## On ageing effects in analogue integrated circuits

- The behaviour of electronic circuits is influenced by ageing effects. Modelling the behaviour of circuits is a standard approach for the design of faster, smaller, more reliable and more robust systems. In this thesis, we propose a formalization of robustness that is derived from a failure model, which is based purely on the behavioural specification of a system. For a given specification, simulation can reveal if a system does not comply with a specification, and thus provide a failure model. Ageing usually works against the specified properties, and ageing models can be incorporated to quantify the impact on specification violations, failures and robustness. We study ageing effects in the context of analogue circuits. Here, models must factor in infinitely many circuit states. Ageing effects have a cause and an impact that require models. On both these ends, the circuit state is highly relevant, an must be factored in. For example, static empirical models for ageing effects are not valid in many cases, because the assumed operating states do not agree with the circuit simulation results. This thesis identifies essential properties of ageing effects and we argue that they need to be taken into account for modelling the interrelation of cause and impact. These properties include frequency dependence, monotonicity, memory and relaxation mechanisms as well as control by arbitrary shaped stress levels. Starting from decay processes, we define a class of ageing models that fits these requirements well while remaining arithmetically accessible by means of a simple structure. Modeling ageing effects in semiconductor circuits becomes more relevant with higher integration and smaller structure sizes. With respect to miniaturization, digital systems are ahead of analogue systems, and similarly ageing models predominantly focus on digital applications. In the digital domain, the signal levels are either on or off or switching in between. Given an ageing model as a physical effect bound to signal levels, ageing models for components and whole systems can be inferred by means of average operation modes and cycle counts. Functional and faithful ageing effect models for analogue components often require a more fine-grained characterization for physical processes. Here, signal levels can take arbitrary values, to begin with. Such fine-grained, physically inspired ageing models do not scale for larger applications and are hard to simulate in reasonable time. To close the gap between physical processes and system level ageing simulation, we propose a data based modelling strategy, according to which measurement data is turned into ageing models for analogue applications. Ageing data is a set of pairs of stress patterns and the corresponding parameter deviations. Assuming additional properties, such as monotonicity or frequency independence, learning algorithm can find a complete model that is consistent with the data set. These ageing effect models decompose into a controlling stress level, an ageing process, and a parameter that depends on the state of this process. Using this representation, we are able to embed a wide range of ageing effects into behavioural models for circuit components. Based on the developed modelling techniques, we introduce a novel model for the BTI effect, an ageing effect that permits relaxation. In the following, a transistor level ageing model for BTI that targets analogue circuits is proposed. Similarly, we demonstrate how ageing data from analogue transistor level circuit models lift to purely behavioural block models. With this, we are the first to present a data based hierarchical ageing modeling scheme. An ageing simulator for circuits or system level models computes long term transients, solutions of a differential equation. Long term transients are often close to quasi-periodic, in some sense repetitive. If the evaluation of ageing models under quasi-periodic conditions can be done efficiently, long term simulation becomes practical. We describe an adaptive two-time simulation algorithm that basically skips periods during simulation, advancing faster on a second time axis. The bottleneck of two-time simulation is the extrapolation through skipped frames. This involves both the evaluation of the ageing models and the consistency of the boundary conditions. We propose a simulator that computes long term transients exploiting the structure of the proposed ageing models. These models permit extrapolation of the ageing state by means of a locally equivalent stress, a sort of average stress level. This level can be computed efficiently and also gives rise to a dynamic step control mechanism. Ageing simulation has a wide range of applications. This thesis vastly improves the applicability of ageing simulation for analogue circuits in terms of modelling and efficiency. An ageing effect model that is a part of a circuit component model accounts for parametric drift that is directly related to the operation mode. For example asymmetric load on a comparator or power-stage may lead to offset drift, which is not an empiric effect. Monitor circuits can report such effects during operation, when they become significant. Simulating the behaviour of these monitors is important during their development. Ageing effects can be compensated using redundant parts, and annealing can revert broken components to functional. We show that such mechanisms can be simulated in place using our models and algorithms. The aim of automatized circuit synthesis is to create a circuit that implements a specification for a certain use case. Ageing simulation can identify candidates that are more reliable. Efficient ageing simulation allows to factor in various operation modes and helps refining the selection. Using long term ageing simulation, we have analysed the fitness of a set of synthesized operational amplifiers with similar properties concerning various use cases. This procedure enables the selection of the most ageing resilient implementation automatically.
- Viele alltägliche Geräte in Haushalt, Verkehr, zur Kommunikation oder Medizintechnik werden seit Mitte des zwanzigsten Jahrhunderts von elektronischen Schaltungen beherrscht. Solche Schaltungen messen, steuern und regeln wichtige Eigenschaften, Funktionen und Prozesse und ermöglichen immer weiter ausgefeilte Anwendungen, höhere Effizienz und neue Einsatzmöglichkeiten. Grundsätzlich besteht ein Interesse an der einwandfreien Funktionalität solcher Geräte. Mit elektronischen Halbleiterschaltungen werden zunehmend kleinere Bauteile in diese Geräte verbaut. Einerseits führt dies zu einer wachsenden Systemkomplexität bei mitunter gleichbleibenden Abmessungen, andererseits werden im Zuge der Miniaturisierung physikalische Grenzen erreicht und bisweilen überwunden. Die Einzelteile eines Systems sind nach Fertigung nicht zugänglich und können nicht ausgetauscht werden. Als Konsequenz erwartet man einen Ausfall, sobald ein Einzelteil nicht mehr funktioniert. Um solchen Ausfällen vorzubeugen, möchte man gerne vor der Serienproduktion in Erfahrung bringen, wie sie zustande kommen. Hierzu bedarf es geeigneten Modellen und Analysemethoden. Die Entwicklung solcher im Falle von Analogschaltungen ist der Schwerpunkt dieser Arbeit...

Author: | Felix Salfelder |
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URN: | urn:nbn:de:hebis:30:3-415788 |

Publisher: | Univ.-Bibliothek |

Place of publication: | Frankfurt am Main |

Referee: | Lars HedrichGND, Oliver Bringmann |

Document Type: | Doctoral Thesis |

Language: | English |

Date of Publication (online): | 2016/09/23 |

Year of first Publication: | 2016 |

Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |

Granting Institution: | Johann Wolfgang Goethe-Universität |

Date of final exam: | 2016/09/22 |

Release Date: | 2016/09/26 |

Page Number: | xiv, 109 |

HeBIS-PPN: | 387246150 |

Institutes: | Informatik und Mathematik / Mathematik |

Informatik und Mathematik / Informatik | |

Dewey Decimal Classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 000 Informatik, Informationswissenschaft, allgemeine Werke |

5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik | |

Sammlungen: | Universitätspublikationen |

Licence (German): | Deutsches Urheberrecht |