CN111693510B - Method for measuring thermal conductivity of two-dimensional layered materials based on temperature-dependent Raman spectroscopy - Google Patents

Abstract

The invention discloses a method for measuring the thermal conductivity of a two-dimensional layered material based on temperature-dependent Raman spectroscopy. The method comprises the following steps: setting a substrate of a sample to be detected, and preparing the sample to be detected based on mechanical stripping and PDMS transfer technology; in the room temperature environment, carrying out Raman spectrum test on a sample to be tested under different powers, and carrying out power-wave number offset coefficient calibration; carrying out Raman spectrum tests at different temperatures on a sample to be tested, and carrying out temperature-wave number offset coefficient calibration; establishing a thermal conductivity relation curve according to a specific theoretical model and corresponding boundary conditions; substituting experimental test data into a thermal conductivity relation curve to extract thermal conductivity, and reversely verifying the rationality of the hypothesized condition by utilizing the extracted thermal conductivity, thereby determining the accuracy of the extracted thermal conductivity. The invention can make up the limit of the prior art on the measurement of the thermal conductivity of the micro-nano size material, and simultaneously ensure the problems of micro-nano measurement precision and the like.

Description

Method for measuring thermal conductivity of two-dimensional layered materials based on temperature-dependent Raman spectroscopy

technical field

The invention relates to the technical field of semiconductor thin film testing, in particular to a method for measuring thermal conductivity of two-dimensional layered materials based on temperature-dependent Raman spectroscopy.

Background technique

In order to meet the future of 5G technology, semiconductors with high power density are increasingly integrated on chips, resulting in greater power consumption and more heat, which will greatly deteriorate the performance and stability of devices. sex. At the same time, the increase in integration level indicates that the volume of semiconductors is constantly shrinking, and it is difficult to accurately measure the thermal conductivity of micron-sized semiconductors by traditional methods.

For example, the 3ω law of electrochemistry is limited by the heating frequency, which will cause damage to the sample to be tested and is no longer suitable for the measurement of thermal conductivity of micro-nano materials. The laser heat reflection method needs to vapor-deposit a heat-absorbing layer on the sample to be tested, which has a large error. Therefore, to advance the R&D and production of large-scale, high-power-density semiconductors, it is important to develop a robust non-contact, non-destructive measurement of thermal conductivity to evaluate and guide thermal management.

At the same time, since the discovery of graphene in 2004, two-dimensional layered materials have received more and more attention and research because of their atomic-level planarity, wearability, tunable bandgap, and strong light-matter interaction. The carrier mobility of graphene is 100 times that of traditional silicon materials, and it also has an ultra-broad spectrum optical resonance response.

The special crystal structure of transition metal sulfide and black phosphorus makes its band gap and electronic properties change with the number of layers, which provides a great opportunity for the development of new light-emitting devices and energy storage devices, as well as the research of emerging energy valley optoelectronics. New material options. Excellent thermal management technology can ensure reliable and stable operation of the device. As 2D materials show great promise for future electronic and optoelectronic devices, it is especially important to explore the thermal conductivity of these materials.

To date, Raman spectroscopy has been one of the most routine and non-destructive techniques for studying the physical properties of low-dimensional nanomaterials. Focusing the laser light locally generates heat in the material, causing the frequency of the phonons to change. At the same time, Raman spectroscopy is particularly sensitive to phonon frequency changes, and can directly detect the vibration of phonons. This makes it possible for Raman spectroscopy to realize low-dimensional thermal performance testing.

Contents of the invention

Aiming at the deficiencies of the prior art, the present invention discloses a method for measuring the thermal conductivity of two-dimensional layered materials based on temperature-dependent Raman spectroscopy, which can make up for the limitations of the prior art on the measurement of thermal conductivity of micro-nano-scale materials, and improve Micro-nano measurement accuracy and other issues.

