INTRODUCTION
GaAs MMIC reliability is the probability that a device will perform its intended
function during a specified period of time under the specified operating environment.
The reliability of MMICs has been extensively investigated (Pecht
and Nash, 1994; Foucher et al., 2002;
Gu and Pecht, 2007). Generally, the method used for reliability prediction
is a matter of contention. It is understood that the benefits of a reliability
prediction depend on the accuracy and completeness of the information used to
conduct the prediction. Unfortunately, on the one hand, the long assessment
time required is not often acceptable; on the other hand, the economic constraints
allow this type of scheme to be used only by large companies. With the reliability
of MMICs improved and the shorter production duration required, the ability
to predict the reliability is very important but very limited nowadays. Thus,
it must draft a test plan to understand the lifetime of MMICs and the tendency
of reliability versus time.
Our proposed approach is usually used for items that are undergoing an enhancement.
It starts with the collection of past experience data. If the product does not
have a direct similar item, then lower level similar circuits can be exploited.
This MMIC reliability test method mainly involves thermal stress (175275°C
channel temperature), shorter test time and smaller sample size. The Arrhenius
law, Weibull and lognormal distributions will be applied in this study. In particular,
a MMIC reliability evaluation approach is presented and a general overview of
the corresponding parameters’ influence are given.
FAILURE MECHANISM
GaAs MMIC failures can be classified as either catastrophic or degradation
failures. Catastrophic failures render the device totally nonfunctional, while
degradation failures result in an electrically operating device that shows parametric
degradation and limited performance. Although, both passive and active components
of MMICs are subject to reliability problems, the active elements are often
the limiting factor and the major limitations have been found to be related
to channel temperature. The most common failure modes can be observed via the
degradation of the MMIC parameters such as I_{DSS}, gain and others
(Kayali et al., 1996; Ponchak
et al., 1994).
In this study, we assume all failure mechanisms obey the Arrhenius law. Thermally
accelerated life tests would be effective. Mittereder et
al. (1997) have shown the Weibull distribution is efficient for predicting
the reliability of MMICs.
CHANNEL TEMPERATURE
The reliability of MMICs, particularly for power devices, depends critically on the operating channel temperature. The reliability at normal operating temperatures is predicted by extrapolating data from accelerated life tests at elevated temperatures. The Weibull slope of the line depends upon the activation energy of the failure mechanism. Incorrect measurement of the channel temperature would create erroneous values of the lifetime and the activation energy. Therefore, it is important that accurate channel temperatures should be used to correlate the reliability life test data. It is obvious that the knowledge of temperatures is fundamental in obtaining accurate reliability data from accelerated temperature tests. It has been demonstrated that precise MMIC channel temperatures can be obtained by combining analytical models and physical measurement techniques.
Recently, a number of simulators have been developed (Flotherm 7.1, 2007; ANSYS
11.0, 2007) and many analytical approaches have also been given. Darwish
et al. (2005) have proposed an accurate closedform expression for
the thermal resistance of FET structures, which predicts the channel temperature
accurately.
DATA EXTRAPOLATING
To acquire MMIC reliability data in a reasonable amount of time, accelerated life test needs to be performed for the MMIC whose lifetime may be several decades. We expose the devices to elevated temperatures such that we can reduce the time to failure of a component, thereby enabling us to obtain the required data in a shorter time. The degradation rate r at which many chemical processes take place is governed by the Arrhenius equation:
where, A is a proportional multiplier, E_{a} is a constant of activation energy, k is the Boltzmann’s constant 8.6x10^{5} (eV/K), T is the absolute temperature in Kelvin.
The above equation has been widely used in the electronics industry. Experimental data acquired from life tests at elevated temperatures are analyzed via the Arrhenius equation to obtain the device behavior model at normal operating temperatures. The link between the lifetime data at different channel temperatures decides the accelerated factor. We can rearrange the Arrhenius equation as:
where, r_{1,2} is the accelerated factor between the temperatures T_{1}
and T_{2}, t_{1 }and t_{2} are time to failures. We
can use the Arrhenius plots, from which the slope of the logarithm of failure
rate versus reciprocal absolute temperature can be extracted, to estimate E_{a}.
Extensive reliability life tests on numerous GaAs MMICs have been performed
since the early 1970s. Typical measured activation energies of MMICs range from
