Method for measuring interfacial thermal resistance and thermal conductivity of multilayer thin film materials

Abstract

The application discloses a method for measuring interface thermal resistance and thermal conductivity of multilayer thin film material, comprising the following steps: arranging a first heating electrode, a second heating electrode and a detecting electrode on the top insulating layer of the multilayer thin film material; changing the frequency of the first alternating current heating current, recording the third harmonic voltage of the first heating electrode, and calculating the alternating current thermal response signal of the first heating electrode and the detecting electrode; changing the frequency of the second alternating current heating current, recording the third harmonic voltage of the second heating electrode, and calculating the alternating current thermal response signal of the second heating electrode and the detecting electrode; fitting the thermal conductivity of the substrate; and fitting the thermal conductivity and the interface thermal resistance of the multilayer thin film material. The substrate thermal conductivity slope method is used for fitting, the slope method is only sensitive to the thermal conductivity of the substrate, and the measurement error caused by the thin film layer is eliminated; the alternating current response signal in the frequency domain is used for the inversion calculation of the thermal conductivity and the interface thermal resistance of the thin film, the data amount is large, and the fitting precision can be improved.

Description

Technical Field

[0001] This invention pertains to thin film measurement methods, specifically a method for measuring the interfacial thermal resistance and thermal conductivity of multilayer thin film materials. Background Technology

[0002] Multilayer thin-film structures have been widely used in microelectronic devices, power semiconductors, MEMS devices, photodetectors, phase-change memories, flexible electronics, and novel thermal functional materials. When devices operate under high power density, high frequency, or fast switching conditions, they generate significant amounts of heat, which needs to be transferred along multilayer thin-film systems composed of metals, dielectrics, semiconductors, and two-dimensional materials. Therefore, the thermal conductivity of each thin film layer and the interlayer thermal resistance (TBR) become key parameters determining the device's heat dissipation capacity, temperature rise distribution, and long-term reliability. However, as material sizes enter the nanoscale, the number of interfaces increases continuously. Factors such as lattice mismatch, differences in chemical bonding, interface roughness, stress, and defects lead to significantly enhanced phonon scattering at the interfaces, making interlayer thermal resistance the main bottleneck limiting overall heat transfer. In many scenarios, interlayer thermal resistance even exceeds the bulk thermal resistance of the thin film layer, becoming the dominant factor controlling the heat dissipation process. Therefore, accurately and repeatedly obtaining the thermal conductivity and interlayer thermal resistance of each single layer in a multilayer thin film is of great significance for material design, optimization of device heat dissipation structures, and verification of theoretical models.

[0003] Among existing thermophysical property testing techniques, photothermal methods such as TDTR (time-domain thermal reflectometry) and FDTR (frequency-domain thermal reflectometry) have high time resolution, but they require high quality of the metal absorption layer on the sample surface, are complex, and have high equipment costs. At the same time, there are coupling problems in parameter inversion in multi-interface systems. Traditional methods such as transient hot wire method and steady-state method are difficult to use for nanofilm structures, and their spatial resolution and sensitivity are insufficient.

[0004] In contrast, the 3ω method offers advantages such as relatively simple setup, high signal-to-noise ratio, wideband modulation capability, and insensitivity to the testing environment, making it widely used for thermal conductivity studies of thin films and substrates. The 3ω method injects an alternating current with frequency ω into a metal heating wire, generating periodic Joule heating with a frequency of 2ω. The temperature change is then converted into a voltage signal with a frequency of 3ω using the temperature coefficient of the metal resistance. By measuring the variation of the 3ω voltage with frequency, the thermal diffusion depth and heat wave propagation behavior can be analyzed, thus deducing the material's thermal parameters. However, the traditional 3ω method primarily targets single-layer thin films or simple thin-film / substrate structures, and its theoretical models are typically based on single-interface or bilayer systems. When the sample consists of multiple thin films and multiple interfaces, the thermal diffusion process exhibits a significant frequency dependence. The contributions of each film and interface to the overall thermal resistance are coupled, making it difficult for traditional models to distinguish between the thermal conductivity of different layers and the interfacial thermal resistance. Furthermore, the thickness of multilayer thin films varies considerably, and the thermal diffusion length may only penetrate part of the film in different frequency ranges, leading to difficulties in parameter sensitivity differentiation. Simultaneously, the interfacial thermal resistance is in the nanoscale phonon scattering-dominated region, typically on the order of 10⁻⁶. -8 -10 -7 m 2 The K / W ratio places higher demands on the frequency selection, phase-locked loop accuracy, and modeling accuracy of the testing method. Existing technologies struggle to achieve independent extraction of multi-level parameters while ensuring measurement repeatability and stability. Summary of the Invention

