Pd, 3.1% for Pt and 0.1% for V₂O₃²²) with chromia. Consequently, we are concerned with understanding the manner in which this influences the resulting dielectric properties of the chromia films. We find clear evidence for space-charge limited conduction (SCLC)^23–25 in the films, and show that the details of this are sensitive to the choice of the underlying substrate. Most notably, the highest resistivity is obtained for chromia films fabricated on V₂O₃ substrates, consistent with the improved lattice matching to this material. We furthermore calculate various electrical properties for chromia, including its effective mobility, its total trap density, and its substrate-dependent trap distributions and energies. Based on these studies, we suggest that chromia thin films formed on V₂O₃ substrates are a promising candidate for next-generation ME spintronics.

To aid the analysis and understanding of our experimental results, in this section we give a brief overview of electrical-conduction mechanisms in thin dielectrics. SCLC is widely exhibited by such materials,^23–25 and arises when current through the insulator becomes limited by the build-up of charge injected from the source electrode. This mechanism dominates once the applied voltage (V) reaches a characteristic value (V_tr), at which point the number of injected charge carriers in the vicinity of the source becomes equivalent to the number of thermally-generated ones.²⁶ At smaller voltages (V < V_tr), in contrast, thermal carriers provide the dominant contribution to the current, and ohmic conduction is consequently obtained. In the presence of these two mechanisms, the total current density may follow the functional form:

where the parameters α and β are associated with ohmic transport and SCLC, respectively. The defining equations for these parameters can be expressed as:^27–30 

In these expressions, n is the density of thermally generated charge carriers, q is the electronic charge, μ is the carrier mobility, d is the film thickness, ε_r is the dielectric constant and ε₀ is the permittivity of free space. $Θ$ is the ratio of free carriers to the total carrier concentration (i.e. free plus trapped charges). Assuming n-type material, this ratio can be expressed as:²⁶ 

where g_n denotes the degeneracy of energy states in the conduction band, N_t is the total trap density, N_c is the effective density of states in the conduction band, E_t is the trap energy, E_c is the energy at the conduction band edge, k_B is the Boltzmann constant and T is the temperature. In samples free of traps, the parameter $Θ$ = 1. In the presence of traps, however, the value of $Θ$ is voltage dependent, ultimately reaching unity once the last trap is filled.³¹ The product $μΘ$ in Eq. (3) may be used to define an effective mobility, the value of which may be inferred directly from the observed current variations (as we demonstrate below).

Quite generally, the interplay of ohmic transport with SCLC leads to a four-stage conduction mechanism in dielectrics, as illustrated schematically in Fig. 1(a).^26,31,32 Starting from the situation at low bias, these mechanisms are as follows: (1) ohmic-like conduction (⁠$I∝Vm$⁠, m = 1); (2) trap-limited SCLC (m = 2); (3) the trap-filled limit (reached at voltage V_TFL, m > 2), and; (4) trap-free SCLC (m = 2). Dependent upon the nature of the defects in the material, a variety of I-V curves may therefore be exhibited. In an insulator free of traps, for example, only stages (1) and (4) will be observed. With discrete traps present (with energy E_T, see Fig. 1(b)), on the other hand, charge will begin to fill the traps at V_tr (see Fig. 1(a)), an estimate for which can be derived by equating both terms on the right side of Eq. (1) and determining the $Θ$ term from Eq. (4). In this way it can be shown that the resulting value for V_tr can be expressed as:²⁶ 

where E_F denotes the Fermi level. From this relation it is apparent that V_tr increases with increasing temperature. At voltages larger than this value, the second (β) term on the right-hand side of Eq. (1) dominates the current, as injected carriers overwhelm thermally-generated ones. However, once all traps are completely filled, implying that the quasi-static Fermi level is precisely aligned with the energy of the shallowest trap, a sudden increase in current (step 3 in Fig. 1(a)) will be observed.³¹ At even larger voltages than this, the I-V curve will once again resume its square-law dependence (step 4 in Fig. 1(a)), reflecting the influence of trap-free SCLC.

