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

Method for measuring thermal conductivity of two-dimensional layered material based on temperature-dependent Raman spectrum Download PDF

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CN111693510B
CN111693510B CN202010582500.6A CN202010582500A CN111693510B CN 111693510 B CN111693510 B CN 111693510B CN 202010582500 A CN202010582500 A CN 202010582500A CN 111693510 B CN111693510 B CN 111693510B
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李亮
檀朝阳
陈家旺
陈利杰
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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 material based on temperature-dependent Raman spectrum
Technical Field
The invention relates to the technical field of semiconductor film testing, in particular to a method for measuring the thermal conductivity of a two-dimensional layered material based on temperature-dependent Raman spectroscopy.
Background
In order to meet the requirement of the 5G technology in the future, the integration level of the semiconductor with high power density on the chip is higher and higher, so that more heat is brought while more power consumption is caused, and the heat accumulation effect can greatly deteriorate the performance and stability of the device. Meanwhile, the increase of the integration level shows that the volume of the semiconductor is continuously reduced, and the traditional method for accurately measuring the thermal conductivity of the micron-sized semiconductor is difficult to realize.
For example, the electrochemical 3 omega rule is limited by the heating frequency, which can lead to damage to the sample to be measured, which is no longer suitable for measuring the thermal conductivity of micro-nano materials. The laser heat reflection rule needs to vapor-deposit a heat absorption layer on a sample to be measured, and has larger error. Therefore, to advance the development and production of large-scale high power density semiconductors, it is important to develop a robust, non-contact, non-damaging thermal conductivity measurement method for assessing and guiding thermal management.
Meanwhile, since the discovery of graphene in 2004, two-dimensional layered materials have been increasingly focused and studied because of atomic level planes, wearability, band gap tunability, and strong light and substance interactions. Graphene has carrier mobility 100 times that of conventional silicon materials, and has an optical resonance response of ultra-wide spectrum.
The transition metal sulfur compound and the black phosphorus have special crystal structures, so that the band gap and the electronic characteristics of the transition metal sulfur compound and the black phosphorus can be changed along with the number of layers, and the transition metal sulfur compound and the black phosphorus provide new material choices for developing novel light-emitting devices and energy storage devices and researching the emerging energy valley optoelectronics. Excellent thermal management techniques can ensure reliable and stable operation of the device. With the wide application prospect of two-dimensional materials for future electronic and optoelectronic devices, the exploration of the thermal conductivity of the materials is also becoming particularly important.
To date, raman spectroscopy has been one of the most conventional and non-destructive techniques to study the physical properties of low-dimensional nanomaterials. Focusing the laser causes localized heating of the material, which changes the phonon frequency. Meanwhile, the Raman spectrum is particularly sensitive to phonon frequency change, and can directly detect the vibration of phonons. This makes it possible to achieve low dimensional thermal performance testing of raman spectra.
Disclosure of Invention
Aiming at the defects of the prior art, the invention discloses a method for measuring the thermal conductivity of a two-dimensional layered material based on temperature-dependent Raman spectrum, which can solve the problems of the prior art that the thermal conductivity of a micro-nano material is limited, the micro-nano measuring precision is improved, and the like.
In order to achieve the above purpose, the invention is realized by the following technical scheme:
a method for measuring thermal conductivity of a two-dimensional layered material based on temperature-dependent raman spectroscopy, comprising the steps of:
s1: setting a substrate of a sample to be detected, and preparing the sample to be detected based on mechanical stripping and PDMS transfer technology;
s2: 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;
s3: carrying out Raman spectrum tests at different temperatures on a sample to be tested, and carrying out temperature-wave number offset coefficient calibration;
s4: calculating a thermal conductivity relation by utilizing MATLAB simulation software according to the specific theoretical model and the corresponding boundary conditions;
s5: and substituting the experimental test data into a simplified formula to extract the heat conductivity.
In a preferred technical solution, the step S1 further includes:
s11: preparing a clean silicon wafer, and spin-coating positive photoresist with a specified thickness on the surface of the clean silicon wafer by using a photoresist homogenizing machine;
s12: using a mask plate and an upper ultraviolet exposure machine to obtain a corresponding pattern template on a silicon wafer with spin-coating photoresist, and then performing patterning under the action of a developing solution;
s13: placing the patterned silicon wafer into hydrofluoric acid and saturated sodium hydroxide solution for corrosion to obtain a silicon wafer with round holes;
s14: and mechanically stripping the block layered semiconductor material by using a transparent adhesive tape to obtain a corresponding few-layer sheet, and transferring the corresponding few-layer sheet onto a silicon wafer with a cavity by using a PDMS dry method.
