Miniaturized Spectrometers with a Tunable van der Waals Junction Hoon Hahn Yoon,1,2,∗ Henry A. Fernandez,1,2 Fedor Nigmatulin,1,2 Weiwei Cai,3 Zongyin Yang,4 Hanxiao Cui,5 Faisal Ahmed,1 Xiaoqi Cui,1,2 Md Gius Uddin,1,2 Ethan D. Minot,6 Harri Lipsanen,1 Kwanpyo Kim,7 Pertti Hakonen,2 Tawfique Hasan,8 Zhipei Sun1,2,∗ 1Department of Electronics and Nanoengineering, Aalto University, Espoo 02150, Finland 2QTF Centre of Excellence, Department of Applied Physics, Aalto University, Aalto 00076, Finland 3Key Lab of Education Ministry for Power Machinery and Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China 4College of Information Science and Electronic Engineering, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China 5School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, China 6Department of Physics, Oregon State University, Corvallis, Oregon 97331, United States 7Department of Physics, Yonsei University, Seoul 03722, Republic of Korea 8Cambridge Graphene Centre, University of Cambridge, Cambridge CB3 0FA, UK ∗To whom correspondence should be addressed; E-mail: hoonhahn.yoon@aalto.fi and zhipei.sun@aalto.fi Miniaturized computational spectrometers, which can obtain incident spectra using a combination of device spectral response and reconstruction algorithm, are essential for on-chip and implantable applications. Highly-sensitive spec- tral measurement using a single detector allows the footprints of such spec- trometers to be scaled down while achieving spectral resolution approach- 1 ing that of benchtop systems. We report a high-performance computational spectrometer based on a single van der Waals junction with an electrically- tunable transport-mediated spectral response. We achieve high peak wave- length accuracy (∼ 0.36 nm), high spectral resolution (∼ 3 nm), broad opera- tion bandwidth (from ∼ 405 to 845 nm), and proof-of-concept spectral imag- ing. Our approach provides a route towards ultra-miniaturization and offers unprecedented performance in accuracy, resolution, and operation bandwidth for single-detector computational spectrometers. Spectrometers are indispensable for various applications, including industrial inspection, chemical/biological characterization, and image sensing/analysis (1, 2). Their miniaturization with high spectral resolution and wide operation bandwidth is highly desirable to meet the emerging and future demands in 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 strict restrictions on ultra-miniaturization (2). Common spectrometer miniaturization approaches therefore replace the functions of these dispersive optical elements through various schemes (Fig. S1), including photonic crystals (3), metasurfaces (4), and compact interferometers (5). Recently, a profound technological leap has seen the emergence of miniaturized computational spectrometers, which leverage the power of mathematical algorithms for spectrum reconstruction (1). Examples of such approaches have used quantum dot filter arrays on to the charged-coupled device sensor (6), bandgap engineered multiple nanowires (7), a single nanowire with bandgap gradation (8), Stark effect in black phosphorus (9), in situ perovskite modulation (10), and a single superconducting nanowire with tunable quantum efficiency (11). However, the performance and usability of these computa- tional spectrometers remain limited: spectral resolution and operation bandwidth are typically restricted by the number of integrated detectors (6–8), bandgap modulation limits (9, 10), and 2 cryogenic operational requirements (11). Photodetection with two-dimensional (2D) layered materials is advantageous due to their strong light-matter interaction, atomically-sharp interface, and electrically-tunable photoresponse (12–14). However, insufficient band structure modulation makes it challenging to achieve high- resolution, broadband spectral sensing using a single 2D material. On the other hand, 2D materials-based van der Waals (vdW) junctions offer highly tunable functionalities beyond the constituent materials (15–17) and could overcome these limitations. In particular, we suggest that wavelength-dependent photodetection with vdW junctions recently