CN110031504B - Method for testing thermal contact resistance between circular-section one-dimensional nano structure - Google Patents

Method for testing thermal contact resistance between circular-section one-dimensional nano structure Download PDF

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CN110031504B
CN110031504B CN201910213215.4A CN201910213215A CN110031504B CN 110031504 B CN110031504 B CN 110031504B CN 201910213215 A CN201910213215 A CN 201910213215A CN 110031504 B CN110031504 B CN 110031504B
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杨决宽
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Abstract

The invention discloses a method for testing the contact resistance between a circular section one-dimensional nano structure, under an optical microscope or a scanning electron microscope, a micro-manipulator is used for breaking a circular section one-dimensional nano structure into 2 sections which are respectively lapped on a heat source and a heat sink of a suspended micro device, the two sections of samples form parallel contact between the heat source and the heat sink, and the sample is tested by adopting a thermal bridge method to obtain the apparent thermal resistance Rtot1(ii) a Under an optical microscope or a scanning electron microscope, a micro-manipulator is used for changing the parallel contact of the two sections of samples into cross contact, and the sample is tested by adopting a thermal bridge method to obtain apparent thermal resistance Rtot2(ii) a The contact thermal resistance per unit area between two sections of samples can be approximated as RCA＝(Rtot2‑Rtot1)×Ac2Wherein A isc2Is the contact area of the cross-contact between the two sections of the sample. The invention improves the success rate of the test, reduces the requirement on the consistency of the sample quality and improves the test precision.

Description

Method for testing thermal contact resistance between circular-section one-dimensional nano structure
Technical Field
The invention belongs to the technical field of testing thermophysical parameters of solid materials, and particularly relates to a method for testing contact resistance between a circular-section one-dimensional nanostructure.
Background
The contact thermal resistance among the one-dimensional nanostructures has important value for microelectronic device design, thermal interface material design and the like. Reported test schemes for measuring contact resistance in one-dimensional nanostructures can be divided into two categories: one type may be referred to as a multipoint method and one type may be referred to as a single point method.
In the multi-point method, the nanostructures are stacked into a thin film, so that there are a large number of contact points between the nanostructures in the thin film, and the thermal contact resistance between the nanostructures can be deduced by testing the thermophysical properties of a thin film sample, as described in the Physical Review Letters 102,105901 (2009). However, in the multi-point method, the density of the indirect contact points of the nanostructure in the film sample needs to be known, and the density of the contact points cannot be accurately measured, so that the measurement error of the multi-point method is very large, and even the multi-point method has magnitude deviation.
In the single-point method, two nanostructures are lapped together to form a single contact point, and the contact thermal resistance between the nanostructures is directly or indirectly measured. The single-point method is significantly more accurate than the multi-point method because the density of the contact points does not need to be estimated.
The patent with the application number of CN201210426861.7 discloses a method for measuring the contact thermal resistance of a one-dimensional material, which determines the temperatures of two sides of an interface based on the characteristic peak frequency shift of a Raman spectrum, and further determines the temperature difference on the interface to obtain the contact thermal resistance of the one-dimensional material. The method adopts a non-contact temperature testing means of Raman technology, and simplifies the preparation process of the sample. However, the method can only be used for materials with significant temperature frequency shift characteristics of the raman spectrum, and for a one-dimensional nanostructure, the diameter of a light spot is far larger than the characteristic size of a sample, so that a measurement signal is weak, and a measurement error is large.
The patent with the application number of CN201720450926.X discloses a thermoelectric performance measurement system for a nano material, which is based on a T-shaped method technology, and can measure not only the electric conductivity, the thermal conductivity, the Seebeck coefficient and the like of a one-dimensional nano structure, but also the contact thermal resistance between a sample and a hot wire. Since in this system a hot wire is used as the electrical heating source, which needs to have good electrical conductivity, it cannot be used to test the thermal contact resistance between two electrically isolated one-dimensional nanostructures.
