Ultralow thermal conductivity of amorphous silicon–germanium thin films for alloy and disorder scattering determined by 3ω method and nanoindentation

The ultralow thermal conductivity (1.3 W/(m∙K)) of amorphous silicon–germanium films for alloy and disorder scattering was investigated using the 3ω method and nanoindentation. The films exhibited the lowest phonon mean free path (MFP) of 0.5 nm compared to that of amorphous silicon (1.1 nm) and germanium (0.9 nm) films, owing to alloy scattering in the silicon–germanium films. Based on Matthiessen’s rule, the phonon MFPs of the amorphous silicon–germanium films contributing to alloy and disorder scattering were calculated to be 1.0 nm for both. Therefore, alloy and disorder scattering contribute equally to the reduction in the phonon MFP.

A morphous materials are solids that consist of atoms and molecules bound together in irregular structures.Unlike crystals, amorphous materials do not exhibit long-range order.Nevertheless, they are not completely disordered, as there exists short-range order between neighboring atoms and molecules.Because of this structure, the material properties of the amorphous phase are significantly different from those of the crystalline phase.For example, in amorphous Si, the electronic band structure transitions from an indirect to a direct one, which significantly increases the light-absorption coefficient.][8][9] Thermoelectric materials are primarily used in thermoelectric generators (TEGs), which produce electrical power directly from thermal energy and are used in various energyharvesting applications.[10][11][12][13] The efficiency of electrical power generation in TEGs increases as the thermal conductivity of the thermoelectric materials decreases.[14][15][16] Thermal conductivity comprises lattice and electronic components, with lattice thermal conductivity playing a key role in the performance of thermoelectric materials.This is because the lattice thermal conductivity decreases as the representative size decreases.This phenomenon suggests that amorphous materials are well-suited for size reduction. Therore, many researchers have attempted to synthesize thermoelectric materials with low lattice thermal conductivities, such as organic materials, [17][18][19][20] low-dimensional materials, [21][22][23][24] and nanostructured materials.[25][26][27][28] Nanostructured materials have diverse nanoarchitectures, including nanocrystals, [29][30][31][32] nanocomposites, [33][34][35] and superlattices.[36][37][38] Given this context, the thermal conductivity of amorphous materials has been extensively studied.Cahill et al. measured the thermal conductivities of various amorphous materials using the 3ω method, 39) and their findings revealed that the mechanism of ultralow thermal conductivity aligns well with the minimum thermal conductivity model proposed by Slack.40) However, to achieve a more detailed understanding of this mechanism, the lattice thermal conductivity must be separated for each element.According to kinetic theory, the lattice thermal conductivity is composed of specific heat, group velocity, and phonon mean free path (MFP).Minnich et al. measured the phonon MFPs of silicon using thermal conductivity spectroscopy and obtained good agreement with first-principles calculations. 41) Inour previous studies, we developed a method to estimate thermal conductivity, group velocity, and phonon MFP by combining thermal conductivity measurements and nanoindentation.[42][43][44][45][46] Consequently, we showed that the primary cause of the ultralow thermal conductivity of amorphous materials is a notable reduction in phonon MFP.47) One approach to further decreasing the lattice thermal conductivity of amorphous materials is to alloy them.In crystals, short-wavelength phonons are scattered by alloy atoms. For exmple, alloys of silicon and bismuth telluride have shown a reduction in lattice thermal conductivity through alloy scattering.[48][49][50] The thermal conductivity of amorphous alloys has been investigated in various alloy materials 51,52) ; however, the phonon transport phenomena have not yet been analyzed by isolating the effects of the alloy from those of the disordered structure.
In this study, to address this unexplored research gap, we prepared amorphous silicon-germanium thin films by sputtering.Additionally, reference samples of amorphous silicon and germanium thin films were prepared using the same method.The thermal conductivity, group velocity, and phonon MFP of the amorphous thin films were measured using the 3ω method and nanoindentation.Finally, to isolate the contribution of alloy scattering to the phonon MFP of amorphous silicon-germanium thin films, we estimated the phonon MFP of the alloy from the measurements using the phonon MFPs of the reference samples.
Three types of amorphous thin films made of silicon, silicon-germanium, and germanium were fabricated using a pressure-gradient sputtering system (PGS, Kenix) without substrate heating.High-purity (99.9%) poly-Si, poly-Si 0.5 Ge 0.5 , and poly-Ge targets (Furuuchi Chemical) with diameters of 50 mm were used for the deposition.Polished alumina substrates with dimensions of 25 mm × 25 mm × 1.0 mm (AO-2525, Furuuchi Chemical) were used.The distance between the target and the substrate was adjusted to 200 mm.Sputtering was performed using highpurity (99.995%)Ar gas under a pressure of 0.6 Pa and a radio frequency power of 30 W. The deposition time was adjusted to achieve a film thickness of approximately 400 nm for all three types of thin films, and the film thickness was measured using a profilometer (DektakXT, Bruker).
