Burn-In, Lifetime Models, and the Bathtub Curve

Reliability data is reported as a failure rate in FITs, where one FIT is one failure per billion device-hours. A part rated at a few FITs is expected to fail at a rate that makes a single failure in a large population an event worth investigating. The number is a summary of three regimes with different physics, and the regimes are what burn-in is designed to exploit.

Three mechanisms, one curve

The infant-mortality regime covers the first few hundred hours of operation. Failures there come from latent defects introduced by manufacturing: a gate oxide that is thinner than spec across a small region, a via with a marginal barrier, a bond with a partial weld, a particle that is not yet a short. Each is a defect that survives the manufacturing test because the test does not stress it hard enough to fail, or because the defect only becomes catastrophic when it is stressed the way the product will stress it. The failure rate falls steeply with time as the subpopulation with latent defects is exhausted.

The useful-life regime is flat. The rate is set by random defects that succeed in causing a failure, and because the number of susceptible elements in the population is not being reduced in a correlated way, the hazard does not change. This is the part of the curve the FIT figure usually describes, and it is the part that is quoted in a datasheet.

The wear-out regime is where the physical degradation mechanisms dominate: electromigration in the metal, time-dependent dielectric breakdown of the gate and inter-metal oxides, hot-carrier injection into the gate oxide, and thermal fatigue of solder joints and bond wires. Each has a threshold-like behaviour: it degrades slowly and then accelerates, so the hazard rises with time. The wear-out onset sets the product’s useful life, and it is the regime that the qualification tests are designed to show lies beyond the warranty period.

The curve connecting the three is the bathtub. Its two ends are not symmetric in their cause or in the manufacturing response: burn-in attacks the left side, and design and process margin attack the right side. A part with a good infant-mortality screen and poor wear-out margin fails late; a part with a poor screen and good wear-out margin fails early and then is stable.

Accelerating time

The mechanisms are thermally activated and are accelerated by temperature according to the Arrhenius relation, in which the rate depends exponentially on activation energy divided by the thermal energy. The acceleration factor between a stress temperature and a use temperature is the ratio of the two exponential terms. An activation energy of 0.7 electron-volts, a commonly used figure for many silicon failure mechanisms, yields an acceleration factor of about 2.4 for each ten kelvin between 25 and 35 degrees, falling to about 2.1 between 55 and 65 and 1.8 near 100 degrees; a lower activation energy accelerates far less.

import math

K_B = 8.617e-5  # eV per kelvin, Boltzmann constant

def arrhenius_af(use_temp_c, stress_temp_c, ea_ev):
    t_use = use_temp_c + 273.15
    t_stress = stress_temp_c + 273.15
    return math.exp((ea_ev / K_B) * (1 / t_use - 1 / t_stress))

# A hundred hours at 125 C compared with 55 C use
print(round(arrhenius_af(55, 125, 0.7), 1))   # ~78x
print(round(arrhenius_af(55, 125, 0.3), 1))   # ~6.5x, weakly accelerated

A hundred hours at 125 degrees with an activation energy of 0.7 electron-volts corresponds to an equivalent use time of roughly eight thousand hours at 55 degrees, about eleven months. That is the basis of a qualification burn-in: a few days of stress stands in for years of use. The premise is that the acceleration does not change the failure mechanism, and that premise is what the qualification is actually testing: if the failure distribution at stress temperature has a different shape from the one at use temperature, the acceleration factor is meaningless.

Voltage accelerates oxide wear through the field across the dielectric, and the field is voltage divided by thickness, so thinner oxides accelerate far more for the same voltage. The exponential dependence on the field means that a modest overvoltage is a strong stress, and that a design with a thinner gate oxide is both more sensitive to overvoltage and more cheaply tested for it.

