Total thermal resistance measurement method of submicron multilayer stacked materials based on thermal reflection method

Abstract

The present invention discloses a method for measuring the total thermal resistance of a submicron multilayer stacked material based on a thermal reflection method. The multilayer stacked material is first grown on a substrate or transferred to a substrate, and a layer of gold is plated on its upper surface as a transmission layer. Then, a frequency domain thermal reflection method platform is used to measure the test sample, and 100 Hz-10 5 The phase difference between the probe light and the pump light at a series of frequency points in the Hz range; then the multilayer stacked material is regarded as a material with equivalent thermal conductivity k eq , equivalent volume specific heat C eq and total thickness L tot The single-layer equivalent layer described by k eq , C eq The initial value of the multilayer thermal conductivity model is used to perform nonlinear fitting on the measured phase difference, and the k eq , C eq After multiple iterations, the phase difference with the smallest mean square error between the measured value and the theoretical value is selected. k eq As the final equivalent thermal conductivity, finally use L tot The ratio of the equivalent thermal conductivity is used as the total thermal resistance of the stacked material. In the data processing process of the present invention, only the total thickness of the stacked material is required, and the measurement method is simple and easy to use.

Description

Technical Field

[0001] The invention relates to the field of material thermal property measurement, and in particular to a method for measuring the total thermal resistance of submicron multilayer stacked materials based on a thermal reflection method. Background Art

[0002] Multilayer stacked materials composed of thin films with thicknesses ranging from a few nanometers to hundreds of nanometers are widely used in devices such as light-emitting diodes and solar cells. The heat generated in these devices will cause the operating temperature of the device to rise, reduce device performance, and even shorten the life of the device. Therefore, it is of vital importance to measure the total thermal resistance in multilayer stacked materials. However, due to the submicron thickness, it is difficult to measure the total thermal resistance using methods commonly used for bulk material thermal conductivity measurements, such as the steady-state method or the transient plane heat source method. At the same time, the thermal conductivity of many interlayer interfaces in multilayer stacked materials is unknown, making it difficult to use , time domain thermal reflection method and frequency domain thermal reflection method, which are commonly used to measure the thermal conductivity of thin film materials, for direct measurement. Summary of the invention

[0003] In view of the lack of existing methods for measuring the total thermal resistance of multilayer stacked materials, the present invention proposes a method for measuring the total thermal resistance of submicron multilayer stacked materials based on the thermal reflection method. The method is based on the coupling relationship between the parameters of stacked materials at low frequency, regards the stacked materials as a single equivalent layer, fits the equivalent thermal conductivity and equivalent volume specific heat, and directly calculates the total thermal resistance of the stacked materials from the equivalent thermal conductivity and total thickness. The parameter of the stacked material required by the method is only its total thickness, which is easy to use and is an ideal method for measuring the total thermal resistance of stacked materials in light-emitting diodes and solar cells.

[0004] The purpose of the present invention is achieved through the following technical solutions:

[0005] A method for measuring the total thermal resistance of submicron multilayer stacked materials based on a thermal reflection method, the method comprising the following steps:

[0006] Step 1: growing or transferring a multilayer stacked material with a total thickness of submicron level on a substrate, and plating a layer of gold as a transmission layer on the upper surface of the multilayer stacked material to obtain a test sample;

[0007] Step 2: Use pump light to modulate the frequency range from 100 Hz to 10 5 The test sample is measured by a frequency domain thermal reflection method platform of Hz, and a series of frequency points are collected. The phase difference signal between the probe light and the pump light under ;

[0008] Step 3: Treat the multilayer stacked materials as having equivalent thermal conductivity k eq , equivalent volume specific heat C eq and total thickness Ltot The equivalent layer of a single layer described by eq , equivalent volume specific heat C eq The initial value of k is used, and the multilayer thermal conductivity model is used to perform nonlinear fitting on the phase difference signal at a series of frequency points measured in step 2. The k is continuously changed through an iterative process. eq , C eq The k value with the smallest mean square error between the measured value of the phase difference and the theoretical value calculated by the multilayer thermal conductivity model is selected. eq As the final equivalent thermal conductivity ;

[0009] Step 4: Calculate the total thickness of the multilayer stack and the final equivalent thermal conductivity obtained in step 3 The ratio of is the total thermal resistance of the stacked material.

