Design method of high-sensitivity graphene temperature sensor

Abstract

This invention discloses a design method for a highly sensitive graphene temperature sensor, belonging to the field of micro-nano sensing technology. The method includes the following steps: S1, constructing a graphene geometric structure model and optimizing the structure; S2, introducing electron-phonon coupling to optimize the structure; S3, calculating the band structure based on the optimized structure; S4, calculating the temperature at a given temperature based on the band data. v F S5, based on v F S6. Calculate resistivity; S7. Set different thermodynamic temperatures and repeat steps S2 to S5; S8. Fit the resistivity-temperature change curve and calculate the temperature coefficient of resistance; S9. Construct a high-sensitivity graphene temperature sensor based on the temperature coefficient of resistance. The method of this invention does not rely on mobility models or empirical fitting parameters. It can self-consistently and quantitatively predict the temperature resistance characteristics of graphene based on the intrinsic response of the electronic structure, providing a theoretical basis for the design of high-sensitivity graphene temperature sensors.

Description

Technical Field

[0001] This invention relates to the field of micro-nano sensing technology, specifically to a design method for a highly sensitive graphene temperature sensor. Background Technology

[0002] Graphene, a two-dimensional material with a single atomic layer thickness, possesses extremely high carrier mobility, excellent mechanical strength, and outstanding thermal conductivity, making it a focus of attention in the fields of micro- and nano-scale thermal management and high-sensitivity sensing. In recent years, temperature sensors based on the thermal resistance effect of graphene (i.e., its resistance changes with temperature) have been regarded as important candidates for the next generation of miniaturized and integrated temperature detection devices due to their advantages such as fast response speed, small size, and low power consumption.

[0003] However, graphene itself is a two-dimensional material, and its physical properties are highly susceptible to external environmental influences. This is especially true when graphene is transferred and placed on various substrates upon which actual devices rely, significantly altering its intrinsic thermal transport characteristics and directly impacting the performance of temperature sensors. In particular, the interface and doping effects of graphene have been shown to have a significant impact on sensor performance. Studies have shown that substrate materials (such as α-Al₂O₃ and SiO₂) alter the electronic structure of graphene through mechanisms such as charge transfer and stress generated by lattice mismatch, thereby affecting its temperature response characteristics. For example, α-Al₂O₃ (sapphire) is widely used in sensor packaging for high-temperature environments due to its high hardness, chemical stability, thermal stability, and excellent electrical insulation properties, but its theoretical prediction of graphene's temperature response remains insufficient. Meanwhile, doping (such as N-doping and B-doping) can control the carrier concentration and type in graphene, thereby changing its temperature coefficient of resistance (TCR), but currently, a systematic theoretical model is lacking to guide the design of doped graphene temperature sensors.

[0004] In existing technologies, there is relatively more research on the temperature response of graphene, but most of it focuses on experimental fabrication and performance testing. Due to the long development cycle, high trial-and-error costs, and significant investment in materials and processes for graphene temperature sensors, research on the temperature response behavior of graphene-substrate heterojunctions (such as α-Al₂O₃ substrates) and doped graphene (such as N-doped graphene) which are more commonly used in practical applications remains relatively scarce. Among these, heterojunctions formed by α-Al₂O₃ substrates and graphene have unique application advantages in high-temperature extreme environments such as aero-engines and gas turbines, but their intrinsic temperature response mechanism has not yet been systematically revealed. N-doped graphene, as an n-type doped material, exhibits significantly different temperature sensitivity characteristics compared to intrinsic graphene and α-Al₂O₃ substrate graphene, and currently lacks theoretical prediction models that can guide performance optimization. Summary of the Invention

[0005] To address the aforementioned shortcomings of existing technologies, the present invention aims to provide a design method for a highly sensitive graphene temperature sensor. This method employs graphene as the sensing element of the temperature sensor. By calculating the band structure of graphene, doped graphene, and graphene heterojunctions, and combining theories such as phonon scattering, the resistivity-temperature curve of the graphene-based temperature sensor is predicted, providing comprehensive theoretical support for the high-performance design of graphene temperature sensors.

