Broadband miniaturized spectrometers with a van der Waals tunnel diode

Miniaturized spectrometers are of immense interest for various on-chip and implantable photonic and optoelectronic applications. State-of-the-art conventional spectrometer designs rely heavily on bulky dispersive components (such as gratings, photodetector arrays, and interferometric optics) to capture different input spectral components that increase their integration complexity. Here, we report a high-performance broadband spectrometer based on a simple and compact van der Waals heterostructure diode, leveraging a careful selection of active van der Waals materials- molybdenum disulfide and black phosphorus, their electrically tunable photoresponse, and advanced computational algorithms for spectral reconstruction. We achieve remarkably high peak wavelength accuracy of ~2 nanometers, and broad operation bandwidth spanning from ~500 to 1600 nanometers in a device with a ~ 30×20 μm2 footprint. This diode-based spectrometer scheme with broadband operation offers an attractive pathway for various applications, such as sensing, surveillance and spectral imaging.


Introduction
Optical spectrometers, which analyze the spectral contents of light, are cornerstone instruments in a wide variety of application fields ranging from fundamental scientific research to industrial inspections 1,2 .Conventional spectrometers are bulky and costly as they typically need several movable dispersive optical components (e.g., motorized gratings, interferometers) and thousands of detectors or filter arrays.Although these benchtop spectrometers offer high resolution and wide spectral range, their large physical dimensions restrict them from being widely adopted in numerous portable applications, such as consumer electronics, smart wearable devices, drone integration and remote sensors 3 .
Over the past few years, various approaches have been developed to realize miniaturized spectrometers with a significant reduction in their cost and footprint by replacing the bulk dispersive optical components with tunable filter arrays or compact interferometers 4,5 .These techniques offer excellent performance in general, but they cannot be scaled down below the submillimetre scale due to fundamental physical limitations in the optical path length.To overcome these restrictions, a "reconstructive-type" operation principle has recently been developed that relies on special computational algorithms for spectral reconstruction 6,7 .Examples of such approaches include spectrometers realized on colloidal quantum dots 8 , in-situ dynamically modulated perovskites 9 , compositionally engineered 10 and superconducting 11 nanowires.Twodimensional (2D) materials 12,13 and their heterostructures 14,15 have been used to fabricate ultracompact computational spectrometers owing to their inherently dangling-bond-free surfaces, atomically sharp interfaces, layer-dependent bandgap, and electrically tunable photoresponse [16][17][18] .
However, the operation bandwidth, precision, and portability of all these miniaturized spectrometers are generally restricted by the bandgap engineering limits of their chosen materials 19 .
In this work, we report a reconstructive broadband spectrometer based on van der Waals heterostructures consisting of an overlapping tunnel junction of two semiconducting 2D materials -molybdenum disulfide (MoS2) and black phosphorus (BP).In contrast to the previous 2D materials-based spectrometers [13][14][15] , which typically use the gate voltage to tune wavelengthdependent photoresponses, here, we propose and demonstrate to use the bias voltage to create an electrically tunable spectral response for spectral reconstruction.In this design, the spectrometers are much more compact and simpler in architecture, as gate contacts and insulation layers are not required.Further, in contrast to the previously reported results (e.g., pure BP 12 , graphene 13 , MoS2/WSe2 14 , ReS2/Au/Wse2 15 ), we choose BP/MoS2 heterostructures because the BP/MoS2 junctions exhibit the transition of band alignment between staggered-and broken-gap.This can effectively switch the charge carrier transport from thermionic emission to band-to-band tunneling only by tuning the source-to-drain bias voltage across the junction without gating [20][21][22][23][24] .This drastically reduces the contact resistance under the reverse bias voltage and enables low-voltage operation without a gate terminal.Our new van der Waals tunneling-diode-driven spectrometer has a broad operation bandwidth from the visible to near-infrared ranges.Additionally, the demonstrated small operation voltage change (~2V) of the diode-based spectrometer design offers immense potential in realizing practical devices for various on-chip applications.

