Evolution of the Ferroelectric Properties of AlScN Film by Electrical Cycling with an Inhomogeneous Field Distribution

This work investigates the evolution of the ferroelectric (FE) performance of the sputtered aluminum scandium nitride (AlScN) thin film, which has a high remanent polarization (Pr, > 100 µC cm−2) and coercive field (Ec, > 6 MV cm−1), with the electric field cycling. The work aims at elucidating the underlying origin of the severe fatigue behavior, even with a relatively small number of endurance cycles (<105). When cycled with a low electric field, an internal field is created by charges trapped between the FE layer and the interfacial dielectric layer (non‐FE). On the other hand, fatigue is observed when cycled with a high electric field cycling. This work proposes a new method to simulate a switching current utilizing an inhomogeneous field mechanism and the appropriate circuit model to assess the thickness change of the non‐FE layer. It is concluded that the thickened non‐FE layer after the field cycling results in fatigue.


Introduction
Ferroelectric (FE) thin films have been intensively studied due to their bistable and switchable remanent polarization (P r ), which could be utilized for non-volatile memory. As a result, FE field-effect transistors (FeFET) and FE random access memory (FRAM) have received much attention, but only a niche market due to defects, resulting in low endurance. According to the recently reported literature, the leakage current of AlScN increased due to the nitrogen vacancies formed during the field cycling, and the Joule-heating-induced leakage current caused the breakdown. [11] Another major reliability problem is fatigue, in which the P r decreases with the increasing number of field cycling. The AlScN films exhibited lower endurance characteristics (<10 5 ) than conventional FE materials. [11,13] Fatigue is observed in other FE materials, such as PZT and HZO thin films, which have been extensively studied. [9,14] However, no systematic investigation on the fatigue of AlScN has been conducted. Ensuring a sufficient cycle number is crucial for the memory application.
Therefore, this work analyzed the fatigue mechanism of the sputtered AlScN by examining the electrical property variation with the electrical cycling. It is known that fatigue is greatly influenced by the interfacial dielectric layer (non-FE) between the electrode and FE. The non-FE interfacial layer can induce charge trapping, which may hinder polarization switching. [15,16] Also, the increased non-FE layer thickness causes a significant depolarization field in the FE layer following field cycling. [17,18] These factors can make the polarization state unstable, leading to fatigue.
Therefore, examining the non-FE layer is required to understand the fatigue phenomenon, but not many methods have been proposed to analyze non-FE experimentally, especially in AlScN film. The pulse-switching measurement (PS), which has been extensively used to examine the interfacial non-FE layer properties in PZT and HZO films, can also be adopted in this case. [19,20] The PS method suggested by Jiang et al. helped extract the capacitance (C i ) of the interfacial non-FE layer and contact resistance during the switching using the switching current measured by square pulse. [19] This method fundamentally assumed a uniform switching of the entire ferroelectric capacitor area, which could be probable only when the coercive voltage (V c ) of all grains in the polycrystalline film is the same.
However, as reported for the randomly oriented polycrystalline HZO film, [21] the uniform switching of all grains in the polycrystalline film may not be guaranteed in this AlScN film. This problem can be ascribed to the circumstance that the local electric field at each grain, which has different crystallographic orientations and defect density, would be applied differently at a given bias voltage. [22] Under this circumstance, the inhomogeneous field mechanism (IFM) model, originally suggested by Zhukov et al., [23] could be useful. The same method was feasibly adopted to identify the various electrical parameters and their distribution in the polycrystalline HZO film. [21] This work further enhanced the accuracy of the analysis by combining the IFM model with an equivalent circuit model of the adopted AlScN film. As a result, the fatigue phenomenon in this new FE material system, observed when cycling with a high electric field, was ascribed to increased non-FE layer thickness.
Nonetheless, AlScN's very high P r (>100 µC cm −2 ) is undesirable for the stable FeFET operation, requiring additional research to decrease the P r but keep the high E c .

