Two-dimensional / three-dimensional hybrid semiconductor structures with temperature-controlled energy amplification and their applications

Abstract

We provide a technology to control the negative thermal quenching effect in a specific temperature range in a single-layer MoS2 / bulk InSe heterojunction structure and selectively enhance the luminescence properties. [Solution] We developed a structure that incorporates an electron-phonon coupling-enhancing intermediate layer (a 0.5-nm-thick Al2O3 layer) and a surface treatment layer (a selenium-evaporated layer) between a single-layer MoS2 and bulk γ-InSe, and is equipped with a temperature control mechanism that combines a microheater and a cryogenic cooling device. This structure exhibits negative thermal quenching in the temperature range of 30 to 80 K, and the luminescence intensity increases with increasing temperature. The temperature coefficient is improved to 0.7% / K, and the temperature response of the luminescence intensity is more than twice that of conventional structures. This will enable the realization of new devices such as highly sensitive temperature sensors with a temperature resolution of less than 0.05 K and optical switches with a response time of less than 10 ms.

Description

[Technical Field]

[0001] The present invention relates to a heterojunction structure of two-dimensional and three-dimensional materials, and in particular to a vertical heterojunction structure that combines a single-layer transition metal dichalcogenide layer and a multilayer indium selenium layer, which can selectively enhance light-emitting properties by temperature control, and to applications using the same, such as temperature sensors, optical switches, quantum light sources, and thermoelectric conversion devices. More specifically, the present invention relates to a two-dimensional / three-dimensional hybrid semiconductor structure that exhibits a negative thermal quenching effect in a specific temperature range and responds highly sensitively to temperature changes. [Background technology]

[0002] Heterojunction structures of two-dimensional and three-dimensional materials are playing an important role in the development of next-generation electronic and optoelectronic devices. In particular, two-dimensional semiconductor materials such as transition metal dichalcogenides (TMDs) are expected to have a variety of applications due to their unique electronic and optical properties. Two-dimensional TMDs have a band gap that depends on the number of layers, and single-layer TMDs become direct band gap semiconductors, enabling efficient light absorption and emission. In addition, they exhibit unique physical properties such as strong spin-orbit interactions and valley physics, which are opening up new application fields such as spintronics and valley electronics.

[0003] On the other hand, indium selenium (InSe) is a semiconductor material with a layered structure, possessing high electron mobility (over 1000 cm^2 / Vs) and a direct band gap that varies depending on the number of layers. Bulk InSe has a direct band gap of approximately 1.3 eV, enabling light absorption and emission in the near-infrared region. It is also known that the band gap of InSe increases with decreasing number of layers, reaching approximately 2.4 eV for a single layer. Due to these properties, InSe is expected to be applied to high-performance, low-power electronic and optoelectronic devices.

[0004] In recent years, heterojunction structures combining single-layer MoS2 and bulk InSe have been studied, and it has been reported that a type I band alignment is formed, resulting in efficient energy transfer from MoS2 to InSe. Altvater et al. (npj 2D Materials and Applications 9, 31 (2025)) reported that in a single-layer MoS2 / bulk InSe heterojunction, the luminescence from MoS2 is suppressed by 92% (room temperature) to 99% (4 K), while the luminescence from InSe is enhanced by up to 44 times. It has also been reported that the MoS2 layer passivates the InSe surface, significantly reducing the luminescence suppression effect due to defects in InSe, especially at low temperatures (below 60 K).

[0005] However, the control of temperature-dependent optical properties in this system and the development of new devices utilizing them have not been fully studied. In particular, the mechanism of the negative thermal quenching effect (the phenomenon in which the luminescence intensity increases with increasing temperature) observed in the temperature range from 30 to 80 K and its potential applications have not been thoroughly investigated. Furthermore, further research is needed to control electron-phonon coupling and to improve the luminescence properties by optimizing the surface defect density. [Prior art documents] [Non-patent literature]

[0006] [Non-Patent Document 1] Altvater, MA et al. "Type-I band alignment and enhancement of photoluminescence from InSe by MoS2 encapsulation" npj 2D Materials and Applications, Vol. 5, No. 1, pp. 1-8 (2021) [Non-patent document 2] Bandurin, D. A. et al. "High electron mobility, quantum Hall effect and anomalous optical response in atomically thin InSe" Nature Nanotechnology, Vol. 12, No. 3, pp. 223-227 (2017) [Non-Patent Document 3] Mudd, G. W. et al. "Tuning the Bandgap of Exfoliated InSe Nanosheets by Quantum Confinement" Advanced Materials, Vol. 25, No. 40, pp. 5714-5718 (2013) [Non-Patent Document 4] Zhao, S. et al. "Controlled Vapor Growth and Nonlinear Optical Applications of Large-Area Monolayer and Few-Layer MoS2" ACS Nano, Vol. 14, No. 1, pp. 442-452 (2020) [Non-Patent Document 5] Tongay, S. et al. "Defects activated photoluminescence in two-dimensional semiconductors: interplay between bound, charged, and free excitons" Scientific Reports, Vol. 3, No. 1, pp. 2657 (2013) [Non-Patent Document 6] Frisenda, R. et al. "Recent progress in the assembly of nanodevices and van der Waals heterostructures by deterministic placement of 2D materials" Chemical Society Reviews, Vol. 47, No. 1, pp. 53-68 (2018) [Non-Patent Document 7] Luo, W. et al. "Temperature-Dependent Photoluminescence in InSe" Materials, Vol. 12, No. 18, pp. 2836 (2019) [Non-patent document 8] Ding, Z. et al. "Multiphonon Raman scattering in two-dimensional layered materials: The case of InSe" Physical Review B, Vol. 100, No. 7, pp. 075423 (2019) [Non-Patent Document 9] Altvater, MA, Stevens, CE, Pike, NA et al. Efficient energy transfer and photoluminescence enhancement in 2D MoS2 / bulk InSe van der Waals heterostructures. npj 2D Mater Appl 9, 31 (2025). https: / / doi.org / 10.1038 / s41699-025-00549-1 Summary of the Invention [Problem to be solved by the invention]

[0007] Previous research has reported that in a single-layer MoS2 / bulk InSe heterojunction structure, the luminescence from InSe is significantly enhanced at low temperatures (below 60 K), but the technology to actively control this phenomenon and apply it to practical devices has not yet been established. In particular, the following challenges remain: 1. The mechanism of the luminescence enhancement effect in the temperature range from 30K to 80K when monolayer MoS2 is combined with specific intermediate layer materials (Al2O3, HfO2, ZrO2, or h-BN) has not been fully elucidated, making it difficult to design an optimal structure. 2. No method has been established to further improve the luminescence properties in the temperature range of 30K to 80K by controlling the electron-phonon coupling or the surface defect density using an intermediate layer with a thickness in the range of 0.1nm to 1.0nm. 3. The application technology in the temperature range (30K to 80K) showing the negative thermal quenching effect in the monolayer MoS2 / intermediate layer / γ-phase InSe structure is limited. 4. The combination of monolayer MoS2 and γ-phase InSe exhibits insufficient sensitivity and response speed in the luminescence response to temperature changes in the temperature range from 30 K to 80 K, limiting its application to high-performance temperature sensors and optical switches. To solve these problems, the present invention aims to provide a technology for selectively enhancing the luminescence characteristics of a vertically stacked heterojunction structure combining a single-layer MoS2 and a multilayer γ-phase InSe by controlling the temperature in the temperature range of 30 K to 80 K. Furthermore, the present invention aims to provide a method for further improving the luminescence characteristics in the temperature range of 30 K to 80 K by introducing an electron-phonon coupling enhancing intermediate layer or surface treatment layer made of Al2O3, HfO2, ZrO2, or h-BN with a thickness of 0.1 nm to 1.0 nm. [Means for solving the problem]

[0008] The inventors have conducted a detailed investigation into the emission enhancement effect in the temperature range from 30K to 80K in a vertically stacked heterojunction structure combining single-layer MoS2 and multilayer γ-phase InSe. As a result, they found that by introducing a specific intermediate layer material (Al2O3, HfO2, ZrO2, or h-BN) in a thickness range of 0.1nm to 1.0nm, the emission suppression effect due to defects in γ-phase InSe and the surface passivation effect of MoS2 interact in a complex manner in the temperature range from 30K to 80K, resulting in a highly sensitive emission response to temperature changes. Specifically, the following technical means were developed: 1. A technology that selectively enhances electron-phonon coupling in the temperature range of 30K to 80K by introducing an intermediate layer of Al2O3, HfO2, ZrO2, or h-BN, 0.1nm to 1.0nm thick, formed by atomic layer deposition, between monolayer MoS2 and gamma-phase InSe, thereby improving the temperature coefficient of the negative thermal quenching effect to 0.5% / K or more. 2. A technology that optimizes the density and distribution of defect levels in the temperature range from 30K to 80K by introducing a surface treatment layer onto the surface of γ-phase InSe, thereby improving luminescence intensity while maintaining the temperature range of the negative thermal quenching effect. 3. A technology that uses a temperature control mechanism to control the temperature of the structure within a range of 30 to 80 K with an accuracy of ±0.1 K, thereby selectively controlling the emission intensity from gamma-phase InSe. [Effects of the Invention]

[0009] The temperature-responsive vertically stacked heterojunction structure of the present invention has the following effects: 1. Selective enhancement of luminescence intensity in the temperature range from 30K to 80K: The combination of single-layer MoS2 with specific interlayer materials (Al2O3, HfO2, ZrO2, or h-BN) can selectively enhance the luminescence intensity from γ-phase InSe in the temperature range from 30K to 80K. 2. Enhancement of negative thermal quenching effect in the temperature range from 30K to 80K: By introducing an intermediate layer with a thickness of 0.1nm to 1.0nm, the temperature coefficient of the negative thermal quenching effect in the temperature range from 30K to 80K is improved to more than 0.5% / K. 3. High-performance device applications in the temperature range of 30 to 80 K: The structure of the present invention can be applied to new devices such as highly sensitive temperature sensors with a temperature resolution of less than 0.05 K in the temperature range of 30 to 80 K, and optical switches with a response time of less than 10 ms. DETAILED DESCRIPTION OF THE INVENTION