Current accelerates electromigration, which is the mass transport of metal atoms driven by the electron wind. The phenomenon is described by Black’s equation, in which the median time to failure falls with the inverse of the current density raised to an exponent commonly between one and two, and is accelerated by temperature through an Arrhenius term. Because both the current density and the temperature are elevated in operation, current density limits are set on every wire, and the limit depends on the wire’s expected temperature and on the allowed fraction of the population that may fail within the product life.

What burn-in actually screens

A burn-in step places the parts at elevated temperature and voltage for a defined time, typically while exercising them with a pattern that toggles internal nodes. The choices are the temperature, the voltage, the duration, and the pattern. Temperature and voltage set the acceleration; the duration sets how much of the infant-mortality population is removed; the pattern sets which circuits are stressed, and a pattern that leaves a node static leaves the defects at that node unaccelerated.

The pattern is the least appreciated part. A defect in a memory array is stressed by writing and reading the cell; a defect in a logic cone is stressed by toggling it. A burn-in that holds the part in a reset state stresses almost nothing, which is why burn-in uses the same structural patterns as scan test, run at temperature. The overlap with test is deliberate: the vectors already exist, as scan chain generation produced them, and running them hot converts a functional test into a stress.

The screening is incomplete by construction. A latent defect whose acceleration is low, or whose stress path is not exercised, survives. The measure of the screen is the outgoing failure rate in the field, and it is a property of the whole flow — manufacturing test, burn-in, and the design’s own margin — not of the burn-in step alone.

The cost of screening, and why it is being cut

Burn-in consumes a burn-in oven’s time, a socket’s life, and the parts’ own time in a flow that would otherwise ship them sooner. The parts occupy an oven for hours to tens of hours at temperature, and the ovens and their boards are a capital item sized to the production volume times the duration. The cost per part is therefore roughly proportional to the burn-in duration, and the duration is chosen to be long enough that the remaining infant-mortality rate is acceptable.

The direct cost is not the only one. Burn-in at temperature stresses every part, including the ones that would never have failed, and the stress consumes some of the part’s wear-out budget. The temperature-cycling fatigue of the solder joints and the electromigration damage accumulated during burn-in are real, and a long screen at high temperature shortens the product’s life at the margin. The duration is therefore bounded from both sides: long enough to screen, short enough not to consume the life it is protecting.

The industry’s response has been to reduce burn-in by finding the latent defects earlier and cheaper. Higher coverage in wafer probe and final test, with patterns targeted at the defect mechanisms that burn-in would otherwise catch, removes the need for the thermal stress; the test economics favour moving coverage upstream when the test can be made as effective. Parts with measured quiescent current or leakage outside a narrow distribution are screened as likely to contain a latent defect, and that parametric screen costs milliseconds rather than hours. The result is that burn-in is applied selectively or replaced, on parts where the mechanism mix and the field data justify the confidence.

Reading a FIT number

The FIT figure for a part is usually a calculated value, not a measured one. It is derived from the accumulated device-hours in qualification tests, divided into the number of failures observed, with a confidence bound applied and the acceleration factor used to convert stress time to use-equivalent time. With zero failures observed, which is common, the upper confidence bound is computed from the device-hours alone rather than from a measured rate, and the result is a statement about the size of the experiment as much as about the part.

The consequence is that a FIT number is comparable only with another computed the same way. A figure from a vendor that ran a larger sample with the same zero failures is smaller; a figure that includes the whole product line’s burn-in data is smaller still. Comparisons across vendors, or across generations of the same part, are therefore only meaningful when the method, the acceleration, the confidence level, and the population are matched, which is why the standards that define the calculation are referenced alongside the number rather than left implicit.

The other caveat is scope. A FIT figure describes the useful-life regime at a specified temperature and voltage. A part operated outside those conditions has a different rate, and the temperature dependence is exponential, so the extrapolation is not gentle. Derating — operating below the rated voltage and temperature — is the practical way to buy margin, and it is the reason a part’s reliability at its rated maximum is not the number to design to when the application’s thermal design can keep it cooler.