CN112816520B - Method for testing film contact thermal resistance - Google Patents

Method for testing film contact thermal resistance Download PDF

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CN112816520B
CN112816520B CN202011600491.5A CN202011600491A CN112816520B CN 112816520 B CN112816520 B CN 112816520B CN 202011600491 A CN202011600491 A CN 202011600491A CN 112816520 B CN112816520 B CN 112816520B
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童浩
杨冠平
缪向水
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Huazhong University of Science and Technology
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Abstract

本发明属于薄膜材料热特性测试领域,具体涉及一种薄膜接触热阻的测试方法,包括:在三个衬底上分别制备第一、第二待测薄膜以及依次层叠的第一、第二待测薄膜,层叠结构表示第三待测薄膜,在每个衬底对应的薄膜上表面制备金属条;每个衬底厚度大于该衬底对应的金属条在该衬底中的热穿透深度,且该衬底上部薄膜厚度小于热穿透深度;向每个金属条通入交流电信号并测试基波电压和三次谐波电压,分别基于三倍频法计算第一、第二和第三待测薄膜的热阻;由第三待测薄膜的热阻与第一、第二待测薄膜热阻加和的差值得到第一、第二待测薄膜间的接触热阻。本发明可测试纳米尺度超薄膜,对多层待测薄膜间的相对厚度无限制,且多层薄膜的接触状态与实际相符合。

Figure 202011600491

The invention belongs to the field of thermal property testing of thin film materials, and in particular relates to a method for testing contact thermal resistance of thin films, comprising: respectively preparing first and second thin films to be tested on three substrates, and successively stacking first and second thin films to be tested. Measuring film, the laminated structure represents the third film to be measured, and metal strips are prepared on the upper surface of the film corresponding to each substrate; the thickness of each substrate is greater than the thermal penetration depth of the metal strip corresponding to the substrate in the substrate, And the thickness of the film on the upper part of the substrate is less than the thermal penetration depth; pass an alternating current signal to each metal strip and test the fundamental wave voltage and the third harmonic voltage, and calculate the first, second and third to be calculated based on the triple frequency method respectively. The thermal resistance of the thin film is measured; the contact thermal resistance between the first and second thin films to be measured is obtained from the difference between the thermal resistance of the third thin film to be measured and the sum of the thermal resistance of the first and second thin films to be measured. The invention can test nano-scale ultra-thin films, has no limitation on the relative thickness of the multilayer films to be tested, and the contact state of the multilayer films conforms to reality.

Figure 202011600491

Description

Method for testing film contact thermal resistance
Technical Field
The invention belongs to the field of testing of thermal characteristics of thin film materials, and particularly relates to a method for testing contact thermal resistance of a thin film.
Background
With the rapid development of microelectronic technology in the information age, in order to meet the requirements of high speed, low power consumption and high integration level of microelectronic devices, the characteristic size of the devices is continuously shrinking, and the thickness of thin films in the devices has entered the nanometer scale. The thermal effect problem caused by the miniaturization of the device enables the regulation of the thermal conductivity of the film and the thermal contact resistance between films to become key factors for improving the reliability, so that the representation of the thermal characteristics of the nanoscale film is important to the design and the manufacture of a microelectronic device.
The measurement of the contact resistance between the multilayer film materials is a hot topic in the field of the research of the thermal characteristics of the materials at present, and common methods for measuring the contact resistance are mainly divided into a steady-state method and a transient method. The steady-state method is the most common method for measuring interface contact thermal resistance at present, the temperature gradient near the interface is obtained by arranging a plurality of temperature measuring points, the testing principle is simple, the measuring precision is higher, but the time spent in the testing of the method is long, and the most important point is that the arrangement of the plurality of temperature measuring points in the film thickness direction limits the thickness of a sample to be at least more than 50mm, so that the testing requirement of a nano-scale film cannot be met. In order to overcome the defects of the steady state method, various transient state methods are developed along with the development of the microelectronic technology, the transient state method greatly shortens the time required by the test, hardly damages the sample by the non-contact test, and further reduces the measurable thickness of the film to be tested.