To achieve the above object, the present invention is achieved through the following technical solutions:

A method for measuring the thermal conductivity of a two-dimensional layered material based on temperature-dependent Raman spectroscopy, comprising the following steps:

S1: Set up the substrate of the sample to be tested, and prepare the sample to be tested based on mechanical peeling and PDMS transfer technology;

S2: At room temperature, conduct Raman spectroscopy tests at different powers on the sample to be tested, and perform power-wavenumber offset coefficient calibration;

S3: Carry out Raman spectrum tests at different temperatures for the sample to be tested, and perform temperature-wavenumber offset coefficient calibration;

S4: According to a specific theoretical model and corresponding boundary conditions, use MATLAB simulation software to calculate the thermal conductivity relationship;

S5: Combined with the experimental test data, substitute the simplified formula to extract the thermal conductivity.

A preferred technical solution, the step S1 also includes:

S11: Prepare a clean silicon wafer, and use a coater to spin coat the surface with a specified thickness of positive photoresist;

S12: Use a mask plate and an upper ultraviolet exposure machine to obtain a corresponding pattern template on a silicon wafer spin-coated with photoresist, and then pattern it under the action of a developer;

S13: Etching the patterned silicon wafer into hydrofluoric acid and saturated sodium hydroxide solution to obtain a silicon wafer with round holes;

S14: Use scotch tape to mechanically peel off the bulk layered semiconductor material to obtain the corresponding few-layer flakes, and then transfer them to silicon wafers with holes by using PDMS dry method.

In a further preferred technical solution, three circular holes with diameters of 3 μm, 4 μm, and 5 μm are respectively provided on the mask plate, the distance between each circular hole is set to 5 μm, and three circular holes are arranged in a matrix.

A further preferred technical solution is to first corrode the patterned silicon wafer with hydrofluoric acid for 1 minute, then put in saturated sodium hydroxide to corrode for 8-9 hours, and finally wash it with deionized water, and then dry it.

A further preferred technical solution is to take the PDMS with the sample under the micro-transfer platform with a microscope, find a suitable few-layer thin slice and transfer it to the silicon wafer substrate with holes.

In a further preferred technical solution, the few-layer sheet completely covers the circular cavity of the substrate, so that the sample to be tested is in a suspended state.

In the preferred technical scheme, in the step S2, the Raman spectrum is used to calibrate the coefficient of the Raman wavenumber of the few-layer sheet to be measured with the power offset,

M=Δω/ΔP

Among them, M is the coefficient of Raman wavenumber offset with power, Δω is the wavenumber offset of the few-layer sheet, ΔP is the offset of laser power, and the range of laser power is selected from 0.1mW to 0.35mW.

In the preferred technical scheme, in the step S3, the Raman spectrum is used to calibrate the coefficient of the Raman wavenumber of the thin film to be measured with the temperature offset,

M'=Δω/ΔT

Among them, M' is the coefficient of Raman wavenumber shift with temperature, Δω is the wavenumber shift of few-layer sheet, ΔT is the shift of temperature, and the temperature range is selected from 80K to 300K.

In the preferred technical solution, in the step S4, according to a specific theoretical model and corresponding boundary conditions, the MATLAB simulation software is used to calculate the heat conduction relational expression;

In the preferred technical scheme, in the step S5, the Raman spectrum is used to calibrate the coefficient of the Raman wavenumber of the few-layer sheet to be measured as the temperature shifts, and the thermal conductivity is extracted in conjunction with the experimental test data, and then the extracted thermal conductivity can be used The temperature distribution graph of the rate simulation temperature along the x-axis verifies the rationality of the assumptions G and K`, and then determines the accuracy of the thermal conductivity.

The invention discloses a method for measuring the thermal conductivity of a two-dimensional layered material based on temperature-dependent Raman spectroscopy, which has the following advantages:

By rationally designing a substrate with large holes, constructing a heat transfer characterization that conforms to Raman tests and theoretical models, the thermal conductivity measurement of nanoscale two-dimensional layered materials is realized; at the same time, it is a non-contact type of test , to minimize the deviation that may be caused by contact, so that the measurement results are more accurate; this scheme has strong feasibility, simple operation, low cost, and is conducive to systematic research on the thermal management of two-dimensional materials.

Description of drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings that are required in the description of the embodiments or the prior art.

Apparently, the drawings in the following description are only some embodiments of the present invention, and those skilled in the art can obtain other drawings according to these drawings without creative efforts.

Fig. 1 is a logical block diagram of an embodiment of the present invention;

Fig. 2 is the schematic diagram of the sample to be tested in the embodiment of the present invention;

Figure 3 is a typical Raman peak shift and fitting image with laser power;

Figure 4 is a typical Raman peak shift and fitting image with temperature.