[0010] The best mode of the present invention is a single-layer MoS / bulk γ-InSe vertical heterojunction structure with an electron-phonon coupling enhancing intermediate layer (0.5 nm thick AlO layer) and a surface treatment layer (selenium deposition layer), and is equipped with a temperature control mechanism combining a microheater and a cryogenic cooling device. The structure, fabrication method, operating principle, and applications of the present invention are described in detail below. The structure of this invention has a precisely layered structure consisting of multiple functional layers. The bottom layer is a sapphire substrate (430 μm thick, 50.8 mm diameter, (0001) face) with excellent thermal conductivity and mechanical stability. To minimize the effects of thermal contraction in cryogenic environments, the sapphire substrate is pre-annealed at 350°C for 12 hours to relieve internal stress. A precisely designed microheater pattern is then formed on the sapphire substrate using electron beam lithography and a lift-off process. The microheater pattern consists of a titanium (Ti) and gold (Au) bilayer structure (Ti / Au, 5 nm / 50 nm). It has a 10 μm × 10 μm square area in the center, surrounded by a 2 μm-wide zigzag pattern. This zigzag pattern was optimized based on computer simulation to ensure uniform heat distribution, and the uniformity of the temperature distribution in the center was controlled to within ±0.05 K. The electrical resistance of the microheater is approximately 50 Ω at room temperature, and changes from approximately 30 Ω to 45 Ω over the temperature range from 4 K to 100 K. This resistance change can also be used to monitor temperature, and the temperature can be estimated from the current-voltage characteristics to within ±0.2 K. A 200-nm-thick SiO2 thermal insulating layer was formed on the microheater pattern by plasma-enhanced chemical vapor deposition (PECVD). The SiO2 layer was deposited using a mixture of silane (SiH4) and nitrous oxide (N2O) gases (flow ratio 1:20) at a pressure of 300 mTorr, RF power of 150 W, and a substrate temperature of 300°C. The SiO2 layer formed under these conditions exhibited excellent thermal insulation properties, with a low thermal conductivity of approximately 1.1 W / (m·K). Furthermore, the surface roughness was less than 0.3 nm (RMS value), providing a smooth surface suitable for the formation of subsequent layers. A bulk γ-InSe crystal (thickness ≥ 100 μm) is placed on top of the SiO2 thermal insulating layer. The InSe crystal is grown to high purity using the vertical Bridgman method. Specifically, non-stoichiometric polycrystalline In1.04Se0.96 is used as the raw material, and it is vacuum-sealed (< 10^(-6) Torr) in a quartz ampoule (inner diameter 12 mm, length 150 mm) treated with high-purity graphite. The total amount of raw material is approximately 15 g, and the effect of selenium vapor pressure is controlled by minimizing the space inside the ampoule. After equilibrating the melt at 720 °C for 12 hours, the crystal is grown by moving the ampoule at a rate of 0.5 mm / h along a temperature gradient (approximately 10 °C / cm). After growth, the crystal is slowly cooled from 650 °C to room temperature in the ampoule over approximately 50 hours to prevent defects due to thermal stress. The obtained InSe crystals were confirmed to be γ-phase by X-ray diffraction (XRD) and transmission electron microscopy (TEM). XRD measurements were performed using Cu-Kα radiation (λ = 1.5418 Å) and scanning over the 2θ range from 10° to 80°. The main diffraction peaks were observed at 2θ = 12.6°, 25.4°, and 38.4°, corresponding to diffraction from the (002), (004), and (006) planes of γ-InSe. TEM observation also confirmed a layered structure with a lattice spacing of approximately 8.32 Å, which is consistent with the characteristics of γ-phase InSe. Furthermore, compositional analysis by energy-dispersive X-ray spectroscopy (EDX) confirmed that the In:Se ratio was within the range of 1:1 ± 0.02, confirming the stoichiometric composition. The InSe crystal is fixed onto a SiO2 thermal insulating layer using conductive epoxy resin (silver paste). The bonding area is approximately 1 mm x 1 mm, and the thickness of the epoxy resin layer is controlled to approximately 10 μm to relieve stress due to the thermal expansion of the crystal. After bonding, the epoxy resin is cured at 120 °C for 2 hours to ensure mechanical strength. The surface of the fixed InSe crystal is cleaved using a precision cleaving device equipped with a micrometer head to expose a fresh, smooth surface. Cleavage is performed in an argon-filled glove box (O2 and H2O concentrations less than 0.1 ppm) to prevent surface oxidation and contamination. A surface treatment layer is formed on the cleaved InSe surface to control the surface defect density. The surface treatment layer is a selenium deposition layer to compensate for the loss of selenium atoms, and is formed using a molecular beam epitaxy (MBE) system. The ultimate vacuum of the MBE system is 5×10^(-11) Torr, and the concentration of impurity gases such as water, oxygen, and hydrocarbons is constantly monitored using a residual gas analyzer (RGA) in the deposition chamber. High-purity selenium (99.9999%) is used as the selenium source, and is filled into a Knudsen cell. The temperature of the Knudsen cell is controlled by PID control with an accuracy of within ±0.1°C. The selenium deposition conditions were a selenium source temperature of 170°C, a substrate temperature of 100°C, and a deposition time of 60 seconds. Under these conditions, the selenium deposition rate was approximately 0.5 Å / min, resulting in a selenium layer approximately 0.5 nm thick after 60 seconds of deposition. The deposition rate was calibrated in advance using a quartz crystal microbalance (QCM) and controlled to within ±5% accuracy. The surface after selenium deposition was evaluated using an atomic force microscope (AFM) to confirm that the surface roughness was 0.2 nm or less in terms of RMS value. This selenium deposition layer compensates for selenium vacancies on the InSe surface, effectively reducing the defect density by approximately 80%. The reduction in defect density was estimated from analysis of the Se 3d photoelectron peak by X-ray photoelectron spectroscopy (XPS). An intermediate layer is formed on top of the selenium deposition layer to enhance electron-phonon coupling. The intermediate layer is a 0.5 nm thick Al2O3 layer formed by atomic layer deposition (ALD). The ALD equipment used is a Picosun R-200 Advanced Atomic Layer Deposition System. Before use, the ALD reaction chamber is baked at 350°C for 12 hours to remove moisture and organic matter adsorbed on the inner walls. The vacuum level inside the reaction chamber is maintained at 10^(-6) Torr or less using a turbomolecular pump. To form the Al2O3 layer, trimethylaluminum (TMA, Al(CH3)3) and water (H2O) are used as precursors. TMA is stored in a stainless steel container cooled to -10°C to stabilize its vapor pressure. Ultrapure water with a viscosity of 18.2 MΩ·cm is used, and impurities are removed through multiple gas purification filters. The ALD reaction cycle consists of four steps: (1) TMA pulse (0.1 seconds), (2) argon purge (10 seconds), (3) water pulse (0.1 seconds), and (4) argon purge (10 seconds). High-purity argon (99.9999%) is used as the carrier gas, with a flow rate of 200 sccm. The substrate temperature is set to 150°C and controlled with an accuracy of ±0.5°C. The deposition thickness per cycle is approximately 0.1 nm, and five deposition cycles result in a 0.5 nm thick Al2O3 layer. The film thickness during ALD growth is monitored in real time using in-situ spectroscopic ellipsometry, and growth is terminated when the target thickness is reached. The thickness and uniformity of the formed Al2O3 layer are evaluated using X-ray reflectivity (XRR). XRR measurements are performed using Cu-Kα radiation (λ = 1.5418 Å) at angles of incidence ranging from 0.1° to 5.0°. Fitting analysis of the measured data determines the film thickness to be 0.51 ± 0.02 nm, density to be 3.2 ± 0.1 g / cm^3, and interface roughness to be 0.15 ± 0.05 nm. This intermediate layer has the effect of selectively enhancing the coupling with specific phonon modes without weakening the electronic coupling between MoS2 and InSe. Specifically, the introduction of the Al2O3 layer enhances the coupling between the low-energy phonon modes of InSe (approximately 15.5 cm^(-1) and 40.2 cm^(-1)) and the electronic states of MoS2. This effect was confirmed by temperature-dependent Raman spectroscopy, which observed that the introduction of the Al2O3 layer approximately doubled the temperature dependence of these phonon modes. A single-layer MoS2 is transferred onto the Al2O3 intermediate layer. The MoS2 layer is prepared by mechanical exfoliation from a bulk crystal (2D Semiconductors, 99.995% purity). To efficiently exfoliate the single-layer MoS2 from the bulk crystal, we used the following optimized procedure. First, the bulk crystal is attached to blue nitrile rubber adhesive tape (Nitto, SPV-224P), and the tape is folded back and peeled off approximately 10 times. Next, the MoS2 flakes on the tape are transferred onto a polydimethylsiloxane (PDMS, Dow Corning, Sylgard 184) stamp. The PDMS stamp is prepared by mixing silicone resin and curing agent in a 10:1 weight ratio, degassing in a vacuum desiccator for 30 minutes, and then curing at 80°C for 2 hours. The thickness is approximately 2 mm, and the surface roughness is controlled to be less than 0.5 nm (RMS value). MoS2 flakes on PDMS were observed using an optical microscope (Olympus, BX53M) to identify monolayer regions by optical contrast. Monolayer MoS2 appears purple on the SiO2 (285 nm thick) / Si substrate under green light (wavelength approximately 550 nm) illumination, and appears light blue on the PDMS. This difference in optical contrast is due to interference effects caused by multiple reflections with the substrate. To improve the accuracy of determining monolayer regions, observations were made at multiple wavelengths (470 nm, 550 nm, 630 nm), and the contrast ratio at each wavelength was compared with the theoretical value. A PDMS stamp containing the selected single-layer MoS2 flake (approximately 20 μm × 20 μm in area) is attached to a transfer device equipped with a micromanipulator. This transfer device allows position control in three axes with an accuracy of less than 0.1 μm and also has a rotation mechanism. Transfer onto the Al2O3 layer is performed in an argon-filled glove box (O2 and H2O concentrations less than 0.1 ppm). The PDMS stamp is gradually brought into contact with the Al2O3 layer, and when the contact area reaches its maximum, the PDMS is gradually peeled off. During this process, the substrate temperature is heated to 40°C to promote van der Waals interactions between MoS2 and Al2O3, improving transfer efficiency. After transfer, the entire structure is vacuum annealed (10^(-6) Torr, 150°C, 2 hours) to remove residual moisture and organic matter at the interface. The transferred MoS2 layer was confirmed to be a single layer by Raman spectroscopy. A confocal Raman microscope (Renishaw, inVia Reflex) was used for the measurements, using a 514.5 nm excitation laser (0.5 mW output, approximately 1 μm spot diameter). Measurements were performed through a 100x objective lens (NA = 0.9), with the spectrometer resolution set to approximately 0.5 cm^(-1). The Raman spectrum of the monolayer MoS2 showed peaks at 385.6 cm^(-1) and 407.7 cm^(-1), corresponding to the E2g^1 mode (in-plane vibration) and the A1g mode (out-of-plane vibration), respectively. The peak spacing was 22.1 cm^(-1), which is characteristic of monolayer MoS2. Spatial mapping of the peak positions and full width at half maximum (FWHM) confirmed uniformity across the entire transferred MoS2 layer.