However, most transient methods have extremely complex testing principles and systems, the cost of experimental equipment is high, and the accuracy cannot be guaranteed due to a large number of factors influencing the testing result. At present, a few transient testing methods of film contact thermal resistance based on a frequency tripling method exist, and the methods have some problems, for example, because of the limitation of a testing model, the thickness of a film to be tested is required to be larger than the heat penetration depth (hundred microns level) of a metal heat source; because the temperature change of a certain film to be measured is required to be ignored and the thickness of the film to be measured is far smaller than that of another film to be measured, the selection scale range of a film sample to be measured is greatly limited; in addition, the methods adopt a pressure loading device to simulate the contact pressure between films, in the actual microelectronic process, when the multilayer films are deposited in sequence, molecular permeation and lattice dislocation are caused due to the uneven tightness of contact surfaces, so that great influence is caused on interface heat resistance, the influence cannot be reflected by the pressure loading device, a film to be measured with smaller thickness is placed between two layers of films to be measured with larger thickness, and the method obviously does not accord with the real contact state of the two films to be measured in sequence deposition.
Therefore, the method for testing the contact thermal resistance of the film is researched, has the advantages of quick response and non-contact of a transient method, can be used for measuring the nanoscale ultrathin film, has no limit on the relative thickness among the multiple layers of thin films to be tested, and has important significance in that the contact state among the multiple layers of thin films to be tested is consistent with the actual microelectronic process.
Disclosure of Invention
The invention provides a method for testing film contact thermal resistance, which is used for solving the technical problem that the existing method for testing film contact thermal resistance has strict requirements on film thickness.
The technical scheme for solving the technical problems is as follows: a method for testing the contact thermal resistance of a thin film comprises the following steps:
respectively preparing a first film to be detected, a second film to be detected and the first film to be detected and the second film to be detected which are sequentially stacked on the three substrates, wherein the stacked structure represents a third film to be detected, and preparing a metal heating sensor on the upper surface of the film corresponding to each substrate; wherein the thickness of each substrate is larger than the thermal penetration depth of the metal heating sensor on the upper part of the substrate in the substrate, and the film thickness on the upper part of the substrate is smaller than the thermal penetration depth;
introducing an alternating current signal into each metal heating sensor and testing fundamental wave voltage and third harmonic voltage so as to calculate and obtain the thermal resistances of the first film to be tested, the second film to be tested and the third film to be tested respectively based on a frequency tripling method;
and obtaining the contact thermal resistance between the first film to be tested and the second film to be tested according to the difference value of the sum of the thermal resistance of the third film to be tested and the thermal resistances of the first film to be tested and the second film to be tested.
The invention has the beneficial effects that: the test structure is formed by laminating a substrate, a film and a metal heating sensor, wherein the thickness of the film is far smaller than the heat penetration depth of the metal heating sensor in the substrate, the heat diffusion time in the film material is ensured to be smaller than the heating period of an alternating current signal, the film can be processed according to the absence of temperature gradient, namely, the whole film to be tested generates a temperature rise irrelevant to frequency, the temperature rise is directly applied to the calculation of triple frequency thermal conductivity and thermal resistance, and in addition, the thickness of the substrate is required to be larger than the heat penetration depth of the metal heating sensor, so that the heat can be completely dissipated in the substrate. Therefore, compared with the existing test method based on the frequency tripling method, the test method can test the nano-scale ultrathin film, the relative thickness among the multiple layers of thin films to be tested is not limited, the contact state of the multiple layers of thin films in the test sample is consistent with the multiple layers of thin films manufactured by the practical microelectronic process, and the problems in the prior art are effectively solved.
On the basis of the technical scheme, the invention can be further improved as follows.
Further, each of the substrates has a thickness greater than 500 μm.
Further, the material of each substrate is a high thermal conductivity material.
Further, the materials of the three metal heating sensors are respectively and independently selected from any one of gold, silver and platinum.
Further, when there is a substrate corresponding to which the thin film material in contact with the metal heating sensor is a semiconductor or a conductor material, an insulating film is prepared before the metal heating sensor is prepared on the upper surface of the thin film.
