Ferroelectric semiconductor junctions based on graphene/In2Se3/graphene van der Waals heterostructures

The miniaturization of ferroelectric devices offers prospects for non-volatile memories, low-power electrical switches and emerging technologies beyond existing Si-based integrated circuits. An emerging class of ferroelectrics is based on van der Waals (vdW) two-dimensional materials with potential for nano-ferroelectrics. Here, we report on ferroelectric semiconductor junctions (FSJs) in which the ferroelectric vdW semiconductor α-In2Se3 is embedded between two single-layer graphene electrodes. In these two-terminal devices, the ferroelectric polarization of the nanometre-thick In2Se3 layer modulates the transmission of electrons across the graphene/In2Se3 interface, leading to memristive effects that are controlled by applied voltages and/or by light. The underlying mechanisms of conduction are examined over a range of temperatures and under light excitation revealing thermionic injection, tunnelling and trap-assisted transport. These findings are relevant to future developments of FSJs whose geometry is well suited to miniaturization and low-power electronics, offering opportunities to expand functionalities of ferroelectrics by design of the vdW heterostructure.


Introduction
Since the pioneering studies in the 1920s by Joseph Valasek on ferroelectricity in Rochelle salt (e.g. KNaC 4 H 4 O 6 ·4H 2 O) [1], ferroelectric materials have had an enormous impact in science and exploited in many technologies ranging from high-energy capacitors and transducers to ultrasound medical imaging [2][3][4]. More recently, the observation of ferroelectricity in van der Waals (vdW) crystals has attracted significant interest [5][6][7][8]. These two-dimensional (2D) layered materials can exhibit ferroelectricity above room temperature and for layer thicknesses down to a few layers of atoms. Their implementation in miniaturized devices could open paths towards multifunctional sensors for digital technologies, nano-electromechanical systems, increased storage capacity of non-volatile memories, neuromorphic computing, etc [9][10][11][12]. For example, resistance switching by ferroelectricity could be exploited in nanoscale memristive devices (or memristors) to store and process information for non-volatile, low-power electrical switches [13]. Thus, understanding the limitations and potential of this emerging class of 2D ferroelectrics is important for future scientific and technological advances.
In a ferroelectric material, the crystal lattice is polarized along a specific direction, generating a macroscopic electrical polarization P that can be reversed by an applied electric field E. The electric polarization arises from a structural asymmetry of the crystal along the direction of the polarization leading to a nonlinear dependence of the polarization amplitude P on the strength of the electric field, E, and an S-shaped hysteresis loop in the P-E curve [3]. For atomically thin layers, the ferroelectric state can be difficult to detect due to a weak polarization signal; it may require a large applied electric field to be reversed, leading to electrical breakdown; finitesize effects, such as depolarization fields at interfaces, can destabilize the ferroelectric polarization [14,15]; furthermore, localization of charge carriers onto defects, crystalline phase changes and/or electrochemical processes can influence ferroelectric properties and device performance [16,17].
Amongst 2D ferroelectrics, the vdW semiconductor α-In 2 Se 3 has emerged as a promising material due to its room temperature in-plane (IP) and out-of-plane (OOP) ferroelectricity [15,[18][19][20] and a low coercive electric field (∼10 7 V m −1 ) [20]. Its use in 2D ferroelectric devices has been reported and includes ferroelectric field effect transistors (FeFETs) with the ferroelectric semiconductor serving as conducting channel [11,16,19,21] or dielectric gate [9,22], and ferroelectric semiconductor junctions (FSJs) based on a thin α-In 2 Se 3 layer embedded between single-layer graphene and few layer graphene electrodes [20]. The geometry of the FSJ is well suited to miniaturization and low-power applications. Furthermore, the conductivity properties of a ferroelectric semiconductor can be modified by temperature and light, providing broad prospects for applications of ferroelectric devices.
