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Tianzhuo Zhan, Chong Zheng, Mao Xu, Zhi Cao, [Yen-Ju Wu](https://orcid.org/0000-0003-2647-3407), [Yibin Xu](https://orcid.org/0000-0001-8600-8748), Ryo Yokogawa, Atsushi Ogura, [Yanming Xue](https://orcid.org/0000-0003-1061-229X), Haidong Wang, Mengjie Song, Wei Wang, Bo Chen, Takanobu Watanabe, Yonggang Jiang, Huawei Chen, Deyuan Zhang

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This document is the Accepted Manuscript version of a Published Work that appeared in final form in ACS Applied Electronic Materials, copyright © 2025 American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://doi.org/10.1021/acsaelm.5c01142.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Thermal Conductivity and Thermal Boundary Resistance of Low–Dielectric Constant Interlayer Dielectrics in Advanced Very Large Scale Integration Interconnects](https://mdr.nims.go.jp/datasets/911f88ea-5175-489d-848b-82c58f6647f8)

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21 Thermal Conductivity and Thermal Boundary Resistance of Low-k Interlayer Dielectrics in Advanced VLSI InterconnectsTianzhuo Zhan1, a, *, Chong Zheng2, a, Mao Xu3, a, Zhi Cao2, Yen-Ju Wu4, Yibin Xu4, Yanming Xue5, *, Haidong Wang6, Mengjie Song7, *, Wei Wang7, Bo Chen8,9, Takanobu Watanabe21School of Mechanical Engineering and Automation, Beihang University, 37 Xueyuan Road, Haidian, Beijing 100191, China2Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan3Department of Basic Science, The University of Tokyo, 3-8-1 komaba, Meguro-ku, Tokyo 153-8902, Japan4National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan5School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, China6School of Aerospace Engineering, Tsinghua University, 30 Shuangqing Road, Haidian, Beijing 100084, China7School of Mechanical Engineering, Beijing Institute of Technology, 5 South Street, Zhongguancun, Haidian, Beijing 100081, China8Aerospace Information Research Institute, Chinese Academy of Science, Beijing 100190, China9University of Chinese Academy of Sciences, Beijing 100049, ChinaAbstract Low-dielectric-constant (low-k) interlayer dielectrics (ILD) are necessary to reduce signal propagation delay and electronic crosstalk in advanced very-large-scale integration (VLSI) circuits. Thermal conductivity of low-k ILDs significantly influences the temperature rise of VLSI interconnects, and therefore the performance and reliability of VLSI circuits. Furthermore, as the technology node is scaled, thermal boundary resistance (TBR) between wires and low-k ILDs becomes increasingly critical for the thermal management of VLSI interconnects. In this study, we experimentally investigated the thermal conductivity and TBR of methylpolysiloxane low-k ILDs. The results show that a 5% increase in methyl content has a minimal effect on the thermal conductivity but significantly increases the TBR. Whereas the cure process enhances the thermal conductivity as well as TBR. Persistent homology (PH) analysis was performed on the transmission electron microscopy (TEM) images of low-k ILDs to extract hidden structural features to quantify the medium-range order, which further elucidates the mechanisms underlying the modification of the thermal conductivity. The enhanced thermal conductivity after the cure process can be attributed to both enhanced phonon group velocity and enhanced effective MFPs of delocalized vibration modes owing to the densification of the films. Fourier transform infrared (FTIR) spectra revealed that variations in TBR are primarily attributed to the modifications of the hydrophilic and hydrophobic functional groups. Increased hydrophobic methyl groups or decreased hydrophilic hydroxyl and silanol groups within the low-k ILDs leads to reduced interfacial bonding between the low-k ILD and its adjacent layers, thereby enhancing the TBR. Contact angle measurements demonstrated the linear relationship between the interfacial bonding strength and TBR. Our findings offer new insights into understanding thermal transport within low-k ILDs and at interfaces, which are essential for the development of next-generation thermally conductive low-k ILDs and composite thermal interface materials for thermal management in VLSI circuits.Keywords: Thermal conductivity; thermal boundary resistance; low-k dielectrics; VLSI interconnects; persistent homology. 