Abstract
A new stochastic process was developed by considering the internal performance of macro-states in which the sojourn time in each one is phase-type distributed depending on time. The stationary distribution was calculated through matrix-algorithmic methods and multiple interesting measures were worked out. The number of visits distribution to a determine macro-state were analyzed from the respective differential equations and the Laplace transform. The mean number of visits to a macro-state between any two times was given. The results were implemented computationally and were successfully applied to study random telegraph noise (RTN) in resistive memories. RTN is an important concern in resistive random access memory (RRAM) operation. On one hand, it could limit some of the technological applications of these devices; on the other hand, RTN can be used for the physical characterization. Therefore, an in-depth statistical analysis to model the behavior of these devices is of essential importance.
Highlights
A new statistical methodology is presented; we will concentrate in the study of resistive memories [11,12], known as resistive random access memories (RRAMs), a subgroup of a wide class of electron devices named memristors [13]
random telegraph noise (RTN) fluctuations can be beneficial, for instance, when used as entropy sources in random number generators, an employment of most interest in cryptography [22,23]. The application in this issue is addressed in the current work, in particular with the statistical description of RTN signals in RRAMs
To study the number of possible latent levels hidden into the signals, we considered hidden Markov models (HMMs) [26,27]
Summary
Advanced statistical techniques are key tools to model complex physical and engineering problems in many different areas of expertise In this context, a new statistical methodology is presented; we will concentrate in the study of resistive memories [11,12], known as resistive random access memories (RRAMs), a subgroup of a wide class of electron devices named memristors [13]. RTN fluctuations can be beneficial, for instance, when used as entropy sources in random number generators, an employment of most interest in cryptography [22,23] The application in this issue is addressed in the current work, in particular with the statistical description of RTN signals in RRAMs. This study, in addition to physically characterizing the devices, can be used for compact modeling and, as explained above, for developing the software tools needed for circuit design. Conclusions related to the main contributions of this work are presented in
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