Further preferable technical scheme is that three circular holes with diameters of 3 μm, 4 μm and 5 μm are respectively arranged on the mask, the distance between each circular hole is 5 μm, and the three circular holes are arranged in matrix.
According to a further preferred technical scheme, firstly, the patterned silicon wafer is corroded by hydrofluoric acid for 1 minute, then saturated sodium hydroxide is put into the silicon wafer to corrode the silicon wafer for 8-9 hours, and finally deionized water is used for cleaning the silicon wafer, and the silicon wafer is dried.
According to a further preferred technical scheme, PDMS with a sample is taken under a micro-transfer platform with a microscope, and a proper few-layer thin sheet is found and transferred onto a silicon wafer substrate with a cavity.
According to the further preferred technical scheme, the few-layer thin sheet completely covers the round cavity of the substrate, so that the sample to be measured is in a suspended state.
In the preferred technical scheme, in the step S2, the Raman spectrum is utilized to calibrate the coefficient of the Raman wave number of the few-layer sheet to be measured along with the power offset,
M=Δω/ΔP
wherein M is a coefficient of Raman wave number offset with power, deltaω is a small-layer sheet wave number offset, deltaP is an offset of laser power, and the range of the laser power is selected to be 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 sheet to be measured along with the temperature shift,
M′=Δω/ΔT
where M' is a coefficient of Raman wavenumber offset with temperature, Δω is a few-layer sheet wavenumber offset, ΔT is a temperature offset, and the temperature range is selected to be 80K to 300K.
In the preferred technical scheme, in the step S4, according to a specific theoretical model and corresponding boundary conditions, a thermal conductivity relation is calculated by utilizing MATLAB simulation software;
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 along with the temperature offset, the thermal conductivity is extracted in combination with experimental test data, and then the extracted thermal conductivity can be used to simulate the temperature distribution diagram of the temperature along the x-axis, so as to verify the rationality of the assumed conditions G and K', and further determine 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 spectrum, which has the following advantages:
by reasonably designing a substrate with larger holes, constructing a heat transmission characterization conforming to a Raman test and a theoretical model, and realizing the measurement of the heat conductivity of the nanoscale two-dimensional layered material; meanwhile, the device is a non-contact type test, so that the deviation possibly caused by contact is reduced to the minimum value, and the measurement result is more accurate; the scheme has strong feasibility, simple operation and low cost, and is beneficial to the system research on the thermal management of the two-dimensional material.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below.
It is evident that the drawings in the following description are only some embodiments of the present invention and that other drawings may be obtained from these drawings without inventive effort for a person of ordinary skill in the art.
FIG. 1 is a logical block diagram of an embodiment of the present invention;
FIG. 2 is a schematic diagram of a sample to be tested in an embodiment of the present invention;
FIG. 3 is a typical Raman peak shift with laser power and fit image;
fig. 4 is a shift and fit image of a typical raman peak with temperature.
FIG. 5 is an image of extracted thermal conductivity in an embodiment of the invention;
FIG. 6 is a plot of temperature profile along the x-axis diameter of a sample in an embodiment of the invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments.
All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, a method for measuring thermal conductivity of a two-dimensional layered material based on temperature-dependent raman spectroscopy according to an embodiment of the present invention includes the following steps:
firstly, preparing a clean silicon wafer, spin-coating positive photoresist with a specified thickness on the surface of the silicon wafer, adding an ultraviolet exposure machine to the mask plate, obtaining a corresponding pattern template on the spin-coated silicon wafer, then patterning under the action of a developing solution, further placing the patterned silicon wafer into hydrofluoric acid to be corroded for 20-40 seconds, and then corroding the silicon wafer with saturated sodium hydroxide solution for 10-12 hours to obtain the silicon wafer with round holes.
Finally, the bulk two-dimensional layered material was mechanically peeled off with tape to give the corresponding thin layer, which was directly transferred to PDMS and then microscopically found to a thin layer of moderate thickness and size, and samples were transferred from PDMS onto round holes of the substrate with the aid of a micromanipulator, as shown in fig. 2.
And in the room temperature environment, carrying out Raman spectrum test on the sample to be tested under different laser powers, calibrating the power-wave number offset coefficient, and aligning the light spot of the laser with the center of the round hole under the suspension sample to be tested. Correspondingly, the Raman spectrum test is carried out on the measured sample at different temperatures, and the calibration of the temperature-wave number offset coefficient is carried out. The light spot of the laser is aligned with the center of the lower round hole of the suspension sample to be measured.
It can be appreciated that the embodiment of the present invention further includes establishing a heat distribution formula:
let I be the unit power density of the laser, alpha be the absorptivity of the few-layer sheet, t be the thickness of the sheet, r 0 Is the radius of the laser spot.
k is the thermal conductivity of the suspended material, T (R) is the distribution of the temperature in the hole, R is the distance from the center of the round hole, and R is the radius of the round hole.
