Mid-infrared (MIR) photonic integration is desirable in the development of MIR spectroscopy and “lab-on-a-chip” sensing. The germanium-on-silicon (GOS) platform offers a promising solution for MIR photonic integration, extending the operational wavelength to a longer band by eliminating the light-absorbing buried oxide layer. However, MIR photodetectors on the GOS platform remain undeveloped due to the challenging heterogeneous integration of active materials on silicon and inadequate light absorption in the photodetection region. Here, we demonstrate a photo-thermoelectric graphene photodetector on the GOS platform, taking advantage of zero-bias operation and easy heterogeneous integration of graphene. By employing split-gate architecture and plasmonic enhancement to strengthen the light-graphene interaction, we achieve a responsivity of 1.97 V W−1 and noise equivalent power of 2.8 nW Hz−1/2 at the wavelength of 3.7 µm. This work enables waveguide-integrated MIR photodetection on the GOS platform for the first time, and it holds great potential for on-chip MIR sensing and imaging applications.

The mid-infrared wavelength band (2–20 µm) is of great significance in trace gas sensing, environmental monitoring, and medical diagnostics since it encompasses the absorption bands of greenhouse gases and the vibrational absorption peaks of biological and chemical molecules.1,2 Efforts have been made to develop MIR spectroscopy devices for chemical and biological sensing systems.3–5 It is remarkable that photonic integrated circuit (PIC) offers a practical and feasible way for creating compact and portable “lab-on-a-chip” integrated sensors,1,3 benefitting from inherent characteristics of miniaturization, light-weighting, and strong light–matter interaction.

However, the monolithic integration of sensing waveguides and photodetectors for MIR on-chip sensors still confronts challenges, limiting the signal-to-noise ratio (SNR) and sensitivity of the sensors. Specifically, integrating narrow bandgap materials like III–V and II–VI compounds with silicon for MIR photodetection encounters severe lattice mismatch.6–8 To overcome this obstacle, waveguide-integrated graphene photodetectors (GPDs) are favored by means of their broadband photoresponse, strong carrier interaction, and straightforward fabrication.9–11 Guo et al.12 proposed a hybrid plasmonic waveguide GPD operating at 2 µm wavelength with a responsivity of ∼70 mA W−1 at a bias voltage of −0.3 V. Nevertheless, the large dark current accompanied with a low SNR for biased graphene cannot be ignored. GPDs based on the photo-thermoelectric (PTE) effect can effectively restrain the dark currents and shot noise through zero-bias operation.13,14 When the graphene channel is optically illuminated, electron–hole pairs are excited and decay rapidly to form a Fermi–Dirac distribution of “hot” carriers. The hot electrons remain at a locally elevated temperature against the lattice temperature before reaching thermal equilibrium via phonon interaction. The temperature difference results in a directional thermal current that generates the photovoltage VPTE, known as the Seebeck effect. Therefore, the photo-thermoelectric response VPTE of graphene under light illumination can be directly read out without external bias. Taking the PTE effect into consideration, a zero-biased waveguide p–n homojunction GPD is reported more recently with a much lower noise.15 Moreover, the silicon-on-insulator (SOI) platform generally adopted for photonics integration is not suitable in the MIR region due to the considerable loss induced by the buried SiO2 layer beyond 3.5 µm. Recently, researchers overcome these challenges with a PTE based GPD on a scalable chalcogenide glass platform,16 exhibiting a responsivity of 1.5 V W−1 and a noise-equivalent power (NEP) of 1.1 nW Hz−1/2 at 5.2 µm wavelength. While the chalcogenide glass GPD architecture enables longer wavelength operation and good sensitivity at zero-bias, it comes at the cost of complex and complementary-metal-oxide-semiconductor (CMOS) incompatible fabricating processes.

In this paper, we propose and demonstrate a split-gate plasmonic enhanced GPD on the germanium-on-silicon (GOS) platform driven by the PTE effect. Thanks to the large refractive index of germanium and its strong confinement in a light field, the GOS platform allows waveguide integration in the absence of a buried oxide layer and, therefore, breaks the limitation of operating wavelength. By employing the split-gate architecture to electrostatically control the doping level of graphene, we can form the p–n homojunction where PTE takes effect. Furthermore, the split-gates on top of the optical waveguide induce a plasmonic effect for optical field enhancement, strengthening light-graphene interaction. A series of standard CMOS-compatible processes are adopted to fabricate the designed GPD, and the experimental characterizations show a responsivity of 1.97 V W−1 under zero bias at 3.7 µm, and the NEP is calculated to be 2.8 nW Hz−1/2. Our work features the first waveguide-integrated GPD on the GOS platform and the first PTE-based GPD at the 3.7 µm band of the MIR atmospheric window.

