激活能的意义.doc

激活能的意义:激活能是晶体中晶格点阵上的原子运动到另一点阵或间隙位置时所需的能量, 是反映温度应力对产品寿命影响的一种指标。对产品而言, 它从正常的未失效状态向失效状态转换的过程中存在着势垒, 这就是激活能。激活能越小, 失效的物理过程越容易进行激活能越大,加速系数越大, 越容易被加速而失效。激活能是不随温度变化的常数。也就是说, 对应于某失效机理, 激活能是不随温度变化的常数, 这就保证了加速寿命试验的可行性。事实上, 当温度大于500K时, 激活能不再为常数。对于电子产品来说, 温度应力一般不会500K超过。激活能会随产品批次的不同和同批不同类的产品而不同,此外, 同一产品的不同失效模式也会使激活能发生变化。因此, 使用已公布的数值并不一定合适Let the Data Speak About Activation EnergyLet the Data Speak About Activation Energy There are many factors to consider when conducting an analysis of accelerated test data. One factor that is often overlooked or misrepresented is the activation energy. When considering accelerated life tesLet the Data Speak About Activation Energy There are many factors to consider when conducting an analysis of accelerated test data. One factor that is often overlooked or misrepresented is the activation energy. When considering accelerated life tests, the activation energy represents the magnitude of effect that the applied stress will have on the product under test. A large activation energy indicates that the applied stress will have a large effect on the life of the product. Understanding activation energy is one thing, but obtaining an accurate value is another. Currently, the published values of activation energy relate to a particular material, technology, or failure mode, but how this value relates to a product, which may be composed of many different materials, is unknown. One possible method to alleviate the problem of selecting the most representative activation energy is to estimate the value based on collected data. Utilizing maximum likelihood theory, the parameters of the Arrhenius model are solved while using the Weibull distribution as the underlying life distribution. Once the parameters have been estimated, the activation energy and acceleration factor can be easily calculated. Arrhenius RelationThe Arrhenius life-stress relationship is given by:where C is a parameter to be estimated, Ea is the activation energy and K is Boltzmans constant (8.617385*10-5 eV/K). The 2-parameter Weibull pdf is given by:The scale parameter (characteristic life) is h. The Arrhenius-Weibull pdf is obtained by setting h = L(T).However, the activation energy, Ea, must be known a priori and this is rarely the case. So another parameter, B, is introduced, where:The Arrhenius-Weibull pdf can be rewritten as:The parameters that need to be estimated are b, B and C. These parameters can be estimated using Maximum Likelihood Estimation (MLE) where the Arrhenius-Weibull log-likelihood equation is:Once the parameters have been estimated, then the activation energy can be calculated using the following equation:Significance of BThe significance of the parameter B can be seen if the life-stress relationship is linearized by taking the natural logarithm of both sides. Therefore:In the above equation, ln(C) is equal to the intercept, the inverse of the stress (temperature) is the variable, and B is the slope of the line. But B is not the slope of the life versus stress; it is the slope of the life versus the inverse of the stress. An example of a life vs. stress plot, also referred to as an Arrhenius plot, is shown in Figure 1.Figure 1: Life vs. Stress PlotIt would seem from Figure 1 that B, and therefore the activation energy, is negative. This is due to the fact that the x-axis is actually a reciprocal scale. The x-axis is plotted on a reciprocal scale simply for practical purposes. It is just easier to read the life at 404 than at 0.00248 (the reciprocal of 404). Figure 1 actually illustrates that B is positive. As the reciprocal of the stress increases, the stress decreases. If the activation energy is small, then you can expect the life of the product to change slowly as the temperature changes.Acceleration FactorOnce the activation energy has been estimated, the acceleration factor can be determined next. The acceleration factor is most often referred to as the ratio of the life between use stress level and some higher (accelerated) test stress level, or:If the activation energy is known a priori (rarely the case), then the acceleration factor can be written as:But since the parameter B is being estimated based on the given accelerated test data, the above equation can become:From this equation, it is possible to estimate the value of the acceleration factor based on the estimated parameter B (which includes the activation energy), as opposed to assuming a value for the activation energy. It can also be seen that the AF depends only on the Ea or B. Therefore, an incorrect assumption on either of these values will have a large effect on the value for acceleration factor.ExampleTo illustrate the process of estimating the activation energy, 399 hard drive systems were thermally stressed at 308K and 328K for 1032 hours and three failures were observed. The collected data set is shown in Table 1, where F indicates that the observation has failed and S indicates a right censored (suspended) observation.Number inGroupF or STime(hrs)Temperature(K)1F483081S60308197S10323081S133281F163281S243281S383281S653281F733281S793281S983281S2503281S361328190S1032328Table 1: Accelerated Life Test DataArrhenius is selected as the life-stress relationship and Weibull as the underlying life distribution. It is also assumed that the use stress level is 308K. The parameters are estimated using ALTA 6:b = 0.3074; B = 11674.2; C = 1.0506E-6Therefore, the estimated