Optical spectrometry can analyze substance characteristics at different wavelengths, which is widely applied in food safety, chemical material analysis, disease detection, environmental monitoring, and other fields [1–5]. Infrared spectroscopy especially provides crucial data [6,7] distinguishing materials [8–10], due to the fingerprint features of substances in the infrared spectrum. By far, traditional infrared spectrometers are well developed. For example, Fourier transform infrared spectroscopy provides rapid acquisition of high-resolution spectral data, widely applied in chemical analysis and materials science [11,12]. Although the set-up significantly enhances convenience and efficiency in laboratory work, it is bulky and costly. There is a growing demand for miniaturized, low-cost, and high-performance infrared spectrometers [13–17]. Many attempts have been made by researchers to miniaturize spectrometers. In 2001, Kong et al. developed a dual-silicon planar grating chip spectrometer consisting of two wafers bonded vertically [18]. The top silicon wafer is scribed with a slit to act as a planar transmission grating, and a line array detector is integrated on the bottom silicon wafer to miniaturize the spectrometer. In 2012, a miniature spectrometer based on linear variable optical filters was proposed by Emadi et al. [19]. This design scheme can circumvent the optical range limitation, thus making it possible to achieve a more compact spectrometer.

The design of discrete dispersion elements, mechanical movable parts, and photodetectors directly affects the miniaturization. The development of nanotechnologies [20–24] and computer technologies [25–28] provides a new method [13,15]. Nanomaterials exhibit many novel optical and electrical properties due to the quantum confinement. Therefore, they show attractive prospects in electrical and optical devices and have attracted wide attention for spectral filters and the photodetectors in spectrometers. For instance, Bao et al. utilized 195 different colloidal quantum dot (CQD) filters, pioneering CQD integrated spectrometers [29]. Utilizing adjustable absorption characteristics of CQD, they have developed fine-transmission filters to replace interferometric optical devices. These filters are integrated with charge coupled device (CCD) cameras, covering the 390–690 nm visible spectrum. Later, Zhu et al. integrated an array of 361 CQD-embedded film filters with a CCD camera, achieving a spectral resolution of $\sim 1.6\mathrm{nm}$ over a broad range from 250 to 1000 nm [30]. In addition, research on CQD-based detector arrays is rapidly advancing. In 2018, Chu et al. explored the application of two nanocrystalline materials, PbS and HgTe, in the short-wave infrared (SWIR) region and successfully integrated HgTe nanocrystal films into multi-pixel devices, demonstrating their potential for high-performance imaging systems [31]. In 2024, Ahn et al. proposed a novel hybrid photodetector by combining graphene with PbS quantum dots [32]. This device achieves spectral analysis through an alternating stacked structure, where photosensitive layers at different positions exhibit distinct spectral responses, thereby broadening the functional scope of the detector.

These achievements present the potential of CQD in high-performance micro spectrometer applications. Recently, the advancement of computer technology has promoted computational spectrometry [25–28]. The reconstruction spectrometer systems typically consist of a set of detectors with unique spectral response characteristics. Yang et al. have proven that utilizing machine learning algorithms for spectral reconstruction significantly reduces the size of spectrometers [33] based on single nanowires.

However, since the nanomaterials are only used as filters, most nanomaterial-based spectrometers are limited in the visible wavelength band due to the detectable wavelength of silicon photodetectors. The configuration of infrared photodetectors in linear or planar arrays for spectral analysis heavily relies on narrow band semiconductor materials. Unfortunately, the epitaxial growth and the silicon incompatibility do come with increased costs from the manufacturing complexity and the specialized equipment. Recent research shows great progress on CQD infrared photodetection, covering near infrared [34], short-wave infrared [35], mid-wave infrared [36–38], long-wave infrared [39,40], and up to very long-wave infrared [40]. The solution processability also promotes the development of infrared spectrometers with CQD photodetector arrays.

In this work, we developed the CQD homojunction photodetector arrays with resonant cavities, with a detectivity of $4.64\times {10}^{11}$ Jones at 2.5 μm at room temperature. Compared to a heterojunction CQD detector, homojunction demonstrates higher quantum efficiency and responsivity due to the well-designed band alignment [38]. What is more, resonant cavity structures have been used to further improve the optical collection efficiency of the CQD film [41]. We then built an infrared spectrometer based on diffraction gratings, CQD photodetector arrays, and computing methods. Diffraction gratings can offer better resolution in diffraction spectrometers because of their superior dispersion capability [42]. The spectrometer was equipped with a total of 256 detector channels. As shown in Fig. 5 (Appendix B), the structure of each pixel and the device fabrication process are identical, and the CQD and SU-8 solutions are spin-coated. An array of contact electrodes is integrated onto the wafer and the entire wafer is then cut into individual array modules. This approach ensures the uniformity of the CQD film and resonant cavity layers and improves the uniformity of the optical response over 256 pixels. The area of a single pixel is $100\mathrm{\mu m}\times 400\mathrm{\mu m}$. The spectrometer displays a detection spectrum spanning 1.4–2.5 μm, and a spectral resolution capability reaching 7 nm confirms the spectrometer’s capabilities.

