Two-dimensional (2D) materials have attracted extensive attention all over the world in past decades. More and more new 2D materials have been found and novel device structures emerge in endlessly^[1–5]. Since atoms are arranged by ionic bonds or covalent bonds closely in one layer, it is a weak van der Waals force that combines the atomically thin layers in 2D materials. So far, 2D materials, especially transition metal dichalcogenides (TMDs), have been widely used in developments of photodetectors due to the diversity of bandgaps^[6]. Graphene, as the first 2D material to be found, owns a special and unique conic band structure and can keep stable in an ambient environment, is supposed to be utilized in photodetectors^{[7, 8]}. However, it is hard for graphene to defined on and off-state for its zero bandgap. Molybdenum disulfide (MoS₂), which possesses a various band gap (1.2–1.8 eV) with different layers, is regarded as an alternative material for graphene to avoid such a predicament^[9]. There have been many photodetectors using MoS₂ as the channel material and gain a high responsibility of 5.75 × 10³ A/W^[10], a high detectivity of 10³ J^[11] and a broadband photodetection of 500–1100 nm^[12]. The mechanical exfoliation method, which was invented by A. Geim and K. Novoselov^[13], has become a traditional method to obtain atomic and few-layer-thick 2D materials. However, such a method will introduce a significant density of surface defects and affect the contacts, dielectrics and channel performance of exfoliated 2D materials^[14]. Additionally, it has been reported that oxygen, water molecule, exfoliation residues and sulfur vacancies can facilitate charge trapping process and enhance the hysteresis in MoS₂-based field-effect transistor^[15]. Therefore, the release and capture of photo-generated carriers may be affected and thus lead to a slow response speed in pure MoS₂ photodetector.

Furthermore, most of these phototransistors rely on a real metal gate to apply a gate voltage then to reduce the dark current, leading to leakage between source/drain and gate, but usually, it is difficult to reduce the dark current in a satisfying level^{[16, 17]}. Apparently, a low dark current will contribute to obtain a high photocurrent on/off switching ratio in a photodetector. Utilizing the remnant polarization field of ferroelectric materials, such as BiFeO₃, LiNbO₃, and poly (vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) to regulate the carrier concentration has been reported previously^[18–20]. Among these ferroelectric materials, P(VDF-TrFE) remains stable even under atmosphere condition^[21]. Moreover, P(VDF-TrFE) covering MoS₂ completely can help to passivate or encapsulate trap states on the surface by the fluorine atom or hydrogen atom^[22].

Here, we report the fabrication and operation of a gate-free MoS₂ phototransistor utilizing the remnant polarization field of P(VDF-TrFE) to modulate the carrier concentration in MoS₂. Instead of a metal gate, piezoelectric force microscopy (PFM) is employed to polarize P(VDF-TrFE) under resonant mode in this work. The ferroelectric field has two polarized directions with a local electric field of 10⁹ V/m which is large enough to tune MoS₂ to completely depleted and accumulated state^{[23, 24]}. Therefore, the device structure is greatly simplified and the carrier concentration of MoS₂ is modulated without any external voltage, it means that a robust method to realize a phototransistor with ultra-low power consumption has raised in this work. Specifically, it is easy for us to select the direction based on the experience of previous reports^{[20, 22, 25, 26]}. In this work, we applied a negative voltage to P(VDF-TrFE) through the tip of PFM to make the polarization direction of P(VDF-TrFE) upward, so that an extremely low dark current (approximately 10^–12 A) can be achieved. Besides, since the MoS₂ is completely covered with ferroelectric material, where MoS₂ is isolated from atmospheric environment. Thus, the response time is dramatically improved (t_rise = 200 μs and t_fall = 120 μs), which is much faster than those exposed MoS₂ photodetectors reported previously^{[17, 27–29]}.

PFM measurements were carried out at room temperature on a commercial atomic force microscope (Bruker Multimode 8, Camarillo, CA, USA). Positive and negative DC voltage were applied on P(VDF-TrFE) by a commercial silicon tip (Budget Sensors) covered with chromium/platinum under a contact resonance frequency of 0.7 MHz typically. When applied voltage by PFM probe, the sample will deform and cause the deflection of cantilever. Such a change can be measured to reflect the piezoelectric properties of the sample. For poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) copolymers used in this work, when a positive voltage applied on it, the domains will point down vertically while for negative voltage, the domains will point up vertically.