1. IntroductionThe ever-increasing demand for high computing performance, driven by the expansion of cloud computing, Internet of Things (IoT), and artificial intelligence, spurs a significant scaling of the technology node in advanced VLSI circuits such as CPUs and GPUs. The reduction in gate length makes the transistors faster and more power efficient. On the other hand, the accompanying scaling of the interconnects, which are used for connecting transistors for power distribution and signal transmission, may lead to deterioration of the performance. In other words, the performance benefits achieved at the front-end-of-line processes will be offset if back-end-of-line processes fail to keep pace. According to the International Roadmap for Devices and Systems (IRDS) [1], the half-pitch of local interconnects, will be reduced to sub-10 nm as the technology node is scaled to 2 nm and beyond. The half-pitch of intermediate and global interconnects will also experience significant reduction with scaling. The reduction in half-pitch implies the interconnect wires have decreased cross-sectional area and wire spacing. The decreased wire cross-sectional area increases the wire resistance, and the reduced wire spacing increases the capacitance, leading to an increase in signal propagation delay, commonly referred to as resistance-capacitance delay (RC delay). [2,3] The RC delay issues exacerbate challenges in advancing speed in VLSI circuits. For instance, transitioning from the 10 nm to the 7 nm technology node is estimated to incur a delay increase of over 30%. Furthermore, charge build up and electronic crosstalk are also critical issues as the wires get closer.[4] Therefore, addressing these problems in interconnects is paramount for improving the overall device performance in future technology nodes. The RC delay can be mitigated by employing an interconnect metal with lower resistivity, such as Cu, thereby reducing resistance.[5] Ruthenium (Ru), with its much shorter electron mean free paths (MFP), is expected to exhibit lower wire resistance than the mainstream Cu interconnects at dimensions below 10 nm, making it a promising candidate to further solve the RC bottleneck for the 2 nm node and beyond. [6,7] Additionally, the RC delay can be reduced by substituting conventional SiO2 ILDs to low-k materials, consequently lowering capacitance. Utilizing low-k ILDs also lowers power consumption and reduces electronic crosstalk.[8] Various materials, including silicates, organosilicates, and porous organosilicates possessing lower relative dielectric constants than SiO2, have been employed as ILDs in VLSI interconnects. These low-k materials are typically deposited by chemical vapor deposition (CVD). Spin-on glass (SOG) polymeric dielectric, such as hydrogen silsesquioxane and methylsilsesquioxane, are also commonly used low-k materials.[9] The current flow through transistor channels and interconnects produces Joule heat as a byproduct, which is known as the self-heating effect (SHE). Even though SHE in interconnects is not a major portion of the total chip power dissipation, the SHE will induce a significant temperature rise in interconnects due to the very low thermal conductivity of low-k ILDs and very high current density induced by the aggressive scaling. Therefore, thermal management of interconnects has emerged as one of the most pivotal factors determining the performance and reliability of deeply scaled VLSI circuits. [10] Figure 1 illustrates the schematic of SHE and heat dissipation path in the multilevel Cu/low-k interconnects used in advanced VLSI circuits, the overall thermal resistance of which mainly comprises the intrinsic thermal resistance of the low-k ILDs (RILD) and thermal boundary resistance (TBR) between the wire and the low-k ILDs (TBRW/ILD). Unfortunately, these two thermal properties, which are essential for rigorous electrothermal simulations of VLSI circuits, are not available in IRDS. Furthermore, in conventional electrothermal analysis of multilevel interconnects, only the effects of RILD were considered, while the effects of TBRW/ILD, have been disregarded. [11] In nanostructures, however, thermal transport exhibits a ballistic or quasi-ballistic nature rather than diffusive behavior. [12-17] As a result, interfaces can present greater hindrance to heat flow than the intrinsic thermal resistance of the constituent materials as the dimension is deeply scaled. Therefore, investigating the effects of TBR on the temperature rise of interconnects in advanced VLSI circuits is of paramount importance.In our previous studies, we experimentally investigated the effects of TBR of the mainstream Cu interconnect [18] and the next generation Ru interconnect [19] on the temperature rise of deeply scaled VLSI circuits. However, the ILDs used in these studies was SiO2. In advanced VLSI interconnects, carbon is incorporated into SiO2 to reduce the dielectric constant of the ILDs, thereby reducing the RC delay. The dopant is believed to exert a significant impact on the TBR between wires and ILDs, which in turn significantly affects the temperature rise in interconnects.In this study, we experimentally investigated the thermal conductivity and TBR of low-k ILDs in advanced VLSI interconnects. We prepared Cu/Ta/TaN/low-k ILDs film stacks to simulate the mainstream Cu interconnect structures used in advanced VLSI circuits. Low-k ILDs were constructed using SOG methylsiloxane polymers with varying methyl group contents. The thermal conductivity of the SOG films and TBR  were measured using the FDTR technique. Transmission electron microscope (TEM) equipped with energy-dispersive X-ray spectroscopy (EDS) was used to characterize the microstructure and elemental mapping of the film stacks. Frequency domain thermoreflectance (FDTR) was employed to analyze the modifications of functional groups in the SOG