A broadband frequency-domain thermoreflectance method for measuring the thermal properties of solid materials

Abstract

The present invention discloses a broadband frequency-domain thermal reflection method for measuring the thermal properties of solid materials, the method comprising: intensity modulating the pump light, irradiating the pump light to the sample surface to cause heating of the sample, reflecting the probe light after reaching the sample surface, and generating a difference frequency signal on the sample surface or in front of a photodetector, measuring the phase of the pump light, the probe light and the mixed light using a phase-locked amplifier, calculating the thermal phase, and fitting the thermal phase to obtain the required thermal property parameters. The present invention proposes an innovative difference frequency method to solve the problem of low signal-to-noise ratio of the frequency-domain thermal reflection method under high-frequency measurement. This method can effectively improve the signal-to-noise ratio when the measurement frequency is greater than 20 MHz, and ultimately achieve a heating frequency of up to 200 MHz. A wider heating frequency range can obtain more data points, and then a suitable range can be selected according to its sensitivity curve for parameter fitting, thereby improving the accuracy of thermal property measurement.

Description

Technical Field

[0001] The invention relates to a broadband frequency domain thermal reflection method, in particular to a broadband frequency domain thermal reflection method for measuring thermal properties of solid materials. Background Art

[0002] Frequency-domain thermoreflectance is an advanced technique for measuring thermophysical properties. It uses a periodically modulated continuous laser as a heat source to heat a sample, causing the sample surface temperature to change periodically. When the temperature change remains within a small range, there is a linear relationship between the light intensity reflectance and temperature. This property allows us to illuminate the sample with another continuous laser beam as a probe light source and analyze the light reflected from the sample surface to measure the amplitude and phase of the surface temperature change. The phase difference between the sample surface temperature and the periodic heat source is closely related to the sample's thermophysical properties. By measuring the phase difference at different heating frequencies and then using inverse analysis, the sample's thermophysical properties, including thermal conductivity, interfacial thermal conductance, and volumetric heat capacity, can be determined. This method not only provides precise measurement results but is also simple to operate, bringing significant benefits to the fields of materials science and thermophysical property research.

[0003] However, experimental measurements often require a relatively wide heating frequency range, as the accuracy of thermophysical property parameters derived through inverse analysis depends on sensitivity. Because the sensitivity of each parameter varies significantly across different heating frequency ranges, the accuracy of the inverse analysis also varies significantly. Therefore, to accurately determine the parameters of the material being measured, measurements over a wide heating frequency range are necessary. This allows accurate inverse analysis to be performed using measurement data from heating frequency ranges with high sensitivity for each parameter.

[0004] In the traditional frequency domain thermoreflectometry method, an electro-optical modulator (EOM) is used to modulate the intensity of the pump light, and a sinusoidal electrical signal is introduced into the pump light path to generate a modulated optical signal. The heating frequency of the traditional method is usually below 20MHz because the frequency response signal of the probe light is Among them, C TR is the light reflection coefficient of the structure surface; Q0 and Q1 are the power of the pump light and the probe light; k is the Hankel transformation; C and D are the matrix elements in the heat conduction matrix; ω0 and ω1 are the radii of the heating light and the probe light. The intensity of the probe light signal is positively correlated with the amplitude R, which is This formula indicates that as the heating frequency increases, the signal amplitude decreases. Furthermore, high frequencies are accompanied by an increase in coherent noise and ambient noise. Specifically, when two cables transmit high-frequency signals, especially those exceeding 20 MHz, the primary noise source is the cable connecting the EOM amplifier and the EOM. The high-voltage signals on these cables produce a broadcast effect at the same frequency as the thermal signal, which is then received by the cable connecting the photodetector and the lock-in amplifier. Because this cable acts as an antenna in this case, the noise signal it receives is superimposed on the thermal signal, further reducing the measurement accuracy. In summary, these factors collectively cause the signal-to-noise ratio of the frequency-domain thermoreflectometry method to decrease significantly at higher heating frequencies. Summary of the Invention

[0005] Purpose of the invention: The present invention aims to provide a broadband frequency-domain thermoreflection method for measuring the thermal properties of solid materials, so as to solve the problem of low signal-to-noise ratio of the frequency-domain thermoreflection method under high-frequency measurement. At the same time, a wider heating frequency range can obtain more data points, and then the appropriate interval can be selected according to its sensitivity curve for parameter fitting, thereby improving the accuracy of thermal property measurement.

[0006] Technical solution: The broadband frequency-domain thermal reflection method for measuring the thermal properties of solid materials described in the present invention can selectively allow the difference frequency to occur on the sample surface or in front of the photodetector.

[0007] When a difference frequency occurs on the sample surface, the method includes: synchronous intensity modulation of the pump laser and the detection laser, and the signal generator can output multiple frequencies, including the difference frequency signal, for use as a reference frequency by the phase-locked amplifier. The pump light is irradiated onto the sample surface, causing the sample to heat up. At the same time, the signal carried by the detection light meets the signal carried by the pump light on the sample surface and mixes. The two beams of light are then reflected back to the photodetector together. The phase of the pump light, detection light, and mixed light is measured using the phase-locked amplifier, and the thermal phase is calculated. After fitting the thermal phase, the required thermal physical parameters are obtained. The calculation formula of the thermal phase is as follows:

[0008]

[0009] in, is the phase of the pump light, is the phase of the detection light, is the phase of the mixed light.