[0005] Purpose of the invention: In order to overcome the shortcomings of the prior art, the purpose of this invention is to provide a method for measuring the interfacial thermal resistance and thermal conductivity of multilayer thin film materials by optimizing the control of thermal diffusion direction.

[0006] Technical solution: The present invention provides a method for measuring the interfacial thermal resistance and thermal conductivity of multilayer thin film materials, comprising the following steps:

[0007] Step 1: Set a first heating electrode, a second heating electrode, and a detection electrode on the top insulating layer of the multilayer thin film material;

[0008] Step 2: Apply a first AC heating current to the first heating electrode and a first DC detection current to the detection electrode. Change the frequency of the first AC heating current, record the third harmonic voltage of the first heating electrode and the second harmonic voltage of the detection electrode, and calculate the AC thermal response signals of the first heating electrode and the detection electrode.

[0009] Step 3: Apply a second AC heating current to the second heating electrode and a second DC detection current to the detection electrode. Change the frequency of the second AC heating current, record the third harmonic voltage of the second heating electrode and the second harmonic voltage of the detection electrode, and calculate the AC thermal response signals of the second heating electrode and the detection electrode.

[0010] Step 4: Fit the substrate thermal conductivity by the relationship between the third harmonic voltage and frequency of the first heating electrode.

[0011] Step 5: Based on the multilayer heat propagation physical model, set the thermal conductivity and interfacial thermal resistance values ​​of each thin film, and input them into the thermal simulation model to obtain the simulated values ​​of the AC thermal response signals of the first heating electrode, the detection electrode, the second heating electrode, and the detection electrode. Adjust one of the parameters, either the thin film thermal conductivity or the interfacial thermal resistance, to minimize the difference between the actual measured value and the theoretical calculated value. Iterate repeatedly to fit the thermal conductivity and interfacial thermal resistance of the multilayer thin film material.

[0012] Furthermore, in step one, the multilayer thin film material is composed of multiple layers of thin films of different types stacked together, with the outermost thin film being an insulating layer.

[0013] Furthermore, in step one, the width of the first heating electrode is greater than the width of the second heating electrode.

[0014] Furthermore, in step two, based on the operating parameters of the first heating electrode and the detection electrode under the first DC detection current, the AC thermal response signals of the first heating electrode and the detection electrode are calculated:

[0015]

[0016]

[0017] Where, ΔT h1 (ω) is the AC thermal response signal of the first heating electrode, V 3ω，h1 I is the third harmonic voltage of the first heating electrode. h1 R is the current passing through the first heating electrode. h1 α is the resistance of the first heating electrode. h1 ΔT is the temperature sensitivity coefficient of the first heating electrode. s1 (ω) represents the AC thermal response signal of the probe electrode, V 2ω，s1 To detect the second harmonic voltage of the electrode, I s1 To detect the current in the probe electrode, R s To detect electrode resistance, α s To detect the temperature sensitivity coefficient of the electrode.