The sketch map of the proposed GPD is illustrated in Figs. 1(a)1(c). The GOS platform with a 1 µm thick germanium (Ge) layer is applied to construct the low-loss waveguide at 3.7 µm. We employ the GOS platform for the sake of CMOS-compatible processing and high-quality epitaxial growth of germanium on silicon. As shown in Fig. 1(b), split-gates consisting of a pair of metallic strips made from gold (Au) are connected to separate gate pads (Gate1 and Gate2). A silicon nitride layer, 8 nm thick, is placed beneath the split-gates and on top of the monolayer graphene to form a capacitor structure. This arrangement enables individual control of doping levels in the left and right parts of the graphene channel through distinct gate voltages. The graphene channel with a width of 8.5 µm and a length of 40 µm is patterned and contacted with source and drain electrodes. Another 8 nm-thick silicon nitride layer is sandwiched between the monolayer graphene and Ge waveguide, acting as the insulating layer, as depicted in Fig. 1(c). Subwavelength gratings (SWGs) are introduced on both sides of the waveguide to prop up the graphene channel, preventing potential tear and damage to graphene due to the suspended architecture. The SWGs are of 400 nm period and separated 200 nm away from waveguides to avoid influence on the light field. In order to monitor the optical power injected into the GPD, we introduce a 1 × 2 multi-mode interference (MMI) based power splitter with a coupling ratio of 1:1. Light is injected through a transverse magnetic (TM) type grating coupler and split by the MMI-coupler, with half of the optical power entering the GPD and the other half coupling out from the chip to monitor the coupling status and calculate the input optical power. The scanning electron microscopy (SEM) view of the fabricated GPD is shown in Fig. 1(d) and the inset.

FIG. 1.

Proposed MIR GPD with split-gate architecture. (a) Overall view of the GPD integrated on the GOS platform. (b) Detailed diagram of the graphene photodetection region. (c) Cross-section view of the graphene photodetection region. (d) Scanning electron microscopy images of the fabricated GPD; the inset shows a zoom-in of the split-gate region. (e) Simulated optical field distribution in the photodetection region; the white rectangle in the middle represents the germanium waveguide, and the horizontal dotted line above the waveguide represents the graphene.

FIG. 1.

Proposed MIR GPD with split-gate architecture. (a) Overall view of the GPD integrated on the GOS platform. (b) Detailed diagram of the graphene photodetection region. (c) Cross-section view of the graphene photodetection region. (d) Scanning electron microscopy images of the fabricated GPD; the inset shows a zoom-in of the split-gate region. (e) Simulated optical field distribution in the photodetection region; the white rectangle in the middle represents the germanium waveguide, and the horizontal dotted line above the waveguide represents the graphene.

Close modal

We perform the finite-different time-domain (FDTD) simulations to investigate the optical field characteristics in the photodetection region and the graphene absorption. Due to the large refractive index and strong light confinement of the Ge waveguide, the power of the leakage field in the upper cladding is quite low, posing challenges for favorable light-graphene interaction. To address this, we introduce a hybrid plasmonic waveguide aimed at boosting the light field energy in the upper cladding where graphene is situated. In addition, TM-mode device structures are designed instead of TE-mode to obtain stronger light field energy in the upper cladding. A pair of Au strips is fabricated on top of the 1.5 μm-wide waveguide to induce surface plasmon polaritons (SPPs), which confine the light beyond the optical diffraction limit and greatly strengthen the light-graphene interaction.17 The cross-section view of the simulated optical field distribution is plotted in Fig. 1(e). A significant improvement of the light field energy can be observed on the upper surface of the waveguide. The height and gap of the Au strips are optimized to obtain an enhanced light-graphene interaction together with a fabrication-friendly feature size. Simulation results indicate that the metal loss decreases and the graphene absorption ratio increases with the decrease of Au height. For the convenience and robustness of the fabrication process, the Au height is set to 10 nm. The Au strips are set to align with the waveguide edges, so that the gap determines the Au width. A small gap is conducive to achieving a stronger localized optical field but may lead to electrical breakdown when applying gate voltages, so we choose a 600 nm gap as a trade-off. The calculated graphene absorption coefficient and metal absorption coefficient, defined as the percentage of optical energy absorbed by graphene or metal per micrometer, are 0.14 dB μm−1 and 0.3 dB μm−1, respectively. This corresponds to a graphene absorption ratio of 32%. Thanks to the carefully designed metallic gate strips, the simulated graphene absorption coefficient of the hybrid plasmonic waveguide is over 10 times higher than that of an ordinary strip GOS waveguide (with simulated absorption of 0.011 dB μm−1), indicating a great enhancement of the light-graphene interaction.