[0006] The technical solution of this invention to solve the above-mentioned technical problems is as follows: A design method for a high-sensitivity graphene temperature sensor is provided, comprising the following steps: S1. Construct a graphene geometric structure model at 0 K and use the GGA-PBE exchange-correlation functional for structural relaxation. S2. Based on the structure relaxed in step S1, electron-phonon coupling is introduced to further optimize the graphene geometry at a given temperature. S3. Based on the optimized graphene geometry at the given temperature in step S2, calculate the band structure and obtain band data. S4. Based on the band structure data obtained in step S3, calculate the Fermi velocity at a given temperature. v F ; S5. Fermi velocity obtained in step S3 v F Calculate the resistivity; S6. Set different thermodynamic temperatures and repeat steps S2 to S5; S7. Fit the resistivity-temperature change curve based on the calculation results of S6, and then calculate the graphene temperature coefficient of resistance (TCR) based on the fitted resistivity-temperature change curve. S8. Construct a highly sensitive graphene temperature sensor based on the temperature coefficient of resistance (TCR) obtained in step S7.

[0007] Furthermore, in step S1, the graphene geometric structure model can be intrinsic graphene, heterogeneous element-doped graphene, a heterojunction composed of a substrate material and graphene, or a graphene structure model with different numbers of layers.

[0008] Furthermore, resistivity is calculated using electroacoustic coupling combined with Boltzmann transport theory, without requiring carrier mobility or carrier concentration as intermediate variables; resistivity is used to characterize the temperature-sensitive performance of graphene temperature sensors.

[0009] Furthermore, the formula for calculating resistivity is shown in equation (Ⅰ): (Formula I) in, The resistivity of the material as a function of temperature. T For temperature, This represents the deformation potential of graphene. Boltzmann's constant, The amount of elementary charge. is Planck's constant. The surface mass density of graphene. The speed of sound for graphene phonons. v F For Fermi velocity, This represents the residual resistivity of graphene that does not change with temperature.

[0010] Furthermore, Fermi speed v F The calculation formula is shown in equation (II): (II) in, To reduce Planck's constant, For band structure energy, wave vector in reciprocal space 。

[0011] Furthermore, the formula for calculating the temperature coefficient of resistance (TCR) in step S5 is shown in (Ⅲ): (III) in, T 0 represents the initial temperature. and These are the resistance and resistivity at the initial temperature, respectively. and Temperature The resistance and resistivity of the material.

[0012] This invention has the following beneficial effects: By using the Fermi velocity as an intermediate variable, it establishes a one-to-one correspondence between microscopic physical quantities (graphene band structure) and macroscopic physical quantities (resistivity), thereby enabling the construction of a temperature coefficient of resistance. In the research of graphene-based temperature sensors, the change in the material's resistance (or resistivity) with temperature is a core indicator for evaluating its temperature-sensitive performance. According to classical transport theory, conductivity... Due to carrier concentration With carrier mobility Joint decision, that is Correspondingly, resistivity Therefore, the response of resistance to temperature is essentially... and The result of coupling changes. If only the mobility variation with temperature is considered, while neglecting the variation in carrier concentration, it will be difficult to accurately predict the temperature resistance characteristics of the device. The electrical transport properties of graphene are mainly regulated by its band dispersion relation, while the Fermi velocity... As a direct representation of band slope, it can quantitatively reflect the perturbation of electronic structure by temperature through electron-phonon coupling. Due to resistivity and Inversely proportional, the band structure at different temperatures is calculated using first-principles calculations, and the energy is extracted. This allows for direct prediction of the temperature dependence of resistivity without the need for a mobility model. This invention systematically studies the temperature response characteristics of three typical structures: intrinsic graphene, α-Al₂O₃ substrate graphene heterojunction, and N-doped graphene. Therefore, the design method of this invention can effectively evaluate the substrate effect and the modulating effect of doping on temperature sensitivity, providing a reliable theoretical basis for the development of highly sensitive graphene temperature sensors. Attached Figure Description