Here, we report on FSJs based on the ferroelectric vdW semiconductor α-In 2 Se 3 embedded between two single-layer graphene electrodes ( figure 1(a)). In the FSJ, the polarization of the nanometrethick In 2 Se 3 layer is controlled by a voltage applied between two graphene electrodes, thus modifying the Schottky-like barrier at the graphene/In 2 Se 3 interface [15,20]: the change in the height of the barrier modulates the transmission of electrons across the interface, leading to memristive effects. We show that this is a robust process over a wide range of temperatures, below and above room temperature. Also, it can be modified by a relatively small applied voltage (∼1 V) and by light: the free carriers generated by light and/or thermionic injection can neutralize the polarization charges at the graphene/α-In 2 Se 3 interface and influence the hysteretic behaviour in the electrical transport, offering opportunities for future developments.

FSJs
For our studies we focus on the α-phase of In 2 Se 3 , which is ferroelectric at room temperature with a Curie temperature T c above 500 K [18]. The preliminary characterization of the α-In 2 Se 3 crystals by x-ray diffraction, piezoresponse force microscopy (PFM), Raman and photoluminescence (PL) spectroscopy is in the Methods section and in figures S1 and S2 (available online at stacks.iop.org/2DM/8/045020/ mmedia) of supplementary material S1. Amongst the different crystalline phases of In 2 Se 3 , the α-phase exhibits either a rhombohedral (3R) or a hexagonal (2H) crystal structure [6,23]. For both structures, the single vdW In 2 Se 3 layer consists of five atomic layers stacked in the sequence Se-In-Se-In-Se (one quintuplet layer, QL), which exhibits reversible spontaneous electric polarization in both OOP and IP orientations [15,[18][19][20]. The asymmetric position of the Se-atoms inside each QL breaks the centro-symmetry of the crystal, providing two degenerate energy states with opposite OOP polarization and IP asymmetry. To reverse the OOP polarization, the middle Se-atom must move along the c-axis and in the ab-plane, leading to a break up and reconfiguration of the In-Se covalent bond [15,21]. The OOP polarization of α-In 2 Se 3 is important for miniaturization of electrical components that require vertical device architectures, such as the FSJ.
Our graphene/In 2 Se 3 /graphene vdW heterostructures are assembled by exfoliation and mechanical stamping of nanometre-thick vdW layers (see section 4). The optical image and schematics of the band alignments for a FSJ with a 30 nm thick α-In 2 Se 3 layer are illustrated in figures 1(a) and (b). Under a voltage applied between the two graphene electrodes of the FSJ, electrons are injected from the negatively biased graphene electrode onto the α-In 2 Se 3 layer and collected at the second graphene electrode ( figure 1(a)). For an electric field larger than the coercive field, the ferroelectric layer becomes polarized and the polarized charges at the graphene/α-In 2 Se 3 interface shift the Dirac cone of graphene relative to the conduction band (CB) of α-In 2 Se 3 , thus lowering (figure 1(b), (i)) or increasing (figure 1(b), (ii)) the potential barrier seen by electrons. The polarization charges decrease the potential barrier at one interface, while they increase it at the other interface. Also, the applied voltage creates an asymmetry in the junction so that the interface between the negatively biased graphene electrode and the α-In 2 Se 3 barrier dominates: once electrons are injected across the first interface, they travel throughout the ferroelectric layer reaching the second interface with graphene where there are available empty states ( figure 1(a)). For an electric field larger than the coercive field, the potential barrier seen by the electrons at the first interface decreases. This leads to an increased transmission of electrons throughout the device, causing resistance switching and memristive behaviours.
The current-voltage |I|-V curves of the FSJ reveal counter-clockwise loops at T = 100 K (figure 1(c)) and T = 300 K (figure 1(d)): the amplitude of the current is larger when sweeping the voltage from high to low positive V (or from high to low negative V). The applied voltage is critical to the observation The transport properties of the FSJ are further probed by monitoring the temporal dependence of the current under different applied voltages and electric poling conditions of the FSJ. The current measured at a low bias (V = +0.5 V) takes different values following a poling of the FSJ at a larger positive or negative voltage (see figure 1(f) for poling at V = +1.5 V). The initial resistive state can be resumed by applying a negative (or positive) bias after poling at V > 0 (or V < 0) (figure 1(f)). Similar counter-clockwise loops in I-V and memristive effects were observed in FSJs with different thicknesses of the α-In 2 Se 3 layer (figure S3 in supplementary material S2). In contrast, they are not observed in FETs based on long (>1 µm) α-In 2 Se 3 channels, whose electrical properties and hysteretic behaviours are dominated by charge injection onto trap sites (supplementary material S3).
