Nonlinear self-calibrated spectrometer with single GeSe-InSe heterojunction device

Computational spectrometry is an emerging field that uses photodetection in conjunction with numerical algorithms for spectroscopic measurements. Compact single photodetectors made from layered materials are particularly attractive since they eliminate the need for bulky mechanical and optical components used in traditional spectrometers and can easily be engineered as heterostructures to optimize device performance. However, such photodetectors are typically nonlinear devices, which adds complexity to extracting optical spectra from their response. Here, we train an artificial neural network to recover the full nonlinear spectral photoresponse of a single GeSe-InSe p-n heterojunction device. The device has a spectral range of 400 to 1100 nm, a small footprint of ~25 × 25 square micrometers, and a mean reconstruction error of 2 × 10−4 for the power spectrum at 0.35 nanometers. Using our device, we demonstrate a solution to metamerism, an apparent matching of colors with different power spectral distributions, which is a fundamental problem in optical imaging.


report on the training of an artificial neural network (ANN) to recover the full nonlinear spectral photoresponse -a nonlinear problem of high dimensionality -of a single GeSe-InSe
p-n heterojunction device.We demonstrate the functionality of a calibrated spectrometer in the spectral range of 400-1100 nm, with a small device footprint of ~ ×  , and we achieve a mean reconstruction error of  ×  ! for the power-spectrum at a spectral resolution of 0.35 nm.Using our device, we demonstrate a solution to metamerism, an apparent matching of colors with different power spectral distributions, which is a fundamental problem in optical imaging.
Optical sensing, the measurement of the properties of light such as its spectrum, polarization, and power, is central to several fields of science and technology. 11,12Accurate optical spectrometers with analytical calibration and resolution are typically expensive table-top machines containing moving optical components. 11,12In contrast, computational optical spectroscopy [7][8][9] and sensing, 13,14 which entails the use of an algorithm and either a single on-chip tunable detector or an array of detectors to replace the optical components in conventional sensing instruments, allows for spectra 9 and polarization 15 measurements efficiently and compact manner.The operational principle of a computational spectrometer based on a single tunable device exploits the electrical tunability of the photodetector, e.g., via voltage bias, for collecting the output photocurrent within a high-dimensional vector space defined by the number of variable input conditions.This process is termed an encoding process and, so far, it has been applied only to linear detectors since the non-linear problem was considered intractable.Linear computational detectors exploit the relation  #$ () = ∫ (, )() , where R is the responsivity, () is the spectral power density to be measured,  #$ () is the photocurrent, and  is the wavelength. 9,16The voltage-dependent responsivity matrix, (; ), 7,9,10 operates as a transformation operator that maps the measured photocurrent  #$ () on to the spectrum ().These linear relations between the responsivity, current and spectrum allow for training a transformation matrix that connects the measured photocurrent to the unknown spectrum, via linear regression techniques. 7,9,10However, most semiconductor devices can also operate in the nonlinear regime. 17,18For example, diodes, field-effect transistors, and bipolar transistors often display a nonlinear response that is considered disadvantageous for high-fidelity analog and digital communication systems 19,20 and in optical spectrometers. 21In the case of nonlinear photoresponse, the existence of a mapping between the photocurrent and spectrum is not guaranteed, and if such a mapping exists, it must rely on a larger parameter space to account for the nonlinearity.In this work, we use a voltage-tunable heterojunction device of p-GeSe/n-InSe (see Figure 1a) that is amenable to tuning of both the spectral response and its higher-order nonlinearities.To resolve the complex mapping transformation between the spectrum and photocurrent, we encode the nonlinear response of the device by training an ANN (Figure 1b-1c) that captures device's response as a function of bias voltage and spectrum.Unknown spectra can then be analyzed by decoding the voltage-dependent photocurrent response of the device (Figure 1d) and performing the inverse mapping via the trained ANN (Figure 1e) to reconstruct the power spectrum (Figure 1f).The voltage-tunable InSe/GeSe heterojunction device (Figure 2a) consist of a stack of ~4 layers of p-type GeSe and ~7 layers of n-type InSe; the GeSe side is in contact with a gold electrode while the InSe side is in contact with transparent graphene electrode, and the entire device is encapsulated in hBN (Figure 1a and Supplementary Figure 1).The Raman spectrum corresponding to this structure is presented in Figure 2b (and Supplementary Figures 2 and 3), and the current-voltage transfer curves confirm the formation of a p-n junction (Figure 2c; also see SI for results of a lateral device as a control experiment).While the principle of voltage-tunable band alignment and spectral response in 2D heterostructures is known, 7,10 the nonlinear response of the GeSe-InSe device is not yet understood.3][24] In the present case, the tunable nonlinear response of the heterostructure device arises from interfacial charge transfer at the p-n junction.When bias voltage is applied to this heterojunction, the built-in potential is modified as well as the optical polarizability associated with the observed voltage and nonlinear spectral response (Figure 3).A general model describing the nonlinear response of the device may be written as where the nonlinear coefficients (, ) are unknown and span a high-dimensional  ×  parameter space,  & is the photocurrent at voltage ,  &,% is the responsivity at voltage  and wavelength , and  % is the component of the power spectrum at wavelength .The dependence of our device's nonlinear response on the applied voltage and spectrum is evaluated from the measurements in Figure 3.  Furthermore, the resolution of the reconstructed power spectra was evaluated with respect to the dimension of the input/output vectors (photocurrent and spectrum) by reducing the dimension of the power spectrum vectors from 2,000 × 1 to 1,000 × 1. Figure 4c shows the measured and reconstructed spectra of a color-printed polymer transparency (such as the one shown in Figure 5), sampled with 2,000 points over the spectral range of 400-1,100 nm.The lower-resolution spectrum of dimension 1,000 × 1 is shown in Figure 4d.The low-resolution spectrum was decoded with a similar MLP with hidden layers of 1024, 512, 256 and 128 neurons.Interestingly, even upon decreasing the vector size by a factor of two, the power calibration (and dynamic range) of the spectrometer is maintained while the spectral resolution deteriorates, as observed from the broadening and loss of spectral details in Figure 4d.Here, the spectral resolution is not defined directly by the reconstruction of the computational spectrometer but based on the resolution of the reference signal that was measured with a tabletop spectrometer.The quality of the computational spectrometer is defined by the reconstruction error relative to the reference signal used to test and match its performance.The normalized reconstruction error, defined as ℰ = The ability to image with high spectral resolution within the visible-to-NIR range using a simple portable device has many potential applications in our daily lives.One such common example is the objectivity of colors in vision and imaging, and their dependence upon illumination, known as metamerism.In metamerism, two objects of different color can appear to have the same color or, alternatively, the same object can appear different under varying illumination.The two different filters in Figure 5a appear indistinguishable under fluorescent ambient light.However, with a cell phone flashlight, the difference between these filters becomes evident (Figure 5b).With our compact nonlinear spectrometer, the reflection spectra of the two filters show a clear difference (Figure 5c) and provide a quantitative measure of the true color of the filters, independent of the lighting conditions.