Apart from inducing plasmonic enhancement, the Au strips also serve as the split-gates to apply gate voltages. We measure the resistance map of the graphene to take a close look at the influence of gate voltages on graphene doping level and conductivity. The resistances of graphene are recorded by a source meter (Keithley 2401) at a fixed source–drain bias of 10 mV as the separate gate voltages (VG1 and VG2) varied from −4 to 4 V. The results are shown in Fig. 2(a), and four quadrants (p–p, p–n, n–n, n–p) of different doping polarities are clearly identified. The crossing point of the resistance map is the charge neutrality point (CNP, also referred to as the Dirac point), with a maximum graphene resistance of 2953 Ω and VCNP ∼ 2 V. It is worth noting that the graphene resistance is asymmetric about the diagonal line of resistance map when the two gate voltages take the same value. This mainly arises from some asymmetry and misalignment of graphene and split-gates introduced by the fabrication error. The diagonal slice (dashed line) in the resistance map indicates the transfer characteristics of the GPD with VG1 = VG2, from which the graphene parameters can be fitted and extracted, as shown in Fig. 2(b). The extracted minimum conductivity σmin and the carrier mobility μ are 1.4 mS and 985 cm2 V−1 s−1, respectively (see Sec. IV). Based on the extracted graphene electrical parameters, the PTE effect modeling is carried out as follows:15,18 first, the PTE effect induced photovoltage can be expressed as
(1)
where x is the position along the graphene channel from drain to source and Tex is the lateral gradient of the average electronic temperature. The Seebeck coefficient Sx is calculated utilizing the following equation:
(2)
where e represents the elementary charge, kB stands for the Boltzmann constant, μc is the chemical potential of graphene, and σ(x) denotes the distribution of graphene electrical conductivity. The graphene electrical conductivity σ(x) can be written as the function of chemical potential μc that is related to the gate voltage VG (see more details in Sec. IV). Therefore, the dependence of chemical potential and Seebeck coefficient on gate voltage is obtained, and the simulated results are shown in Fig. 3(a).
FIG. 2.

Characterization and analysis of the graphene electrical properties. (a) Measured resistance map of the graphene channel as a function of the two gate voltages (VG1 and VG2). (b) Fitting results for graphene electrical parameter extraction; the measurement data are obtained from the dashed line in the resistance map.

FIG. 2.

Characterization and analysis of the graphene electrical properties. (a) Measured resistance map of the graphene channel as a function of the two gate voltages (VG1 and VG2). (b) Fitting results for graphene electrical parameter extraction; the measurement data are obtained from the dashed line in the resistance map.

Close modal
FIG. 3.

Modeling and calculating results of the PTE effect. (a) The dependence of chemical potential and Seebeck coefficient on gate voltage. (b) The lateral electronic temperature distribution calculated from the heat diffusion equation. (c) Simulated VPTE map of the GPD.

FIG. 3.

Modeling and calculating results of the PTE effect. (a) The dependence of chemical potential and Seebeck coefficient on gate voltage. (b) The lateral electronic temperature distribution calculated from the heat diffusion equation. (c) Simulated VPTE map of the GPD.

Close modal
Second, the electronic temperature Tex is solved using the heat equation
(3)
where κ represents the electronic thermal conductivity and Lc is the cooling length. The absorbed power density Px is obtained from the optical field distribution and the graphene absorption coefficient mentioned earlier. Figure 3(b) presents the lateral distribution of Te in the graphene channel with an input optical power of 1 mW. A significant increase in electron temperature can be observed at the position of Au strips on account of the optical field enhancement. Finally, the photovoltage VPTE is calculated utilizing Eq. (1). Figure 3(c) shows the simulation results of the VPTE map under different gate voltages. A six-fold pattern indicates the typical PTE-dominated photoresponse, suggesting lager photovoltages in the bipolar doped regions (n–p and p–n) where the graphene p–n homojunction is formed.19 Under the circumstances, both the electronic temperature gradient and Seebeck coefficients for the two gated regions of graphene channel are contrary, leading to an enlarged integral of product in Eq. (1). A maximum responsivity of 3.2 V W−1 is obtained. The simulation helps to further understand the intrinsic mechanism of PTE-dominated photodetectors and analyze the experimental results below.

