Stress test acceleration factor calculator

How it works

An acceleration factor says how many hours (or cycles) of use one hour (or cycle) of a stress test stands for. This tool covers the models reliability engineers use most: Arrhenius, Eyring, Peck, Coffin-Manson, Norris-Landzberg, voltage, Black's equation and stress migration, and a product of factors for tests that stress more than one thing. It converts test time to use time, and works out the test time a use life needs.

1. Arrhenius temperature factor. For a thermally activated mechanism, the rate follows exp(−Ea / kT). The factor is the ratio of the rate at the stress temperature to the rate at the use temperature. Temperatures are in kelvin and k = 8.617 x 10^−5 eV/K.AF = exp[(Ea / k) x (1 / Tuse − 1 / Tstress)]
2. Eyring: a temperature prefactor and a second stress. The Eyring model adds a prefactor that grows with temperature and a term for a second stress S such as humidity or voltage. With p, B and C at zero it reduces to Arrhenius. The forms of the stress term differ between authors; this tool uses one common form.AF = (Tstress / Tuse)^p x exp[(Ea / k) x (1 / Tuse − 1 / Tstress)] x exp[(B + C / Tstress) x Sstress − (B + C / Tuse) x Suse]
3. Peck: temperature and humidity. Peck's model multiplies the Arrhenius factor by a power of the humidity ratio, with an exponent near 2.7 for aluminium corrosion. An optional power of the voltage ratio covers biased tests.AF = (RHstress / RHuse)^n x exp[(Ea / k) x (1 / Tuse − 1 / Tstress)] x (Vstress / Vuse)^m
4. Coffin-Manson and Norris-Landzberg: cycling. Fatigue is driven by the temperature swing. Coffin-Manson raises the ratio of the swings to an exponent q. Norris-Landzberg, for solder, adds a cycle-frequency term (a slower cycle gives more creep damage per cycle) and an Arrhenius term on the peak temperature. These factors compare cycles to failure, so time follows from the cycles per day.Coffin-Manson: AF = (dTstress / dTuse)^q; Norris-Landzberg: AF = (dTstress / dTuse)^n x (fuse / fstress)^m x exp[(Ea / k) x (1 / Tmax,use − 1 / Tmax,stress)]
5. Voltage, current density and stress migration. Voltage acceleration is exponential (a constant gamma per volt, or per MV/cm for oxide field) or a power law. Black's equation gives electromigration life as a power of current density times an Arrhenius term; the same form with a negative Ea covers hot carrier injection. Stress migration adds a thermomechanical term that falls as the stress temperature nears the stress-free temperature T0 of the metal.voltage: AF = exp[gamma x (Vstress − Vuse)] or (Vstress / Vuse)^n; Black: AF = (Jstress / Juse)^n x exp[(Ea / k) x (1 / Tuse − 1 / Tstress)]; stress migration: AF = ((T0 − Tuse) / (T0 − Tstress))^(−n) x exp[(Ea / k) x (1 / Tuse − 1 / Tstress)]
6. Combined factors and time. When a test stresses several things at once and they act independently, the factors multiply. Equivalent use time is the factor times the test time; the test time a use life needs is the life divided by the factor. For cycling models the same ratios apply to cycles, and cycles per day convert them to time.AF total = AF1 x AF2 x ...; equivalent use time = AF x test time; test time needed = use life / AF

Sources

The methods and default figures rest on these public sources. The wording here is our own; read the source for its full text.

• JEP122, Failure Mechanisms and Models for Semiconductor Devices (JEP122H) (opens in a new tab), JEDEC Solid State Technology Association, September 2016. The standard list of mechanisms, model forms and activation energies. The forms here are written in our own words.
• Semiconductor Device Reliability Failure Models (Technology Transfer 00053955A-XFR), Richard Blish and Noel Durrant (opens in a new tab), International SEMATECH, 31 May 2000. Open report with the model forms, typical constants and worked examples for hot carrier, stress migration and temperature cycling.
• Automotive Electronics Reliability Testing Starts and Ends with the Mission Profile, Thomas Eikenberg (opens in a new tab), Monolithic Power Systems, published by Power Electronics News, 14 May 2021. The worked example of 12,000 hours at 87 C against a 125 C life test.
• An Acceleration Model for Lead-Free (SAC) Solder Joint Reliability under Thermal Cycling, Vasu Vasudevan and Xuejun Fan, IEEE, 2008 Electronic Components and Technology Conference, 2008. The Norris-Landzberg form and its constants for tin-lead solder, and a comparison with lead-free fits.
• Reliability of Controlled Collapse Interconnections, K. C. Norris and A. H. Landzberg, IBM Journal of Research and Development, volume 13, 1969. The original thermal cycling model for solder joints.