[0010] Furthermore, the pump light laser and the probe light laser are independently and differently intensity modulated by their respective signal generators and electro-optical modulators (EOMs), at frequencies f1 and f2, respectively.

[0011] When the difference frequency occurs in front of the photodetector, the method includes: the electro-optic modulator applies intensity modulation of the pump light with a frequency of f1, the pump light is irradiated to the sample surface, causing the sample to heat up, so that the sample surface temperature changes periodically, and then the unmodulated detection light reaches the sample surface. Due to the periodic reflectivity change caused by the temperature change, the detection light carries a signal with a frequency of f1 and a thermal phase after being reflected by the sample surface. This signal is then further modulated by the electro-optic modulator in front of the photodetector, and after passing through a low-pass filter, the signal frequency is converted to f1-f2 and finally captured by a phase-locked amplifier. The phase of the pump light, detection light and mixed light is measured using the phase-locked amplifier, and the thermal phase is calculated. The thermal phase is fitted to obtain the required thermal physical parameters. The calculation formula of the thermal phase is the same as above.

[0012] Furthermore, two signal generators are connected to the mixer, and a reference signal with a frequency of f1-f2 is generated by the mixer and supplied to the lock-in amplifier.

[0013] Furthermore, the frequency difference Δf during mixing is between 100 kHz and 50 MHz. The present invention maintains the difference between the two modulation frequencies (Δf = f1 - f2) at a low, fixed value, and sets this difference as the reference frequency of the lock-in amplifier. This design has the advantage of enabling direct frequency differentiation at the sample interface or in front of the photodetector, thereby avoiding the effects of coherent noise in traditional solutions and improving signal processing efficiency and measurement accuracy.

[0014] Furthermore, a beam splitter is provided on the pump light path, a long-wavelength dichroic mirror is provided on the detection light path, and filters corresponding to the two types of light are installed in front of the photodetector.

[0015] Furthermore, the thermophysical parameters include thermal conductivity, volumetric heat capacity and interface thermal conductance.

[0016] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: the method can effectively improve the signal-to-noise ratio when the measurement frequency is greater than 20 MHz, and ultimately achieve a heating frequency of up to 200 MHz. A wider heating frequency range can obtain more data points, and then the appropriate interval can be selected according to its sensitivity curve for parameter fitting, thereby improving the accuracy of thermal property measurements. In addition, the present invention can realize the difference frequency signal measurement of the reflected detection light under high pump light modulation frequency, and maintain an excellent signal-to-noise ratio. A higher heating frequency allows for the capture of more abundant data points under high-frequency modulation conditions. The increase in these data points provides a wider range of choices to select the appropriate interval for parameter fitting according to the sensitivity curve. This solution significantly improves the accuracy and reliability of thermal property measurements, and lays a solid foundation for the accurate analysis of experimental data. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a diagram of the optical path design structure of Example 1;

[0018] Figure 2 This is a comparison chart of the signal-to-noise ratios obtained by testing the present invention and the traditional method;

[0019] Figure 3 is the thermal phase fitting diagram;

[0020] Figure 4 This is a sensitivity curve diagram of Example 1;

[0021] Figure 5 This is the optical path design structure diagram of Example 2. DETAILED DESCRIPTION

[0022] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0023] Figure 1 and Figure 5 The reference numerals in the figures are: 1-signal generator, 2-electro-optic modulator, 3-locked amplifier, 4-photodetector, 5-mixer.

[0024] Example 1

[0025] This embodiment uses a pump laser and a probe laser (pump light 400nm, probe light 800nm) to perform intensity modulation through a signal generator 1 and an EOM. The signal generator 1 can output multiple frequencies, including difference frequency signals, for use as a reference frequency by the phase-locked amplifier 3. A beam splitter is provided on the pump light path, and a long-wavelength dichroic mirror is provided on the probe light path. The pump light irradiates the sample surface, causing the sample to heat up. At the same time, the signal carried by the probe light meets the signal carried by the pump light on the sample surface and mixes. The two beams of light are then reflected back to the photodetector 4 together. In order to accurately separate and detect the two types of light, two filters corresponding to the light are installed in front of the photodetector 4. The phase-locked amplifier 3 can lock multiple frequencies at the same time and perform phase measurement in a specific frequency range. In this way, the phases of the pump light, the probe light, and the mixed probe light are measured respectively. Based on these measurement results, the thermal phase can be calculated. Finally, the thermal phase is fitted in combination with the heat transfer model to obtain the required thermal physical parameters.

[0026] Schematic diagram of the pump light and probe light carrying signals with frequencies f1 and f2, respectively, after being modulated by signal generator 1 and EOM. Since ω = 2πf, the pump light is Y1 = A1sin(ω1t) and the probe light is Y2 = A2sin(ω2t).