Further, a volumetric gaussian beam heating equation is obtained:
Figure GDA0004156734660000061
further, a volumetric gaussian beam heating equation is obtained:
Figure GDA0004156734660000062
T 2 (r) is the distribution of the out-of-hole temperature, k' is the thermal conductivity of the layered sheet overlying the substrate, G is the thermal conductivity of the interface, and the temperature at infinity is defined as T a
Further, the thermal diffusion equation outside the cavity is obtained:
Figure GDA0004156734660000063
the weighted average temperature of the further cavity centers is:
Figure GDA0004156734660000064
further, the boundary conditions are:
T 1 (R)=T 2 (γ)| r=R
T 2 (r→∞)=T a
Figure GDA0004156734660000065
Figure GDA0004156734660000066
further, the approximate conditions are:
k=k′
G=50MW/m 2 k
the present invention will be described in detail with reference to examples.
PtS (PtS) test for thermal conductivity of two-dimensional layered semiconductor material platinum disulfide 2 The substrate is a silicon wafer with a thickness of 3nm and 300nm SiO2 deposited.
Designing a substrate of a sample to be tested, and transferring the sample to be tested onto the substrate: firstly, preparing a clean silicon wafer, spin-coating positive photoresist with a certain thickness on the surface of the silicon wafer, adding an ultraviolet exposure machine to a mask designed in advance, obtaining a corresponding pattern template on the silicon wafer spin-coated with the photoresist, then patterning under the action of a developing solution, further placing the patterned silicon wafer into hydrofluoric acid to be corroded for 20-40 seconds, and then corroding the patterned silicon wafer with saturated sodium hydroxide solution for 10-12 hours to obtain the silicon wafer with the round cavity. Finally, the bulk two-dimensional layered material is mechanically peeled off by using an adhesive tape to obtain a corresponding thin layer, the corresponding thin layer is directly transferred to PDMS, then a microscope is used for finding out the thin layer with proper thickness and size, and a sample is transferred from the PDMS to a round hole of a substrate with the help of a micromanipulator.
PtS to be tested in room temperature environment 2 Raman spectroscopic testing of samples spread at different laser powers here we select E 1 2g The wave number of the vibration mode peak changes along with the power and the power-wave number offset coefficient is calibrated: setting the power of the laserThe method comprises the following steps: 0.1mW to 0.35mW, with intervals of 0.034mW, for a total of 10 points. And the wave number under the corresponding wave peak is marked by Raman according to the formula: M=Δω/ΔP by linear fitting to obtain peak wavenumber shift-laser power variation coefficient M of-7.87 cm -1 FIG. 3 shows typical Raman peak shift with laser power and fitted data.
To PtS to be tested 2 Raman spectroscopy at different temperatures of sample development, where we select E 1 2g Variation of wave number of vibration mode peak with temperature and calibration of temperature-wave number offset coefficient: the temperature was set to: 80K to 300K, spaced 20K apart for a total of 11 points. And the wave number under the corresponding wave peak is marked by Raman according to the formula: m=Δω/Δt by linear fitting to obtain peak wavenumber shift-temperature change coefficient M' of-0.028 cm -1 FIG. 4 shows typical Raman peak shift and fit data with temperature.
Establishing a heat distribution formula by utilizing MATLAB software: the volumetric gaussian beam heating equation is:
Figure GDA0004156734660000071
i is the unit power density of laser, alpha is the absorptivity of the few-layer sheet, t is the thickness of the sheet, r 0 Is the radius of the laser spot. Volumetric gaussian beam heating equation: />
Figure GDA0004156734660000081
Wherein k is the thermal conductivity of the suspended material, T (R) is the distribution of the temperature in the hole, R is the distance from the center of the round hole, and R is the radius of the round hole.
Equation of thermal diffusion outside the cavity:
Figure GDA0004156734660000082
obtaining T 2 (r) is the distribution of the temperature outside the hole, k' is the thermal conductivity of the lamellar sheet covered on 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: />
Figure GDA0004156734660000083
According to boundary conditions: t (T) 1 (R)=T 2 (γ)| r=R ,T 2 (r→∞)=T a ,/>
Figure GDA0004156734660000084
Figure GDA0004156734660000085
And approximate conditions: g=50 MW/m 2 k,k=k′。
And substituting the experimental test data into a formula to extract the heat conductivity: referring to the material to obtain PtS with thickness of 3nm 2 Is 3.4% and will be experimentally measured
Figure GDA0004156734660000086
As shown in fig. 4, substituting the thermal conductivity formula to obtain a final thermal conductivity of 12W/mK., changing the sizes of the assumed conditions G and K', substituting the thermal conductivity extracted before, and calculating the temperature distribution of the temperature along a certain diameter X axis by using the formula established by MATLAB. As shown in FIG. 6, the thermal conductivity was 12Wm -1 K -1 In the case of (2) changing the values of the hypothetical conditions G and K', the curves were found to be substantially coincident, indicating that they have little effect on the temperature distribution and thermal conductivity. Thereby ensuring that the thermal conductivity can be accurately extracted even under the assumption.