films. The contact angles of water on the surface of SOG films were measured to evaluate hydrophobic and hydrophilic surface properties, which significantly influences the interfacial bonding. Characterization of the structural features of amorphous solids is difficult owing to the lack of long-range order (LRO), which makes building structure-property relationships challenging. Despite the absence of LRO, amorphous solids can exhibit medium-range order (MRO) at various length scales (1–20 Å), which is closely related to the delocalized vibrational modes that contribute to thermal transport. [20,21] Conventional experimental and simulation methods cannot provide a complete description of MRO. Recently, topological data analysis (TDA) has provided tools in the analysis of complex datasets in material science field, offering unique insights that conventional methods often overlook. Persistent homology (PH), a key technique in TDA, captures and tracks the persistence of topological features of various dimensions, such as connected components, holes, rings, and voids at multiple scales. Therefore, PH analysis can provide a description of MRO in amorphous solids by capturing topological features. Using molecular dynamics simulation dataset, PH has been used for characterizing the MRO structural features of amorphous solids [22-24]. In this paper, we perform PH analysis on TEM images of SOG films to extract hidden structural features to quantify the difference in MRO, which further elucidates the mechanisms underlying the modification of the thermal conductivity of different low-k SOG films. 2. Experimental and simulation2.1. Sample Preparation. Low-k dielectric films were coated on a silicon substrate using a spin coater (MS-A200, MIKASA Inc.). Prior to spin coating, the Si substrates were cleaned using acetone in an ultrasonic bath. Two types of commercially available methylsiloxane SOG low-k materials, (Series No. T-111 and T-512B, Honeywell ACCUGLASS®) were utilized. These SOG materials are widely employed for ILD planarization and gap filling in VLSI circuits. Material properties of the two types of low-k materials are presented in Table 1. T-512B and T-111 contain 15 wt% and 10 wt% methyl groups, respectively. T-512B exhibits a lower dielectric constant due to its higher methyl content than T-111, because Si–CH3 bonds have a lower polarizability than Si-O bonds. The molecular structure of the methylsiloxane low-k materials is schematically presented in Fig. 2(a). Terminal methyl groups (-CH3) and hydroxyl groups (-OH) are bonded to Si atoms in the Si-O-Si backbone. Table 1 Material properties of the two types of low-k materials. Series No. Metryl content Dielectric constant Viscosity (cP) Coefficient of Thermal Expansion(×10-6K-1) T-512B 15 wt% 3.1  2.15 5 T-111 10 wt% 3.8 1.43 5To measure the thermal conductivity and TBR of SOG films using the FDTR method, SOG films with three different thickness are required. Spin speeds were adjusted to vary the thickness of the SOG films. Following a 20 sec spin coating, the films were baked at 150 ℃ for 1 min to evaporate solvents and solidify the films. The baked films were then cured at 425 ℃ for 1 h in a nitrogen atmosphere for densification. The curing temperature was limited to 425 ℃ because methylsiloxanes begin to lose methyl groups above 450 °C.[25] For the deposition of Au/Cu/Ta/TaN film stacks onto the spin coated SOG films, magnetron sputtering was employed. The Cu/Ta/TaN film stacks were deposited on SOG films to simulate the commonly used interconnect structures in advanced VLSI circuits. The schematic of Au/Cu/Ta/TaN/low-k ILD film stacks is shown in Fig. 2(b). Cu and methylsiloxane served as the metal wire and low-k ILD, respectively. TaN acted as the barrier layer to prevent Cu diffusion into the low-k ILD, and it was deposited using reactive sputtering with a Ta target and an Ar/N2 mixing atmosphere with a flux ratio of 16:4. The total flow of the Ar/N2 mixing gas was 20 sccm. Ta was used as the liner layer to enhance the adhesion between Cu and TaN layer. Au was employed as the transducer layer in the ω method. The thicknesses of the Au, Cu, Ta, and TaN layers were 100, 10, 10, and 10 nm, respectively. All films were deposited at a substrate temperature of 25 °C using a sputtering power of 300 W. The base pressure of the sputtering chamber was 1×10-5 Pa for all depositions. 