Ferroelectric Properties of 40 nm-Thick AlScN
40 nm-thick AlScN film was deposited on TiN(50 nm)/SiO 2 /Si substrate by radio frequency (RF) reactive sputtering using the AlN and metal Sc target. The Sc concentration was adjusted to 30%. The film deposition process was reported elsewhere and in the Experimental Section. [24] A 50 nm-thick TiN top electrode was deposited by direct current (DC) reactive sputtering. The top electrode was biased during the electrical tests, while the bottom electrode was grounded. Figure 1a shows the current density versus electric field (J-E, red line) and polarization versus electric field (P-E, black line) curves measured by the positive-up-negative-down (PUND) measurement with triangular pulses of 50 kHz. The PUND measurement was used to eliminate the contribution of leakage current, which could be substantial in AlScN. The ferroelectricity of the film was proved through the switching current peak in the J-E curve. However, the rounded P-E curve shape in a high electric field indicated that the PUND method is still inappropriate for eliminating the adverse effects. Also, the estimated double remanent polarization (2P r ) was as high as ≈300 µC cm −2 , which must be an exaggeration by adverse effects such as the DC leakage contribution. The PUND test was suggested initially to eliminate the distortion of the P-E curve by subtracting the components of capacitive charging and the DC leakage current (U and D) from the total measured current (P and N). [25] However, suppose the adverse charge effects during the polarization-switching step (P and N) and the non-switching step (U and D) are different. In that case, the PUND cannot be the appropriate method to identify the P-E property precisely. In this work, the voltage polarity-dependent leakage current of FE and detrapping current during the FE switching could make it hard to eliminate the adverse charge contribution through the PUND measurement. [26,27] The contribution of leakage current can be reduced by increasing measurement frequency. However, when the frequency of the triangular pulse increases over 100 kHz, a time mismatch between the voltage source and current response occurs due to the RC delay, making it challenging to measure the P-E curve. [28] Therefore, this work adopted a modified PUND (P1-P2-N1-N2) test using square pulses with a length of 1 µs, as shown in the inset figure of Figure 1b, to determine the precise P r value of the AlScN. As the pulse length was much shorter than the 50 kHz triangular pulse (10 µs), the adverse effect of the unremoved leakage current was mitigated significantly. Figure 1b shows an example of current-time responses of the modified PUND test, where a pulse height of 7.5 MV cm −1 was applied to a pristine sample, of which E c was ≈6.6-6.9 MV cm −1 . Figure 1c shows the sum of positive and negative P r (2P r ) measured using 1 µs square-pulse modified PUND as a function of the applied electric field. The black square and red circle represent 2P r measured when positive switching (∫(P1−P2) dt, 2P r+ ) and negative switching occurred (∫(N1−N2)dt, 2P r-), respectively. The stable saturation of the estimated 2P r value to ≈175 µC cm −2 at the electric fields >7 MV cm −1 indicates that the P r overestimation in the standard P-E test is effectively www.advelectronicmat.de suppressed. Nonetheless, it can be immediately noted that the ∫(P1−P2)dt (red curves) and ∫(N1−N2)dt (blue curves) are not identical in Figure 1b. Previous studies demonstrated that most AlScN domains were aligned in one direction in the pristine state, even without poling. [24] The predominant orientation was impacted by oxygen concentration, substrate, and deposition conditions. [29,30] To measure the upward-polarization domain portion (P + ) in the pristine state, positive square pulses P1 and P2 (1 µs, 7.5 MV cm −1 ) were consecutively applied, and the currents were measured as shown in Figure 1b. Also, the downward-polarization domain portion (P − ) could be similarly measured by employing two consecutive negative pulses, N1 and N2. The experiments were conducted without pre-poling when measuring P + and P − , in contrast to when measuring 2P r utilizing PUND. The calculated P (P P ) + − + − value was ≈0.81, meaning that most domains were aligned downward in the pristine state, as shown in Figure 1d. The positive coercive field (E c+ ) and the negative coercive field (E c− ) are represented by the red dotted lines in Figure 1a, where E c+ is ≈0.27 MV cm −1 lower than E c− . The imprint appeared in the pristine state due to its initially downward-preferred domain configuration, which will be discussed in more detail below.
Next, the variations in the FE performance of the AlScN film with the field cycling are examined at field strengths lower and higher than E c .

Field Cycling Under the Low Electric Field
For this test, a high electric field of 7.5 MV cm −1 was first applied to pole the film in one direction, and the samples were field cycled ≈10 2 -10 6 times at a low electric field of 4.5 MV cm −1 at 50 kHz. As the E c of the AlScN used in this study was higher than ≈6.5 MV cm −1 , the electric field of 4.5 MV cm −1 did not cause the FE switching. After the elapses of each targetted cycle number, the change in E c was measured through 50 kHz triangular pulse PUND and 1 µs squarepulse PUND methods. Figures 2a,b show the changes in the J-E curves from the 50 kHz triangular pulse PUND for the downward and upward, respectively, polarized samples as the number of field cycles increases. The shape of the J-E curves and intensity of the switching current peak did not change significantly after field cycling for both samples. Similarly, E c+ and E c− remained almost constant after field cycling when the film was polarized downward, as shown in the solid lines in Figure 2c. However, when the film was poled upward before the cycling, E c+ increased and E c− decreased with an increase in the number of field cycles, leading to an even higher E c+ than E c− by ≈0.37 MV cm −1 after 10 6 cycles, as shown in the dashed lines in Figure 2c.
