In recent years, with the rapid development of the semiconductor industry, the volume of semiconductor components has decreased dramatically, which is crucial for the thermophysical properties of chip or thin film materials, which provides a development demand for ultra-small thermophysical detection technology, and the development of optical-based thermal reflectometry has made it easy to measure the thermal conductivity of small (submicron) samples. In frequency-domain thermal reflectometry FDTR measurements, the reference phase of the lock-in amplifier needs to be precisely calculated to reduce the effect on the phase lag signal.
SDTR - SpecialDomain Thermal Reflection) is also a laser-pumped-thermal reflection detection technique, which can be used to measure the in-plane thermal physical properties of small-sized thin film samples. Compared with other laser-pumped detection methods (e.g., TDTR, FDTR), it has the advantage of being able to test the in-plane thermal physical properties of thin film samples at a low costLike FDTR, it is based on CW laser, but the current FDTR is usually modulated at a frequency of more than 5 kHz, so it can only measure in-plane thermal conductivity above 10 W mK, but SDTR can measure in-plane thermal conductivity below 10 W (m·k) by changing the phase and amplitude signals of the pump and the spatial position of the detection spot.
1.SDTR test
Figure 1 shows the optical path of the experimental system for SDTR. A pump laser beam is modulated by a sine wave and focused on the surface of the sample, which is periodically heatedAnother detection laser with different wavelengths passes through a polarization beamsplitter prism (the transmittance can be changed by adjusting the direction of linear polarization), the transmitted light is focused on the sample surface, and the temperature response of the sample surface is detected, and the detection light can be irradiated through the dichroic mirror and focused to the sample and reflected, carrying the thermal reflectance information of the periodic changes of the sample surface, the pump light is reflected at the dichroic mirror and focused to the sample to periodically heat the sample, and the sample surface generates periodic changes in thermal reflectivity due to the periodic thermal field. The photodetector converts the detection light signal into an electrical signal, which is then transmitted to a lock-in amplifier to extract the amplitude and phase of the signal. A sinusoidal signal of a given frequency can be output by the lock-in amplifier or output to the lock-in amplifier and pump laser through an external signal generator, transmitted to the pump laser to modulate the pump laser, and transmitted to the lock-in as an internal reference to achieve lock-in analysis of the acquired signal.
In the SDTR experiment, a metal film about 100 nm thick is required to coat the surface of the sample as a temperature sensing layer. By adjusting the angle of the mirror in the optical path that reflects the beam to the sample, the position of the pump spot on the sample surface relative to the detection spot can be adjusted, and the lock-in amplifier records the data of the offset distance xc between the pump spot and the detection spot on the sample surface. Taking the phase and amplitude signals at xc = 0 as the reference, the difference value of the phase signal at any xc is taken.
The amplitude signal is normalized to its normalized value.
By fitting the differential phase signal and the normalized amplitude signal at the same time, the in-plane thermal conductivity kx and the laser spot size wx in the direction of the spot shift of the sample can be extracted.
Figure 2: Fused silica sample with 100 nm titanium plated at 150 Hz pump modulation frequency and 11Plots of SDTR test phase (A) and normalized amplitude (B) at a 5 m spot size.
Figure 2 shows the measurement data and fitting curves of a fused silica sample coated with a 100 nm titanium film at 150 Hz pump frequency modulation. By fitting the phase difference signal in Fig. 2(a), the in-plane thermal conductivity of the fused silica along the spot offset direction is 14w/(m·k)。The thermal conductivity measured by SDTR is very close to the literature value;Similarly, the thermal conductivity of each anisotropy along the surface can be measured by changing the direction of the pump spot and the probe spot relative to the sample (although the fused silica in this example is an isotropic material, so it is not necessary to test the anisotropy in different directions). Figure 2(a) also shows the curve for a 30% change in the best fit value of zui, which is represented by a dotted line in the plot to illustrate the sensitivity of this signal pair. On the other hand, the normalized amplitude signal shown in Figure 2(b) can be fitted to accurately obtain a laser spot size of 11 in the offset direction5 μm。
2.Sensitivity analysis
Figure 3 illustrates the sensitivity coefficients of the measured signal in Figure 1 to different parameters in the system. These parameters include the thermal conductivity kxm, kym, kzm (where the corner mark m represents the physical properties of the metal sensing) and kx, ky, kz, volume specific heat capacity cm and c, the thickness of the metal sensing layer hm, the interfacial thermal conductivity g, and the laser spot size wx and wy in different directions on the surface of the pump spot sample.
Figure 3: Schematic diagram of the sensitivity of the SDTR test results of a 100 nm AU Sapphire sample with a modulation frequency of 9 kHz to the individual thermal physical properties of the sample. (a) Phase gradient signal δ Sensitivity to different parameters;(b) Sensitivity of amplitude to different parameters.
Figure 3 shows that the thermal conductivity kx along the x-direction of the sample surface and the volumetric specific heat capacity c of the sample are highly sensitive to δ, so it is necessary to know the more accurate and reliable sample volume specific heat capacity c in advance to obtain more accurate thermal conductivity resultsThe spot size wx in the x-direction is highly sensitive to the amplitude half-height width, so the spot size wx on the sample surface can be determined more accurately by the amplitude half-height width, which is less affected by other sample parameters.
3.Test results
Figure 4: Comparison of in-plane thermal conductivity measurements of a series of standard samples performed by SDTR with reference values in the literature.
The in-plane thermal conductivity of sapphire, silicon, silica, highly directional pyrolytic graphite (HOPG) and X-cut quartz was measured by SDTR method, and the results are shown in Figure 4, in which the results obtained are highly consistent with the reference values of the literature, and the errors are less than 5%.
References: 1] p jiang, d. wang, z. xiang, r. yang, h. ban, a new spatial-domain thermoreflectance method to measure a broad range of anisotropic in-plane thermal conductivity, int. j. heat mass transfer, 191 (2022) 122849.
2] Shangzhi Song, Kexin Zhang, Puqing Jiang, Novel Optical AC Calorimetry to Accurately Measure In-Plane Thermal Conductivity of Small-Sized Samples, Energy Science and Technology, 1 (2022) 33-38