2.2. TBR Measurement. The illustration of measurement system and the details for the FDTR method can be found elsewhere. [26,27] A thermoelectric cooling system maintained the sample stage temperature at 25 °C. The vacuum chamber was evacuated to a pressure of ~0.1 Pa. A pump laser heated the sample, while a probe laser measured the surface temperature of the Au sensing film through the temperature dependence of the reflectivity. The pump and probe laser beams were coaxially focused on the film stack surface using an objective lens. The pump laser, a multimode diode laser with a 405 nm wavelength and an output power of 360 mW, was modulated at different frequencies ω (1, 2, 4, and 8 kHz) by a transistor-transistor logic (TTL) signal from the function generator in a DSP lock-in amplifier (Stanford SR830). The probe laser, a single-mode diode laser with a 635 nm wavelength and 5 mW output power, was used for temperature measurements. Given the pump laser's larger beam size compared to the probe laser and the thermal diffusion length, one-dimensional heat conduction in the normal-to-plane direction was assumed. Measurements were conducted at three different locations on each sample, with each measurement repeated three times for error reduction. Measurement uncertainties were estimated from the standard deviations of the intercepts in the straight-line fits.For an Au/target film/substrate three-layer sample system, the in-phase surface temperature of the Au transducer T(0) can be expressed as a function of the properties of the films and the substrate as [26]T(0)qd0=e−iπ42λ2C2ω−12+1−λ0C0λ2C2d0λ0+1−λ1C1λ2C2dTλT+R  (1)where q is the heat flux, d is the thickness, λ is the thermal conductivity, C is the volumetric heat capacity. The subscripts 0, 1, and 2 denote the Au transducer, target film, and substrate, respectively. R is the sum of the TBR at the Au/target film and target film/substrate interfaces. As ω is varied from 1 to 8 KHz, a plot of T(0)/(qd0) versus ω-1/2 gives a straight line, the intercept Ri is the sum of the second to the fourth terms of the right side of the equation. If we change the thickness of the target film d and plot Ri as a function of d, a linear relationship between Ri and d is expected. The thermal conductivity of the target film can be calculated from the slop of the straight line, and R equals the intercept. In this study, the thickness of Cu, Ta, and TaN layers is only 10 nm, the Au/Cu/Ta/TaN film stacks was treated as a single layer. Thus, R gives the total TBR at TaN/SOG and SOG/Si interfaces.2.3. Characterization. A high-resolution TEM equipped with an EDS spectrometer was employed to image the cross-sectional microstructures and elemental mapping. An ellipsometer was employed to measure the thicknesses of the SOG films. X-ray reflectometry (XRR) was utilized to determine the density of the SOG films. FTIR spectra were acquired in the attenuated total reflectance (ATR) mode using a Thermo Fisher Scientific Nicolet iS50 analyzer. The background spectrum of each silicon substrate was measured before the film deposition. The contact angle measurements were performed under ambient air at room temperature, employing a measuring system (B100, ASUMIGIKEN, Limited, Tokyo, Japan). A distilled ultrapure water drop with a volume of 1 microliter was deposited on the surfaces of SOG films. A real-time CMOS video camera was utilized to visualize the droplet for contact angle calculation. All measurements were repeated three times and averaged for accuracy. 2.4. PH Analysis. Before PH analysis, the TEM images were preprocessed to ensure clarity and noise reduction. Specifically, we first select a subset of each image, consisting of 10×10 nm area of each sample. A gaussian denoising filter is then applied to reduce noise in these subsets. From the processed images, we generate the connected components by computing the sub-level set with a threshold value of 5. Each connected component is represented by a single point, which results in a point cloud dataset representing the microstructure of the materials.Next, we construct alpha complex to the data and compute one-dimensional PH using Homcloud software [24]. Alpha complexes are a type of scaled simplicial complex providing a multiscale representation of the point cloud. One-dimensional PH captures the number and shape of rings (holes) across different scales. The persistence of these features is recorded, resulting in persistence diagrams (PDs) that visually summarize the birth and death of each ring. In a PD, each ring is represented as a point in a two-dimensional plane, where the x-coordinate indicates the "birth" of the ring (the scale at which it appears) and the y-coordinate indicates the "death" of the ring (the scale at which it disappears). Rings that persist over a wide range of scales (i.e., those far from the diagonal of the PD) are considered significant, while those that appear and disappear quickly are considered noise. The structural properties among the TEM images are quantitatively given by further computations of the average persistence of each PD. 3. Results and discussionThe cross-sectional high-resolution TEM images for T-111 and T-512B film stacks were shown in Fig. 2(c) and (d), respectively. The T-512B SOG film has a much larger thickness than the T-111 SOG film. The corresponding EDS elemental mappings of Cu, Ta, O, and Si elements for T-111 and T-512B film stacks were presented in Fig. 2(e) and (f), respectively. From the EDS elemental mapping images, it is observed that Cu diffused into the Au layer but not the SOG layer, owing to the barrier function of the TaN layer.  