Miniaturized spectrometer with tunable van der Waals junction

Abstract

According to an example aspect of the invention, a spectrometer is provided. Comprising a molybdenum disulfide layer and a tungsten diselenide layer between which a Van der Waals heterojunction is formed, a hexagonal boron nitride layer facing a portion of the molybdenum disulfide layer and the tungsten diselenide layer, a second hexagonal boron nitride layer covering the molybdenum disulfide layer and the tungsten diselenide layer, a single-layer graphene film facing the hexagonal boron nitride layer, and a third hexagonal boron nitride layer covering the single-layer graphene film. And a tunable gate-source voltage source is provided for electrically connecting the single-layer graphene film and the molybdenum disulfide layer.

Description

Technical Field

[0001] The present disclosure relates to the field of spectroscopy. Background of the Invention

[0003] Miniaturized computational spectrometers are essential for on-chip and implantable applications, using a combination of the device spectral response and a reconstruction algorithm to obtain the incident spectrum. High-sensitivity spectral measurements using only a single detector are key to future advances to significantly reduce the footprint of such spectrometers while allowing spectral resolution approaching that of benchtop systems. Summary of the invention

[0004] According to some aspects, the subject matter of the independent claims is provided. Some embodiments are defined in the dependent claims.

[0005] According to a first aspect of the present disclosure, a spectrometer is provided, comprising a molybdenum disulfide layer and a tungsten diselenide layer forming a van der Waals heterojunction therebetween, a hexagonal boron nitride layer facing a portion of the molybdenum disulfide layer and the tungsten diselenide layer, a second hexagonal boron nitride layer covering the molybdenum disulfide layer and the tungsten diselenide layer, a single-layer graphene film facing the hexagonal boron nitride layer, and an electrical connection connecting the single-layer graphene film and the molybdenum disulfide layer, wherein the electrical connection is provided with a tunable gate-source voltage source. BRIEF DESCRIPTION OF THE DRAWINGS

[0006] Figure 1 : Concept of ultra-miniaturized spectrometer with single vdW junction. A, Typical gate-tunable band arrangement at the vdW junction interface (top) and its obvious gate-tunable spectral response matrix (bottom). E C (E V ) indicates the conduction (valence) band edge. B, Schematic diagram of various application examples using our single-junction spectrometer: a wavelength meter that distinguishes the peak wavelength of monochromatic light (top), a spectrometer that resolves broadband spectra (middle), and a spectroscopic imager that analyzes the spectral information of an image (bottom).

[0007] Figure 2: Demonstration of a single-junction spectrometer. A, Schematic diagram of our MoS2 / WSe2 heterojunction spectrometer (left) and its optical images on h-BN and graphene layers before (middle) and after (right) deposition of electrodes and stacking of the top h-BN passivation layer. For better visualization, the top h-BN layer is not shown in the upper panels. B and C, Transfer curves of the MoS2 and WSe2 channels and their heterojunctions with graphene gates without (B) and with (C) illumination of different wavelengths at a fixed power of ∼20 μW. D, Color contour plot of the spectral response matrix. E and F, Quasi-monochromatic (E, bandwidth: ∼10 nm) and two different broadband (F) spectra reconstructed with our spectrometer (solid lines) and measured with a commercial spectrometer (dashed lines). G, Peak signal-to-noise ratio between the reconstructed and reference spectra as a function of the learning step size.

[0008] Figure 3 : High-performance wavelength resolution and spectral resolution. A, Color contour plot of a high-density spectral response matrix with a learning step size of ∼0.1 nm. B, Monochromatic (bandwidth: ∼2 nm) spectra reconstructed with our spectrometer (solid line) and measured with a commercial spectrometer (dashed line). C, Peak wavelength of the reconstructed and measured spectra as a function of the input wavelength. D, Peak wavelength difference between the reconstructed and reference spectra (upper panel), and the wavelength resolution of our single-junction spectrometer (lower panel). E, Composite spectrum of the reconstructed (solid line) and measured (dashed line). F, Future prospects of our single-junction spectrometer aiming to achieve ultra-high resolution.

[0009] Figure 4 : Proof-of-concept demonstration of spectral imaging. A, Spectral imaging configuration using our single-junction spectrometer with spatial scanning method. A broadband light source filtered with a color image is incident on our spectrometer for spectral imaging. B, Spectral imaging with different V GS Photocurrent mapping data scanned down. C, Spectral images reconstructed at different wavelengths, covering the visible range to the near-infrared range. Higher intensity at each wavelength indicates more broadband light is transmitted through the color image. The pixel intensities in B and C are normalized by each maximum intensity.

[0010] Figure 5 : Spectrometer miniaturization. Historical perspective on major miniaturization strategies (1-11, 39-41). (Left) Typical conventional spectrometers, including bulky dispersive optics and arrays of thousands of detectors (1, 2). (Middle) State-of-the-art spectrometers with minimized optics or reduced detectors (3-8, 39-41). (Right) Miniaturized single-detector spectrometers using tunable spectral detectors (9-11). In this work, we exploit single vdW junctions for interlayer transport-mediated spectral response engineering.

[0011] Figure 6 : Summarized workflow diagram. A, Simplified version. B, Detailed version. As shown in the figure, a computational method is required to reconstruct the unknown spectrum by solving a constrained least squares solution using an adaptive Tikhonov regularization (1, 8). Based on the spectral response matrix encoded during the learning process and an advanced reconstruction algorithm, the incident light with unknown spectral information measured during the test process can be computationally obtained from the photocurrent data measured by our single vdW junction spectrometer.