However, the adverse current components were still present in J-E curves at a high electric field, which could be identified from the rounded shape of the curve at the highest field regions. Therefore, the trends of E c change were further www.advelectronicmat.de confirmed by the 1 µs square-pulse PUND tests. First, the film was polarized upward before the low field cycling and cycled ≈10 2 -10 6 times using the triangular pulses. Figures 2d,e show the variation in 2P r+ and 2P r− as a function of the applied electric field of the 1 µs square-pulse PUND, respectively. In all cases, 2P r saturated at ≈175 µC cm −2 in the high electric field (>7 MV cm −1 ). It was discovered that the field cycling under a low electric field did not influence P r . However, 2P r -electric field curve (2P r -E) shifted along the electric field in a different direction after field cycling, depending on the switching direction. When positive (negative) switching took place, the 2P r -E curves moved in the direction of a higher (lower) electric field after field cycling, as shown in Figure 2d (Figure 2e). Figure  S1a,b, Supporting Information, shows the derivative of 2P r to the electric field. They show that their maximum position, which corresponds to the E c of the FE layer free from the series resistance effect, under the positive (E c,max+ ) and negative (E c,max− ) switching shifted in the same trends as E c value from the 50 kHz triangular PUND tests. E c,max+ (E c,max− ) changed from 5 to 5.7 MV cm −1 (5.45 to 5 MV cm −1 ) after 10 6 cycles, as shown in Figure 2f. Figure S1c,d, Supporting Information, shows the change in 2P r+ and 2P r− as a function of the applied electric field when the film was polarized downward before field cycling. 2P r -E curve and E c,max did not shift, which corroborated the E c trends of the downward polarized film measured by the 50 kHz triangular PUND tests.
In the previous investigations to explain the phenomenon in which imprints evolved differently depending on the polarity, an interface screening model (ISM) was employed. [31] According to the ISM model, the presence of the non-FE layer between the FE and electrode creates a relatively strong electric field across the non-FE layer because the charges on the electrode do not entirely screen polarization charges. The electric field injects electrical charges from the electrode, which are trapped at the interface between FE and non-FE layers after a long time or many cycling numbers, even with a low electric field. [31][32][33] At the same time, an imprint emerges due to the internal field (E int ) generated by trapped charges at the interface. Therefore, when thin films with a different polarity are cycled with a low electric field, the E int can be developed differently as the charges are trapped in the opposite direction. [33] When the upward polarized film is cycled under the low electric field, holes (electrons) are likely trapped at the non-FE/ FE interface near the bottom (top) electrode. These trapped charges produce an E int toward the top electrode, which causes E c+ to increase and E c− to decrease. On the contrary, when the downward polarized film is cycled, charges are trapped in the opposite direction, generating the E int toward the bottom electrode. However, as the AlScN domains were aligned toward a downward direction in the pristine state, charges were already trapped in a way to stabilize downward polarization before field cycling. Due to these trapped charges, E c+ was ≈0.27 MV cm −1 smaller than E c− in the pristine state ( Figure 1a). Therefore, E c did not change significantly when the film was polarized downward before field cycling, as there was already an E int directed toward the bottom electrode in the pristine state. Figure 3 summarizes how the trapped charges and internal field evolved differently after field cycling depending on the polarization direction.
The above experiments proved that the imprint in the pristine state was caused by the charges trapped between FE/ non-FE interface. When cycled under the low electric field, an E int was generated differently depending on the direction of the polarization, and fatigue did not occur.

Effects of Field Cycling on Ferroelectric Characteristics
In this experiment, the film was cycled with a 7.5 MV cm −1 triangular pulse of 50 kHz. The 7.5 MV cm −1 was high enough to induce ferroelectric switching, so it was unnecessary to pole the film in one direction before the field cycling. First, J-E curves were measured through the PUND method with triangular pulses of 50 kHz to measure the variation in E c . Figure 4a shows the changes in the J-E curves after the different numbers of field cycling (0 (pristine), 1000, 5000, and 10 000 cycles). It was observed that both E c+ and E c− decreased with increasing the number of field cycling. Previous research suggested that increasing nitrogen vacancies in the film following field cycling under the high electric field caused the ferroelectric switching barrier to decrease, but further study is needed. [11] In addition, the imprint (E c− − E c+ ) decreased from ≈0.27 to ≈0.02 MV cm −1 after 10 000 cycles, which means the internal field in the film disappeared. The trapped charges at the FE/non-FE interface that produced the internal field could be released when cycled under a high electric field, resulting in a symmetrical J-E curve. Nonetheless, such a triangular pulse-based PUND is vulnerable to an error by the adverse charge effects. Therefore, 2P r was measured using a 1 µs square-pulse PUND to assess the impact of field cycling in a high electric field on P r .