Further, the total thickness of the films on the upper portion of each substrate satisfies the following conditions:
the total thickness of the thin film is less than one tenth of the depth of thermal penetration of the metal heating sensor in the substrate above the substrate.
Further, the thickness of the first film to be tested and the thickness of the second film to be tested are 0.5 nm-5 μm, and the thickness of the third film to be tested is 1 nm-10 μm.
Furthermore, the line width of each metal heating sensor is 10-50 μm, and the length is 1-5 mm.
Drawings
FIG. 1 is a flow chart of a method for testing thermal contact resistance of a thin film according to an embodiment of the present invention;
FIG. 2 is a flowchart of a method for testing thermal contact resistance of a thin film according to an embodiment of the present invention;
fig. 3 is a schematic structural diagram of a first sample to be tested according to an embodiment of the present invention;
fig. 4 is a schematic structural diagram of a second sample to be tested according to an embodiment of the present invention;
fig. 5 is a schematic structural diagram of a third sample to be tested according to an embodiment of the present invention;
fig. 6 is a schematic diagram of a thermal conductivity testing system by a frequency tripling method according to an embodiment of the present invention;
fig. 7 is a schematic diagram of a method for testing thermal contact resistance of a thin film according to an embodiment of the present invention.
The same reference numbers will be used throughout the drawings to refer to the same or like elements or structures, wherein:
1 is a substrate; 2 is a first film to be detected; 3 is a metal heating sensor; 4 is a second film to be tested; 5 is an alternating current source; 6 is a computer; 7 is a phase-locked amplifier; 8 is an adjustable resistance box; 9 is a first operational amplifier; and 10 is a second operational amplifier.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Example one
A method for testing thermal contact resistance of a thin film, as shown in fig. 1, comprising:
respectively preparing a first film to be detected, a second film to be detected, and a first film to be detected and a second film to be detected which are sequentially laminated on the three substrates, wherein the laminated structure represents a third film to be detected, and preparing a metal heating sensor on the upper surface of the film corresponding to each substrate; wherein, the thickness of each substrate is larger than the thermal penetration depth of the metal heating sensor on the upper part of the substrate in the substrate, and the film thickness on the upper part of the substrate is smaller than the thermal penetration depth;
introducing an alternating current signal into each metal heating sensor and testing fundamental wave voltage and third harmonic voltage so as to calculate and obtain the thermal resistances of the first film to be tested, the second film to be tested and the third film to be tested respectively based on a frequency tripling method;
and obtaining the contact thermal resistance between the first film to be tested and the second film to be tested according to the difference value of the sum of the thermal resistance of the third film to be tested and the thermal resistances of the first film to be tested and the second film to be tested.
The metal heating sensor is a metal strip and plays a role in heating and sensing. When the embodiment is actually applied and executed, as shown in fig. 2, reference may be made to the following specific steps:
step 1: depositing a first film 2 to be tested on a substrate 1, and then depositing a metal heating sensor 3 to form a whole structure called a first sample to be tested, wherein the structure is shown in FIG. 3;
step 2: depositing a second film 4 to be tested on the substrate 1, and then depositing a metal heating sensor 3, wherein the formed whole structure is called a second sample to be tested, and the structure is shown in fig. 4;
and step 3: sequentially depositing a first film to be detected 2 and a second film to be detected 4 on a substrate 1, then depositing a metal heating sensor 3, wherein a multilayer film formed by the first film to be detected 2 and the second film to be detected 4 is called a third film to be detected, the whole formed structure is called a third sample to be detected, and the structure is shown in fig. 5;
and 4, step 4: alternating current is conducted on the metal heating sensor on the surface of the first sample to be tested, and fundamental wave voltage V at two ends of the first sample to be tested is testedωAnd third harmonic voltage VThereby obtaining the temperature rise delta T of the metal heating sensor and the temperature rise delta T of the substrates(ii) a Then according to the formula
Figure BDA0002870871800000051
Calculating to obtain the thermal conductivity k of the first film to be measured1In the formula, P is the thermal power on the metal heating sensor, d is the thickness of the film to be measured, and b and l are the line width and the length of the metal heating sensor respectively; further according to formula R1=d1/k1Obtaining the thermal resistance R of the first film to be measured1Wherein d is1Is the thickness of the first film to be measured;
and 5: connecting the metal heating sensor 3 on the surface of the second sample to be tested into a test system, and obtaining the thermal conductivity k of the second film 4 to be tested by using the same method as the step 42Further according to formula R2=d2/k2Obtaining the thermal resistance R of the second film to be measured2Wherein d is2The thickness of the second film to be measured;
step 6: connecting the metal heating sensor 3 on the surface of the third sample to be tested into the test system, and obtaining the thermal conductivity k of the third film to be tested by using the same method as the step 43Further according to formula R3=d3/k3To find outThermal resistance R of three films to be measured3Wherein d is3Is the thickness of the third film to be measured, and d3=d1+d2
And 7: thermal contact resistance R between the first film to be tested 2 and the second film to be tested 4 in the third sample to be testedCCan be represented by the formula RC=R3-R1-R2And (4) obtaining.