A large electric field is required to induce a ferroelectric polarization in α-In 2 Se 3 by displacements of the In-and Se-atoms within each vdW layer. PFM demonstrates switching of the polarization at the nanoscale and possibility to create local stable OOP domains (figure S2 in supplementary material S1). The calculated amplitude of the electric dipoles is 0.11 and 0.03 eÅ per α-In 2 Se 3 unit cell for the two oppositely polarized configurations, influencing the atomic orbitals and energy band alignments at the graphene/α-In 2 Se 3 interface [15]: the chemical potential in graphene moves upward or downward according to the sign of the polarization charges so that more or fewer electrons can transverse the junction. At low T (figure 1(c)), the steeper increase of the current at |V| > 1 V suggests a switchable polarization of the ferroelectric layer, thus increasing the current throughout the junction; this behaviour is also observed at room temperature, but it is less pronounced (figure 1(d)).

Thermionic injection and tunnelling
We probe the mechanisms of conduction in the FSJ and the robustness of the memristive behaviour against a rising temperature by considering the I-Vs over a range of temperatures from T = 100 K to T = 380 K. As shown in figure 2(a), the counterclockwise loop in I-V persists above T = 300 K, although is significantly reduced at T = 340 K. For T < 150 K, the current and hysteretic behaviours are weakly dependent on T; in contrast, at higher temperatures, the current tends to increase exponentially with T, following a dependence described by I ∼ exp(−E a /k B T), where k B is the Boltzmann constant and E a is an activation energy ( figure 2(b)). From the Arrhenius plots of figure 2(b), we extract the value of E a and its dependence on V (figure 2(c)): with increasing V, E a first decreases, reaches a constant value between V ∼ 0.5 V and V ∼ 1 V, and then it decreases for V >1 V.
The temperature dependence of the current suggests a contribution to the transport from thermionic injection of electrons from the graphene electrode onto the CB of α-In 2 Se 3 (figure 2(c), (i)). For thermionic injection, the emission current density can be described as J = J s [exp(qV/k B T) − 1] [24], where J s = A * T 2 exp(−qϕ B /k B T), A * is the effective Richardson constant, q = e is the elementary electron charge, and qϕ B is the Schottky barrier height at the graphene/semiconductor interface. The current is thermally activated with an activation energy E a that increases with decreasing V extrapolating to qϕ B at V = 0 V. As shown in figure 2(c), our FSJs reveal this dependence at low V with E a = qϕ B = (0.38 ± 0.01) eV at V = 0. From the measured position of the Fermi level, E F , in our p-type graphene electrode at V = 0, we deduce that the neutral Dirac point of graphene lies at ∆E = qϕ B − E F ≈ 0.25 eV below the CB edge of α-In 2 Se 3 at V = 0 V (supplementary material S1).
The Schottky barrier model is in agreement with that expected from density functional theory for a graphene/α-In 2 Se 3 interface [15]. However, the graphene/α-In 2 Se 3 interface does not behave as a simple Schottky contact. The constant value of E a with increasing V from V ∼ +0.5 V to V = +1 V followed by a steep decrease for V > +1 V (figure 2(c)) cannot be explained by thermionic injection. On the other hand, under a large applied electrical field, electrons can tunnel from the electrode onto the CB of α-In 2 Se 3 through a triangular potential barrier (Fowler-Nordheim tunnelling, figure 2(c), (ii)), causing a weaker dependence of the current on temperature than for thermionic injection. Furthermore, as the voltage increases beyond the coercive field, the polarization charges at the graphene/α-In 2 Se 3 interface induce an effective lowering of the Schottky barrier (figure 2(c), (iii)). This can account for the decrease of E a at high V and the corresponding increase of conduction in the low-resistive ferroelectric state of the FSJ. In summary, the modulation of the graphene/α-In 2 Se 3 interface by polarization switching can be modelled as a tuneable Schottky barrier: a change in the height of the barrier modulates the transmission of electrons across the FSJ. At low T (<150 K) charge injection is dominated by tunnelling, whereas thermal injection becomes more prominent as the temperature increases above T = 150 K. The reduced memristive effects with increasing T arise from the increased current in the FSJ acting to diminish the polarization of α-In 2 Se 3 .