The proposed GPD is fabricated on a commercial GOS wafer with a 1 μm-thick Ge waveguide layer and a 500 μm-thick silicon substrate. The passive devices, including grating couplers, waveguides, power splitters, and SWGs, are constructed using electron beam lithography (EBL) followed by inductively coupled plasma (ICP) etching. After that, the 8 nm thick silicon nitride insulating layer is deposited by plasma-enhanced chemical vapor deposition (PECVD). Source and drain electrodes are grown through e-beam evaporation (EBE) and the liftoff process, with a metal composition of 10/90 nm-thick Ni/Au. Afterward, a CVD-grown monolayer graphene is wet-transferred onto the chip and patterned by ultraviolet (UV) lithography and reactive ion etching (RIE). Another silicon nitride layer is deposited as the dielectric layer and gate electrodes are grown on it. Finally, the Au strips are lithographed by EBL and grown by EBE.

We characterize the photovoltage response of the fabricated GPD using a lock-in amplifier (STANFORD SR830) to read out the photoelectronic signals. The experimental setup is shown in Fig. 4. Light at 3.7 µm is emitted from a quantum cascade laser (QCL) and then collimated into a chalcogenide MIR fiber (IRF-S-7) by a reflective collimator. After coupling into the chip through the grating coupler, it goes through the optical power splitter and injects into the GPD, with a tested power splitting loss of −3.4 dB. As mentioned earlier, we use a power meter at the end of the output fiber to monitor the coupling status during the measurements. A chopper is placed at the output end of the QCL to modulate the light at a frequency of 0.2 kHz, with a clock signal being sent into the lock-in amplifier for reference. Gate voltages are applied by a binary-channel source meter (Keysight B2902A), and the photovoltage is amplified by a low-noise preamplifier (STANFORD SR560) before being received by the lock-in amplifier.

FIG. 4.

Experimental setup for photovoltage response measurement.

FIG. 4.

Experimental setup for photovoltage response measurement.

Close modal

The GPD is measured under zero bias, and the recorded open circuit voltage map (VPTE) is presented in Fig. 5(a) under an input optical power of 10.5 µW (with deduction of insertion losses from the grating coupler and power splitter). Along the dashed lines in the photovoltage map, the sign of VPTE changes twice during a single gate voltage sweep while the other is fixed, confirming the working mechanism of the PTE effect, as shown in Fig. 5(b). Changes of the sign arise from the non-monotonic relationship between gate voltage and Seebeck coefficient, aligning with the simulations presented in Fig. 3(a). The maximum photovoltage response occurs in the second and fourth quadrants, with the doping states to be p–n or n–p, which is in good agreement with the theoretical results. A maximum photovoltage of −20.7 µV is achieved when VG1 = 2.2 V and VG2 = −2.6 V, as indicated by the star symbol in the VPTE map. The calculated maximum responsivity is 1.97 V W−1. The difference between the simulated responsivity and the measured one mainly comes from the uneven distribution of chemical potential and Seebeck coefficient of the graphene sheet. In simulation, we assume that the chemical potential and Seebeck coefficient of graphene change linearly. However, the uneven doping level of the graphene sheet induced by impurities during the fabrication process and the wrinkles and unevenness on the graphene surface can cause nonlinear and abrupt changes of the chemical potential and Seebeck coefficient, degrading the GPD responsivity. Therefore, the performance of the device can be further improved by optimizing the fabrication process with a higher quality graphene sheet and cleaner transfer and patterning procedures. Wavelength-dependent responsivity is also explored, and the results are depicted in Fig. 5(c). Similar responsivities around 1.9 V W−1 are observed across different wavelengths, showing a broadband photovoltage response in the 3.61–3.7 µm MIR wavelength range. Limited by the output power of the QCL source and loss of the optical link (fibers and grating couplers), the power dependence of responsivity is investigated with input power below 10.5 µW, and the GPD shows a linear photoresponse in this region, as shown in Fig. 5(d).

FIG. 5.

Measured photovoltage performance of the proposed GPD. (a) Measured VPTE map under different gate voltages; the star symbol represents the maximum photovoltage response. (b) Curves of the photovoltage when a single gate voltage varies along the dotted line in the VPTE map. (c) Measured responsivity under different wavelengths varying from 3.61 to 3.7 µm. (d) Measured photovoltage as a function of the input optical power.