Figure 4(a) and (b) show the Ri of the Au/Cu/Ta/TaN/SOG/Si film stacks as a function of thickness of the SOG film for T-512B and T-111 samples, respectively. The thicknesses of the SOG films, coated using spin speeds of 2000, 3500, and 5000 rpm, are listed in Table 2. T-512B SOG films exhibit a much larger thickness than their T-111 counterparts due to the higher viscosity of the SOG liquid. The thickness of SOG films measured by the ellipsometer is in good agreement with that depicted in the TEM images in Fig. 2(c) and (d). Furthermore, minor shrinkage in thickness for all SOG films was observed after the cure process. As presented in Table 2, the mass densities of the as baked T-512B and T-111 SOG films measured by XRR were 1.45 and 1.5 g/cm3, respectively, which increased to 1.6 and 1.7 g/cm3 respectively, after the cure process. In comparison with fully dense amorphous SiO2 (~2.2 g/cm3), the Si-O-Si backbone is interrupted by the methyl functional groups, resulting in a less dense matrix and lowered connectivity, and therefore a mass density deficit.[28] The observed shrinkage in thickness and increase in density of SOG films indicate densification of SOG films occurred after the cure process.[29]  The thermal conductivities of all the SOG films were calculated from the slopes of the straight lines fitting the three Ri data points, as depicted in Fig. 4(a) and (b). The thermal conductivities of the as-baked T-512B and T-111 SOG films were 0.333±0.002 and 0.334±0.004 W/mK, respectively. The obtained density and thermal conductivity results are close to the values reported in the literature.[28,30] Despite a 5% difference in methyl content, the difference in the thermal conductivity was marginal. After the cure process, the thermal conductivities of the T-512B and T-111 SOG films increased significantly to 0.458±0.003 and 0.469±0.01 W/mK, respectively, as illustrated in Fig. 4(c). The results show that the SOG films exhibit similar thermal conductivity irrespective of the methyl content, both before and after the cure process. This indicates that the thermal conductivity of the SOG films primarily depends on the Si-O-Si backbone, with minimal influence from the terminal -CH3 groups. This should be attributed to the nonpolar nature of -CH3 groups, which cannot form hydrogen bonds with neighboring chains to facilitate thermal transport. This observation is similar with the behavior of thermal transport in  polymers, where intrachain axial conduction via covalent bonds dominates, while interchain van der Waals conduction is marginal. [31,32] In crystalline materials, according to the classical kinetic theory, the thermal conductivity of a solid is described as λ=j13Cjvjlj, where j is the polarization (one longitudinal and two transverse), C is the volumetric heat capacity, v is the phonon group velocity, and l is the phonon mean free path (MFP). While in amorphous materials, the definition of phonons is questionable due to the lack of periodicity, vibration modes can be classified into three types: propagons, diffusons, and locons, corresponding to the delocalized propagating, delocalized diffusive, and localized modes, respectively. [33,34] Phonon-like propagons with long effective MPFs are known to contribute significantly to the thermal conductivity of amorphous Si and amorphous Ge. [35-38] By comparison, thermal conductivity of amorphous SiO2 is primarily contributed by non-propagating diffusons with short effective MFPs.[39] We next discuss potential mechanisms underlying the enhancement of thermal conductivity of the SOG films induced by the cure process. The observed differences in thermal conductivity among samples should be caused by the differences in one or more of three parameters C, v, and l. During the cure process, the cross-linking reactions can occur by the following reactions [28], Si−OH+Si−OH→Si−O−Si+H2Owhich can be confirmed by the loss of -OH groups and increase of the Si–O–Si band area in the FTIR spectra shown later. The cross-linking density improvement will induce an increase of the elastic modulus. For example, Iacopi et al. have found that a ~45% increase in elastic modulus was achieved in organosilicate glasses after an ultraviolet-assisted cure process. Since the velocity of sound is directly proportional to the square root of the elastic modulus, a ~45% increase in elastic modulus will lead to a ~20% increase in velocity of sound. However, the increase in thermal conductivity was only ~6%. [28] Therefore, in this study, the enhancement in phonon group velocity due to the cross-linking density improvement should not be the only factor causing the ~40% enhancement in thermal conductivity. Typically, a density deficit is expected to result in corresponding decrease in the volumetric heat capacity. However, Ju et al. have found that the volumetric heat capacities of the SiO2 films deposited by LPCVD decrease after annealing, a trend opposite to what is observed for the thermal conductivity. This is attributed to the loss of water and Si-OH groups with a much larger volumetric heat capacity than SiO2.