[0018] Furthermore, in step three, based on the operating parameters of the second heating electrode and the detection electrode under the second DC detection current, the AC thermal response signals of the second heating electrode and the detection electrode are calculated:

[0019]

[0020]

[0021] Where, ΔT h2 (ω) is the AC thermal response signal of the second heating electrode, V 3ω，h2 I is the third harmonic voltage of the second heating electrode. h2 R is the current passing through the second heating electrode. h2 α is the resistance of the second heating electrode. h2 The temperature sensitivity coefficient of the second heating electrode; ΔT s2 (ω) represents the AC thermal response signal of the probe electrode, V 2ω，s2 To detect the second harmonic voltage of the electrode, I s2 To detect the current in the probe electrode, R s To detect electrode resistance, α s To detect the temperature sensitivity coefficient of the electrode.

[0022] Furthermore, in steps two and three, frequency domain testing is conducted by changing the frequencies of the first AC heating current and the second AC heating current, and recording the corresponding harmonic signal values.

[0023] Furthermore, in steps two and three, the frequencies of the first AC heating current and the second AC heating current are both 100~5000Hz, with a frequency step size between 20~500Hz. At each frequency point, the automatic control software records the operating parameters of the heating electrode and the detection electrode.

[0024] Furthermore, in step four, the differential relationship between the third harmonic voltage and frequency is as follows:

[0025]

[0026] Among them, V 3ω，h1 V is the third harmonic voltage, V1 is the average value of the fundamental voltage, l is the electrode length, R is the electrode resistance, T is the temperature, and ω is the frequency.

[0027] Furthermore, the slope method is used to fit V globally. 3ω，h1 The slope m of -ln(ω), according to the relationship between slope m and thermal conductivity k The thermal conductivity k of the substrate was calculated.

[0028] Furthermore, in step five, the thermal conductivity and interfacial thermal resistance of the multilayer thin film material satisfy the following formula:

[0029]

[0030]

[0031]

[0032]

[0033] in, For the electrode temperature rise under isothermal boundary conditions, P represents the electrode temperature rise under adiabatic boundary conditions. l Where b1 is the heating power, b2 is the half-width of the first heating electrode or the half-width of the second heating electrode, and b2 is the detector half-width; A, B, C, and D are multilayer coupling coefficients; i is the imaginary unit, and d is the multilayer coupling coefficient. ht R represents the distance between the first heating electrode and the detection electrode, or the distance between the second heating electrode and the detection electrode, where λ is the integral variable; (j-1)j It is the interfacial thermal resistance between the (j-1)th layer and the jth layer; γ j For calculating coefficients; d j It is the thickness of the j-th layer, k jy It is the interlayer thermal conductivity of the j-th layer, k jx It is the thermal conductivity within the j-th layer, ρc p It is the product of the layer's density and specific heat. It is the thermal angular frequency.

[0034] Beneficial effects: Compared with the prior art, the present invention has the following significant features:

[0035] 1. The thermal conductivity of the substrate is obtained by fitting the logarithm of the third harmonic signal and frequency on the wide first heating electrode using the slope method. The slope method is only sensitive to the thermal conductivity of the substrate, thus eliminating the measurement error introduced by the thin film layer.

[0036] 2. The substrate thermal conductivity can be directly measured without the need for external data, which reduces the measurement error of thin film thermal conductivity and interface thermal resistance and improves accuracy;

[0037] 3. The AC response signal in the frequency domain is measured for inversion calculation of thin film thermal conductivity and interfacial thermal resistance. The large amount of data can improve the fitting accuracy.

[0038] 4. No other reference samples are required to achieve in-situ characterization of multiple parameters such as substrate thermal conductivity, thin film thermal conductivity, and interfacial thermal resistance of a single sample. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the sample structure during the testing of this invention. Detailed Implementation

[0040] like Figure 1 The test structure for measuring the interfacial thermal resistance and thermal conductivity of multilayer thin film materials includes a three-electrode sensor: a wide first heating electrode 1, a narrow second heating electrode 2, and a probe electrode 3. The width of the first heating electrode is W1, which is 20 μm to 60 μm. The width of the second heating electrode 2 is W2, which is 500 nm to 10 μm. The width of the probe electrode 3 is W... sW s The wavelength range is 500 nm to 5 μm. The distance between the first heating electrode 1 and the detection electrode 3 is d. h1 d h1 The distance between the two heating electrodes is 4μm to 35μm. h2 d h2 The effective region length of the electrode is 500 nm to 6 μm. The effective region length of the electrode is l, which is 500 to 3000 μm.

