When nonlinear electronics meets thermal noise at the nanoscale : A stochastic thermodynamics approach

Stochastic thermodynamics has significantly advanced the understanding of non-equilibrium systems, providing fundamental relations and bounds characterizing the thermal fluctuations, relevant at the nanoscale. Although these results have been experimentally validated in biological systems and low-temperature devices, their application to technologically relevant systems, such as modern computing devices, remains unexplored. The exponential growth in information processing capability in the past 50 years has been mainly driven by the steady miniaturization of complementary metal-oxide-semiconductor (CMOS) devices, leading to increasingly efficient, faster, and densely integrated computing devices. As CMOS technology continues to miniaturize, energy scales are approaching thermal energies, making thermal fluctuations and single-electron effects increasingly significant, especially in low-power applications. Addressing this gap, this thesis applies modern tools of stochastic thermodynamics for the analysis of noisy circuits with low-power CMOS and single-electron devices.
In the first part of the thesis, we characterize the voltage and current fluctuations in CMOS circuits using a weak noise approximation. This approximation is naturally reached for large physical dimensions of the device, such that logical states are represented by a macroscopic number of electrons. Using a CMOS inverter (NOT gate) as a case study, we demonstrate that large deviation theory accurately captures the fluctuations even in devices involving a few tens of electrons. This approach also provides a thermodynamically consistent alternative to the traditional Gaussian approaches. Additionally, we analytically characterize the limit cycle oscillations and its phase noise in CMOS-based ring oscillators near a Hopf bifurcation, revealing that thermal noise induces oscillations below the bifurcation, which are absent in the deterministic dynamics.
In the second part, we analyze circuits coupling the underdamped inductive/mechanical elements with the CMOS/single-electron devices. As a first step, we investigate the thermodynamic cost of precision in timekeeping using an electronic clock circuit, where we explore the violation of the thermodynamic uncertainty relation (TUR) in underdamped systems, for different device sizes and damping. Importantly, we show that the TUR violation occurs only in the single-electron regime of the circuit and is restored at macroscopic scales. Finally, we extend the framework of information thermodynamics to hybrid systems that couple discrete-state charge transport with inertial dynamics, with direct application in nanoelectromechanical systems (NEMS). By studying the self-oscillating behavior of a single-electron shuttle, the interplay between energy and information flows is analyzed on steady-state behavior, in regimes where the electrical power input leads to mechanical oscillations.
By applying stochastic thermodynamics to these technologically relevant systems, the work advances the understanding of nonequilibrium phenomena in modern electronic devices and provides insights that may inform future developments in computing technology.