[39] Therefore, the volumetric heat capacities of the SOG films in this study should decrease after the cure process due to the loss of water and Si-OH groups, as demonstrated in the FTIR spectra shown later. The above discussions indicate that the ~40% enhancement in thermal conductivity cannot be explained by considering the small enhancement of phonon group velocity and the opposite effects of the decreased volumetric heat capacity. Therefore, the variation in the third factor, namely effective MPFs of heat carriers, should be the primary factor for the enhanced thermal conductivity. One-dimensional PH analysis of high-resolution TEM images was performed to extract hidden structural features with respect to MRO in SOG films. Fig.3(a) shows a conceptual illustration of PH analysis. Starting with a point cloud, one-dimensional PH analyzes the formation (birth) and vanishing (death) of rings, as a radius parameter grows. The lifetimes of these rings are visualized using a PD, where their birth and death times are recorded. Fig.3(b)-(d) show one-dimensional PDs of T-111, T-512B, and cured T-512B SOG films, consisting of 1152, 945, and 936 generators (rings), respectively. Each point of the PDs corresponds to a one-dimensional generator of the PH of each structure. One-dimensional generators represent the information about one-dimensional holes in the spaces, including not only the existence of the corresponding holes, but also the “size” of the holes. Given a persistent diagram X consisting of points x1,x2,…,xn, we define the average persistence of the X as the average of the persistence of each generator, denoted as AVR(X), which can be expressed as follows.AVRX≔idi−biXwhere di,bi denote the death time and birth time of xi, and X denotes the number of points of X. We calculate the average persistence of the points whose persistence time larger than 3 to eliminate noise for each PD. The AVR(X) for T-111, T-512B, and cured T-512B samples are 5.58, 5.57, and 6.50, respectively. The results show that the structural difference between T-111 and T-512B is minimal, indicating a ~5% difference in -CH3 groups have minimal effect on the MRO structural features, and therefore almost the same thermal conductivity. In comparison, the structural difference between T-512B and cured T-512B is significant, resulting in a large difference in MRO structural features, and therefore the large different thermal conductivity of two SOG films. The trend found in the PH analysis coincides with the experimental results.Table 2 Thicknesses, densities, thermal conductivities, and total TBRs of the as-baked and cured T-512B and T-111 SOG films. SOG film Thickness (nm)/2000, 3500, 5000 rpm Density (g/cm3)/5000 rpm λ (W/mK) TBR (m2K/GW) T-512B (as-baked) 693, 535, 440 1.45 0.333±0.016 53.4±5.4 T-512B (cured) 680, 515, 437 1.6 0.458±0.012 77.3±6.4 T-111 (as-baked) 166, 124, 103 1.5 0.334±0.039 46.1±5 T-111 (cured) 156, 114, 94 1.7 0.469±0.049 61.6±5.9The total TBRs at the TaN/SOG and SOG/Si interfaces for all the SOG films were calculated by extrapolating the total thermal resistance to zero SOG film thickness, namely the intercepts of the straight lines. As shown in Fig.4(d), the total TBR of T-512B samples is higher than that of T-111 counterparts. Interfacial bonding has been shown to significantly affect thermal transport at interfaces. [40-44] Therefore, the differing TBR should be attributed to the difference in methyl content in the two types of SOG films. Methyl groups are nonpolar molecules because each C-H covalent bond equally attracts electrons from the center. Methyl groups are hydrophobic because they cannot form hydrogen bonds with polar compounds such as water. Therefore, interfaces with hydrophobic methyl groups typically exhibit lower interfacial adhesion energy than interfaces with polarized hydrophilic groups such as hydroxyl or carbonyl groups, resulting in a higher TBR.[45-49] Hence, the higher methyl content in T-512B SOG film leads to lower bonding strength of TaN/SOG and SOG/Si interfaces, resulting in a higher TBR than T-111 sample. It is known that in addition to interfacial bonding strength, interfacial disorder also affects TBR.[50] Fig. 5(a)-(d) show the high-resolution cross-sectional TEM images of TaN/SOG and SOG/Si interfaces for T-512B samples before and after the cure process. No evident difference in interface disorder between the as-baked and cured samples can be observed. Therefore, the difference in TBR should be attributed to the change in functional groups in the SOG films induced by the cure process. The change in functional groups in SOG will affect the adhesion strength at the TaN/SOG and SOG/Si interfaces, resulting in the increased TBR. FTIR was employed to characterize the chemical modifications in SOG films induced by the cure process to understand the mechanisms. The FTIR spectra of the as-baked and cured T-512B SOG films coated using a spin speed of 3500 rpm are shown in Fig. 6(a) and (b). The absorption peak around 1275 cm–1 is ascribed to the stretching vibration of the C–H bonds in Si–CH3. [51,52] No remarkable change in the intensity of these peaks is observed, indicating that the methyl groups were not removed at 425 ℃ in the cure process. The as-baked T-512B film exhibits a broad absorption peak around 3400 cm–1, attributed to the stretching vibration of -OH groups, which are physically adsorbed on the film surface. [53] The absorption peaks around 900 cm−1 are ascribed to silanol groups (Si-OH).