exploited for optoelec- tronic logic computing (18, 19) and color sensing (20, 21) could also be key to high-resolution computational spectral sensing. Here, we demonstrate a high-performance ultra-miniaturized computational spectrometer utilizing a single vdW junction with an electrically-tunable transport-mediated spectral re- sponse. Our device, with its footprint defined by the junction size (∼ 22 × 8 µm2) shows unprecedented performance for a single detector computational spectrometer, with the ability to resolve peak monochromatic wavelengths with ∼ 0.36 nm accuracy, reconstruct broadband spectra with ∼ 3 nm resolution, and acquire spectral images by scanning. Our single-junction spectrometer concept can be extended to other tunable junctions for achieving high spectral resolution and broad operation bandwidth with its ultra-compact size, representing the ultimate miniaturization strategy without sacrificing spectrometer performance. The performance of computational spectrometers relies on the variability of their wavelength- dependent photoresponsivity (1,6–11). The single-detector miniaturized spectrometers reported thus far are limited by their performance (9, 10) and usability (9, 11) due to the limited band structure modulation and consequently, the spectral response. In contrast, electrical tuning of the interfacial band alignment of a vdW junction (Fig. 1A, upper panel) enables controllable and unique interlayer transport (15–17). This allows a tunable spectral response (Fig. 1A, lower 3 panel) with high sensitivity and variability over a wide spectral range (12–14). This suggests that a single-vdW-junction spectrometer could achieve significantly higher performance than previously reported spectrometers (section ST1 and table S1). We combine an electrically- tunable single-vdW-junction with computational reconstruction algorithms for various applica- tions (Fig. 1B). To experimentally realize our spectrometer concept, the following three steps are required (Fig. S2): measuring the gate-tunable spectral responses with multiple known in- cident spectra (learning process); measuring the gate-tunable photocurrent of the unknown in- cident light to be analyzed (testing process); and computing the spectral information of the Spectral imager A Electrically-tunable spectral response matrix Electrically-tunable vdW junction B Wavelength meter In te n s it y Wavelength Monochromatic light Gate tuning R e s p o n s iv it y W avelength E v E c Spectrometer In te n s it y Wavelength Broadband light W a v e le n g th Image Figure 1: Ultra-miniaturized spectrometer concept with a single-vdW-junction. A, A typ- ical gate-tunable band alignment at the vdW junction interface (upper) with its distinct gate- tunable spectral response matrix (lower). EC (EV) represents the conduction (valence) band edge. B, Schematic of various application examples using single-junction spectrometer: wave- length meter to distinguish peak wavelengths of monochromatic light (upper), spectrometer to resolve broadband spectra (middle), and spectral imager to analyze spectral information of images (lower). 4 unknown incident light based on the results obtained in learning and testing processes with the reconstruction algorithm (reconstructing process). The distinct and varied photoresponse of a vdW junction, tuned at different gate voltages and incident light wavelengths, is critical to our spectrometer (1). We choose a MoS2/WSe2 heterojunction (Fig. 2A) as an example for its distinct spectral response due to the gate-tunable photovoltaic effect from the visible to the near-infrared. (22–28) The MoS2/WSe2 heterojunc- tion is encapsulated by top and bottom h-BN layers for insulation and passivation, respectively (section MM1). A monolayer graphene film below the stack is used as a local gate electrode for effective gate tuning. Each stacking layer was characterized by Raman spectroscopy and atomic force microscopy (Fig. S3) to confirm the quality of the vdW heterostructure. The transfer curves (drain-source current IDS as a function of the gate-source voltage V GS) of the MoS2 or WSe2 channels and their heterojunction are measured at drain-source voltage