Reliability Physics and Engineering

Frontmatter

Chapter 1. Introduction

Abstract

It is very frustrating (and often very expensive) to buy a device only to have it to fail with time. However, all devices (from integrated circuits to automobile tires) are fabricated from materials that will tend to degrade with time. The materials degradation will continue until some critical device parameter can no longer meet the required specification for proper device functionality. At this point, one usually says—the device has failed. The failure could be due to an increase in capacitor leakage (in the case of the integrated circuits) or the inability of an automobile tire to hold proper pressure (blowout). Materials degradation and eventual device failure are the subjects of Reliability Physics and Engineering. Reliability physics is normally associated with understanding the kinetics (temperature and stress dependence) of failure mechanisms. Reliability engineering is usually associated with establishing: proper design rules, robust materials selection criteria, and good manufacturing guidelines for reliable device fabrication and use.

J. W. McPherson

Chapter 2. Physics of Degradation

Abstract

Regardless how carefully crafted, devices are made of materials that generally exist in metastable states. A state is referred to as being metastable if it is only apparently stable and susceptible to change/degradation. The driving force for materials degradation is a lower Gibbs Potential. When we apply a generalized stress ξ to a material, it tends to increase (not lower) the Gibbs Potential. Therefore, a stressed material is even more unstable and even more susceptible to degradation. Since devices are fabricated from materials (and materials degrade with time), then devices will degrade with time. Engineers are confronted with the very difficult situation—they must manage the degradation rate in order to prevent failure.

J. W. McPherson

Chapter 3. Time-Dependence of Materials and Device Degradation

Abstract

Degradation is seemingly fundamental to all things in nature. Often this is described as one of the consequences of the Second Law of Thermodynamics—entropy (disorder) of isolated systems will tend to increase with time. The evidence for degradation is apparently everywhere in nature. A fresh coating of paint on a house will eventually crack and peel. The finish on a new automobile will oxidize with time. The tight tolerances associated with finely meshed gears will deteriorate with time. The critical parameters associated with precision semiconductor devices (threshold voltages, drive currents, interconnect resistances, capacitor leakage, etc.) will degrade with time. In order to understand the useful lifetime of the device, it is important to be able to model how critically important materials/device-parameters degrade with time.

J. W. McPherson

Chapter 4. From Material/Device Degradation to Time-to-Failure

Abstract

In Chap. 3, it was suggested that material/device degradation will occur with time and that this continuing degradation will eventually cause device failure. Methods were presented in Chap. 3 which can be used for modeling the time-dependence of degradation. The question that we would like to address in this chapter is—how does one go from the time-dependence of degradation to the time-to-failure for the device? The time-to-failure (TF) equations are critically important, for device failure mechanisms, and will be the focus of the remaining chapters in this book.

J. W. McPherson

Chapter 5. Time-to-Failure Modeling

Abstract

All materials tend to degrade, and will eventually fail, with time. For example, metals tend to creep and fatigue; dielectrics tend to trap charge and breakdown; paint tends to crack and peel; polymers tend to lose their elasticity and become more brittle, teeth tend to decay and fracture; etc. All devices (electrical, mechanical, electromechanical, biomechanical, bioelectrical, etc.) will tend to degrade with time and eventually fail. The rate of degradation and eventual time-to-failure (TF) will depend on the electrical, thermal, mechanical, and chemical environments to which the device is exposed.

J. W. McPherson

Chapter 6. Gaussian Statistics: An Overview

Abstract

The Gaussian distribution (normal or bell-shaped distribution) is a widely used statistical distribution and it is generally used as the foundation for statistical quality control. Simply measuring the time-zero values of a parameter (resistor values, mechanical tolerances, children heights, class grades on a test, etc.) can result in a distribution of values which can be described by a normal distribution.

J. W. McPherson

Chapter 7. Time-to-Failure Statistics

Abstract

When nearly identically processed materials/devices are placed under the same set of stress conditions, they will not fail exactly at the same time. An explanation for this occurrence is that slight differences can exist in the materials’ microstructure, even for materials/devices processed nearly identically. This means that not only are we interested in time-to-failure but, more precisely, we are interested in the distribution of times-to-failure. Once the distribution of times-to-failure is established, then one can construct a probability density function f(t) which will permit one to calculate the probability of observing a failure in any arbitrary time interval between t and t + dt, as illustrated in Fig. 7.1.