[54] These absorption peaks completely disappear after the cure process, indicating the removal of -OH groups by the cure process. OH groups are polarized hydrophilic groups, which can promote its adhesion to other surfaces such as SiO2, etc.[55] Thus, the loss of hydrophilic -OH groups decreases the interfacial adhesion energy, leading to an increase in TBR after the cure process. The absorption peak at 1105 cm–1 is attributed to the large angle Si-O-Si bonds in a cage structure, while the absorption peak at 1043 cm–1 is attributed to the small angle Si-O-Si bonds in a network structure.[28] A decrease in the peak intensity of the large angle Si-O-Si bonds and an increase in the peak intensity of the small angle Si-O-Si bonds are clearly observed after the cure process. The structural rearrangement in the Si–O–Si backbone leads to an increase in network connectivity. The larger fraction of stable small angle bonding configuration is expected to form a higher rigid network, which is favorable for phonon transport.[28] Furthermore, increase of the Si–O–Si band area can be observed, which is attributed to the the cross-linking reactions between Si-OH groups, resulting in decreased volumetric heat capacity. Therefore, the enhanced thermal conductivity after the curing process should be attributed to the enhanced phonon group velocity as well as enhanced effective MFPs of delocalized vibration modes induced by the improvement of Si–O–Si backbone network rigidity.The contact angle can be correlated with the work of adhesion, representing the minimum work required to separate water from the film surface. In other words, the contact angle can offer a metric for assessing the bonding strength at the interface. [45] We conducted contact angle measurements of water on the surfaces of as-baked and cured T-111 and T-512B films. The contact angle of water on a thermally grown SiO2 surface was also measured for comparison as a reference. The contact angles of water on the surfaces of thermally grown SiO2, as-baked T-111, and as-baked T-512B films are 63.9±2°, 81.1±2°, and 88.1±2°, respectively, with a higher methyl content in the film corresponding to a larger contact angle. The increase in contact angle can be attributed to the increase of methyl groups with hydrophobic nature. Furthermore, the contact angles of water on the surfaces of cured T-111 and T-512B films increase to 91.1±2° and 97.2±2°, respectively, which are larger than their as-baked counterparts. This can be attributed to the removal of hydrophilic hydroxyl and silanol groups by the curing process. Contact angle images for all the samples are presented in Fig. 7(a). According to Young’s equation, the work of adhesion is proportional to (1+cosθ), with the air-water surface tension serving as the proportionality coefficient, where θ denotes the contact angle.[45] Hence, a larger contact angle corresponds to a smaller work of adhesion. Fig. 7(b) depicts the TBR of all the SOG samples as a function of (1+cosθ), indicating a linear relationship between TBR and the work of adhesion at the interface. The results demonstrate that TBR is proportional to the interfacial bonding strength, despite the simultaneous effects of interfacial disorder on the TBR.4. ConclusionsWe performed an experimental work on the thermal conductivity and TBR of low-k ILDs.. We prepared Cu/Ta/TaN/low-k ILDs film stacks on Si substrates to simulate the mainstream Cu interconnect structures wildly used in advanced VLSI circuits. Low-k ILDs were constructed using two types of commercially available methylpolysiloxane SOG films containing 15 wt% and 10 wt% methyl groups, respectively. The cure process was performed to densify the SOG films after baking. The results show that the SOG films exhibit similar thermal conductivity irrespective of the methyl content, both before and after the cure process, indicating that the thermal conductivity of the SOG films primarily depends on the Si-O-Si backbone, with marginal influence from the terminal methyl groups. The thermal conductivity of the SOG films increased significantly after the cure process, which can be attributed to the enhanced phonon group velocity as well as enhanced effective MFPs of delocalized vibration modes induced by the densification of the films. Furthermore, PH analysis of high-resolution TEM images was performed to extract hidden structural features with respect to MRO in the SOG films. The results show that a ~5% difference in methyl groups have no effect on the MRO structural features, resulting in almost the same thermal conductivity. In comparison, the structural difference with respect to MRO between T-512B and cured T-512B is significant, resulting in the significantly different thermal conductivity. Both increased methyl content and the cure process enhance the total TBRs of the SOG films. FTIR analyses revealed that an increase in hydrophobic methyl groups and a decrease in hydrophilic hydroxyl and silanol groups within the SOG films result in reduced interfacial bonding strength between the SOG film and its adjacent layers, thereby enhancing the TBR. Contact angle measurements demonstrate the linear relationship between the interfacial bonding strength and TBR. Our findings offer new insights into understanding thermal transport within low-k ILDs and at interfaces, which are essential for the development of next-generation thermally conductive low-k ILDs and composite thermal interface materials for thermal management in VLSI circuits.AcknowledgementThis work was supported by a grant from a Grant-in-Aid for Scientific Research (C) (21K04886) from the Japan Society for the Promotion of Science (JSPS). We gratefully thank Kagami Memorial Research Institute for Materials Science and Technology in Waseda University for the support of TEM-EDS characterization.