[0041] The GaN / AlN / SiC structure sample was tested. To avoid leakage current on the GaN surface, a 40nm thick SiO2 insulating layer was grown on the GaN surface, forming the SiO2 / GaN / AlN / SiC structure. The GaN was 2μm thick, the AlN was 300nm thick, and the SiC was 500um thick. The SiC was the sample substrate. Since the AlN was inside the sample and its thickness was very small compared to the GaN, it could be regarded as an interface layer.

[0042] A method for measuring the interfacial thermal resistance and thermal conductivity of multilayer thin film materials includes the following steps:

[0043] Step S1: Using photolithography, evaporation coating and other processes, a first heating electrode 1, a second heating electrode 2 and a detection electrode 3 are set on the upper surface of the SiO2 insulating layer on the top of the GaN / AlN / SiC structure sample. The width of the first heating electrode 1 is 40 μm and the width of the second heating electrode 2 is 8 μm.

[0044] Step S2: Connect an AC heating current of 40mA to the first heating electrode 1 and a DC detection current of 5mA to the detection electrode 3. Change the frequency of the AC heating current, starting from 800Hz with frequency intervals of 50Hz, up to 5000Hz. Record the third harmonic voltage V of the heating electrode 1 at each frequency point. 3ω，h1 and the second harmonic voltage V of the detection electrode 3 2ω，s Based on the operating parameters of the first heating electrode 1 and the detection electrode 3, the AC thermal response signal ΔT of the first heating electrode 1 is calculated. h1 (ω), and the AC thermal response signal ΔT of the detection electrode 3. s1 (ω).

[0045] Step S3: Connect the second AC heating current to the second heating electrode 2 with a current amplitude of 10mA, and connect the DC detection current to the detection electrode 3 with a DC detection current of 2mA. Change the frequency of the AC heating current, starting from 800Hz and increasing in 500Hz intervals up to 5000Hz. Based on the operating parameters of the second heating electrode 2 and the detection electrode 3 under the second DC detection current, calculate the AC thermal response signal ΔT of the second heating electrode 2.h2 (ω), and the AC thermal response signal ΔT of the detection electrode 3 s2 (ω);

[0046] Step S4, using the third harmonic voltage V detected on the first heater 3ω，h1 The relationship with frequency ω is used to fit the substrate thermal conductivity. Based on the semi-infinite heat propagation model, the third harmonic voltage V is calculated. 3ω，h1 The differential relationship with frequency ω is:

[0047]

[0048] Using the slope method to fit V as a whole 3ω，h1 The slope m of -ln(ω), according to the relationship between slope m and thermal conductivity k The thermal conductivity of the substrate can be calculated from the measured Vt at 800-5000 Hz. 3ω，h1 The thermal conductivity of SiC was obtained by fitting the data points of -ln(ω) to a value of 394.56 W / (m·K).

[0049] Step S5, based on the multilayer heat propagation physical model, the electrode thermal response ΔT and heating power P l Relationship between electrode dimensions (heater half-width b1, detector half-width b2), thermal conductivity of each layer, and interfacial thermal resistance:

[0050]

[0051]

[0052]

[0053]

[0054] in, For the electrode temperature rise under isothermal boundary conditions, P represents the electrode temperature rise under adiabatic boundary conditions. l Where b1 is the half-width of the first heating electrode 1 or the half-width of the second heating electrode 2, and b2 is the half-width of the detector; A, B, C, and D are multilayer coupling coefficients, calculated from the above matrix; i is the imaginary unit, and d... ht R is the distance between the first heating electrode 1 and the detection electrode 3, or the distance between the second heating electrode 2 and the detection electrode 3, where λ is the integral variable; (j-1)j It is the interfacial thermal resistance between the (j-1)th layer and the jth layer; γ j The coefficients are calculated using the fourth formula above; d j It is the thickness of the j-th layer, k jy It is the interlayer thermal conductivity of the j-th layer, k jx It is the thermal conductivity within the j-th layer, ρcp It is the product of the layer's density and specific heat; It is the thermal angular frequency, defined as twice the angular frequency of alternating current.

