The challenges of the current von Neumann computing architecture mainly stem from three aspects: insufficient processor cache, time-consuming data movement between memory and processor, and high energy consumption. These collectively form the well-known von Neumann bottleneck^[1−3]. As a potential solution to address the bottleneck, the non-volatile memory device called "memristor" has garnered widespread research interest due to its advantages such as simple structure and fabrication, fast computation speed due to needless of data movement between memory and processor, low energy consumption, and so on^{[4, 5]}. In comparison to memristors fabricated with traditional materials, those based on two-dimensional (2D) semiconductor materials, especially the transition-metal dichalcogenides (TMDs), have attracted significant attention because of their merits including ultra-high-density storage capacity, very low energy consumption, fast data movement speed, natural flexibility, and great potential applicable to integrating into processor chips^{[6, 7]}. However, only some 2D semiconductor materials show memristive properties but must suffer from poor performance, which becomes a significant obstacle for the practical application of 2D semiconductor memristors^[8−12].

Mechanism researches of 2D-material memristors have indicated that moderated defects in 2D materials are crucial for memristive performance, and the defects may be introduced in many fabrication steps such as 2D material growth, transfer, and building processes of the memristor, and so on. This results in defect modulations in both controllable defect concentration and desired defect region are very difficult to be realized controllably. Controllable doping used for silicon-based materials through ion implantation^{[13, 14]} seems to be a referential route for improving and modulating 2D memristive characteristics. However, due to the lattice structure of atomic-scale thickness 2D material is easily damaged during this process, leading to it not being applied effectively. Additionally, doping methods based on interface molecular modification or controlling gate voltage through electrostatic means often face issues like poor stability and electrical breakdown. Therefore, the development of new doping strategies for 2D semiconductors to achieve precise and stable control of defects is of great value for improving the performance of memristors and other devices.

Owing to laser direct writing (LDW) implements easily diverse modulation manners including patterned modulation, gradient modulation, and uniform modulation and for forth, utilizing LDW to dope defects into 2D materials being a promising strategy, which has been identified in bandgap modulation and polarity change of the semiconductor, and so forth^[15]. Very recently, appearance of a memristive effect after laser modulation to MoS₂ grown by chemical vapor deposition (CVD) has verified effectiveness of the laser modulation^[16]. Noted that the laser-modulation needs to be investigated in deep, especially the mechanism of laser-modulation not yet clear, which may open a door for performance modulation of 2D semiconductor memristors. However, inevitable defects existing in CVD-growth MoS₂ confounds source of the defects in the laser-induced MoS₂ memristor, and thereby hindering elucidation of the memristive mechanism which originates whether from only laser-induced defects or not.

For clearing the mechanism of laser-induced memristive features, we utilized LDW technology to modulate mechanically-exfoliated MoS₂ for removing the influence of defects from CVD-growth MoS₂. Based on experiment results, dynamic Monte Carlo simulations and first-principles calculations were employed to elucidate the operational principles of LDW-induced planar MoS₂ memristors, and confirmed laser-induced oxygen-doping mechanism and the band structures and barriers of MoS₂ with varying levels of oxygen doping. Furthermore, we verified the universality of the laser modulation by other 2D materials of TMDs. This work achieved some interesting results: (1) realizing memristive feature in defect-free intrinsic materials by laser-modulation with precise and stable control of defect concentrations, (2) clearing the laser-induced memristive mechanism and establishing a correlation between oxygen-ion doping concentration and memristive characteristics, and (3) verifying the laser-modulation's universality. Our work is helpful in experiment and theory to insight into mechanism of laser-modulation and to modulate and optimize performance of 2D semiconductor memristive devices.

The few-layer MoS₂ was obtained by mechanical exfoliation, and then the sample was transferred on the SiO₂/Si substrate. The thickness of the silicon oxide is about 300 nm. For the planar two terminal devices, the electrodes were patterned by the LDW (HWN-LDW-L4) lithography, and then deposited 3 nm Ti (adhesion layer) and 50 nm Au by e-beam evaporation. After that, doping patterns could be directly uploaded to LDW as a laser scanning path for laser-doping to 2D materials. The laser spot is a circle with a diameter of 300 nm. Here the parameters of laser (such as power, pulse width) could be adjusted. The direct current (DC) characteristics of the devices based on different multilayer MoS₂ memristors were measured on a Lakeshore probe station with Keithley 2635A, 2602B, and Keithley 4200A-SCS parameter analyzer. A cyclic scanning rate of 1 s for positive scanning and about 4 s for one cycle. All the electrical measurements were conducted on a manual probe station (Lakeshore, TTP4) equipped with a vacuum pump.