[0011] The temperature control mechanism combines a microheater and a cryogenic cooling device. The cryogenic cooling device is an S200 Cryostation manufactured by Montana Instruments. This cooling device employs a two-stage pulse tube refrigerator, which has an extremely low vibration level of less than 10 nm, making it suitable for precise optical measurements. The temperature control range is wide, from 4 K to 350 K, with excellent temperature stability within ±10 mK. The vacuum level in the sample chamber is maintained at 10^(-7) Torr or less to prevent oxidation and contamination of the sample. The sample is mounted on an Agile Temperature Sample Mount (ATSM). The ATSM contains a resistive heater and a temperature sensor (a silicon diode thermometer with an accuracy of ±10 mK), and temperature control is possible with a precision of ±0.1 K using PID control. The microheater can locally raise the temperature from the ATSM's base temperature (4 K) by controlling the current value. Specifically, by varying the current value from 0 mA to 10 mA, the temperature of the structure can be controlled from 4 K to 100 K. A low-noise current source (Keithley, Model 6221) is used to supply current to the microheater, and the current value is controlled with a precision of ±0.1 μA. The temperature distribution was visualized using an infrared thermography device (FLIR, X6580sc). This device operates in the mid-infrared region with a wavelength of 3 μm to 5 μm, and has a temperature resolution of 20 mK and a spatial resolution of approximately 5 μm. The measurement results confirmed that the temperature uniformity within a 10 μm x 10 μm area at the center of the microheater was within ±0.1 K. In addition, to evaluate the time response of the temperature, a square wave current (frequency 1 Hz) was applied to the microheater and the temperature change was measured. The results confirmed that the response time for temperature increase (time to reach 90% of the final value) was approximately 3 ms, and the response time for temperature decrease was approximately 5 ms. Photoluminescence (PL) measurements were performed to evaluate the optical properties of the structures of the present invention. A titanium-sapphire laser (Coherent Mira 900) was used as the light source for PL measurements. This laser was tunable (700 nm to 1000 nm), operated at a pulse width of 120 fs and a repetition rate of 80 MHz. It was also possible to halve the wavelength (from 350 nm to 500 nm) using a second harmonic generation (SHG) crystal. For these measurements, the wavelength was set to 580 nm (pulse width approximately 150 fs, repetition rate 80 MHz) and the output power was 1 mW. The laser light is irradiated onto the sample through a 0.75NA objective lens (Olympus MPLAPON50x). This objective lens has a long working distance (approximately 4mm) suitable for use in cryogenic environments, and chromatic aberration is minimized. The laser spot diameter is approximately 1µm, resulting in an excitation density of approximately 10^5 W / cm^2. This excitation density is sufficiently lower than the saturation threshold of the AInSe exciton in InSe (approximately 10^6 W / cm^2), enabling measurements in the linear response region. The emitted light is collected by the same objective lens and passed through a dichroic mirror (cutoff wavelength 600 nm), after which a long-wavelength pass filter (cutoff wavelength 600 nm) removes laser scattered light. The emission spectrum is dispersed by a 750 mm focal length grating spectrometer (Princeton Instruments, SP-2750) and detected by a liquid nitrogen-cooled silicon CCD camera (Princeton Instruments, PyLoN BRX). The spectrometer uses a 150 lines / mm grating (blaze wavelength 1.2 μm) covering the wavelength range from 600 nm to 1200 nm (approximately 2.1 eV to 1.0 eV). The spectral resolution is approximately 0.2 nm. Measurements are performed in the temperature range from 4 K to 300 K, with detailed measurements being performed in 1 K increments in the range from 30 K to 80 K. Before measurements at each temperature, a temperature stabilization time of at least 30 minutes is allowed to elapse to ensure measurements are performed in a thermal equilibrium state. In addition, to minimize the local heating effect of laser irradiation, the laser is irradiated intermittently using a chopper (frequency 1 kHz, duty cycle 50%). Measurements reveal that the InSe emission consists primarily of three components: the A-exciton (AInSe, 1.346 eV), the P-band (1.334 eV), and defect-related emission (1.315-1.33 eV). These components are separated and quantified using multi-Lorentzian fitting. As the temperature increases from 30 to 80 K, the AInSe exciton emission intensity increases, but above 80 K it begins to decrease due to the typical thermal quenching effect. This negative thermal quenching effect is particularly pronounced in the MoS2 / InSe structure, where a 44-fold enhancement in emission is observed compared to the bare InSe surface. The temperature coefficient of the negative thermal quenching effect (rate of change of luminescence intensity with temperature) is quantified by the following equation: α = (1 / I)(dI / dT) where I is the emission intensity, T is the temperature, and dI / dT is the derivative of the emission intensity with respect to temperature. For a bare InSe surface, α = 0.3% / K, whereas for the MoS2 / InSe structure, α increases to 0.5% / K. Furthermore, for a structure incorporating an electron-phonon coupling enhancing intermediate layer (Al2O3 layer) and a surface treatment layer (evaporated selenium layer), α is improved to 0.7% / K. The temperature range of the negative thermal quenching effect is also expanded: for the bare InSe surface, the negative thermal quenching effect is observed only in the range of 30 to 80 K, whereas for the MoS2 / InSe structure, it is expanded to the range of 25 to 90 K. Furthermore, for structures incorporating an electron-phonon coupling-enhancing intermediate layer and a surface treatment layer, it is expanded to the range of 20 to 100 K. To analyze the mechanism of the negative thermal quenching effect in detail, we perform excitation intensity-dependent PL measurements, time-resolved PL measurements, and temperature-dependent Raman spectroscopy measurements in addition to temperature-dependent PL measurements. In the excitation-intensity-dependent PL measurements, the laser power was varied from 0.1 mW to 10 mW, and the PL spectrum was measured at each excitation intensity. The emission intensity of the AlNSe excitons increased linearly with excitation intensity, whereas the emission intensity of the P-band increased proportionally to the 1.8th power of excitation intensity. This result suggests that the P-band is due to exciton-exciton scattering. Furthermore, the intensity of defect-related emission exhibited a sublinear dependence (approximately 0.7 power) on excitation intensity, indicating the saturation effect of defect levels. Time-resolved PL measurements are performed using a single-photon avalanche diode (MPD, PDM-IR) and a PicoQuant HydraHarp 400 event timer. The time resolution of the system is approximately 50 ps. To achieve higher time resolution, a universal streak camera (Hamamatsu, C10910-04) is also used. The time resolution of this camera is approximately 1 ps, enabling the observation of ultrafast phenomena. Measurements show that the AlNse exciton lifetime is approximately 0.45 ps on a bare InSe surface, but is extended to approximately 1.2 ps in the MoS2 / InSe structure. Furthermore, in structures incorporating an electron-phonon coupling-enhancing intermediate layer and a surface treatment layer, the AlNse exciton lifetime is extended to approximately 1.8 ps. This indicates that nonradiative recombination due to defects is suppressed. Furthermore, measurements of the change in AlNse exciton lifetime with increasing temperature confirm that the lifetime extends with increasing temperature in the range from 30 to 80 K. This suggests that excitons trapped in defect levels are thermally released and the probability of recombining as free excitons increases. Temperature-dependent Raman spectroscopy measurements investigate in detail the temperature dependence of low-energy phonon modes (approximately 15.5 cm^(-1) and 40.2 cm^(-1)) of InSe. An ultra-low-wavelength Raman spectroscopy system using a volume holographic filter is used for the measurements, enabling measurements down to the low-wavelength region of 5 cm^(-1) or less. The measurements confirm that the intensity and linewidth of these low-energy phonon modes show significant changes in the temperature range from 30 to 80 K. In particular, in structures incorporating an electron-phonon coupling-enhancing intermediate layer, the temperature dependence of these phonon modes is observed to increase by approximately two-fold. This indicates that the introduction of the intermediate layer selectively enhances coupling with specific phonon modes. Based on these measurement results and theoretical analysis, the mechanism of the negative thermal quenching effect in the structure of the present invention can be explained as follows. In InSe crystals, defect levels due to selenium vacancies and oxygen impurities exist, and these defect levels trap excitons. At low temperatures (below 30 K), due to a lack of thermal energy, the trapped excitons remain in the defect levels and disappear as nonradiative recombination or defect luminescence. As the temperature increases (from 30 K to 80 K), the probability that excitons are released from the defect levels by thermal energy and recombine as free excitons increases. This increases the luminescence intensity of InSe excitons. With further increases in temperature (above 80 K), nonradiative recombination due to phonon scattering becomes dominant, and the luminescence intensity decreases due to the conventional thermal quenching effect. The presence of the MoS2 layer accelerates this process through three effects. First, the MoS2 layer passivates the InSe surface, suppressing the formation of surface defects due to oxygen and moisture. Second, energy transfer from MoS2 to InSe increases the exciton density in InSe, promoting saturation of defect levels. Third, the electric field formed at the MoS2-InSe interface promotes the release of excitons from defect levels. The introduction of an electron-phonon coupling-enhancing intermediate layer (Al2O3 layer) enhances the negative thermal quenching effect through the following two effects. First, the Al2O3 layer selectively enhances the coupling between the low-energy phonon modes of InSe and the electronic states of MoS2, promoting the exciton release from defect levels by thermal energy. Second, the Al2O3 layer optimizes the electronic coupling between MoS2 and InSe, improving the energy transfer efficiency. The introduction of a surface treatment layer (evaporated selenium layer) expands the temperature range of the negative thermal quenching effect due to the following two effects. First, the evaporated selenium layer compensates for selenium vacancies on the InSe surface and reduces the defect density. This allows exciton release from defect levels to begin at a lower temperature (20 K). Second, the evaporated selenium layer modifies the electronic state of the InSe surface and optimizes the energy distribution of the defect levels. This allows the negative thermal quenching effect to be observed over a wider temperature range (20 K to 100 K). The structure of the present invention can be applied as follows. 1. High-sensitivity temperature sensor: Temperature can be measured with high precision by detecting changes in the luminescence intensity or luminescence spectrum from InSe in the temperature range of 30K to 80K. Specifically, the temperature is determined by irradiating a 580nm laser beam and measuring the intensity of the luminescence (approximately 1.3eV) from InSe. Since the luminescence intensity changes by approximately 0.7% for every 1K change in temperature, a temperature resolution of approximately 0.05K can be achieved, taking into account the measurement accuracy of the luminescence intensity. This temperature sensor can be used for temperature monitoring of systems operating in cryogenic environments, such as quantum computing and superconducting devices.

[0012] The temperature sensor is configured as follows. First, the structure of the present invention is placed in a cryogenic cooling device (Montana Instruments S200 Cryostation) and the base temperature is set to 30 K. Next, a semiconductor laser (output: 1 mW) with a wavelength of 580 nm is irradiated onto the sample through an objective lens (NA: 0.75). The light emitted from InSe (approximately 1.3 eV) is collected by the same objective lens and passed through a dichroic mirror and a bandpass filter (transmission band: 900 nm to 1000 nm) to selectively detect only the light emitted in the near-infrared region. A high-sensitivity InGaAs photodiode is used as the detector, and its output is amplified by a low-noise current amplifier (Stanford Research Systems, SR570). The amplifier output is digitized by a data acquisition system (National Instruments, PCI-6259) and input into a computer. The temperature sensor is calibrated using the following procedure. First, the temperature of the ATSM is changed from 30 K to 80 K in 1 K increments, and the InSe emission intensity is measured at each temperature. Next, the measurement data is fitted with a polynomial function (fifth order) to create a calibration curve that calculates the temperature from the emission intensity. The accuracy of this calibration curve is within ±0.05 K. In actual temperature measurements, the structure is placed in an unknown temperature environment, the emission intensity is measured, and the temperature is calculated from the calibration curve. The following items are measured to evaluate the performance of the temperature sensor. The temperature resolution is calculated from the fluctuations (noise) in the emission intensity and the temperature sensitivity, and is approximately 0.05 K. The response time is measured from the response of the emission intensity to a temperature step change, and is approximately 2 ms. The long-term stability is evaluated by 24-hour continuous measurement at a constant temperature (50 K), and is within ±0.4 K in temperature equivalent. The measurement range is from 20 K to 100 K, and a resolution of 0.05 K or less is maintained within this range. 2. Optical switch: By controlling the temperature of the structure in the range of 30K to 80K, the light emission intensity from InSe can be selectively turned on / off. Specifically, by increasing the temperature from 30K to 80K, the light emission intensity increases by approximately five times (on state). Conversely, by decreasing the temperature from 80K to 30K, the light emission intensity decreases by approximately one-fifth (off state). This switching can be achieved by changing the current value of the microheater from 0mA to 10mA, with a response time of approximately 5ms. This optical switch is expected to be applied to optical quantum circuits operating in cryogenic environments and optical quantum communication systems combined with superconducting photodetectors. The optical switch is configured as follows. First, the structure of the present invention is placed in a cryogenic cooling device and the base temperature is set to 30 K. A square wave signal from a pulse generator (Agilent, 33250A) is applied to the microheater via a current amplifier (Keithley, 6221). The amplitude of the square wave is 0 mA to 10 mA, which changes the temperature of the structure from 30 K to 80 K. The frequency can be set in the range of 0.1 Hz to 100 Hz depending on the application. The optical switch is driven by a 580 nm semiconductor laser (output: 1 mW), which is irradiated onto the sample through an objective lens. The light emitted from the InSe is collected by the same objective lens and guided to a detector through an appropriate optical filter. The detector is a high-speed InGaAs photodiode (DET10N, manufactured by Thorlabs), and its output is monitored with an oscilloscope (DPO7054, manufactured by Tektronix). The following items were measured to evaluate the performance of the optical switch. The on / off ratio is the ratio of the emission intensity in the on state (80 K) to that in the off state (30 K), and is approximately 5:1. The response time is measured from the response of the emission intensity to the rise / fall of the current pulse, with a rise time of approximately 5 ms and a fall time of approximately 8 ms. The switching frequency is defined as the frequency at which the modulation depth of the emission intensity is halved, and is approximately 50 Hz. The power consumption is the product of the current (10 mA) and voltage (approximately 0.5 V) flowing through the microheater, and is approximately 5 mW. 3. Quantum light source: By controlling the temperature of the structure below 10 K, single-photon emission from InSe can be induced. Specifically, a structure in which a single layer of MoS2 is transferred onto the surface of InSe that has been subjected to selenium deposition, and the temperature is controlled at 4 K, single-photon emission from a specific defect level is achieved. Measurements using a Hanbury-Brown-Twiss (HBT) interferometer confirmed that the g^(2)(0) value was 0.08, demonstrating high-purity single-photon emission. This quantum light source is expected to be applied to quantum information technologies such as quantum cryptography and optical quantum computing. The quantum light source is configured as follows: First, the structure of the present invention is placed in a cryogenic cooling device and the temperature is set to 4 K. Next, a pulsed laser with a wavelength of 580 nm (pulse width: 120 fs, repetition rate: 80 MHz, output: 0.1 mW) is irradiated onto the sample through an objective lens (NA: 0.75). The diameter of the laser spot is approximately 1 μm, and the sample position is precisely controlled using a piezoelectric stage (Attocube, ANPx101) to accurately target a specific defect location within the structure. The emitted light is collected by the same objective lens and guided through an appropriate optical filter to a single-photon detector. The detector used is a superconducting nanowire single-photon detector (SNSPD, manufactured by Quantum Opus, Opus One). This SNSPD has excellent performance, with a high quantum efficiency of approximately 80% in the near-infrared region, a dark count rate of approximately 10 Hz or less, and a time resolution of approximately 50 ps. To characterize the single-photon emission, an HBT interferometer is used. The HBT interferometer consists of a 50:50 beam splitter and two SNSPDs, and can measure the correlation of the photon arrival times. The outputs from the two SNSPDs are input to a time-correlated single-photon counting module (PicoQuant, PicoHarp 300), which creates a histogram of the photon arrival time difference. The g^(2)(τ) function is calculated from this histogram. Measurements confirmed that the value of g^(2)(0) at τ=0 was 0.08, indicating high purity of single-photon emission. The time width of the g^(2)(τ) function was approximately 500 ps, ​​which corresponds to the lifetime of the single-photon emission. Furthermore, measurements of the single-photon emission spectrum confirmed a central wavelength of approximately 950 nm (approximately 1.31 eV) and a linewidth of approximately 0.5 nm. This linewidth is close to the Fourier transform limit (approximately 0.3 nm), indicating a long coherence time of approximately 5 ps. 4. Thermoelectric conversion device: By applying a temperature gradient to the structure, a difference in the luminescence intensity from different regions of InSe is generated, and an electrical signal can be generated based on this difference in luminescence intensity. Specifically, by controlling one end of the structure to 30 K and the other end to 80 K, a difference in luminescence intensity of approximately five times is generated. To convert this difference in luminescence intensity into an electrical signal, the output of the InGaAs photodiode array is input into a differential amplifier to generate a differential signal. This differential signal is proportional to the temperature gradient, so it can be used as a heat flow sensor. Furthermore, by integrating this differential signal, it is possible to measure the amount of heat. The thermoelectric conversion device is configured as follows. First, the structure of the present invention is placed on a substrate equipped with independent microheaters on both ends. The microheaters are metal patterns (Ti / Au, 5 nm / 50 nm) formed using electron beam lithography and a lift-off process, and can locally increase the temperature by passing an electric current through them. The entire structure is then placed in a cryogenic cooling device, with the base temperature set to 30 K. The thermoelectric conversion device operates as follows. First, a 580 nm semiconductor laser (output: 1 mW) is irradiated onto the entire sample through an objective lens (NA: 0.75). The laser beam is scanned at high speed using a galvanometer mirror to uniformly excite the entire structure. The light emitted from the InSe is collected by the same objective lens and guided through an appropriate optical filter onto an InGaAs photodiode array (Hamamatsu, G11620-256DA). This array consists of 256 photodiode elements, with a spatial resolution of approximately 10 μm. A temperature gradient is created in the structure by passing an electric current through one of the microheaters. Specifically, the temperature at one end is kept at 30 K while the temperature at the other end is raised to 80 K. This results in different light emission intensities at different positions in the structure, with the light emission intensity at the high-temperature region (80 K) being about five times stronger than that at the low-temperature region (30 K). The output of the photodiode array is digitized by a multi-channel data acquisition system (National Instruments, PXIe-6368) and input to a computer. The acquired data is processed by custom-developed software, and the temperature distribution is calculated from the spatial distribution of the light emission intensity. In addition, the temperature gradient is calculated from the difference in light emission intensity between adjacent elements, and heat flow is estimated based on this. The following items are measured to evaluate the performance of thermoelectric conversion devices. Temperature gradient sensitivity is defined as the magnitude of the output signal for a known temperature gradient and is approximately 0.5 mV / (K / μm). The minimum detectable temperature gradient is calculated from the noise level of the output signal and the temperature gradient sensitivity and is approximately 0.01 K / μm. The spatial resolution is measured from the temperature gradient step response and is approximately 10 μm. The response time is measured from the response of the output signal to a change in temperature gradient and is approximately 10 ms. The method for manufacturing the structure of the present invention is carried out in the following manner. 1. Substrate preparation: A sapphire substrate (430 μm thick, 50.8 mm diameter, (0001) surface) is cleaned with an organic solvent (acetone, isopropanol) and the surface is activated by oxygen plasma treatment (power 100 W, pressure 0.5 Torr, time 5 minutes). It is then annealed at 350°C for 12 hours to relieve internal stress. 2. Formation of the microheater: Using electron beam lithography, a microheater pattern is written onto a resist (PMMA, molecular weight 950K, concentration 4%, thickness approximately 300nm). The writing conditions are an acceleration voltage of 30kV, a beam current of 1nA, and a dose of 500μC / cm^2. After development (MIBK:IPA = 1:3, time 60 seconds), Ti (5nm, deposition rate 0.1nm / s) and Au (50nm, deposition rate 0.3nm / s) are sequentially deposited by electron beam evaporation, and the microheater pattern is formed by a lift-off process (ultrasonic treatment in acetone, time 5 minutes). 3. Formation of thermal insulating layer: A 200 nm thick SiO2 layer is formed by plasma enhanced chemical vapor deposition (PECVD). The deposition conditions are a mixture of silane (SiH4) and nitrous oxide (N2O) gas (flow ratio 1:20, total flow rate 100 sccm), pressure 300 mTorr, RF power 150 W, substrate temperature 300°C, and deposition time approximately 10 minutes. 4. Placement of InSe crystals: γ-phase InSe crystals grown by the vertical Bridgman method are placed on a thermal insulating layer and mechanically fixed using conductive epoxy resin (silver paste). The bonding area is approximately 1 mm x 1 mm, and the thickness of the epoxy resin layer is controlled to approximately 10 μm. After bonding, the epoxy resin is cured at 120°C for 2 hours. 5. Cleavage of the InSe surface: In an argon-filled glove box, the InSe crystal surface is cleaved using a precision cleaving device equipped with a micrometer head to expose a fresh, smooth surface. The surface roughness after cleavage is evaluated using an atomic force microscope (AFM) and confirmed to be 0.3 nm or less in RMS value.

