1、JEDEC STANDARD Methods for Calculating Failure Rates in Units of FITs JESD85 JULY 2001 (Reaffirmed: JANUARY 2014) JEDEC SOLID STATE TECHNOLOGY ASSOCIATION NOTICE JEDEC standards and publications contain material that has been prepared, reviewed, and approved through the JEDEC Board of Directors leve
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9、North 10th Street Suite 240 South Arlington, VA 22201-2107 or refer to www.jedec.org under Standards-Documents/Copyright Information. JEDEC Standard No.85-i-IntroductionThe calculation of failure rates is an important metric in assessing the reliability performance of aproduct or process. This data
10、can be used as a benchmark for future performance or anassessment of past performance, which might signal a need for product or process improvement.Reliability data are expressed in numerous units of measurement. This document uses the unitsof FITs (Failures-In-Time), where one FIT is equal to one f
11、ailure occurring in 109device-hours.These methods are assembled here to provide a reference to the way failure rates are calculated inFITs.Most of these methods only apply to constant failure rates. They assume that a 2distribution isa reasonable approximation of the failure distribution over time.
12、The examples given use failuresthat exhibit an Arrhenius behavior. Other failure models can also be applied to these methods,but care must be used for those models that do not simulate a constant failure rate.Please note that the methods described in this document represent simplified ways of calcul
13、atingfailure rates using various forms of data. More detailed methods exist in other publications, suchas EIA/JESD63 Standard Method for Calculating the Electromigration Model Parameters forCurrent Density and Temperature and JESD37 Standard for Lognormal Analysis of UncensoredData and of Singly Rig
14、ht-Censored Data Using the Persson and Rootzen Method.JEDEC Standard No. 85-ii-JEDEC Standard No. JESD85Page 1METHODS FOR CALCULATING FAILURE RATES IN UNITS OF FITs(From JEDEC Board Ballot JCB-01-02, formulated under the cognizance of the JC-14.3Subcommittee on Silicon Devices Reliability Qualificat
15、ion and Monitoring.)1 ScopeThe methods described in this document apply to failure modes and mechanisms whose failuresexhibit a constant failure rate, e.g., an Arrhenius behavior characterized by an activation energyfor failure. If data on the distributions of failure with time exist, these activati
16、on energies can beassumed from prior knowledge or failure analysis signatures. If the default activation energiesare not known or cant be determined, an activation energy can be used as a default. Refer toJEP122 Activation Energies for Failure Mechanisms to obtain initial estimates.The purpose of th
17、is method is to provide a reference to the way failure rates are calculated inFITs.2 Terms and definitionsprobability density function of the time-to-failure; mortality function f(t): The probabilityof failure at a given instant of time t. F(t)dt is the probability of failure in the interval t to t
18、+ dt.cumulative distribution function of the time-to-failure; cumulative mortality functionF(t): The probability that a device will have failed by time t or the fraction of units that havefailed by time t. It is the integral of f(t).cumulative reliability function R(t): The probability that a device
19、 will function at time t orthe fraction of units surviving to time t. R(t) = 1 F(t)instantaneous (or hazard) failure rate h(t): The rate at which devices are failing referencedto the survivors. h(t) = f(t) / R(t)cumulative hazard function H(t): The integral of h(t).FIT (failure in time): The number
20、of failures per 109device-hours. Typically used to express thefailure rate. Similarly, it can be defined as 1 PPM per 1000 hours of operation or one failure per1000 devices run for one million hours of operation.population failure distributions: The frequency of occurrence of failures over segments
21、oftime. Typically seen failure distributions are Normal, Lognormal (wearout), Weibull andExponential.JEDEC Standard No. JESD85Page 22 Terms and definitions (contd)bathtub curve: A plot of hazard rate versus time that exhibits three phases of life: infantmortality (initially decreasing failure rate w
