Interface thermal conductance of van der Waals monolayers on amorphous substrates

Nonequilibrium Phonon Thermal Resistance at MoS2/Oxide and Graphene/Oxide Interfaces

Accurate measurements and physical understanding of thermal boundary resistance (R) of two-dimensional (2D) materials are imperative for effective thermal management of 2D electronics and photonics. In previous studies, heat dissipation from 2D material devices was presumed to be dominated by phonon transport across the interfaces. In this study, we find that, in addition to phonon transport, thermal resistance between nonequilibrium phonons in the 2D materials could play a critical role too when the 2D material devices are internally self-heated, either optically or electrically. We accurately measure the R of oxide/MoS₂/oxide and oxide/graphene/oxide interfaces for three oxides (SiO₂, HfO₂, and Al₂O₃) by differential time-domain thermoreflectance (TDTR). Our measurements of R across these interfaces with external heating are 2-4 times lower than the previously reported R of the similar interfaces measured by Raman thermometry with internal self-heating. Using a simple model, we show that the observed discrepancy can be explained by an additional internal thermal resistance (R_int) between nonequilibrium phonons present during Raman measurements. We subsequently estimate that, for MoS₂ and graphene, R_int ≈ 31 and 22 m² K GW^-1, respectively. The values are comparable to the thermal resistance due to finite phonon transmission across interfaces of 2D materials and thus cannot be ignored in the design of 2D material devices. Moreover, the nonequilibrium phonons also lead to a different temperature dependence than that by phonon transport. As such, our work provides important insights into physical understanding of heat dissipation in 2D material devices.

Thermal boundary conductance of monolayer beyond-graphene two-dimensional materials on SiO2and GaN

Two-dimensional (2D) materials have emerged as a platform for a broad array of future nanoelectronic devices. Here we use first-principles calculations and phonon interface transport modeling to calculate the temperature-dependent thermal boundary conductance (TBC) in single layers of beyond-graphene 2D materials silicene, hBN, boron arsenide (BAs), and blue and black phosphorene (BP) on amorphous SiO₂and crystalline GaN substrates. Our results show that for 2D/3D systems, the room temperature TBC can span a wide range from  7 to 70 MW m^-2K^-1 with the lowest being for BP and highest for hBN. We also show that 2D/3D TBC has a strong temperature dependence that can be alleviated by encapsulating the 2D/3D stack. Upon encapsulation with AlO_x, the TBC of several beyond-graphene 2D materials can match or exceed reported values for graphene and numerous transition-metal dichalcogendies which are in the range of 15-40 MW m^-2K^-1. We also compute the room temperature TBC as a function of van der Waals spring coupling (K_a) where the TBC falls in the range of 50-150 MW m^-2K^-1 at coupling strengths ofK_a = 2-4 N m^-1 for silicene, BAs, and blue phosphorene. We further identify group III-V materials with ultra-soft flexural branches as being promising 2D materials for thermal isolation and energy scavenging applications when matched with crystalline substrates.

Thermal interface materials with graphene fillers: review of the state of the art and outlook for future applications

We review the current state-of-the-art graphene-enhanced thermal interface materials for the management of heat in the next generation of electronics. Increased integration densities, speed and power of electronic and optoelectronic devices require thermal interface materials with substantially higher thermal conductivity, improved reliability, and lower cost. Graphene has emerged as a promising filler material that can meet the demands of future high-speed and high-powered electronics. This review describes the use of graphene as a filler in curing and non-curing polymer matrices. Special attention is given to strategies for achieving the thermal percolation threshold with its corresponding characteristic increase in the overall thermal conductivity. Many applications require high thermal conductivity of composites, while simultaneously preserving electrical insulation. A hybrid filler approach, using graphene and boron nitride, is presented as a possible technology providing for the independent control of electrical and thermal conduction. The reliability and lifespan performance of thermal interface materials is an important consideration towards the determination of appropriate practical applications. The present review addresses these issues in detail, demonstrating the promise of graphene-enhanced thermal interface materials compared to alternative technologies.

Theoretical analysis of thermal boundary conductance of MoS2-SiO2 and WS2-SiO2 interface

Understanding the physical processes involved in interfacial heat transfer is critical for the interpretation of thermometric measurements and the optimization of heat dissipation in nanoelectronic devices that are based on transition metal dichalcogenide (TMD) semiconductors. We model the phononic and electronic contributions to the thermal boundary conductance (TBC) variability for the MoS2-SiO2 and WS2-SiO2 interface. A phenomenological theory to model diffuse phonon transport at disordered interfaces is introduced and yields G = 13.5 and 12.4 MW K-1 m-2 at 300 K for the MoS2-SiO2 and WS2-SiO2 interface, respectively. We compare its predictions to those of the coherent phonon model and find that the former fits the MoS2-SiO2 data from experiments and simulations significantly better. Our analysis suggests that heat dissipation at the TMD-SiO2 interface is dominated by phonons scattered diffusely by the rough interface although the electronic TBC contribution can be significant even at low electron densities (n ≤ 1012 cm-2) and may explain some of the variation in the experimental TBC data from the literature. The physical insights from our study can be useful for the development of thermally aware designs in TMD-based nanoelectronics.

