# Tunable Non-Volatile Memory by Conductive Ferroelectric Domain Walls in Lithium Niobate Thin Films

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{2}, consisting of Cr/Au with a thickness of 100 nm, were evaporated and lithographically structured to enable the electrical characterization.

^{2}and a thickness of 100 nm on a LNO film with a thickness of 600 nm and Ti/Pt back electrode.

## 3. Results

#### 3.1. Conductive AFM Investigation

^{−2}nA). At the DW position, however, there is a strong nonlinear increase in current with applied voltage. At all points, a significant increase over several orders of magnitude (at least three) can be observed, which sufficiently separates these states from the background. The temporal stability measurements show a small increase in current over time. An example is given in Figure 1e. Local probe measurements on these CDWs reveal a stable conductance after 3 h with a minute increase over the measurement of 5% between 1 h and 3 h, hence influences by drift can be ruled out for the given shorter-term measurement.

#### 3.2. Phase-Field Simulation

_{S}sin α.

#### 3.3. Resistive Switching Investigations

_{set}= 21.05 V with an accuracy of ∆V

_{set}/V

_{set}= 10

^{−3}, which is proven to be the local coercive voltage from PFM measurements. This value of V

_{set}is not only reproduced for a single device, but also for 50 individual devices on a single wafer, which clearly underlines the very precise and reproducible behavior of single-crystalline resistive switching devices. Up to a voltage of −3 V, a very symmetric current–voltage relation can be observed. Yet, for larger negative biases, the absolute value of the current saturates and is not stable anymore but reduces with time. The given cycles in Figure 3d are obtained with a cycle frequency of 1.5 mHz. The observed behavior is very similar to back-switching observed upon current injection from the top electrode at small voltages confirmed by PFM. Hence, we suppose, upon the application of a negative bias, insulating straight or tail-to-tail DWs are formed or domain inversion is invoked; thus, there is no complete conductive channel anymore, which prohibits a current flow.

^{−8}A at −210 V. We can observe the reproducible set voltage. However, below this specific voltage, a slight increase in current can be observed. In general, this current, which deviates from the first cycle, is smaller the lower the current at V = −210 V. It saturates after several cycles. Several reasons are possible, e.g., deep traps, which are incorporated into the film upon large current flow. Hence, for endurance testing high voltage treatment was kept as short as possible. In Figure 3f the endurance upon such cycling is shown. The resistance is measured after every cycle. The LRS is created on application of V

_{set}= 21.1 V. The system is released into the HRS upon application of V = −210 V. This results in a very enduring resistive switching device over at least 10

^{5}cycles. The states can be read out without destruction. The temporal stability of the LRS is given in Figure 3g. As is visible, the conductance is very stable over at least 10

^{4}s. Hence, assuming an exponential decrease and a minimum current of 80%, a stability over 10

^{8}s or 10 years can be predicted. Similar measurements with an AFM tip revealed the stability of the current on CDWs over at least 3 h, which is about the longest time to measure due to probe drift. The statistical results given in Figure 3h show a sufficiently high margin for the application as a nonvolatile memory.

#### 3.4. Conductance Type Extraction

^{2}in a log–log plot. A fit is given, which shows a perfect fit over almost two voltage magnitudes. In Figure 4b the I–V curve is linearized according to Shottky thermioninc emission (STE). A good fit can be seen in a medium voltage range, but both for a small and large voltage significant deviations are visible. Similarly, in the case of Poole–Frenkel (PF) linearization given in Figure 4c, we obtain a reasonable fit for medium voltages, but discrepancies for very low and high voltages. Yet, it would be not sufficient to formally exclude these two transport mechanisms. Likewise, the linearization with Fowler–Nordheim (FN) tunneling does not give a decent fit. In the LRS we obtain a flat line. Hence, the first three transport mechanisms still have to be considered. Thus, we used the abrupt junction approximation, which assumes a pn-junction with an abrupt doping profile [31] Even though the main advantage of this method is to understand impedance upon a DC bias, it is still helpful to analyze the plain DC I–V curves as dlog(I)/dV is independent on most parameters, especially the contact area; it is, hence, more robust, especially upon temperature changes, and it is possible to differentiate between FN and PF. Hence, in Figure 4d, the I–V curves in a temperature range T between 300 K and 340 K are given. Only SCLC and PF [both dlog(I)/dV ∼ V