In some studies,^33,34 it has been suggested that the traps in insulators should be distributed exponentially in energy (with a characteristic energy range E_t, see Fig. 1(c)). Under such an assumption, the trap distribution is expressed as:

where T_C is a temperature scale that defines the characteristic energy (E_t = k_BT_C) of the traps and E is the energy measured from the bottom of conduction band (again, assuming an n-type semiconductor). In this situation, the transition to the third stage of SCLC in Fig. 1(a) will no longer be sharply defined and the current will rather follow the expression:

where l = T_C/T.

Single-crystal chromia films (300-nm thick) were prepared on α-Al₂O₃ (0001) substrates, after first depositing a conductive layer to serve as a bottom electrode in electrical measurements. Our main focus here was on understanding the influence of this electrode material on the resulting dielectric properties of the films, to which end platinum, palladium, and vanadium oxide (V₂O₃) were utilized. Pt and Pd were selected since they are commonly used metals in semiconductor microfabrication, while V₂O₃ was utilized since it is a conductive oxide and so expected to be compatible, in many ways, with chromia. In a recent study where we explored the morphology of chromia synthesized on these films,²² we used conductive AFM to show that electrical leakage was significantly reduced for chromia on V₂O₃, a result that was attributed to the absence of twinning defects in that system. That having been said, no analysis was made of the leakage mechanisms in these films and it is this issue that forms the focus of this study.

The various conductive layers used to seed the chromia growth were synthesized via different methods, dictated by the specific properties of these crystalline layers. Molecular beam epitaxy (MBE) was used for the growth of a Pd(111), while Pt(111) films were deposited by DC magnetron sputtering, and V₂O₃(0001) was grown by pulsed laser deposition (PLD). Typical thickness of these layers was around 25 nm.²² Following the growth of the bottom electrode, the samples were transferred to a PLD system and held at 700 °C. Chromia was then ablated from a (99.99% pure) ceramic target to deposit a thickness of 300 nm on the samples. X-ray diffraction analysis confirmed the good (0001) texture achieved for the chromia with different back electrodes. Twinning (i.e. 60° rotated domains) was observed in the Pd- and Pt-based crystalline films,²² consistent with previous observations.³⁵ (For further details on the synthesis and structural characterization of such films we refer the reader to Refs. 22, 35–38.)

Following thin-film growth, Cr(50nm)/Au(150nm) electrodes of area 50 x 50 μm² were fabricated on top of the chromia via a standard, photolithography and lift-off. Metal deposition was performed by electron-beam deposition, under a vacuum of less than 5 μTorr. I-V measurements of the films were then made with the samples mounted on the cold finger of a closed-cycle cryostat, under vacuum conditions below 1 μTorr and over the temperature range of 200 – 400 K. The latter range was chosen since V₂O₃ undergoes a metal-insulator transition near 160 K,^39,40 below which this layer is unable to function as an efficient electrode.

In our previous analysis of the electrical conductivity of chromia, grown on different metallic substrates, we found a significant statistical spread in the resistivity values, exhibited in measurements of nominally identical electrodes.²² In the study here, we focus on a comparison of the conductivity mechanisms exhibited by the most resistive of these contacts, since these are considered to be most indicative of the “intrinsic” nature of these materials. In Figs. 2(a)–2(c) we display representative I-V curves for the different chromia films. The main panels plot this data on linear axes, while in the lower insets the current is indicated on a logarithmic scale. Data are provided for the temperature range of 200 – 400 K and the overall behavior is qualitatively reminiscent of that observed for (bulk) chromia crystals.¹² The I-V curves exhibit pronounced nonlinearity, and the current increases strongly with increasing temperature, both indicators of the insulating nature of this material. In the upper inset to Fig. 2(c), we show the corresponding change of resistivity (calculated for an electric field of 33 kV/cm) of these films, as a function of temperature. From a comparison of these data we see that chromia exhibits its highest resistivity (∼5 TΩcm at 300 K) when synthesized on V₂O₃, for which substrate the resistivity is close to that of crystalline chromia (∼10 TΩcm at 300 K).¹² The highest leakage, on the other hand, is found for chromia on Pd, for which the corresponding resistivity (∼50 MΩcm at 300 K) is almost six orders of magnitude smaller than that of chromia on V₂O₃.