SUMMARY AND CONCLUSIONS
In summary, we have demonstrated a power-calibrated spectrometer based on a single, voltagetunable GeSe-InSe p-n heterojunction device.Using ANNs to decode the nonlinear photocurrent response of this device allows us to achieve high-resolution spectral measurements over the entire visible-to-near-IR range of the optical spectrum.Specifically, with a small device footprint of ~25 × 25  and a trained ANN, we were able to reconstruct complex power spectra within the spectral range of 400-1100 nm with accuracy better than 5pW/nm and a spectral resolution of 0.35 nm.Our results pave the way for expanding the role of computational spectroscopy as a viable alternative to traditional optical spectrometry, potentially leading to single-element, on-chip spectrometers for rapid and inexpensive optical sensing.

Device fabrication:
The following steps were taken to fabricate an encapsulated hBN/Graphene/InSe/GeSe vdW heterojunction using the dry transfer method inside a glovebox to prevent contamination and degradation of the exfoliated samples.First, Si/SiO2 substrates were cleaned with deionized water, acetone, and isopropanol in succession, then dried with nitrogen gas.
Mechanical exfoliation was used to obtain the desired thickness of hBN, graphene, InSe, and GeSe flakes from their parental crystals on top of Si/SiO2 substrates.Next, the dry-transfer technique was utilized to encapsulate the vertical hetero-junction with hBN, creating a vertical hBN/Gr/InSe/GeSe heterostructure.The successive layers were picked up from a 285 nm Si/SiO2 wafer using a polycarbonate membrane, starting with the top layer of hBN, followed by the graphene flake, InSe, and finally the bottom layer of GeSe.The entire stack was deposited on a clean pre-patterned back electrode (Ti/Au: 5/50 nm) at 150°C and the PC membrane was then dissolved using chloroform.

Figure 1 .
Figure 1.Illustration of the nonlinear learning and reconstruction process: Schematic atomistic

Figure 2 . 27 Figure 3 .
Figure 2. A schematic depicting the voltage-adjustable band alignment of InSe/GeSe (a) and the

Figure 4 .
Figure 4. Nonlinear reconstruction of power spectra.Schematic of the fully-connected MLP Figure 4f.Clearly, the reconstructed spectra follow the reference, as evident from these small

Figure 5 .
Figure 5.A photo of two filters with different color taken and the lighting of a fluorescent lamp Photoresponse Characterization: All measurements of photocurrent as a function of bias voltage were performed at room temperature (25 ± 0.1 ℃) under vacuum conditions at ~10 -5 Torr.Photocurrent was measured with incident light modulated by a mechanical chopper at frequency of 1 kHz, and with low noise current pre-amplifier (Femto DLPCA-200) and lock-in amplifier (Model SR830).In this photocurrent measurement, the heterojunction was illuminated by seven light-emitting diodes and a Laser Driven Light Source (LDLS) as a white-light source combined with a set of bandpass filters and also with transparency printed filters (see supplementary information for details).The reference spectrum of each light source was measured with a Thermo Fisher Scientific Nicolet-iS50R Fourier Transform Infrared (FTIR) spectrometer connected to an external silicon detector (Thorlabs FDS100) and the spectra were normalized to the silicon detector's calibrated responsivity.