Operation principle
where Iph, λ, and P represent the generated photocurrent, the wavelength of the incident light, and the optical power of the incident light, respectively.In the testing step, as shown in Fig. 1(b), the bias-dependent photocurrent response of the device corresponding to the incident light with an unknown spectrum is measured.For signal processing, the incident light is assigned to an unknown spectrum function (S(λ)).The photo-response data measured in the testing step, together with the calibrated response functions obtained in the learning step, are then processed to reconstruct (S(λ)) by solving a system of linear equations 10 : where λmin and λmax refer to the operational bandwidth of the spectrometer.We compute its constrained least-squares solution to reconstruct the unknown incident light spectrum (Fig. 1(c)).We fabricate electrodes on both BP and MoS2 flakes to analyze their electrical characteristics.

Device scheme and characterization
In this work, we use multilayer flakes to fabricate the BP/MoS2 heterostructure to achieve high photoresponse.Atomic force microscopy (AFM) mapping on the heterostructure spectrometer presented in Fig. 2(b) reveals the thicknesses of the BP and the MoS2 flakes as ~45 and ~33 nm, respectively (Supplementary Fig. S1).To confirm material quality, we perform Raman measurements on pure channels and overlapping regions of the devices.Figure 2(c) shows the Raman spectra of bare MoS2 (black line), BP (blue line), and their heterostructure regions (red line) excited by a 532 nm laser at room temperature.Two distinct Raman modes of MoS2 are observed in the range of ~330-510 cm −1 : E2g 1 at ~383 cm −1 and A1g at ~407 cm −1 ; while BP shows three phonon modes: Ag 1 at ~362 cm −1 , B2g at ~439 cm −1 , and Ag 2 at ~467 cm −1 , in good agreement with previous reports 22,25 .Raman peaks of the heterostructure region comprise the contribution from both flakes, indicating the formation of a high-quality van der Waals heterojunction.
We perform electrical measurements on the tunnel diode to reveal its intrinsic properties.
For the heterojunction, drain bias is applied to BP, while MoS2 is connected to the source terminal.
In this measurement configuration, electrons are injected from the source electrode to the MoS2 flake and subsequently transported to the BP flake through the heterostructure region.Eventually, the electrons are collected by the drain electrode.Figure 2(d) presents the output characteristics of our BP/MoS2 heterostructure on a logarithmic scale.The junction offers comparable conduction for forward and reverse Vds.The superior current level under reverse bias is attributed to the bandto-band tunnelling (BTBT) mechanism, as discussed later.Since we use multilayer BP and MoS2 flakes, the quantum confinement effect can be ignored.Consequently, their band profiles are considered the same as their bulk counterparts.BP and MoS2 have electronic bandgaps of ~0.3 and 1.29 eV, respectively.Multilayer BP typically behaves as a degenerate p-type semiconductor whose Fermi level lies in the valence band, while multilayer MoS2 shows normal n-type behaviour (Supplementary Fig. S2).When a forward Vds is applied across the heterojunction, as shown in Fig. 2(e), the band of BP shifts downward compared to its equilibrium state.Consequently, the interface barrier height decreases.Therefore, valence band holes (majority carriers) of BP and conduction band electrons (majority carriers) of MoS2 effectively surmount the reduced junction barrier height, enabling forward conduction.This forward conduction is a thermionic emission process where the forward current increases exponentially with increasing Vds in the ideal case.Since BP is a strong p-type and MoS2 is an n-type semiconducting material, their respective minority carrier concentration is intrinsically low, limiting their contribution to the forward conduction.Figure 2(f) shows a heterostructure band diagram under reverse bias.BP flake offers high doping concentration, and its electrons can tunnel from the filled valence band states to the empty conduction band states of MoS2.