Interfacial Thermal Conductance between Monolayer WSe2 and SiO2 under Consideration of Radiative Electron-Hole Recombination

This work reports the interfacial thermal conductance (G) and radiative recombination efficiency (β), also known as photoluminescence quantum yield (PL QY), of monolayer WSe₂ flakes supported by fused silica substrates via energy-transport state-resolved Raman (ET-Raman). This is the first known work to consider the effect of radiative electron-hole recombination on the thermal transport characteristics of single-layer transition-metal dichalcogenides (TMDs). ET-Raman uses a continuous-wave laser for steady-state heating as well as nanosecond and picosecond lasers for transient energy transport to simultaneously heat the monolayer flakes and extract the Raman signal. The three lasers induce distinct heating phenomena that distinguish the interfacial thermal conductance and radiative recombination efficiency, which can then be determined in tandem with three-dimensional (3D) numerical modeling of the temperature rise from respective laser irradiation. For the five samples measured, G is found to range from 2.10 ± 0.14 to 15.9 ± 5.0 MW m^-2 K^-1 and β ranges from 36 ± 6 to 65 ± 7%. These values support the claim that interfacial phenomena such as surface roughness and two-dimensional (2D) material-substrate bonding strength play critical roles in interfacial thermal transport and electron-hole recombination mechanisms in TMD monolayers. It is also determined that low-level defect density enhances the radiative recombination efficiency of single-layer WSe₂.

Current Rerouting Improves Heat Removal in Few-Layer WSe2 Devices

Few-layer (FL) transition-metal dichalcogenides have drawn attention for nanoelectronics applications due to their improved mobility, owing to the partial screening of charged impurities at the oxide interface. However, under realistic operating conditions, dissipation leads to self-heating, which is detrimental to electronic and thermal properties. We fabricated a series of FL-WSe₂ devices and measured their I-V characteristics, while their temperatures were quantified by Raman thermometry and simulated from first principles. Our tightly integrated electrothermal study shows that Joule heating leads to a significant layer-dependent temperature rise, which affects mobility and alters the flow of current through the stack. This causes the temperatures in the top layers to increase dramatically, degrading their mobility and causing the current to reroute to the bottom of the FL stack where thermal conductance is higher. We discover that this current rerouting phenomenon improves heat removal because the current flows through layers closer to the substrate, limiting the severity of self-heating and its impact on carrier mobility. We also observe significant lateral heat removal via the contacts because of longer thermal healing length in the top layers and explore the optimum number of layers to maximize mobility in FL devices. Our study will impact future device designs and lead to further improvements in thermal management in van der Waals (vdW)-based devices.

Probing thermal transport across amorphous region embedded in a single crystalline silicon nanowire

While numerous studies have been carried out to characterize heat transport behaviours in various crystalline silicon nanostructures, the corresponding characteristics of amorphous one-dimension system have not been well understood. In this study, we amorphize crystalline silicon by means of helium-ion irradiation, enabling the formation of a completely amorphous region of well-defined length along a single silicon nanowire. Heat conduction across both amorphous region and its crystalline/amorphous interface is characterized by an electron beam heating technique with high measurement spatial resolution. The measured thermal conductivity of the amorphous silicon nanowire appears length-independence with length ranging from ~30 nm to few hundreds nm, revealing the fully diffusons governed heat conduction. Moreover, unlike the size-dependent interfacial thermal conductance at the interface between two one-dimensional crystalline materials, here for the first time, we observe that the interface thermal conductance across the amorphous/crystalline silicon interface is nearly independent of the length of the amorphous region. This unusual independence is further supported by molecular dynamics (MD) simulation in our work. Our results provide experimental and theoretical insight into the nature of interaction between heat carriers in crystalline and amorphous nano-structures and shed new light to design innovative silicon nanowire based devices.

Mapping Hot Spots at Heterogeneities of Few-Layer Ti3C2 MXene Sheets

Structural defects and heterogeneities play an enormous role in the formation of localized hot spots in 2D materials used in a wide range of applications from electronics to energy systems. In this report, we employ scanning thermal microscopy (SThM) to spatially map the temperature rise across various defects and heterogeneities of titanium carbide (Ti₃C₂T _x; T stands for surface terminations) MXene nanostructures under high electrical bias with sub-50 mK temperature resolution and sub-100 nm spatial resolution. We investigated several Ti₃C₂T _x flakes having different thicknesses as well as heterogeneous MXene structures incorporating line defects or vertical heterojunctions. High-resolution temperature rise maps allow us to identify localized hot spots and to quantify the nonuniformity of the temperature fields across various morphological features. The results show that the local heating is most severe in vertical junctions of MXene flakes and is highly affected by nonuniform conduction due to the presence of line defects. These results provide a direct insight into the power dissipation of MXene-based devices and the roles of various heterogeneities that are inherent to the material synthesis process. This study provides a guideline for how a better understanding of the structure-property-processing correlations and further optimization of the synthesis routes could improve the lifetime, safety, and operation limits of the MXene-based devices.

