Large–Area Graphene Electrode for Ferroelectric Control of Pb(Mg1/3Nb2/3)O3–PbTiO3 Single Crystal

Large‐area monolayer graphene is utilized as a metallic electrode for a ferroelectric single‐crystal [Pb(Mg1/3Nb2/3)O3]m–[PbTiO3]n (PMNPT). Unlike conventional metal, whose properties remain unaffected by field‐induced charge carriers, graphene's unique Dirac‐cone band structure causes its carrier density to vary in response to the polarization state of contacting dielectrics. PMNPT capacitors with graphene‐only and graphene/Cr/Au electrodes exhibit similar polarization versus electric‐field curves. However, polarization switching in PMNPT and corresponding charge‐state conversion in the graphene electrode are observed in the device configuration of a graphene‐ferroelectric field‐effect transistor. Systematic analysis of graphene's source‐drain current variation reveals that experimental results align well with a theoretical model considering the intrinsically doped state in graphene and ferroelectric surface charge state in PMNPT. Furthermore, interfacial charge trapping discussed in many previous reports is not observed. These findings suggest that large‐area monolayer graphene effectively serves as an electrode for ferroelectric single‐crystal materials, irrespective of its atomically thin structure and ambipolar metallic nature.


Introduction
Spontaneous polarization in ferroelectrics is a highly intriguing phenomenon and has been extensively investigated in DOI: 10.1002/aelm.202300339solid-state physics.The inversion symmetry breaking inside a crystalline material induces a deviation between the center of positive charges and that of negative charges in the unit cell, and the dynamics of these spontaneous polarizations have been utilized for various applications. [1]Even though such ferroelectric polarization is a bulk property, its manifestation in real applications heavily relies on the contacting materials.[10] It is worth noting the difference between the metal-ferroelectric contacts and the semiconductor-ferroelectric contacts.Due to the large number of charges induced on the surface of the ferroelectric materials, the effect on conventional metals is negligible because the metal has many conduction electrons.However, the influence on semiconductors can be substantial because of the relatively small number of free carriers.Therefore, the semiconductorferroelectric contacts are more sensitive to the interface properties between the two materials.[12] The combination of ferroelectrics with 2D materials has also been an interesting topic from the viewpoint of basic research as well as applications. [8]15][16][17][18][19][20] Even though there is no bandgap in graphene, its Dirac-cone  1a.b) A schematic drawing of the devices in (a), including elements such as align marks, graphene areas, and interdigitated pattern electrodes.c) Ferroelectric polarization versus electric field curves for each device using the bottom gate metal as one electrode and the graphene with the interdigitated metal electrode as the other electrode.In this case, the area of the square-shaped graphene remains the same, but the ratio of the metal-deposited area on graphene differs for all three devices.band structure enables conductance variation, which inversely reflects the status of contacting ferroelectrics.][17]22,27] However, when in contact with a ferroelectric oxide such as Pb(Zr,Ti)O 3 , graphene's conductance wasn't notably controlled by the oxide's ferroelectricity.][25][26][27] Here, we demonstrate macroscopic polarization switching in a ferroelectric singlecrystal [Pb(Mg 1/3 Nb 2/3 )O 3 ] m -[PbTiO 3 ] n (PMNPT) oxide block with a 100 μm thickness, employing large-scale, centimeter-area graphene as an electrode. [29]For the conductance variation of graphene, the obtained data curves match well with the ideal cases expected in the graphene-on-ferroelectrics system, indicating that no interfacial traps are required in the data analysis.All results indicate that graphene works well as an electrode for ferroelectric oxides by compensating for surface charges on PM-NPT, which was verified by the systematic analysis of multiple devices.The newly designed electrical measurement scheme for the graphene/PMNPT devices confirms the position of ferroelectric switching and its influence on the contacting graphene's conductance explicitly.