Spectroscopy demonstration
Upon optical irradiation of the heterojunction, the generation of photocurrent occurs depending on the signatures of excitonic states in the absorption spectrum of constituent flakes 26,27 .When the BP/MoS2 diode is excited with light in the visible wavelength region, as shown in Fig. 3(a), the electrons in the valence bands of both MoS2 and BP can be excited to their respective conduction In the learning process of the spectrometer, we first measure the output curves of the BP/MoS2 heterojunction diode under multiple known incident lights with a spectral width of ∼10 nm.For the operation demonstration at the visible spectral region, we vary the incident excitation from ∼500 nm to 800 nm in a step of 10 nm. Figure 3(b) shows the calculated photoresponsivity (R), also called responsivity in short, as a function of the wavelength of incident lights and the bias voltage applied across the heterojunction.The responsivity is defined as R=Iph/P; where Iph and P represent the photocurrent and the optical power of incident light, respectively.After encoding the spectral response matrix for the learning process, we measure unknown incident light spectra following the spectrum reconstruction process (Supplementary S3).In brief, we first measure the bias-tunable photocurrent of the unknown incident light (Fig. 1(b)).Afterwards, we compute its constrained least-squares solution to reconstruct the spectrum using an adaptive Tikhonov method 10,14 .Details of the optical setup, electrical, and optoelectrical measurements are provided in the Methods section.As shown in Fig. 3(c), the quasi-monochromatic spectra reconstructed with our spectrometer agree with the reference spectra measured using a commercial spectrometer.
The average peak wavelength difference (∆λ) between reconstructed and reference spectra is calculated as ∼2.5 ± 0.9 nm (Fig. 3(c)).The small second peak at ∼675 nm is a computational error.In principle, such artifacts can be suppressed by filtering or improving the base model.We also carry out broadband measurement (Supplementary Fig. S4), which agrees well with that of the commercial spectrometer.
We now demonstrate the operation of our spectrometer at the near-infrared (NIR) spectral region.Under NIR illumination at the heterojunction tunnel diode, as shown in Fig. 4(a), the photocurrent generation process is mainly attributed to the direct-bandgap transition in BP since the incident photons cannot provide sufficient energy to excite the electrons in MoS2 from its valence band to the conduction band.Under reverse bias (right panel of Fig. 4(a)), the photoexcited electrons in the BP drift to the MoS2 conduction band.To demonstrate operation capability at the NIR region with high spectral resolution using our single-junction ultraminiaturized spectrometer, we construct a spectral response matrix by choosing a small learning step.Figure 4(b) presents the responsivity matrix obtained in the learning process for monochromatic incident lights ranging from ∼1550 to 1560 nm in a step of ~0.5 nm.After learning, we test our spectrometer.The results shown in Fig. 4(c) indicate our broadband spectrometer is highly efficient in resolving NIR signals.
It can successfully distinguish two wavelengths at ∼1557 nm and ∼1558 nm.With larger learning steps, the peak-to-peak wavelength accuracy would be compromised, mainly due to a lower peak signal-to-noise ratio 11,14 , as shown in Supplementary Fig. S5.We also conduct spectrometer stability and reproducibility measurements (Supplementary Fig. S6), which confirm operational stability over a ∼10-day period and good device-to-device variation (∼1.2 nm in the visible range and ∼0.02 nm in the NIR range).However, currently, we cannot demonstrate the operation in the mid-infrared range due to the unavailability of tunable light sources in the mid-infrared range for the learning and reconstruction process.In contrast to the previously reported triode-based spectrometers 12,14,15 , where high gate voltage (typically > 15 V) is required for operation, our tunnel-diode-based spectrometer needs a lower voltage for tuning, which in principle reduces power consumption.Our diode-based spectrometer concept has the following main advantages: 1) simple and compact device structure without the gate terminal; 2) low driving voltage (<2V) for low power consumption; and 3) broadband operation from the visible to mid-IR for a much wider range of applications.

Discussion
In conclusion, we have successfully demonstrated a reconstruction-type tunneling-diode-based broadband spectrometer.The spectrometer is electrically reconfigurable, and it does not require any filter or, photodetector array, or other bulky dispersive components to achieve high resolution with nanometer accuracy.The low operation voltage and compact footprint of the spectrometers offer immense possibility of integration with numerous portable applications such as consumer photonics and affordable on-chip spectral imaging (e.g., smart agriculture, remote sensing, and environmental monitoring).

Device fabrication and characterization
We used Si substrates with a 285 nm thick SiO2 capping layer for device fabrication.hBNencapsulated high-quality van der Waals heterostructures were prepared with commercially available hBN, BP, and 2H-phase MoS2 crystals (2D Semiconductors, HQ Graphene) following the deterministic dry-transfer method.First, BP/MoS2/bottom-hBN heterostructures were realized Photonics) that allowed us to tune the spectral bandwidth to ~10 nm.For photo-measurements at the NIR region, we used a distributed-feedback laser source (Photonetics Osics 3610RA00).All measurements were done at room temperature, and data acquisition was performed with a customized LabVIEW program.For spectral references, the visible and the NIR spectra were measured by commercial spectrometers (FLAM-S and Anritsu MS9740A from OceanOptics).