Fig. 5 is the image that extracts thermal conductivity in the embodiment of the present invention;

Fig. 6 is a temperature distribution diagram of the sample along the x-axis diameter in the embodiment of the present invention.

Detailed ways

In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. the embodiment.

Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

As shown in Figure 1, a method for measuring the thermal conductivity of a two-dimensional layered material based on temperature-dependent Raman spectroscopy described in the embodiment of the present invention includes the following steps:

First, prepare a clean silicon wafer, spin-coat positive photoresist with a specified thickness on its surface, and then use a mask plate and a UV exposure machine to obtain a corresponding pattern template on the silicon wafer with photoresist spin-coated, and then Patterning is performed under the action of a developer, and then the patterned silicon wafer is etched in hydrofluoric acid for 20-40 seconds, and then etched with saturated sodium hydroxide solution for 10-12 hours to obtain a silicon wafer with round holes.

Finally, the bulk two-dimensional layered material is mechanically peeled off with adhesive tape to obtain the corresponding thin layer, which is directly transferred to PDMS, and then a thin layer with a moderate thickness and size is found using a microscope. With the help of a micromanipulator, the sample is transferred from PDMS to on the round hole of the substrate, as shown in Figure 2.

At room temperature, the sample to be tested is tested for Raman spectroscopy under different laser powers, and the power-wavenumber offset coefficient is calibrated. The laser spot is aligned with the center of the circular hole under the suspended sample to be tested. Correspondingly, the Raman spectrum test at different temperatures is carried out on the test sample, and the temperature-wavenumber shift coefficient is calibrated. The laser spot is aligned with the center of the circular hole under the suspended sample to be tested.

It can be understood that the embodiment of the present invention also includes establishing the heat distribution formula:

Let I be the unit power density of the laser, α the absorptivity of the few-layer flake, t the thickness of the flake, and _r0 the radius of the laser spot.

k is the thermal conductivity of the suspended material, T(r) is the temperature distribution in the hole, r is the distance from the center of the hole, and R is the radius of the hole.

Further, the volumetric Gaussian beam heating equation is obtained:

Further, the volumetric Gaussian beam heating equation is obtained:

T ₂ (r) is the temperature distribution outside the hole, kˊ is the thermal conductivity of the layered sheet covering the substrate, G is the thermal conductivity of the interface, and the temperature at infinity is defined as T _a .

Further, the heat diffusion equation outside the cavity is obtained:

The weighted average temperature of the further void center is:

Further, the boundary conditions are:

T ₁ (R) = T ₂ (γ) | _{r = R}

T ₂ (r→∞)=T _a

Further, the approximate conditions are:

k=k'

G＝50MW/m ² k

The content of the present invention will be described in detail below in conjunction with examples.

For the test of the thermal conductivity of the two-dimensional layered semiconductor material platinum disulfide, the thickness of _PtS2 is 3nm, and the substrate is a silicon wafer deposited with 300nm SiO2.

Design the substrate of the sample to be tested, and transfer the sample to be tested onto the substrate: first, prepare a clean silicon wafer, spin-coat the surface with a certain thickness of positive photoresist, and then use the mask designed in advance The template is added with a UV exposure machine, and the corresponding pattern template is obtained on the silicon wafer with spin-coated photoresist, and then patterned under the action of the developer, and then the patterned silicon wafer is etched in hydrofluoric acid for 20-40 seconds Then corrode with saturated sodium hydroxide solution for 10-12 hours to obtain a silicon wafer with round holes. Finally, the bulk two-dimensional layered material is mechanically peeled off with adhesive tape to obtain the corresponding thin layer, which is directly transferred to PDMS, and then a thin layer with a moderate thickness and size is found using a microscope. With the help of a micromanipulator, the sample is transferred from PDMS to hole in the substrate.

At room temperature, the Raman spectrum test of the PtS ₂ sample to be tested under different laser powers is carried out. Here we choose the change of the wave number of the E ¹ _2g vibrational mode peak with the power and calibrate the power-wave number shift coefficient: the laser The power setting is: 0.1mW to 0.35mW, the interval is 0.034mW, a total of 10 points. And use Raman to mark the wave number under the corresponding peak, according to the formula: M=Δω/ΔP, the peak wave number shift-laser power variation coefficient M is -7.87cm ^-1 /mw through linear fitting, and Figure 3 shows a typical Raman Mann peak shifted and fitted data with laser power.