Polarization Switching of PMNPT Single Crystal by Graphene as a Metal Electrode of Ferroelectric Capacitor
Figure 1a displays stitched optical microscope images of the three graphene/PMNPT devices on a single-crystal ferroelectric PM-NPT sample.The design plan of the graphene/PMNPT hybrid devices with different interdigitated electrode pattern shapes is depicted in Figure 1b.The PMNPT substrate had a back-side metal contact on the bottom and was covered by a large-area monolayer graphene on top.Interdigitated patterns of metal electrodes were formed on top of the graphene to enable stable electrical contact and to measure the conductance variation of graphene upon changes in the polarization status of PM-NPT.The three devices were separated by etching out the outside area except the graphene channel.Figure 1a also provides a bird's-eye view of the fabricated graphene/PMNPT device, which has a basic FET structure.The bottom metal electrode, PMNPT block, graphene layer, and top-most interdigitated metal patterns correspond to the gate electrode, gate dielectric, semiconductor channel, and source/drain electrodes, respectively.If graphene is effectively coupled with the ferroelectricity of PMNPT, then the charge carriers in graphene will compensate for the surface charges on PMNPT, inducing conductance variation in the graphene.
There was concern that polarization switching of this graphene/PMNPT ferroelectric capacitor might be mainly driven by the metal/graphene/PMNPT area rather than the grapheneonly/PMNPT part.To address this concern, we measured the P-E curves for all samples, varying the relative ratio of the area between the graphene-only electrode and metal/graphene stacked electrode.As we fabricated the three graphene devices on a single-crystal PMNPT substrate, the ferroelectric characteristics of all capacitors are expected to be similar, assuming that the graphene-only electrode and metal/graphene electrode play identical roles.All the P-E curves of the three devices with different relative area ratios overlapped in Figure 1c, showing a saturated polarization of ≈20 μC/cm 2 and coercive field below 3 kV cm −1 , similar to high-quality ferroelectric PMNPT capacitors. [12,24,34]espite substantial variation in the ratio of the metal-deposited area, there was little difference in ferroelectric properties such as saturated polarization and coercive field.Therefore, it is evident that graphene serves as a 2D electrode, providing sufficient charges to maintain the stable polarization of ferroelectrics like ordinary metals.

Conductance Variation of Graphene during the Ferroelectric Switching of PMNPT
Figure 2a shows the standard device and measurement configuration of graphene/PMNPT FET, in addition to the detailed information for the graphene and the interdigitated electrode pattern for three samples.In this FET device configuration, the formation of defect-free homogeneous interfaces between graphene and PMNPT is ensured by the similar I G − V G curves in Figure 2b.Because the three graphene device regions with the same size of 9 mm 2 were made of a centimeter-sized single graphene sheet (followed by the separation of devices through dry etching), the similar current flow passing through the PM-NPT substrate in Figure 2b indicates that the graphene-only layer works effectively as the electrode for the ferroelectric PMNPT single-crystal bulk capacitor.Unlike the similarity in I G − V G curves in Figure 2b, the I D − V G curves in Figure 2c for three graphene/PMNPT devices are different depending on the shape of the interdigitated metal electrode patterns.Apparently, the I D level of the device #3 is much higher than those of the other two because of the elongated channel width and the shortened channel length of the graphene transistor due to the higher-density interdigitated pattern shape.However, the overall shape did not change irrespective of the electrode shape, which indicates that the three devices are qualitatively identical, but quantitatively different.