[0012] Figure 7 : Optical and structural properties of single junction spectrometers. The h-BN / MoS2 / WSe2 / h-BN / graphene heterostructure was characterized using an optical microscope, an atomic force microscope (AFM) using tapping mode, and a Raman spectroscopy device equipped with a 532nm continuous wave laser. Bright field (A) and dark field (B) optical microscopy images confirm the absence of scattered light near the heterojunction and single channels, indicating that the surface morphology is free of defects or wrinkles. The thickness of the top h-BN, MoS2, WSe2, and bottom h-BN sheets measured by AFM (C and D) are ~19, 28, 33, and 53nm, respectively. 1g 、E 1 2g , 2D and E 2g Peak reconstruction of Raman intensity mapping images of MoS2, WSe2, graphene, and h-BN sheets (E, F, G, and H). The corresponding Raman spectra are shown in I and J.

[0013] Figure 8 : Electrical characteristics of the spectrometer device. Gate-tunable output curves of a single MoS2 (A), WSe2 (B) channel and its heterojunction (C).

[0014] Fig. 9 : Rectification ratio and diode ideality factor. Rectification ratio of MoS2 / WSe2 heterojunction (top, ) and ideality factor (lower, ), where I DS，F and I DS，R They are drain-source voltage V DS =3 and -3V drain-source current I DS , q is the charge, and T is the absolute temperature. GS The rectifying behavior is determined by the competition between tunneling and recombination (22–28).

[0015] Fig.10 :Fowler-Nordheim plot analysis. a, b, at V DSFowler-Nordheim (FN) tunneling diagram of MoS2 / WSe2 heterojunction for V > 0 (A) and V < 0 (B) (50). The colored area indicates the V where FN tunneling occurs. DS Each figure shows that the transition point from direct tunneling to FN tunneling, the charge carrier transport mechanism, is gate-tunable.

[0016] Fig.11 : Bias-dependent band alignment and carrier transport mechanisms. Tunable MoS2 / WSe2 heterojunctions with inversion layers involving free-carrier tunneling and recombination (22–28).

[0017] Fig.12 : Power-dependent spectral response matrix. Under different powers and wavelengths of light, at V DS =3 V. Corresponding colored contour plots of the power-dependent gate-tunable spectral response of the MoS2 / WSe2 heterojunction. (A, E) 4 μW, (B, F) 20 μW, (C, G) 100 μW, and (D, H) 500 μW.

[0018] Fig.13 : Gate-tunable charge carrier transport mechanism under dark conditions or illumination. A, MoS2 / WSe2 heterojunction with graphene gate at V DS =3 V under dark conditions. For different charge carrier transport mechanisms (cases A, B and C), V GS The range is indicated by the red, green, and blue regions. B, C, and D, Gate-tunable charge carrier dynamics at the MoS2 / WSe2 heterointerface. (22–28) E, Color contour plot of the spectral response matrix, depending on V GS and incident light wavelength, with a fixed power of 20 μW. The boundaries of each case shown in A are marked by black dashed lines. F, G, and H, the gate can tune the dynamics of photoexcited charge carriers generated at the MoS2 / WSe2 heterointerface. (22–28) Case A (B and F): The gate is driven by a negative V GS The induced staggered band gap blocks electrons from MoS2 to the conduction band of WSe2 and holes from WSe2 to the valence band of MoS2. The dark current corresponds to the interlayer recombination of MoS2 electrons and WSe2 holes. The interlayer recombination is limited by the electron supply from MoS2. Thus, light absorbed by MoS2 causes photogenerated electrons in MoS2 to dominate the photoresponse. Case B (C and G): The dark current is mainly due to the interlayer recombination of MoS2 electrons and WSe2 holes. The interlayer recombination is limited by the hole supply from WSe2. Light absorbed by WSe2 causes photogenerated holes in WSe2, which dominate the photoresponse. Case C (D and H): Positive V GSThe energy of the WSe2 band edge is lowered, changing the staggered band gap. (27, 28) Due to the high density of states at the MoS2 Fermi level, the energy of the MoS2 band edge is significantly affected by the V GS Less sensitive. (61–63) The dark current is dominated by the flow of electrons from MoS2 to WSe2. The photocurrent is dominated by the tunneling of electrons excited from MoS2 to WSe2 and holes excited from WSe2 to MoS2. Thus, the photoresponse is sensitive to light absorption in both materials.

[0019] Fig.14 : Gate-tunable photovoltaic effect. Photovoltaic effect on MoS2 / WSe2 heterojunction. (22–28) In the dark or under illumination at wavelengths of ~550 and 750 nm, the photoluminescence intensity of the photons increases with the V GS Short-circuit current, zero voltage current, open circuit voltage, and zero current voltage were obtained. The photovoltaic effect confirmed the spectral detection performance with giant grating tunability. (37, 38)

[0020] Fig.15 : Optical switching characteristics. A and B, Photocurrent measured as a function of time for a MoS2 / WSe2 heterojunction with a silicon gate (A) or a graphene gate (B) under 532 nm laser irradiation switched on / off every ~5 seconds. The photocurrent of the silicon gate decreases over time, leading to errors, while the photocurrent measured using the graphene gate is almost constant and independent of time, ensuring stable and fast encoding of the spectral response matrix during the learning process.

