(Invited, Digital Presentation) Nonlinear and Electro-Thermo-Mechanical Effects in Heterogeneous Electronics at Microwave Frequencies
Authors: Booth James C. , Orloff Nathan , Long Christian , Hagerstrom Aaron , Stelson Angela , Jungwirth Nicholas , Suriyasena Liyanage Luckshitha 
Published: November 2022

Materials properties are an essential component for the accurate modeling of integrated devices and circuits. The accuracy of such models depends explicitly on the accuracy of the input material parameters and interfaces between them. With the trend toward increasing heterogeneous integration, the relationships between electromagnetic, thermal, and mechanical material properties of heterogeneously integrated devices are even more important. Recent trends toward co-design emphasize the optimization of all aspects of circuit performance from the beginning, rather than sequentially optimizing the electromagnetic, thermal, mechanical characteristics. It can be critical for modeling success to understand, for example, where losses due to an electromagnetic signal are significant, as those losses can lead to energy dissipation with the subsequent temperature rise being a function of local thermal properties such as the thermal conductivity and heat capacity. Beyond losses, nonuniform temperature distributions generate mechanical stress that can impact interfaces between materials with dissimilar coefficients of thermal expansion. Furthermore, change in temperature and stress can lead to changes in the linear electromagnetic properties, resulting in changes in signal propagation and the generation of nonlinear effects.
Material properties are also important as they connect device response to underlying materials physics. This connection allows one to exploit different physical phenomena to add functionality at materials level, and to understand and mitigate non-idealities such as nonlinear response. As such, it is critically important to quantify nonlinear electromagnetic and electro-thermo-mechanical properties of heterogeneous integrated devices. In Fig. 1, the Heckmann diagram shows the electro-thermo-mechanical relations in a crystal, where T, S, E, D, θ, and σ are stress, strain, electric field, electric displacement, temperature, and entropy, respectively. This diagram illustrates the various nonlinear interactions that can be important for determining the overall response of microelectronic devices composed of a wide range of material systems.
Here, we present an overview of experimental efforts designed to accurately characterize the linear electromagnetic properties of materials relevant for microelectronics, including dielectrics and conductors as a function of frequency from 100 kHz through 220 GHz. Dispersion and absorption imply frequency dependence of complex quantities such as the dielectric permittivity and magnetic permeability, and this in turn necessitates broadband characterization techniques. We describe efforts to characterize broadband frequency-dependent linear electromagnetic properties over a wide range of temperatures, including cryogenic temperatures relevant for quantum computing, and augment these techniques with approaches to characterize the relevant thermal material parameters. We then describe measurements of nonlinear response of different material systems to quantify the nonlinear relationships between different thermodynamic fields in integrated structures. We conclude with a discussion of the needs for additional metrology to characterize these complex interactions inside complex 3D and packaged microelectronic devices and at buried interfaces within these heterogeneous integrated structures.

Figure 1