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Figures 4b,c show the changes in 2P r+ and 2P r− as a function of the applied electric field of the 1 µs square-pulse PUND tests, respectively. 2P r saturated (≈175 µC cm −2 ) in the high electric field (>7 MV cm −1 ) and did not change significantly after 1000 cycles. However, the saturated 2P r began to decrease after 5000 cycles and became ≈135 µC cm −2 after 10 000 cycles. Additionally, E c,max+ and E c,max− decreased with increasing the number of cycles and reached the value (≈4.75 MV cm −1 , open symbols) after 10 000 cycles, as shown in Figure 4d. E c measured from the J-E curve shown in Figure 4a (closed symbols) was also included in Figure 4d, and both parameters (E c , E c,max ) exhibited the same trend.
Interestingly, such fatigue was not as severe when 2P r was measured using 3 µs-long square pulses. Figure 4e,f shows the variation of 2P r+ and 2P r− measured by 3 µs square-pulse PUND as a function of the applied electric field. 2P r of the pristine film saturated to ≈180 µC cm −2 , close to the value determined by 1 µs square-pulse PUND. However, 2P r decreased by only ≈15 µC cm −2 after 10 000 cycles (from ≈180 to ≈165 µC cm −2 ), a substantially lower amount than when 2P r was measured with 1 µs-long square pulses.
This difference could be ascribed to the different degrees of compensation charge injection during the PUND tests depending on the length of the square pulse. [34] The depolarization field in FE created by unscreened FE-bound charges makes the polarization state unstable and suppresses P r . [17,18] When the charge injection across the non-FE interfacial layer was fluent and sufficiently compensated for the FE-bound charges, the estimated P r should not be decreased. [34] Additional conditions for such an unsuppressed P r is the fluent trapped charge exchange with the changing bias application. As the charge injection and exchange require time, the shorter the bias application time, the less efficient bound charge compensation and the decreased P r . [34] This effect must become more evident as the non-FE layer thickness increases. Therefore, the 1 µs pulse duration in Figure 4b,c is insufficient to confirm the charge injection and exchange, so the decreasing P r with increasing cycle number indicates the thickening of the non-FE layer at the interface. In contrast, the 3 µs pulse duration was relatively long to guarantee the compensating charge injection and exchange even with the increased non-FE layer thickness at the higher cycle numbers. Therefore, the fatigue phenomenon was less critical when 2P r was measured using 3 µs-long square pulses due to the weak depolarization field across the FE. The E c,max+ and E c,max− estimated from the 3 µs-long square pulses PUND showed similar trends to the 1 µs-long square pulse PUND test (data not shown).
Next, the properties of the evolving non-FE layer were examined in more detail using the PS measurement. The main intention of this analysis was to achieve quantitative data on the non-FE capacitance C i and possible series resistance. [19,20] For this experiment, the film was pre-poled in one direction, and a switching pulse was applied in the opposite direction to measure the switching current (I SW ) as a function of time.
When a switching pulse is applied to an ideal FE capacitor without involving the non-FE layer, the current peak due to the capacitor charging develops initially. Subsequently, when the voltage applied to the FE reaches the V c of the FE layer at a time t = t o , the FE switching occurs. Assuming that switching occurs at the same voltage in all domains, the voltage applied to the FE layer remains constant at V c during switching. Therefore, the difference between the applied voltage (V P ) and V c is applied to the load resistance of the measurement circuit (R L ) during the switching, and the I SW remains constant at if a non-FE layer with a capacitance of C i exists, I SW decreases with time and is expressed as Equation (1).
where t sw is the time when switching is completed. Therefore, I SW is not constant during the switching, and from Equation (1), R L and C i can be estimated from the I SW at t = t o and the slope of the ln(I SW ) versus t graph, respectively. [19,20] However, in a polycrystalline AlScN, film properties could be spatially inhomogeneous due to the non-uniform distribution of defects, grain size, and interfacial non-FE layers. [22] Under this circumstance, each domain (or grain) may have a specific V c . As a result, the voltage applied to the FE during switching may not be constant, which causes I SW to vary during switching. [21] Under this circumstance, the precise C i value can not be determined from the slope of the ln(I SW ) versus t graph based on Equation (1).