Figure 1 shows the characterization of a single-pixel photodetector. The device structure design is shown in Fig. 1(a), combining a homojunction photodiode and a Fabry-Perot cavity. For a PIN photodiode, N-type and P-type CQD films are used as the electron and hole transport layers, respectively. The homojunction design not only avoids carrier lost at the interface but also benefits a larger built-in electric field. The Fabry-Perot cavity mainly consists of a gold contact electrode (lower gold layer), an optical spacer layer (SU-8 photoresist), and a high-reflectivity upper gold back-reflector. The bottom lighting is used to maximize the light collection efficiency. As the SEM image shows in Fig. 1(a), an indium tin oxide (ITO) layer about 50 nm thick is used as the bottom contact on the ${\mathrm{Al}}_2{\mathrm{O}}_3$ substrate. Stacked in sequence to form the PIN homojunction are layers of N-type CQD with 50 nm, intrinsic with 300 nm, and P-type with 50 nm [43]. Then, the resonant cavity structure was prepared on top of the CQD film, which includes a 10 nm thick contact gold electrode, 1.3 μm SU-8 photoresist, and 40 nm upper gold as the reflective layer. Detailed information on the device fabrication can be found in Appendix A.

COMSOL simulation is used to determine the parameters of the device, mainly the thickness of the SU-8 photoresist, the lower gold layer, the upper gold, and the CQD layer. The left and right sides were set as periodic boundary conditions. For the CQD layer, we set the real part of the refractive index at 2.3 and the value of the imaginary part changed with the wavelength, determined by extracting the distribution of extinction coefficients from the absorption. The refractive index of the air was $1\text{+}\text{0i}$. The thickness of CQD was pre-set to 400 nm, determined by the typical thickness used. With the SU-8 photoresist thickness of 1.3 μm, the electric field distribution of the device under resonant conditions is shown in Fig. 1(b). The incident light was confined within the Fabry-Perot cavity, forming standing waves, which caused a strong spatial overlap between the CQD absorber and the optical field [44,45].

The resonant cavity structure is spectrally selective. To achieve the optimal device performance, we explored the variation in optical spacer layers and CQD thicknesses. As shown in Fig. 1(c), by tuning the optical spacer layers thicknesses from 1 to 2.1 μm, the peak absorption would be tuned from 5800 to $6100{\mathrm{cm}}^{-1}$. The peak absorption was increased from 45% (no cavity) to 85% (1.3 μm cavity thickness). In the simulation, sharp absorption peaks appeared at $3800{\mathrm{cm}}^{-1}$, $5000{\mathrm{cm}}^{-1}$, and $6600{\mathrm{cm}}^{-1}$, which may be from the absorption of the two layers of gold in the device. Figures 1(d) and 1(e) show the effect of different thicknesses of the lower and upper gold layers on the simulated absorption of the device when the SU-8 photoresist is 1.3 μm and the CQD layer is 400 nm. From the results, when the thickness of the lower gold layer was varied, there was a notable change in the sharp absorption at $5000{\mathrm{cm}}^{-1}$, with a small blue shift. When the lower gold layer was fixed at 10 nm, changing the thickness of the upper gold layer, there was a significant absorption at $5000{\mathrm{cm}}^{-1}$ and the intensity of absorption was maximum at 40 nm of the upper gold layer, while the absorption at other positions was almost unchanged. Figure 1(f) shows the simulation varying the CQD thickness, which determined the cavity length and the resonance peak absorption from 4800 to $6500{\mathrm{cm}}^{-1}$. As expected [46,47], reducing the CQD thickness caused a blue shift of the resonance peak. The 400 nm CQD film with the resonant cavity exhibits a more significant absorption enhancement effect. Based on the simulation, we have prepared resonant-cavity-enhanced CQD homojunction arrays, with the length of 4 cm and the width of 2.8 mm containing 256 pixels.

