SPRADI9 June   2024 AM623 , AM625

 

  1.   1
  2.   Abstract
  3.   Trademarks
  4. 1Introduction
  5. 2Design-Based Approach
  6. 3Background
    1. 3.1 Process Delivery Kit (PDK)
    2. 3.2 SPICE Models for Circuit Behavior
    3. 3.3 Electronic Design Automation (EDA) Tools
    4. 3.4 Package Reliability
  7. 4Comparison of Design-Based Approach vs. HTOL Approach
  8. 5AM625/623 Lifetime Reliability Analysis Results
  9. 6Conclusion
  10. 7Revision History
  11.   A Appendix – The HTOL-Based Approach
  12.   B Appendix – The Mathematic Basis for EM Reliability Estimates

A Appendix – The HTOL-Based Approach

HTOL-based models are limited in two ways that do not apply for design-based reliability approach.

Typically, HTOL-based models apply a constant failure rate assumption. This is bottom of the bathtub curve as shown in Figure 8-1. Importantly, this paradigm does not credibly represent the useful lifetime of the product, as logically, lifetime coincides with the onset of the wear-out stage, characterized by increasing instantaneous failure rate.


AM625 AM623 Bathtub Curve – Mnemonic for Product Reliability Life Cycle

Figure A-1 Bathtub Curve – Mnemonic for Product Reliability Life Cycle

Reliability estimates are limited by fixed HTOL sample size and test duration. Usually one or both of these factors lead to a result of no observed failures. This limits viability of the model to characterize lifetime because no failures means minimal information to asses changes in failure rate vs. time. Mathematically, the case of terminating the test at a fixed duration (usually due to practical reasons) regardless of number of failures is called Type I right censoring. The term right censoring is used because when the test is terminated, it is unknown when the survivors at that point can later fail. The failure rate (in reciprocal time dimension) for Type I right censoring is represented by the following equation as shown in Equation 1.

Equation 1. F . R .   =   Χ 2 2 × f + 2,1 - α 2 × S S   x   t H T O L × A F

Where

Equation 2. Χ 2 2 × f + 2,1 - α
  • = Inverse Chi
  • Squared Cumulative Distribution Function (CDF) with f fail count at (1 - a) one-sided confidence level
  • SS = HTOL Sample Size
  • tHTOL = duration of HTOL test (hours)
  • AF = Acceleration Factor (HTOL to application)

To convert the Average Failure Rate (AFR) to CDF (Fail Fraction), use the following general identity:

Equation 3. F t = 1 - e - A F R × t

In this case, the Average Failure Rate is the same as the Constant Failure Rate. However, more boradly, AFR is a non-constant function of time.