FIG. 5.

Measured photovoltage performance of the proposed GPD. (a) Measured VPTE map under different gate voltages; the star symbol represents the maximum photovoltage response. (b) Curves of the photovoltage when a single gate voltage varies along the dotted line in the VPTE map. (c) Measured responsivity under different wavelengths varying from 3.61 to 3.7 µm. (d) Measured photovoltage as a function of the input optical power.

Close modal
As depicted in Eq. (1), the PTE response arises from the different Seebeck coefficient distribution in the graphene channel and the photo-induced gradient of electronic temperature. Therefore, there are two main methods to enlarge the PTE photovoltage. One is to maximize the Seebeck coefficient by improving the carrier mobility μ and decreasing the minimum conductivity σmin, which calls for a clean and smooth graphene channel with fewer defects and higher quality. The other is to maximize the lateral electronic temperature gradient Tex by introducing a tightly confined light field to achieve a highly localized temperature rise. For instance, silicon slot ridge waveguides,18 ring resonators,14 and plasmonic slot waveguides19 have been proposed to confine the light field and strengthen the light-graphene interaction in the previously reported works. Here, we use the Au strips to induce SPP enhancement of the light field, and an effective improvement in temperature gradient can be observed in Fig. 3(b). We analyzed the NEP to study the noise characteristics and evaluate the sensitivity of the proposed GPD. The bias-free feature of the PTE-based GPD evades shot noise caused by dark current. Therefore, the thermal noise is the major contribution to NEP,15,
(4)
where vt represents the thermal noise voltage, R is the responsivity, and Rg is the graphene resistance. According to the resistance map and photoresponse, the NEP for our GPD is calculated to be 2.8–3.5 nW Hz−1/2 in the bipolar doped region. By reducing the graphene resistance, for example, using mechanically exfoliated graphene and optimizing the contact resistance, the NEP can be further improved. Limited by the experimental facilities, the frequency response of our GPD is not characterized. However, the literature suggests that high-speed frequency response for PTE-based GPD is attainable due to the ultra-fast hot carrier dynamics in graphene,19–21 indicating the potential of our GPD for high-speed operation. In general, for a PTE-based GPD, the response speed is related to both the electrical circuit’s resistance–capacitance (RC) constant and the photoresponse time dominated by the electron–phonon cooling time of hot electrons in graphene. To estimate the response speed of our device, the RC-limited 3-dB bandwidth is discussed first. An equivalent electrical circuit model of the proposed GPD is established [Fig. 6(a)].12 Then, we use a vector network analyzer (VNA, Anritsu MS4647B) to measure the reflection coefficient S11 of the device, from which the RC parameters of the equivalent circuit can be fitted and extracted, as shown in Fig. 6(b). After that, the S21 response based on the circuit's RC parameters is calculated and plotted as the inset of Fig. 6(b). The RC-limited bandwidth is estimated to be 143 GHz. On the other hand, we take the value of electron–phonon cooling time (τ) to be 50 ps as reported in Ref. 16, and the frequency response dependence of (1+2πτf2)0.5 can be obtained.16 The product of the RC-limited frequency response and τ-limited frequency response is then calculated, from which the bandwidth of this device is estimated to be 3.2 GHz, as shown in the inset of Fig. 6(b).
FIG. 6.

Bandwidth analysis of the proposed GPD. (a) Equivalent circuit model. In this model, RL = 50 Ω is the load resistance. CGP + Cpad is the total capacitance of the graphene and pads. RGP represents the graphene channel resistance and the contact resistance. CSiN is the capacitance of the SiN layer, and Rcore is the resistance from Ge layer and substrate. (b) Measured and fitted results of reflection coefficient S11. The inset shows the RC-limited bandwidth curve calculated from the equivalent circuit model and the combined frequency response of τ and RC limited bandwidth.

FIG. 6.

Bandwidth analysis of the proposed GPD. (a) Equivalent circuit model. In this model, RL = 50 Ω is the load resistance. CGP + Cpad is the total capacitance of the graphene and pads. RGP represents the graphene channel resistance and the contact resistance. CSiN is the capacitance of the SiN layer, and Rcore is the resistance from Ge layer and substrate. (b) Measured and fitted results of reflection coefficient S11. The inset shows the RC-limited bandwidth curve calculated from the equivalent circuit model and the combined frequency response of τ and RC limited bandwidth.