V DS = 3 V in dark condition (Fig. 2B). The individual MoS2 and WSe2 channels exhibit n(p)- type characteristics due to the donor (acceptor) impurities in MoS2 (WSe2). Thus, a depletion region and built-in electric field are expected at their vdW interface (22–28). The MoS2/WSe2 heterojunction is characterized by positive V DS applied to the WSe2 side, corresponding to the forward biasing of the diode. The sign change of transconductance, dIDS dVGS , occurs at V GS = ∼ -5 V, matching the hole current from WSe2 with the electron current from MoS2. This “anti-ambipolar” behavior and other transport properties (Figs. S4 to S7) are typical of the MoS2/WSe2 heterojunctions (22–28), providing clearly distinguishable V GS-dependence. The transfer curves of the MoS2/WSe2 heterojunction measured under multiple known inci- dent lights with a bandwidth of∼ 10 nm indicate a strong wavelength dependence (Fig. 2C). The photoresponsivity, R = Iph P , measured at different V GS and incident light wavelengths is used to encode the spectral response matrix, where the photocurrent is defined as Iph = I light − Idark, with I light and Idark representing IDS with and without light illumination at V DS = 3 V, respec- 5 WSe 2V DS V GS h-BN MoS 2 Graphene 50E G A C D F Quasi-monochromatic spectra (E) Complex broadband spectra (F) 100 50 25 12.5 0 10 20 30 40 P e a k s ig n a l- to -n o is e r a ti o ( d B ) Learning step (nm) λ (nm) 845 800 750 700 650 600 550 500 450 405 I D S ( A ) Wavelength (nm) -13 R (mA·W-1) 0 -20 -10 0 10 20 400 500 600 700 800 V G S ( V ) -20 -10 0 10 10 -9 10 -8 10 -7 V DS = 3 V MoS 2 /WSe 2 V GS (V) B -30 -20 -10 0 10 20 30 10 10 10 10 MoS 2 MoS 2 /WSe 2 WSe 2 I D S ( A ) V DS = 3 V V GS (V) 0.0 0.4 P ( a .u .) 20 400 500 600 700 800 0.8 0.0 0.4 1.2 P ( a .u .) Commercial spectrometer Single-junction spectrometer Wavelength (nm) Wavelength (nm) 400 500 600 700 800 0.8 0.0 0.4 0.8 1.2 10 μm Top h-BN MoS 2 WSe 2 Graphene 10 μm Bottom h-BN -10 -8 -6 -4 Figure 2: Single-junction spectrometer demonstration. A, Schematic of our MoS2/WSe2 heterojunction spectrometer (left) and its optical images on the h-BN and graphene layers before (middle) and after (right) depositing electrodes and stacking the top h-BN passivation layer. The top h-BN layer is not present in the upper panel for better visibility. B and C, Transfer curves of the MoS2 and WSe2 channels and their heterojunction with the graphene gate without (B) and with (C) light illumination at different wavelengths with a fixed power of ∼ 20 µW. D, Color contour plot of the spectral response matrix. E and F, Quasi-monochromatic (E, bandwidth: ∼ 10 nm), two different broadband (F) spectra reconstructed with our spectrometer (solid) and measured using a commercial spectrometer (dashed). G, Peak signal-to-noise ratio between reconstructed and reference spectra as a function of learning step. 6 tively, and P is the incident light power (Fig. S8). The gate-tunable spectral response with high sensitivity over a wide spectral range is due to the wavelength-dependent absorption (29) of MoS2 and WSe2 as well as the controllable charge carrier transport (22–28) through the MoS2/WSe2 interface, unlike the individual material. The spectral response matrix (Fig. 2D) inherits a rich structure from the dynamics of photoexcited charge carriers generated across the tunable MoS2/WSe2 heterojunction (22–29), confirming fast and stable spectral detection with giant gate-tunability in our MoS2/WSe2 heterojunction (Figs. S9 to S13). After encoding this spectral response matrix (Fig. 2D) for the learning process, our single- junction spectrometer is ready to measure unknown incident light spectra, following the work- flow diagram (Fig. S2). Briefly, we measure the gate-tunable photocurrent of the unknown in- cident light and then compute its constrained least-square solution to reconstruct the spectrum using adaptive Tikhonov regularization by minimizing the residual norm with a regularization factor (1, 8). Details of the optical setup, electrical/optoelectrical measurements, and computa- tional reconstruction are provided in Fig. S14 and sections MM2 to MM4. The quasi-monochromatic and complex