The domain-wall/metal-electrode injection barrier in lithium niobate: Which electrical transport model fits best?

Abstract

The comprehensive description of both the electrical transport along conductive domain walls (CDWs) in lithium niobate (LNO) single crystals and the charge injection at the interfacing metal electrodes, emerged to be a complex challenge. Recently, a heuristic evaluation allowed to postulate the "R2D2" equivalent-circuit model (consisting of two parallel resistor-diode pairs) to appropriately match the DC current-voltage (I-V) characteristics. Here, we carefully revisit the interfacial electrical behavior, i.e., the diode part of the equivalent circuit model, since many more processes beyond the diode-related electron hopping transport (HT) assumed so far, may concurrently occur, such as thermionic emission (TE), Fowler-Nordheim tunneling (FNT), space-charge limited conduction (SCLC), and others more. The "R2D2" model thus needs to be generalized into an "R2X2" circuit model (with X = HT, TE, FNT, and others) to fit to the experimental data. Moreover, to double check for the best I-V curve fitting to the different theories, we apply a higher-harmonic DW current-contribution (HHCC) analysis, i.e., an AC I-V inspection, that allows us to discriminate between all these possible models with much higher precision than from pure DC I-V curve fitting. Both the AC and DC analysis reveal well consistent results, finally finding that the FNT model accounts best for the domain-wall/electrode junctions investigated here.

Figures (10)

• Figure 1: DC I-V characteristics of the two conductive LiNbO3 domain-wall samples of the present study and their equivalent circuits. (a) I-V curve of sample DW-1 that can be fitted with the "R2D2" model (inset) of ref. zahn_equivalentcircuit_2024, which would correspond to an assignment of the forward and reverse diode-like circuit parts to hopping transport (HT) in terms of \ref{['tab:conduction_mechanisms']}. (b) In contrast, the reverse current path is only weakly developed in the second exemplary sample of this work, DW-2, exhibiting a rectifying behavior, where the "R2D2" circuit model can be reduced to one branch: "RD". A "positive" voltage means here that the positive electrode is connected to the z+ side of the LNO crystal. The indices $f$ and $b$ refer to the forward and backward direction, while $R$, $I_\text{HT}$, and $U_\text{HT}$ symbolize the resistance, the diode's saturation current, and the diode's characteristic voltage (which bears the ideality factor), respectively (also cf. ref. zahn_equivalentcircuit_2024).
• Figure 2: Principle of higher-harmonic current contributions' (HHCC) acquisition of a structure consisting of a conductive ferroelectric domain wall in LNO single crystal contacted with Cr electrodes on the z+ and z- side. (a) Scheme of the electric circuit including signal generator, sample with two pairs of electrodes of the same area (one contacting the DW, the other contacting the pure bulk as a reference), and lock-in amplifier. The sample incorporates here an artificially poled single cylindrical ferroelectric DW as shown in the 3D close-up view. More details on the experimental setup are provided in sec. C of the Supplemental Material supplement. (b) Within the HHCC measurement, a sinusoidal voltage $U(t)$ is applied around the DC offset voltage $U_0$, see \ref{['equ:exc_voltage']}. Due to non-ohmic conduction behavior (here, exemplarily, the I-V curve of a single diode is shown), the electric current, as induced by the excitation field, follows a non-harmonic oscillation with the same periodicity in time as the excitation signal, which can be expressed in the trigonometric orthonormal base of sine and cosine functions with angular frequency $\omega_1$ and their integer multiples $\omega_m = m \cdot \omega_1$ (Fourier series). The HHCCs are characterized by their harmonic order $m$ and their complex amplitude $I_m$. (c) Nyquist diagram of the complex Fourier coefficients of the electric-current response, illustrated for the single-diode case, exhibiting a characteristic pattern in amplitude and phase as derived in \ref{['sec:methods:math']} and represented in \ref{['equ:diode_fourier_coefficients']}. The harmonic orders are color-coded from $m = 1$ to $m = 6$ in black, red, blue, green, grey, and orange, respectively.
• Figure 3: AC conductance of MgO:LiNbO3 domain walls, represented as absolute value $\lvert I_m \rvert$ (upper panels) and phase angle $\arg(I_m)$ (lower panels) of higher harmonic current contributions (HHCCs). The color coding for the harmonic orders $m$ is the same as in \ref{['fig:ac_principle:complex_plane']}. Experimental data is illustrated with dots, while theoretical predictions based on the I-V curve of the best-fitting R2D2 model are shown with solid lines. (a), (b) HHCC amplitude and phase as a function of the DC offset voltage on sample DW-1 (constant excitation parameters: $\omega_1/2 \pi = 1.5kHz$, $U_1 = 0.71V$) within a small voltage range. They fulfill several relations discussed in \ref{['sec:results:consistency']}, acting as consistency checks for the measurement working principle. (c), (d) Full-range DC offset voltage dependence, extending the view shown in panel (a) and (b) that is indicated in gray in the panel (c). A good agreement with the R2D2 model is observed for the amplitudes and phases of the first to third harmonic order, as discussed in mich more detail in the text. (e), (f) HHCCs of sample DW-2 under variable AC amplitude (constant parameters: $\omega_1/2 \pi = 23Hz$, $U_0 = 0.7V$).
• Figure 4: Static I-V characteristics (recorded with $\text{d}V/\text{d}t = 0.5V/s$) of samples DW-1(a) and DW-2(b) modeled with different equivalent circuits of the R2X2 type. The space charge limited conduc-tion (SCLC) model (light green) is plotted next to the hopping transport (light blue), the thermionic emission (orange), and Fowler-Nordheim tunneling models (dark green). Since the latter three models are hard to distinguish visually, the residuals between experimental data and fit curves, are plotted in the the lower panels (c) and (d). The grayish ranges were excluded from the fitting procedure. The inset within panel (a) sketches the three best-fitting X-part processes within a simplified band scheme.
• Figure 5: Comparison of measured and (on the basis of the static-I-V curve fit parameters) predicted/calculated HHCCs for sample DW-1. The predictions are shown for the three best-performing equivalent-circuit models of the R2X2 type, using the hopping-transport/classical-diode description (light blue solid line), the thermionic emission model (orange solid line) and the Fowler-Nordheim tunneling (dark green solid line) for the X-part. Separately shown are the measured absolute values of the (a) first (black dotted), (c) second (red dotted) and (e) third (blue dotted) harmonic order current contributions. Note that the experimental data and acquisition parameters are the same as in \ref{['fig:ac_results:offset:amp']}, that the complete data sets including also the HHCC phases and the weaker-performing SCLC and TFE models can be found in SI-fig. S4, and that the grayish ranges were excluded from fitting. The lower panels (b,d,f) contain the corresponding residuals $\mathcal{D}_i$ for the three best-performing models showing that with rising harmonic order, it becomes clearer and clearer that the FNT model shows the lowest residuals.