[0013] Figure 1 This is a diagram of the intrinsic graphene 4×4 supercell structure in Example 1; Figure 2 The image shows the band structure of intrinsic graphene under EPC at different temperatures in Example 1. Figure 3 The curve showing the change in relative resistivity of intrinsic graphene with temperature in Example 1; Figure 4 In Example 2 <0001> A heterojunction structure model composed of a 1×1 supercell of α-Al2O3 and a 2×2 graphene supercell; Figure 5 The image shows the band structure of the graphene / α-Al2O3 heterojunction under EPC in Example 2 at different temperatures. Figure 6 The curve showing the change in relative resistivity of the graphene / α-Al2O3 heterojunction with temperature in Example 2; Figure 7 This is the N-doped graphene structure model in Example 3; Figure 8 The image shows the band structure of N-doped graphene under EPC at different temperatures in Example 3. Figure 9 The curve showing the change in relative resistivity of N-doped graphene with temperature in Example 3; Figure 10 A schematic diagram of a suspended graphene sensor chip prepared according to the design method of Example 1; Figure 11 The graphene sensor prepared according to the design method of Example 1 is shown as a test curve of the relative resistance as a function of temperature. Detailed Implementation

[0014] The examples given below are for illustrative purposes only and are not intended to limit the scope of the invention. Unless otherwise specified, conditions in the examples are performed under standard conditions or as recommended by the manufacturer. Reagents or instruments whose manufacturers are not specified are all commercially available products.

[0015] Example 1: A design method for a highly sensitive graphene temperature sensor includes the following steps: S1. Construct an intrinsic graphene 4×4 supercell model using MedeA software. Optimize the structure using the GGA-PBE exchange-correlation functional with the help of the VASP 6 module in MedeA software. The energy convergence criterion is 10. -5 The stress converges to below 0.05 eV / Å. The optimized structural model is as follows: Figure 1 As shown.

[0016] S2. Using the VASP 6 software package with electron-phonon coupling (EPC), calculate the band structure of intrinsic graphene at 0 K, 200 K, 400 K, 600 K, 800 K, and 1000 K in 200 K steps. Figure 2 As shown. By Figure 2 It can be seen that the band gap value E corresponding to the above temperature is g The band gap values ​​E are 0.277 eV, 0.281 eV, 0.291 eV, 0.307 eV, 0.327 eV, and 0.351 eV, respectively. The results indicate that the band gap value E increases with increasing temperature. g Gradually increase.

[0017] S3. Combining the energy band data obtained in step S2 at different temperatures, use the formula... (in, To reduce Planck's constant, For band structure energy, Calculate the Fermi velocity for the wave vector in reciprocal space, and then substitute it into... (in, The resistivity of the material as a function of temperature. T For temperature, This represents the deformation potential of graphene. Boltzmann's constant, The amount of elementary charge. is Planck's constant. The surface mass density of graphene. The speed of sound for graphene phonons. v F For Fermi velocity, The resistivity of graphene at different temperatures was calculated to represent the residual resistivity that does not change with temperature, as shown below. Figure 3 The curve showing the relative resistivity of intrinsic graphene as a function of temperature is shown. Its temperature coefficient of resistance is also mentioned. (in, T 0 represents the initial temperature. and These are the resistance and resistivity at the initial temperature, respectively. and Temperature (The resistance and resistivity of the material at that time).

[0018] Example 2: A design method for a highly sensitive graphene temperature sensor includes the following steps: S1. Model construction using MedeA software: Construct a hexagonal unit cell for α-Al₂O₃, along... <0001> Directional slices were prepared and expanded into 1×1 surface supercells to construct 2×2 graphene supercells. These supercells were then combined with α-Al₂O₃ to form a heterojunction model. Using the VASP 6 module in MedeA software, GGA-PBE exchange-correlation functionals were employed for structural optimization, with an energy convergence criterion of 10⁻⁶. -5 The stress converges to below 0.05 eV / Å. The optimized structural model is as follows: Figure 4 As shown in the figure. Calculations show that the heterojunction binding energy is -0.2 eV, indicating that the heterojunction structure is stable.