The morphology and structure of the multilayer MoS₂ were characterized with optical microscopy (Olympus LEXT-OLS4000), transmission electron microscope Tecnai (TEM, G2 F20 U-TWIN), scanning electron microscopy (SEM, Hitachi S-4800, 10 kV, 10 µA) and atom force microscope (AFM, Bruker Multimode 8HR). The element ratio of Mo/S of the pristine MoS₂ was tested by energy dispersive spectrometer (EDS) and auger electron spectroscopy (AES, Ulvac-PHI 710). The photoluminescence (PL) spectrum was tested by Renishaw in-Via system using a 514 nm wavelength source.

As is known to all, MoS₂ is a widely used 2D semiconductor in various applications due to its simple preparation, suitable forbidden bandwidth, and stable material properties^[17]. In order to ensure meanwhile that the material has no defects, the stable electrical performance in the device, and suitable for laser energy absorption, we use mechanical exfoliation method to prepare few-layer (thickness of 7−8 nm) MoS₂. The SEM characterization of MoS₂ of different thicknesses under the action of the laser at the same power density is shown in Fig. S1. The device fabrication process is schematically shown in Fig. S2 and its optical pictures are shown in Fig. S3. The AFM characterization of the thickness of interlay MoS₂ is shown in Fig. S4. To show the laser modulation effect, one two-terminal device with a structure of Au/multilayer-MoS₂ (10 μm length, 7−8 nm thick)/Au was fabricated (Fig. 1(a)) and another the same structure device, in which half MoS₂ was doped by laser (Fig. 1 (b)). The AFM characterization of the material in laser action area is shown in Fig. S5. SEM and EDS line scan characterization of the material after laser action on half of the region are shown in Fig. S6. The TEM images before and after laser action are shown in Fig. S7. DC measurements are performed on devices without (pristine) and with the laser treatment, and the result is shown in Figs. 1(d) and 1(e). The device with pristine MoS₂ shows no storage window and presents an approximate ohmic contact, while the I−V curve of the laser-doped device shows stable memristor characteristics under DC voltage sweep. From the memristive curve (Fig. 1(e)), the set and reset voltage is around ±10 V, and the memristive window between the high resistance state (HRS) and the low resistance state (LRS) is 69.2 times. As shown in Fig. 1(c), the retention time of both HRS and LRS can reach up to 2 × 10⁴ s. The above results strongly support that laser doping can induce the memristive characteristics of the MoS₂ device from absence to presence.

To determine the origin of the memristive characteristics induced by laser doping, the MoS₂ semiconductor property is analyzed. It has been found that the MoS₂ device with half-modulated region by laser doping, MoS_2−xO_y is formed in the action region, thus may generate a junction at the interface with another-half pristine MoS₂^[16]. Since the material does not form conductive filaments at 0−3 V, we fit the experimental results for 0−3 V. The experimental data I−V curve shows high consistency with the I−V curve of a homojunction (Fig. 2(f)), which can be described by Eq. (1)^[18−20]:

1J=J0[exp(qVkT)−1],

where J and J₀ refer to current density and saturation current density, respectively, q denotes the electronic charge, k is the Boltzmann constant, T is the absolute temperature, and V is the applied voltage. This consistency with Eq. (1) indicates the formation of one homojunction at the interface between the modulated area and pristine area in the MoS₂ memristor. That is, the laser action possesses the ability to bring variations to pristine MoS₂.

In order to verify that the doping degree of MoS₂ can be adjusted by the laser energy, a more precise elemental analysis is performed with AES to quantitatively determine the regulation between doping level and laser energy. As illustrated in Fig. 2(a) and Table S1, the AES results indicate that the oxygen concentration in MoS₂ gradually increases with increasing power density for a constant pulse width at the non-destructive range (below 280 kW·mm⁻²). The memristive features induced under different power densities are tested and shown in Fig. 2(b). The device without laser action shows no memristive feature at all, and as the power density increases and the local doping concentration rises, the memristive properties of the device gradually become obvious and the memristive window becomes larger. This means laser-doping is a feasible and precise method for manipulating the properties of 2D material memristors.