To carry out the Raman spectrum test at different temperatures on the PtS ₂ sample to be tested, here we choose the wave number of the E ¹ _2g vibration mode peak to change with temperature and perform temperature-wave number offset coefficient calibration: set the temperature to: 80K to 300K, The interval is 20K, a total of 11 points. And use Raman to mark the wave number under the corresponding peak. According to the formula: M=Δω/ΔT, the peak wave number offset-temperature variation coefficient M' is -0.028cm ^-1 /K through linear fitting. Figure 4 shows a typical Raman Mann peak shift and fit data with temperature.

I为激光的单位功率密度，α为少层薄片的吸收率，t为薄片的厚度，r₀为激光光斑的半径。体积高斯光束加热方程：/>

其中k为悬浮材料的热导率，T(r)为孔内温度的分布，r为距离圆孔中心得距离，R为圆空洞的半径。Use MATLAB software to establish the heat distribution formula: the volumetric Gaussian beam heating equation is:

I is the unit power density of the laser, α is the absorption rate of the few-layer flake, t is the thickness of the flake, and _r0 is the radius of the laser spot. Volumetric Gaussian beam heating equation: />

Where k is the thermal conductivity of the suspended material, T(r) is the temperature distribution in the hole, r is the distance from the center of the hole, and R is the radius of the hole.

得到T₂(r)为孔外温度的分布，k′为覆盖在衬底上层状薄片的热导率，G为界面的热导率，无穷远处的温度定义为T_a。加权平均温度为：/>

在根据边界条件：T₁(R)＝T₂(γ)|_r＝R，T₂(r→∞)＝T_a，/>

和近似条件：G＝50MW/m²k，k＝k′。The heat diffusion equation outside the cavity:

It is obtained that T ₂ (r) is the temperature distribution outside the hole, k' is the thermal conductivity of the layered sheet covering the substrate, G is the thermal conductivity of the interface, and the temperature at infinity is defined as T _a . The weighted average temperature is: />

According to the boundary conditions: T ₁ (R) = T ₂ (γ) | _{r = R} , T ₂ (r→∞) = T _a , />

And approximate conditions: G=50MW/m ² k, k=k'.

如图4所示，代入热导率公式最后得到的热导率为12W/mK.再改变假设条件G和K`的大小，代入之前提取的热导率，利用MATLAB建立的公式计算温度沿着某条直径X轴的温度分布。如图6所示，在热导率为12Wm<sup>-1</sup>K<sup>-1</sup>的情况下，改变假设条件G和K`的值，发现曲线基本重合，表明它们对温度分布和热导率影响很小。进而保证了即便在假设条件下也能准确的提取热导率。Combined with the experimental test data, substitute the formula to extract the thermal conductivity: look up the material and get the absorption rate α of PtS ₂ with a thickness of 3nm is 3.4%, and the experimentally measured

As shown in Figure 4, the final thermal conductivity obtained by substituting the thermal conductivity formula is 12W/mK. Then change the size of the assumptions G and K`, substitute the previously extracted thermal conductivity, and use the formula established by MATLAB to calculate the temperature along the The temperature distribution along the x-axis of a certain diameter. As shown in Fig. 6, in the case of thermal conductivity of 12Wm <sup>-1</sup> K <sup>-1</sup> , changing the values of the assumed conditions G and K`, it is found that the curves basically coincide, indicating that they have little influence on the temperature distribution and thermal conductivity. This in turn ensures accurate extraction of thermal conductivity even under hypothetical conditions.

It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that there is a relationship between these entities or operations. There is no such actual relationship or order between them.

Furthermore, the term "comprises", "comprises" or any other variation thereof is intended to cover a non-exclusive inclusion such that a process, method, article, or apparatus comprising a set of elements includes not only those elements, but also includes elements not expressly listed. other elements of or also include elements inherent in such a process, method, article, or device. Without further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article or apparatus comprising said element.