■ AUTHOR INFORMATION Corresponding AuthorsTianzhuo Zhan - School of Mechanical Engineering and Automation, Beihang University, 37 Xueyuan Road, Haidian, Beijing 100191, ChinaEmail:zhantianzhuo@buaa.edu.cn Yanming Xue - School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, ChinaEmail:ym.xue@hebut.edu.cn  Mengjie Song - School of Mechanical Engineering, Beijing Institute of Technology, 5 South Street, Zhongguancun, Haidian, Beijing 100081, China Email:mengjie.song@bit.edu.cn Authors Chong Zheng - Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan Mao Xu - Department of Basic Science, The University of Tokyo, 3-8-1 komaba, Meguro-ku, Tokyo 153-8902, Japan Zhi Cao - Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan Yen-Ju Wu - National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan Yibin Xu - National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan Haidong Wang - School of Aerospace Engineering, Tsinghua University, 30 Shuangqing Road, Haidian, Beijing 100084, China Wei Wang - School of Mechanical Engineering, Beijing Institute of Technology, 5 South Street, Zhongguancun, Haidian, Beijing 100081, China Bo Chen - Aerospace Information Research Institute, Chinese Academy of Science, Beijing 100190, China；University of Chinese Academy of Sciences, Beijing 100049, China Takanobu Watanabe - Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan Author contributionsT.Z.:conceptualization, funding acquisition, project administration, supervision, data curation, formal analysis, investigation, validation, visualization, writing−original draft. writing−review and editing. 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Sci. 253, 4220-4225 (2007).Fig. 1 Schematic of multilevel Cu/low-k interconnects used in advanced VLSI circuits. The overall thermal resistance mainly comprises the intrinsic thermal resistance of the low-k ILDs (RILD) and TBR between the interconnect wire and the low-k ILDs (TBRW/ILD).Fig. 2. (a) Schematic molecular structure of methylsiloxane SOG low-k materials. Terminal methyl (denoted as R) and hydroxyl (-OH) groups are bonded to Si atoms in the Si-O-Si backbone. (b) Schematic of Au/Cu/Ta/TaN/SOG/Si film stacks to simulate the mainstream Cu interconnect structures used in advanced VLSI circuits. Au film is used as a temperature sensor in the FDTR measurement. Cross-sectional high-resolution TEM images for T-111 (c) and T-512B (d) film stacks. Corresponding EDS elemental mapping images of Cu, Ta, O, and Si elements (from top to bottom) for T-111 (e) and T-512B (f) film stacks.Fig. 3 (a) A conceptual illustration of PH. Starting with a point cloud, one-dimensional PH analyzes the formation (birth) and vanishing (death) of rings, as a radius parameter grows. The lifetimes of these rings are visualized using a PD, where their birth and death times are recorded. (b) One-dimensional PD of T-111 (c) One-dimensional PD of T-512B (d) One-dimensional PD of cured T-512BFig. 4. Ri of the Au/Cu/Ta/TaN/SOG/Si film stacks (as-baked and cured) as a function of the thickness of SOG film for T-111 (a) and T-512B (b) samples. Thermal conductivity (c) and total TBR at the TaN/SOG and SOG/Si interfaces for all the SOG samples calculated from the slopes and intercepts of the straight lines fitting the three Ri data points, respectively. Fig. 5 High-resolution cross-sectional TEM images of TaN/SOG and SOG/Si interfaces for T-512B samples before and after the cure process. Smoother and less disordered interfaces can be observed in the samples after the cure process.Fig. 6 FTIR spectra of the as-baked and cured T-512B SOG films. No remarkable change in the intensity of the peaks around 1275 cm–1 is observed before and after the cure process, indicating that the -CH3 groups were not removed at 425 ℃. While absorption peaks around 3400 cm–1 and 900 cm–1 disappear after the cure process, indicating the removal of -OH and Si-OH groups.Fig. 7 (a) Contact angle values and images of water on the surfaces of thermally grown SiO2, as-baked T-111, as-baked T-512B, cured T-111, and cured T-512B films. The contact angle increases with increasing methyl content and loss of hydroxyl and silanol groups induced by the cure process. (b) TBR for all the SOG samples plotted as a function of (1+cosθ), which is proportional to the work of adhesion at the interface. aEqual contributionsimage3.jpegimage4.tiffimage5.tiffimage6.tiffimage7.tiffimage1.jpegimage2.tiff