It should be noted that the first film to be measured 2 and the second film to be measured 4 may be any film material, and through the above calculation process, it can be determined that there is no correlation requirement between the substrate materials and the substrate sizes among the three substrates, and it only needs to satisfy that the thickness of each substrate is greater than the thermal penetration depth of the corresponding metal heating sensor in the substrate; in addition, there is no requirement for correlation between materials and sizes of the three metal heating sensors.
In addition, regarding the test structure diagram of step 4, as shown in fig. 6, the metal heating sensor 3 has four lead terminals, the outer two lead terminals 31 and 32 are connected to the ac current source 5 through lead wires to obtain the excitation current, and the inner two lead terminals 33 and 34 are connected to the first operational amplifier 9 through lead wires to output the harmonic voltage signal. The metal heating sensor 3 is connected with the adjustable resistance box 8 in series; when the alternating current source outputs the alternating current with the frequency omega, the resistance of the adjustable resistance box 8 is adjusted, so that the difference value between the fundamental wave voltage at the two ends of the adjustable resistance box 8 and the fundamental wave voltage at the two ends of the metal heating sensor 3 is as small as possible, and the numerical value of the fundamental wave voltage at the moment is read as the V value at the two ends of the metal heating sensor 3ω(ii) a Voltage signals of the metal heating sensor 3 and the adjustable resistance box 8 are respectively input into an A port and a B port of the phase-locked amplifier 7 through the first operational amplifier 9 and the second operational amplifier 10, and the phase-locked amplifier 7 extracts frequency tripled voltage V at two ends of the metal heating sensor 3(ii) a The computer 6 establishes a communication link with the ac current source 5 and the lock-in amplifier 7 to collect and process data in real time. In step 4, the temperature rise Δ T of the metal heating sensor can be obtained by the following formula:
Figure BDA0002870871800000071
in the formula, VωFor fundamental voltage, V, across the metal heating sensorThe temperature coefficient alpha is the resistance temperature coefficient of the metal heating sensor;
in the above step 4, the temperature rise Δ T of the substrateSCan be obtained by the following formula:
Figure BDA0002870871800000072
in the formula, KSIs the thermal conductivity of the substrate, rho is the density of the substrate, C is the specific heat of the substrate, eta takes a constant of 0.923, omega is the angular frequency of the alternating current, wherein the thermal conductivity K of the substrateSCan be obtained by the following formula:
Figure BDA0002870871800000073
wherein R is the resistance value of the metal heating sensor at room temperature.
The thermal penetration depth of the metal heating sensor 3 in the substrate 1 is expressed by the formula
Figure BDA0002870871800000074
And (6) obtaining. In the formula, Ksρ, C are the thermal conductivity, density and specific heat, respectively, of the substrate 1, ω is the angular frequency of the alternating current in the metal heating sensor 3.
