Laser Diode Lifetime: How an MTTF Claim Is Built

Scope

This article explains where a laser diode lifetime number comes from and what it means: the acceleration models that let a short, hot, overdriven test stand in for years of service, the statistics that turn a handful of devices into a mean time to failure with a confidence level, the definition of a failure that the number silently depends on, and how to derate from the claim to your own operating point. It is a reference on the reasoning; the screening procedure itself is the burn-in entry, and the operating-point limits it interacts with are in Why L-I curves kink and the catastrophic optical damage entry.

What fails, and what counts as failing

A laser diode wears out gradually through the growth of non-radiative defects in and near the active region, degradation of the facets, and creep in the contacts and solder. The visible symptoms are a rising threshold current, a falling slope efficiency, and, in a constant-power loop, a rising drive current. A lifetime number therefore requires a failure criterion, and the common ones are a 20% or 50% increase in the operating current needed to hold rated power, or a 20% rise in threshold, or a fixed drop in output at constant current. The same population reaches these criteria at different times, so a mean time to failure without its criterion is not a number; a data sheet that quotes "MTTF > 1,000,000 hours" should say "to a 50% increase in operating current at 25 °C case temperature," and a good one does.

Two separate populations of failures exist. Infant mortality, the early failures from defects present at manufacture (dark-line defects, contact and solder flaws, facet contamination), is what burn-in exists to remove: a few tens to a few hundred hours at elevated temperature and current accelerate those failures to the first days and screen them out. Wear-out, the slow degradation of the survivors, is what the lifetime claim describes, and burn-in does not measure it, shorten it, or predict it. A lifetime test is a separate, longer, and more expensive exercise run on a sample after burn-in.

Acceleration

Wear-out is accelerated by temperature and by current, and the lifetime test uses both to compress years into weeks. The temperature dependence follows an Arrhenius law with an activation energy $E_a$:

$$\mathrm{AF}_T = \exp\!\left[\frac{E_a}{k}\left(\frac{1}{T_\mathrm{use}} - \frac{1}{T_\mathrm{stress}}\right)\right],$$

with temperatures in kelvin at the junction, not the case. Activation energies reported for laser diode wear-out span 0.3 to 0.7 eV depending on the material system and the dominant mechanism. The current dependence is usually modelled as a power law, $\mathrm{AF}_I = (I_\mathrm{stress}/I_\mathrm{use})^n$, with $n$ between 1.5 and 2 in most published work, and the two factors multiply.

The numbers show how much leverage the model has. For a use junction temperature of 45 °C and a stress junction temperature of 85 °C, the temperature acceleration is 3.4 at $E_a = 0.3$ eV, 7.7 at 0.5 eV, and 17 at 0.7 eV. Driving the stress at 1.5 times the use current with $n = 2$ adds a factor of 2.25. With $E_a = 0.5$ eV and that current, the combined acceleration is 17: one hour at stress represents 17 hours at the use point. The sensitivity to $E_a$ is the first thing to notice. The same test data extrapolated with 0.7 eV instead of 0.5 eV claims a lifetime 2.3 times longer, and the activation energy is itself estimated from tests at two or three temperatures with its own uncertainty, so a lifetime claim carries, hidden inside it, an assumption that is worth asking about.

From a test to a number

Suppose 20 devices run for 5000 hours at the stress condition above and none reaches the failure criterion. The test has accumulated $20 \times 5000 \times 17 = 1.7 \times 10^6$ equivalent device-hours at the use condition with zero failures. The standard treatment assumes an exponential (constant-rate) failure distribution and puts a lower bound on the mean time to failure from the chi-squared distribution: with zero failures, $\mathrm{MTTF} \ge T_\mathrm{total} / 0.916$ at 60% confidence and $\mathrm{MTTF} \ge T_\mathrm{total} / 2.303$ at 90% confidence. The example gives an MTTF of at least $1.9 \times 10^6$ hours at 60% confidence and $7.5 \times 10^5$ hours at 90%, or in the other common unit, at most 530 failures per $10^9$ device-hours (530 FIT) at 60% confidence.

Three features of that arithmetic deserve attention. The million-hour figure is a lower bound, not an estimate of when a typical device fails; the test saw no failures and cannot say more than "at least." The bound scales directly with the acceleration factor, so it inherits the activation-energy assumption in full. And it applies to a population whose failures are assumed to arrive at a constant rate, which wear-out mechanisms do not obey; a population that fails in a narrow band around 200,000 hours would pass the same 5000-hour test with the same zero failures and the same million-hour bound. Tests that run to failure and fit a lognormal or Weibull distribution to the failure times say much more, and a supplier who can show a distribution of failure times rather than a zero-failure bound is showing better evidence.

Derating

The user's job is to translate the claim to the operating point. The steps are these.

1. Find the junction temperature at which the claim is made and the junction temperature of the application, using the package thermal resistance and the dissipated power, as in Measuring laser diode junction temperature. Convert with the Arrhenius factor at the stated (or, if unstated, a conservative) activation energy: running 20 K hotter than the claim's condition costs a factor of 1.9 to 4.5 in life for $E_a$ of 0.3 to 0.7 eV.
2. Do the same for current. A constant-power loop raises the drive current as the laser ages, which accelerates the aging; a laser run at 80% of its rated current gains a factor of $1.25^n$, 1.4 to 1.6, over one run at rating.
3. Add the operating margins that are not in the lifetime model: the kink-free rating, which narrows with age, and the facet intensity limit, which the coating and the aging facet share.
4. Decide what failure means for the application, and if it is stricter than the supplier's criterion (a 10% current rise rather than 50%), scale the expectation down; degradation is roughly linear early in life for many mechanisms, so a criterion at 10% arrives in about a fifth of the time of one at 50%.

The result is usually an operating point at 50 to 80% of rated current and a junction temperature held as low as the package allows, which is what a data sheet's derating curve encodes without explaining.

Reading the claim

A lifetime specification is complete when it states the failure criterion, the junction (not case) temperature, the drive current, the activation energy and current exponent used, the number of devices and hours tested, the number of failures observed, and the confidence level. Most data sheets state two or three of these. The absent ones can be asked for, and the answers are more informative than the headline. A supplier who runs to failure and fits a distribution, states $E_a$ from multi-temperature data, and quotes the criterion is describing a measurement; a supplier who quotes a round number of hours at 25 °C with no criterion is describing a hope.

References: Telcordia GR-468-CORE, Generic Reliability Assurance Requirements for Optoelectronic Devices Used in Telecommunications Equipment; M. Fukuda, Reliability and Degradation of Semiconductor Lasers and LEDs (Artech House, 1991); JEDEC JEP122, Failure Mechanisms and Models for Semiconductor Devices, for the Arrhenius and current-acceleration forms and the chi-squared confidence bounds. The acceleration factors and bounds above are computed from the stated parameters; the activation-energy and exponent ranges are representative of published laser reliability studies.