[0019] S2. Using the VASP 6 software package and incorporating electron-phonon coupling EPC, calculate the heterojunction band structure at 0 K, 100 K, 200 K, 300 K, 400 K, 500 K, 600 K, 700 K, and 800 K with a step size of 100 K (see...). Figure 5 ).Depend on Figure 5 It can be seen that the band gap value E corresponding to the above temperature is g The values ​​were 0.412 eV, 0.424 eV, 0.430 eV, 0.431 eV, 0.432 eV, 0.427 eV, 0.418 eV, 0.419 eV, and 0.419 eV, respectively. The results indicate that the Fermi level of the heterojunction enters the valence band, suggesting that the α-Al₂O₃ substrate introduced p-type doping, i.e., hole doping, into the graphene.

[0020] S3. Combining the energy band data obtained in step S2 at different temperatures, use the formula... (in, To reduce Planck's constant, For band structure energy, Calculate the Fermi velocity for the wave vector in reciprocal space, and substitute it into... (in, The resistivity of the material as a function of temperature. T For temperature, This represents the deformation potential of graphene. Boltzmann's constant, The amount of elementary charge. is Planck's constant. The surface mass density of graphene. The speed of sound for graphene phonons. v F For Fermi velocity, The resistivity of graphene at different temperatures was calculated to represent the residual resistivity that does not change with temperature, as shown below. Figure 6 The graphene / α-Al₂O₃ heterojunction is shown as a function of temperature. Its temperature coefficient of resistance was calculated. (in, T 0 represents the initial temperature. and These are the resistance and resistivity at the initial temperature, respectively. and Temperature (The resistance and resistivity of the material at that time).

[0021] Example 3: A design method for a highly sensitive graphene temperature sensor includes the following steps: S1. Construct an N-doped graphene crystal structure using MedeA software. Optimize the structure using the GGA-PBE exchange-correlation functional with the VASP 6 module in MedeA, setting the energy convergence criterion to 10. -5 When the stress converges to below 0.05 eV / Å, the optimized crystal structure is as follows: Figure 7 As shown. Calculations show that the formation energy of N-doped graphene is -0.77 eV, indicating that the N-doped graphene structure is stable.

[0022] S2. Using the VASP 6 software package and incorporating electron-phonon coupling EPC, calculate the band structure of N-doped graphene at 0 K, 200 K, 400 K, 600 K, 800 K, and 1000 K with a step size of 200 K (see...). Figure 8 ).Depend on Figure 8 It can be seen that the band gap value E corresponding to the above temperature is g The values ​​were 0.376 eV, 0.372 eV, 0.368 eV, 0.368 eV, 0.372 eV, and 0.378 eV, respectively. The results indicate that the Fermi level enters the conduction band after N-doping graphene, and N-doping introduces n-type doping, i.e., electronic doping, into the graphene.

[0023] S3. Combining the energy band data obtained in step S2 at different temperatures, use the formula... (in, To reduce Planck's constant, For band structure energy, Calculate the Fermi velocity for the wave vector in reciprocal space, and substitute it into... (in, The resistivity of the material as a function of temperature. T For temperature, This represents the deformation potential of graphene. Boltzmann's constant, The amount of elementary charge. is Planck's constant. The surface mass density of graphene. The speed of sound for graphene phonons. v F For Fermi velocity, The resistivity of graphene at different temperatures was calculated to represent the residual resistivity that does not change with temperature, as shown below. Figure 9 The curve showing the intrinsic graphene resistivity versus temperature is shown, and its temperature coefficient of resistance is... (in, T 0 represents the initial temperature. and These are the resistance and resistivity at the initial temperature, respectively. and Temperature (The resistance and resistivity of the material at that time).

