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

For our studies we focus on the α-phase of In₂Se₃, which is ferroelectric at room temperature with a Curie temperature T_c above 500 K [18]. The preliminary characterization of the α-In₂Se₃ 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 In₂Se₃, the α-phase exhibits either a rhombohedral (3R) or a hexagonal (2H) crystal structure [6, 23]. For both structures, the single vdW In₂Se₃ 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, 18–20]. 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-In₂Se₃ is important for miniaturization of electrical components that require vertical device architectures, such as the FSJ.

Our graphene/In₂Se₃/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-In₂Se₃ 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-In₂Se₃ 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-In₂Se₃ interface shift the Dirac cone of graphene relative to the conduction band (CB) of α-In₂Se₃, 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-In₂Se₃ 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 of the hysteretic behaviour in I–V. As shown in figure 1(e), the counter-clockwise loop becomes more pronounced at larger V. Weaker clockwise loops are instead observed at low V. For the device of figure 1, a voltage |V| = 1 V corresponds to an electric field E = |V|/t > 0.3 × 10⁸ V m⁻¹, where t ≈ 30 nm is the thickness of the α-In₂Se₃ layer.

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-In₂Se₃ layer (figure S3 in supplementary material S2). In contrast, they are not observed in FETs based on long (>1 µm) α-In₂Se₃ 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-In₂Se₃ 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-In₂Se₃ unit cell for the two oppositely polarized configurations, influencing the atomic orbitals and energy band alignments at the graphene/α-In₂Se₃ 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)).

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 counter-clockwise 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.

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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-In₂Se₃ (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*T²exp(−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 ΔE = qφ_B − E_F ≈ 0.25 eV below the CB edge of α-In₂Se₃ 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-In₂Se₃ interface [15]. However, the graphene/α-In₂Se₃ 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-In₂Se₃ 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-In₂Se₃ 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-In₂Se₃ 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-In₂Se₃.

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-In₂Se₃ 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-In₂Se₃ [26]. Their existence is supported by Hall effect measurements of bulk α-In₂Se₃, giving a Hall electron density of up to n = 4.9 × 10¹⁷ 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-In₂Se₃ 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.

Light provides a non-invasive method for switching ferroelectric properties and probe ferroelectrics [11, 27–30]: 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-In₂Se₃ (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 ΔI and reduces the hysteretic loops in I–V. We examine the photoresponse of the FSJ by considering the dependence of the photoresponsivity, R = ΔI/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.

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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-In₂Se₃ layer are swept by the electric field in opposite directions and extracted at the graphene electrodes (figure 4(e), (i)) to generate a photocurrent ΔI= [qtαP_i/hv]τ_l /τ_t, where α is the absorption coefficient of α-In₂Se₃ at the photon energy hv, t is the thickness of the α-In₂Se₃ 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-In₂Se₃. In these FSJs, the majority carriers are electrons due to residual n-type doping of α-In₂Se₃ (n = 4.9 × 10¹⁷ cm⁻³ at T = 300 K). Thus, we express R as R= ΔI/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 β = −0.71 ± 0.03 for t= 200 nm. The largest values of R (up to R = 10⁶ A W⁻¹) are reached for low P_i = 10⁻¹² W. For t = 30 nm, V = +1 V and α = 10⁶ m⁻¹ at hv= 1.96 eV, we estimate that τ_l/τ_t decreases from ∼2 × 10⁶ to ∼2 × 10⁴ with P_i going from 10⁻¹² W to ∼10⁻⁸ W. A value of τ_l/τ_t = 2 × 10⁶ corresponds to a large internal gain with IQE = 2 × 10⁶, EQE = R[hv/e] = 7 × 10⁴ and D* = R(A/2eI)^1/2 ∼ 5 × 10¹¹ m W⁻¹s^−1/2, where A = 20 µm² is the area of the device and I = 0.8 µA is the dark current at V= +1 V.

The decrease of R, EQE and D* with increasing P_i is similar to that reported for other 2D materials [31–35] 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.

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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 In₂Se₃-based devices in the literature [31, 36–39]. 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 In₂Se₃ 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-In₂Se₃ 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 band-to-band impact ionization, the threshold energy for impact ionization, _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 _th would be larger than ${E_{{\text{th}}}}$ ∼ 2.4 × 10⁹ 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 < ${E_{{\text{th}}}}$.