Reversible Electrical Control of Interfacial Charge Flow across van der Waals Interfaces

Bond-free integration of two-dimensional (2D) materials yields van der Waals (vdW) heterostructures with exotic optical and electronic properties. Manipulating the splitting and recombination of photogenerated electron–hole pairs across the vdW interface is essential for optoelectronic applications. Previous studies have unveiled the critical role of defects in trapping photogenerated charge carriers to modulate the photoconductive gain for photodetection. However, the nature and role of defects in tuning interfacial charge carrier dynamics have remained elusive. Here, we investigate the nonequilibrium charge dynamics at the graphene–WS2 vdW interface under electrochemical gating by operando optical-pump terahertz-probe spectroscopy. We report full control over charge separation states and thus photogating field direction by electrically tuning the defect occupancy. Our results show that electron occupancy of the two in-gap states, presumably originating from sulfur vacancies, can account for the observed rich interfacial charge transfer dynamics and electrically tunable photogating fields, providing microscopic insights for optimizing optoelectronic devices.


II. Supplementary sections
Section S1 Estimation of initial Fermi energy and carrier density in graphene Section S2 Thermalized hot carrier distribution in graphene

(A) Fabrication of graphene-WS 2 van der Waals heterostructures
CVD-grown WS 2 monolayers supported by sapphire substrates were commercially available and purchased from SixCarbon Technology (Shenzhen). Afterwards, CVDgrown graphene was transferred onto the WS 2 monolayer according to the following procedure. First, cellulose acetate butyrate (CAB) was dissolved in ethyl acetate (30 mg/mL) and spin-coated on graphene supported by copper foil at 4000 rpm. After baked at 180 °C for 3 min, the copper foil was etched with 3 g/100 ml aqueous ammonium persulfate solution. Subsequently, the CAB-coated graphene was rinsed 5 times with Milli-Q water to remove etchant residues, and then transferred onto the WS 2 monolayer to form the graphene-WS 2 vdW heterostructure. After 2 days of natural drying, CAB was removed by soaking with acetone (12 h) and isopropanol (1 h). Ti/Au (5/50 nm) was deposited on the heterostructure through a shadow mask to form source, drain, and gate electrodes. LiClO 4 dissolved in polyethylene oxide was deposited on the heterostructure and used as a high-capacitance gate dielectric to perform electrochemical gating. The sample preparation process was performed in a dust-free environment to avoid potential contaminants.

(B) Operando optical-pump THz-probe spectroscopy
Operando optical-pump THz-probe (OPTP) spectroscopy was employed to monitor in situ the photoconductivity of the heterostructure under device operation. The OPTP spectroscopy was driven by a regenerative amplified and mode-locked Ti:sapphire system, which generated femtosecond laser pulses with a central energy of 1.55 eV, a pulse duration of ~50 fs, and a repeating frequency of 1 kHz. Optical excitation directly utilized the generated 1.55 eV laser pulses. Single-cycle THz pulses of ~1 ps duration were generated via optical rectification by pumping a (110) ZnTe crystal with 1.55 eV ultrafast laser pulses. The resulting THz pulses were collimated and focused onto the sample by a pair of off-axis parabolic mirrors. The transmitted THz pulses were then re-collimated and focused onto the second (110) ZnTe crystal to map out the time-varying electric field by free-space electro-optic sampling. The measurements were performed at room temperature under a dry N 2 atmosphere. The resistance of the graphene layer was monitored simultaneously by the four-point probe method during OPTP measurements.

Section S1 Estimation of initial Fermi energy and carrier density in graphene
We estimate in graphene from its G-band frequency (w G ), following equation is found to be ~0.15 eV with respect to the Dirac point. On this basis, we further calculate the carrier density ( ) in graphene, following equation (S2). 2 where is the reduced Planck constant and is the Fermi velocity. The calculated ℏ is ~1.4 × 10 12 cm −2 .

