Reliability of Nanoelectronic Devices

Transcription

1 Reliability of Nanoelectronic Devices M. A. Alam Purdue University West Lafayette, IN Reliability: Physics of how things break A child drops a glass Lighting in a rain-soaked night Volcano, landslides, and forest fire Check-out queues Bridges (Tacoma Narrows) and Shuttle (Challenger) A stochastic process terminated by a threshold 1

2 A Brief History of Reliability Phase 1: Antiquity to Based on empirical study and over-design Phase 2: 1900 onward Based on system design principles Introduction of rigorous statistical principles Phase 3: 1970 onward Development on physical principles of reliability and other complex and emergent phenomena Phase 1: Empirical Approach Phase 1: Antiquity to Based on empirical study and over-design 3000 year old Pyramid, 2000 year old Pont du Gard stone bridge in Southern France, the 300 year old first iron Bridge on the Savern River still stand. Stone age vs. Cu age (performance vs. BC) Stone vs. Steel (e.g. Lui Sullivan building in Chicago) Power-law for Earthquake and forest fires Corrosion in battery Light bulb and Edison 2

3 Phase 2: Introduction of Statistics and System Theory Urgency of WWII (50% equipment unserviceable, MTTF 20h for bombers, etc.) forces people to look at reliability issues as a scientific branch. 1. DARPA introduces AGREE program (Advisory group of reliability of electronic equipments). Results in MIL-HDBK-217 Handbook. Many books books begin to appear in 1960s. Statistical theories bring discipline to reliability physics (e.g. Von-Neuman theory of fault-tolerant computing). 2. Queuing theory of sofware and computer systems. 3. ATT builds trans-atlantic cable, must ensure 40 year lifetime. Phase 3: Physical Principles Pervasive use of physical models to explain reliability phenomena Mechanical/Aeronautical Engineering: Theory of Fracture, excellent theory, many books, embedded in software Software Development: Formal methods of verification, embedded in software, courses taught in the university Natural Phenomena Volcanic eruption: Sandpile models Forrest fires: Percolation theory Courses in statistical physics and emergent phenomena Electronic Devices: Significant work since 1940s (Bardeen, Shockley), 1960s in Fairchild, whole industry in 1980s and 1990s. Not embedded in software and not formally taught in universities. 3

4 An example of Three Types of Reliability Study Empirical approach: Sell a set of computers and observe the frequency of field-returns. Put together a historical data-base for various products to predict what is likely to happen to your next product. Statistical Approach and System Theory: Assume that each component (blue boxes) has a certain failure rate (e.g. exp(-λt), one need not know the physics of λ) and a certain connectivity. Use the rules of probability to predict overall reliability of the system. Physical Approach: Study the physics of individual devices to find the origin Of l as a function of voltage, temperature, etc. and use it in statistical model and compare with empirical results. Another example Empirical approach: To study the reliability of a molecular bridge, one may observe and tabulate the failure rates as a function of time, F(t). Statistical Approach and System Theory: One may realize that if there are N atoms holding the bridge, then if they can dissociate from the bridge independent from Each other, then F(t)=1-p N. If N is large and p is small, then the bridge will fail. The strength of the bonds define p. Reliability Physics: E B One further realizes that the dissociation probability of individual molecule is given by q=v0exp(-eb/kt)tobs where v0 is the attempt frequency, EB is the energy barrier for dissociation (bonding energy), and T is the temperature, and t is the time. Since F(t)=1-p N =1-(1-q) N ~ qn = v 0 exp(-e B /kt)t obs N Failure times depends linearly with bridge size and observation time, and exponentially on temperature and bond strength. Compare with empirical results for confirmation. 4

5 Conclusions! We have broadly illustrated the use of empirical information, statistical concepts and physical modeling.! In the next class, we will use a A blind fish in a river model to illustrate these formulation concretely.! Check out the MATLAB code provided to see how the concepts are linked to each other and the general structure of the reliability theory. 5