Modeling of Graphene-Ferroelectric Field-Effect Transistor
The ideal operation models of this graphene/PMNPT FET device are presented in Figure 3a-c for three cases of different intrinsic doping levels in graphene.In each figure, three plots are combined, which are (i) the P-E curve of a ferroelectric layer, (ii) the carrier density (Q) versus the conductance curve of graphene, and (iii) the gate voltage (V G ) versus the drain current (I D ) curve, i.e., the I D − V G curve of a graphene/ferroelectric hybrid FET device.Under the assumption of coupling between ferroelectrics and graphene, the polarization charge of the ferroelectric layer in (i) is directly related to the charge density in graphene with the opposite sign in (ii).The electric field in the P-E curve in (i) is controlled by V G in (iii), as indicated by the dashed lines.Additionally, the I D in (iii) is equivalent to the conductance in (ii) with the linear relationship between P in (i) and Q in (ii).Figure 3a shows a graphene/ferroelectric FET device under the assumption that there is no intrinsic doping or no residual charge remaining in graphene (for example, induced by contamination).From the spontaneous polarization in ferroelectrics, the conductance variation of graphene is hysteretic upon the V G sweep, which results in two points of conductance minima corresponding to the charge neutrality points (CNPs), as illustrated in Figure 3a (iii).It is noteworthy that the shapes of the I D − V G curves near the two CNPs are similar, and their positions are symmetric at V G = 0.In contrast, Figure 3b,c show the cases of finite doping level to graphene, where lightly doped and heavily doped graphene samples are considered as shown in the panel (ii) of Figure 3b,c, respectively.Here, the criteria for light doping versus heavy doping are determined by the relative position of the conductance minimum of graphene with respect to the hysteretic surface charge state of PMNPT.As indicated by the dashed lines, the overall shape changes of the I D − V G curves are significant, and the details, such as the movement of V G corresponding to CNPs and the I D slope variation near CNPs depending on the V G sweep direction, should be carefully examined.

Field-Effect Transistor Operation of Graphene -PMNPT Device
The FET characteristics of the graphene/PMNPT hybrid device are presented in Figure 4 for the device '#3′ whose measurement setup and top-view optical image are presented in Figure 2a.The I D − V G and I G − V G curves at various V G sweep ranges are plotted together to investigate the correlation between the conductance variation of graphene and ferroelectric switching of PM-NPT.Figure 4a shows the experimental data for the sample measured under a high vacuum condition of 2 × 10 −6 Torr.When V G is swept from +60 to −60 V, I D (red curve in the top panel) decreases continuously in the region of V G > −10 V, and increases abruptly in the region of V G between -10 to −18 V.After a sud-  the type of carriers in graphene, it may not be spatially uniform, and there could be many electron-hole puddles distributed over the whole graphene sample during the carrier-type conversion.Therefore, the minimum conductance might not be small, which corresponds to the case of I D during the V G sweep from +60 to −60 V in the top panel of Figure 4a.
When we compare these experimentally obtained I D − V G curves in Figure 4a with the models in Figure 3, we find that the comparison matches well with the case of lightly hole-doped graphene with ferroelectric hysteresis, as shown in Figure 3b.First, two V CNP positions deviate slightly from the points of most rapid polarization switching.Another factor is the enhanced hole-type conduction with a higher current level on the left side of the V CNP .37][38] Figure 4b shows the results of the same sample used in Figure 4a but measured in an ambient condition.Intriguingly, the conductance minima obtained under opposite V G sweep directions, where one is very sharp, and the other is very dull, are located nearly in the same region of the I D − V G plot.When we compare this with the models in Figure 3, we notice that this is identical to the case of Figure 3c, where the graphene channel in the FET device configuration is highly p-doped, and CNPs are shifted to the region of saturated ferroelectric polarization.We can understand the coincidence of the model in Figure 3c and the experimental result in Figure 4b by considering the fact that significant hole-doping effects are reported in the graphene sample under ambient conditions, where adsorp-tion of water or oxygen molecules might give a hole-type doping effect. [8,39]t is worth noting that the above experimental results, which show normal hysteresis of I D − V G curves of graphene, are distinguished from many previous reports on graphene on ferroelectric oxide showing anti-hysteresis effect, where interfacial charge traps should have been considered to explain the anomaly. [8,14,38,40]This difference can be explained simply by saying that the direct coupling between graphene and PMNPT was achieved in this experiment.