[0021] Fig.16 :Wavelength-dependent photoresponse mechanism. A, MoS2 / WSe2 heterojunction at different V GS The obvious photoresponse at 750nm corresponds to the exciton absorption resonance of WSe2. The 750-nm feature appears at positive V when WSe2 is not doped with holes. GS When WSe2 is doped with holes, it disappears at negative V GS Two mechanisms may contribute to modulating this feature. First, it is known that in strongly doped semiconductors, the strength of the exciton oscillator is reduced due to screening by Pauli blocking and Coulomb interactions. (29, 64, 65) Second, negative V GS Change the band alignment of the staggered gap and block the photoexcited carriers from passing through the MoS2 / WSe2 interface. B, V GSThe band energy in WSe2 is strongly modulated, but the band energy in MoS2 is weakly modulated. There are two reasons for this asymmetry. First, MoS2 has a large doping impurity concentration due to its sulfur vacancies, (61–63) which brings the Fermi level close to the conduction band edge. On the other hand, due to the unpinned nature of the Fermi level of WSe2, (61–63) the Fermi level can be easily displaced to a neutral position inside its band gap, where exciton absorption increases. Second, MoS2 is stacked on top of WSe2, thus WSe2 shields the gate when it is strongly doped. The generation, separation, and extraction of photoexcited charge carriers depend on the incident photon energy and V GS In generating a value greater than E g,WSe2 and E g,MoS2 After photoexcitation of carriers by photon energies of (C and E), carrier extraction relies on the interplay of tunneling and recombination. For example, the photocurrent is dominated by interlayer recombination of photogenerated electrons (holes) from MoS2 (WSe2) in C. In contrast, the photocurrent is dominated by direct interlayer tunneling of photogenerated electrons (holes) from MoS2 (WSe2) in E. Due to the band gap difference, E g,WSe2 and E g,MoS2 The photon energy between them is absorbed only by WSe2 (D and F). Depending on the band alignment, direct tunneling of photogenerated holes from WSe2 to MoS2 affects the photocurrent.

[0022] Fig.17 : Compared with silicon gate, the gate using graphene gate can tune the photoresponse. MoS2 (A and D) and WSe2 (B and E) channels and their heterojunctions (C and F) with silicon gate (A, B and C) or graphene gate (D, E and F) at V DS =3 V in dark conditions and under 532 and 730 nm illumination at 20 μW. A schematic diagram of the device structure and electrical configuration is provided in each panel. The corresponding hysteresis window (G) and current (H) confirm the giant gate tunability of graphene gates (37, 38) compared to silicon gates (using small V GS achievable saturation current level) and a low hysteresis window (minimum error in the measured current for gate sweep).

[0023] Fig.18 : Optical setup for spectrometer measurements. Schematic diagram of the optical setup used to compare the reconstructed spectrum obtained using our single junction spectrometer and the reference spectrum measured using a commercial spectrometer. Note that the wavelength selector represents a single tool of a tunable wavelength filter, a grating monochromator, a color filter, or a coupled system thereof to generate a monochromatic or broadband light source used in our measurements.

[0024] Fig.19: Peak wavelength analysis of broadband spectra. The resolving power of our single junction spectrometer can resolve the peak wavelengths of two broadband spectra that are close to each other. Two peaks at ~683nm were successfully resolved in the green and blue spectra, and the interval between the two peaks was ~0.9nm.

[0025] Fig. 20 : Transmission through color filters. A, Optical setup for broadband light source and color filters. Broadband light filtered using color filters was incident on our setup, and the transmission spectrum was obtained using the reconstruction algorithm. B, Reconstructed spectrum of the transmitted light through the color filters.

[0026] Fig.21 : Comparison of different miniaturized spectrometers.

[0027] Fig. 22 An exemplary single junction spectrometer capable of supporting at least some embodiments of the present disclosure is shown. DETAILED DESCRIPTION

[0028] We report a high-performance computational spectrometer based on a single van der Waals junction with an electrically tunable transmission-mediated spectral response. We achieve high peak wavelength accuracy (~0.36 nm), high spectral resolution (~3 nm), wide operating bandwidth (~405 to 845 nm), and proof-of-concept spectral imaging. Our approach not only defines a new path toward ultraminiaturization, but also provides single-detector computational spectrometers with unprecedented performance in terms of accuracy, resolution, and operating bandwidth.

[0029] Spectrometers are essential for a variety of applications, including industrial inspection, chemical / biological characterization, and image sensing / analysis (1, 2). Their miniaturization with high spectral resolution and wide operating bandwidth is highly desirable to meet emerging and future requirements for portable and on-chip applications (1). However, conventional spectroscopy systems typically rely on bulky dispersive optical components (e.g., gratings) and detector or filter arrays, which impose severe limitations on ultra-miniaturization (2).

[0030] Therefore, the conventional spectrometer miniaturization method is through various schemes ( Figure 5) have replaced the functionality of these dispersive optical elements, including photonic crystals (3), metasurfaces (4), and compact interferometers (5). In the past decade, a profound technological leap has seen the advent of miniaturized computational spectrometers that fully exploit the power of mathematical algorithms for spectral reconstruction (1). Examples of this approach have well established the use of quantum dot filter arrays for charge-coupled device sensors (6), multiple nanowires with engineered band gaps (7), single nanowires with band gap grading (8), the Stark effect in black phosphorus (9), in situ perovskite modulation (10), and single superconducting nanowires with tunable quantum efficiency (11). However, the performance and usability of these computational spectrometers remain limited: spectral resolution and operating bandwidth are typically limited by the number of integrated detectors (6–8), band gap modulation limitations (9, 10), and cryogenic operation requirements (11).