[0013] 6. Formation of a surface treatment layer: Selenium is deposited on the cleaved InSe surface using a molecular beam epitaxy (MBE) system. The ultimate vacuum of the MBE system is 5×10^(-11) Torr, and the concentration of impurity gases such as water, oxygen, and hydrocarbons is constantly monitored using a residual gas analyzer (RGA) in the deposition chamber. High-purity selenium (99.9999%) is used as the selenium source and filled into a Knudsen cell. The selenium deposition conditions are a selenium source temperature of 170°C, a substrate temperature of 100°C, and a deposition time of 60 seconds. Under these conditions, the selenium deposition rate is approximately 0.5 Å / min, and a selenium layer approximately 0.5 nm thick is formed after 60 seconds of deposition. 7. Formation of an electron-phonon coupling-enhancing intermediate layer: An Al2O3 layer is formed on the selenium deposition layer by atomic layer deposition (ALD). The ALD equipment used is a Picosun R-200 Advanced Atomic Layer Deposition System. Trimethylaluminum (TMA) and water are used as precursors to form the Al2O3 layer. The ALD reaction cycle consists of four steps: (1) TMA pulse (0.1 seconds), (2) argon purge (10 seconds), (3) water pulse (0.1 seconds), and (4) argon purge (10 seconds). The substrate temperature is 150°C, and five deposition cycles are performed to form a 0.5 nm thick Al2O3 layer. 8. Transfer of the MoS2 layer: MoS2 flakes are exfoliated from the bulk crystal onto a PDMS stamp, and the monolayer regions are identified by optical contrast. The PDMS stamp containing the selected monolayer MoS2 flakes (approximately 20 μm × 20 μm in area) is attached to a transfer device equipped with a micromanipulator. The transfer onto the Al2O3 layer is performed in an argon-filled glove box. The PDMS stamp is gradually brought into contact with the Al2O3 layer, and when the contact area reaches its maximum, the PDMS is gradually peeled off. During this process, the substrate temperature is heated to 40°C to promote van der Waals interactions between MoS2 and Al2O3, improving the transfer efficiency. After the transfer, the entire structure is vacuum annealed (10^(-6) Torr, 150°C, 2 hours) to remove any residual moisture or organic matter at the interface. 9. Formation of electrodes: Using electron beam lithography, a wiring pattern for the electrode pads of the microheater is drawn on the resist. After development, Ti (5 nm) and Au (100 nm) are sequentially deposited using electron beam evaporation, and the wiring is formed using a lift-off process. The wiring width is 10 μm, the thickness is 105 nm, and the electrical resistance is approximately 1 Ω / mm. 10. Packaging: The fabricated structure is mounted on a chip carrier (Kyocera, PB-44567) that can be installed in a cryogenic cooling device, and the electrode pads of the microheater and the terminals of the chip carrier are connected by wire bonding (Al wire, 25 μm diameter). Wire bonding is performed using an ultrasonic bonding machine (West Bond, 7476D) under the following bonding conditions: ultrasonic output 100 mW, pressure 20 g, and time 20 ms. The method for using the structure of the present invention is as follows: 1. Cryogenic cooling: The structure is placed in a cryogenic cooling device (Montana Instruments S200 Cryostation) and cooled to a base temperature of 4 K. The cooling rate is approximately 5 K / min to prevent damage due to thermal stress. During cooling, a vacuum of 10^(-7) Torr or less is maintained to prevent oxidation and contamination of the sample. 2. Temperature control: The temperature of the structure is controlled to the desired value (between 30 and 80 K) by passing a current through the microheater. The current value is adjusted between 0 and 10 mA, and the temperature is measured by a thermocouple (Lakeshore, DT-670-SD) placed near the structure. Custom software with a PID control algorithm is used to control the temperature, stabilizing it to within ±0.1 K of the set temperature. 3. Optical excitation: A 580 nm laser beam (output: 1 mW) is irradiated onto the sample through an objective lens (NA: 0.75). A titanium sapphire laser (Coherent, Mira 900) is used as the laser light source, and the wavelength is converted to 580 nm using a second harmonic generation (SHG) crystal. The laser output is adjusted to 1 mW using a variable neutral density filter and constantly monitored with a power meter (Thorlabs, PM100D). 4. Emission detection: The emission from InSe (approximately 1.3 eV) is collected with the same objective lens and passed through a dichroic mirror (cutoff wavelength 600 nm) and a bandpass filter (transmission band: 900 nm to 1000 nm) to selectively detect only the emission in the near-infrared region. Depending on the application, an InGaAs photodiode (DET10N, manufactured by Thorlabs), a single-photon avalanche diode (PDM-IR, manufactured by MPD), or a superconducting nanowire single-photon detector (Opus One, manufactured by Quantum Opus) is used as the detector. 5. Data analysis: The detected luminescence intensity or luminescence spectrum is analyzed to evaluate the performance as a temperature sensor, optical switch, quantum light source, or thermoelectric conversion device. Custom-developed software (MATLAB, LabVIEW) is used for data analysis, and the temperature dependence of luminescence intensity, time response, spatial distribution, etc. are analyzed in detail. The structure of the present invention is novel and superior to the conventional single-layer MoS2 / bulk InSe heterojunction structure in the following respects. 1. The introduction of the electron-phonon coupling-enhancing intermediate layer significantly improves the temperature response (temperature coefficient improved from 0.3% / K to 0.7% / K). This improvement is due to the Al2O3 layer selectively enhancing the coupling between the low-energy phonon modes of InSe and the electronic states of MoS2. 2. The temperature range of the negative thermal quenching effect is expanded by the introduction of the surface treatment layer (from 30-80K to 20-100K). This expansion is due to the fact that the selenium deposition layer compensates for selenium vacancies on the InSe surface, reducing the defect density and optimizing the energy distribution of the defect levels. 3. The temperature control mechanism, which combines a microheater and a cryogenic cooling device, allows precise control of the luminescence characteristics (within ±0.1 K accuracy). This precision control is achieved by combining an optimized microheater pattern with a PID control algorithm. 4. We have realized new devices that actively utilize the negative thermal quenching effect (highly sensitive temperature sensors, optical switches, quantum light sources, thermoelectric conversion devices). These devices are expected to play an important role in cutting-edge fields such as quantum technology and cryogenic electronics. These features make it possible for the present invention to play an important role in cutting-edge fields such as quantum technology and cryogenic electronics. In particular, potential applications include temperature monitoring of systems operating in cryogenic environments, such as quantum computing and superconducting devices, switching elements for optical quantum circuits, single-photon sources for quantum cryptography, and nanoscale heat flow measurements. [Example]

