Analytical Thermal Modeling of Cylindrical Nanostructures

The continued miniaturization of electronic components has led device architectures to evolve toward fully three-dimensional structures, with transistors featuring nanoscale dimensions and adopting gate-all-around topologies. Consequently, power dissipation and self-heating have emerged as critical challenges regarding performance, reliability, and lifetime estimates. This thesis investigates by analytical and numerical means the thermal behavior of cylindrical nanodevices, such as nanowires and nanosheets, which are promising candidates for advanced nanowire transistors, multi-gate transistors, gate-all-around transistors, and crossbar memory cells. The work begins with an introductory summary of the limitations resulting from scaling; notably, power dissipation, which has fueled the need for predictive thermal models at different levels of abstraction. Equivalent thermal network models are introduced to describe device heating within the same abstraction level as electronic design. The core of the study focuses on deriving closed-form analytical models for radial heat transfer in homogeneous and heterogeneous cylinders. The heterogeneous problem is formulated in a state-space representation that depicts each material layer as a thermal quadrupole, effectively incorporating thermal boundary resistances between adjacent layers. The study is then expanded to include two-dimensional conduction in both radial and longitudinal directions, enabling the analysis of localized heat sources. Both steady-state and transient conditions are investigated and validated against thermal simulations using a professional TCAD suite. The results provide practical formulas, calculation procedures, and physical insights into temperature distribution, thermal resistances, and thermal capacitances for complex cylindrical heterostructures and transistors. These results are useful to interpret time-resolved temperature measurements. Ultimately, this work addresses the definition of physics-based lumped thermal equivalent circuit models derived from the mathematical properties of heat transport rather than empirical assumptions.