## 1 Introduction  
The self-heating effect (SHE) in semiconductor devices refers to the phenomenon of temperature rise caused by the generation of joule heat as a current flows through transistor channels during operation [1; 2; 3; 4; 5]. The channel temperature rise reduces the carrier mobility and the drain current, and it can also induce a shift in the threshold voltage, leading to performance degradation [6]. Furthermore, based on the Arrhenius relationship, which correlates the channel temperature and mean time to failure (MTTF) of a device, an increase in the operating temperature can substantially reduce its lifetime [7; 8]. As shown in Figure 1, the current flow through interconnects, which is utilized to connect transistors for power distribution and signal transmission, also causes SHE [9]. Before the 45 nm technology node, the temperature rise within the interconnects was small and negligible. However, aggressive scaling of interconnects notably increased metal resistivity and current density, resulting in a significant increase in temperature owing to the SHE [10; 11]. Temperature increase in the interconnects also causes performance degradation and reliability issues owing to electromigration effects. Because of the extremely high thermal resistance of the top printed circuit board (PCB) package layers, the generated heat is dissipated through the heat sink connected to the substrate [10; 11; 12; 13]. Therefore, the thermal conductivity of the substrate materials plays an important role in the heat dissipation of semiconductor devices. The SHE in conventional planar bulk silicon (Si) CMOS devices does not cause a substantial increase in temperature owing to the high thermal conductivity of bulk Si (\(\sim\)150 W/mK). The heat generated in the channel is efficiently dissipated through the Si substrate, preventing a significant temperature increase. Several advanced techniques have been developed to improve the electrical performance of semiconductor devices. For example, silicon-on-insulator (SOI) devices improve performance by reducing the parasitic capacitance. An insulating buried oxide layer, typically SiO\({}_{2}\), impedes heat dissipation from the channel to the Si substrate because of its low thermal conductivity (\(\sim\)1 W/mK), resulting in severe SHE [3]. Fully depleted silicon-on-insulator (FDSOI) technology has been developed to overcome the short-channel effect. The low in-plane thermal conductivity of ultrathin top Si layers in FDSOI devices also intensifies the SHE [14]. The transition from planar metal-oxide-semiconductor field-effect transistors (MOSFET) to fin-field effect transistor (FinFETs) and gate-all-around field-effect transistor (GAAFET) technologies could significantly improve the performance of transistors. However, in advanced FinFET and GAAFET designs, the SHE becomes more pronounced owing to the encapsulation of the channel by a gate dielectric, with low thermal conductivity coupled with limited heat dissipation paths to the substrate provided by the three-dimensional (3D) structures [15]. Wide-bandgap semiconductors, such as gallium nitride (GaN) and silicon carbide (SiC), offer significant advantages over traditional Si-based semiconductors in terms of high-power and high-frequency operations. The SHE in these semiconductor devices is more severe because of their relatively higher power dissipation. The temperature increase could be as high as 350 \({}^{\circ}\)C in the active region of a GaN-on-Si device [16]. The overall thermal resistance of a semiconductor device is the lumped thermal resistance, which comprises the intrinsic thermal resistance of the constituent materials and the thermal boundary resistance (TBR) present at the interfaces between them. At the macroscale, the thermal conductivity of the constituent materials plays a crucial role in determining the heat-dissipation capability of semiconductor devices.