A similar issue has been dealt with by Hyun et al. for the polycrystalline HZO film. [21] They simulated the I SW using the equivalent circuit model of the test circuit and the IFM model that considered the inhomogeneous field distribution. Their study ascribed the decaying I SW to the inhomogeneous switching over the HZO film area. However, the impact of the non-FE layer was not considered in that study. Also, the AlScN exhibits significant leakage current, unlike HZO, and thus, the equivalent circuit for the AlScN FE film was revised in this work. [10] Figure 5 illustrates the equivalent circuit of the test device when a voltage pulse with an amplitude of V P is applied to the FE capacitor. R L is the test circuit's series resistance, which is composed of the internal resistance of the semiconductor characterization system and parasitic resistance. Using a short-circuited configuration, R L was estimated to be 104 Ω from the pulse measurement. [20,35] R c is the contact resistance between the film and electrodes. R c contains the differential resistance of the non-FE layer if the non-FE layer is conducting during the switching. [36] If the non-FE layer is insulating during the switching, the non-FE layer works as a dielectric capacitor with the capacitance of C i . C P is the background capacitance of the FE, and C PF represents the non-linear ferroelectric switching element. It is known that when the voltage applied to the FE layer reaches V c , the FE layer behaves as resistance during the ferroelectric switching. [19,36] However, polycrystalline AlScN is likely to have V c distribution shown in the inset of Figure 5, and thus, C PF is represented with multiple parallel resistances with various V c values. J L is the DC leakage current density across www.advelectronicmat.de the entire FE + non-FE layer, V F is the voltage applied to FE, and V i is the voltage applied to the non-FE layer. Therefore, the I sw (t) analysis becomes much more complicated than the simple form of Equation (1).

Ferroelectric Switching Model Considering Inhomogeneous Field Distribution
Nonetheless, the recently developed IFM model provides a quantitative method to solve this problem. It also provides crucial clues to understanding the bulk property variation with cycling. [23] Therefore, before discussing the variations in C i and R c by cycling, the bulk property variations, estimated from the IFM model application, are discussed first. Then, the same model was used to identify the C i and R c variations, which are interface-related properties.
Bulk Property Variation by Field Cycling: The current flowing through the resistance R L (i R ) is a sum of the non-FE layer charging current (i i ) and leakage current (i L ). Furthermore, i i is a sum of the FE switching current (i F ) and FE charging current (i P ); thus, the i R can be represented by Equation (2) dV , dV where E F is an electric field applied to the FE layer, and A is the electrode area. The C P and J L must be identified, and the polarization, p, should be described as a function of time and E F to solve Equation (2). First, a 5 V (1.2 MV cm −1 ) triangular pulse of 50 kHz, which is low enough not to cause the FE switching, was used to measure the background capacitance C P of the FE, as shown in Figure S2, Supporting Information. As the C P could be overestimated due to the domain wall vibration, the film was pre-poled in the downward direction by applying a 7.5 MV cm −1 triangular pulse before measuring the C P value. Because the charge versus voltage (Q-V) curve did not show hysteresis, the Q-V response did not include the DC leakage and ferroelectric switching currents. Additionally, the contribution from the C i could be dis-regarded as the non-FE layer thickness must be significantly thinner than the film thickness (so, C i >> C P ). Therefore, C P was extracted from the slope of the Q-V curve and calculated as ≈0.33µF cm −2 . The dielectric constant, estimated using the C P value, was determined to be ≈14, comparable to the reported dielectric constant of AlScN. [37] Second, J L was measured in the positive and negative bias regions after the film was stressed with various switching cycles. In previous studies, Schottky emission was used to explain the conduction mechanism of AlScN. [38] However, when the thickness of the dielectric film exceeds the electronic mean free path, the thermal electron is also impacted by the traps in the film. [39] Therefore, Schottky emission should be modified into Equation (3) where α = 300 A sm −3 K 3/2 , T is the absolute temperature, μ is the electronic mobility, m 0 is free electron mass, m* is effective electron mass, qφ b is the Schottky barrier height, ε r is the optical dielectric constant, ε 0 is the permittivity in a vacuum, and K is the Boltzmann constant. Since the thickness of AlScN employed in the experiment was thicker than the reported electronic mean free path of other dielectric materials (<10 nm), Equation (3) was utilized to fit the measured J L . [39] Figures 6a,b show the       J T E ln L 1.5 versus E 0.5 plots in the positive and negative bias regions, respectively. They show a feasible fit to the modified Schottky model at voltages above 1 V, and the ε r value calculated from the slope of the fitted graph was between 4 and 4.6, comparable to the published optical-frequency ε r value (4.6) of Al 0.7 Sc 0.3 N. [40] In addition, leakage current increased as the number of field cycles increased.