22、ith time), intrinsic or useful life (relatively constantfailure rate) and wearout (increasing failure rate with time).acceleration factor (AF): A multiplier relating failure times during an accelerated life testversus those during useful life application conditions, assuming the same cumulative perc
23、entfailures and sigma for the two different stress conditions.activation energy (EA): The excess free energy over the ground state that must be acquired byan atomic or molecular system in order that a particular process can occur. Examples are theenergy needed by the molecule to take part in a chemi
24、cal reaction, by an electron to reach theconduction band in a semiconductor, or by a lattice defect to move to a neighboring site.apparent activation energy (EA): Activation energy that is calculated using the principles ofthe physical relationship between stress and failure rate but is not directly
25、 related to a basicchange in physical processes. It may be based on too many possible physical “effects” that, whenstressed as a unit, produce a cumulative effect. It is similar to the concept of activation energybut measures the probability of not exceeding some measurable attribute. A plot of ther
26、eciprocal or absolute temperature (1/T(K) versus the log of percent failed is linear.3 Methods for calculating failure ratesThe methods detailed below are arranged in an order such that an increasing amount of detailregarding the failure data is available for each successive model3.1 Case I: Single
27、activation energy procedure for constant failure rate distributionsAssumptions: NO TEST INTERVALS (single read point of 2000 hours) UNKNOWN FAILURE MECHANISMS NOMINAL VOLTAGES DURING STRESS TESTThis method assumes knowledge of the number of failures in a known sample size from a lifetest with a sing
28、le stress temperature and single end point test. The failures have not beensegregated or analyzed to determine the applicable failure mechanism, so an apparent activationenergy is assumed for all failures.JEDEC Standard No. JESD85Page 33.1 Case I: Single activation energy procedure for constant fail
29、ure rate distributions(contd)3.1.1 Summarize the data f = # of failures = 15 ss = sample size = 500 TSTRESS= stress temperature = 125 C T USE= use temperature = 55 C EA(avg) = apparent activation energy = 0.7 eV Very low power consumption during life test (negligible self heating) Apparent activatio
30、n energy may or may not be an average.3.1.2 Calculate the acceleration factorUsing the Arrhenius equation (1), calculate the acceleration factor for the failures at the givenstress and use temperatures.AFEkT TAUSE STRESS= exp11(1)+=KKKeVeV)273125(1)27355(1/106.87.0exp5= 78.6Usually devices draw powe
31、r during life test. Junction temperature can be derived from theambient temperature, power dissipation and the thermal impedance, and should be used foraccurate estimation of the acceleration factor. The self-heating in a device is package-dependent.The thermal dissipation property of a package (The
32、ta ja, ja) determines the amount of self-heating for the package. ja is a function of the air velocity around the package body. A good ruleof thumb is that jais reduced by as much as 30% for moving air compared to still air. As anexample, if we were to assume that jawere 60 C/watt, the power dissipa
33、tion were 0.1 watt at125 C, and 0.12 watts at 55 C, then there would be 7.2 C (60*0.12) difference betweenjunction temperature and ambient at 55 C and 6 C (60*0.1) difference at 125 C. Thus, theacceleration factor would be calculated based on 131 C as stress temperature vs. 62.2 C as theactual use t
34、emperature. The net effect of the self-heating would reduce acceleration factor to62.5, compared to 78.6 calculated earlier without a self -heating consideration.Some mechanisms such as oxide and inter-layer dielectrics may also be accelerated due to theapplied electric fields. Appropriate models ma
35、y be used to calculate acceleration due to voltageapplied. Refer to JEP122 for the most commonly used models.JEDEC Standard No. JESD85Page 43.1 Case I: Single activation energy procedure for constant failure rate distributions(contd)3.1.3 Calculate the point estimate of the failure ratePOINTft ssAF=