New Electrical Characterization Scheme of Ferroelectric Field-Effect Transistor Device
To go one step further in analyzing the coupling between graphene and PMNPT, we measured the conductance hysteresis of the graphene/PMNPT device as a function of V G sweep range, as shown in Figure 5a.Conventional symmetric V G sweeps with different V G ranges show complicated hysteretic conductance variation, where the relationship between the ferroelectric coercive voltage and the appearance of conductance hysteresis in graphene is unclear.Therefore, for a deeper analysis, we propose a new measurement scheme changing the cyclic V G sweep sequence systematically, as introduced below.The hysteresis loop of ferroelectrics in Figure 5b indicates that the status of polarization at a given voltage depends on the history of the previous polarization status.However, if this fact is not considered strictly, then well-defined I D − V G curves for the graphene FET with a ferroelectric gate insulating layer cannot be obtained, in the case of Figure 5a.Therefore, to define the initial polarization states clearly, we designed the test method described in Figure 5c,d involving sequential V G sweeps after the preset of polarization to the saturated regime.As a result, this new scheme provides us with definite information on the polarization states for every single measurement step, allowing a direct comparison between each curve.
Specifically, in the case of Figure 5c, all V G sweeps start from the fixed large negative V G value (denoted as V init ), ensuring the initially saturated polarization state.Then, V G sweeps toward the positive V G direction and returns to V init .When the maximum V G value (denoted as V max ) increases step-by-step in the repetitive V G sweeps, hysteretic ferroelectric switching starts to appear when V max is larger than the coercive voltage of ferroelectrics.Furthermore, once ferroelectric switching occurs for the V G sweep from V init to V max , reverse ferroelectric switching should also occur in the opposite sweep direction of V G moving from V max to V init , as denoted by the green and red colors in Figure 5c.The main advantage of this newly proposed scheme is that we can check the point of ferroelectric switching clearly.In addition, the same method can be applied to the opposite cyclic V G sweeps, which start from a large positive V G value, as illustrated in Figure 5d.By combining both schemes in Figure 5c and d, ferroelectric switching can be systematically monitored and analyzed to determine if there is any hidden factor preventing the explicit appearance of ferroelectric switching.
Figure 6a,b show the experimental data of I D − V G and corresponding I G − V G curves for the V G sweeps, all starting from V G = −60 V, which corresponds to the saturated polarization 'down' state (by definition).The cyclic V G sweep range becomes wider, first between −60 and −50 V, second between −60 and −40 V, between −60 to −30 V, and finally between −60 to +60 V with increasing V max value at 10 V intervals.Then, we collected the data curves for the increasing V G direction starting from V G = −60 V (plotted in Figure 6a) and those for the decreasing V G direction ending at V G = −60 V (plotted in Figure 6b), respectively.Because all data curves initially start from V G = −60 V, the data curves in Figure 6a follow a single curve showing that a sudden change in I D occurs when V max exceeds the coercive voltage of this graphene/PMNPT device, as expected.However, in Figure 6b, the starting point of the curve, which is the maximum V G value in the previous V G sweep, determines the behavior of hysteresis.If it is smaller than the coercive voltage, the initially saturated polarization does not change, so that the I D − V G curve simply follows the previous curves without hysteresis.However, if the maximum V G value is larger than the coercive voltage, then the initially saturated polarization is altered substantially, which results in the I D − V G curves being different from the initial curves in Figure 6a.Then, such hysteretic behavior disappears when it again passes the coercive voltage in the negative V G regime, which recovers the initial saturated polarization.All these experimental results are compatible with the expectation schematically illustrated in Figure 5c, with different colors indicating the variation of polarization for different V G sweep ranges.
The similar results are also obtained in Figure 6c,d under the condition of initial V G = +60 V, which defines the saturated polarization "up" state.In Figure 6c, all curves starting from V G = +60 V and moving in the decreasing V G direction follow an identical pattern, which qualitatively resembles the case in Figure 6a, except for the opposite V G polarity.In Figure 6d, for the increasing V G direction that finishes at V G = +60 V, the hysteretic behaviors in I D − V G curves can be categorized into three different groups, which depend on the appearance of the ferroelectric switching peak in the I G − V G plot.If a clear peak appears in the I G − V G curves in Figure 6d, the V G sweep range covers the entire ferroelectric switching region.However, if the peak shape is incomplete, such V G sweep ranges cover the coercive voltage region, but the ferroelectric polarizations are not fully saturated.The absence of any peak-like signature in the I G − V G indicates that the V G sweep range is too narrow to cover the ferroelectric switching region.
Among the data curves in Figure 6d, the V G sweeps from 0 to +60 V and the narrower ranges (i.e., V min ≥ 0 V) show no signature of ferroelectric switching.Additionally, when the V G sweeps from −10 to +60 V (i.e., V min = −10 V), an incomplete switching behavior occurs, as explained in detail in Figure S1 in the Electronic Supporting Material (ESM).In contrast, when V G sweeps from −20 to +60 V, as well as in wider V G sweep ranges (i.e., V min ≤ −20 V), a full ferroelectric switching behavior occurs.All the results in Figure 6 indicate that the conductance of graphene effectively depicts the history and status of polarization in PMNPT owing to the direct coupling between graphene and PMNPT.This confirms that the graphene/PMNPT system shows normal ferroelectric switching behavior without the need to employ additional mechanisms, such as interfacial charge trapping.