[0055] First, assume the thermal conductivity and interfacial thermal resistance of each thin film, then substitute them into the above formula to obtain a set of simulated electrode thermal response data {ΔT}. h1,s (ω), ΔT s1,s (ω), ΔT h2,s (ω), ΔT s2,s (ω)}, adjust one of the parameters, thin film thermal conductivity or interfacial thermal resistance, to make the actual measured electrode thermal response {ΔT} h1 (ω), ΔT s1 (ω), ΔT h2 (ω), ΔT s2 (ω)} and the theoretically calculated electrode thermal response {ΔT} h1,s (ω), ΔT s1,s (ω), ΔT h2,s (ω), ΔT s2,s The difference between (ω)} The minimum value is determined by the value of i, where i represents the AC thermal response signal of the four sets of electrodes: the first heating electrode 1 and its corresponding detection electrode 3, the second heating electrode 2 and its corresponding detection electrode 3. Then, the thermal conductivity or interface thermal resistance parameter of the next thin film is adjusted to minimize the difference between the actual measured electrode thermal response and the theoretically calculated electrode thermal response. The thermal conductivity and interface thermal resistance of each thin film layer are iteratively fitted repeatedly. After multiple iterations, the substrate thermal conductivity k... SiC The AlN layer, i.e., the thermal resistance R at the GaN / SiC interface I GaN thermal conductivity k GaN SiO2 thermal conductivity k SiO2 The convergence is at {392.12 W / (m·K), 9.21 m}. 2 K / GW, 127.28 W / (m·K), 1.26 W / (m·K)}.

Claims

1. A method for measuring the interfacial thermal resistance and thermal conductivity of multilayer thin film materials, characterized in that, Includes the following steps: Step 1: A first heating electrode (1), a second heating electrode (2), and a detection electrode (3) are disposed on the top insulating layer of the multilayer thin film material. Step 2: Apply a first AC heating current to the first heating electrode (1) and a first DC detection current to the detection electrode (3). Change the frequency of the first AC heating current, record the third harmonic voltage of the first heating electrode (1) and the second harmonic voltage of the detection electrode (3), and calculate the AC thermal response signals of the first heating electrode (1) and the detection electrode (3). Step 3: Apply a second AC heating current to the second heating electrode (2) and a second DC detection current to the detection electrode (3). Change the frequency of the second AC heating current, record the third harmonic voltage of the second heating electrode (2) and the second harmonic voltage of the detection electrode (3), and calculate the AC thermal response signals of the second heating electrode (2) and the detection electrode (3). Step 4: Fit the substrate thermal conductivity by the relationship between the third harmonic voltage and frequency of the first heating electrode (1); Step 5: Based on the multilayer heat propagation physical model, set the thermal conductivity and interface thermal resistance values ​​of each thin film, and input them into the thermal simulation model to obtain the simulation values ​​of the AC thermal response signal of the first heating electrode (1), the AC thermal response signal of the detection electrode (3), the AC thermal response signal of the second heating electrode (2), and the AC thermal response signal of the detection electrode (3). Adjust one of the parameters, either the thermal conductivity of the thin film or the interface thermal resistance, to minimize the difference between the actual measured value and the theoretical calculated value. Iterate repeatedly to fit the thermal conductivity and interface thermal resistance of the multilayer thin film material. In step one, the multilayer thin film material is composed of multiple layers of thin films of different types stacked together, with the outermost thin film being an insulating layer. In steps two and three, the frequency of the first AC heating current and the frequency of the second AC heating current are both 100~5000Hz, and the frequency step is between 20~500Hz. At each frequency point, the automatic control software records the working parameters of the heating electrode and the detection electrode (3). In step five, the thermal conductivity and interfacial thermal resistance of the multilayer thin film material satisfy the following formula: in, For the electrode temperature rise under isothermal boundary conditions, P represents the electrode temperature rise under adiabatic boundary conditions. l For heating power, b1 is the half-width of the first heating electrode (1) or the half-width of the second heating electrode (2), b2 is the half-width of the detection electrode (3); A, B, C, and D are multilayer coupling coefficients, which are calculated by the third formula above. i is the imaginary unit, d ht R is the distance between the first heating electrode (1) and the detection electrode (3) or the distance between the second heating electrode (2) and the detection electrode (3), where λ is the integral variable; (j-1)j It is the interfacial thermal resistance between the (j-1)th layer and the jth layer; γ j The coefficients are calculated using the fourth formula above; d j It is the thickness of the j-th layer, k jy It is the interlayer thermal conductivity of the j-th layer, k jx It is the thermal conductivity within the j-th layer, ρc p It is the product of the layer's density and specific heat. It is the thermal angular frequency.

