Semiconductor Lifetime: How Temperature Affects Mean Time to Failure
Device reliability is an important issue across industries - we don’t want military radars or cell transmitters dropping out at the most critical times. There are a variety of factors that go into device reliability, but often underappreciated is the thermal contribution. Just how do semiconductor device lifetimes depend on device temperature, and how do semiconductor fabrication facilities predict how long their devices will last?
Usually, semiconductor manufacturers determine a device lifetime by an accelerated life test (ALT). Essentially, this means they pick a temperature for the device to operate, and measure how long the device runs at this temperature before it fails. In this case, failure is typically defined by a certain percentage decrease in performance. The temperature at which they test is usually much higher than the recommended device temperature so the device will fail on a time scale that they can actually see (hence accelerated life test). The results of the test are fed into the following equation, called the Arrhenius Equation, which allows us to approximately predict the lifetime of a semiconductor device:
where MTTF is the mean time to failure of a device operating at temperature T_operation, TTF_test is the lifetime of the device measured in an accelerated life test at temperature T_test, k_B the Boltzmann constant, and E_a is the apparent activation energy. The apparent activation energy E_a is a fitted parameter representing the dependence of lifetime on temperature, often specific to a given semiconductor material.
Now, this is a highly simplified formulation to predict device lifetime. There are some well-documented reasons to apply caution when using this equation [1,2]. Predicting your device lifetime with high accuracy would require a very thorough study for each individual device you want to characterize.
However, this formulation can show us general trends, particularly that device operating temperature has a significant effect on device lifetime. Let’s take a look at a plot of lifetime plotted against temperature to develop some intuition on this. For the purpose of illustration, we’ll apply parameters of an example gallium nitride (GaN) device of TTF_test=7E10 hours at T_test=127°C, at an activation energy of E_a=1.7eV. An interesting note here: the lifetime from the datasheet 7E10 hours is around 8 million years, where GaN devices have been around for maybe 10 years. The actual life test must have been done at a much higher temperature than what is listed, but the listed conditions correspond to the actual life test via the Arrhenius equation.
Note that the y-axis is logarithmic. What we see is the lifetime changes by a factor of ≈1E15 in the typical range of temperatures we may see from an electronic device. However, this plot has quite a range - let’s zoom into a section near where GaN devices are typically operated and convert it to a linear scale to get a better feel for what smaller changes in temperature may mean.
On this linear scale, we can clearly see the strong sensitivity to temperature. By increasing the device temperature by just 10°C, we have reduced the lifetime by over 2x. You may have heard a rule of thumb along the lines of a 50% lifetime decrease for each 10°C increase in channel temperature; that seems consistent with this formulation at this point in the Arrhenius curve. Even more significant, by increasing the temperature by 25°C from 225°C to 250°C, the lifetime dropped by almost an order of magnitude. This is equivalent to going from a ≈500 year lifetime to a ≈50 year lifetime on these devices, which will make operators of this device very happy if the lifetime ranges are a few times longer than a standard technology cycle.
In short, keeping devices cool can have a major, major impact on device reliability. This underscores the importance of good thermal management techniques as well as appropriate characterization of the device operating temperature, which if not applied properly can cause early onset of thermal issues, resulting in costly replacements or premature mission failure.
(1) O'connor, Patrick DT. "Arrhenius and electronics reliability." Quality and Reliability Engineering International 5.4 (1989): 255-255.
(2) Hakim, Edward B. "Reliability prediction: is Arrhenius erroneous?" Solid State Technology 33.8 (1990): 57-58.