FAQ 7: How do operating conditions influence GaAs failures?


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By common definition, the acceleration factor (temperature) is the median life at low temperature divided by the median life at higher temperature. The median lives are determined by life testing to failure. The remaining unknown value is the activation energy. With just two temperatures, the activation energy can be determined by direct substitution. For more temperatures, the activation energy can be determined by graphical plotting. As with lognormal plotting, activation energy plotting can be more precisely done mathematically. This was accomplished by converting the time scale to log, and inverting the temperature, then performing a least squares linear fit. Once the slope of the time/temperature relationship is known, it can be divided into Boltzmann's constant to determine the activation energy. The conversions can also be performed prior to graphing by converting each axis, then plotting.

The Arrhenius Equation can also be depicted graphically by using a log scale for time and an inverse Kelvin scale for temperature. Although either time or temperature can be used as the independent variable, temperature was selected since "goodness" is more easily perceived in the vertical direction and the times being analyzed are more akin to lifetimes than elapsed times. The parameters that are plotted on this graph are, by convention, median lives. Using an Arrhenius graph, the relationship between temperature and lifetimes can be identified by plotting the median lives. Since the resulting relationship has a large (negative) slope, small changes in temperature can be expected to produce large changes in median lives. Since the ratios of any two median lives determines an acceleration factor, the slope of the Arrhenius graph is equivalent to the Ea/K term. In other words, the slope multiplied by Boltzmann's Constant is the activation energy for any particular failure mechanism shown on the Arrhenius Graph. For this reason, the Arrhenius graph is sometimes called an activation energy graph.

The activation energy for MesFETs is roughly 2.5eV. Compared to failure mechanisms for silicon devices which have activation energies from 0.3 to 1.2eV, this is extremely high (remember, its an exponential term). Although high, its not unexpected since the activation energy expected for the diffusion of Au in GaAs is 2.64eV and titanium in GaAs is 2.93eV.

Now that a method of determining acceleration has been defined, the previous question about when GaAs failures will occur can be adequately answered. Since the maximum specified operating temperature of TriQuint GaAs devices is 150°C, that will be used as the basis of definition. The most pessimistic median life for FETs at 150°C is about 1 billion hours, or 114 thousand years! This makes it more obvious why we don't consider sinking gates as a failure mechanism that needs fixing, at least for the next few thousand years. In addition to FETs, the accelerating effects on the other elements can be examined.

As we have discussed in a previous FAQ, the failure mechanism for interconnects and resistors is a combination of metal interdiffusion and electromigration. The interdiffusion can be handled as the FETs were, but electromigration requires a different technique for investigating acceleration factors.

Electromigration mechanisms are accelerated by current density as well as temperature. The general relationship is sometimes referred to as Black's Equation. Just as with the Arrhenius equation, we can observe the electromigration effects on lifetimes using a graphical approach.

The slope from this graph is the exponent in the electromigration equation, sometimes called "n" or the "n factor." This is called the "J exponent." For silicon devices, this J exponent is often considered a constant which is fixed at 1 or 2. This consideration is logical for silicon devices since all metal interconnects are aluminum with small amounts of silicon and copper. For GaAs, one constant is not a logical choice. We have empirically determined that the J exponent is different for each metal structure. This is rational since the metal structures all have different compositions. Unfortunately, each metal has its own specified maximum rating for current density, so there is not a common basis for comparison. The failure mechanisms for each element can be analyzed. For example, the metals with the higher J exponents have lower activation energies. The results of high sensitivity to current density and lower sensitivity to temperature, for plated metal in particular, are characteristic of electromigration failure mechanisms.

The metal least sensitive to current density is deposited titanium/platinum/gold. For this metal, an extra review into failure criteria provides some interesting data on failure mechanisms. For example, different failure criteria result in different J exponents. The first 50% change in resistance has very low sensitivity to current density, and the first 250% change has a much higher J exponent. In a similar but inverse manner, acceleration factors decrease with increasing failure criteria, particularly for unbiased life tests. These two results indicate that at least two failure mechanisms are operating. Early resistance changes are most highly accelerated by temperature as the interdiffusion mechanism progresses, but as the resistance continues to increase, the activation energy decreases as the interdiffusion is completed. Eventually, the current density exponent increases as the electromigration mechanism begins to take effect.