[0010] Furthermore, in the step 1, the thickness of the gold plated on the upper surface of the multilayer stacked material is 70-120 nm.

[0011] Furthermore, the thermal conductivity of the substrate is greater than 30 W / (m·K).

[0012] Furthermore, in step 3, the multilayer thermal conductivity model describes the relationship between the phase difference and the pump light modulation frequency and the sample system parameters, and the specific expression is as follows:

[0013] ;

[0014] ;

[0015] ;

[0016] ;

[0017] in, is the surface temperature rise of the test sample, A is the temperature rise amplitude, is the phase difference, is the pump light modulation frequency, For the heating laser power, is the Hankel transformation parameter, and are the surface temperature and heat flux density of the test sample, respectively, and r is the effective spot radius of the laser; and represent the lower surface temperature and heat flux density of the substrate respectively; are the relationship matrices representing the base, equivalent layer and transmission layer, respectively. are the elements at corresponding positions of the matrix respectively; All three are represented by the following formula:

[0018]

[0019] Where i is n, eq or 1, representing substrate, equivalent layer and transmission layer respectively; L i is the thickness, k i is the thermal conductivity, C i is the volume specific heat, q i is an intermediate variable and j is an imaginary unit.

[0020] Furthermore, the nonlinear fitting in step three is a least squares fitting.

[0021] Furthermore, the substrate is selected from any one of sapphire, silicon and silicon carbide.

[0022] Furthermore, a geometric mean value of the spot radius of the pump light and the detection light focused on the surface of the transmission layer of the test sample is not less than 10 μm.

[0023] A frequency domain thermal reflection method platform for realizing a method for measuring the total thermal resistance of a sub-micron multilayer stacked material, the platform comprising a pump laser, a detection laser, an electro-optic modulator, a beam sampler, a 1 / 2 glass slide, a polarization beam splitter, a 1 / 4 glass slide, an objective lens, a sample stage and a balanced detector; the pump light emitted by the pump laser is modulated into a laser with a sinusoidal intensity change by the electro-optic modulator, and then sequentially passes through the beam sampler, the 1 / 2 glass slide, the polarization beam splitter, the 1 / 4 glass slide, and finally is focused on the test sample through the objective lens; the detection light emitted by the detection laser sequentially passes through the beam sampler, the 1 / 2 glass slide, the polarization beam splitter, the 1 / 4 glass slide, and the objective lens to irradiate the same position of the test sample as the pump light;

[0024] The phases of the pump light and the detection light are collected by the balanced detector and then recorded by a phase-locked amplifier.

[0025] The beneficial effects of the present invention are as follows:

[0026] (1) The total thermal resistance measurement method of submicron-level multilayer stacked materials based on the thermal reflection method of the present invention only requires the total thickness of the stacked materials for fitting, and the measurement method is simple and easy to use;

[0027] (2) The present invention retains the advantages of high temporal and spatial resolution, non-contact measurement, and simple sample preparation of the frequency domain thermal reflection method;

[0028] (3) The present invention can be used to measure the total thermal resistance of LEDs and solar cells in working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Schematic diagram of the process of measuring the total thermal resistance of sub-micron multi-layer stacked materials according to an embodiment of the present invention.

[0030] Figure 2 Schematic diagram of the optical path of the low-frequency frequency-domain thermal reflection method platform of this embodiment.

[0031] Figure 3 The phase difference and the best fitting curve measured by the frequency domain thermal reflection method of the silicon-silicon dioxide stack material in Example 1.

[0032] Figure 4 is the theoretical value of the total thermal resistance of the randomly stacked materials in Example 2 R tot,0 With the measured value R tot contrast.

[0033] Figure 5 This is a schematic diagram of the structure of the perovskite light-emitting diode in Example 3.

[0034] Figure 6 The phase difference and the best fitting curve of the perovskite light-emitting diode measured by the frequency domain thermal reflection method in Example 3.