Regarding the principle of the solution of this embodiment, as shown in fig. 7, the left diagram is a schematic diagram of a conventional testing method based on a frequency tripling method, a gray area in the diagram is a heat penetration area of a metal heating sensor in a film to be tested, and in order to completely dissipate heat in the film and thus accurately calculate temperature change of the film, the thickness of the film to be tested is required to be greater than the heat penetration depth of the metal heating sensor. And the right diagram of fig. 7 is a test schematic diagram of the solution of the present embodiment, and the gray area in the diagram is the heat penetration area of the metal heating sensor in the substrate. The thickness of the film to be measured is far less than the thermal penetration depth of the metal heating sensor in the substrate, which is required in this embodiment because only if the condition is satisfied, the thermal diffusion time inside the film material to be measured can be considered to be shorter than the heating period, and the inside of the film can be processed according to the absence of the temperature gradient, that is, the whole film to be measured generates a temperature rise unrelated to the frequency, and the temperature rise is directly applied to the calculation of the thermal conductivity and the thermal resistance in this embodiment, so that the embodiment can be applied to the film to be measured in the nano scale. The solution of this embodiment also requires that the thickness of the substrate is larger than the thermal penetration depth of the metal heating sensor in order to allow the heat to be completely dissipated in the substrate to accurately calculate the temperature change of the substrate.
Therefore, in summary, the solution of the present embodiment has significant advantages over the prior art: the method can realize the contact thermal resistance test of the nano-scale film material and has the advantages of simplicity, rapidness and high precision. Specifically, compared with the existing steady-state method, the method is based on the transient test method, the time required by the test is greatly shortened without waiting for the stability of heat flow, and the size limit of a test sample is broken through without setting a temperature test point; compared with most of the existing transient methods, the method converts the thermal signal into the electric signal for testing, the testing principle and the testing system are relatively simple, and the testing system has good accuracy and stability due to the fact that the heat exchange area of the sample and the air is extremely small. Compared with the existing test method based on the frequency tripling method, the test model can test the nano-scale ultrathin film, the relative thickness among the multilayer thin films to be tested is not limited, and the contact state of the multilayer thin films in the test sample conforms to the multilayer thin films manufactured by the practical microelectronic process.
Preferably, the thickness of each substrate is greater than 500 μm. Since the heat penetration depth of the metal heat source is in the order of hundreds of micrometers, the thickness of each substrate is selected to be greater than 500 μm in consideration of the general situation of actual processing.
Preferably, the material of each substrate is a high thermal conductivity material, such as Si. The low heat conductivity of the substrate can cause the temperature rise of the film to be tested to be small, and cause a large test error, therefore, the material of each substrate adopts a high heat conductivity material to improve the test precision of the film contact thermal resistance.
Preferably, the materials of the three metal heating sensors are independently selected from any one of gold, silver and platinum. The gold, the silver and the platinum are all inert metals, so that samples are easy to store, the resistance temperature coefficient is small, temperature rise measurement is facilitated, and meanwhile, the manufacturing process is mature.
Preferably, when there is a substrate corresponding to a semiconductor or conductor material of the thin film material in contact with the metal heating sensor, an insulating thin film is formed before the metal heating sensor is formed on the upper surface of the thin film. When the metal heating sensor is communicated with an alternating current signal, the film and the metal heating sensor are insulated, so that the fact that the electric signal is completely communicated on the metal heating sensor is guaranteed, and the accuracy of the measured voltage is further guaranteed.
Preferably, the total thickness of the films on the upper portion of each substrate satisfies the following condition: the total thickness of the film is less than one tenth of the heat penetration depth of the metal heating sensor on the upper part of the substrate, under the condition, the heat diffusion time (the time for heat to penetrate through the film) in the film material is less than the heating period (the period corresponding to the frequency of alternating current) of an alternating current signal, the film can be processed according to the absence of temperature gradient, namely, the whole film to be measured generates a temperature rise which is independent of the frequency, and the temperature rise is directly applied to the calculation of the heat conductivity and the heat resistance of the invention.
The thicknesses of the first test film, the second film to be tested and the third film to be tested are all far smaller than the thermal penetration depth of the metal heating sensor 3 in the substrate 1.