We have examined FSJs with different layer thickness (see figures S3 and S4 in supplementary material S2). All structures show similar hysteretic behaviours in the electrical transport. Although the transmission of electrons by direct tunnelling is reduced in thicker layers, trap-assisted tunnelling can dominate at high applied voltages. Under a large applied electrical field, the conduction electrons in the α-In 2 Se 3 layer can acquire sufficient energy to ionize charge trap sites, generating additional electrons by inelastic collisions. Electron emission from traps is also influenced by the electric field due to Poole-Frenkel emission [25]. Carrier traps can arise from In-vacancies and/or residual n-type dopants that reside in the interlayer gaps of α-In 2 Se 3 [26]. Their existence is supported by Hall effect measurements of bulk α-In 2 Se 3 , giving a Hall electron density of up to n = 4.9 × 10 17 cm −3 at T = 300 K (see Methods sections and figures S3 and S4 in supplementary material S2). The ionization of impurities and/or defects at high electric fields and/or temperature is pivotal to the operation of FSJs, requiring optimization of the doping properties of the ferroelectric semiconductor. We note that the thermal excitation of electrons from the valence band to the CB of α-In 2 Se 3 creates free carriers whose density depends on the band gap energy (E g ) and temperature (E g = 1.4 eV at 300 K) (figure S1 in supporting materials S1). The thermal activation energy for this process is significantly larger than that derived from the thermally activated behaviour of the current in the FSJ ( figure 2). Thus, we infer that the intrinsic thermal excitation of carriers can be neglected.

FSJs under light
Light provides a non-invasive method for switching ferroelectric properties and probe ferroelectrics [11,[27][28][29][30]: The built-in electric field due to the ferroelectric polarization can induce photovoltaic effects [27,28] and modify the ferroelectric polarization by screening of polarization charges [30]. Here, we examine light-polarization interactions in our FSJs using laser light of energy hv = 1.96 eV (λ = 633 nm) above the band gap of α-In 2 Se 3 (E g = 1.4 eV at 300 K) (figure S1 in supporting materials S1). In these experiments the FSJ is illuminated through the transparent top graphene electrode.
As shown in figure 3, an increasing laser power P i induces a positive photocurrent ∆I and reduces the hysteretic loops in I-V. We examine the photoresponse of the FSJ by considering the dependence of the photoresponsivity, R = ∆I/P i , on V and P i for two FSJs with different layer thicknesses (t = 30 and 200 nm in figures 4(a)-(c) and (b)-(d), respectively). As can be seen in figure 4, for both FSJs R increases by several orders of magnitude with increasing V and is larger at low powers.
At first glance, the photoresponse of the FSJ can be understood by considering the dynamics of photocreated carriers (figure 4(e)). Under an applied voltage V, electrons and holes that are photoexcited in the α-In 2 Se 3 layer are swept by the electric field in opposite directions and extracted at the graphene electrodes (figure 4(e), (i)) to generate a photocurrent ∆I = [qtαP i /hv]τ l /τ t , where α is the absorption coefficient of α-In 2 Se 3 at the photon energy hv, t is the thickness of the α-In 2 Se 3 layer, and τ l /τ t is the ratio of the minority carrier lifetime (τ l ) to the transit time (τ t ) of majority carriers in α-In 2 Se 3 . In these FSJs, the majority carriers are electrons due to residual n-type doping of α-In 2 Se 3 (n = 4.9 × 10 17 cm −3 at T = 300 K). Thus, we express R as R = ∆I/P i = [etα/hv]τ l /τ t and the external and internal quantum efficiencies as EQE = R(hv/e) = [tα]τ l /τ t and IQE = τ l /τ t , respectively. These relations indicate that large values of R, EQE and IQE are achieved if the lifetime of holes is longer than the transit time of electrons.