As shown in Equation (3) Figure 6c shows the relationship between ln and T −1 of the pristine film with an electric field ranging from 0.5 to 3 MV cm −1 . At a given E, the slope of the linear fit (β) is equal to ). Figure 6d shows the change in β as a function of E 0.5 , and the linear dependence of the β is in line with the modified Schottky emission model. qφ b value was ≈0.4 eV obtained from the y-axis intercept of the plot. This value is much lower than the theoretical qφ b value (≈1.6 eV) of the epitaxial lattice-matched TiN/AlScN interface. [41] Previous studies also reported qφ b value of the TiN/AlScN interface exhibited low value due to the defects such as nitrogen vacancies and unscreened polarization charges. [11,38,26] Also, the m* value was obtained from the y-axis inter-  . Previous studies also reported a considerably low m* value than the theoretical value because the injected electrons were scattered in the dielectric film. [42,43] Nonetheless, this does not preclude the thermionic injection mechanism of carriers.
Finally, the IFM model was used to determine the time and electric field-dependent polarization variation (p(t, E F )). A detailed description of the physical implication and derivation steps of the IFM model can be found elsewhere. [23] The following provides a brief description of the model. The fundamental idea behind this model is that when an electric field (E app ) is applied to a film, a different local field (E loc ) is applied to each ferroelectric domain. Under this circumstance, the local polarization p(t, τ) is given as Equation (4) , where κ is the dimension of the nucleation growth, and κ = 2 is frequently utilized for thin films. [44] τ is the local switching time and is represented by Equation (5) using the local electric field E loc . τ 0 is the characteristic switching time and E a is an activation field.
After applying E app , the total switched polarization ΔP determined by adding up local polarization can be expressed as Equation (6) , , d is the distribution function of the normalized local field, and E th (t) is the threshold field and determined by solving the equation t = τ(E loc ). Assuming that p(t, τ(E loc )) switches instantaneously when the pulse is applied for a time longer than τ(E loc ) p(t, τ(E loc )) can be estimated using the Heaviside step function with the field, as shown in Equation (7). Then, the total polarization ΔP(E app ,t) can be simplified as Equation (8). Normalized logarithmic derivative of ΔP(E app ,t) to E app is represented by Equation (9).

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Equation (9) indicates that logarithmic derivatives for various switching times have the same intensity at their maximum position (E max (t)) and scale to the identical master curve which serves as the model's fingerprint. When these conditions are satisfied, E th (t) should be proportional to E max (t), that is, E max (t) = γE th (t). Constant γ is determined using the normalization condition for f(x). Then, the electric field distribution can be determined from the master curve, as shown in Equation (10).
The switched polarization ΔP was first measured as a function of the E app for different pulse times to apply this IFM model. The length and amplitude of the write pulse varied between ≈10-5000 µs and ≈3-6 MV cm −1 , respectively, as shown in Figure 7a. 1 µs-long 7.5 MV cm −1 square pulse was used to read the amount of switched polarization (R1, R2). To remove the non-switching component, the switched polarization value was calculated from the difference between the integrated current responses to the R1 and R2 pulses. Figure 7b shows the variation of the ΔP as a function of the E app for the different pulse lengths when positive switching took place in the pristine state (data points) and fitted graphs following Equation (8) (lines). Figure 7c shows the calculated logarithmic derivatives, revealing that all curves had a similar shape, and the maximum values were almost identical regardless of the writing pulse length. This behavior confirmed the validity of the IFM model for this film. The normalization of each curve to its E max (t) leads to the master curve, Figure 7d, which was used to derive the local field distribution, Figure 7e. This field distribution was fitted using extreme value distribution (Equation (11)) where Ψ is the location parameter, σ is the scale parameter, which determines the broadness of the distribution function. The electric field distribution of the film became broad as the σ value increased. The obtained values were Ψ = 1.03 and σ = 0.034, respectively.
Finally, the E a and τ 0 required to calculate the ΔP(E app ,t) were obtained through the max 1 E − versus ln t graph shown in Figure 7f. The extracted values were E a = 96 MV cm −1 and τ 0 = 5.98 × 10 −14 s, respectively.