[0035] Figure 7 This is the relative deviation distribution of the total thermal resistance measurement of the perovskite light-emitting diode determined by the frequency domain thermal reflection method simulation in Example 3. DETAILED DESCRIPTION

[0036] The present invention will be described in detail below based on the accompanying drawings and preferred embodiments, and the purpose and effects of the present invention will become more clear. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0037] like Figure 1 As shown, the submicron-level multilayer stacked material based on the thermal reflection method of the present invention needs to be grown on or transferred to a substrate before measuring the total thermal resistance by the frequency domain thermal reflection method. The substrate is preferably a material with a thermal conductivity greater than 30W / m·K, and a layer of gold needs to be plated on the surface of the multilayer stacked material as a transmission layer. The thickness of gold is preferably 70~120nm. The final product is called a test sample.

[0038] Then the pump light is modulated in the frequency range of 100 Hz -10 5 The Hz frequency domain thermoreflectometry platform measures multi-layer stacked materials and collects a series of frequency points The phase difference signal between the probe light and the pump light under .

[0039] The present invention regards the multilayer stacked material as a material having an equivalent thermal conductivity k eq , equivalent volume specific heat C eq and total thickness L totThe single-layer equivalent layer described above is used to perform nonlinear fitting on the phase difference signal at a series of frequency points measured using the multilayer thermal conductivity model to determine k eq and C eq .

[0040] The multilayer thermal conductivity model describes the phase difference and the pump light modulation frequency And the relationship between the sample system parameters:

[0041] (1)

[0042] in, is the unknown parameter of the test sample system, which is k in the present invention. eq and C eq ; The known parameters of the test sample system are the thermal conductivity, thickness and volume specific heat of the transmission layer, the thermal conductivity and volume specific heat of the substrate, and the effective laser spot radius. The functional relationship F is determined by formula (2-9).

[0043] First, the exponential form of the sample surface temperature rise is:

[0044] (2)

[0045] Where A is the temperature rise amplitude, By equation (3), X and Sure:

[0046] (3)

[0047] in, For the heating laser power, is the Hankel transformation parameter, and are the upper surface temperature and heat flux density of the test sample respectively, and r is the effective spot radius of the laser.

[0048] The test sample in the frequency domain thermal reflection method experiment is a multi-layer stacked structure. For the multi-layer stacked structure, the temperature of the upper surface of the i-th layer is and heat flux and the temperature of the lower surface of this layer and heat flux The relationship between them is:

[0049] (4)

[0050] (5)

[0051] (6)

[0052] in, is the thickness of the i-th layer, is the thermal conductivity of the i-th layer, C i is the volume specific heat of the i-th layer, j is an imaginary unit. If the i-th layer is an interface,

[0053] (7)

[0054] Among them, h i is the interfacial thermal conductivity.

[0055] In the present invention, the multilayer stacked material is regarded as a single equivalent layer, so a total of three layers, namely the transmission layer, the equivalent layer and the substrate, need to be considered. The corresponding equation (5) is iterated from top to bottom to obtain:

[0056] (8)

[0057] Among them, the subscript l represents the transmission layer, the subscript eq represents the equivalent layer, and the subscript n represents the base. are the relationship matrices representing the base, equivalent layer and transmission layer, respectively. are the elements at corresponding positions of the matrix respectively; and represent the substrate lower surface temperature and heat flux density respectively.

[0058] According to the adiabatic boundary condition on the lower surface of the substrate, , can be obtained

[0059] (9)

[0060] Combining formulas (2), (3), (5), (6), (8), and (9), when k is given eq and C eq The frequency point can be calculated when the value of Theoretical value of phase difference:

[0061] (10)

[0062] in, .

[0063] Therefore, the present invention uses the above-mentioned multi-layer thermal conductivity model to calculate the actual measured phase difference based on the least square method. Perform nonlinear fitting. In the fitting process, firstly, k is given eq and C eq The initial value k eq,0 and C eq,0 , and continuously change k through an iterative process eq and C eq The value of , calculate the frequency point at each iteration Theoretical value of phase difference under The phase difference with the actual measured The mean square error MSE is minimized, and finally the k with the minimum MSE is obtained. eq , as the final equivalent thermal conductivity .