^{−1}] can describe such a curve, whereas STE [dlog(I)/dV ∼ V

^{−3/4}] cannot describe this behavior. Yet, in the case of PF, a very strong component ∝ V

^{−1/2}should also be present, which cannot be seen in the measurements. The I–V SCLC curve fit is almost perfect over two orders of magnitude and, thus, significantly better than those of PF and STE.

^{−18}m

^{2}/s, which is derived from experimental values of lithium transport in Li

_{x}Si [32], the estimated ionic movement over 100 ms is about ∼0.8 nm at a field of 2 × 10

^{7}V/m and room temperature T = 300 K, which is about three orders of magnitude smaller than the film thickness. Reported values for the ionic transport diffusion constants in LNO (e.g., Li, H, D, Na, Mg) at elevated temperatures and interpolated to room temperature are significantly smaller. Hence, we can exclude ionic current having a major share.

_{eff}9εμ(T)V

^{2}/8d

^{3}with A

_{eff}the effective contact area, d the thickness of the dielectric film, ε the static permittivity, and μ(T) the mobility of the major charge carrier. Using the current extracted from cAFM measurements, we can derive a mobility of about 5 ± 3 × 10

^{−2}cm

^{2}/Vs, which is in good agreement with previously reported macroscopic photo-induced current measurements [34]. The temperature dependence in an SCLC transport regime is solely determined by the temperature dependence of the mobility of the major charge carrier.

#### 3.5. Temperature Dependent Conductance

_{Li}

^{4+}+ Nb

_{Nb}

^{5+}→ Nb

_{Li}

^{5+}+ Nb

_{Nb}

^{4+}, Ea ∼ 0.65 eV

_{Li}

^{4+}+ Nb

_{Li}

^{5+}→ Nb

_{Li}

^{5+}+ Nb

_{Li}

^{4+}, Ea ∼ 0.2 eV

_{Li}

^{4+}+ Fe

_{Li}

^{3+}→ Nb

_{Li}

^{5+}+ Fe

_{Li}

^{2+}, Ea ∼ 0.03 eV.

^{2+}is given to be 0.35 eV [36], hence, only a little larger than Li for bound and free polarons, but as the hopping rate follows w ∼ e

^{−r/a}≈ e

^{−r[Å]}, hopping transport is very unlikely for the given concentrations and even for lightly doped Fe:LNO not relevant. A conversion to bound and small polarons is unlikely due to the high binding energy of 1.22 eV.

## 4. Discussion and Conclusions

_{Li}is < t

_{NbLi4+}≥ 100 Å and for the free polaron is < t

_{NbNb4+}≥ 80 Å. These values were derived by interpolation from the data of Mhaouech and Guilbert [35] under consideration of the smaller iron impurity concentration c

_{Fe}= 10

^{17}cm

^{−3}and a niobium antisite defect concentration of c

_{NbLi}= 10

^{21}cm

^{−3}. Upon drift condition, these values can be larger. Hence, the bound polaron has a larger mean free path. However, the hopping rate of bound polarons is only w

_{NbLi4+}= 10

^{7}s

^{−1}. Assuming the hopping rate to depend mainly on the nearest neighbor distance, like w~e

^{r[Å]}, we can calculate, that the hopping rate of free polarons is two orders of magnitude larger, hence w

_{NbLi4+}= 10

^{9}s

^{−1}. Thus, the electric current with free polaron transport as in Mg:LNO can be significantly larger. This again explains why, for the case of bulk material only, congruent Mg:LNO revealed a conductance upon UV illumination. For the ultrathin LNO films in use in this study, even undoped material can give measureable conductance.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**DW conductance in the congruent LNO thin films: (