[0031] Photodetection using two-dimensional (2D) layer materials has great advantages due to their strong light-matter interactions, atomically sharp interfaces, and electrically tunable photoresponses (12–14). However, insufficient band structure modulation makes it challenging to achieve high-resolution, broadband spectral sensing using single 2D materials. On the other hand, van der Waals (vdW) junctions based on 2D materials offer highly tunable functionalities beyond the constituent materials (15–17) and are able to overcome these limitations. In particular, we believe that wavelength-dependent photodetection of vdW junctions, which has recently been used for optoelectronic logic computing (18, 19) and color sensing (20, 21), may also be the key to high-resolution computational spectral sensing.

[0032] We establish this hypothesis by demonstrating a high-performance ultraminiaturized computational spectrometer that exploits a single vdW junction with electrically tunable spectral responsivity. Our device, whose footprint is determined by the junction size (~22 × 8 μm 2 ) definition, showing unprecedented performance of a single-detector computational spectrometer, capable of resolving peak monochromatic wavelengths with an accuracy of ∼0.36 nm, reconstructing broadband spectra with a resolution of ∼3 nm, and acquiring spectral images by scanning. Our single-junction spectrometer concept can be extended to other tunable junctions, achieving high spectral resolution and wide operating bandwidth with its ultra-compact size, representing the ultimate miniaturization strategy without sacrificing spectrometer performance.

[0033] The performance of computational spectrometers relies on the variability of their wavelength-dependent photoresponsivity (1, 6–11). Single-detector spectrometers reported so far are limited in their performance (9, 10) and availability (11) by limited band structure modulation and hence spectral response. In contrast, electrical tuning of the interfacial band alignment of vdW junctions ( Figure 1A, upper panel) enables controllable and unique interlayer transport (15-17). This allows for a tunable spectral response with high sensitivity and variability over a wide spectral range ( Figure 1 A, lower panel) (12-14). This shows that a single vdW junction spectrometer can achieve significantly higher performance than previously reported spectrometers (ST1 section and Fig.21 We demonstrate this by combining an electrically tunable single vdW junction with a computational reconstruction algorithm for various applications ( Figure 1 B). To realize our spectrometer concept experimentally, the following three steps are required ( Figure 6 ): measuring the gate-tunable spectral response with multiple known incident spectra (learning process); measuring the gate-tunable photocurrent of the unknown incident light to be analyzed (testing process); and calculating the spectral information of the unknown incident light based on the results obtained in the learning and testing processes by using a reconstruction algorithm (reconstruction process).

[0034] The distinct and variable photoresponse of the vdW junction tuned at different gate voltages and incident light wavelengths is extremely important for our spectrometer miniaturization concept (1). We chose the MoS2 / WSe2 heterojunction ( Figure 2 A) As an example, it has a distinct spectral response due to its gate-tunable photovoltaic effect from the visible to the near-infrared. (22–28) The MoS2 / WSe2 heterojunction is encapsulated by top and bottom h-BN layers for insulation and passivation, respectively (section MM1). The monolayer graphene film underneath the stack is used as a local gate electrode for efficient gate tuning. Each stack layer is characterized by Raman spectroscopy and atomic force microscopy ( Figure 7 ) to confirm the quality of the vdW heterostructure.

[0035] Transfer curves of MoS2 or WSe2 channels and their heterojunctions (drain-source current I DS and the gate-source voltage V GS的 function) is the drain-source voltage V under dark conditions DS =3V measured ( Figure 2 B). Due to the donor (acceptor) impurities in MoS2 (WSe2), the individual MoS2 and WSe2 channels exhibit n(p)-type characteristics. Therefore, a depletion region and a built-in electric field are expected at their vdW interfaces (22–28). The MoS2 / WSe2 heterojunction is characterized by a positive V applied to the WSe2 side. DS , corresponds to the forward bias of the diode. The sign of the transconductance changes, Occurs at V GS = ~ -5 V, matching the hole current from WSe2 and the electron current from MoS2. This "anti-bipolar" behavior and other transport properties ( Figure 8 , 9, 10, and 11) are typical MoS2 / WSe2 heterojunctions (22–28), providing clearly distinguishable V GS Dependency.

[0036] The transfer curves of MoS2 / WSe2 heterojunctions measured under multiple known incident lights with a bandwidth of ~10 nm indicate a strong wavelength dependence ( Figure 2 C) At different V GS and the photoresponsivity measured at the incident light wavelength, is used to encode the spectral response matrix, where the photocurrent is defined as I ph =I 光 -I 黑暗 , where I 光 and I 黑暗 Respectively, V DS = 3V with and without illumination I DS , and P is the incident light power ( Fig.12 Unlike individual materials, the gate-tunable spectral response with high sensitivity over a wide spectral range is due to the wavelength-dependent absorption of MoS2 and WSe2 (29) and the controllable charge carrier transport through the MoS2 / WSe2 interface (22–28). The spectral response matrix ( Figure 2 D) inherits the rich structure of the dynamics of photoexcited charge carriers generated across the tunable MoS2 / WSe2 heterojunction (22–29), demonstrating fast and robust spectroscopic probing with giant-gate tunability in our MoS2 / WSe2 heterojunctions ( Fig.13 , 14 , 15, 16 and 17).