Figure 1
Figure 1 illustrates the operation principle of our diode-based broadband spectrometer concept.It involves three distinct steps: (a) learning, (b) testing, and (c) reconstruction.The optoelectronic properties of a diode can be tuned in a controlled manner by applying a tunable external electric bias potential across the junction.As shown in Fig. 1(a), the responses of the diode are first studied with multiple known monochromatic optical inputs individually.This leads to a distinct photoresponse matrix of the device.The corresponding photoresponsivity can be treated as a function of both the incident light wavelength (λ) and the external electric bias potential (Vds) applied across the junction.The entire photo-response information is encoded into a single responsivity matrix (R, Right panel of Fig.1(a)) whose electrically tunable spectral response elements (Rij) are denoted as-

Figure 1 .
Figure 1.Schematic of working principle of our diode-based broadband miniaturized spectrometers.(a) In the learning step, the diode is excited with multiple known monochromatic inputs (Left panel).The bias-dependent (Vds) spectral responses (Middle panel) are encoded into responsivity matrix elements (Right panel).(b) In the testing process, the electrical response (Right panel) of the incident light with unknown spectral information is recorded (Left panel).(c) Spectral information of unknown incident light is then reconstructed using results obtained in the learning and testing steps with computational algorithms.

Figure 2 (
Figure 2(a) illustrates the schematic view of our BP/MoS2 diode-based spectrometer fabricated on a Si substrate with a 300 nm thermally grown SiO2 capping layer.Note that hexagonal boron nitride (hBN) passivation layers encapsulate the device.There is an additional Al2O3 encapsulation on top of the hBN.The device fabrication process is described in the Methods section.A corresponding optical microscope image of the spectrometer is provided in Fig. 2(b), where multilayer BP and MoS2 flake edges are depicted with dashed yellow and black lines, respectively.

Figure 2 .
Figure 2. Characterization of our broadband diode based spectrometer.(a) Schematic of our BP/MoS2 diode spectrometer.The junction is encapsulated by hBN passivation flakes.The top hBN and an additional Al2O3 protection layer are not shown.(b) Corresponding optical microscope image.The black and yellow dashed lines indicate MoS2 and BP flakes, respectively.Dashed grey and white lines mark the edges of the bottom and top hBN flakes.Scale bar: 10 μm.(c) Raman spectra of bare MoS2, BP, and the BP/MoS2 heterostructure.(d) Log plot of Ids-Vds characteristics of the BP/MoS2 diode.(e-f) Band diagram and carrier transport mechanisms across the BP/MoS2 heterodiode under forward (e) and reverse (f) bias conditions.

Figure 3 .
Figure 3. Demonstration of our spectrometer at the visible range.(a) Schematic of photocurrent generation mechanism when the junction is excited with the visible light under forward bias (left panel) and reverse bias (right panel) conditions.(b) Colour contour plot of experimentally obtained spectral response matrix (31 different spectra, 41 voltage values per spectrum).(c) Quasi-monochromatic spectra reconstructed with our spectrometer (solid curves).Dashed curves represent corresponding spectra obtained with a commercial spectrometer.

Figure 4 .
Figure 4. Demonstration of our spectrometer at the NIR range.(a) Schematic of photocurrent generation mechanism under the NIR light excitation under forward bias (left panel) and reverse bias (right panel) conditions.(b) Colour contour plot of spectral response matrix obtained with a small learning step of ~0.5 nm (21 different spectra, 41 voltage values per spectrum).(c) Reconstruction of typical quasimonochromatic spectra with our spectrometer (solid curves).Dashed curves represent corresponding spectra measured with a commercial spectrometer.

Figure 5
Figure 5 compares our results with state-of-the-art miniaturized spectrometers.Our singlejunction tunnel diode-based spectrometer offers comparably high peak-wavelength accuracy with a broad operational window spanning the visible and NIR regions.Note that the operation bandwidth of our device is expected to cover ∼4 μm, as the bandgap of multilayer BP is ∼0.3 eV 27 .

Figure 5 .
Figure 5.Comparison of different reconstruction-type miniaturized spectrometers with bandgap engineering.Systems are categorized according to their active materials.Solid lines in distinct colours mark corresponding operation bandwidth.The red dashed line suggests the theoretical extent of the operation bandwidth of our devices.