broadband spectra reconstructed with our single- junction spectrometer agree well with the reference spectra measured using a commercial spec- trometer, demonstrating the viability of single-junction spectrometer concept (Fig. 2, E and F). While the demonstrated bandwidth (from ∼ 405 to 845 nm) is limited due to the availability of the light wavelengths in our laboratory, the MoS2/WSe2 heterojunction exhibits photore- sponse from ∼ 400 to 2400 nm (25). Indeed, the vdW junctions are known to exhibit pho- todetection capability for incident light whose wavelength corresponds to around half (or even much smaller than) the bandgap of each material (15–17, 25). Therefore, in principle, single- junction spectrometer is not limited by the material bandgap and likely offers operation band- width broader than our demonstration. Our single-junction spectrometer using the interlayer- transport-mediated photoresponse is fundamentally different from the previously demonstrated 7 spectrometer concepts, such as bandgap engineering and grading (7–10). Detailed compar- isons of our work with the current state-of-the-art miniaturized spectrometers (including black- phosphorus-based spectrometers with the Stark effect (9)) are given in section ST2 and table S1. To evaluate deviations between the reconstructed and reference spectra, the peak signal-to- noise ratio (PSNR) has previously been used to analyze the mean squared error (section ST3). The maximum PSNR estimated from the extrapolation is ∼ 35.7 and 33.6 dB for the quasi- monochromatic and complex broadband spectra, respectively (Fig. 2G). A reasonable learning step (i.e. step in wavelength for encoding the spectral response matrix) can be chosen based on the saturated PSNR. Therefore, a high-speed learning process is achievable with a large learning step and slightly reduced accuracy (11). The wavelength resolving power is an important measure of spectrometers in practical ap- plications (1, 2). To demonstrate high spectral resolution capability with our single-junction ultra-miniaturized spectrometer, we construct a high-density spectral response matrix through an ultra-small learning step of ∼ 0.1 nm using monochromatic light from ∼ 675 nm to 685 nm for the learning process (Fig. 3A). Our single-junction spectrometer encoded by the high- density spectral response matrix can resolve monochromatic light with high accuracy (Fig. 3, B and C). The average peak wavelength difference (∆λ) between reconstructed and reference spectra is ∼ 0.36 ± 0.06 nm, with a minimum of ∼ 0.04 nm (Fig. 3D). This is comparable to the learning step of ∼ 0.1 nm. The wavelength resolving power ( Rλ = λ ∆λ ) at a given input wavelength (λ) is ∼ 3470 ± 880. Furthermore, we measure complex incident spectra to study spectral resolution. Two peaks at ∼ 679 nm, separated by ∼ 3 nm, are successfully distinguished (Fig. 3E). Our spectrometer can also resolve broadband spectra and identify their peak wavelengths with high resolution (∼ 0.9 nm demonstrated in Fig. S15). This indicates that our spectrometer has spectral resolu- 8 tion comparable to or better than the current state-of-the-art miniaturized spectrometers (1–11) with footprint (∼ 22 × 8 µm2) comparable to or smaller than most. This is several orders of magnitude smaller than commercial miniaturized spectrometers (30) and recently demonstrated spectrometers with metasurfaces (4), quantum dots (6), or a single-dot perovskite (10); see Ta- ble S1 for a detailed comparison. We note that the demonstrated accuracy (∼ 0.36 nm) and 103 16 C 676 678 680 682 684 676 678 680 682 684 P e a k w a v e le n g th (n m ) Input wavelength (nm) A B 676 678 680 682 684676 678 680 682 684 -20 -10 0 10 20 -17 R (mA·W-1) 0 V G S ( V ) Wavelength (nm) 676 678 680 682 684 3.0 nm D F NPDR change per wavelength (W-1·nm-1) Commercial spectrometer R = 1 A·W-1 0.8 0.0 0.4 1.2 P (a .u .) 