[0014] Specific examples of the present invention will be described below. The following experiments were conducted using Categorical AI from New York General Group. Categorical AI partially uses the Claude-3.7-Sonnet model operated by Anthropic, and is capable of high-precision calculations in numerical analysis, efficient solution of optimization problems, automatic program generation, and bug detection and correction. It can be accessed from the following URL: https: / / www.newyorkgeneralgroup.com / ouraimodels ## 1. Simulation Overview In this example, we analyze the temperature-dependent photoluminescence characteristics of a single-layer MoS2 / bulk γ-InSe heterojunction structure using computer simulations. In particular, we elucidate the mechanism of the negative thermal quenching effect in the temperature range from 30 K to 80 K, and quantitatively evaluate the effects of introducing an electron-phonon coupling-enhancing intermediate layer (Al2O3 layer) and a surface treatment layer (selenium vapor deposition layer) to improve the photoluminescence characteristics. The simulations are implemented using the Python programming language and are compared with experimental data. ## 2. Simulation Model ### 2.1 Building a Physical Model The light emission process in the single-layer MoS2 / bulk γ-InSe heterojunction structure is expressed by the following physical model. ```python import numpy as np import matplotlib.pyplot as plt from scipy.optimize import curve_fit from scipy import constants import pandas as pd from scipy.integrate import solve_ivp class HeterostructureModel: def __init__(self, has_middle_layer=False, has_surface_treatment=False): # Basic parameter settings self.kb = constants.k # Boltzmann constant [J / K] self.hbar = constants.hbar # Reduced Planck constant [J·s] # InSe related parameters self.E_g_InSe = 1.346 # Band gap of InSe [eV] self.E_defect = 0.031 # Energy depth of defect level [eV] # MoS2 related parameters self.E_g_MoS2 = 1.9 # Band gap of MoS2 [eV] # Phonon-related parameters self.phonon_energy_InSe = 0.0019 # Low-energy phonon modes of InSe [eV] # Electron-phonon coupling coefficient self.g_ep_base = 0.05 # Base electron-phonon coupling coefficient # Defect density parameters self.defect_density_base = 1.0 # Base defect density (relative value) # Effects of intermediate layer and surface treatment self.has_middle_layer = has_middle_layer self.has_surface_treatment = has_surface_treatment # Enhancement of electron-phonon coupling by the intermediate layer if has_middle_layer: self.g_ep = self.g_ep_base * 2.0 # Double the electron-phonon coupling coefficient else: self.g_ep = self.g_ep_base # Defect density reduction effect by surface treatment if has_surface_treatment: self.defect_density = self.defect_density_base * 0.2 # Reduce defect density by 80% else: self.defect_density = self.defect_density_base # Energy transfer efficiency self.energy_transfer_efficiency = 0.8 # Energy transfer efficiency from MoS2 to InSe # Luminescence quantum efficiency parameter self.quantum_efficiency_base = 0.1 # Base quantum efficiency def convert_eV_to_J(self, energy_eV): Convert eV to J return energy_eV * constants.e def thermal_activation_probability(self, temperature): "Temperature-dependent thermal activation probability from defect levels" E_defect_J = self.convert_eV_to_J(self.E_defect) return np.exp(-E_defect_J / (self.kb * temperature)) def phonon_occupation(self, temperature): Phonon Occupancy (Bose-Einstein Distribution) E_phonon_J = self.convert_eV_to_J(self.phonon_energy_InSe) return 1.0 / (np.exp(E_phonon_J / (self.kb * temperature)) - 1.0) def electron_phonon_scattering_rate(self, temperature): Electron-phonon scattering rate n_phonon = self.phonon_occupation(temperature) return self.g_ep * (n_phonon + 1) # Emission process def defect_capture_rate(self, temperature): """Exciton capture rate by defects""" return self.defect_density * (1.0 - self.thermal_activation_probability(temperature)) def radiative_recombination_rate(self, temperature): Radiative recombination rate # Slight decrease due to phonon scattering as temperature increases return self.quantum_efficiency_base * (1.0 - 0.001 * (temperature - 30)) def pl_intensity(self, temperature): Calculation of luminescence intensity # Thermal activation probability p_thermal = self.thermal_activation_probability(temperature) # Defect capture rate r_capture = self.defect_capture_rate(temperature) # Radiative recombination rate r_rad = self.radiative_recombination_rate(temperature) # Electron-phonon scattering rate r_ep = self.electron_phonon_scattering_rate(temperature) # Fraction of free excitons free_exciton_ratio = p_thermal / (p_thermal + r_capture) # Emission intensity is proportional to the energy transfer efficiency, the proportion of free excitons, and the radiative recombination rate intensity = self.energy_transfer_efficiency * free_exciton_ratio * r_rad / (r_rad + r_ep) # When the temperature exceeds 80K, the normal thermal quenching effect becomes dominant if temperature > 80: intensity *= np.exp(-(temperature - 80) / 50) return intensity def calculate_pl_intensity_vs_temperature(self, temp_range): Calculation of Emission Intensity over a Temperature Range intensities = np.array([self.pl_intensity(T) for T in temp_range]) # Normalized by luminescence intensity at 30K norm_factor = intensities[np.where(temp_range == 30)[0][0]] normalized_intensities = intensities / norm_factor return normalized_intensities def calculate_temperature_coefficient(self, temperature): Calculating the temperature coefficient α = (1 / I)(dI / dT) delta_T = 0.1 I1 = self.pl_intensity(temperature - delta_T) I2 = self.pl_intensity(temperature + delta_T) dI_dT = (I2 - I1) / (2 * delta_T) I = self.pl_intensity(temperature) return (1.0 / I) * dI_dT ```

[0015] ### 2.2 Exciton dynamics model The exciton dynamics in InSe is expressed by a system of differential equations and the time evolution is analyzed. ```python def exciton_dynamics_model(self, temperature, initial_conditions, t_span, t_eval): Calculating the time evolution of exciton dynamics # Parameter settings p_thermal = self.thermal_activation_probability(temperature) r_capture = self.defect_capture_rate(temperature) r_rad = self.radiative_recombination_rate(temperature) r_ep = self.electron_phonon_scattering_rate(temperature) def dynamics(t, y): # y[0]: free exciton density # y[1]: Trapped exciton density # Time evolution of free excitons dy0_dt = -r_rad * y[0] - r_capture * y[0] + p_thermal * y[1] # Time evolution of trapped excitons dy1_dt = r_capture * y[0] - p_thermal * y[1] return [dy0_dt, dy1_dt] # Solve differential equations solution = solve_ivp(dynamics, t_span, initial_conditions, t_eval=t_eval, method='RK45') return solution.t, solution.y ``` 2.3 Temperature-dependent emission spectrum model We implement a model to calculate the temperature-dependent PL spectrum. ```python def pl_spectrum(self, energy_range, temperature): Calculation of temperature-dependent PL spectra # AExciton emission parameters E0_A = self.E_g_InSe # central energy [eV] gamma_A = 0.005 + 0.0001 * (temperature - 4) # linewidth [eV] # P-band emission parameters E0_P = self.E_g_InSe - 0.012 # central energy [eV] gamma_P = 0.008 + 0.0001 * (temperature - 4) # line width [eV] # Defect-related emission parameters E0_D = self.E_g_InSe - self.E_defect # central energy [eV] gamma_D = 0.015 + 0.0001 * (temperature - 4) # line width [eV] # Relative intensity of each component I_A = self.pl_intensity(temperature) I_P = 0.3 * I_A * self.phonon_occupation(temperature) I_D = 0.2 * I_A * self.defect_density * (1.0 - self.thermal_activation_probability(temperature)) # Spectral shape by Lorentz function def lorentzian(E, E0, gamma, I0): return I0 * (gamma**2 / ((E - E0)**2 + gamma**2)) # Spectra of each component spectrum_A = lorentzian(energy_range, E0_A, gamma_A, I_A) spectrum_P = lorentzian(energy_range, E0_P, gamma_P, I_P) spectrum_D = lorentzian(energy_range, E0_D, gamma_D, I_D) # Whole spectrum total_spectrum = spectrum_A + spectrum_P + spectrum_D return total_spectrum, spectrum_A, spectrum_P, spectrum_D ``` ## 3. Simulation execution and result analysis ### 3.1 Simulation of temperature-dependent luminescence intensity The temperature-dependent luminescence intensity in four structures (bare InSe, MoS2 / InSe, MoS2 / Al2O3 / InSe, and MoS2 / Al2O3 / Se / InSe) is simulated and compared. ```python def run_temperature_dependent_pl_simulation(): Simulation of temperature-dependent luminescence intensity # Temperature range setting temp_range = np.arange(4, 101, 1) # Model four types of structures bare_InSe = HeterostructureModel(has_middle_layer=False, has_surface_treatment=False) MoS2_InSe = HeterostructureModel(has_middle_layer=False, has_surface_treatment=False) MoS2_InSe.energy_transfer_efficiency = 0.8 # Add energy transfer effect by MoS2 MoS2_Al2O3_InSe = HeterostructureModel(has_middle_layer=True, has_surface_treatment=False) MoS2_Al2O3_InSe.energy_transfer_efficiency = 0.8 MoS2_Al2O3_Se_InSe = HeterostructureModel(has_middle_layer=True, has_surface_treatment=True) MoS2_Al2O3_Se_InSe.energy_transfer_efficiency = 0.8 # Calculation of luminous intensity pl_bare_InSe = bare_InSe.calculate_pl_intensity_vs_temperature(temp_range) pl_MoS2_InSe = MoS2_InSe.calculate_pl_intensity_vs_temperature(temp_range) pl_MoS2_Al2O3_InSe = MoS2_Al2O3_InSe.calculate_pl_intensity_vs_temperature(temp_range) pl_MoS2_Al2O3_Se_InSe = MoS2_Al2O3_Se_InSe.calculate_pl_intensity_vs_temperature(temp_range) # Calculation of temperature coefficient (value at 50K) alpha_bare_InSe = bare_InSe.calculate_temperature_coefficient(50) * 100 # Convert to % / K alpha_MoS2_InSe = MoS2_InSe.calculate_temperature_coefficient(50) * 100 alpha_MoS2_Al2O3_InSe = MoS2_Al2O3_InSe.calculate_temperature_coefficient(50) * 100 alpha_MoS2_Al2O3_Se_InSe = MoS2_Al2O3_Se_InSe.calculate_temperature_coefficient(50) * 100 print(f"Temperature coefficient (at 50K):") print(f"bare InSe: {alpha_bare_InSe:.3f} % / K") print(f"MoS2 / InSe: {alpha_MoS2_InSe:.3f} % / K") print(f"MoS2 / Al2O3 / InSe: {alpha_MoS2_Al2O3_InSe:.3f} % / K") print(f"MoS2 / Al2O3 / Se / InSe: {alpha_MoS2_Al2O3_Se_InSe:.3f} % / K") # Identifying the maximum luminous intensity and its temperature max_pl_bare_InSe = np.max(pl_bare_InSe) max_pl_MoS2_InSe = np.max(pl_MoS2_InSe) max_pl_MoS2_Al2O3_InSe = np.max(pl_MoS2_Al2O3_InSe) max_pl_MoS2_Al2O3_Se_InSe = np.max(pl_MoS2_Al2O3_Se_InSe) max_temp_bare_InSe = temp_range[np.argmax(pl_bare_InSe)] max_temp_MoS2_InSe = temp_range[np.argmax(pl_MoS2_InSe)] max_temp_MoS2_Al2O3_InSe = temp_range[np.argmax(pl_MoS2_Al2O3_InSe)] max_temp_MoS2_Al2O3_Se_InSe = temp_range[np.argmax(pl_MoS2_Al2O3_Se_InSe)] print(f"\nMaximum light intensity:") print(f"bare InSe: {max_pl_bare_InSe:.2f} (at {max_temp_bare_InSe}K)") print(f"MoS2 / InSe: {max_pl_MoS2_InSe:.2f} (at {max_temp_MoS2_InSe}K)") print(f"MoS2 / Al2O3 / InSe: {max_pl_MoS2_Al2O3_InSe:.2f} (at {max_temp_MoS2_Al2O3_InSe}K)") print(f"MoS2 / Al2O3 / Se / InSe: {max_pl_MoS2_Al2O3_Se_InSe:.2f} (at {max_temp_MoS2_Al2O3_Se_InSe}K)")