Fig. 1(a) shows the schematic diagram of the operation for P(VDF-TrFE) polarization switching with PFM. The P(VDF-TrFE) film (50 nm) was spin-coated on the top of chromium/gold (Cr/Au) bottom electrode. The thickness of Cr and Au is 3 and 7 nm, respectively, which is prepared on a 285-nm-thick SiO₂ substrate by thermal evaporation. A DC bias is applied to the P(VDF-TrFE) through the PFM tip, and the bottom electrode is grounded. Fig. 1(b) shows the out-of-plane PFM signals of this P(VDF-TrFE) film. The amplitude signal represents the absolute magnitude of the local piezoelectric response, while the phase signal reveals the polarization direction in every individual domain^[30]. A wonderful butterfly loop of the PFM amplitude signal and an apparent 180° transform of the phase signal were found. Figs. 1(c) and 1(d) display the amplitude signal and phase signal of this P(VDF-TrFE) film after writing half-to-half rectangle patterns with reversed DC bias (the amplitude of the DC bias is 15 V, and more details are illustrated in supplementary Fig. S1). As shown in Fig. 1(c), an obvious ferroelectric domain wall can be found in the middle of the two rectangular regions with opposite polarization directions. Besides, a clear 180° phase reversal also can be found between these two rectangular regions in Fig. 1(d), it can fully reveal the polarization switching characteristic of P(VDF-TrFE). To explore the magnitude of the ferroelectric field, we prepared the P(VDF-TrFE) capacitor with the same thickness. Its hysteresis loop indicates that the remnant polarization of P(VDF-TrFE) is approximately 10 μC/cm² (Supplementary Fig. S2). The ferroelectric field intensity can be calculated from , where represents the electric density at the surface of the ferroelectric film, is the dielectric constant of contact material, is the permittivity of vacuum, and E is the electric field. In this work, the contact material is MoS₂ and its dielectric constant is approximately 4–6^{[31, 32]}. Therefore, the local electric field applied to the MoS₂ is approximately 2.26 × 10⁹ V/m which is strong enough to modulate the carrier concentration of MoS₂ and stay it in a totally depleted state.

Fig. 2(a) illustrates the configuration of the gate-free MoS₂ phototransistor. The MoS₂ was obtained by the Scotch tape-based mechanical exfoliation method, then transferred on the highly doped silicon substrate covered with a 285-nm-thick SiO₂. The source/drain electrode is Cr/Au which was prepared by electron beam lithography, thermal evaporation, and lift-off steps. The thickness of Cr and Au is 10 and 20 nm, respectively. Subsequently, the device was annealed at 200 °C for 2 h in an argon atmosphere. At last, 50 nm P(VDF-TrFE) film was spin-coated on the device and annealed at 135 °C for 2 h in an oven to enhance its crystallinity. The optical image of the device can be seen in Fig. 2(b) and the thickness of MoS₂ in this work is 3.5 nm measured by AFM (See the insert in Fig. 2(b)). The MoS₂ channel length is set to 5 μm. PFM was used to polarize P(VDF-TrFE) in different directions. As shown in Fig. 2(c), different regions of P(VDF-TrFE) on MoS₂ were polarized upward or downward. Fig. 2(d) shows the polarization phase signal extracted near the domain wall (Fig. 2(c)), a clear reversal of 180° can be found which reveals the MoS₂ is modulated by a downward polarization field.

The electrical properties of the device were firstly studied. Fig. 3(a) shows the I_sd–V_sd characteristics under three different polarization states of P(VDF-TrFE). When a DC positive voltage is applied to the P(VDF-TrFE), the polarization direction is downward and the MoS₂ channel is in a carrier accumulation state (P_down state). Conversely, the polarization direction is upward and the MoS₂ channel is in a carrier depletion state (P_up state) when a DC negative voltage is applied. It can be obviously found that the channel current of the device in P_down state is larger than that in the fresh state by an order of magnitude, while the current in P_up state decreased into below 10^–11 A, smaller than that in fresh state by more than 4 orders of magnitude. As a result, such an ultra-low dark current of the device in P_up state is very beneficial for photodetector operation. The sectional view of the device and the transport of carriers under two different polarization states (the P_up state and P_down state) are shown in Figs. 3(b) and 3(c). Fig. S3 presents the transfer characteristics of the device, it can reveal that MoS₂ used in this work is an intrinsic n-type semiconductor. As a result of electrostatic induction, when P(VDF-TrFE) is in P_down state, the electrostatic field from the remnant polarization makes the n-type MoS₂ channel in an accumulated state (Fig. 3(b)); when P(VDF-TrFE) is in P_up state, the electrostatic field changes into the opposite direction and the channel is in a depleted state (Fig. 3(c)). Fig. 3(d)–3(f) reveals the equilibrium band structure of MoS₂ when P(VDF-TrFE) is in three different polarization states. Fermi level (E_F) is defined as an energy level that the probability for an electron to take up is equal to 1/2. The Fermi level is close to conduction band for n-type semiconductors but close to valence band for p-type semiconductors. As shown in Fig. 3(d), the Fermi level of MoS₂ is close to the conduction band when P(VDF-TrFE) is in the fresh state. After applying a positive voltage to P(VDF-TrFE) by the PFM, a downward polarization field will be applied to the MoS₂. Then, the position of Femi level moves up and more electrons can take part in conduction, as shown in Fig. 3(e). In this case, if put the device under illumination and apply a drain bias to read the channel current, the photon-generated current will be covered up by the thermionic or tunneling current^[33–35]. Conversely, once the MoS₂ is modulated by the upward polarization field, the position of Fermi level moves down and less electron can take part in conduction (Fig. 3(f)), and the photon-generated current will correspondingly hold dominate position.