Section S2 Thermalized hot carrier distribution in graphene
We simulate the thermalized hot carrier distribution in graphene after photoexcitation by considering energy conservation and particle number conservation. 3 For energy conservation, the total energy of the graphene electronic system before photoexcitation contains the energies of electrons and holes, and can be 0 ( ) written as equation (S3).
where is the lattice temperature, is the energy, is the density of states ( ) (DOS) at a given energy , is the Fermi-Dirac distribution for electrons, and is the Fermi-Dirac distribution for holes. For simplicity, we assume is 298 K before photoexcitation, and approximate the chemical potential in graphene at room temperature as . After photoexcitation, the absorbed photon energy ( ) is converted into electronic heat, increasing the effective temperature ( ) ∆ of the electron bath in graphene. According to energy conservation, the total energy of the graphene electronic system after photoexcitation can be written as can be expressed as equation (S5).
where = 2.3% 4 is the optical absorption of graphene at the pump wavelength used (i.e., 800 nm), represents the energy of the incident laser pulse, and stands ℎ for the heat efficiency described in reference 5 and is assumed to be 70 % here, and is the chemical potential after photoexcitation.
For particle number conservation, the total carrier density (n) in graphene is a constant defined by the initial chemical potential regardless of photoexcitation, and can be written as equation (S6).
Based on energy conservation and particle number conservation, we can numerically calculate the changes in the effective temperature of the electron bath ( ) and chemical potential ( ) in graphene caused by an incident laser pulse → → with energy input , thereby obtaining the thermalized hot electron distribution and hot hole distribution after photoexcitation.

Section S3 Pure photo-thermionic emission (PTE) model
Based on early studies 6-8 , we set the band alignment of the graphene-WS 2 vdW heterostructure as follows: the conduction ( ) and valence ( ) bands of WS 2 are located at 0.9 eV above and 1.4 eV below the Dirac point, respectively. In the pure PTE model without considering any defect states, the conduction band of WS 2 can harvest thermalized hot electrons with energy higher than and the valence band of WS 2 can harvest thermalized hot holes with energy higher than . At given and , the net electron loss ( ) in graphene due to PTE can be obtained by calculating the ∆ difference between the number of thermalized hot electrons distributed above and the number of thermalized hot holes distributed below , following equation (S7).
Note that we use the majority conducting carrier density change to ∆ describe the charge carrier gain or loss in graphene, as its sign can be easily linked to the photoconductivity . We define in n-doped graphene and ∆ ∆ = ∆ ∆ in p-doped graphene, respectively. = -∆ = ∆ ℎ

Section S4 PTE model involving one defect state
In this section, we consider one in-gap defect state with either a fixed density or fixed energy, and discuss the PTE model based on the occupancy of the in-gap defect state. We define the energy and density of this defect state as and , respectively.
When is energetically lower than , this defect state is unoccupied and behaves as electron acceptor. In this case, can be calculated by equation (S8), and the ∆ defect-assisted contribution can be written as equation (S9).
When is energetically higher than , this defect state is occupied and acts as hole acceptor channel. In this case, can be calculated by equation (S10), and the ∆ defect-assisted contribution can be written as equation (S11).
Note that we set the upper bounds of and ∫ ( ) ( , , ) to be . Similar to Section S3, we define in ∫ n-doped graphene and in p-doped graphene, respectively.

Section S5 PTE model involving two defect states
In this section, we consider the presence of two in-gap defect states and discuss the PTE model according to the occupancy of the two in-gap defect states. Inspired by early studies 9 , we set the energetically higher defect state ( ) and the energetically lower In the p-doped heterostructure where is energetically lower than , these 2 two defect states are unoccupied and can be seen as electron acceptors. In this case, ∆ can be calculated by equation (S12), and the defect-assisted contribution ∆ _ can be written as equation (S13).
In the undoped heterostructure where is located between and , 1 2 1 remains unoccupied and acts as electron acceptor, whereas is electrically 2 passivated and serves as hole acceptor. In this case, can be calculated by equation ∆ (S14), and the defect-assisted contribution can be written as equation (S15).
In the n-doped heterostructure where is located above , both and are electrically passivated and serves as hole acceptors. In this case, can be ∆ calculated by equation (S16), and the defect-assisted contribution can be ∆ _ written as equation (S17).