It is noted that relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions.
Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (6)

1. A method for measuring the thermal conductivity of a two-dimensional layered material based on temperature-dependent raman spectroscopy, comprising the steps of:
s1: setting a substrate of a sample to be detected, and preparing the sample to be detected based on mechanical stripping and PDMS transfer technology;
s2: 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;
in the step S2, the raman spectrum is used to calibrate the coefficient of the raman wavenumber of the less-layer sheet to be measured along with the power offset:
M=Δω/ΔP
wherein M is a coefficient of Raman wave number offset along with power, deltaω is a less-layer sheet wave number offset, deltaP is an offset of laser power, and the range of the laser power is selected to be 0.1mW to 0.35mW;
s3: carrying out Raman spectrum tests at different temperatures on a sample to be tested, and carrying out temperature-wave number offset coefficient calibration;
in the step S3, the raman spectrum is used to calibrate the coefficient of the raman wavenumber of the sheet to be measured with the temperature shift:
M′=Δω/ΔT
wherein M' is a coefficient of the shift of the Raman wave number with temperature, deltaω is a shift of the wave number of the few-layer sheet, deltaT is a shift of the temperature, and the temperature is selected to be 80K to 300K;
s4: establishing a simplified formula of heat distribution according to a specific theoretical model and corresponding boundary conditions;
in the step S4, according to a specific theoretical model and corresponding boundary conditions, calculating a thermal conductivity relation by utilizing MATLAB software;
s5: combining experimental test data, substituting the experimental test data into a simplified formula to extract heat conductivity, and reversely verifying the rationality of the hypothesized condition by utilizing the extracted heat conductivity to further determine the accuracy of the extracted heat 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 along with the temperature offset, and the thermal conductivity is extracted in combination with experimental test data, and then the extracted thermal conductivity can be used to simulate the temperature distribution diagram of the temperature along the diameter of the round hole, so as to verify the rationality of the assumed conditions G and K', and further determine the accuracy of the thermal conductivity.
2. The method for measuring thermal conductivity of a two-dimensional layered material based on temperature-dependent raman spectroscopy according to claim 1, wherein said step S1 further comprises:
s11: preparing a clean silicon wafer, and spin-coating positive photoresist with a specified thickness on the surface of the clean silicon wafer by using a photoresist homogenizing machine;
s12: using a mask plate and an upper ultraviolet exposure machine to obtain a corresponding pattern template on a silicon wafer with spin-coating photoresist, and then performing patterning under the action of a developing solution;
s13: placing the patterned silicon wafer into hydrofluoric acid and saturated sodium hydroxide solution for corrosion to obtain a silicon wafer with round holes;
s14: and mechanically stripping the block layered semiconductor material by using a transparent adhesive tape to obtain a corresponding few-layer sheet, and transferring the corresponding few-layer sheet onto a silicon wafer with a cavity by using a PDMS dry method.
3. The method for measuring the thermal conductivity of a two-dimensional layered material based on temperature-dependent raman spectroscopy according to claim 2, wherein: round holes with the diameter of 8 mu m are respectively arranged on the mask, the distance between each round hole is 5 mu m, and three round holes are arranged in a matrix.
4. The method for measuring the thermal conductivity of a two-dimensional layered material based on temperature-dependent raman spectroscopy according to claim 2, wherein: etching the patterned silicon wafer for 20-40 seconds by using hydrofluoric acid, then putting saturated sodium hydroxide into the silicon wafer to etch for 8-9 hours, finally washing the silicon wafer by using deionized water, and then drying the silicon wafer.
5. The method for measuring the thermal conductivity of a two-dimensional layered material based on temperature-dependent raman spectroscopy according to claim 2, wherein: and taking the PDMS with the sample under a micrometric transfer platform with a microscope, finding out a proper few-layer thin sheet, and transferring the thin sheet to a silicon wafer substrate with a cavity.
6. The method for measuring thermal conductivity of a two-dimensional layered material based on temperature-dependent raman spectroscopy according to claim 5, wherein: the few-layer thin sheet completely covers the round cavity of the substrate, so that the sample to be measured is in a suspended state.
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