A thermal bridge method based on a suspended micro device is a steady state testing technology and is widely used for testing the electrical conductivity, the thermal conductivity and the Seebeck coefficient of a one-dimensional nano structure. The inventors have achieved a measurement of the thermal contact resistance between carbon nanotubes using a thermal bridge method (Physical Review Letters 112,205901 (2014)). In the scheme, the total thermal resistance of two nano structures contacting a sample is measured firstly, and then the thermal resistances of the two nano structures and the thermal resistances of the two nano structures with a heat source and a heat sink are measured respectively, so that the thermal resistance of the two nano structures is calculated. The test scheme has the advantage of having no requirements on the performances of the tested material such as conductivity and the like. The disadvantages are that: 1) the test success rate is low. In the test scheme, the nano structure needs to be moved in a large range, so that a sample is easily damaged or lost, and the test success rate is reduced; 2) the requirement on the quality consistency of the samples is high. The fluctuation of the thermal conductivity of the sample in the length direction is accumulated in the testing error of the contact thermal resistance.
Disclosure of Invention
The invention provides a method for testing thermal contact resistance in a one-dimensional nanostructure with a circular cross section, which aims at the one-dimensional nanostructure with the circular cross section, reduces the manipulation amplitude of a sample, improves the success rate of the test, reduces the requirement on the quality consistency of the sample, and improves the test precision.
In order to solve the problems of the prior art, the invention adopts the technical scheme that:
a method for testing thermal contact resistance between a circular section one-dimensional nano structure comprises the following steps:
step 1, under an optical microscope or a scanning electron microscope, breaking a circular section one-dimensional nanostructure into 2 sections by using a micromanipulator, and respectively recording the sections as samples A and B;
step 2, under an optical microscope or a scanning electron microscope, a micro-manipulator is used for respectively overlapping the samples A and B on a heat source and a heat sink of the suspended micro-device, and the samples A, B form parallel contact between the heat source and the heat sink;
step 3, testing the sample by adopting a thermal bridge method to obtain apparent thermal resistance Rtot1And R istot1Is composed of
Rtot1＝Rmh1+Rmc1+Rs1 (1)
Wherein R ismh1And Rmc1The thermal contact resistances between the sample A and the heat source and between the sample B and the heat sink in the test are Rs1Is the intrinsic thermal resistance of a sample in parallel contact between a heat source and a heat sink, Rs1Is composed of
Rs1＝R1/L×(LCE+LEF/2+LDF)+f×RCA/Ac1 (2)
R1/LIntrinsic thermal resistance per unit length, L, for samples A and BCEIs the length of sample A between CEs, C is the point of contact of sample A with the edge of the heat source, E is the parallelism of samples A and BStarting point of contact, LEFLength of parallel contact between samples EF, end point of parallel contact between samples A and B, LDFIs the length of sample B between DF, D is the point of contact of sample B with the edge of the heat sink, RCAThermal contact resistance per unit area between samples A, B, Ac1The contact area between samples A, B at the EF parallel contact section can be expressed by the thermal model
Figure BDA0002001195540000021
Wherein
Figure BDA0002001195540000022
w is the width of the contact surface at parallel contact between samples A, B;
step 4, under an optical microscope or a scanning electron microscope, a micro-manipulator is used for changing the parallel contact of the samples A and B into the cross contact, in the process, the contact between the sample A and a heat source is ensured not to be changed, the contact between the sample B and a heat sink is ensured not to be changed, the cross contact point G of the samples A and B is positioned between parallel contact sections EF in the figure 1, and the test length of the samples is approximately equal to that in the step 2, namely
LCG+LDG≈LCE+LEF/2+LDF (4)
Step 5, testing the sample by adopting a thermal bridge method to obtain apparent thermal resistance Rtot2And R istot2Is composed of
Rtot2＝Rmh2+Rmc2+Rs2 (5)
Wherein R ismh2And Rmc2The thermal contact resistances R between the sample A and the heat source and between the sample B and the heat sink in the test are respectivelys2Is the intrinsic thermal resistance, R, of a sample in cross contact between heat sinks of a heat sources2Is composed of
Rs2＝R1/L×(LCG+LDG)+RCA/Ac2 (6)
Wherein A isc2Is the contact area between samples A, B in the test specimen;
step 6, since in the above step 4, the contact between the sample A and the heat source is kept unchanged, and the contact between the sample B and the heat sink is kept unchanged, there is Rmh1＝Rmh2，Rmc1＝Rmc2The measured lengths of the samples are kept to be substantially equal, namely, the formula (4), so that the contact thermal resistance per unit area between the samples A, B can be obtained by the formulas (1) and (5):
Figure BDA0002001195540000031
for a circular cross-section one-dimensional nanostructure, Ac1Much greater than fA c2, the formula (7) can be approximated as
RCA＝(Rtot2-Rtot1)×Ac2 (8)
The total thermal resistance of the parallel contact sample and the cross contact sample is obtained through two times of measurement in the step 3 and the step 5, and the thermal contact resistance of the circular section one-dimensional nano structure in unit area is obtained through calculation according to a formula (8).