As shown in figures 4(c) and (d), R follows a power dependence described by P i β with β = −0.48 ± 0.02 for t = 30 nm and The decrease of R, EQE and D * with increasing P i is similar to that reported for other 2D materials [31][32][33][34][35] and can be accounted for by the decrease of τ l/ τ t with increasing P i due to either a decrease of τ l and/or an increase of τ t with increasing P i . The transit time of majority electrons can increase with P i due to enhanced carrier scattering. The lifetime of minority holes is limited by Shockley-Read and surface recombination and is reduced at high carrier densities (or high P i ) due to Auger recombination [24]. The dependence of R on P i is more pronounced in the thicker FSJs, suggesting a stronger contribution from trap-assisted carrier recombination (figure 4(e), (ii)). All our FSJs reveal a similar high, fast temporal photoresponse. Figure 5(a) shows the temporal dependence of the current under illumination of an FSJ with t = 200 nm (see also figure S6 in the supplementary material S5). The rise (τ r ) and decay (τ d ) times of the current are derived from an exponential fit to the data ( figure 5(b)): they are both short (0.1-1 ms) with τ d > τ r and both decreasing with increasing V and/or P i .
We examine the data on photoresponsivity under different applied voltages and powers to examine the role of the ferroelectric polarization on the photoresponse of the FSJs. The photoresponsivity increases by several orders of magnitude with increasing V (figures 4(a) and (b)), reaching values comparable to or higher than those reported for other In 2 Se 3based devices in the literature [31,[36][37][38][39]. The strong dependence of the photocurrent on V is also seen in tunnel junctions without the ferroelectric layer [34], suggesting that the ferroelectric polarization of the In 2 Se 3 layer does not play a critical role in the high values of R or in the dependence of R on V. The high photoresponsivity of the FSJ is primarily caused by a large internal gain and is not influenced by polarization charges at the graphene/α-In 2 Se 3 interface. On the other hand, photocreated carriers act to neutralize polarization charges, reducing the hysteresis loops in I-V ( figure 3).
We assign the superlinear dependence of R on V to avalanche multiplication of carriers due to impact ionization of traps inside the band gap (figure 4(e), (iii)). This process can occur at lower fields than those required for band-to-band ionization as traps require a smaller ionization energy and their binding energy is reduced due to Poole-Frenkel effect [25]. For bandto-band impact ionization, the threshold energy for impact ionization, ε th , should be larger than the band gap energy (E g = 1.4 eV at 300 K for bulk crystals). A simple diffusive model of electron motion indicates that the electric field required for an electron to acquire such energy ε th would be larger than E th ∼ 2.4 × 10 9 V m −1 , much larger than that considered in our experiments (supplementary material S4). On the other hand, an avalanche creation of free carriers by ionization of defects and/or impurities can occur for E < E th .

Conclusions
In conclusion, the polarization of the ferroelectric vdW semiconductor α-In 2 Se 3 can be manipulated by applying a voltage across the two graphene electrodes of a graphene/α-In 2 Se 3 /graphene junction. This acts to modify the Schottky barrier at the graphene/α-In 2 Se 3 interface: a change in the height of the barrier modulates the transmission of electrons across the interface, leading to memristive effects. This is a robust process over a wide range of temperatures. However, it can be influenced by ionization of defects and impurities that reside in n-type α-In 2 Se 3 , a phenomenon that tends to weaken the memristive effect. The additional free carriers generated by impact ionization, tunnelling and thermionic injection can neutralize the polarization charges at the graphene/α-In 2 Se 3 interface and influence the hysteretic behaviour in the electrical transport. Light provides an effective route for modifying electronic properties and memristive effects. In particular, the FSJs reveal a high photoresponsivity and fast modulation of the photocurrent that exploit the optical absorption properties of α-In 2 Se 3 and its favourable interface with graphene for charge extraction. Further research into device design, mechanisms and fabrication are crucial for reliable, optimized and predictable memristive behaviours and graphene-based vdW heterostructures with ferroelectric tunnelling barriers. Also, the development of ferroelectric semiconductors with controlled n-and ptype doping is critical to future implementation of ferroelectrics in multi-functional devices.

