Sourabh Lahiri

Kinetics of oxidation of copper alloy leadframes

Abstract Delamination of the oxide film from copper alloy leadframes is considered a serious reliability problem for microelectronics packages. In an effort to identify the factors which may lead to the formation of brittle and/or poorly adhering oxides, kinetics of oxidation of leadframes in air was investigated by measuring the oxide thickness as a function of time at temperatures ranging from 200 to 300°C. The oxidation was found to occur fairly rapidly in this temperature range. The oxide has the appearance of incoherent platelets and it consists of CuO and Cu2O. Analysis of the oxidation data indicates a logarithmic growth law in the 100–1400 nm thickness range, and an activation energy of about 19 kJ/mol, which is much smaller than that reported for the oxidation of unalloyed copper by a diffusion mechanism. The results of this investigation are presented here, indicating the important role of defects in the oxidation of leadframes.

Fluctuation theorems in the presence of information gain and feedback

In this study, we rederive the fluctuation theorems in the presence of feedback by assuming the known Jarzynski equality and detailed fluctuation theorems. We find that both the classical and quantum systems can be analyzed using a similar treatment in terms of state space trajectories. We first briefly reproduce the already known work theorems for a classical system in order to show its equivalence with the quantum treatment. We then extend the treatment to arrive at new results, namely the generalizations of Seifert’s entropy production theorem and the Hatano–Sasa fluctuation theorem, in the presence of feedback. We have also derived the extended version of the Tasaki–Crooks fluctuation theorem for a quantum particle in the presence of multiple loop feedback. For deriving the extended quantum fluctuation theorems, we have considered open systems. No assumption is made on the nature of environment and the strength of system–bath coupling. However, it is assumed that the measurement process involves classical errors.

Fluctuation theorems and atypical trajectories

In this work, we have studied simple models that can be solved analytically to illustrate various fluctuation theorems. These fluctuation theorems provide symmetries individually to the distributions of physical quantities such as the classical work (Wc), thermodynamic work (W), total entropy (Δstot) and dissipated heat (Q), when the system is driven arbitrarily out of equilibrium. All these quantities can be defined for individual trajectories. We have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level. As the time of observation increases, the fraction of such atypical trajectories decreases, as expected at the macroscale. The distributions for the thermodynamic work and entropy production in nonlinear models may exhibit a peak (most probable value) in the atypical regime without violating the expected average behaviour. However, dissipated heat and classical work exhibit a peak in the regime of typical behaviour only.

Quantum Jarzynski equality with multiple measurement and feedback for isolated system

In this paper, we derive the Jarzynski equality (JE) for an isolated quantum system in three different cases: (i) the full evolution is unitary with no intermediate measurements, (ii) with intermediate measurements of arbitrary observables being performed, and (iii) with intermediate measurements whose outcomes are used to modify the external protocol (feedback). We assume that the measurements will involve errors that are purely classical in nature. Our treatment is based on path probability in state space for each realization. This is in contrast with the formal approach based on projection operator and density matrices. We find that the JE remains unaffected in the second case, but gets modified in the third case where the mutual information between the measured values with the actual eigenvalues must be incorporated into the relation.

Fluctuation relations for heat engines in time-periodic steady states

A fluctuation relation for heat engines has been derived recently. In the beginning, the system is in contact with the cooler bath. The system is then coupled to the hotter bath and external parameters are changed cyclically, eventually bringing the system back to its initial state, once the coupling with the hot bath is switched off. In this work, we lift the condition of initial thermal equilibrium and derive a new fluctuation relation for the central system (heat engine) being in a time-periodic steady state (TPSS). Carnot?s inequality for classical thermodynamics follows as a direct consequence of this fluctuation theorem even in the TPSS. For the special cases of the absence of hot bath and no extraction of work, we obtain the integral fluctuation theorem for total entropy and the generalized exchange fluctuation theorem, respectively. Recently, microsized heat engines have been realized experimentally in the TPSS. We numerically simulate the same model and verify our proposed theorems.

Fluctuation theorems in inhomogeneous media under coarse graining

Abstract We compare the fluctuation relations for work and entropy in underdamped and overdamped systems, when the friction coefficient of the medium is space-dependent. We find that these relations remain unaffected in both cases. We have restricted ourselves to Stratonovich discretization scheme for the overdamped case.

Extended fluctuation theorems for repeated measurements and feedback within Hamiltonian framework

Abstract We derive the extended fluctuation theorems in presence of multiple measurements and feedback, when the system is governed by Hamiltonian dynamics. We use only the forward phase space trajectories in the derivation. However, to obtain an expression for the efficacy parameter, we must necessarily use the notion of reverse trajectory. Our results show that the correction term appearing in the exponent of the extended fluctuation theorems is non-unique, whereas the physical meaning of the efficacy parameter is unique.

Energy fluctuations in a biharmonically driven nonlinear system

We study the fluctuations of work done and dissipated heat of a Brownian particle in a symmetric double well system. The system is driven by two periodic input signals that rock the potential simultaneously. Confinement in one preferred well can be achieved by modulating the relative phase between the drives. We show that in the presence of pumping the stochastic resonance signal is enhanced when analysed in terms of the average work done on the system per cycle. This is in contrast with the case when pumping is achieved by applying an external static bias, which degrades resonance. We analyse the nature of work and heat fluctuations and show that the steady state fluctuation theorem holds in this system.