- Application note
- No. SEN001-IFCF-20230315-001
Thermal conductivity measurement of amorphous Ge1-xSnx thin ﬁlms using frequency-domain thermoreﬂectance
- Frequency-domain thermoreflectance
- InFocus BB-FDTR
The thermal conductivities of amorphous Ge1-xSnx thin ﬁlms with diﬀerent Sn compositions were measured using frequency-domain thermoreﬂectance (FDTR). The results show that the thermal conductivity of the thin ﬁlms decreases from 0.50 W/mK to 0.44 W/mK with increasing Sn composition, consistent with the amorphous limit calculated by the minimum thermal conductivity model.
Published Online: Mar. 24th, 2023Download PDF
The optimization of the thermal design of semiconductor devices is crucial for improving their performance and reliability. This requires a deep understanding of the thermal transport properties of the constituent materials, especially as semiconductor materials continue to become ﬁner and thinner. Therefore, it is important to develop accurate and reliable methods for measuring the thermal properties of thin-ﬁlm and nanoscale materials.
Laser ﬂash analysis is a widely used technique for measuring thermal diﬀusivity of bulk materials. However, this method is not suitable for measuring the thermal properties of thin-ﬁlm materials with fast temperature response. An alternative method, frequency-domain thermoreﬂectance (FDTR), is an optical pump-probe technique that can measure various thermal properties of thin ﬁlms with thicknesses ranging from tens of nanometers to several micrometers.
In this application note, the thermal conductivities of amorphous Ge1-xSnx thin ﬁlms with diﬀerent Sn compositions were measured using ScienceEdgeʼs InFocus FDTR.
Four a-Ge1-xSnx thin ﬁlms with diﬀerent Sn compositions were prepared by RF co-sputtering on a silicon substrate (resistivity: 1-20 Ωcm, thickness: 404 µm). All samples were coated with a 62 nm thick Au as a transducer and a 5 nm thick Cr layer was added between Au and thin ﬁlm to improve adhesion. Sn composition and thickness of four a-Ge1-xSnx thin ﬁlms are shown in Table 1.
Table 1. Sn composition and thickness of four a-Ge1-xSnx thin ﬁlm samples. The thickness of the silicon substrate is 404 µm.
The thermal conductivities of thin ﬁlms were measured using ScienceEdgeʼs InFocus FDTR (frequency-domain thermoreﬂectance microscope).
An intensity-modulated 488 nm pump laser was used to create a periodic heat ﬂux on the sample surface, and a 532 nm probe laser was used to monitor the surface temperature through a change of thermoreﬂectance signal. While changing the modulation frequency of the pump laser from 200 kHz to 10 MHz, the phase response of the reﬂected probe beam to the incident heat ﬂux was recorded with a lock-in ampliﬁer. It took 4 minutes to obtain a phase lag plot from 200 kHz to 10 MHz, and each sample was measured three times to ensure repeatability.
The thermal conductivity of thin ﬁlms was determined by comparing the averaged phase lag of each sample and the calculated phase lag using a thermal transport model with unknown thermal conductivity as the ﬁtting parameter. The multilayer sample model and nominal values for ﬁtting are shown in Figure 1 and Table 2. Volumetric heat capacity of the thin ﬁlms were calculated from literature values of Ge (1644.8 kJ/m3K) and Sn (1671.7 kJ/m3K) and their composition ratios.
Figure 1. The multilayer sample model where each layer includes thermal conductivity k, volumetric heat capacity C, the thermal boundary conductance G, and layer thickness (not shown). Table 2. Nominal values for ﬁtting analysis.
As shown in Figure 2, the phase data for the four a-Ge1-xSnx thin ﬁlms show clear diﬀerences with good reproducibility. Thereafter, ﬁtting analysis was performed on the average phase data of three measurements for each sample.
Figure 3 (a) presents the averaged phase data (dots) and best-ﬁt curve (solid line) obtained using a thermal conductivity value of 0.55 W/mK for the a-Ge thin ﬁlm. This value is in close agreement with predictions from the minimum thermal conductivity model (0.62 W/mK)*1, as well as with values measured by Cahill et al. (0.51 W/mK)*2 and by Alvarez-Quintana et al. (0.64 W/mK)*3. Simulated curves obtained by varying the thermal conductivity by ±10% (0.50 to 0.61 W/mK) and ±20% (0.44 to 0.66 W/mK) are also shown. The variability of the three measurements is small compared to the ±10% range (Figure 3 (b)), and the uncertainty is approximately ±5%.
Table 3 summarizes the thermal conductivity results for the rest of the samples, which exhibit a decrease in thermal conductivity from 0.50 W/mK to 0.44 W/mK with increasing Sn composition. These values are close to the amorphous limit calculated by the minimum thermal conductivity model*4.
Figure 2. Phase vs frequency data obtained from FDTR measurements of the a-Ge1-xSnx thin ﬁlms. Three diﬀerent spots were measured for all samples.
Figure 3 (a). The averaged phase data of three a-Ge data (dots) and best-ﬁt curve (solid line) are shown along with solutions obtained by varying thermal conductivity (k) by ±20% (dotted lines). (b). Variation in phase data of three measurements (dots) and solutions obtained by varying k by ±10% and ±20% (dotted lines).
Table 3. A summary of measured thermal conductivity.
We successfully measured the thermal conductivities of amorphous Ge1-xSnx thin ﬁlms with diﬀerent Sn compositions using ScienceEdgeʼs InFocus FDTR. The experimental setup and methodology demonstrated in this study provide an accurate and reliable method for measuring the thermal properties of thin-ﬁlm and nanoscale materials. This highlights the excellent performance of ScienceEdgeʼs InFocus FDTR, and its potential for optimizing the thermal design of semiconductor devices.
We sincerely thank Dr. Kurosawa and Mr. Oiwa of Nagoya University for providing samples and for their helpful comments on the measurements and the draft of application note.
*1: Cahill et al., Phys. Rev. B 46, 6131 (1992).
*2: Cahill et al., Phys. Rev. B 37, 8773 (1988).
*3: Alvarez-Quintana et al., J. Appl. Phys 104(7) 074903 (2008).
*4: Khatami et al., Appl. Phys. Rev. 6, 014015 (2016).