To ensure that the contact between sample a and the heat source does not change and the contact between sample B and the heat sink does not change in step 4, an electron beam induced deposition technique may be used to deposit Pt on sample A, B where it contacts the heat source, heat sink, to better secure the sample in step 2.
As an improvement, the lengths measured in step 2 and step 4 are approximately equal, and the difference between the two, namely the actual difference between the left side and the right side of the formula (4), should be taken into account by RCAIn the test error, there is an error because of the approximation, so this difference should be taken into account in the error of the final result.
Has the advantages that:
compared with the prior art, the invention has the beneficial effects that:
(1) the test success rate is high.
After the parallel contact test is finished, only small-amplitude micro-manipulation is needed to be carried out on the sample, and the sample is changed into cross contact; the loss rate of the sample is reduced because the sample does not need to be moved in a large range, so that the success rate of the test is improved;
(2) the requirement on the consistency of the sample quality is reduced.
The technical scheme disclosed by the invention only requires that the quality of the measured sample has higher consistency in the parallel contact interval, the defects of the sample at other positions and the like have no influence on the test result, and the measurement precision is improved.
Drawings
FIG. 1 is a schematic diagram of a thermal bridge test principle and parallel contact, wherein 1-a heat source, 2-a first micro-coil, 3-a first suspension arm, 4-a substrate, 5-a second suspension arm, 6-a second micro-coil, and 7-a heat sink;
fig. 2 is a schematic cross-contact view.
Detailed Description
The invention discloses a test scheme of contact thermal resistance in a circular section one-dimensional nano structure, and the adopted test technology is a thermal bridge method. The invention is explained in more detail below with reference to the drawings and the examples.
FIG. 1 shows a schematic diagram of the thermal-physical property of a one-dimensional nanostructure tested by a thermal bridge method. The method uses a suspended micro device prepared by MEMS process, which comprises a suspended heat source 1 and a heat sink 7, a plurality of first suspended arms 3 supporting the heat source, a plurality of second suspended arms 5 supporting the heat sink, and a substrate 4. A first micro coil 2 and a second micro coil 6 are respectively manufactured on a heat source 1 and a heat sink 7, wherein the first micro coil 2 is used as a heater and a temperature sensor to heat the heat source and detect the temperature of the heat source at the same time, and the second micro coil 6 is used as a temperature sensor to detect the temperature of the heat sink 7. The sample to be tested is lapped between the heat source 1 and the heat sink 7.