Experimental section
Materials and device fabrication The α-In 2 Se 3 crystals were grown using the Bridgman method from a polycrystalline melt of In and Se with atomic ratio of 40:60. The crystal structure of the α-In 2 Se 3 single crystals was studied by x-ray diffraction using a DRON-3M diffractometer. The crystals exhibit either a rhombohedral (3R) or a hexagonal (2H) crystal structure. Here we focus on the hexagonal (2H) phase with lattice parameters a = b = 4.031 ± 0.003 Å and c = 19.210 ± 0.009 Å. For the rhombohedral (3R) phase, a = b = 4.017 ± 0.003 Å and c = 28.870 ± 0.009 Å. Raman spectroscopy and imaging studies on flakes and bulk crystals reveal the characteristic vibrational modes of 2H α-In 2 Se 3 , providing a means to distinguish it from other phases (figure S1 in the supplementary materials). The PL emission of bulk α-In 2 Se 3 is centred at about 1.4 eV at 300 K and blue-shifts with decreasing layer thickness. In its bulk form, α-In 2 Se 3 contains native donors. Hall effect measurements on bulk α-In 2 Se 3 at T = 300 K indicate an electron density n = 4.9 × 10 17 cm −3 and an electron mobility in the layer plane of µ = 405 cm 2 V −1 s −1 . The relatively high electron density arises from impurities residing in the interlayer spaces. These limit the OOP mobility, which is 50 times smaller (8 cm 2 V −1 s −1 ) than in the layer plane [26]. Figure 1(a) in the main text shows a schematic illustration of our devices. These graphene/α-In 2 Se 3 /graphene heterostructures are assembled onto a SiO 2 /p-Si substrate (SiO 2 layer thickness of 300 nm) using chemical vapour deposition (CVD) graphene and α-InSe 3 flakes. For the stamping of top and bottom graphene, we use a needle-assisted transfer process of patterned graphene microsheets, as described in [40]. The top and bottom graphene flakes are deposited sequentially onto prepared metal contacts (Au/Ti (100 nm/10 nm)) using a dry transfer method under ambient conditions. Flakes of α-In 2 Se 3 are exfoliated onto polydimethylsiloxane (PDMS) from a lowtack, low-residue tape and identified using transmission and reflection mode optical microscopy. Then, using a micromanipulator stage, an exfoliated flake of α-In 2 Se 3 on PDMS is aligned to the predeposited bottom graphene flake and brought into contact. The PDMS is then slowly retracted in order to deposit α-In 2 Se 3 . Finally, the top graphene contact is aligned to the α-In 2 Se 3 and Au/Ti metal contact.
Optical, electrical and microscopy studies Images of the layers' topography were acquired by atomic force microscopy (MFP3D) in non-contact mode under ambient conditions.
Local reversible polarisation of ferroelectric domains [41] and PFM maps of α-In 2 Se 3 films were conducted using a commercial scanning probe microscope (Multimode with Nanoscope-V controller, Bruker, USA) in ambient atmosphere using small contact radius conductive tips (PtSi-CONT, Nanosensors, Switzerland) in both resonance and nonresonance contact mode [42]. Transport measurements in the dark and under light illumination were conducted in vacuum (2 × 10 −6 mbar). All experiments were conducted with the bottom-graphene electrode grounded. The experimental setup for the micro-Raman and micro-PL spectroscopy studies at room temperature comprises a He-Ne laser (λ = 633 nm), an x-y-z motorized stage and an optical confocal microscope system equipped with a 0.5 m long monochromator with 1200 g mm −1 and 150 g mm −1 gratings. The laser beam was focused to a diameter d ∼ 1 µm using a 50× objective. The signal was detected by a Si-charge-coupled device camera. The optical studies were performed at low excitation power to avoid excessive heating. The temporal dynamics of the photocurrent was investigated under constant bias voltage and illumination by a mechanically modulated He-Ne laser with λ = 633 nm and frequency f < 200 Hz. The photocurrent signal was measured using a Tektronix DPO 4032 digital oscilloscope and a Keithley2400 was used as a DC voltage source. For the time-resolved measurements of the current, the device was connected in series with a 1 MΩ resistor and the voltage on the 1 MΩ resistor recorded using the oscilloscope with a low-noise level.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.