J. W. McPherson

Chapter 8. Failure Rate Modeling

Abstract

For a collection of devices, it is critically important to be able to understand the expected failure rate for the devices. For the supplier of such devices, the expected failure rate will be an important indicator of future warranty liability. For the customer, the expected failure rate will be an important indicator of future satisfaction. For mission-critical applications, it is of paramount importance for one to know that the expected failure rate will be extremely low.

J. W. McPherson

Chapter 9. Accelerated Degradation

Abstract

In Chap. 2 we learned that a stressed material was at a higher Gibbs Potential and therefore more unstable. The stressed material will spontaneously degrade, but at what rate? We might suspect, and rightfully so, that higher stress levels will make a material even more unstable and therefore accelerate the degradation rate; also, our intuition might suggest that the degradation rate for a material is temperature dependent. This chapter will develop the needed equations that show that this is indeed the case.

J. W. McPherson

Chapter 10. Acceleration Factor Modeling

Abstract

In reliability physics and engineering, the development and use of the acceleration factor (AF) is fundamentally important to the theory of accelerated testing. The AF permits one to take time-to-failure (TF) data very rapidly under accelerated stress conditions, and then to be able to extrapolate the accelerated TF results (into the future) for a given set of operational conditions. Since experimental determination of the AF could actually take many years, the AF must be modeled using the TF models introduced in Chap. 5. Since the AF must be modeled, it brings up another important question—how does one build some conservatism into the models without being too conservative?

J. W. McPherson

Chapter 11. Ramp-to-Failure Testing

Abstract

Engineers are constantly confronted with time issues. Applying a constant stress and waiting for failure can be very time-consuming. Thus, it is only natural to ask the question—does a rapid time-zero test exist that can be used on a routine sampling basis to monitor the reliability of the materials/devices? The answer to this question is often yes and it is called the ramp-to-failure test. While the test is destructive in nature (one has to sacrifice materials/devices), it is generally much more rapid than conventional constant-stress time-to-failure tests. The relative quickness of the test also enables the gathering of more data and thus the gathering of better statistics.

J. W. McPherson

Chapter 12. Time-to-Failure Models for Selected Failure Mechanisms in Integrated Circuits

Abstract

Advanced integrated circuits (ICs) are very complex, both in terms of their design and in their usage of many dissimilar materials (semiconductors, insulators, metals, plastic molding compounds, etc.). For cost reductions per device and improved performance, scaling of device geometries has played a critically important role in the success of semiconductors. This scaling—where device geometries are generally reduced by 0.7 × for each new technology node and tend to conform to Moore’s Law—has caused the electric fields in the materials to rise (bringing the materials ever closer to their breakdown strength) and current densities in the metallization to rise causing electromigration (EM) concerns. The higher electric fields can accelerate reliability issues such as: time-dependent dielectric breakdown (TDDB), hot-carrier injection (HCI), and negative-bias temperature instability (NBTI). In addition, the use of dissimilar materials in a chip and in the assembly process produces a number of thermal expansion mismatches which can drive large thermomechanical stresses. These thermomechanical stresses can result in failure mechanisms such as stress migration (SM), creep, fatigue, cracking, delaminating interfaces, etc.

J. W. McPherson

Chapter 13. Time-to-Failure Models for Selected Failure Mechanisms in Mechanical Engineering

Abstract

The mechanical properties of materials are related to the fundamental bonding strengths of the constituent atoms in the solid and any bonding defects which might form. A molecular model is presented so that primary bond formation mechanisms (ionic, covalent, and metallic) can be better understood. How these bonds form and respond to mechanical stress/loading is very important for engineering applications. A discussion of elasticity, plasticity and bond breakage is presented. The theoretical strengths of most molecular bonds in a crystal are seldom realized because of crystalline defects limiting the ultimate strength of the materials. Important crystalline defects such as vacancies, dislocations, and grain boundaries are discussed. These crystalline defects can play critically important roles as time-to-failure models are developed for: creep, fatigue, crack propagation, thermal expansion mismatch, corrosion and stress-corrosion cracking.