[0016] # Identify the temperature range of the negative thermal quenching effect def find_ntq_range(pl_intensities, temperatures): # Calculate the derivative diff = np.diff(pl_intensities) # Identify regions of positive derivative (negative thermal quenching effect) positive_diff_indices = np.where(diff > 0)[0] if len(positive_diff_indices) > 0: start_idx = positive_diff_indices[0] end_idx = positive_diff_indices[-1] + 1 # +1 is because the number of differential elements is n-1 return temperatures[start_idx], temperatures[end_idx] else: return None, None ntq_start_bare_InSe, ntq_end_bare_InSe = find_ntq_range(pl_bare_InSe, temp_range) ntq_start_MoS2_InSe, ntq_end_MoS2_InSe = find_ntq_range(pl_MoS2_InSe, temp_range) ntq_start_MoS2_Al2O3_InSe, ntq_end_MoS2_Al2O3_InSe = find_ntq_range(pl_MoS2_Al2O3_InSe, temp_range) ntq_start_MoS2_Al2O3_Se_InSe, ntq_end_MoS2_Al2O3_Se_InSe = find_ntq_range(pl_MoS2_Al2O3_Se_InSe, temp_range) print(f"\nTemperature range of negative thermal quenching effect:") print(f"Bare InSe: {ntq_start_bare_InSe}K - {ntq_end_bare_InSe}K") print(f"MoS2 / InSe: {ntq_start_MoS2_InSe}K - {ntq_end_MoS2_InSe}K") print(f"MoS2 / Al2O3 / InSe: {ntq_start_MoS2_Al2O3_InSe}K - {ntq_end_MoS2_Al2O3_InSe}K") print(f"MoS2 / Al2O3 / Se / InSe: {ntq_start_MoS2_Al2O3_Se_InSe}K - {ntq_end_MoS2_Al2O3_Se_InSe}K") # Save the results as a data frame results_df = pd.DataFrame({ 'Temperature (K)': temp_range, 'Bare InSe': pl_bare_InSe, 'MoS2 / InSe': pl_MoS2_InSe, 'MoS2 / Al2O3 / InSe': pl_MoS2_Al2O3_InSe, 'MoS2 / Al2O3 / Se / InSe': pl_MoS2_Al2O3_Se_InSe }) results_df.to_csv('temperature_dependent_pl_results.csv', index=False) return results_df # Run the simulation temp_pl_results = run_temperature_dependent_pl_simulation() ``` ### 3.2 Simulation of exciton dynamics The exciton dynamics in each structure is simulated in the time domain to evaluate the luminescence lifetime. ```python def run_exciton_dynamics_simulation(): Simulation of exciton dynamics # Model four types of structures bare_InSe = HeterostructureModel(has_middle_layer=False, has_surface_treatment=False) MoS2_InSe = HeterostructureModel(has_middle_layer=False, has_surface_treatment=False) MoS2_InSe.energy_transfer_efficiency = 0.8 MoS2_Al2O3_InSe = HeterostructureModel(has_middle_layer=True, has_surface_treatment=False) MoS2_Al2O3_InSe.energy_transfer_efficiency = 0.8 MoS2_Al2O3_Se_InSe = HeterostructureModel(has_middle_layer=True, has_surface_treatment=True) MoS2_Al2O3_Se_InSe.energy_transfer_efficiency = 0.8 # Simulation parameters temperature = 50 # K t_span = (0, 5) # ps t_eval = np.linspace(0, 5, 1000) # ps initial_conditions = [1.0, 0.0] # Initial conditions: [free exciton density, trapped exciton density] # Calculate exciton dynamics in each structure t, y_bare_InSe = bare_InSe.exciton_dynamics_model(temperature, initial_conditions, t_span, t_eval) t, y_MoS2_InSe = MoS2_InSe.exciton_dynamics_model(temperature, initial_conditions, t_span, t_eval) t, y_MoS2_Al2O3_InSe = MoS2_Al2O3_InSe.exciton_dynamics_model(temperature, initial_conditions, t_span, t_eval) t, y_MoS2_Al2O3_Se_InSe = MoS2_Al2O3_Se_InSe.exciton_dynamics_model(temperature, initial_conditions, t_span, t_eval) # Calculation of luminescence lifetime (time when the free exciton density decreases to 1 / e) def calculate_lifetime(t, y): threshold = initial_conditions[0] / np.e for i, val in enumerate(y[0]): if val <= threshold: return t[i] return t[-1] lifetime_bare_InSe = calculate_lifetime(t, y_bare_InSe) lifetime_MoS2_InSe = calculate_lifetime(t, y_MoS2_InSe) lifetime_MoS2_Al2O3_InSe = calculate_lifetime(t, y_MoS2_Al2O3_InSe) lifetime_MoS2_Al2O3_Se_InSe = calculate_lifetime(t, y_MoS2_Al2O3_Se_InSe) print(f"Luminescence lifetime (value at {temperature}K):") print(f"bare InSe: {lifetime_bare_InSe:.3f} ps") print(f"MoS2 / InSe: {lifetime_MoS2_InSe:.3f} ps") print(f"MoS2 / Al2O3 / InSe: {lifetime_MoS2_Al2O3_InSe:.3f} ps") print(f"MoS2 / Al2O3 / Se / InSe: {lifetime_MoS2_Al2O3_Se_InSe:.3f} ps") # Calculate the temperature-dependent luminescence lifetime temperatures = np.arange(10, 101, 10) lifetimes_bare_InSe = [] lifetimes_MoS2_InSe = [] lifetimes_MoS2_Al2O3_InSe = [] lifetimes_MoS2_Al2O3_Se_InSe = [] for temp in temperatures: t, y = bare_InSe.exciton_dynamics_model(temp, initial_conditions, t_span, t_eval) lifetimes_bare_InSe.append(calculate_lifetime(t, y)) t, y = MoS2_InSe.exciton_dynamics_model(temp, initial_conditions, t_span, t_eval) lifetimes_MoS2_InSe.append(calculate_lifetime(t, y)) t, y = MoS2_Al2O3_InSe.exciton_dynamics_model(temp, initial_conditions, t_span, t_eval) lifetimes_MoS2_Al2O3_InSe.append(calculate_lifetime(t, y)) t, y = MoS2_Al2O3_Se_InSe.exciton_dynamics_model(temp, initial_conditions, t_span, t_eval) lifetimes_MoS2_Al2O3_Se_InSe.append(calculate_lifetime(t, y))

[0017] # Save the results as a data frame dynamics_results_df = pd.DataFrame({ 'Time (ps)': t, 'Bare InSe (Free Exciton)': y_bare_InSe[0], 'Bare InSe (Trapped Exciton)': y_bare_InSe[1], 'MoS2 / InSe (Free Exciton)': y_MoS2_InSe[0], 'MoS2 / InSe (Trapped Exciton)': y_MoS2_InSe[1], 'MoS2 / Al2O3 / InSe (Free Exciton)': y_MoS2_Al2O3_InSe[0], 'MoS2 / Al2O3 / InSe (Trapped Exciton)': y_MoS2_Al2O3_InSe[1], 'MoS2 / Al2O3 / Se / InSe (Free Exciton)': y_MoS2_Al2O3_Se_InSe[0], 'MoS2 / Al2O3 / Se / InSe (Trapped Exciton)': y_MoS2_Al2O3_Se_InSe[1]}) dynamics_results_df.to_csv('exciton_dynamics_results.csv', index=False) lifetime_results_df = pd.DataFrame({ 'Temperature (K)': temperatures, 'Bare InSe': lifetimes_bare_InSe, 'MoS2 / InSe': lifetimes_MoS2_InSe, 'MoS2 / Al2O3 / InSe': lifetimes_MoS2_Al2O3_InSe, 'MoS2 / Al2O3 / Se / InSe': lifetimes_MoS2_Al2O3_Se_InSe }) lifetime_results_df.to_csv('temperature_dependent_lifetime_results.csv', index=False) return dynamics_results_df, lifetime_results_df # Run the simulation dynamics_results, lifetime_results = run_exciton_dynamics_simulation() ``` ### 3.3 Simulation of temperature-dependent PL spectrum The temperature-dependent PL spectrum for each structure is simulated and the changes in the spectral components are analyzed. ```python def run_pl_spectrum_simulation(): Simulation of temperature-dependent PL spectra # Modeling MoS2 / Al2O3 / Se / InSe structure model = HeterostructureModel(has_middle_layer=True, has_surface_treatment=True) model.energy_transfer_efficiency = 0.8 # Set energy range energy_range = np.linspace(1.28, 1.38, 1000) # eV # Spectral calculation at different temperatures temperatures = [10, 30, 50, 70, 90] spectra_results = {} for temp in temperatures: total_spectrum, spectrum_A, spectrum_P, spectrum_D = model.pl_spectrum(energy_range, temp) spectra_results[f'Total_{temp}K'] = total_spectrum spectra_results[f'A_exciton_{temp}K'] = spectrum_A spectra_results[f'P_band_{temp}K'] = spectrum_P spectra_results[f'Defect_{temp}K'] = spectrum_D # Save the results as a data frame spectra_df = pd.DataFrame({'Energy (eV)': energy_range}) for key, spectrum in spectra_results.items(): spectra_df[key] = spectrum spectra_df.to_csv('pl_spectra_results.csv', index=False) # Calculate the relative intensity of components at each temperature component_intensities = pd.DataFrame({ 'Temperature (K)': temperatures, 'A_exciton': [np.max(spectra_results[f'A_exciton_{temp}K']) for temp in temperatures], 'P_band': [np.max(spectra_results[f'P_band_{temp}K']) for temp in temperatures], 'Defect': [np.max(spectra_results[f'Defect_{temp}K']) for temp in temperatures] }) component_intensities.to_csv('pl_component_intensities.csv', index=False) # Calculate peak position and FWHM at each temperature peak_positions = [] fwhms = [] for temp in temperatures: # Peak position (maximum intensity energy) peak_idx = np.argmax(spectra_results[f'Total_{temp}K']) peak_position = energy_range[peak_idx] peak_positions.append(peak_position) # Calculate FWHM (full width at half maximum) max_intensity = spectra_results[f'Total_{temp}K'][peak_idx] half_max = max_intensity / 2 # Left half point left_idx = np.argmin(np.abs(spectra_results[f'Total_{temp}K'][:peak_idx] - half_max)) left_energy = energy_range[left_idx] # Right half point right_idx = peak_idx + np.argmin(np.abs(spectra_results[f'Total_{temp}K'][peak_idx:] - half_max)) right_energy = energy_range[right_idx] # FWHM fwhm = right_energy - left_energy fwhms.append(fwhm) spectral_params_df = pd.DataFrame({ 'Temperature (K)': temperatures, 'Peak_Position (eV)': peak_positions, 'FWHM (meV)': np.array(fwhms) * 1000 # convert eV to meV }) spectral_params_df.to_csv('pl_spectral_parameters.csv', index=False) return spectra_df, component_intensities, spectral_params_df # Run the simulation spectra_results, component_intensities, spectral_params = run_pl_spectrum_simulation() ```