The atomic composition of the silicon-germanium thin films was determined using an electron probe micro analyzer (EPMA-8050G: Shimadzu), confirming a Si:Ge composition ratio of 50:50.The surface morphologies of the three types of thin films were analyzed using scanning probe microscopy (SPM; SPM-9700, Shimadzu).The structural characteristics of the films were analyzed through X-ray diffraction (XRD; X'Pert-MRD, Philips) and Raman spectroscopy (XploRA, Horiba).Cu Kα radiation (λ = 0.154 nm) was used to obtain the XRD patterns, and an Ar+ laser beam excited at 514.5 nm was used to obtain the Raman spectrum.
][55] In brief, this method involves using a thin metal wire for both heating and temperature sensing, where the temperature amplitude is obtained by detecting the 3ω component voltage of the alternating current applied to the heater.The group velocity of the films was estimated at approximately 300 K through nanoindentation (ENT-NEXUS, Elionix).Nanoindentation is a technique used for evaluating the hardness and elastic modulus of a material by applying a microindenter and recording the load-displacement curve.In this study, a Berkovich indenter operating in continuous stiffness mode was used, and the indentation depth was set to 10% of the film thickness.The process of determining group velocity through nanoindentation has been described in our previous reports. 44,45)he surface morphologies of the amorphous thin films analyzed using SPM are shown in Fig. 1.None of the films exhibited cracks, and their surfaces were relatively smooth.These characteristics are favorable for the measurement of thermal conductivity and group velocity using the 3ω method and nanoindentation, respectively.
The phase structure analysis results obtained from XRD are shown in Fig. 2(a).Peaks exhibited by the silicon, silicon-germanium, and germanium thin films were obtained from the alumina substrate, indicating that the three thin films had very low crystallinity.The Raman spectra of the thin films are shown in Fig. 2(b).Broad peaks are observed in the spectra of the three thin films.Therefore, the XRD and Raman spectroscopy analyses indicate that the three thin films of silicon, silicon-germanium, and germanium attained an amorphous phase.In addition, the silicon-germanium thin film obtains two broad peaks at approximately 250 and 370 cm −1 .The peak at 250 cm −1 is almost identical to the peak position of the germanium film, but the peak intensity of the silicon-germanium thin film is lower than that of the germanium thin film.These phenomena indicate that small amounts of germanium are dispersed and solid soluble in the silicon-germanium thin film.
Figure 3 shows the thermal conductivity of the amorphous silicon-germanium thin films (measured using the 3ω method at approximately 300 K) compared to those of amorphous silicon and germanium thin films.The thermal conductivity measured in this study corresponded to the lattice thermal conductivity because the amorphous silicongermanium, silicon, and germanium thin films were undoped (i.e. the electronic thermal conductivity was negligible).The thermal conductivity of the amorphous silicon-germanium thin films was estimated to be 1.3 W/(m•K), whereas those of amorphous silicon and amorphous germanium thin films were obtained as 3.3 and 1.8 W/(m•K), respectively.Therefore, the thermal conductivity of the amorphous silicon-germanium thin film was the lowest among the three types of amorphous thin films, indicating that alloying can reduce thermal conductivity even though the structure is an amorphous phase.In Table I, the thermal conductivities of the amorphous silicon-germanium thin films in this study are compared with those of previously reported silicon-germanium thin films with different structures.The thermal conductivity of the amorphous silicon-germanium thin film in this study was lower than those of single-crystalline and polycrystalline thin films because these crystalline films exhibited less phonon scattering and had longer phonon MFPs. 56,57)Moreover, the thermal conductivity of the amorphous silicon-germanium thin film is low compared to that of the superlattice, which exhibits increased phonon scattering at the interfaces. 58)When the grain size decreases to the nanocrystalline level, the thermal conductivities of amorphous and nanocrystalline materials are similar. 59,60)igure 4 shows the group velocity of the amorphous silicon-germanium thin films (measured at approximately 300 K) compared to those of amorphous silicon and amorphous germanium thin films.The longitudinal group 011005-2 © 2024 The Author(s).Published on behalf of The Japan Society of Applied Physics by IOP Publishing Ltd velocity v L and transverse group velocity v T were estimated using Young's moduli and shear moduli, respectively, obtained via nanoindentation.The average group velocity v ave is expressed as 3/v ave 3 = 1/v L 3 + 2/v T 3 .The longitudinal, transverse, and average group velocities of the amorphous silicon-germanium thin films were 6208, 3926, and 4320 m s −1 , respectively.The average group velocity of the amorphous silicon-germanium thin films was approximately 24% lower than that of the amorphous silicon thin films and 21% higher than that of the amorphous germanium thin films.Therefore, the group velocity of the amorphous silicon-germanium thin film fell between that of the amorphous silicon and that of amorphous germanium thin films.This result indicates that the group velocity was unaffected by alloy scattering; that is, if the alloy scattering effect is present, the group velocity of the amorphous silicongermanium thin films should have been the lowest among those of the three types of amorphous thin films.