J. W. McPherson

Chapter 14. Conversion of Dynamical Stresses into Effective Static Values

Abstract

The time-to-failure models which were developed in the previous chapters assume that the stress remains constant with time until the material fails. Even when we discussed fatigue (a failure mechanism caused by a cyclical stress), it was assumed that the stress range Δσ remained constant with time. However, seldom is the applied stress constant with time, as illustrated in Fig. 14.1. In integrated circuits, the currents and fields are continually changing during operation and generally depend on the frequency of operation. In mechanical devices, the mechanical stress usually varies with time (the mechanical stress in a metal light pole changes with wind direction and with wind speed while the mechanical stress in the shaft of a rotor changes with the number of rpm). Therefore, a question naturally arises: how does one convert dynamical stresses (time-dependent stresses) ξ(t) into an effective static form ξeffective so that all of the previously developed time-to-failure models can be used? This chapter presents a methodology for that conversion.

J. W. McPherson

Chapter 15. Resonance and Resonance-Induced Degradation

Abstract

The time-to-failure models (developed in Chap. 14) for periodic stresses assumed that the periodic stresses were not associated with any resonant frequencies for the component/system. However, nearly every component/system has certain natural (or resonant) frequencies that must be avoided. If the applied time-dependent stress ξ(t) is periodic, with a frequency close to a system’s natural frequency υ, then this condition is referred to as resonance. Resonance can produce unexpectedly large-amplitude oscillations. This is true for both mechanical systems and electrical systems. Because of resonance, what might have been thought initially to be a rather benign stress condition can actually be a severe stress condition.

J. W. McPherson

Chapter 16. Increasing the Reliability of Device/Product Designs

Abstract

Design engineers are continually asked reliability questions such as: (1) how long is your newly designed device/product expected to last and (2) how can you make cost-effective design changes to improve the reliability robustness of the device? Often the designer will attempt to answer these questions by stating a safety factor v which was used for a design:

J. W. McPherson

Chapter 17. Screening

Abstract

It would be a great accomplishment if we could simply design and build devices without defects. That should always be our goal—but, obtaining perfection is indeed a difficult/impossible challenge. Given that all devices will likely have a small fraction of the population which is defective, the question that we want to address in this chapter is: can a relatively short-duration stress be used to eliminate the defective/weak devices without causing significant degradation to the good/ strong devices? The use of a short-duration stress to eliminate weak devices is generally referred to as screening. We will find that screening can sometimes be very effective, but not always. Screening effectiveness depends on the exact details of the strength distribution for the devices plus the magnitude and duration of the screening stress.

J. W. McPherson

Chapter 18. Heat Generation and Dissipation

Abstract

The adverse impact of temperature on device/material reliability has been emphasized often in this book. The degradation rate for most devices/materials tends to accelerate exponentially with increasing temperature. Therefore, for reliability reasons, lower temperature device operation is usually preferred. However, many devices (both electrical and mechanical) can generate significant amounts of heat as they are being operated. Once device operation begins, the rate of increase in temperature of the device/material will depend upon on the heat generation within the device, the heat capacity of the materials, and the heat dissipation from the device to the heat sink (which is often the ambient). Elevated device temperature during operation (versus the ambient temperature) creates a thermal gradient which serves to drive heat flow from the device. In thermal equilibrium the heat dissipation from the device will just match the heat generation within the device. Managing device heat dissipation may require a significant engineering effort—but the improvements in reliability can be worth the effort.

J. W. McPherson

Chapter 19. Sampling Plans and Confidence Intervals

Abstract

Before purchasing a large number of devices, a customer will likely ask the supplier about the defect level for the product being offered. The customer’s reliability inquiry is often expressed as: what is the defect level for the population of such devices in terms of number of defective devices per hundred, number of defective devices per thousand, number of defective devices per million (dpm), etc.? To determine the fraction defective, a sample of the devices is randomly selected from the population and this sample is tested/stressed to determine the fraction defective. After the fraction defective is determined for the sample, then it is only natural to ask: based on the sample size used, what is the confidence interval for the population fraction defective? To answer this critically important question, we must understand the basics of sampling theory.

J. W. McPherson

Backmatter