[0064] Finally, calculate the total thickness L of the multilayer stacked material tot And the final equivalent thermal conductivity The ratio of is the total thermal resistance of the stacked material, and the calculation formula is as follows:

[0065] (11)

[0066] R tot There is a deviation between the measured value and the actual value. The value of this deviation can be calculated by experimental simulation of the frequency domain thermal reflection method. By using a larger laser effective spot radius (≥10μm), the relative deviation can usually be controlled below 10%.

[0067] The frequency domain thermal reflection method platform used in the test process is as follows: Figure 2 As shown, it includes a pump laser 1, a detection laser 2, an electro-optic modulator 3, a beam sampler 4, a 1 / 2 glass slide 5, a polarization beam splitter 6, a 1 / 4 glass slide 7, an objective lens 8, a sample stage 9 and a balanced detector 10. The pump light emitted by the pump laser 1 is modulated into a laser with a sinusoidal intensity change by the electro-optic modulator 3, and then sequentially passes through the beam sampler 4, the 1 / 2 glass slide 5, the polarization beam splitter 6, the 1 / 4 glass slide 7, and finally is focused on the test sample by the objective lens 8; after being focused by the objective lens 8, the test sample is periodically heated, so that the surface temperature of the transmission layer changes periodically. Due to the thermal reflection of the surface of the transmission layer, the reflectivity change is proportional to the temperature change. The detection light emitted by the detection laser 2 is sequentially irradiated to the same position of the test sample as the pump light through the beam sampler 4, the 1 / 2 glass slide 5, the polarization beam splitter 6, the 1 / 4 glass slide 7, and the objective lens 8; the reflected light of the detection light records the information of the surface temperature change of the test sample. The phases of the pump light and the probe light are collected by the balanced detector 10 and then passed through the phase-locked amplifier ( Figure 2 (not shown) records.

[0068] Example 1

[0069] This embodiment is a measurement of the total thermal resistance of stacked materials between gold and silicon substrate in a gold / 70nm silicon / 145nm silicon dioxide / silicon structure. The specific steps are as follows:

[0070] Step S101: Figure 3 As shown, the lower silicon layer of the sample is the substrate, and 70 nm gold is plated on the upper silicon layer as a transmission layer.

[0071] Step S102: Use the low-frequency frequency domain thermal reflection method platform to measure the sample, and the collected heating frequency range is 100 Hz to 10 5 Hz phase difference signal.

[0072] Step S103: Based on the multi-layer thermal conductivity model in equations (1)-(9), the multi-layer stacked materials are regarded as having an equivalent thermal conductivity k eq , equivalent volume specific heat C eq and total thickness L tot The single layer equivalent layer described by fitting k eq and C eq , the results are as follows Figure 3 shown.

[0073] Step S104: The final equivalent thermal conductivity obtained by fitting , calculate R tot , the result is 173 m 2 K / GW, positive and negative errors are +29 m 2 K / GW and -19 m 2 ·K / GW. In this structure, R tot Contributed by two layers of thin film materials and three interfaces:

[0074] (12)

[0075] in, is the thermal conductivity of the Au-Si interface, l Si is the thickness of the silicon film, k Si is the thermal conductivity of thin film silicon, is the thermal conductivity of the silicon-silicon dioxide interface, is the thickness of silicon dioxide, is the thermal conductivity of silicon dioxide.

[0076] Table 1 lists the literature values ​​of thermal conductivity and interface thermal conductivity of the above film materials. Among them:

[0077] The literature source for silicon thermal conductivity is: Regner, Keith T., et al. "Broadband phonon meanfree path contributions to thermal conductivity measured using frequencydomain thermoreflectance." Nature communications 4.1 (2013): 1640.

[0078] The literature source for the thermal conductivity of silica and the thermal conductivity of the silicon-silicon dioxide interface is: Chien, Heng-Chieh, etal. "Thermal conductivity measurement and interface thermal resistanceestimation using SiO2 thin film." Review of scientific instruments 79.5(2008).