Figure 2 shows the photodetection property on the device. The 600°C blackbody is used as the light source with an incident power $P$ of 1.24 μW. Figure 2(a) shows the I–V curves of the detector with and without a resonant cavity. At zero bias, the photocurrent ($I_{\mathrm{ph}}$) of the device with the resonant cavity is two-fold that without the cavity, which are 1.44 μA and 0.68 μA, respectively. Responsivity $R=\frac{I_{\mathrm{ph}}}{P}$ is 1.16 A/W and 0.54 A/W with and without the resonant cavities, respectively. The two-fold difference is consistent with the simulation results where the resonant cavity increases the total photon absorption of the QD film. The noise of the photodetector with a cavity is increased by a factor of 1.6 compared to the photodetector without a cavity as shown in Fig. 2(b); the measured noise of PIN homojunction detectors with and without a resonant cavity is $0.{05\mathrm{pA}\mathrm{Hz}}^{-1/2}$ and $0.03{\mathrm{pA}\mathrm{Hz}}^{-1/2}$, respectively. The 50 Hz industrial frequency interference noise may come from the test instrument. In our case, the noise spectrum is measured in the dark without an external bias, indicating the main noise is from Johnson noise and generated complex noise. The Johnson noise is related to the device dark resistance, expressed as $I_{\mathrm{Johnson}}=\sqrt{4K_{B}TB/R}$, where $K_B$ is the Boltzmann constant, $R$ the resistance, $B$ the bandwidth, and $T$ the temperature. As Fig. 2(a) shows, the slope of the dark current, which is the dark resistance, increases with the FP cavity. The increasement of dark resistance is possibly from the change of the internal electric field with the cavity, since the metal-insulator-metal layer basically forms a capacitor. Besides, the process of the SU-8 layer and additional Au layer may also slightly affect the QD layers’ property. Although the noise increases with the cavity, the specific detectivity ($D^{*}$) is calculated as $D^{*}=\frac{R\sqrt{A}}{I_n}$, where $I_n$ is the current noise, and $A$ is the area of the device.

Resonant cavity devices increase the transmission efficiency and gain of light, enhancing their detectivities, which are $4.64\times {10}^{11}$ Jones and $3.6\times {10}^{11}$ Jones for devices with and without a resonant cavity, respectively. The external quantum efficiency of the photodetector is defined as $\mathrm{EQE}=\frac{1.24R}{\lambda (\mathrm{\mu m})}$. The device can achieve an EQE of more than 57%, which is comparable to epitaxially grown HgCdTe detectors at the same wavelength. The response speed of the single-pixel detector is within 10 μs as shown in Fig. 6 (Appendix B). The spectrometer could work as high as 50 kHz with the current design.

We have prepared detectors with different CQD thicknesses to further verify the simulation results, as shown in Fig. 7 (Appendix B). The photocurrents of the homojunction resonance-enhanced CQD detectors with 300 nm, 500 nm, and 600 nm thicknesses were all increased compared to the detectors without the resonant cavity, while the 400 nm CQD thickness device exhibits the most superior performance. We also verified the I–V curves of other channels among the 256 pixels, and both the photocurrent and rectification characteristics showed high consistency, which is attributed to our fabrication method, as shown in Fig. 8 (Appendix B). Figure 2(c) shows the spectral response of detectors with and without the resonant cavity at the cut-off of 2.5 μm. The peak response of the device enhanced by the resonant cavity is nearly twice that without the cavity, which also matches our simulation. The spectral response shows two smooth absorptions. To test the model reliability, we also show that the CQD devices’ simulation results are consistent with the actual measurement response spectra at the cut-off of 2.1 μm in Fig. 9 (Appendix B).

Figure 3 shows a CQD homojunction photovoltaic array. A grating is used as a compact dispersive element, with the microscope image shown in Fig. 10 (Appendix B). The spectral reconstruction process includes learning, processing, and reconstruction stages [48,49]. The basic steps of spectrum reconstruction are as shown in Fig. 3(a), where the right figure shows the circuit diagram of the spectrometer operation. This work uses a 16-bit, 256-channel ADC with parallel sampling and current inputs, which allows for the simultaneous measurement of up to 256 channels of current signals. The physical picture is shown in Fig. 11 (Appendix B).

