Schmitt-Trigger circuits are the method of choice for converting general signal shapes into clean, well-behaved digital ones. In this context these circuits are often used for metastability handling, as well. However, like any other positive feedback circuit, a Schmitt-Trigger can become metastable itself. Therefore, its own metastable behavior must be well understood; in particular the conditions that may cause its metastability.In this paper we will build on existing results from Marino to show that (a) a monotonic input signal can cause late transitions but never leads to a non-digital voltage at the Schmitt-Trigger output, and (b) a non-monotonic input can pin the Schmitt-Trigger output to a constant voltage at any desired (also nondigital) level for an arbitrary duration. In fact, the output can even be driven to any waveform within the dynamic limits of the system. We will base our analysis on a mathematical model of a Schmitt-Trigger's dynamic behavior and perform SPICE simulations to support our theory and confirm its validity for modern CMOS implementations. Furthermore, we will discuss several use cases of a Schmitt-Trigger in the light of our results.

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Schmitt-Triggers (S/Ts) are often utilized to clean noisy analog signals at intermediate voltage values in digital circuits. However, they are vulnerable to metastability, which may cause the same undesired non-digital output behavior that was supposed to be removed in the first place. To enable an efficient characterization of static and dynamic metastability properties of S/Ts (e.g., the metastable voltages, the resolution time constants and the overall total resolution times), this work introduces multiple simulation approaches based on control theory, AC, DC and transient analyses. The accuracy and runtime of all methods are compared and discussed by applying them to an analytically describable idealized circuit model as well as three common circuit implementations. Altogether, this work represents a comprehensive resource for investigating the metastable behavior in S/Ts. Even more, the proposed methods are applicable beyond the S/T, enabling an efficient characterization of static and dynamic metastable behavior in general circuits as well.

Semiconductor heterostructures are well characterized experimentally and provide a solid basis for electronic and optoelectronic devices ranging from single interface to complex superlattice structures. Yet, structural and electronic models commonly describe the material properties in a continuum approach, which neglects the crystalline structure, as well as potential local variations of the composition and resulting strain. Empirical interaction potentials provide an efficient way to model chemical bonds and therefore allow a structural description of multi‐layer structures. This work provides a detailed introduction on methods to minimize the total energy of semiconductor heterostructures at an atomistic level. We present an algorithm to minimize the total energy and generate optimized interface configurations. The relaxed structures are then evaluated with respect to interfacial strain, where different strain calculation methods are evaluated and compared with experimental data.

Despite their attractiveness as metastability filters, Schmitt-Triggers can suffer from metastability themselves. Therefore, in the selection or construction of a suitable Schmitt-Trigger implementation, it is a necessity to accurately determine the metastable behavior. Only then one is able to compare different designs and thus guide proper optimizations, and only then one can assess the potential for residual metastable upsets. However, while the state of the art provides a lot of research and practical characterization approaches for flip-flops, comparatively little is known about Schmitt-Trigger characterization. Unlike the flip-flop with its single metastable point, the Schmitt-Trigger exhibits a whole range of metastable points depending on the input voltage. Thus the task of characterization gets much more challenging.In this paper we present different approaches to determine the metastable behavior of Schmitt-Triggers using novel methods and mechanisms. We compare their accuracy and runtime by applying them to three common circuit implementations. The achieved results are then used to reason about the metastable behavior of the chosen designs which turns out to be problematic in some cases. Overall the approaches proposed in this paper are generic and can be extended beyond the Schmitt-Trigger, i.e., to efficiently characterize metastable states in other circuits as well.