Conclusions
In this study, we report the ferroelectric polarization switching of a 100-μm-thick PMNPT single-crystal block using large-area graphene as an electrode.A comprehensive investigation from the viewpoint of graphene-ferroelectric FET device configura-tion, in which PMNPT functions as a gate dielectric layer, reveals that the charge carrier in graphene is effectively modulated by the ferroelectric states of PMNPT, consistent with the ideal model of a graphene/ferroelectric hybrid system.Our newly proposed electrical measurement technique, employing the voltage bias conditions of a pre-poled V G sweep sequence, enables the observation of the charge carrier modulation in graphene reflecting the polarization state of ferroelectric materials.Consequently, the chargetrapping effect at the interface appears negligible.Furthermore, it has been demonstrated that direct contact between PMNPT and a graphene electrode alone can result in successful charge compensation during ferroelectric switching, similar to the case of graphene/metal stacked electrodes.
All these experimental observations suggest that graphene may serve as an electrode for ferroelectric oxide materials, monitoring ferroelectric polarization switching in graphene/ferroelectric hybrid systems.Our analysis emphasizes the electrode application of graphene in direct contact with ferroelectrics.One of such examples is its use as a source or drain metal contact in 2D semiconductor devices of ferroelectric field-effect transistors.The other is the implementation of large-area graphene electrodes in piezoelectric devices, either with Pb(Zr,Ti)O 3 ceramic or single-crystal PMNPT, expecting the advantages due to its atomic thickness over conventional metals.We anticipate that this will enhance our understanding of the graphene/PMNPT interface and pave the way for the development of 2D electrodes for ferroelectric or piezoelectric systems.