[0027] When the two beams of light reach the sample surface, the pump light generates heat on the sample surface, and the heat propagates in the sample, causing the surface temperature change to produce a phase delay. It contains information closely related to the thermal properties of the sample. Under the condition of a small temperature rise, the change in light reflectivity on the sample surface maintains a linear relationship with the temperature change. Due to the heating effect of the pump light, the surface temperature will show a periodic change following the heating frequency. This periodic change will also affect the reflection characteristics of the probe light. In addition, since the probe light and the pump light have undergone different instrument paths and reflection processes, they each carry an additional phase. and Then during reflection, where Y 混 It represents the mixed light in the reflected probe light. It is obtained by mathematically calculating the reflectivity change caused by the probe light and the surface temperature change. The high-frequency (ω1+ω2) signal is omitted here because it is not the signal we need and will be filtered out by the phase-locked amplifier.

[0028] When the two beams of light reach the photodetector, they will also carry additional phases due to the different optical paths they have experienced. and Mixed light carries additional phase but because The distance from the sample surface to the photodetector is the same for the three beams, so By replacing the corresponding filters in front of the photodetector, the pump light and the probe light can be allowed to pass through separately, so that their phases can be measured separately. In particular, the reflected probe light signal with a difference frequency is used here, and its frequency is significantly lower than the modulation frequency of the pump light. This method effectively reduces the coherent noise, thereby significantly improving the signal-to-noise ratio, such as Figure 2 As shown, the yellow curve is the noise measured after frequency mixing according to the present invention, and the black curve is the noise measured using a conventional method (reference: Schmidt AJ, Cheaito R, Chiesa MA frequency-domain thermoreflectance method for the characterization of thermal properties [J]. Review of Scientific Instruments, 2009, 80 (9): 617.).

[0029] Based on this, we can get By fitting the thermal conductivity model, thermal physical parameters such as thermal conductivity and interface thermal conductivity can be obtained.

[0030] Fitting process: This experiment mainly measures the thermal phase angle The theoretical calculation formula is as follows. The lsqcurvefit model is used in MATLAB to fit the unknown parameters. The remaining parameters are substituted into the literature values or actual measured values. The fitting range of each parameter is set as the initial value according to the actual situation, as shown in Table 1 and Figure 3 As shown in the sensitivity curve Figure 4 shown.

[0031] The frequency response function is

[0032] Thermal phase angle

[0033] Table 1

[0034]

[0035] *: Thermophysical parameters obtained by fitting

[0036] Example 2

[0037] This embodiment uses an electro-optical modulator 2 to modulate the pump light intensity at a frequency of f1. The probe light then carries a signal at a frequency of f1 after being reflected from the sample surface. This signal is then further modulated by the electro-optical modulator (EOM) in front of the photodetector 4. After passing through a low-pass filter, the signal frequency is converted to f1-f2 and ultimately captured by the lock-in amplifier 3. Simultaneously, two signal generators 1 generate a reference signal at a frequency of f1-f2 through a mixer 5, which is then fed to the lock-in amplifier 3. For a diagram of the optical path design, see [1]. Figure 5 , The calculation method and the fitting process of the thermal phase are similar to those in Example 1.

Claims

1. A broadband frequency domain thermal reflection method for measuring the thermal properties of solid materials, characterized in that: The method includes: modulating the intensity of pump light at a frequency f1 and irradiating it onto the sample surface, causing the sample to heat; synchronously modulating the intensity of probe light at a frequency f2, so that the two beams meet on the sample surface to generate mixed light, which is reflected back to the photodetector; using a lock-in amplifier to measure the phase of the pump light, probe light, and mixed light; and using the formula: Calculate the thermal phase and obtain the thermal physical property parameters after fitting the thermal phase; is the phase of the pump light, is the phase of the detection light, is the phase of the mixed light.

2. The broadband frequency domain thermal reflection method for measuring the thermal properties of solid materials according to claim 1, characterized in that: The pump laser and the detection laser are synchronously intensity modulated by a signal generator and / or an electro-optical modulator.

3. The broadband frequency domain thermal reflection method for measuring the thermal properties of solid materials according to claim 1, characterized in that: The frequency difference Δf during mixing is 100KHz-50MHz.

4. The broadband frequency domain thermal reflection method for measuring the thermal properties of solid materials according to claim 1, characterized in that: A beam splitter is provided on the pump light path, and a long-wavelength dichroic mirror is provided on the detection light path.

5. The broadband frequency domain thermal reflection method for measuring the thermal properties of solid materials according to claim 1, characterized in that: Filters corresponding to the two types of light are installed in front of the photodetector.

6. The broadband frequency domain thermal reflection method for measuring the thermal properties of solid materials according to claim 1, characterized in that: This method is applicable to heating frequencies up to 200 MHz.

7. The broadband frequency domain thermal reflection method for measuring the thermal properties of solid materials according to claim 1, characterized in that: The thermophysical parameters include thermal conductivity, volumetric heat capacity and interface thermal conductance.

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