The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: it can still be described in the foregoing embodiments Modifications are made to the recorded technical solutions, or equivalent replacements are made to some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (6)

1. The method for measuring the thermal conductivity of a two-dimensional layered material based on temperature-dependent Raman spectroscopy, is characterized in that, comprising the following steps: S1: Set up the substrate of the sample to be tested, and prepare the sample to be tested based on mechanical peeling and PDMS transfer technology; S2: At room temperature, conduct Raman spectroscopy tests at different powers on the sample to be tested, and perform power-wavenumber offset coefficient calibration; In the step S2, the Raman spectrum is used to calibrate the coefficient of the Raman wavenumber of the few-layer sheet to be measured with the power offset: M=Δω/ΔP Among them, M is the coefficient of Raman wavenumber offset with power, Δω is the wavenumber offset of a few-layer sheet, ΔP is the offset of laser power, and the range of laser power is selected from 0.1mW to 0.35mW; S3: Carry out Raman spectrum tests at different temperatures for the sample to be tested, and perform temperature-wavenumber offset coefficient calibration; In the step S3, the Raman spectrum is used to calibrate the coefficient of the Raman wavenumber of the thin film to be measured as the temperature shifts: M'=Δω/ΔT Among them, Mˊ is the coefficient of Raman wavenumber offset with temperature, Δω is the wavenumber offset of few-layer sheet, ΔT is the offset of temperature, and the range of temperature is selected from 80K to 300K; S4: Establish a simplified formula for heat distribution based on a specific theoretical model and corresponding boundary conditions; In said step S4, according to a specific theoretical model and corresponding boundary conditions, then use MATLAB software to calculate the heat conduction relational expression; S5: Combined with the experimental test data, substitute the simplified formula to extract the thermal conductivity, and then use the extracted thermal conductivity to reversely verify the rationality of the assumed conditions, and then determine the accuracy of the extracted thermal conductivity; In the step S5, the Raman spectrum is used to calibrate the coefficient of the Raman wavenumber of the few-layer sheet to be measured with the temperature offset, and the thermal conductivity is extracted in combination with the experimental test data, and then the extracted thermal conductivity can be used to simulate the temperature along the circle The temperature distribution diagram of the hole diameter verifies the rationality of the assumptions G and K`, and then determines the accuracy of the thermal conductivity. 2. the method for measuring the thermal conductivity of two-dimensional layered materials based on temperature-dependent Raman spectroscopy according to claim 1, is characterized in that, described step S1 also comprises: S11: Prepare a clean silicon wafer, and use a coater to spin coat the surface with a specified thickness of positive photoresist; S12: Use a mask plate and an upper ultraviolet exposure machine to obtain a corresponding pattern template on a silicon wafer spin-coated with photoresist, and then pattern it under the action of a developer; S13: Etching the patterned silicon wafer into hydrofluoric acid and saturated sodium hydroxide solution to obtain a silicon wafer with round holes; S14: Use scotch tape to mechanically peel off the bulk layered semiconductor material to obtain the corresponding few-layer flakes, and then transfer them to silicon wafers with holes by using PDMS dry method. 3. The method for measuring the thermal conductivity of two-dimensional layered materials based on temperature-dependent Raman spectroscopy according to claim 2 is characterized in that: circular holes with a diameter of 8 μm are respectively set on the mask plate, and the distance between each circular hole is set 5μm, three circular holes arranged in matrix. 4. the method for measuring the thermal conductivity of two-dimensional layered materials based on temperature-dependent Raman spectroscopy according to claim 2 is characterized in that: first use hydrofluoric acid to corrode the patterned silicon wafer for 20-40 seconds, and then place Add saturated sodium hydroxide to corrode for 8-9 hours, and finally wash it with deionized water, and then dry it. 5. according to the method for measuring the thermal conductivity of two-dimensional layered materials based on temperature-dependent Raman spectroscopy according to claim 2, it is characterized in that: the PDMS with sample is taken under the micro-transfer platform with microscope, find out suitable Few-layer flakes are transferred to silicon wafer substrates with voids. 6. The method for measuring the thermal conductivity of two-dimensional layered materials based on temperature-dependent Raman spectroscopy according to claim 5, characterized in that: the few-layer flakes are completely covered on the circular cavity of the substrate, so that the sample to be measured is in suspension status.

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