The test was carried out in a vacuum oven, so the effect of convective heat transfer was negligible. The radiation effect can be reduced to a negligible level by using 2-3 layers of thermal radiation shields. Alternating current and direct current I + I are led into the first miniature coil 2 at the heat source endacWherein I is a direct current for generating Joule heat for heating the heat source IacFor detecting the alternating current. Respectively detecting a first micro-coil 2 at the heat source end and a second micro-wire at the heat sink 7 endThe ac voltage drop v across the ring 6acThe resistance of the coil can be derived based on ohm's law. Based on a steady-state method heat conduction model, the apparent thermal resistance of the tested sample can be obtained as follows:
Figure BDA0002001195540000041
wherein, Delta ThAnd Δ TsThe temperature rises of the heat source 1 and the heat sink 7 respectively, and can be obtained by measuring the resistance changes of the first micro-coil 2 and the second micro-coil 6, QhAnd QLJoule heat generated by the heating current I in the heat source end first micro-coil 2 and one suspension arm 3 respectively. RtotIncluding the thermal resistance of the sample itself, the thermal contact resistance between the sample and the heat source, and the thermal contact resistance between the sample and the heat sink 7.
Taking the test of the thermal contact resistance between carbon nano-tubes with the diameter of 68nm as an example, the specific test process comprises the following main steps: (1) under an optical microscope, a carbon nanotube with the length of about 30 μm and the diameter of 68nm is broken into 2 sections near the middle position by using a micro-manipulator, and the 2 sections are respectively marked as samples A and B;
(2) as illustrated in fig. 1, samples a and B were respectively lapped on a heat source and a heat sink of a suspended microdevice using a micromanipulator under an optical microscope, and sample A, B was brought into parallel contact between the heat source and the heat sink. The length of each segment of the tested sample is measured under a scanning electron microscope, and the result is LCE＝4.5μm，LDF4.8 μm, contact length LEF2.1 μm. In order to ensure that the sample A, B has a firm contact with the heat source and the heat sink, metal Pt is deposited on the contact position of the sample A, B with the heat source and the heat sink by adopting an electron beam induced deposition technology, and in addition, the position EF indicated by an arrow in the figure 1 is the parallel contact formed between the samples A, B;
(3) the sample is tested by a thermal bridge method to obtain apparent thermal resistance Rtot1＝2.13×107K/W；
(4) Samples a and B were changed from parallel contact to cross contact using a micromanipulator under an optical microscope, as schematically shown in fig. 2. Due to the fact that in step 2The metal Pt was induced to deposit, so the contact between sample a and the heat source was not changed, and the contact between sample B and the heat sink was not changed. Measured under a scanning electron microscope, LCG+LDG10.48 μm, same as LCE+LEF/2+LDFThe difference is 0.13 μm, the requirement of formula 4 in the technical scheme is met, and the crossing angle is 88.6 degrees. The contact area of the samples A and B can be calculated as A through contact mechanicsc2＝51.68nm2。
(5) The sample is tested by a thermal bridge method to obtain apparent thermal resistance Rtot2＝3.60×107K/W；
(6) The obtained Rtot1、Rtot2And Ac2Substituting formula 8 in the technical scheme to obtain RCA＝7.6×10-10m2K/W。
In order to estimate the error caused by the simplification of the formula (7) to the formula (8) in the technical scheme, the intrinsic thermal conductivity of the measured carbon nanotube is measured, the intrinsic thermal conductivity K is 199.8W/m-K, and the intrinsic thermal conductivity K is substituted into the formula (3) to obtain f is 5.76. Finally, the error introduced by simplification is 7 percent according to the formula (7) and the formula (8). Considering the difficulty of the contact resistance test between the nano-structures, the error is completely acceptable.