Close modal

Table I compares our device with other reported MIR waveguide-integrated GPDs. Thanks to the elaborately designed architecture, our work features the first waveguide-integrated GPD on the GOS platform and the first PTE-based GPD operating at 3.7 µm band. By integrating our GPD with other devices on the GOS platform, such as sensing waveguides,22,23 (de)multiplexers,24 and modulators,25 one can achieve practical MIR spectroscopy PICs for toxic gas detection, biomedical sensing, and free-space communications in the future.

TABLE I.

Comparison of waveguide-integrated MIR GPDs.

ReferencePlatformWavelength (μm)MechanismZero-biasedResponsivityNEP (nW Hz−1/2)
12  SOI Bolometric No 70 mA W−1 0.062–0.073 
15  SOI PTE Yes 2.78 V W−1 1.37–2.02 
26  SOI 3.8 ⋯ No 2.2 mA W-1 ⋯ 
27  Silicon-on-sapphire 3.4 PTE Yes 0.21 A W−1 (simulation) 0.001 (simulation) 
16  Chalcogenide glass 5.2 PTE Yes 1.5 V W−1 1.1 
This work GOS 3.7 PTE Yes 1.97 V W−1 2.8 
ReferencePlatformWavelength (μm)MechanismZero-biasedResponsivityNEP (nW Hz−1/2)
12  SOI Bolometric No 70 mA W−1 0.062–0.073 
15  SOI PTE Yes 2.78 V W−1 1.37–2.02 
26  SOI 3.8 ⋯ No 2.2 mA W-1 ⋯ 
27  Silicon-on-sapphire 3.4 PTE Yes 0.21 A W−1 (simulation) 0.001 (simulation) 
16  Chalcogenide glass 5.2 PTE Yes 1.5 V W−1 1.1 
This work GOS 3.7 PTE Yes 1.97 V W−1 2.8 

In conclusion, we propose and demonstrate waveguide-integrated GPD based on the GOS platform. Utilizing Au strips as plasmonic waveguides and split-gates to generate a graphene p–n homojunction, our GPD achieves an effective photovoltage response through the PTE effect. The proposed GPD exhibits a bias-free operating mode and a broadband photoresponse spanning from 3.61 to 3.7 µm, with a responsivity of 1.97 V W−1 and a NEP of 2.8–3.5 nW Hz−1/2. The COMS-compatible fabrication process and the CVD-grown graphene also enable the large-scale and scalable on-chip integration of graphene-based photodetectors and systems. This work addresses the gap in MIR photodetectors on the GOS platform and paves the way for sensing and spectroscopy applications of MIR PICs.

The graphene electrical parameters (σmin and μ) are extracted by fitting the resistance dependence on the gate voltage using the equations below:
(5)
(6)
where R0 includes the contact resistance and the resistance of the ungated graphene channel, L and W represent the length and width of the graphene channel (8.5 and 40 µm for our device, respectively). CG is the capacitance of the silicon nitride dielectric layer in the form of CG = ɛ0ɛSiN/dSiN. Therefore, the graphene electrical parameters can be fitted and extracted from the measured resistance, as depicted in Fig. 2(b).
The chemical potential μc of the graphene channel is controlled by the gate voltages through the modulation of charge-density n, which is described as follows:
(7)
where represents the reduced Planck constant and vF is the Fermi velocity (∼106 m s−1 in graphene). On the other hand, the conductivity σ as a function of μc is given by
(8)

Substituting Eqs. (7) and (8) into Eq. (2), one can establish the relationship between the Seebeck coefficient and gate voltages.

This work was supported by the National Key Research and Development Program of China (Grant No. 2022YFA1404001), the National Natural Science Foundation of China (Grant Nos. 61922034 and 62135004), the Key Research and Development Program of Hubei Province (Grant No. 2021BAA005), and the Innovation Project of Optics Valley Laboratory (Grant No. OVL2021BG005). The authors acknowledge the ShanghaiTech University Quantum Device Lab (SQDL) for technical support.

The authors have no conflicts to disclose.

H.C. and C.Y. contributed equally to this work.

Hongjun Cai: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Changming Yang: Data curation (equal); Formal analysis (lead); Investigation (equal). Yuheng Liu: Investigation (equal); Methodology (equal). Xinliang Zhang: Project administration (equal); Resources (equal); Supervision (equal). Yi Zou: Methodology (equal); Resources (equal); Software (equal). Yu Yu: Funding acquisition (equal); Investigation (equal); Methodology (equal); Supervision (equal); Writing – review & editing (equal).

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

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