[0037] In encoding the spectral response matrix used for the learning process ( Figure 2 D) After that, our single junction spectrometer is ready to follow the workflow diagram ( Figure 6 ) to measure the unknown incident light spectrum. Briefly, we measure the grating-tunable photocurrent for the unknown incident light and then use adaptive Tikhonov regularization to reconstruct the spectrum by minimizing the residual norm with the regularization factor and computing its constrained least squares solution (1, 8). Fig.18 Details of the optical setup and computational reconstruction are provided in sections MM3 and MM4.

[0038] The quasi-monochromatic and composite broadband spectra reconstructed with our single-junction spectrometer are in good agreement with reference spectra measured using a commercial spectrometer, demonstrating the feasibility of our single-junction spectrometer concept ( Figure 2, E, and F). Note that while the bandwidth of the demonstrated spectrometer is limited (from ∼405 to 845 nm) due to the wavelength of light available in our laboratory, the MoS2 / WSe2 heterojunction exhibits photoresponse from ∼400 to 2400 nm (25). In fact, vdW junctions are known to exhibit photodetection capabilities for incident light with wavelengths corresponding to approximately half (or even less) of the band gap of each material (15–17, 25). Therefore, in principle, our single-junction spectrometer is not limited by the material band gap and can provide a wider operating bandwidth than our demonstration. Our single-junction spectrometer uses interlayer transport-mediated photoresponse, which is fundamentally different from previously demonstrated spectrometer concepts such as band gap engineering and binning (7–10).

[0039] To assess the deviation between the reconstructed and reference spectra, the peak signal-to-noise ratio (PSNR) has been used to analyze the squared error (ST2 section). The maximum PSNR estimated by extrapolation is ∼35.7 and 33.6 dB for the quasi-monochromatic and composite broadband spectra, respectively ( Figure 2 G). A reasonable learning step size (i.e., the step size in wavelength used to encode the spectral response matrix) can be chosen based on the saturated PSNR. Therefore, a high-speed learning process (11) can be achieved with a large learning step size and slightly reduced accuracy.

[0040] In practical applications, wavelength resolution is an important measure of spectrometers (1, 2). To demonstrate the high spectral resolution capability of our single-junction ultra-miniaturized spectrometer, we constructed a high-density spectral response matrix using monochromatic light from ∼675 nm to 685 nm with an ultra-small learning step size of ∼0.1 nm for the learning process ( Figure 3 A). Our single-junction spectrometer is encoded by a high-density spectral response matrix that can resolve monochromatic light with high precision ( Figure 3 , B and C). The average peak wavelength difference (Δλ) between the reconstructed spectrum and the reference spectrum is ∼0.36±0.06 nm, with a minimum of ∼0.04 nm ( Figure 3 D). This corresponds to a learning step size of ~0.1 nm. Wavelength resolution for a given input wavelength (λ) It is ~3470±880.

[0041] In addition, we measured composite incident spectra to investigate the spectral resolution. Two peaks at ∼679 nm were successfully distinguished, separated by ∼3 nm ( Figure 3 E). Our spectrometers can also resolve broadband spectra and identify their peak wavelengths with high resolution (e.g. Fig.19 This indicates that our spectrometer has a spectral resolution comparable to or better than that of current state-of-the-art miniaturized spectrometers (1–11), which occupy an area of ​​​​~22 × 8 μm 2) is comparable to or smaller than most spectrometers. This is several orders of magnitude smaller than commercial miniaturized spectrometers (30) and recently demonstrated spectrometers with metasurfaces (4), quantum dots (6), or single-dot perovskites (10); for a detailed comparison, see Fig.21 We note that the demonstrated accuracy (~0.36 nm) and resolution (~3 nm) are limited by the smallest incident wavelength step available in our laboratory and can be further improved by minimizing the learning step size during the learning process. We propose that such a learning process is practical for applications, similar to the calibration process in conventional spectrometers.

[0042] Many strategies can be considered to improve the resolution, accuracy, and speed of our single-junction spectrometers (1). These strategies include: (A) increasing the dataset size to create a higher density spectral response matrix by minimizing the learning step size (7–11), (B) designing junctions with higher responses and larger wavelength or gate dependencies (15–17), and (C) optimizing the reconstruction algorithm (e.g., using more advanced regularization to suppress perturbations (1, 8) or using convolution processing to improve accuracy (20, 21)). Ideally, reducing the learning step size is a straightforward way to form a denser spectral response matrix for more accurate spectral reconstruction. However, there is a trade-off: differences in the signal measured in small learning steps, comparable to the measurement noise, can lead to errors during reconstruction.