Enhanced Thermal Boundary Conductance in Few-Layer Ti3 C2 MXene with Encapsulation

Van der Waals interactions in 2D materials have enabled the realization of nanoelectronics with high-density vertical integration. Yet, poor energy transport through such 2D-2D and 2D-3D interfaces can limit a device's performance due to overheating. One long-standing question in the field is how different encapsulating layers (e.g., contact metals or gate oxides) contribute to the thermal transport at the interface of 2D materials with their 3D substrates. Here, a novel self-heating/self-sensing electrical thermometry platform is developed based on atomically thin, metallic Ti₃ C₂ MXene sheets, which enables experimental investigation of the thermal transport at a Ti₃ C₂ /SiO₂ interface, with and without an aluminum oxide (AlO_x ) encapsulating layer. It is found that at room temperature, the thermal boundary conductance (TBC) increases from 10.8 to 19.5 MW m^-2 K^-1 upon AlO_x encapsulation. Boltzmann transport modeling reveals that the TBC can be understood as a series combination of an external resistance between the MXene and the substrate, due to the coupling of low-frequency flexural acoustic (ZA) phonons to substrate modes, and an internal resistance between ZA and in-plane phonon modes. It is revealed that internal resistance is a bottle-neck to heat removal and that encapsulation speeds up the heat transfer into low-frequency ZA modes and reduces their depopulation, thus increasing the effective TBC.

Power Dissipation of WSe2 Field-Effect Transistors Probed by Low-Frequency Raman Thermometry

The ongoing shrinkage in the size of two-dimensional (2D) electronic circuitry results in high power densities during device operation, which could cause a significant temperature rise within 2D channels. One challenge in Raman thermometry of 2D materials is that the commonly used high-frequency modes do not precisely represent the temperature rise in some 2D materials because of peak broadening and intensity weakening at elevated temperatures. In this work, we show that a low-frequency E_2g² shear mode can be used to accurately extract temperature and measure thermal boundary conductance (TBC) in back-gated tungsten diselenide (WSe₂) field-effect transistors, whereas the high-frequency peaks (E_2g¹ and A_1g) fail to provide reliable thermal information. Our calculations indicate that the broadening of high-frequency Raman-active modes is primarily driven by anharmonic decay into pairs of longitudinal acoustic phonons, resulting in a weak coupling with out-of-plane flexural acoustic phonons that are responsible for the heat transfer to the substrate. We found that the TBC at the interface of WSe₂ and Si/SiO₂ substrate is ∼16 MW/m² K, depends on the number of WSe₂ layers, and peaks for 3-4 layer stacks. Furthermore, the TBC to the substrate is the highest from the layers closest to it, with each additional layer adding thermal resistance. We conclude that the location where heat dissipated in a multilayer stack is as important to device reliability as the total TBC.

Reduced Thermal Transport in the Graphene/MoS2/Graphene Heterostructure: A Comparison with Freestanding Monolayers

The thermal conductivity of the graphene-encapsulated MoS₂ (graphene/MoS₂/graphene) van der Waals heterostructure is determined along the armchair and zigzag directions with different twist angles between the layers using molecular dynamics (MD) simulations. The differences in the predictions relative to those of the monolayers are analyzed using the phonon power spectrum and phonon lifetimes obtained by spectral energy density analysis. The thermal conductivity of the heterostructure is predominantly isotropic. The out-of-plane phonons of graphene are suppressed because of the interaction between the adjacent layers that results in the reduced phonon lifetime and thermal conductivity relative to monolayer graphene. The occurrence of an additional nonzero phonon branch at the Γ point in the phonon dispersion curves of the heterostructure corresponds to the breathing modes resulting from stacking of the layers in the heterostructure. The thermal sheet conductance of the heterostructure being an order of magnitude larger than that of monolayer MoS₂, this van der Waals material is potentially suitable for efficient thermal packaging of photoelectronic devices. The interfacial thermal conductance of the graphene/MoS₂ bilayer as a function of the heat flow direction shows weak thermal rectification.

Measurement of specific heat and thermal conductivity of supported and suspended graphene by a comprehensive Raman optothermal method

The last decade has seen the rapid growth of research on two-dimensional (2D) materials, represented by graphene, but research on their thermophysical properties is still far from sufficient owing to the experimental challenges. Herein, we report the first measurement of the specific heat of multilayer and monolayer graphene in both supported and suspended geometries. Their thermal conductivities were also simultaneously measured using a comprehensive Raman optothermal method without needing to know the laser absorption. Both continuous-wave (CW) and pulsed lasers were used to heat the samples, based on consideration of the variable laser spot radius and pulse duration as well as the heat conduction within the substrate. The error from the laser absorption was eliminated by comparing the Raman-measured temperature rises for different spot radii and pulse durations. The thermal conductivity and specific heat were extracted by analytically fitting the temperature rise ratios as a function of spot size and pulse duration, respectively. The measured specific heat was about 700 J (kg K)^-1 at room temperature, which is in accordance with theoretical predictions, and the measured thermal conductivities were in the range of 0.84-1.5 × 10³ W (m K)^-1. The measurement method demonstrated here can be used to investigate in situ and comprehensively the thermophysical properties of many other emerging 2D materials.