Figure 5 shows the phonon MFP of the amorphous silicon-germanium thin films compared to that of the amorphous silicon and amorphous germanium thin films.The phonon MFP Λ eff was determined from the average group velocity v ave and lattice thermal conductivity κ l based on the kinetic theory (Λ eff = 3κ l /Cv ave ).The values of specific heat C of amorphous silicon-germanium, silicon, and germanium are 1.678 × 10 6 , 1.675 × 10 6 , and 1.669 × 10 6 J/(m 3 •K), respectively. 61)As a result, the phonon MFP Λ eff of the amorphous silicon-germanium thin films was calculated to be 0.5 nm, whereas those of amorphous silicon and amorphous germanium thin films were calculated to be 1.1 and 0.9 nm, respectively.Therefore, the phonon MFP Λ eff of the amorphous silicon-germanium thin film exhibited the lowest value among the three types of amorphous thin films owing to the influence of alloy scattering.
To further investigate the effect of alloy and disorder scattering on amorphous silicon-germanium thin films, we estimated the phonon MFPs for different scattering mechanisms using the phonon MFPs of amorphous silicon and amorphous germanium thin films, as shown in Table II.Based on Matthiessen's rule, the effective (measured) phonon MFP Λ eff can be expressed as 62) ( ) where Λ um , Λ dis , and Λ alloy are the phonon MFPs corresponding to Umklapp, disorder, and alloy scattering mechanisms, respectively.In our previous study on amorphous silicon thin films, Λ um was significantly longer than Λ dis , indicating that Λ eff was almost the same as Λ dis . 47)Therefore, when we calculate the phonon MFPs of Λ dis and Λ alloy , the value of Λ um can be neglected.Because alloy scattering does not occur in amorphous silicon and germanium thin films, the values of Λ eff correspond to those of Λ dis .For amorphous silicon-germanium thin films, the value of Λ dis can be estimated to be 1.0 nm by averaging the Λ dis values of   011005-3 © 2024 The Author(s).Published on behalf of The Japan Society of Applied Physics by IOP Publishing Ltd amorphous silicon (1.1 nm) and germanium (0.9 nm) thin films.This is because the atomic composition of the silicongermanium thin film in this study was Si:Ge = 50:50.Finally, the value of Λ alloy of the amorphous silicongermanium thin film was calculated to be 1.0 nm using Matthiessen's rule from the values of Λ eff and Λ dis .Therefore, we conclude that alloy and disorder scattering contribute equally to the decrease in the phonon MFP.In summary, alloy and disorder scattering in amorphous alloy materials were investigated using a combination of the 3ω method and nanoindentation.We prepared amorphous silicon-germanium thin films by sputtering, and amorphous silicon and germanium thin films were also prepared using the same method as the reference samples.The amorphous silicon-germanium thin films exhibited an ultralow thermal conductivity of 1.3 W/(m•K).This value was lower than that of both the amorphous silicon and germanium thin films, indicating that alloying can reduce thermal conductivity, even in an amorphous structure.The group velocity of amorphous silicon-germanium (4320 m s −1 ) was intermediate between those of amorphous silicon and germanium thin films; however, the phonon MFP of amorphous silicon-germanium (0.5 nm) was the lowest among the three types of amorphous thin films.These results indicate that alloy scattering in amorphous silicon-germanium affects the phonon MFP but not the group velocity.Based on Matthiessen's rule, the phonon MFPs of amorphous silicon-germanium thin films attributed to alloy and disorder scattering were calculated to be 1.0 nm for both.Therefore, alloy and disorder scattering contributed equally to the decrease in the phonon MFP.The insights gained from these findings could prove pivotal to the development of alloy materials with extremely low thermal conductivities.011005-4 © 2024 The Author(s).Published on behalf of The Japan Society of Applied Physics by IOP Publishing Ltd

Table I .
Thermal conductivity of the amorphous silicon-germanium thin film in this work and that of previously reported silicon-germanium thin films with different structures.