[0043] The higher the photoresponsivity, the better it is for distinguishing different V GS The wavelength-dependent photoresponse at λ is given by the wavelength dependence of the photoresponse. More specifically, high gradients of the spectral response matrix components are required to produce high spectral resolution (1, 6–11). To illustrate the future development possibilities of single-junction spectrometers, we consider the change in the normalized photocurrent-to-dark current ratio (NPDR) per wavelength step for the two resolved peaks (section ST3). Figure 3 The extrapolated lines in F demonstrate the potential of our approach, with improved photoresponsivity and higher resolution than commercial miniaturized spectrometers (30). Based on the recently reported photoresponse of MoS2 / WSe2 heterojunctions (~0.1 to 1 A·W at 532 nm), the -1 ), highlighting the achievable resolution (25). Further improvements in resolution and bandwidth can be achieved by engineering the junction using different combinations of various 2D materials or integrating waveguides (15–17). Additional strategies for improving performance are provided in Section ST4. Our single-junction spectrometer has the potential for significant performance improvements and can be adapted to other tunable junction architectures as well as integrated with CMOS (complementary metal oxide semiconductor) compatible platforms.

[0044] Our single-junction spectrometer could benefit from recently developed large-scale 2D material synthesis to build arrays for future spectral imaging. Here, we demonstrate proof-of-concept spectral imaging of a color filter consisting of red, blue, and transparent regions using our spectrometer for spatial scanning ( Figure 4 A). At each mapping position, at different V GS The photocurrent data measured at different V GS A series of photocurrent mapping data scanned under Figure 4 B) and converts it into a series of spectral data reconstructed at different wavelengths ( Figure 4 C). The spectral image indicates that the red and blue filters absorb more incident broadband light from ~405 to 580 nm and from ~600 to 700 nm, respectively. As a result, the spectra of the red capital letter "A" (from ~450 to 700 nm) and the blue exclamation mark "!" (from ~405 to 845 nm) can be distinguished from the spectrum of the background. Note that the strong light signal of the exclamation mark "!" around 800 nm can be fully detected, highlighting the advantage of spectral imaging over traditional RGB color imaging ( Fig. 20 , using different color filters). In our demonstration, the image resolution was defined by the mapping step size. However, our concept has great potential for large-scale spectral imaging via future array devices, providing high spatial resolution with micrometer or nanometer-scale junctions.

[0045] We have demonstrated a high-performance ultra-miniaturized spectrometer using a single vdW junction. In our spectrometer concept, no photodetector arrays, filter arrays, or other bulky dispersive components are required to achieve high resolution, sub-nm accuracy, and wide operating bandwidth. The ultra-compact footprint of our single-junction spectrometer can provide scalability and is compatible with current photonic integrated circuits and CMOS-compatible processes for straightforward integration into modern smartphones, lab-on-a-chip systems, and other customized devices ranging from biological implants to drones and satellites.

[0046] MM1: Device fabrication and characterization.

[0047] Our single junction spectrometer was fabricated by assembling graphene, MoS2, WSe2, and h-BN sheet-by-sheet into a vdW heterostructure. Here, we employed a semidry transfer method using Kapton tape for graphene (31–33) and a dry release transfer method using polypropylene carbonate and polydimethylsiloxane films for MoS2, WSe2, and h-BN (34–36). Monolayer graphene grown from graphene by chemical vapor deposition was transferred onto a highly doped Si substrate with a 285 nm thick SiO2 layer pretreated by solvent cleaning. The graphene layers were patterned by electron beam lithography (EBL, Vistec EBPG 5000) and dry etched by reactive ion etching (RIE, Oxford Instruments PlasmaLab 80Plus) to define each sample electrically isolated from each other. MoS2, WSe2, and h-BN sheets were mechanically exfoliated from their bulk single crystals (2D semiconductors). h-BN sheets were deterministically placed on each graphene gate to control the fraction of covered and uncovered areas. WSe2 and MoS2 sheets were subsequently transferred onto the h-BN-covered graphene. All electrodes and pads were patterned with EBL and deposited by electron beam evaporation (MASAIM-9912), followed by a lift-off process. Note that Ti / Au (10 / 50 nm) and PD / Au (10 / 50 nm) electrodes are used to facilitate electron (hole) injection in MoS2 (WSe2) (22–28). As a passivation layer, additional h-BN sheets were transferred to encapsulate the MoS2 and WSe2 sheets to prevent the surface modification from being affected by the adhesion of gas or water molecules. After device fabrication, the h-BN / MoS2 / WSe2 / h-BN / graphene vdW heterostructures ( Figure 7 ).

[0048] MM2: Optical setup.

[0049] A spectrally filtered supercontinuum laser source (SuperK Extreme, NKT Photonics) was used to photoexcite the charge carriers in the heterostructure. The spectral bandwidth of this source was controlled by a tunable spectral filter (SuperK Varia, NKT Photonics) or a grating-based monochromator (Andor Shamrock 750, silver-coated grating, 600 lines / mm, 1200 nm blaze). Note that the tunable spectral filter allows control of the wavelength from ~10 nm ( Figure 2E) up to spectral bandwidths of ~100 nm, while grating-based monochromators allow spectral bandwidths of ~2 nm with peak wavelength steps of ~0.1 nm ( Figure 3 B). The spectrum was measured by a commercial spectrometer (OceanOptics, Flame VIS). A filtered laser source was used for reference. The laser beam was directed and fully focused onto the heterojunction of the single junction spectrometer using an objective (Mitutoyo, 50X Plan Apo NIR Infinity corrected, NA0.2) that allowed a spot size of 1 to 2 μm. A schematic diagram of the optical setup is shown in Figure 4 and Fig.18 shown.

[0050] MM3: Electrical and photoelectric measurements.