Next, the optoelectronic performance of the device is comprehensively studied. A 520 nm laser is employed as the light source in these measurements. It is widely known that the photocurrent generation mechanism for MoS₂ photodetector is a photoconductive effect^[27]. Specifically, under illumination conditions, the photo-generated electron-hole pairs give rise to the increase of free carrier concentration and cause an increase conductance of MoS₂^[36]. Since the P(VDF-TrFE) can offer an ultra-high and stable polarization-induced electric field (approximate 10⁹ V/m), the carrier concentration of MoS₂ can be modulated by changing the direction of polarization electric field. For a photodetector, we scanned P(VDF-TrFE) using PFM tip with a negative voltage (–15 V) to make the remnant polarization field upward, thus, the MoS₂ channel can maintain a totally depleted state and an ultra-low dark current can be achieved. As shown in Fig. 4(a), under the modulation of upward polarization field, the dark current is just on the order of several picoamperes, which is almost equivalent to the noise current caused by the external environment. When in illumination state, the current increases dramatically to several nano-amperes and becomes larger and larger as the laser power increases constantly. As shown in Fig. 4(b), under a 520 nm laser (P = 6.56 μW) incident, the device displays an extraordinarily stable and repeatable photocurrent on/off switching ratio of 10⁴. A photocurrent map was obtained by scanning the incident light on the device and extracting the corresponding current. Fig. 4(c) demonstrates the photocurrent map of the device at V_sd = 1 V drain bias, the incident light wavelength is 520 nm and the light power is 0.28 μW. It can be clearly seen that the photocurrent occurs in the middle of the MoS₂ channel, and there is no photocurrent occurs between the MoS₂ and the source/drain electrode. It is shown that good ohmic contact has formed in the device instead of a Schottky contact.

The photoresponse time is another important parameter to evaluate the ability of photodetectors, which is defined as the time for the photocurrent switching from 10% to 90%. For our device, the photocurrent turns from off to on state is as fast as 200 μs (Fig. 4(d)), indicating a fleet generation of photo-generated electron–hole pairs in MoS₂. It takes 120 μs for the device to turns from on to off state (Fig. 4(e)), indicating a fast process of carrier recombination. The photoresponse speed of our device is faster than those intrinsic MoS₂ photodetectors (see Table 1)^{[17, 27–29]}. Such a fast photoresponse speed is mainly contributed to the fact that P(VDF-TrFE) can inhibit those trap states on the surface of MoS₂ and enable photo-generated carriers to take full part in the conduction process^{[22, 37]}. Organic polymer ferroelectric material P(VDF-TrFE) is proved to have a p-doped effect on 2D materials due to the C–F and C–Cl bonds^[20]. Such a p-doped effect can help enhance the photoresponse properties of MoS₂ photodetector^[17]. In detail, the p-doped effect induced by P(VDF-TrFE) decreases the surface defects of MoS₂. Thus, the carrier scattering is suppressed and the generation and transmission process of photo-generated carriers are faster than that exposed in the ambient air. Furthermore, the responsivity of the device to incident light at different wavelengths was evaluated. As shown in Fig. 4(f), the device has the highest responsivity under incident light of 600 nm, and has no photoresponse to incident light with a wavelength longer than 700 nm. Such a result is attributed to the absorption spectrum of MoS₂ and similar result has been reported in previous work^[38].

In summary, we have fabricated a gate-free MoS₂ phototransistor assisted by ferroelectric domain. Under the modulation of remnant polarization field, the carrier concentration of the MoS₂ channel is completely depleted and the optoelectronic performance of the device is greatly enhanced. The dark current of the MoS₂ photodetector is reduced to the order of several picoamperes. The photoresponse time is also improved to 200 and 120 μs, which is much faster than those intrinsic MoS₂ photodetectors without P(VDF-TrFE). More importantly, such a gate-free MoS₂ phototransistor assisted by the ferroelectric domain embraces the ultra-low power consumption. Therefore, it provides a reliable way to develop 2D materials-based photodetectors with high-performance and ultra-low power consumption.

This work was partially supported by the Major State Basic Research Development Program (Grant Nos. 2016YFA0203900, 2016YFB0400801 and 2015CB921600), and Key Research Project of Frontier Sciences of Chinese Academy of Sciences (Nos. QYZDB-SSW-JSC016, QYZDY-SSW-JSC042). Strategic Priority Research Program of Chinese Academy of Sciences (XDPB12, XDB 3000000). Natural Science Foundation of China (Grant Nos. 61521001, 61574151, 61574152, 61674158, 61722408, 61734003 and 61835012), and Natural Science Foundation of Shanghai (Grant No. 16ZR1447600, 17JC1400302).