The previous study indicated that the values of E a and τ 0 of HZO film were 8.94 MV cm −1 and 1 × 10 −10 s, respectively, which are far different from the values in this study. [21] Since AlScN is a much "harder" ferroelectric material, that is, much higher electrostatic energy is required to switch than HZO, the E a value is approximately one order of magnitude higher. Since HZO was already "harder" than PZT, this value is almost www.advelectronicmat.de two orders of magnitude higher than that of the PZT. [45] The E c of AlScN (≈6 MV cm −1 ) is likewise higher than the E c of HZO (≈1 MV cm −1 ) and PZT (≈0.1 MV cm −1 ) due to this substantial switching barrier.
In contrast, τ 0 value of AlScN is shorter than those of HZO and PZT (1 × 10 −11 s) by 3 and 2 orders of magnitude, respectively, indicating that AlScN has a significantly faster-switching speed than the other ferroelectric materials. [21,45] Such a faster switching speed might be ascribed to the (002) preferred crystallographic orientation, which does not involve a non-180° domain wall, unlike other materials. Therefore, the FE switching in AlScN may not include the slow domain wall movement. This aspect has not been reported before, but it is an encouraging aspect of AlScN for applications requiring a fast switching speed.
The experimental data and fitting graphs similar to Figure 7b are included in Figure S3, Supporting Information. The same analyses were performed for the AlScN film after the different number of cycle numbers, and the extracted σ, E a , and τ 0 values are summarized in Table 1. As the number of cycles increased, the inhomogeneous characteristics in the thin film grew, resulting in the broader field distribution as illustrated in Figure S3a,f, Supporting Information. [46] The σ value increased from ≈0.03 to ≈0.06 after 10 000 cycles. In contrast, the E a decreased from ≈96-100 to ≈88 MV cm −1 . This decrease in switching barrier after field cycling corroborated the decreasing E c shown in Figure 4a. τ 0 value was insensitive to the cycling numbers but depended on the switching polarity. The interpretation of such τ 0 behavior also requires further study. The discussed σ, E a , and τ 0 values are relevant to the bulk portion of the AlScN film.
Interface Property Variation by Field Cycling: The following discussions are related to the interface properties such as R c and C i . Such parameters were estimated from the tunnelswitch effect for the PZT film, where the V c values of all domains were assumed to be identical. [36] However, the discussions related to the IFM indicated that this assumption could not be applied to this AlScN case. Therefore, Equation (2) was used to estimate them. The parameters needed to solve Equation (2) (C P , J L , and p(t, E F )) were obtained through the experiments shown in Figure 7. Figure 8a,b shows the I SW variation as a function of time when the square pulses shown in the inset figures were applied to the AlScN film. The 1 µs-long 7.5 MV cm −1 square write pulse was first applied to pole the film in one direction, followed by the read pulse field in the opposite direction with the amplitude from 5.75 to 6.75 MV cm −1 . As a result, the capacitor charging current initially emerged before I SW (along path 1 in Figure 5). After completing the capacitor charging, the domain switching current appeared (along path 2 in Figure 5), which decayed with time. Such a decay could be ascribed to the V c -distribution (or E loc -distribution), that is, the domains with the lowest V c (or highest E loc ) switch first for the given read pulse field. Once the ferroelectric switching is over at ≈9 µs, a substantial leakage current was observed. To fit these data quantitatively to Equation (2), the E loc -distribution must be identified, which could be determined by the IFM model, as shown in Figure S4a, Supporting Information. The local polarization of each grain When p(t, E loc ) was substituted into Equation (2), I SW (t) became the function of R c and C i values. R c and C i were first adjusted to see how these two factors influenced I SW , as illustrated in Figure S4b,c, Supporting Information. It was proven that R c determined the intensity of I SW at the moment when the ferroelectric switching started (black dots in Figure S3b, Supporting Information), and C i influenced the slope of the I SW versus t graph, respectively. (see Section S1, Supporting Information). Figures 8a,b show the positive and negative I SW (t) variation, respectively, at different read pulse conditions (data points) of the pristine sample and their fitting results (red lines) based on Equation (2). Similarly, fittings were performed while changing the number of cycles, as shown in Figure S5, Supporting Information.
The C i values were estimated to be above 500 µF cm −2 regardless of the cycling number. However, the C i value of 500 µF cm −2 corresponds to a dielectric thickness of ≈0.03 nm, assuming a dielectric constant of 14, meaning that it does not bear any physical implications. Additionally, there was little difference in I SW between the cases when C i was 500 µF cm −2 and ∞, as shown in Figure S4c, Supporting Information. In other words, there was no C i involved during the ferroelectric switching. Nonetheless, this finding does not imply that the non-FE layer was not developed during the fatigue cycle test, as discussed below.