2. The method for measuring the interfacial thermal resistance and thermal conductivity of multilayer thin film materials according to claim 1, characterized in that: In step one, the width of the first heating electrode (1) is greater than the width of the second heating electrode (2).

3. The method for measuring the interfacial thermal resistance and thermal conductivity of multilayer thin film materials according to claim 1, characterized in that: In step two, the AC thermal response signals of the first heating electrode (1) and the detection electrode (3) are calculated based on their operating parameters under the first DC detection current. Where, ΔT h1 (ω) is the AC thermal response signal of the first heating electrode, V 3ω，h1 I is the third harmonic voltage of the first heating electrode. h1 R is the current passing through the first heating electrode. h1 α is the resistance of the first heating electrode. h1 ΔT is the temperature sensitivity coefficient of the first heating electrode. s1 (ω) represents the AC thermal response signal of the probe electrode, V 2ω，s1 To detect the second harmonic voltage of the electrode, I s1 To detect the current in the probe electrode, R s To detect electrode resistance, α s To detect the temperature sensitivity coefficient of the electrode.

4. The method for measuring the interfacial thermal resistance and thermal conductivity of multilayer thin film materials according to claim 1, characterized in that: In step three, based on the operating parameters of the second heating electrode (2) and the detection electrode (3) under the second DC detection current, the AC thermal response signals of the second heating electrode (2) and the detection electrode (3) are calculated: Where, ΔT h2 (ω) is the AC thermal response signal of the second heating electrode, V 3ω，h2 I is the third harmonic voltage of the second heating electrode. h2 R is the current passing through the second heating electrode. h2 α is the resistance of the second heating electrode. h2 The temperature sensitivity coefficient of the second heating electrode; ΔT s2 (ω) represents the AC thermal response signal of the probe electrode, V 2ω，s2 To detect the second harmonic voltage of the electrode, I s2 To detect the current in the probe electrode, R s To detect electrode resistance, α s To detect the temperature sensitivity coefficient of the electrode.

5. The method for measuring the interfacial thermal resistance and thermal conductivity of multilayer thin film materials according to claim 1, characterized in that: In steps two and three, frequency domain testing is conducted by changing the frequencies of the first AC heating current and the second AC heating current, and recording the corresponding harmonic signal values.

6. The method for measuring the interfacial thermal resistance and thermal conductivity of multilayer thin film materials according to claim 1, characterized in that: In step four, the differential relationship between the third harmonic voltage and the frequency is as follows: Among them, V 3ω，h1 V is the third harmonic voltage, V1 is the average value of the fundamental voltage, l is the electrode length, R is the electrode resistance, T is the temperature, and ω is the frequency.

7. The method for measuring the interfacial thermal resistance and thermal conductivity of multilayer thin film materials according to claim 6, characterized in that: Using the slope method to fit V as a whole 3ω，h1 The slope m of -ln(ω), according to the relationship between slope m and thermal conductivity k The thermal conductivity k of the substrate was calculated.

Images