We outline the spectrum reconstruction process using mathematical formulations, beginning with computational methods for spectral reconstruction [13,33,50]. In spectrometer operation, $r(\lambda )$ is the normalized spectral response of our homemade photodetector, which is consistent for each pixel. $f(x_n,\lambda )$ denotes the spectral distribution of the certain light shined on the $n$th photodetector. $G(x_n)$ represents photovoltage of the $n$th photodetector under certain illumination. The function $f$ can be described as a linear combination of basic functions. Since the shape of the Gaussian function is similar to the shape of the contours of the source spectral lines, we choose the Gaussian function $u(\lambda )$ for fitting. To reduce the effect of noise, we introduce Tikhonov regularization along a generalized cross-validation approach to determine the appropriate parameters. Refer to the support information diagram for a detailed algorithm flowchart in Fig. 12 (Appendix B):$$G(x_n)={\int }_{{\lambda }_{\min }}^{{\lambda }_{\max }}r(\lambda )f(x_n,\lambda )\mathrm{d}\lambda ,n=1,2,\dots ,256,$$(1)setting the wavelength range for spectrometer operation: $$G=RF.$$(2)Here, $G$ represents the measured photovoltage, $R$ denotes the mapping matrix, and $F$ denotes the initial spectrum.

In the reconstruction process of the spectrometer described in this work, the initial step involves a learning process. The spectral distribution $f$ of a particular light beam incident on the $n$th photodetector is a function of the position $x$ and the wavelength $\lambda$. During this phase, the learning data consist of photovoltages ($G$) and the spectral distribution $f$ recorded at position ($x$) under light excitation. The photovoltage $G(x)$ is the integral of the product of the incident spectral distribution and the responsivity over the entire wavelength range ${\lambda }_{\min }\sim {\lambda }_{\max }G(x_n)={\int }_{{\lambda }_{\min }}^{{\lambda }_{\max }}r(\lambda )f(x_n,\lambda )\mathrm{d}\lambda$, where $x_n=x_1$, $x_2$,..., $x_{256}$. Figure 3(c) shows schematically the incident spectral distribution at different positions. At different positions $x$, optical voltages can be measured for each channel of the spectrometer, where each $x_n$ corresponds to a specific voltage value, as depicted in Fig. 3(b2). In this learning process, we derive a total of $n$ equations from $x_1$ to $x_n$, which can be expressed as matrix equations: $$(G(x_1),G(x_2),\cdots ,G(x_n))=(r({\lambda }_1),r({\lambda }_2),\cdots ,r({\lambda }_c))\left(\begin{array}{cccc}f(x_1,{\lambda }_1)& f(x_2,{\lambda }_1)& \cdots & f(x_n,{\lambda }_1)\\ f(x_1,{\lambda }_2)& f(x_2,{\lambda }_2)& \cdots & f(x_n,{\lambda }_2)\\ ⋮& ⋮& & ⋮\\ f(x_1,{\lambda }_c)& f(x_2,{\lambda }_c)& \cdots & f(x_n,{\lambda }_c)\end{array}\right).$$(3)

To achieve greater accuracy in $r(\lambda )$, we employ an iterative algorithm [51]. Since the photovoltage $G(x)$ is the integral of the product of the incident spectral distribution and the responsivity over the wavelength range, we display its integral result, as shown in Fig. 3(b1). Subsequently, we substitute the obtained integral result back into Eq. (1) and solve iteratively until $r(\lambda )$ stabilizes. For two adjacent spectral curves, the main difference is the band edge of the spectral response, lying mainly in the specific spectral distribution of the neighboring photodetectors. The main bodies between the two adjacent spectral curves are approximately the same, so differentiation is naturally considered to visualize more intuitively the difference between neighboring $f(x_n,\lambda )$. Here, we perform a spectral difference discretization of its two neighboring $f(x_n,\lambda )r(\lambda )$, as shown in Eq. (4). Since both sides of Eq. (4) have the same $r(\lambda )$, the spectral distribution difference map can be obtained as shown in Fig. 3(d): $$h(x_n,\lambda )r(\lambda )=f(x_{n+1},\lambda )r(\lambda )-f(x_n,\lambda )r(\lambda ).$$(4)

By solving Eq. (2), the mapping matrix $r(\lambda )$ can be obtained. Here, the response vector terminates at ${\lambda }_c$, determined by the detector. Noise present during the operation of the spectrometer may affect the reconstruction results. To solve matrix Eq. (3) and mitigate the impact of noise and errors on the reconstruction results, a reliable algorithm is necessary. Previous studies have demonstrated various reconstruction algorithms such as simulated annealing, nonnegative least squares, sparse optimization, and machine learning [52–56]. In this work, nonnegative constraint Tikhonov regularization and machine learning algorithms are employed to address these issues. In this learning process, 256 different positions are utilized to generate spectral responsivity vectors. Subsequently, the spectral mapping matrix $R$ is reconstructed from these 256 response vectors. Figure 3(c) illustrates that the spectrometer’s cut-off wavelength in this study spans approximately 1.4–2.5 μm.