R c variation with the cycling numbers is summarized in Figure 8c and Table 1. The initial value of R c was 169 (positive switching) and 186 Ω (negative switching), which decreased slightly after 1000 cycles. However, it increased after 5000 cycles and reached a value of 236 (positive switching) and 285 Ω (negative switching) after 10 000 cycles.
The R c may represent the resistance of the non-FE layers at the electrode interfaces. During the FE switching, the interfacial non-FE layers undergo a tunnel-switch effect due to the significant voltage application on them. [36] The tunnel-switch effect means that the non-FE layers play a role as a series resistor, not an insulating layer, by the significant tunneling current flow. The transported carriers across the non-FE layers are trapped at the non-FE/FE layer interface, compensating for the FE-bound charges. Therefore, the R c will increase if the non-FE layer thickness increases with the increasing cycle number.
The voltage-polarity-dependent R c value could be understood as follows. Assuming the asymmetric non-FE layer structure, that is, the top and bottom interfaces have different non-FE layer thicknesses, would be reasonable. Among the two non-FE layers at the top and bottom interfaces, the non-FE layer, where the holes are transported during the switching, would dominantly govern the R c . This assertion is because the holes generally have higher effective mass than electrons. The hole-injecting non-FE layer is located at the top interface during the positive switching and at the bottom during the negative switching. Therefore, the larger R c value under the negative switching indicated the thicker non-FE layer at the bottom interface. Understanding the origin of such asymmetric non-FE layers needs further research.
The presence of finite R c and its increase with the increasing cycle number implied that the increasing non-FE layer thickness may have caused the ferroelectric fatigue due to the development of the depolarization field and inhibition of domain nucleation.

Conclusion
The changes in ferroelectric characteristics that occurred when 40 nm-thick AlScN was field cycled in both low and high electric fields were analyzed. After cycling with a low electric field, there was little change in the shape of the J-E curve, and the E int was generated in a different direction depending on the polarity. The polarity-dependent E int was developed due to the charges trapped in the interface between the FE and non-FE layers during field cycling.
When the film was cycled with the high electric field, 2P r decreased from ≈175 to ≈135 µC cm −2 after 10 000 cycles. The cause of this fatigue was considered to be an increase in the thickness of the non-FE layer. Further analysis of the ferroelectric switching current using the equivalent circuit model that represented the test device combined with the IFM model revealed characteristic features of this new type of ferroelectrics compared with the HZO and PZT. The AlScN film had an activation field of 90-100 MV cm −1 , larger than that of the HZO and PZT by one and two orders of magnitude, respectively. This factor comprises the primary reason for the much higher E c of this material.
Interestingly, the switching time constant was lower than the others by ≈2-3 orders of magnitude, suggesting the possibility of a very high switching speed. It also showed a relatively narrower E c distribution than the HZO. [21,45] The high switching speed and narrower E c distribution could be related to the highly c-axis-oriented crystal structure of the film, which may eliminate the slow domain wall motion. The increasing cycle number, which has caused the fatigue, slightly increased and decreased the E c distribution and activation field, respectively, while the characteristic switching time was not influenced.

Experimental Section
AlScN film was deposited on the TiN(50 nm)/SiO 2 /Si substrate by RF reactive magnetron sputtering using 4-in. diameter AlN and metal Sc targets. The base pressure was kept at 7 × 10 −8 Torr to maintain the low oxygen concentration in the film. The total sputtering power of each target was held at 500 W, and the film was deposited under 5 mtorr working pressure at 300 °C substrate temperature. The composition of the film was determined by X-ray fluorescence spectrometry (Thermo Scientific, Quant'X EDXRF), and the Al:Sc ratio was fixed at a 7:3 value. When the Sc concentration in the film was 25% or 35%, the films showed a too-high E C value (≈7.2 MV cm −1 ) or higher leakage current than the 30%-Sc-containing film. Therefore, this work adopted a 30% Sc-concentration. Film thickness was measured using spectroscopic www.advelectronicmat.de ellipsometry (SE, J.A. Woollam, M-2000), and the thickness was set to 40 nm. More detailed explanations of the film growth process and property optimization are reported elsewhere. [24] The 50nm-thick TiN top electrode was deposited by DC reactive sputtering under 500 W power and 2 mTorr working pressure at room temperature to test the electrical properties. Following the TiN deposition, photolithography was used to create a circular top electrode with a 110 µm diameter, followed by a dry etching process. Electrical characteristics were measured using a semiconductor characterization system (Keithley, 4200A-SCS).
The vacuum was broken before the AlScN and the top electrode TiN deposition. However, as reported elsewhere, the vacuum break did not produce a noticeable oxide layer at the interface. [24]

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.