[0024] Experimental example: This invention fabricates a highly sensitive graphene temperature sensor based on the design method of Example 1. The specific operation is as follows: (1) A 200 nm silicon nitride insulating layer was deposited on both sides of a 200 μm silicon wafer using low-pressure chemical vapor deposition; then, a 15 nm / 25 nm Cr / Au metal electrode was grown on the front side of the silicon wafer by magnetron sputtering (where Cr is the adhesion layer and Au is the conductive layer). (2) The silicon nitride on the back side of the silicon wafer obtained in step (1) was etched by reactive ion etching process to create a cavity with a depth of 200 nm and a width of 372 μm; then the exposed silicon was selectively removed by wet etching process until the etching reached the bottom surface of the silicon nitride front layer. (3) The silicon nitride on the front side of the silicon wafer obtained in step (3) is etched by reactive ion etching process to form a through hole with a diameter of 20 μm and a depth of 200 nm at the center of the silicon wafer electrode; then, the monolayer graphene is transferred to the silicon wafer surface by wet transfer and patterned to obtain a suspended graphene temperature sensor chip (see Figure 10 ).

[0025] The chip was placed on the probe stage, and the probe was moved to ensure reliable contact with the sensor electrode. The resistance was tested using the van der Bauer method to avoid the influence of contact current. The test temperatures were 288.15 K, 303.15 K, 323.15 K, 343.15 K, 363.15 K, 383.15 K, 403.15 K, 423.15 K, 443.15 K, 463.15 K, and 483.15 K. The test results are as follows: Figure 11 As shown. Fitting the test results yields the functional relationship between the output resistance and temperature of the graphene temperature sensor: R = 20.33T - 2842.9; its temperature coefficient of resistance is calculated to be: The error was only 8.4% compared to the TCR predicted in Example 1.

[0026] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A design method for a highly sensitive graphene temperature sensor, characterized in that, Includes the following steps: S1. Construct a graphene geometric structure model at 0 K and use the GGA-PBE exchange-correlation functional for structural relaxation. S2. Based on the structure relaxed in step S1, electron-phonon coupling is introduced to further optimize the graphene geometry at a given temperature. S3. Based on the optimized graphene geometry at the given temperature in step S2, calculate the band structure and obtain band data. S4. Based on the band structure data obtained in step S3, calculate the Fermi velocity at a given temperature. v F ; S5. Fermi velocity obtained in step S3 v F Calculate the resistivity; S6. Set different thermodynamic temperatures and repeat steps S2 to S5; S7. Fit the resistivity-temperature change curve based on the calculation results of S6, and then calculate the graphene temperature coefficient of resistance (TCR) based on the fitted resistivity-temperature change curve. S8. Construct a highly sensitive graphene temperature sensor based on the temperature coefficient of resistance (TCR) obtained in step S7.

2. The design method according to claim 1, characterized in that, The graphene geometric model mentioned in step S1 is an intrinsic graphene, a heterojunction composed of a substrate material and graphene, or a graphene structure model with different numbers of layers.

3. The design method according to claim 1, characterized in that, The resistivity is calculated using electroacoustic coupling combined with Boltzmann transport theory, without requiring carrier mobility or carrier concentration as intermediate variables; the resistivity is used to characterize the temperature-sensitive performance of the graphene temperature sensor.

4. The design method according to claim 1, characterized in that, The formula for calculating the resistivity is shown in equation (Ⅰ): （Ⅰ）； in, The resistivity of the material as a function of temperature. T For temperature, This represents the deformation potential of graphene. Boltzmann's constant, The amount of elementary charge. Let be Planck's constant. The surface mass density of graphene. The speed of sound for graphene phonons. v F For Fermi velocity, This represents the residual resistivity of graphene that does not change with temperature.

5. The design method according to claim 1, characterized in that, The Fermi velocity v F The calculation formula is shown in equation (II): （Ⅱ）； in, To reduce Planck's constant, For band structure energy, Let be the wave vector in reciprocal space.

6. The design method according to claim 1, characterized in that, The formula for calculating the temperature coefficient of resistance (TCR) in step S5 is shown in (Ⅲ): （Ⅲ）； in, T 0 represents the initial temperature. and These are the resistance and resistivity at the initial temperature, respectively. and Temperature The resistance and resistivity of the material.

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