1.2 to 2.3 eV (Mittereder et al., 1997).
Empirically, as a rule, the reliability of a semiconductor device will decrease to half with every 10°C increase in the junction temperature. Mathematically,
LIFE TEST METHODOLOGY
In order to analyze the lifetest data properly, we should adopt a suitable
mathematical failure distribution, which can be selected from several commonly
used distributions, such as the normal, lognormal, exponential and Weibull distributions.
It has been shown that the Weibull distribution provides better fit when many
defects compete to cause failures (Mittereder et al.,
1997). The Weibull distribution is defined by two parameters, i.e., the
characteristic life and the Weibull slope β. Its cumulative distribution
function is
It is obvious that with zero fails one cannot fit a failure distribution. However, Weibull and lognormal distributions provide the necessary background for establishing a reliability test methodology. The test method is described as below.
We first set a target life requirement in the field, e.g., MTTF (Mean time to failure) or λ. According to the MTTF value, we can calculate the Weibull slope value from the past collecting data. Besides the Weibull distribution, MMIC lives also yield to the lognormal distribution, thus we can get the following formula:
where, t_{m} is the median time. Based on the relationship between Weibull and lognormal distributions, we can get σ by
where, Γ (.) is the Gamma function. We then compute the characteristic
parameter á_{1} for the field using the following Eq.
7 or 8 obtained by rearranging Eq. 4
as:
At this point, the value α_{2} for the test can be calculated from the accelerated factor based on Eq. 2 and 3 as:
Next, the following equation is proposed to determine the required test time t_{test} with zero fails for a sample size of n, such that there is a 90% confidence that exceeds a target design value:
where, B is the confidence multiplier for the exponential distribution.
More details can be found by Breyfogle (1972). The approach
uses a transformation from the exponential distribution to the Weibull distribution
such that the confidence multiplier B is also transformed. For the commonly
used confidence value 90% with zero fails, we can obtain B = 2.303. In fact,
the value B can be looked up from tables in standard reliability tests.
APPLICATIONS OF THE PROPOSED MODEL
Now we apply the proposed model to the following example problem: for an InAlAs/InGaAs
HEMT MMIC with the sample size of 10 as depicted (Dammann
et al., 2004), how many testing hours with zero fails are required
to demonstrate an MTTF of 1x10^{6} h at the operating channel temperature
125°C in the field (approximately 1000 FITs)? To solve this problem, we
can select a test channel temperature and compute its corresponding acceleration
factor and then use the factor in the Arrhenius model as defined in Eq.
2. Dammann et al. (2004) has shown that the
value E_{a} is 1.3 eV, assume that the test channel temperature is 240°C,
the acceleration factor r_{1,2}= 4.9x10^{3} can be calculated
from Eq. 2. The characteristic value á_{1}
is calculated by Eq. 7 as follows:
Assume that the Weibull slope is 3.0 and the confidence is 90%, the required test time t_{test} can be calculated by Eq. 10 as follows:
Under the above assumptions, during the 140 h life testing, if there are no failures occur, we can promise an extrapolated MTTF of 1x10^{6} h at the channel temperature 125°C.
Nowadays, the failure rate of highreliability MMICs has reached 1 FIT or less. Thus, in our experiments, we assume that the failure rate is 1 FIT. Figure 1 shows how the required test time decreases with the sample size n. From this figure, we can easily see that the sample size impacts the test time significantly. We can reduce the test time by using a large number of samples. Ideally, the accelerated life tests should be conducted with very large sample sizes. However, this is not always practical or economical. In fact, due to difficult availability of samples or test equipments, we often adopt a smaller sample size as a compromise that adversely affects demonstrating a particular reliability in the field. From Fig. 1, we can see that it is suitable to choose the sample size as 10 or more. Figure 2 and 3 show the impact of different assumed Weibull slopes β on the required test time with all other parameters unchanged. For Fig. 2, the Weibull slopes range from 0.5 (defects) to 5 (wear out), while for Fig. 3, from 2 to 4.5. Here, the aim of Fig. 3 is to clearly show the part of Fig. 2 with slopes ranging from 2 to 4.5. From these results, we can see that the proposed approach can be appropriately used in the product inspection.

Fig. 1: 
Required test time vs. sample size 

Fig. 2: 
Required test time vs. Weibull slope (from 0.5 to 5) 

Fig. 3: 
Required test time vs. Weibull slope (from 2 to 4.5) 
CONCLUSION
This study suggests a quick reliability test method that can be adopted by smallsize industries in order to obtain the reliability figures. It is effective in improving the prediction accuracy. We strongly stress that it is seriously important to provide the reliability evaluation with the field data collection and the failure analysis of failed parts.