Turning to a more detailed analysis of the current variations exhibited by the different films, for Cr₂O₃ on Pd we find that the I-V curves are well described by the form of Eq. (1). To illustrate this, in Fig. 2(a) we have used this relation to perform a two-parameter (α & β) fit to the measured currents. The fits are indicated by the solid lines and closely follow the experimental data, which are plotted using the open circles (for clarity, only 10% of data points are shown). The β term enables an estimate of the effective mobility (⁠$μΘ$⁠, see Eq. (3)), and in the main panel of Fig. 3 we plot the variation of this quantity as a function of temperature. Much like the behavior reported for bulk chromia, and for numerous other insulators (See Ref. 12 and references therein), we find that this mobility increases exponentially with increasing temperature. Another parameter that may be inferred from the fits is the voltage (V_tr) at which SCLC exceeds ohmic conduction (defined as $Vtr=α/β$⁠, see Eq. (1)). For these particular films, V_tr increases with increasing temperature, a result that is consistent with the prediction of Eq. (5) for SCLC in the presence of discrete traps. To establish this connection explicitly, in the inset to Fig. 3 we plot $ln(Vtr)$ vs. $1/kBT$ and find that the resulting data fall on a straight line. The slope of this line yields information on the trap energy E_T, and from the data in the figure we obtain E_T − E_F ∼ 50 meV. While the value of the Fermi level in this material is not known a priori, its insulating character would tend to suggest a position somewhat close to midgap. Consequently, the inferred value of E_T points to the presence of deep traps, located well away from the conduction band. This conclusion can be reconciled with the results of a recent structural study,²² which has demonstrated a preponderance of twinning defects in chromia when it is grown on Pd. Calculations,⁴¹ based on density functional theory, suggest that these defects may give rise to a local reduction of the bandgap (by as much as 65%), in those regions corresponding to the boundary between neighboring, twinned domains. Such a reduction could be considered to be consistent with the presence of deep traps.

To understand the nature of the current variations exhibited by the other two types of film, in Fig. 4 we replot their I-V curves on double-logarithmic scales. In each of these panels, we observe a transition from ohmic conduction (⁠$I∝Vm$⁠, m ≈ 1) to SCLC (m ≥ 2), as the magnitude of the applied voltage is increased. In contrast to the behavior exhibited by Cr₂O₃ on Pd, the voltage scale (V_TFL) associated with this transition is found to shift to smaller values with increasing temperature. Such behavior is consistent with expectations for materials whose traps are distributed exponentially within the gap (see Fig. 1(c) & Eq. (6)). Behavior of this kind has been reported previously for numerous dielectric materials,^42–45 and is especially clear in the V₂O₃-based films (Fig. 4(b)), in which the power-law exponent (m = l + 1) associated with SCLC increases from around 3 to 7 as the temperature is lowered over the indicated range.

In the insets Figs. 5(a) and 5(b), we plot the variation of the power-law index (l) as a function of 1/T. The resulting data fall on a reasonable straight line, consistent with the definition of l in Eq. (7). The slope of the resulting straight line allows an estimate of the characteristic range (E_t) of the exponential trap distribution, and from the insets in Fig. 5 we infer E_t= 27- & 90-meV for Cr₂O₃ on Pt and on V₂O₃, respectively. In contrast to the case of the Pd-based films, these values correspond to trap distributions that are relatively shallow, lying close to the conduction band.