**a**) domain configuration by PFM; (

**b**) cAFM scan at a bias voltage of 3 V; (

**c**) Local I–V measurements on conductive DWs at four marked spots; (

**d**) logarithmic plot of the detected current; (

**e**) temporal development of the current at spot 4 at an external bias voltage of 10 V.

**Figure 2.**(

**a**) Three-dimensional phase field simulation of CDW formation under an AFM tip for a 20 nm thick lm at 20 V. ① Nucleation, ② through domain formation until equilibrium under external bias, ③ equilibrium domain after removal of bias. (

**b**,

**c**) evolution of inclination angle for film thicknesses, d, of 50 nm and 20 nm respectively; (

**d**) equilibrium inclination angle after removal of bias as a function of applied field; (

**e**) measured current I

_{read}at a bias voltage of 10 V for domains written at various writing voltages V

_{write}, for comparison PFM scans; (

**f**) extracted maximum domain wall current.

**Figure 3.**Investigation of the switching behavior, endurance, stability, and tunability of resistive switching of the Pt/LNO/Cr/Au stack with a contact area of 2000 μm

^{2}. (

**a**) film stack configuration (

**b**) PFM scan of a written domain (

**c**) cAFM scan at a bias voltage of 3V; (

**d**) full I-V cycle (f = 1.5 mHz) with a very defined set voltage V

_{set}= 21.05 V (DVset/Vset~10

^{−3}), hence a comparably small electric field E

_{switch,off}= 0.3 MV/cm and strongly rectifying behavior without significant leakage upon an electric field of E

_{switch,off}= 3.4 MV/cm with a resistance of >20 TW, (

**e**) switch-on I-V cycle with constant switch-off voltage V

_{switch,off}= −210 V, (

**f**) endurance of high resistance and low-resistance state (HRS, LRS, respectively) over at least 10

^{5}cycles with a resistance window of >10

^{4}and a read voltage of 10 V, (

**g**) time stability of low resistant state over 104 s, which yields an 80% reliability over 108 s or 3 years, (

**h**) probability of the current in HRS and LRS at 10 V for 50 tested devices on the same single crystalline thin-film (

**i**) tunability of readout current I

_{read,on}under modulation of writing time t

_{write}and writing voltage V

_{write}. The read-out current I

_{read,on}reduces for larger writing voltages V

_{write,on}. I

_{read,on}is the average value over 100 writing cycles each.

**Figure 4.**Conductance type analysis on CDWs in LNO (

**a**) SCLC I–V plot; (

**b**) STE I–V plot; (

**c**) PF I–V plot; (

**d**) derivative plot. The I–V curves show the first cycle and the stationary cycles after 20 cycles. The off-state was obtained by applying V = −210 V until the current is reduced to 10

^{−8}A.

**Figure 5.**Temperature dependence of the current for thin-film LNO. Measured current at different voltages from 360 K to 77 K. We can observe different regimes of thermal activation ① above 300 K with Ea = 0.63 eV, at ② between 300 K and 100 K with Ea = 0.18 eV and ③ below 100 K with a thermal activation of Ea = 0.03 eV. These are overlaid with the inverse bound polaron lifetime, as calculated by Monte Carlo (MC) simulations.

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## Share and Cite

**MDPI and ACS Style**

Kämpfe, T.; Wang, B.; Haußmann, A.; Chen, L.-Q.; Eng, L.M.
Tunable Non-Volatile Memory by Conductive Ferroelectric Domain Walls in Lithium Niobate Thin Films. *Crystals* **2020**, *10*, 804.
https://doi.org/10.3390/cryst10090804

**AMA Style**

Kämpfe T, Wang B, Haußmann A, Chen L-Q, Eng LM.
Tunable Non-Volatile Memory by Conductive Ferroelectric Domain Walls in Lithium Niobate Thin Films. *Crystals*. 2020; 10(9):804.
https://doi.org/10.3390/cryst10090804

**Chicago/Turabian Style**

Kämpfe, Thomas, Bo Wang, Alexander Haußmann, Long-Qing Chen, and Lukas M. Eng.
2020. "Tunable Non-Volatile Memory by Conductive Ferroelectric Domain Walls in Lithium Niobate Thin Films" *Crystals* 10, no. 9: 804.
https://doi.org/10.3390/cryst10090804