[0051] The fabricated device chips were wire bonded to a custom designed printed circuit board assembled to our optical setup. A self-built optical system allowed us to focus the laser beam at the desired location. All electrical and optoelectronic measurements were performed under ambient conditions in our self-built optical system in conjunction with two source meters (Keithley 2400 and 2401). The source, drain, and gate electrodes were connected to MoS2, WSe2, and graphene, respectively. The gate-source voltage V GS is applied between graphene (37, 38) and MoS2, and the drain-source voltage V DS applied between WSe2 and MoS2. In order to reduce the measurement noise according to the sweep direction, V GS Always sweep from 0 to 20 V (or 30 V) and -20 V (or -30 V), then sweep back to 0 V. All measurements were repeated more than three times to verify reproducibility.

[0052] MM4: Computational reconstruction.

[0053] Based on the spectral response matrix encoded with multiple known monochromatic lights during the learning process and the response data measured during the testing process, the reconstruction algorithm obtains the unknown spectrum of the incident light on our single vdW junction spectrometer (1, 6–11). During the reconstruction process, the measured response data correspond to the photocurrent data set by integrating the unknown spectral function and the spectral response matrix over the wavelength range. In order to extract the unknown spectrum, a set of wavelength-independent weight coefficients should be determined for the linear expansion of the spectrum using simple basis functions. The basis functions for the linear expansion of the spectrum are chosen as Gaussian functions. Note that the discretization of the integral formula combining the unknown spectral function, the response matrix and the photocurrent data allows the integral formula to be expressed in the form of a system of linear equations. In the given matrix form, the residual norm (squared error) must be minimized by solving a non-negative least squares problem. The direct minimization of the residual norm leads to instability of the solution due to high-frequency noise signals. To address this problem, Tikhonov regularization is used in our code to stabilize the minimization procedure. In this method, an auxiliary term defined by a regularization factor (damping coefficient) is added to the residual norm. This regularization factor should be chosen appropriately to satisfy the robustness condition and reflect the signal noise level. The optimal value of the regularization factor is found using a generalized cross-validation adaptive method. The vector of coefficients that provides the global minimum of the modified residual norm enables the reconstruction of unknown spectra by replacing them in the initial expansion of the basis functions. All spectra reconstructed with our spectrometer and measured with commercial spectrometers are normalized with the maximum intensity. Figure 6 More details are provided in .

[0054] ST1: Spectrometer Miniaturization Strategy

[0055] Most conventional spectrometers rely on arrays of dispersive components and detectors or filters (3–5, 39–41). Some dispersive components can be stacked vertically, but detectors or filters cannot (1, 2). Therefore, for ultimate spectrometer miniaturization, the array structure must be minimized, and it is best to implement the spectrometer with a single detector.

[0056] Tunable wavelength-dependent photoresponse is the most important key parameter for the performance of miniaturized computational spectrometers (1, 6–11). However, in the case of approaches relying on material bandgaps, their spectral resolution and bandwidth are usually limited by the number of integrated detectors (6–8) or the bandgap modulation limit (9, 10). For example, spectrometers using multiple nanowires (7) or single nanowires with graded bandgaps (8) require photodetector arrays for their demonstrated resolution. Each nanowire channel with a different bandgap represents a single detector with a different filter, which requires detector arrays and limits further reduction of the footprint. On the other hand, the single-detector spectrometers reported so far (9–11) are limited in their performance (~90 nm resolution) (9) and availability (11) due to insufficient spectral response tunability.

[0057] In contrast, vdW junctions exhibit tunable spectral responses with high sensitivity over a wide spectral range due to controllable and unique interlayer transport. vdW junctions can also be stacked vertically with different bandgaps to minimize the footprint of the spectrometer. Fig.21 (3-11, 39-41) have shown that our single vdW junction spectrometer can achieve higher performance than other computational spectrometers under ambient conditions (6-11).

[0058] ST2: Peak signal-to-noise ratio

[0059] The peak signal-to-noise ratio (PSNR) is used to evaluate the reconstruction of the single-junction spectrometer (S 重建 ) and measured with a commercial spectrometer (S 参考 ) spectra. All reconstructions (S 重建 ) and reference (S 参考 ) The spectra are first normalized by the maximum intensity. PSNR is defined by the mean square error (MSE) as expressed in the following equation, where MAX is the maximum possible value of the spectrum (11).

[0060]

[0061] The spectral or peak wavelength accuracy of the reconstructed spectrum is highly dependent on the number of sampled elements encoded in the spectral response matrix. We introduce a learning step defined by the wavelength step size used during the learning process (11). We set the wavelength learning step size to ∼25 nm to reconstruct Figure 2 , E and F spectra. By increasing the wavelength step size, the increased learning step size means fewer wavelength sampling elements ( Figure 2 G). For quasi-monochromatic and composite broadband spectra, Figure 2The maximum PSNRs of the extrapolated estimates in G are ~35.7 and 33.6 dB, respectively. In our case, our spectral response matrix is ​​constructed with monochromatic light during the learning process. Therefore, more accurate reconstruction can be easily achieved for quasi-monochromatic spectra with larger learning steps than for composite broadband spectra.