Next, we used a machine learning approach. Our goal was to read the light information under different positions by spectral measurements. A training database was first created that contained datasets of photovoltaic and spectral eigenvalues from 256 detectors. The spectral data were measured using a commercial Fourier transform spectrometer (FTIR) (as shown in Figs. 13 and 14, Appendix B) [54,57–59]. The known incident data are used to train a multilayer artificial neural network (ANN), consisting of input, hidden, and output layers. We used a one-dimensional convolutional neural network followed by a fully connected network. Spectra are fed to the input layer of the network, and the hidden layer converts the input data into a form that favors the prediction of the output. Besides, in the output layer, each bit sequence is attributed to a neuron. Therefore, the input-output mapping for predicting spectral eigenvalues can be built directly by providing enough training data to the ANN. Additionally, the machine learning algorithm incorporates a feedback adjustment module. The mapping matrix $r(\lambda )$ obtained from the training dataset can be adjusted in time to further optimize the reconstructed spectra.

To achieve higher reconstruction accuracy, we conducted a deeper investigation into our reconstruction methods. The training dataset directly affects the reconstruction accuracy. By making subtle adjustments to the positions of the detector array, we can alter the light signals received by each channel of the detector array, thereby changing the information captured in each channel. So, we adjust the position of the detector arrays to obtain an additional dataset. The calculated spectra could be expressed as $f(\lambda )=\frac{1}{N}{\sum }_{i=1}^N{f}_i(\lambda )$. $N$ is the number of the detector array movement. Then the error between the calculated spectra and measured spectra could be converged with $\sqrt{N}$. In this work, we measured the responsivity of the photodetectors at new positions [denoted as $f^{\prime }(x_n,\lambda )$ and the photovoltage $g^{\prime }(x_n)$ at these positions]. More details can be found in Fig. 15 (Appendix B).

We present the spectral reconstruction process for broadband spectra, as depicted in Fig. 4. Initially, the spectral responsivity matrix $r(\lambda )$ is obtained during the learning phase, which is put into our processing chip. Then, we measured the photovoltage as a function of the position $x$. In the absence of samples, the line array optical voltages were measured at the $x$ and $x^{\prime }$ positions (respectively denoted as $\text{reference}@x$, $\text{reference}@x^{\prime }$). Then, with the sample positioned in the path of the optical beam, we again measured the photovoltage at positions $x$ and $x^{\prime }$ (denoted as $\text{sample}@x$, $\text{sample}@x^{\prime }$). These photovoltage values are functions of $x$, as illustrated in Fig. 4(a). Here, photovoltage $g(x_n)={\int }_{{\lambda }_{\min }}^{{\lambda }_{\max }}f(x_n,\lambda )·r(\lambda )\mathrm{d}\lambda$, where $r(\lambda )$ denotes the mapping matrix to be determined. Schematic spectral response curves for 256 different positions $x_n$ are shown in Fig. 4(b). Reconstruction of the unknown spectra is achieved by fitting the photocurrent data to the relationship with position $x_n$ akin to the initial learning phase.

As shown in Fig. 4(c), we compared the differences between spectra obtained from the commercial Fourier transform spectrometer and our reconstructed spectra. The dashed line corresponds to the measurement results from the commercial spectrometer, while the solid line depicts the results from our spectrometer. It is evident that our reconstruction captures all major spectral features. In addition, by expanding the channel of the detector, it is theoretically possible to obtain higher reconstruction accuracy.

In this work, we have developed a miniaturized reconstruction spectrometer. A grating is used to spatially separate the optical information. The reconstruction of the spectrum is achieved through a CQD detector line array. The performance of the device is further improved by the resonant-cavity-enhanced homojunction structure. In addition, solution processing of our detector arrays significantly reduces the complexity of epitaxial growth processing and significantly reduces device preparation costs. In the spectral reconstruction process, we use a machine learning algorithm to train the corresponding matrices and reduce the effect of noise through a regularization law. The spectrometer covers the spectral range from 1.4 to 2.5 μm and achieves high-resolution spectral reconstruction with a resolution of about 7 nm. The resolutions are comparable to those of the reported high-performance NIR miniature spectrometers (Table 1). This research proposed a new path for the development of miniaturized spectroscopic systems, which represents significant advances in spectral analysis and in practical applications.Table 1.

Comparison of NIR Spectrometers between Reported Works and This Work