36、1096.78500200010159=h= 190.84 191 FITs3.1.4 Calculate the upper confidence bound of the failure rateCLCL ft ssAF= +2229102%,6.7850020002104.339%60=hCL (2for 15 failures is 33.4 for 60% confidence)= 212.46 212 FITs6.7850020002106.429%90=hCL (2for 15 failures is 42.6 for 90% confidence)= 270.99 271 FI
37、Ts3.2 Case II: multiple activation energy procedure for constant failure rate distributionsAssumption: NO TEST INTERVALS (single read point of 2000 hours) KNOWN FAILURE MECHANISMS NOMINAL VOLTAGES DURING STRESS TESTFor this method, the data set is the same as in section 5.1, but now it is known that
38、 the devicesfailed due to several different failure mechanisms to which can be assigned the appropriateactivation energies.JEDEC Standard No. JESD85Page 53.2 Case II: Multiple activation energy procedure for constant failure rate distributions(contd)3.2.1 Summarize the additional data available FM#1
39、 from 3 failures at EA= 0.5 eV FM#2 from 5 failures at EA= 0.7 eV FM#3 from 7 failures at EA= 1.0 eVTotal # of failures = 153.2.2 Calculate the acceleration factorsCalculate the acceleration factors for each failure mechanism (known activation energy) at thegiven stress and use temperatures using th
40、e Arrhenius equation (1) AF(FM#1) 0.5 eV = 22.6 AF(FM#2) 0.7 eV = 78.6 AF(FM#3) 1.0 eV = 5103.2.3 Calculate the failure ratesCalculate the point estimate of the failure rate for each failure mechanism and add to obtain thepoint estimate of the total failure rate.POINTft ssAF=1096.22500200010391#=hFM
41、 (0.5 eV)= 132.74 133 FITs6.78500200010592#=hFM (0.7 eV)= 63.6 64 FITs510500200010793#=hFM (1.0 eV)= 13.7 14 FITsJEDEC Standard No. JESD85Page 63.2 Case II: Multiple activation energy procedure for constant failure rate distributions(contd)3.2.3 Calculate the failure rates (contd)TOTAL POINT FMn,#=1
42、= 132.74 + 63.6 + 13.7= 210.4 210 FITs3.2.4 Calculate the upper confidence bound of the total failure rateTOTAL CL TOTAL POINTCL ff,%,=+2222TOTAL CL,.60%210 33430= 233.8 234 FITsTOTAL CL,.90%210 42 630= 298.2 298 FITsJEDEC Standard No. JESD85Page 73 Methods for calculating failure rates (contd)3.3 C
43、ase III: Multiple activation energy procedure for constant failure rate distributionswith known test intervalFor this method, the data set is the same as in sections 5.1 and 5.2, but the stress was nowperformed using different test intervals to determine when each of the failures occurred. Thistype
44、of detail enables a calculation of the average failure rate within a given time interval. Theearly life, or nonconstant failure rate, segment can be calculated using a Weibull distribution(m 10,000 h constant failure rate (operational life)It is assumed that this particular life test does not stress
45、 the devices to the wearout portion of theirlifetime. If the data shows a nonconstant (increasing) failure rate before the end of the stresstime, then the failure rate for that segment can be calculated using the method described belowfor a Weibull distribution (m 1).Assumption: KNOWN TEST INTERVALS
46、 KNOWN FAILURE MECHANISMS NOMINAL VOLTAGES DURING STRESS TEST3.3.1 Summarize the additional data availableStress Timebarb2right 48 h 168 h 500 h 1000 h 2000 hAcceleration Sample Sizebarb2right 500 497 495 493 490Factor # Failedbarb2right 32 2 3 522.6 FM # 1 0.5 eV 0 0 10 278.6 FM # 2 0.7 eV 1 002 25
47、10 FM # 3 1.0 eV 2 2 1 1 1JEDEC Standard No. JESD85Page 83.3 Case III: Multiple activation energy procedure for constant failure rate distributionswith known test interval (contd)3.3.2 Separate the data into early life and inherent life periodsThe field equivalent hours of 10,000 (depending on the a
48、pplication, different times may also beused) is used to find the equivalent time for each mechanism as follows:0.5 eV = 10,000/22.6 = 177 hours0.7 eV = 10,000/78.6 = 50.9 hours1.0 eV = 10,000/510 = 7.8 hoursThis means that the first two read points of 48 and 168 hours for the 0.5 eV belongs in the e
49、arlylife period. The first read point of 48 hours read point for the 0.7 eV group also belongs in theearly life period while all the rest of the read points will belong to the inherent life group (theconstant or steady state failure rate). The early life data points are highlighted in the table in3.3.1. This data is rearranged separating the early life portion from the inherent li