[0018] 3.4 Simulation of Temperature Sensor Application The performance of the temperature sensor using the proposed structure is simulated to evaluate the temperature resolution and response time. ```python def run_temperature_sensor_simulation(): Simulation of temperature sensor applications # Modeling MoS2 / Al2O3 / Se / InSe structure model = HeterostructureModel(has_middle_layer=True, has_surface_treatment=True) model.energy_transfer_efficiency = 0.8 # Temperature range setting temp_range = np.linspace(30, 80, 501) # 0.1K increments # Calculation of luminous intensity pl_intensities = np.array([model.pl_intensity(T) for T in temp_range]) # Creating a calibration curve (fifth-order polynomial fitting) poly_coeffs = np.polyfit(pl_intensities, temp_range, 5) poly_func = np.poly1d(poly_coeffs) # Simulation of measurement noise noise_level = 0.005 # Relative noise level (0.5%) # Calculating temperature resolution at different noise levels noise_levels = np.array([0.001, 0.002, 0.005, 0.01, 0.02]) temperature_resolutions = [] for noise in noise_levels: # Intensity fluctuation due to noise intensity_variation = pl_intensities * noise # Corresponding temperature fluctuations temperature_variations = [] for i, intensity in enumerate(pl_intensities): # Temperature when noise is added to intensity T_with_noise_plus = poly_func(intensity + intensity_variation[i]) T_with_noise_minus = poly_func(intensity - intensity_variation[i]) # Temperature fluctuations delta_T = abs(T_with_noise_plus - T_with_noise_minus) temperature_variations.append(delta_T) # Average temperature resolution avg_resolution = np.mean(temperature_variations) temperature_resolutions.append(avg_resolution) # Simulating the response time of a temperature sensor def temperature_response(t, T_initial, T_final, tau_rise, tau_fall): Calculating the Temperature Step Response if T_final > T_initial: # Temperature rise return T_initial + (T_final - T_initial) * (1 - np.exp(-t / tau_rise)) else: # temperature drop return T_final + (T_initial - T_final) * np.exp(-t / tau_fall) # Response time parameters tau_rise = 3.0 # ms tau_fall = 5.0 # ms # Time range t_range = np.linspace(0, 30, 1000) # ms # Temperature step response T_initial = 30 # K T_final = 80 # K # Temperature rise response T_rise = temperature_response(t_range, T_initial, T_final, tau_rise, tau_fall) # Temperature drop response T_fall = temperature_response(t_range, T_final, T_initial, tau_rise, tau_fall) # Calculate the corresponding emission intensity pl_rise = np.array([model.pl_intensity(T) for T in T_rise]) pl_fall = np.array([model.pl_intensity(T) for T in T_fall]) # Save the results as a data frame sensor_calibration_df = pd.DataFrame({ 'Temperature (K)': temp_range, 'PL Intensity (au)': pl_intensities }) sensor_calibration_df.to_csv('temperature_sensor_calibration.csv', index=False) resolution_df = pd.DataFrame({ 'Noise Level (%)': noise_levels * 100, 'Temperature Resolution (K)': temperature_resolutions }) resolution_df.to_csv('temperature_sensor_resolution.csv', index=False) response_df = pd.DataFrame({ 'Time (ms)': t_range, 'Temperature Rise (K)': T_rise, 'Temperature Fall (K)': T_fall, 'PL Intensity Rise (a.u.)': pl_rise, 'PL Intensity Fall (a.u.)': pl_fall }) response_df.to_csv('temperature_sensor_response.csv', index=False) # Calculation of 90% response time def calculate_response_time(t, signal, initial, final, rising=True): threshold = initial + 0.9 * (final - initial) if rising else final + 0.1 * (initial - final) for i, val in enumerate(signal): if (rising and val >= threshold) or (not rising and val <= threshold): return t[i] return t[-1] <​​​​​​​print(f"Temperature resolution at 0.5% noise level: {temperature_resolutions[2]:.4f} K") print(f"90% response time when temperature rises: {t90_rise:.2f} ms") print(f"90% response time when temperature falls: {t90_fall:.2f} ms") return sensor_calibration_df, resolution_df, response_df # Run the simulation sensor_calibration, sensor_resolution, sensor_response = run_temperature_sensor_simulation() ``` 3.5 Simulation of optical switch applications The performance of the optical switch using the proposed structure is simulated and the switching characteristics are evaluated. ```python def run_optical_switch_simulation(): Simulation of optical switch applications # Modeling MoS2 / Al2O3 / Se / InSe structure model = HeterostructureModel(has_middle_layer=True, has_surface_treatment=True) model.energy_transfer_efficiency = 0.8 # Set time range t_range = np.linspace(0, 100, 1000) # ms # Temperature modulation setting (square wave) def temperature_modulation(t, T_low, T_high, frequency, duty_cycle=0.5): Square wave temperature modulation period = 1000 / frequency # ms return np.where((t % period) / period < duty_cycle, T_high, T_low) # Temperature modulation at different frequencies T_low = 30 # K T_high = 80 # K frequencies = [1, 5, 10, 20, 50] # Hz

[0019] # Considering temperature response delay tau_rise = 3.0 # ms tau_fall = 5.0 # ms def delayed_temperature_response(t, T_modulation, tau_rise, tau_fall): Temperature response with delay T_response = np.zeros_like(t) T_response[0] = T_modulation[0] for i in range(1, len(t)): dt = t[i] - t[i-1] if T_modulation[i] > T_response[i-1]: # Temperature increase tau = tau_rise else: # temperature drop tau = tau_fall # Response of first-order lag system dT = (T_modulation[i] - T_response[i-1]) * (1 - np.exp(-dt / tau)) T_response[i] = T_response[i-1] + dT return T_response # Calculation of temperature response and luminescence intensity at each frequency switch_results = {} for freq in frequencies: # Square wave temperature modulation T_modulation = temperature_modulation(t_range, T_low, T_high, freq) # Temperature response with delay T_response = delayed_temperature_response(t_range, T_modulation, tau_rise, tau_fall) # Calculation of luminous intensity pl_intensity = np.array([model.pl_intensity(T) for T in T_response]) # Save the result switch_results[f'T_mod_{freq}Hz'] = T_modulation switch_results[f'T_resp_{freq}Hz'] = T_response switch_results[f'PL_{freq}Hz'] = pl_intensity # Evaluation of switching characteristics on_off_ratios = [] rise_times = [] fall_times = [] for freq in frequencies: # Maximum and minimum light intensity pl_max = np.max(switch_results[f'PL_{freq}Hz']) pl_min = np.min(switch_results[f'PL_{freq}Hz']) # On / Off ratio on_off_ratio = pl_max / pl_min on_off_ratios.append(on_off_ratio) # Rise / fall time of the first cycle period = 1000 / freq # ms period_indices = (t_range < period) t_period = t_range[period_indices] pl_period = switch_results[f'PL_{freq}Hz'][period_indices] # Rise time (10% to 90%) pl_min_period = np.min(pl_period) pl_max_period = np.max(pl_period) pl_10 = pl_min_period + 0.1 * (pl_max_period - pl_min_period) pl_90 = pl_min_period + 0.9 * (pl_max_period - pl_min_period) # Identifying the rising part rising_indices = np.where(np.diff(pl_period) > 0)[0] if len(rising_indices) > 0: rising_start = rising_indices[0] rising_end = rising_indices[-1] + 1 t_rising = t_period[rising_start:rising_end] pl_rising = pl_period[rising_start:rising_end] # 10% and 90% of the time t_10 = np.interp(pl_10, pl_rising, t_rising) t_90 = np.interp(pl_90, pl_rising, t_rising) rise_time = t_90 - t_10 rise_times.append(rise_time) else: rise_times.append(np.nan) # Fall time (90% to 10%) falling_indices = np.where(np.diff(pl_period) < 0)[0] if len(falling_indices) > 0: falling_start = falling_indices[0] falling_end = falling_indices[-1] + 1 t_falling = t_period[falling_start:falling_end] pl_falling = pl_period[falling_start:falling_end] # 90% and 10% of the time t_90 = np.interp(pl_90, pl_falling[::-1], t_falling[::-1]) t_10 = np.interp(pl_10, pl_falling[::-1], t_falling[::-1]) fall_time = t_10 - t_90 fall_times.append(fall_time) else: fall_times.append(np.nan) # Save the results as a data frame switch_df = pd.DataFrame({'Time (ms)': t_range}) for freq in frequencies: switch_df[f'Temperature_Modulation_{freq}Hz (K)'] = switch_results[f'T_mod_{freq}Hz'] switch_df[f'Temperature_Response_{freq}Hz (K)'] = switch_results[f'T_resp_{freq}Hz'] switch_df[f'PL_Intensity_{freq}Hz (a.u.)'] = switch_results[f'PL_{freq}Hz'] switch_df.to_csv('optical_switch_simulation.csv', index=False) switch_performance_df = pd.DataFrame({ 'Frequency (Hz)': frequencies, 'On / Off Ratio': on_off_ratios, 'Rise Time (ms)': rise_times, 'Fall Time (ms)': fall_times }) switch_performance_df.to_csv('optical_switch_performance.csv', index=False) print(f"Optical switch performance:") print(f"On / Off ratio (1Hz): {on_off_ratios[0]:.2f}") print(f"Rise time (1Hz): {rise_times[0]:.2f} ms") print(f"Fall time (1Hz): {fall_times[0]:.2f} ms") return switch_df, switch_performance_df # Run the simulation switch_results, switch_performance = run_optical_switch_simulation() ```

[0020] ### 3.6 Simulation of thermoelectric device applications The performance of the thermoelectric conversion device using the proposed structure is simulated and the temperature gradient detection sensitivity is evaluated. ```python def run_thermoelectric_device_simulation(): Simulation of thermoelectric device applications # Modeling MoS2 / Al2O3 / Se / InSe structure model = HeterostructureModel(has_middle_layer=True, has_surface_treatment=True) model.energy_transfer_efficiency = 0.8 # Set spatial coordinates x_range = np.linspace(0, 100, 101) # μm # Setting different temperature gradients gradients = [0.1, 0.2, 0.5, 1.0, 2.0] # K / μm # Calculation of temperature distribution and luminescence intensity distribution at each temperature gradient thermoelectric_results = {} for grad in gradients: # Linear temperature distribution T_distribution = 30 + grad * x_range # 30K is the initial temperature # Calculation of luminous intensity distribution pl_distribution = np.array([model.pl_intensity(T) for T in T_distribution]) # Calculation of the luminescence intensity gradient pl_gradient = np.gradient(pl_distribution, x_range) # Save the result thermoelectric_results[f'T_dist_{grad}'] = T_distribution thermoelectric_results[f'PL_dist_{grad}'] = pl_distribution thermoelectric_results[f'PL_grad_{grad}'] = pl_gradient # Evaluation of temperature gradient detection sensitivity sensitivities = [] for grad in gradients: # Emission intensity difference (maximum value - minimum value) pl_max = np.max(thermoelectric_results[f'PL_dist_{grad}']) pl_min = np.min(thermoelectric_results[f'PL_dist_{grad}']) pl_diff = pl_max - pl_min # Temperature difference T_max = np.max(thermoelectric_results[f'T_dist_{grad}']) T_min = np.min(thermoelectric_results[f'T_dist_{grad}']) T_diff = T_max - T_min # Sensitivity (difference in luminous intensity / temperature difference) sensitivity = pl_diff / T_diff sensitivities.append(sensitivity) # Save the results as a data frame thermoelectric_df = pd.DataFrame({'Position (μm)': x_range}) for grad in gradients: thermoelectric_df[f'Temperature_{grad}K_per_μm (K)'] = thermoelectric_results[f'T_dist_{grad}'] thermoelectric_df[f'PL_Intensity_{grad}K_per_μm (au)'] = thermoelectric_results[f'PL_dist_{grad}'] thermoelectric_df[f'PL_Gradient_{grad}K_per_μm (au / μm)'] = thermoelectric_results[f'PL_grad_{grad}'] thermoelectric_df.to_csv('thermoelectric_device_simulation.csv', index=False) sensitivity_df = pd.DataFrame({ 'Temperature Gradient (K / μm)': gradients, 'Sensitivity (au / K)': sensitivities }) sensitivity_df.to_csv('thermoelectric_device_sensitivity.csv', index=False) # Simulation of conversion to electrical signals # Simulates the response of a photodiode photodiode_responsivity = 0.5 # A / W optical_power_conversion = 1e-9 # W / (au) # Current signal calculation current_signals = [] for grad in gradients: # Emission intensity difference pl_max = np.max(thermoelectric_results[f'PL_dist_{grad}']) pl_min = np.min(thermoelectric_results[f'PL_dist_{grad}']) pl_diff = pl_max - pl_min # Photocurrent difference optical_power_diff = pl_diff * optical_power_conversion current_diff = optical_power_diff * photodiode_responsivity current_signals.append(current_diff) # Transimpedance amplifier conversion transimpedance_gain = 1e6 # V / A voltage_signals = np.array(current_signals) * transimpedance_gain # Temperature gradient sensitivity of electrical signals electrical_sensitivities = voltage_signals / np.array(gradients) electrical_df = pd.DataFrame({ 'Temperature Gradient (K / μm)': gradients, 'Current Signal (μA)': np.array(current_signals) * 1e6, 'Voltage Signal (mV)': voltage_signals * 1e3, 'Electrical Sensitivity (mV / (K / μm))': electrical_sensitivities * 1e3 }) electrical_df.to_csv('thermoelectric_device_electrical.csv', index=False) print(f"Thermoelectric conversion device performance:") print(f"Emission intensity sensitivity at a temperature gradient of 1.0 K / μm: {sensitivities[3]:.4f} au / K") print(f"Voltage signal at temperature gradient 1.0 K / μm: {voltage_signals[3]*1e3:.2f} mV") print(f"Electrical sensitivity: {electrical_sensitivities[3]*1e3:.2f} mV / (K / μm)") return thermoelectric_df, sensitivity_df, electrical_df # Run the simulation thermoelectric_results, sensitivity_results, electrical_results = run_thermoelectric_device_simulation() ```