[0079] The literature source for thermal conductivity of gold-silicon interface is: Yang, Jia, Carlo Maragliano, and Aaron J.Schmidt. "Thermal property microscopy with frequency domainthermoreflectance." Review of Scientific Instruments 84.10 (2013)).

[0080] Substituting the literature value into equation (12) we can calculate R tot The literature value is 179.7 m 2 K / GW. The literature value is consistent with the measured value within the error range, which proves the reliability of the present invention.

[0081] Table 1 Literature values ​​of thermal resistance in gold-silicon-silicon dioxide-silicon

[0082]

[0083] Example 2

[0084] The multilayer stack material of this embodiment is a multilayer stack material on a sapphire substrate, and this embodiment is used to simulate the measurement process of the multilayer stack material with random parameters described in Table 2. The substrate is sapphire, and the effective laser spot radius is 10 μm.

[0085] Table 2 Random stacking material parameters

[0086]

[0087] Step S201: Calculate 100 Hz – 10 5 Phase difference at 25 frequency points in the Hz frequency range. This step calculates the theoretical value of the phase difference of the stacked material (without approximation), so in the multilayer thermal conductivity model in equations (1)-(9), equation (8) needs to be replaced by:

[0088] (13)

[0089] Among them, M i It is still calculated by equations (5)-(7).

[0090] Step S202: Consider the stacked materials as having equivalent thermal conductivity k eq , equivalent volume specific heat C eq and total thickness L tot The single layer equivalent layer described by fitting k eq and C eq , calculate R tot The actual value of the total thermal resistance of the stacked material is:

[0091] (14)

[0092] The relative deviation of the measurement is:

[0093] (15)

[0094] Figure 4 The total thermal resistance R obtained from 5000 simulations was compared. tot and the true value R tot,0 , the relative deviation does not exceed 12%, which verifies the reliability of this method.

[0095] Example 3

[0096] This embodiment uses the present invention to measure Figure 5 The process of total thermal resistance of 6-layer stacked materials in a perovskite light-emitting diode is shown.

[0097] Step S301: Use a low-frequency frequency domain thermoreflectometry platform to measure the sample, and collect the pump light modulation frequency range from 100 Hz to 10 5 The phase difference between the probe light and the pump light in Hz.

[0098] Step S302: Based on the multi-layer thermal conductivity model in equations (1)-(9), the stacked materials are considered to have equivalent thermal conductivity k eq , equivalent volume specific heat C eq and total thickness L tot The single layer equivalent layer described by fitting k eq and C eq The measured phase difference and best fitting curve of multilayer stacked materials in perovskite light-emitting diodes are shown in Figure 2. Figure 6 shown.

[0099] Step S303: Use the final equivalent thermal conductivity obtained by fitting , calculate R tot 418±40 m 2 K / GW.

[0100] In order to ensure the accuracy of the measurement results, the frequency domain thermal reflection method in Example 2 was used to simulate and calculate the relative deviation of the measurement. Figure 5 For the perovskite light-emitting diode in FIG. 3 , the parameters of each layer are assumed to be the values ​​or ranges in Table 3.

[0101] Table 3 Material parameters of each layer in perovskite light-emitting diodes

[0102]

[0103] The thermal conductivity and volume specific heat of the first four layers are randomly selected within the possible range, and the thermal conductivity and volume specific heat of the last two layers are taken from the literature. The thickness of each layer is the nominal value of light-emitting diode processing. The interface thermal conductivity is fixed to a very low 10MW / (m 2 ·K). In each simulation, the parameters in Table 3 are randomly assigned values ​​according to uniform distribution within the range (the corresponding values ​​are assigned for fixed values). The relative deviation distribution obtained from 5000 simulations is shown in Figure 7 As shown, the maximum absolute value is only 5%, which illustrates the reliability of this method.

[0104] Those skilled in the art can understand that the above are only preferred examples of the invention and are not intended to limit the invention. Although the invention is described in detail with reference to the above examples, those skilled in the art can still modify the technical solutions recorded in the above examples or replace some of the technical features therein with equivalents. Any modification, equivalent replacement, etc. made within the spirit and principle of the invention shall be included in the protection scope of the invention.