[0062] ST3: Future prospects of single vdW junction spectrometers

[0063] Our single vdW junction spectrometer achieves single-detector spectroscopy measurements by engineering the spectral response via electrical tuning. This dispersion-free, filter-free, and detector array-free computational spectrometer concept provides the ultimate miniaturization strategy. Unlike commonly used computational spectrometers that rely on detector arrays (6-8), the resolution and accuracy of single-detector spectrometers (9-11) are highly dependent on the performance of the detector. Note that encoding the spectral response matrix of a single junction spectrometer can be a process similar to calibrating the grating angle in a conventional commercial spectrometer by measuring spectra with known incident wavelengths. In general, a high-performance spectrometer should display spectra with high resolution and high accuracy. For computational spectrometers, high photosensitivity can lead to high performance, but this is not always the case because the photosensitivity is normalized in the reconstruction algorithm. Therefore, at different V GS The variability of its photoresponsivity with respect to wavelength and incident light is an important factor. In this sense, our single vdW junction spectrometer can offer the ultimate in miniaturization with unprecedented performance. Here, we use our single junction spectrometer concept to estimate the spectral resolution as a function of the variation of the average normalized photocurrent-dark current ratio (NPDR) per wavelength spacing of the two resolved peaks, which can be obtained from the spectral response matrix. Extrapolation lines are used to predict the future development of ultra-high resolution single vdW junction spectrometers ( Figure 3 F)(15–17, 22–28, 42–45). Based on anticipated developments, the single-junction spectrometer concept could be used to pursue ultra-high resolutions that outperform commercial high-resolution spectrometers.

[0064] ST4: Performance Improvement Strategy

[0065] In general, the rational design of vdW junction interfaces pursuing other unique bandgap contrasts or arrangements can further enhance the resolution and broaden the bandwidth (15–17). Advanced programming schemes can also be employed in the reconstruction algorithms to improve the performance of the spectrometer.

[0066] Detailed strategies to improve the performance of the single-junction spectrometer concept are as follows: increasing the diversity of wavelength-dependent photoresponses by (A) tunable interlayer transport across other vdW junction interfaces (15–17, 42–45); (B) tunable internal photoemission via highly modulated Schottky barriers (46–49); (C) hybrid / switchable / negative photoresponses (50–52); (D) vertical vdW heterostructure stacking or superlattices (53–55); (E) large-area array integration (56–59), or by upscaling reconstruction algorithms, (F) convolutional processes or other deep learning algorithms (20, 21, 60); and (G) other basis functions for linear expansion (1, 8).

[0067] Industrial Applicability

[0068] At least some embodiments of the present invention find industrial application in spectroscopy.

[0069] List of abbreviations

[0070] AFM Atomic Force Microscope

[0071] CMOS Complementary Metal Oxide Semiconductor

[0072] EBL Electron Beam Lithography

[0073] FN Fowler-Nordheim

[0074] MSE mean square error

[0075] NPDR Normalized photocurrent-dark current ratio

[0076] PSNR Peak Signal-to-Noise Ratio

[0077] RIE Reactive Ion Etching

[0078] V DS Drain-Source Voltage

[0079] V GS Gate-source voltage

[0080] vdW van der Waals

[0081] Reference numerals list

[0082] 110 <![CDATA[MoS2]]> 120 <![CDATA[WSe2]]> 130 <![CDATA[SiO2]]> 140 <![CDATA[p ++ -Yes,]]> 150 h-BN bottom layer 160 Graphene 170 h-BN top layer 180 Gate-Source Voltage Connection 181 <![CDATA[Additional electrode on MoS2]]> 182 Gate-Source / Drain-Source Voltage Connections 183 Drain-Source Voltage Connection 184 <![CDATA[Additional electrode on WSe2]]>

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Claims

1. A spectrometer, comprising: - a molybdenum disulfide layer and a tungsten diselenide layer, forming a van der Waals heterojunction therebetween; - a hexagonal boron nitride layer facing a portion of the molybdenum disulfide layer and the tungsten diselenide layer; - a second hexagonal boron nitride layer, covering the molybdenum disulfide layer and the tungsten diselenide layer; - a single-layer graphene film facing the hexagonal boron nitride layer, and - an electrical connection, provided with a tunable gate-source voltage source, connecting the single-layer graphene film and the molybdenum disulfide layer.

2. The spectrometer according to claim 1, wherein: The spectrometer comprises only a single van der Waals junction.

3. The spectrometer of claim 1 or 2, further comprising an electrical connection connecting the molybdenum disulfide layer to the tungsten diselenide layer.

4. The spectrometer according to any one of claims 1 to 3, configured to determine the wavelength of radiation incident on the spectrometer based on a spectral response matrix and a gate-source voltage value.

5. The spectrometer according to any one of claims 1 to 3, configured to determine the spectrum of radiation incident on the spectrometer based on a spectral response matrix and a tunable photocurrent value of the heterojunction, wherein the tunability of the photocurrent value of the heterojunction is obtained by changing a gate-source voltage value.

6. The spectrometer according to any one of claims 1 to 5, wherein: The tungsten diselenide layer is partially between the molybdenum disulfide layer and the hexagonal boron nitride layer.

7. The spectrometer according to any one of claims 1 to 6, wherein: The spectrometer has a footprint of 22×8 square micrometers.

8. The spectrometer according to any one of claims 1 to 7, wherein: The spectrometer does not include a photodetector array or a filter array.

9. The spectrometer according to any one of claims 1 to 8, further comprising a silicon oxide layer attached to a side of the single-layer graphene film that does not face the hexagonal boron nitride layer.

10. The spectrometer of claim 9, further comprising a silicon substrate attached to the silicon oxide layer.

Images