Dynamic Monte Carlo is a simulation method that models the time evolution of complex systems by stochastically simulating the sequence of events and their timings based on transition probabilities or rate constants. To deepen our understanding of how laser energy influences the doping degree of MoS₂ and its resultant memristive behavior, we employed the dynamic Monte Carlo method to simulate the dynamic processes of set and reset in memristors subjected to varying laser power densities. This simulation approach is pivotal for modeling the stochastic nature of vacancy migration and conductive path formation, directly linking the microscopic behavior of the material under laser doping to its macroscopic electrical properties. The vacancy mobility is calculated by combining each Monte Carlo step with a time-dependent parameter, which is obtained from the probability of following the Boltzmann distribution. The probability of each Monte Carlo step occurring can be calculated from its activation energy E_a, the vibrational frequency of the electron v, and the temperature T, as shown in Eq. (2):

2P=ve−EakT.

The simulations were conducted under a range of controlled laser doping concentration with random position, reflecting the experimental conditions and ensuring the reliability of the insights gained regarding the memristive properties of the devices. With the bias applied to the system, the energy produced by the electric field even the activation energy, increasing the likelihood of the atom migration in the dynamic Monte Carlo simulation, which is considered as one iteration. For each iteration, the horizontal conductivity of the system is calculated and recorded and a threshold for LRS and HRS was set for the termination of the Monte Carlo process. As shown in Fig. 2(e), for a low doping concentration (low power density action), the conductive path presents a weaker tip discharge effect, forms a more dispersed hole path, and has a smaller memristive window, although they exhibit a certain memristive characteristic. This is consistent with the trend of the curves tested in our experiment. As shown in Figs. 2(d) and 2(f), abundant holes are introduced to the system when the doping concentration is higher, which will help to construct the conductive path. Under this circumstance, the device becomes stable and the memristive window becomes larger. In addition, simulations were carried out for devices with different doping regions and the results are shown in Fig. S8. The simulation results prove and support the mechanism of the device's conductive path.

According to the Monte Carlo simulation results, the laser induced memristive feature originates from the directional movement of oxygen vacancies, which is further proved through first-principles calculations using Atomistix ToolKit (ATK). The scan path of the Brillouin zone is shown in Fig. S9. An examination of diverse distributions of holes and oxygen atoms is conducted to scrutinize their impact on the material's energy band structure, offering additional insights into the laser modulation principle on MoS₂. The atomic structures and local density of states of undoped MoS₂ are shown in Figs. 3(a) and 3(e), respectively. The local density of states of intrinsic MoS₂ without doping is consistent with the energy band structure (shown in Fig. S10), featuring a band gap of approximately 1.14 eV and no barrier due to its symmetric structure (as shown in Fig. 3(i)). The atomic structures and local density of states of lightly doped oxygen and heavily doped oxygen are depicted in Figs. 3(b) and 3(f), and Figs. 3(c) and 3(g), respectively, with corresponding potential barrier schematics in Figs. 3(j) and 3(k). Laser-induced doping in the middle position introduces defect levels and impurity levels into the energy band, significantly reducing the bandgap on the right side to 0.32 eV (Fig. 3(f)), which leads to the formation of a barrier between the doped and undoped regions. The height of the barrier varies with the doping concentration. The local density of states reveals that under heavy doping, the MoS₂ on the right side changes from a semi-metallic state to a metallic state (Fig. 3(g)). When a voltage is applied to the oxygen-doped MoS₂ memristor, the height of the barrier gradually decreases due to the movement of oxygen atoms and vacancies under the electric field. This results in a gradual change in the resistance of the device, as shown in Figs. 3(d) and 3(h). When oxygen ions and vacancies reach equilibrium within the material, the entire material becomes metallic, and the memristor switches to a low-resistance state. In this case, although the channel is fully doped, a conductive path forms throughout the MoS₂ channel, and there is no barrier in the device (Fig. 3(l)). Only when a reverse voltage is applied to the device, the oxygen ions and holes will be driven back to the initial doping region, causing the conductive bridge to break again and produce a barrier. The elucidation of memristive behavior in laser-doped MoS₂ through first-principles calculations corroborates the induction effect of laser on memristive properties.