0.8 0.0 0.4 1.2 P (a .u .) E 0.0 0.4 0.8 1.2 Δ λ (n m ) 676 678 680 682 684 102 103 104 R e s o lv in g p o w e r Input wavelength (nm) Commercial spectrometer Single-junction spectrometer Commercial spectrometer Single-junction spectrometer Commercial spectrometer Single-junction spectrometer Wavelength (nm) Wavelength (nm) S p e c tr a l re s o lu ti o n (n m ) 1013 1014 1015 10 10-5 10-3 10-1 101 R = 0.1 A·W-1 Achieved in this work Achievable with improvement Figure 3: High-performance wavelength resolving power and spectral resolution. A, Color contour plot of the high-density spectral response matrix with a learning step of ∼ 0.1 nm. B, Monochromatic (bandwidth: ∼ 2 nm) spectra reconstructed with our spectrometer (solid) and measured using a commercial spectrometer (dashed). C, Peak wavelengths of the reconstructed and measured spectra as a function of input wavelength. D, Peak wavelength difference be- tween reconstructed and reference spectra (upper panel), and wavelength resolving power of our single-junction spectrometer (lower panel). E, Complex spectra reconstructed (solid) and measured (dashed). F, Future prospect of our single-junction spectrometer aiming for ultra- high-resolution. 9 resolution (∼ 3 nm), which are limited by the smallest incident wavelength step available in our laboratory, can be further improved by minimizing the learning step during the learning process. We suggest that such a learning process is practical for applications, similar to the calibration process in traditional spectrometers. Many strategies can be considered to improve the resolution, accuracy, and speed of our single-junction spectrometer (1). These include: (A) increasing the dataset size to create higher- density spectral response matrix by minimizing the learning step (7–11), (B) designing junctions with higher response and larger wavelength or gate dependence (15–17), and (C) optimizing the reconstruction algorithm (e.g., suppressing the perturbation with more advanced regularization (1, 8) or increasing the accuracy with convolutional processing (20, 21)). Ideally, decreasing the learning step is a straightforward approach to forming a denser spectral response matrix for more accurate spectral reconstruction. However, there is a trade-off: signal difference, measured at small learning steps, comparable to the measurement noise could result in errors during reconstruction. To illustrate the future development possibilities of single-junction spectrometers, we con- sider the normalized photocurrent-to-dark current ratio (NPDR) change per wavelength step of two resolved peaks (section ST4). The extrapolated line in Fig. 3F indicates the potential of our approach with improved photoresponsivity for higher resolution than the commercial miniaturized spectrometers (30). The achievable resolution is highlighted based on recently reported photoresponse (∼ 0.1 to 1 A·W−1 at 532 nm) of MoS2/WSe2 heterojunctions (25). The resolution and bandwidth can be further improved by engineering junctions with different combinations of various 2D materials or integrating waveguides (15–17). Additional strategies for improving performance are provided in section ST5. With a significant potential to improve performance, our single-junction spectrometer can not only be adapted to other tunable junc- tion architectures but also integrated with CMOS(complementary metal-oxide-semiconductor)- 10 compatible platforms. Our single-junction spectrometer can benefit from the recently developed large-scale 2D material synthesis to construct an array for future spectral imaging. Here, we demonstrate proof- of-concept spectral imaging of a color filter consisting of red, blue, and transparent areas with spatial scanning using our spectrometer (Fig. 4A). At each mapping position, the measured pho- tocurrent data at different V GS are recorded in the spatial response data cube for spectral recon- struction. A series of photocurrent mapping data scanned at different V GS is displayed (Fig. 4B) and converted to a series of spectral data reconstructed at different wavelengths (Fig. 4C). The B C -10 V 10 V7.5 V5 V2.5 V-2.5 V-5 V-7.5 V I p h ( a .u .) 