Experimental Section
Materials: A single-crystal PMNPT substrate oriented in the (001) direction with a thickness of 100 μm (IBULE photonics, Republic of Korea) and a centimeter-sized monolayer graphene sheet on a copper foil (Graphene Square Inc., Republic of Korea) were used as the ferroelectric substrate and graphene electrode.One side of PMNPT had the Cr(20 nm)/Au(200 nm) bimetal layer that was used as a gate electrode, and the other side was mirror-polished by chemical and mechanical methods. [24]The 1.7 cm × 1.7 cm free-standing PMNPT substrate having the 30% mole fraction of PbTiO 3 was attached to the conventional silicon wafer substrate to prevent damage during the device fabrication processes owing to its fragile feature of PMNPT.
Device Fabrications: The CVD-grown graphene was transferred onto a PMNPT substrate using the conventional polymethyl-methacrylateassisted wet-transfer technique.The interdigitated metal electrodes were formed on graphene by photolithography, which uses the spin-coating of photoresist LOR-2A (4000 rpm for 60 s) / GXR-AZ-601-46cp (4000 rpm for 60 s) and post-baking (100 °C for 1 min), followed by exposure to ultraviolet light (350 W Xe arc lamp), and the development process with AZ-MIF-300 developer.Metallization with Cr (5 nm)/Au (50 nm) was conducted using a thermal evaporator at 2 × 10 −6 Torr.Lift-off was conducted by soaking the entire substrate in the AZ-100 remover for 12 h, followed by washing in acetone for 10 min and in isopropyl alcohol for 5 min.The same lithography processes with spin coating, baking, UV exposure, and development were performed to define multiple graphene areas with a size of 3 mm × 3 mm.Then, the active graphene channel areas were masked by the photoresist, and the O 2 plasma etching process was applied under a pressure of 1 mTorr with 20 W power for 30 s.
Electrical Characterization: The polarization versus electric-field (P-E) curves were obtained using a "Precision LC II ferroelectric tester" (Precision LC II,Radiant Technologies, US). Three-terminal electrical measurements of the graphene/PMNPT FET device, which include the drain current measurement as a function of gate voltage (I D − V G ) and the gate current measurement as a function of gate voltage (I G − V G ), were performed using the semiconductor characterization system (4200SCS, Keithley Instruments).The measurements were performed inside the vacuum probe station (VPX-M600, WIT, Korea) with pumping (for 5 × 10 −7 Torr) and without pumping (for the ambient environment) conditions.
Framework of Experimental Data Analysis: In this work, the centimeterscale, large-area graphene on PMNPT serves as an atomically thin electrode for ferroelectric and piezoelectric bulk materials.For quantitative evaluation of the ferroelectric coupling between PMNPT and graphene, a device structure of graphene-ferroelectric FET was configured and examined its operation to assess the quality of carrier modulation by PMNPT.Despite the high piezoelectric coefficient of PMNPT indicating a possible strain effect, [30][31][32][33] our analysis of graphene conductance cannot clearly differentiate the impacts of the electrical polarization and the mechanical strain.This ambiguity arises due to the simultaneous occurrence of ferroelectric switching and converse piezoelectric effect in PMNPT under a varying electric field.We assumed, for the following analysis, that the influence of piezoelectric strain on the graphene conductance was limited and ignorable compared to that of ferroelectric polarization.The former mainly affects the mobility of graphene, while the latter pertains to the carrier density and type in graphene.This assumption was supported by the fact that the graphene-PMNPT sample was firmly adhered to a silicon wafer substrate, substantially suppressing lateral dimensional change.

Figure 1 .
Figure 1.Large-area graphene/PMNPT sample and its ferroelectric polarization switching.a) A stitched optical photograph showing three graphene/PMNPT devices fabricated on a single PMNPT substrate, each featuring different interdigitated metal electrode shapes.Each device comprises a CVD-synthesized monolayer graphene sheet with an area of 3 mm × 3 mm (equal to 9 mm 2 ), featuring the structure depicted in Figure1a.b) A schematic drawing of the devices in (a), including elements such as align marks, graphene areas, and interdigitated pattern electrodes.c) Ferroelectric polarization versus electric field curves for each device using the bottom gate metal as one electrode and the graphene with the interdigitated metal electrode as the other electrode.In this case, the area of the square-shaped graphene remains the same, but the ratio of the metal-deposited area on graphene differs for all three devices.

Figure 2 .
Figure 2. Detailed information for the three graphene/PMNPT devices presented in Figure 1a.a) The field-effect transistor device configuration and the shapes of interdigitated electrode patterns.b,c) The I G − V G and I D − V G curves of all three devices under FET operation.Notably, the shape of the I G curves as a function of V G is almost identical for all samples in (b), confirming that the entire graphene area serves as an electrode.The level of I D values in (c) changes depending on the effective graphene geometry between the source-drain interdigitated electrodes.