Preferably, the thickness of the first film to be tested and the thickness of the second film to be tested are 0.5nm to 5 μm, and the thickness of the third film to be tested is 1nm to 10 μm.
Preferably, each metal heating sensor has a line width of 10 to 50 μm and a length of 1 to 5 mm.
The method for testing the contact thermal resistance of the nanoscale film is further described by combining the test result of an actual experiment.
Selecting the first film to be tested as SiO with the thickness of 1000nm2The second film to be measured is 90nm thickGeTe, the third film to be measured is 1000nmSiO2And 90nm GeTe, and the total thickness is 1090 nm. Si with the thickness of 500 mu m is selected as a substrate for depositing a film to be measured
The thermal conductivity of the first film to be tested is 1.150Wm by the testing method in the step 4-1K-1Thermal resistance of 8.696X 10-7m2KW-1(ii) a The thermal conductivity of the second film to be measured is 0.151Wm-1K-1Thermal resistance of 5.690X 10-7m2KW-1The thermal conductivity of the third film to be tested was 0.650Wm-1K-1Thermal resistance of 1.677X 10-6m2KW-1
Subtracting the thermal resistance of the first film to be tested and the thermal resistance of the second film to be tested from the thermal resistance of the third film to be tested to obtain 1000nmSiO2The thermal contact resistance of the second film to be tested with 90nm GeTe is 2.384 multiplied by 10-7m2KW-1
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (5)

1. A method for testing the contact thermal resistance of a film is characterized by comprising the following steps:
respectively preparing a first film to be detected, a second film to be detected and the first film to be detected and the second film to be detected which are sequentially stacked on the three substrates, wherein the stacked structure represents a third film to be detected, and preparing a metal heating sensor on the upper surface of the film corresponding to each substrate; wherein the thickness of each substrate is larger than the thermal penetration depth of the metal heating sensor on the upper part of the substrate in the substrate, and the film thickness on the upper part of the substrate is smaller than the thermal penetration depth;
introducing an alternating current signal into each metal heating sensor and testing fundamental wave voltage and third harmonic voltage so as to calculate and obtain the thermal resistances of the first film to be tested, the second film to be tested and the third film to be tested respectively based on a frequency tripling method; obtaining the contact thermal resistance between the first film to be tested and the second film to be tested according to the difference value of the thermal resistance of the third film to be tested and the sum of the thermal resistances of the first film to be tested and the second film to be tested;
wherein the thickness of each substrate is more than 500 μm, and the material of each substrate is a high-thermal-conductivity material;
the thickness of the first film to be tested and the thickness of the second film to be tested are 0.5 nm-5 mu m, and the thickness of the third film to be tested is 1 nm-10 mu m; performing thermal resistance calculation treatment on the interior of each film to be measured according to the absence of temperature gradient, namely generating a temperature rise irrelevant to frequency in each film to be measured integrally according to a formula
Figure FDA0003418312360000011
Calculating the thermal conductivity k of each film to be measured, and calculating the thermal resistance R of each film to be measured according to a formula R ═ d/k, wherein P is the thermal power on the metal heating sensor, d is the thickness of the film to be measured, b and l are the line width and the length of the metal heating sensor respectively, and delta TsThe temperature rise of the metal heating sensor and the temperature rise of the substrate are respectively.
2. The method for testing thermal contact resistance of a thin film as claimed in claim 1, wherein the materials of the three metal heating sensors are respectively and independently selected from any one of gold, silver and platinum.
3. The method as claimed in claim 1, wherein when there is a substrate corresponding to the semiconductor or conductor material of the film in contact with the metal heater sensor, an insulating film is formed on the upper surface of the film before the metal heater sensor is formed thereon.
4. The method for testing thermal contact resistance of thin film according to any one of claims 1 to 3, wherein the total thickness of the thin film on the upper portion of each substrate satisfies the following condition:
the total thickness of the thin film is less than one tenth of the depth of thermal penetration of the metal heating sensor in the substrate above the substrate.
5. The method as claimed in claim 1, wherein each of the metal heating sensors has a line width of 10 μm to 50 μm and a length of 1mm to 5 mm.
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