In order to verify the effectiveness and generality of laser doping in 2D materials, laser raster scanning with various powers and a fixed laser pulse width of 2000 ns was performed on MoS₂, HfS₂, and WS₂, respectively. As shown in Figs. 4(a)−4(c), the laser pulse power increases from 0 to 715 kW·mm⁻² with the step of 3 kW·mm⁻² (from left to right). It has been known that the PL spectrum peak height increases with the increase of defects and oxygen doping, and the peak position also shows a corresponding blue shift^[21], thus we chose PL to characterize the TMDs after the action of different power densities. As illustrated in Figs. 4(d)−4(f), the PL peak intensity increases with the increase of power density, while the peak position occurs a blue shift. With the increase of gray value, a strong MoS₂−O interaction is obtained by chemical adsorption. The partial S replaced by O can be described as MoS₂ + O₂ → MoS_2−xO_y. The main reasons of such huge PL enhancement include the following: (1) the oxygen chemical adsorption induced heavy p doping and the conversion from trion to exciton; (2) the suppression of nonradiative recombination of excitons at defect sites^[19]. This represents a gradual increase in the concentration of defects and oxygen doped in all three materials, showing a strong adaptability of the laser doping method. It should be noted that for MoS₂, the peak intensity starts a decrease when the power density exceeds 280 kW·mm⁻² (Fig. S11), corresponding PL peak shifts to 1.875 eV from 1.86 eV. This is probably due to too much power density causing MoS₂ to be destroyed. To confirm the speculation, the MoS₂ treated under 715 kW·mm⁻² laser (maximum power) and pristine MoS₂ were characterized by SEM and EDS for comparison. The SEM results show that cracking and thinning occurred after laser action (Fig. S12), and the EDS analyses indicate a significant reduction in both molybdenum and sulfur elements in the laser-activated region. These verify that excessive laser energy can cause damage to the 2D material and thus generate a negative effect for the doping. Therefore, only in a proper range of laser energy, the laser treatment can effectively dope the defects to TMDs and the doping degree can be regulated by controlling the laser energy. The above results prove that the located oxygen doping can be realized by laser action on other 2D materials, and that the oxygen vacancy-induced memristive effect is one of the recognized mechanisms of memristor, which has the same mechanism as MoS₂. Thus, we speculate that the laser action on other 2D materials will also result in the modulation of memristive effects similar to that of MoS₂, which offers a new opportunity for precisely adding vacancies into the TMDs to fulfill the preconditions in TMO (transition metal oxide) memristors, thus proposing a feasible road for building memristors^[22].

In summary, our study demonstrates the interaction between laser and mechanically exfoliated MoS₂, realizing precise and stable doping in the targeted regions. The memristive feature is from absence to presence in defect-free MoS₂ memristor after and before laser-modulation, and exhibits a switch ratio of 69.2 (approximately 100), and maintains stability for over 2 × 10⁴ s. By combining experimental results and dynamic Monte Carlo simulations, laser-doping-induced formation of conductive filaments through oxygen vacancy generation has been cleared and confirmed. The resistive switching depending on laser doping concentration provides a critical guideline for modulating and optimizing performance of 2D-material memristor. Furthermore, using the first-principles calculations, we explored the impact of defects and oxygen atom distribution on the memristor's band structure, clarifying the relationship between oxygen doping levels and electrical properties. In addition, we also investigated laser-modulating other 2D materials and verified that there exists in the same mechanism and versatility of the laser-modulation in 2D materials. The work unequivocally showed the effectiveness of laser-induced doping in modulating the memristive characteristics of 2D materials, offering groundbreaking concepts for optimizing and modulating such devices. This method allows for controlled tuning of memory characteristics in any desired region through laser energy modulation (adjustable via power density, pulse width, and scanning step size), showcasing a huge potential in various applications. Our research not only expands the understanding of laser-induced doping in 2D materials but also provides a universal and effective means for modulating memristive properties and other characteristics in 2D materials.

This work was supported by the National Natural Science Foundation of China (Nos. 51971070, 10974037, and 62205011), the National Key Research and Development Program of China (No. 2016YFA0200403), Eu-FP7 Project (No. 247644), CAS Strategy Pilot Program (No. XDA 09020300), Fundamental Research Funds for the Central Universities (No. buctrc202122), the Open Research Project of Zhejiang province Key Laboratory of Quantum Technology and Device (No. 20220401), and the Open Research Project of Special Display and Imaging Technology Innovation Center of Anhui Province (No. 2022AJ05001). The FEA software was supported by assistant professor Lirong Qian, School of Integrated Circuit Science and Engineering, Tianjin University of Technology. This work was funded by the Ph. D Foundation of Hebei University of Water Resources and Electric Engineering (No. SYBJ2202). Funded by Science and Technology Project of Hebei Education Department (No. BJK2022027).