Figure 3 .
Figure 3. Operational model of a graphene/ferroelectric hybrid system in a field-effect transistor configuration.a) The ferroelectric P-E curve (i), graphene's conductance change with respect to the amount of injected charges (ii), and corresponding I D − V G of graphene/ferroelectric hybrid system in ideal case (iii).b,c) The same interpretation is applied to describe the system with lightly hole-doped graphene on ferroelectrics in (b), and heavily hole-doped graphene on ferroelectrics in (c).The yellow shading in (b) indicates the hysteretic regime in the P-E curve of the ferroelectric substrate.The cyan shading in (c) represents the saturation regime of the ferroelectric substrate's polarization.The magenta dashed lines indicate the correlation of charge neutrality points with the polarization states of the ferroelectric substrate.
den saturation from −19 V, I D does not change until V G reached −60 V.These I D variations match the I G variation in the corresponding I G − V G curves (red curve in the bottom panel for the V G sweep from +60 to −60 V).Because I G indicates the time derivative of accumulated charges on graphene passing through PMNPT, the negative peak of I G , having the onset at ≈ V G = −10 V and the peak near V G = −19 V corresponds to characteristic points of I D variation, mentioned above.Similarly, in the opposite sweep direction, when V G is swept from −60 to +60 V, I D (black curve in the top panel) is initially constant for V G less than −40 V and decreases slowly until it reaches the minimum of approximately V G = +8 V corresponding to the CNP.Then, I D starts to increase as V G increases, and saturates roughly when V G exceeds +25 V.The variation of I G (black curve in the bottom panel) also demonstrates the correlation between I D variations and ferroelectric polarization switching of the PMNPT substrate.This overall tendency is similar even in different V G sweep ranges.In the case of V G sweep between ± 30 V, for example, the slight movement of the negative peak position in I G − V G curves (cyan color) is well matched with the movement of I D − V G curve, that is, V G = −5 V for the I D minimum and V G = −16 V for the starting of I D saturation after the sharp increase of I D between −5 and −16 V.In addition, there is one thing to note about the minimum I D values in Figure 4a during V G sweeps in both directions.If everything is perfect, there is no reason for the I D minimum values to be different depending on the V G sweep direction, because the polarization field added to the external electric field only shifts the CNP position horizontally in the I D − V G curve.The magnitude difference of the two I D minima at the CNPs needs to be understood in relation to the electron-hole puddle phenomena and ferroelectric switching.In other words, if all charge carriers are converted from electron to hole instantaneously, the conductance minimum becomes very small, which resembles the case of I D during the V G sweep from −60 to +60 V.However, if ferroelectric switching occurs in the PMNPT substrate to change

Figure 4 .
Figure 4.The electrical characteristics of the graphene/PMNPT FET for device #3 and a comparison with the model presented in Figure 3. a) I D − V G and I G − V G curves at V G sweep ranges of ±30, ±40, ±50, and ±60 V, respectively, under a high-vacuum condition of 2 × 10 −6 Torr.They exhibit similarities with the lightly-doped case shown in Figure 3b.b) The curves measured at ambient conditions, demonstrating similarities with the heavily-doped case in Figure 3c.The source-drain voltage (V D ) is fixed to 5 mV, and the sweep speed of V G is 1.5 V s −1 .

Figure 5 .
Figure 5. Necessity of the new V G sweep measurement scheme.a) The I D − V G curves obtained using the conventional cyclic sequence of V G sweep with symmetric V G sweep ranges from ±10 to ±60 V. b) The simplified ferroelectric polarization versus electric field curve.c,d) The newly proposed V G sweep scheme, ensuring that the initial ferroelectric polarization state is definitely "down" in (c) and "up" in (d), achieved by using a large negative initial V G bias in (c) and a large positive initial V G bias in (d).

Figure 6 .
Figure 6.Electrical characterization of the graphene/PMNPT FET using the newly proposed V G -sweep scheme.a,b) I D − V G and I G − V G curves measured following the sequence in Figure 5c in the V G range between -60 V and V max , with V max varying from −50 to + 60 V.The data curves in the positive sweep direction are collected in (a), while those in the negative sweep direction are collected in (b).(c, d) Data curves measured following the sequence in Figure 5d in the V G range between +60 V and V min , with V min varying from +50 to −60 V.The data curves in the negative sweep direction are collected in (c), and those in the positive sweep direction are collected in (d).