Correlation of Physical and Information Entropies in Reliability Theory for Nanoscale Elements

Modern nanostructures and nanomaterials used as the base for electronic components are characterized by a high degree of heterogeneity and nonequilibrium. During the operation of a device under thermal, electrical, and other effects, its characteristics deteriorate as a result of physical and chemical processes. The tasks of providing fault-tolerance and the failure-free operation of nanodevices under conditions of autonomous operation are extremely urgent and require the significant development of mathematical apparatus in the theory of reliability. The physical–statistical approach to the problem of the reliability of nanodevices, in particular, from very-large-scale integration (VLSI) fragments to the level of the component base, is considered. More accurate formulations are given for solving the basic equation of this approach. A solution in quadratures for the one-dimensional steady-state case is obtained. The most significant advantages of the proposed approach for nanodevices over the traditional approach of the physics of failures are justified. At the same time, the similarity between the formality of the physical–statistical approach and the specifics of testing modern nanodevices with the classical Boltzmann–Arrhenius–Zhurkov (BAZ) model is noted. It is shown that, on the basis of the dynamics of distribution function of products in the space of their characteristics, both evolution of the reliability function and information entropy can be obtained. The weak and strong sides of the hypothesis concerning the relationship between the information entropy of such a distribution (based on tests) and the physical entropy of a nanodevice are discussed. The proposed approach in the theory of reliability combines the advantages of a physical approach based on the specifics of degradation mechanisms and a statistical approach using the reliability function.