With an exponential distribution of traps, it is possible to make an estimate of the total trap density (N_t), by extrapolating the space-charge limited component of the current back to larger voltages. As we demonstrate in the main panels of Fig. 5, this yields a temperature-independent fixed point (V_c) at which the various I-V curves intersect one another. To obtain an analytical solution of V_c, we follow the treatment in Ref. 47 by writing Eq. (7) in an Arrhenius form to isolate the temperature dependence of the current. After some algebraic calculations, Eq. (7) may then be expressed as:⁴⁶ 

where:

At the voltage V_c, the space-charge limited current is temperature independent and the form of Eq. (8) implies that:

By making use of Eq. (10), and the experimentally determined values of V_c from Fig. 5, we obtain the total trap densities N_t = 2.1 × 10¹⁹ cm^-3 & 3.2 × 10¹⁸ cm^-3 for Cr₂O₃ on Pt and on V₂O₃, respectively. These values fall within the range expected of high-quality insulating thin films.^25,46,47 Interestingly, we note that the trap density is an order of magnitude smaller for Cr₂O₃ on V₂O₃, which might be related to the improved lattice matching (with just 0.1% mismatch) in this system.

In this report, we have demonstrated how it is possible to use temperature-dependent measurements of current leakage in epitaxial chromia films, grown on different conducting substrates, and to infer quantitative information on the microscopic characteristics of their defects. The studies here suggest a fundamental difference between chromia films grown on Pd, and those formed on Pt and V₂O₃ substrates, with the former being dominated by deep, discrete traps while the latter are characterized by the presence of exponentially-distributed, fairly shallow traps. This difference is consistent with what we have learned previously,²² from structural investigations of these films. These have shown that growth on Pd results in films with a preponderance of twinning defects, which function as highly-effective leakage paths. Theoretically, the leakage has been attributed to a 65% reduction of the chromia bandgap, which arises at the boundaries between neighboring twinning domains.⁴¹ At the same time, our analysis has shown that the leakage in these particular films may be attributed to the presence of deep traps, a result that could be consistent with such bandgap narrowing at localized positions. Our earlier work²² showed that the twinning defects can be suppressed through the growth of chromia on either Pt or V₂O₃, consistent with which the microscopic nature of the defects in these films is found to be very different to that in Cr₂O₃ on Pd. The resulting traps are much shallower in energy, and distributed exponentially within the forbidden gap, in contrast to the discrete, deep traps inferred for Cr₂O₃ on Pd. The presence of such different trap distributions should, perhaps, not be altogether surprising; while the twinning defects are suppressed by growing chromia on either Pt or V₂O₃, these materials are nonetheless known to exhibit dislocations that may function as an alternative source of trap(s).^48–51 

In conclusion, we have measured the temperature dependent (200 – 400 K) dielectric breakdown of high-quality, epitaxial chromia films, synthesized on various conductive substrates (Pd, Pt and V₂O₃). While we find evidence of SCLC in all of these materials, Pd-based chromia is found to exhibit behavior consistent with the presence of deep, discrete traps. The Pt- and V₂O₃-based films, in contrast, show behavior typical of insulators with shallow, exponentially-distributed traps. The total trap density is approximately an order of magnitude smaller in the V₂O₃-based films, a characteristic that appears consistent with the fact that the resistivity in this film system approaches that of bulk chromia. Overall, our results suggest that V₂O₃-based Cr₂O₃ is a promising candidate for the implementation of next-generation spintronic devices.

This work was supported in part by Antiferromagnetic Magneto-electric Memory and Logic (AMML), one of the centers in nCORE as task 2760.001, a Semiconductor Research Corporation (SRC) program sponsored by the NSF through ECCS 1740136. It was also supported by the Center for Nanoferroic Devices (CNFD), an SRC-NRI Nanoelectronics Research Initiative Center under Task ID 2398.001.