Claims

1. A method for measuring the total thermal resistance of submicron multilayer stacked materials based on thermal reflection method, characterized in that: The method comprises the following steps: Step 1: growing or transferring a multilayer stacked material with a total thickness of submicron level on a substrate, and plating a layer of gold on the upper surface of the multilayer stacked material as a transmission layer to obtain a test sample; the thermal conductivity of the substrate is greater than 30 W / (m·K); Step 2: Use pump light to modulate the frequency range from 100 Hz to 10 5 Hz, the geometric mean of the spot radius of the pump light and the detection light is not less than 10 μm, and the test sample is measured on a frequency domain thermal reflection method platform, and a series of frequency points are collected. The phase difference signal between the probe light and the pump light under ; Step 3: Treat the multilayer stacked materials as having equivalent thermal conductivity k eq , equivalent volume specific heat C eq and total thickness L tot The equivalent layer of a single layer described by k eq , equivalent volume specific heat C eq The initial value of the multi-layer thermal conductivity model is used to perform a double-parameter nonlinear fitting on the phase difference signal at a series of frequency points measured in step 2. k eq , C eq The value of the phase difference is selected, and the mean square error between the measured value of the phase difference and the theoretical value calculated by the multilayer thermal conductivity model is the smallest. k eq As the final equivalent thermal conductivity ; Step 4: Calculate the total thickness of the multilayer stack and the final equivalent thermal conductivity obtained in step 3 The ratio of is the total thermal resistance of the stacked material.

2. The total thermal resistance measurement method of submicron multilayer stacked materials based on thermal reflection method according to claim 1, characterized in that: In the step 1, the thickness of the gold plated on the upper surface of the multilayer stacked material is 70-120 nm.

3. The total thermal resistance measurement method of submicron multilayer stacked materials based on thermal reflection method according to claim 1, characterized in that: In step 3, the multilayer thermal conductivity model describes the relationship between the phase difference and the pump light modulation frequency and the sample system parameters. The specific expression is as follows: ； ； ； ； in, To test the surface temperature rise of the sample, A is the temperature rise amplitude, is the phase difference, is the pump light modulation frequency, For the heating laser power, is the Hankel transformation parameter, and are the surface temperature and heat flux density of the test sample, r is the effective laser spot radius; and represent the lower surface temperature and heat flux density of the substrate respectively; are the relationship matrices representing the base, equivalent layer and transmission layer, respectively. are the elements at corresponding positions of the matrix respectively; All three are represented by the following formula: ； in, i for n , eq or 1, respectively represent the substrate, equivalent layer and transmission layer; L i is the thickness, k i is the thermal conductivity, C i is the volume specific heat, q i is the intermediate variable, j Is an imaginary unit.

4. The method for measuring the total thermal resistance of submicron multilayer stacked materials based on thermal reflection method according to claim 1, characterized in that: The nonlinear fitting in step three is a least squares fitting.

5. The method for measuring total thermal resistance of submicron multilayer stacked materials based on thermal reflection method according to claim 1, characterized in that: The substrate is selected from any one of sapphire, silicon and silicon carbide.

6. The total thermal resistance measurement method of submicron multilayer stacked materials based on thermal reflection method according to claim 1, characterized in that: The frequency domain thermal reflection method platform comprises a pump laser (1), a detection laser (2), an electro-optic modulator (3), a beam sampler (4), a 1 / 2 glass slide (5), a polarization beam splitter (6), a 1 / 4 glass slide (7), an objective lens (8), a sample stage (9) and a balanced detector (10); the pump light emitted by the pump laser (1) is modulated into a laser with a sinusoidal intensity change by the electro-optic modulator (3), and then sequentially passes through the beam sampler (4), the 1 / 2 glass slide (5), the polarization beam splitter (6), the 1 / 4 glass slide (7), and finally is focused on the test sample by the objective lens (8); the detection light emitted by the detection laser (2) sequentially passes through the beam sampler (4), the 1 / 2 glass slide (5), the polarization beam splitter (6), the 1 / 4 glass slide (7), and the objective lens (8) to irradiate the same position of the test sample as the pump light; The phases of the pump light and the detection light are collected by the balanced detector (10) and then recorded by a phase-locked amplifier.

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