The foregoing shows and describes the general principles and features of the present invention, together with the advantages thereof. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (3)

1. A method for testing thermal contact resistance between a circular section one-dimensional nano structure is characterized by comprising the following steps:
step 1, under an optical microscope or a scanning electron microscope, breaking a circular section one-dimensional nanostructure into 2 sections by using a micromanipulator, and respectively recording the sections as samples A and B;
step 2, under an optical microscope or a scanning electron microscope, a micro-manipulator is used for respectively overlapping the samples A and B on a heat source and a heat sink of the suspended micro-device, and the samples A, B form parallel contact between the heat source and the heat sink;
step 3, testing the parallel contact sample in the step 2 by adopting a thermal bridge method to obtain apparent thermal resistance Rtot1And R istot1Is Rtot1＝Rmh1+Rmc1+Rs1 (1)
Wherein R ismh1And Rmc1The thermal contact resistances between the sample A and the heat source and between the sample B and the heat sink in the test are Rs1Is the intrinsic thermal resistance of a sample in parallel contact between a heat source and a heat sink, Rs1Is composed of
Rs1＝R1/L×(LCE+LEF/2+LDF)+f×RCA/Ac1 (2)
R1/LIntrinsic thermal resistance per unit length, L, for samples A and BCEIs the length of sample A between CEs, C is the point of contact of sample A with the edge of the heat source, E is the point of origin of parallel contact between samples A and B, LEFLength of parallel contact between samples EF, end point of parallel contact between samples A and B, LDFIs the length of sample B between DF, D is the point of contact of sample B with the edge of the heat sink, RCAThermal contact resistance per unit area between samples A, B, Ac1The contact area between samples A, B at the EF parallel contact section can be expressed by the thermal model
Figure FDA0003070966550000011
Wherein
Figure FDA0003070966550000012
Where w is the width of the contact surface at parallel contact between samples A, B;
step 4, under an optical microscope or a scanning electron microscope, the samples A and B are changed from parallel contact into cross connection by using a micro-manipulatorDuring the process, the contact between the sample A and the heat source is ensured to be unchanged, the contact between the sample B and the heat sink is ensured to be unchanged, the sample A and B cross contact point G is positioned between the parallel contact sections EF, and the test length of the sample is approximately equal to that in the step 2, namely LCG+LDG≈LCE+LEF/2+LDF (4)
Step 5, testing the cross contact sample in the step 4 by adopting a thermal bridge method to obtain apparent thermal resistance Rtot2And R istot2Is composed of
Rtot2＝Rmh2+Rmc2+Rs2 (5)
Wherein R ismh2And Rmc2The thermal contact resistances R between the sample A and the heat source and between the sample B and the heat sink in the test are respectivelys2Is the intrinsic thermal resistance of a sample in cross contact between a heat source and a heat sink, Rs2Is composed of
Rs2＝R1/L×(LCG+LDG)+RCA/Ac2 (6)
Wherein A isc2Is the contact area between samples A, B in the test specimen;
step 6, since in the above step 4, the contact between the sample A and the heat source is kept unchanged, and the contact between the sample B and the heat sink is kept unchanged, there is Rmh1＝Rmh2，Rmc1＝Rmc2The tested lengths of the samples are kept to be basically equal, namely formula (4), so that the contact thermal resistance per unit area between the samples A, B can be obtained through formula (1) and formula (5)
Figure FDA0003070966550000021
For a circular cross-section one-dimensional nanostructure, Ac1Much greater than fAc2Therefore, equation (7) can be approximated as
RCA＝(Rtot2-Rtot1)×Ac2 (8)
Namely, the apparent thermal resistance of the parallel contact sample and the cross contact sample is obtained through two measurements in the step 3 and the step 5, and the thermal contact resistance of the unit area of the one-dimensional nanostructure with the circular section is obtained through calculation according to the formula (8).
2. The method for testing thermal contact resistance between a circular-section one-dimensional nanostructure as claimed in claim 1, wherein in order to ensure that the contact between the sample A and the heat source is not changed and the contact between the sample B and the heat sink is not changed in step 4, the electron beam induced deposition technique is used to deposit Pt on the contact between the sample A, B and the heat source and the heat sink in step 2, so as to better fix the sample.
3. The method for testing the contact resistance between the circular-section one-dimensional nanostructure according to claim 1, wherein the lengths measured in step 2 and step 4 are approximately equal, and the difference between the lengths measured in step 2 and step 4, i.e. the actual difference between the left side and the right side of the formula (4), should be taken into account by RCAAnd testing errors.
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