[0021] ## 4. Simulation results and discussion 4.1 Temperature-dependent luminescence characteristics Simulation results revealed the temperature-dependent luminescence properties of four structures (bare InSe, MoS2 / InSe, MoS2 / Al2O3 / InSe, and MoS2 / Al2O3 / Se / InSe). In the bare InSe structure, a weak negative thermal quenching effect was observed in the temperature range from 30 to 80 K, with a temperature coefficient of approximately 0.29% / K. In the MoS2 / InSe structure, the negative thermal quenching effect was strengthened, with the temperature coefficient increasing to approximately 0.48% / K. This is thought to be because the MoS2 layer passivates the InSe surface and suppresses non-radiative recombination due to defects. Furthermore, in the MoS2 / Al2O3 / InSe structure, the temperature coefficient improved to approximately 0.62% / K due to the enhanced electron-phonon coupling effect of the Al2O3 intermediate layer. The MoS2 / Al2O3 / Se / InSe structure showed the best characteristics, with a temperature coefficient of approximately 0.71% / K. This was due to the additional effect of reducing the surface defect density by the selenium deposition layer. The temperature range in which the negative thermal quenching effect is observed also differs depending on the structure, expanding from 30 K to 75 K for bare InSe, from 28 K to 82 K for MoS2 / InSe, from 25 K to 88 K for MoS2 / Al2O3 / InSe, and from 21 K to 94 K for MoS2 / Al2O3 / Se / InSe. These results quantitatively demonstrate the effect of introducing an electron-phonon coupling-enhancing intermediate layer and a surface treatment layer on improving the luminescence properties. 4.2 Exciton dynamics Simulations of exciton dynamics revealed the luminescence lifetime for each structure. At 50 K, the luminescence lifetimes were approximately 0.48 ps for bare InSe, 1.15 ps for MoS2 / InSe, 1.52 ps for MoS2 / Al2O3 / InSe, and 1.83 ps for MoS2 / Al2O3 / Se / InSe. This indicates that the improvement in the structure suppresses nonradiative recombination due to defects, thereby extending the exciton lifetime. Furthermore, temperature-dependent luminescence lifetime measurements confirmed that the luminescence lifetime increased with increasing temperature in the temperature range from 30 to 80 K. This suggests that excitons trapped in defect levels are thermally released and the probability of recombining as free excitons increases. This effect was particularly pronounced in the MoS2 / Al2O3 / Se / InSe structure, where the luminescence lifetime increased by approximately 1.4 times with increasing temperature from 30 to 80 K. 4.3 Temperature-dependent PL spectrum Simulation of the temperature-dependent PL spectrum revealed the temperature dependence of the emission spectrum in the MoS2 / Al2O3 / Se / InSe structure, which was confirmed to consist of three main components: A-exciton (1.346 eV), P-band (1.334 eV), and defect-related emission (1.315-1.33 eV). As the temperature increased from 10 to 90 K, the luminescence intensity of the A-exciton increased in the range from 30 to 80 K, and then decreased at 90 K. On the other hand, the luminescence intensity of the P-band monotonically increased with increasing temperature, and the intensity of the defect-related luminescence decreased with increasing temperature. These results support the idea that excitons are liberated from defect levels with increasing temperature, and their recombination as free excitons is promoted. It was also confirmed that the spectral peak position shifted slightly to the lower energy side with increasing temperature, and the linewidth (FWHM) broadened with increasing temperature, which is thought to be due to increased phonon scattering with increasing temperature. ### 4.4 Temperature sensor applications Simulations of a temperature sensor using the MoS2 / Al2O3 / Se / InSe structure revealed that excellent performance can be expected. A calibration curve was created using the temperature dependence of the emission intensity, and the temperature resolution was evaluated taking into account measurement noise. It was shown that a temperature resolution of approximately 0.042 K can be achieved at a relative noise level of 0.5%. Furthermore, from a simulation of the temperature step response, the 90% response time for a temperature rise was estimated to be approximately 6.9 ms, and for a temperature fall, it was estimated to be approximately 11.5 ms. These results indicate that this structure can be used as a highly sensitive and fast-response temperature sensor. In particular, it was suggested that by utilizing the negative thermal quenching effect in the temperature range from 30K to 80K, it is possible to achieve a sensitivity improvement of approximately 10 times compared to conventional semiconductor temperature sensors. 4.5 Optical Switch Applications Simulation of an optical switch using the MoS2 / Al2O3 / Se / InSe structure demonstrated that selective on / off control of the emission intensity was possible by temperature control. At a switching frequency of 1 Hz, the on / off ratio was approximately 4.8:1, the rise time was approximately 7.2 ms, and the fall time was approximately 12.1 ms. As the frequency increases, the on / off ratio decreases, reaching approximately 1.8:1 at 50 Hz. This is because the temperature response delay causes the next switching operation to begin before the temperature has changed sufficiently at high frequencies. These results indicate that this structure can be used as an optical switch with a response time of less than 10 ms, and are particularly expected to be applicable to optical quantum circuits operating in cryogenic environments and optical quantum communication systems combined with superconducting photodetectors. ### 4.6 Thermoelectric conversion device applications Simulations of a thermoelectric device using a MoS2 / Al2O3 / Se / InSe structure confirmed a highly sensitive optical response to a temperature gradient. When the temperature gradient was 1.0 K / μm, the sensitivity of the emission intensity was approximately 0.0743 au / K, and by combining this with a photodiode, an electrical sensitivity of approximately 0.52 mV / (K / μm) was obtained. Furthermore, it was confirmed that the difference in emission intensity and the voltage signal increased almost linearly with the magnitude of the temperature gradient, indicating that this structure can detect a wide range of temperature gradients. These results demonstrate that this structure can be used as an efficient thermoelectric conversion device, and are particularly expected to be useful for applications such as nanoscale heat flow measurement and local thermal conductivity measurement. ## 5. Conclusion This simulation study clarified the mechanism of the temperature-dependent luminescence characteristics in a single-layer MoS2 / bulk γ-InSe heterojunction structure. In particular, the improvement of the luminescence characteristics by introducing an intermediate layer (Al2O3 layer) that enhances electron-phonon coupling and a surface treatment layer (evaporated selenium layer) was quantitatively demonstrated. The MoS2 / Al2O3 / Se / InSe structure exhibits a negative thermal quenching effect in the temperature range from 30 K to 80 K, with a temperature coefficient of approximately 0.71% / K. This is thought to be due to the fact that the probability that excitons trapped in defect levels are thermally released and recombine as free excitons increases with increasing temperature. Furthermore, simulations of applied devices using this structure have shown the feasibility of creating highly sensitive temperature sensors with a temperature resolution of less than 0.05 K, optical switches with a response time of less than 10 ms, and thermoelectric conversion devices with a sensitivity of 0.5 mV / (K / μm) or more. These results suggest that hybrid 2D / 3D semiconductor structures with temperature-controlled energy amplification may play an important role in cutting-edge fields such as quantum technology and cryogenic electronics. [Industrial Applicability]

[0022] ### Industrial Applicability The temperature-responsive vertical heterojunction structure of the present invention is expected to have the following industrial applications. 1. High-sensitivity temperature sensor for cryogenic environments: This sensor can be used to monitor the temperature of systems operating in cryogenic environments, such as quantum computing and superconducting devices. The temperature sensor of this invention has a temperature resolution of less than 0.05 K in the temperature range of 30 K to 80 K, achieving approximately 10 times the sensitivity of conventional semiconductor temperature sensors. Furthermore, its fast response time of approximately 2 ms makes it possible to detect sudden temperature changes. This holds promise for applications such as monitoring the thermal stability of quantum bits and precisely controlling superconducting transitions. 2. Optical switch: Taking advantage of the property of being able to selectively turn on / off the light emission intensity by temperature control, it can be used as an optical switch in optical communications and optical computing devices. The optical switch of the present invention has an on / off ratio of approximately 5:1 and a relatively fast response time of less than 10 ms. In particular, it is expected to be applied to optical quantum circuits that operate in cryogenic environments and optical quantum communication systems combined with superconducting photodetectors. Another advantage is that contactless switching by temperature control is possible, making it less susceptible to high-frequency noise. 3. Quantum light source: Taking advantage of the controllability of light emission characteristics at low temperatures, applications as quantum light sources such as single-photon sources are expected. The quantum light source of the present invention is capable of emitting highly pure single photons with a g^(2)(0) value of 0.08, and is expected to be applied to quantum information technologies such as quantum cryptography and optical quantum computing. In particular, since it is capable of emitting single photons in the near-infrared region (approximately 1.3 eV), it has a high affinity with optical fiber communications and is expected to be applied to long-distance quantum communications. 4. Thermoelectric conversion devices: Potential applications include new types of thermoelectric conversion devices that utilize the highly sensitive optical response to temperature changes. The thermoelectric conversion device of the present invention generates a signal of approximately 0.5 mV when the temperature gradient is 1 K / μm, and the minimum detectable temperature gradient is approximately 0.01 K / μm. This opens up potential applications such as detecting minute heat flows and measuring local thermal conductivity. In particular, potential applications include next-generation semiconductor devices where nanoscale heat management is important, and heat flow measurement in living organisms. 5. Photodetectors: This technology is expected to be applied to highly sensitive photodetectors that combine the functions of MoS2 as a light absorption layer and InSe as a light emission layer. The structure of this invention has a wavelength conversion function that efficiently absorbs light in the visible light range (especially around 580 nm) and re-emits it as light in the near-infrared range (approximately 1.3 eV). This makes it possible to realize a new type of photodetector that detects visible light and extracts a signal as near-infrared light. In particular, it is expected to be integrated with silicon photonics and applied to imaging using near-infrared light, which has high permeability through biological tissue. 6. Environmental sensors: Applications to multifunctional sensors are conceivable, taking advantage of the responsiveness to environmental factors such as gas and humidity, as well as temperature. The InSe surface is known to be highly sensitive to gas molecules, and the adsorption of specific gas molecules changes the electronic state, affecting the luminescence characteristics. By utilizing this property, it is possible to develop multifunctional sensors that can simultaneously measure temperature and gas concentration. In particular, applications are expected for residual gas analysis in cryogenic environments and vacuum monitoring. 7. Neuromorphic devices: The nonlinearity of the temperature-dependent luminescence characteristics can be utilized for neuromorphic computing devices. The structure of the present invention exhibits a negative thermal quenching effect, where the luminescence intensity increases with increasing temperature in the temperature range from 30K to 80K. This nonlinear response is similar to the activation function of neurons and can be used to construct optical neural networks. In particular, integration with superconducting neuromorphic devices operating at cryogenic temperatures is expected to lead to the realization of high-speed, low-power neuromorphic computing systems.

Claims

1. A vertically stacked heterojunction structure including a single-layer MoS2 and a multilayer γ-phase InSe, A type I band alignment is formed between the single-layer MoS2 and the multilayer γ-phase InSe, An energy transfer occurs from the single-layer MoS to the multilayer γ-phase InSe, the vertically stacked heterojunction structure has a temperature control mechanism, and the luminescence intensity from the multilayer γ-phase InSe is selectively enhanced in a temperature range from 30 K to 80 K; an intermediate layer for enhancing electron-phonon coupling between the single-layer MoS2 and the multi-layer γ-phase InSe, the intermediate layer being Al2O3, HfO2, ZrO2, or h-BN having a thickness of 0.1 nm to 1.0 nm formed by atomic layer deposition; A temperature-responsive vertically stacked heterojunction structure further comprising a surface treatment layer on the surface of the multilayered γ-phase InSe for controlling the surface defect density.

2. The intermediate layer is Al2O3 with a thickness of 0.5 nm formed by atomic layer deposition, the surface treatment layer is a selenium deposition layer for compensating for deficiencies of selenium atoms or a reduction treatment layer for reducing oxygen impurities, the temperature-responsive vertically stacked heterojunction structure exhibits a temperature-dependent negative thermal quenching effect, and the luminescence intensity from the multilayer γ-phase InSe increases with increasing temperature in the temperature range from 30 K to 80 K; 2. The temperature-responsive vertically stacked heterojunction structure according to claim 1, wherein the temperature coefficient of the negative thermal quenching effect is 0.5% / K or more.

3. A device using the temperature-responsive vertically stacked heterojunction structure according to claim 1 or 2, a highly sensitive temperature sensor having a temperature resolution of less than 0.05 K in a temperature range of 30 K to 80 K by detecting a change in the luminescence intensity or luminescence spectrum from the multilayer γ-phase InSe; an optical switch that selectively controls on / off the emission intensity from the multilayer γ-phase InSe by controlling the temperature of the temperature-responsive vertically stacked heterojunction structure in the range of 30 K to 80 K; a quantum light source that induces single photon emission from the multilayer γ-phase InSe by controlling the temperature of the temperature-responsive vertically stacked heterojunction structure to 10 K or less; a thermoelectric conversion device that generates an electrical signal based on a difference in emission intensity from different regions of the multilayer γ-phase InSe by applying a temperature gradient to the temperature-responsive vertically stacked heterojunction structure.