405 nm 580 nm450 nm 500 nm 550 nm 800 nm630 nm 650 nm P ( a .u .) Photocurrent data cube I ph (x, y, V GS ) x y V GS Spectral data cube P (x, y, λ) x y λ Spectral reconstruction Image scanning Single-junction spectrometer x y Broadband light source Transmission mapping Near-infraredVisible A Figure 4: Proof-of-concept demonstration of spectral imaging. A, Configuration of spectral imaging using our single-junction spectrometer with a spatial scanning method. A broadband light source filtered with a color image is incident to our spectrometer for spectral imaging. B, Photocurrent mapping data scanned at different V GS. C, Spectral images reconstructed at different wavelengths, covering the visible to near-infrared ranges. Higher intensity at each wavelength indicates more broadband light is transmitted through the color image. The pixel intensity in B and C is normalized with each maximum intensity. 11 spectral images indicate 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 uppercase alphabet "A" (from∼ 450 to 700 nm) and the blue exclamation mark "!" (from∼ 405 to 845 nm) are distinguishable from that of the background. Note that a strong light signal at near 800 nm for the exclamation mark "!" can be fully detected, highlighting the advantages of spectral imaging over conventional RGB color imaging (Fig. S16 with different color filters). In our demonstration, the image resolution is defined by the mapping step. However, our concept has great potential for large-scale spectral imaging by future array devices, offering high spatial resolution with the junction at the micrometer- or nanometer-scale. In our spectrometer, no photodetector array, filter array, or other bulky dispersive compo- nents are required to achieve high resolution, sub-nm accuracy, and broad operation bandwidth. 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Nigmatulin, Spectral Reconstruction Based on Tunable vdW Junction Spectrometers, version 1.0, Zenodo (2022) https://doi.org/10.5281/ zenodo.7012876. Acknowledgments We acknowledge the provision of facilities and technical support from the Otaniemi research in- frastructure (OtaNano-Micronova Nanofabrication Centre and OtaNano-Nanomicroscopy Cen- tre). We thank Andreas Liapis, Mingde Du, Yunyun Dai, Suvi-Tuuli Akkanen, Juan Camilo Arias, and Xueyin Bai for valuable discussions and Mikko Turunen, Diao Li, Yi Zhang, Vin- cent Pelgrin, and Susobhan Das for access to the optical instruments and components. Fund- ing: This work was supported by the Academy of Finland (Grant No. 314810, 333982, 336144, 336813, 336818, and 348920), Academy of Finland Flagship Programme (Grant No. 320167, PREIN), the EU H2020-MSCA-RISE-872049 (IPN-Bio), EPSRC (Grant No. EP/T014601/1), ERC (Grant No. 834742), and National Natural Science Foundation of China (Grant No. 51976122 and 52061135108). Pertti Hakonen was supported by the Jane and Aatos Erkko foundation and the Technology Industries of Finland centennial foundation (Future Makers 2021). Author contributions: Z.S. conceived the ideas during the discussion with H.H.Y. and F.A.. H.H.Y designed the experiments and carried out the characterizations/measurements. H.H.Y., H.A.F., F.N., and M.G.U. fabricated the van der Waals heterostructures and spectrom- eter devices. H.A.F. provided the home-built optical system and prepared the optical instru- ments and components. F.A. and X.C. helped with the electrical and optoelectrical measure- ments. H.H.Y., F.N., W.C., Z.Y., and H.C. developed the reconstruction code. W.C., Z.Y., 19 H.C., and T.H. shared the processing strategies. H.H.Y., H.A.F., F.N., F.A., and Z.S. ana- lyzed the data. W.C., E.D.M., P.H., K.K., H.L., and T.H. commented on the experimental results and helped with the data analysis. H.A.F. and X.C. helped with the graphic design. H.H.Y. wrote the manuscript, and Z.S. supervised the research. All authors participated in the scientific discussion extensively and contributed to the manuscript writing. Correspon- dence: addressed to H.H.Y. or Z.S.. Competing interests: The authors declare no com- peting interests. Data and materials availability: All data needed to evaluate the conclu- sions in the paper are present in the main text or the supplementary materials. Code used for spectral reconstruction based on tunable vdW junction spectrometers is available at https: //github.com/fonig/Reconstruction and archived at Zenodo (66). Supplementary Material Materials and Methods Supplementary Text Figs. S1 to S16 Table S1 References (31-66) 20