Basis of the theory behind FIDES Methodology

Transcription

1 Basis of the theory behind FIDES Methodology ASTR Workshop, St. Paul 0 th to 2 th September 204 Franck Bayle Thales Avionics Chanthachith Souvanthong ON Semiconductor

2 Assumptions of reliability prediction Reliability prediction is one step of the reliability process. Some assumptions must be checked during the Design For Reliability activities performed during the development phase as : q Product robustness to reduce induced failures (overstresses) Derating analysis Worst case analysis Highly Accelerated Stress (HALT) q Life limited component analysis to reject wear-out failure mechanisms after the product service life q Accelerated tests for specific components q Optimized screening (HASS) q Life profile (stress type, stress level, operational phases)

3 FIDES global modelisation Origin cause of failure Components Process impact Process Process failure distribution versus life Cycle components technologies TECHNOLOGY RELIABILITY Technologies Electronic Component family Classification Detailed technologies =>Recent technologies covered Profile Description Phases breakdown Duration of each phase Functioning condition (on/off) Ambient temperature (constant) Thermal cycling (duration, frequency, amplitude) Relative Humidity Vibrations Chemical (pollution) Life cycle Audit 70 Questions PROCESS USE System Life Profile What are the goals of FIDES [REF06]: realistic prediction Usable for reliability assessment and building (DFR) Usable for all types of items, including COTS sub-assemblies

4 FIDES global modelisation λ = λ Physical Π PM Π Process Sedyakin principle Quality of manufacturer Quality of component Experience of supplier Processes management (Quality & Control) λ. λphase i Π Physical i induced i Tphasei i = Tphase Influence of technology Influence of mission profile Unexpected overstress Operational use of the product

5 Different type of failures λ = λ Physical Π PM Π Process Defaults from production Defaults from Design - Weak components - Overstress(Pi induced) - Mission profile Mavericks lots - Mavericks lots - Weak components Overstress Weak components - Overstress - Default from production - Wrong spec, bug Wear-out failures

6 Constant failure justification q Early failures due to flaws in manufacturing process are only observed on a small part of the population, these failures are becoming very low with a screening activity in place. Furthermore, a great quantity of failure mechanisms at equipment level can be observed: F It is impossible to model these phenomena by Weibull distribution q Catalectic failures are usually modeled by the exponential distribution or Homogeneous Poisson Process (HPP) q Premature wear-out failures are only observed on few components. Following Occam s razor principle, as Early failures, HPP model is better than Power Low Process (PLP) model when the number of failures is low [REF04]. q Wear-out mechanisms, during DFR activities, are released after the service life. Even, in some cases, it is not possible, renewal process (AGAN maintenance) at component level leads to an approximately behavior of the failure rate [REF0]. q Drenick [REF03] has proven that this assumption is correct for a series system with a large number of components and maintenance actions. Constant failure rate model

7 Non-repairable system Reliability background Reliability requirement Probability of mission success R t ( t) = exp ( ) λ u. du 0 Reliability metric Failure mechanism block architecture Failure rate Catalectic failure Series system Constant failure rate Independent events λ = n i= λ i

8 Repairable system Reliability background Reliability requirement Reliability metric Failure mechanism MTBF Failure intensity Product maturity MTBF = exp t ( ) = λ( u) m t 0 + ( m( t) ). exp( m( u) ). du Homogeneous Poisson Process 0. du whatever System architecture Series system Poisson Process superposition MTBF = = n λ λ i= i Improvement Maturity Deterioration

9 FIDES physical modelisation q Physical failure rate / intensity is based on Cox models defined by: ( t, X ) λo( t) AF( X ) λ = Physical. where λo is a base failure rate in reference conditions AF is an acceleration factor based on Physic Of Failure X is stress vector t is the calendar time q Constant failure rate / Intensity ( X ) o AF( X ) λ = λ Physical.

10 q Component reliability prediction is very difficult as: Base failure rate estimation Reliability improvement with technology change (Moore s Law is still valid since 964). Physic of failure mechanisms change with technology. λ Physical ( X ) = λo. AF( X ). Πinduced λ 0 can be determined by using: Reliability tests take a long time and will be very expensive: High pressure on development time and cost in combination with high level requirement on reliability for systems with increasing complexity. Has to be done for all electronic components. Manufacturers reliability data report: However for the same equivalent component the reliability can be different. In FIDES, λ 0 was calculated from multiple semiconductor providers: Need more data for statistical reasons. Multisource could be used or supplier could change during lifetime of the equipment. Observation time of the λ 0 is limited due to fast technology change.

11 Base failure rate estimation q Base failure rates are estimated from manufacturer test. This is the component intrinsic reliability and are based on manufacturer reliability tests as follows: Sigle Signification C.I. Discrets Passifs HTOL High Temperature Operating Life X X HTS High Temperature Storage X X HTRB High Temperature Reverse Bias X HTGB High Temperature Gate Bias X HAST Humidity Accelerated Stess Test X THB Temperature Humidity Bias X X H3TRB High Humidity, High Temperature X Reverse Bias PCT ou AC Pressure Cooker Test / Autoclave X TC / TS Temperature Cycle / Thermal Shock X X X

12 FIDES physical modelisation q Physic of Failure are based on modified GLL models [REF02] : L s ( X ) exp α + α g ( X ) = i=. 0 i i i where s is the number of stress α is a parameter vector of the corresponding POF law L is given quantile of the underlying distribution q Acceleration factors are so given by: AF ( X ) ( Xo) ( X ) s L = = exp α. i L i= q Acceleration factors are based on POF [REF05]: [ g ( Xo ) g ( X )] i i i i Stress Steady-state temperature Thermal cycling Vibration Humidity POF Law Arrhenius Law Norris-Landzberg Basquin Hallberg - Peck

13 POF in FIDES : example of Arrhenius law theory FIDES physical modelisation q Chemical reactions (not only for gas) are active by steady-state temperature. This reaction rate R(T) was proposed by Svante Arrhenius [REF07] as follows: a ( ) = C.exp K. T b R T The Boltzmann constant Kb, which links the temperature T to the energy E Kb.T, gives a mechanical significance to the temperature notion. This fundamental constant hasn t sense for a particle and is defined only in the limit of statistical physic i.e. the limit of a great number of particles (~ 0 23 ). The constant C is specific to the reaction and is the fastest reaction that could ever proceed if the temperature is very large. Arrhenius argued that molecules must acquire a minimum amount of energy, called activation energy E a to get transformed into chemical products. He also argued that the proportion of molecules that have kinetic energy greater than Ea can be calculated from Maxwell Boltzmann distribution. E

14 FIDES physical modelisation q Arrhenius concept and reasoning have been widely accepted and widely applied not only to chemical reactions but also to various physical processes involving solids. The inventors of the transistor (Bardeen, Shockley & Brattain) were physicists and this is perhaps why Arrhenius law have been widely used in reliability physics problem during the last 50 years or so to assess the reliability for semiconductor materials and devices. q The reaction rate depends in fact of the proportion of particles having a minimal energy called activation energy. The activation energy is characteristic of the failure mechanisms meaning that failure mechanisms are more or less sensitive to temperature Low activation energy High activation energy

15 FIDES physical modelisation If we take the example of the Peck law. We have 2 stress (RH & T), so s=2 è Set g (RH)=ln(RH) and g 2 (T)=/T. We obtain: AF ( T RH ) = exp α ( ln( RHo) ln( RH )) + α, 2 To T è AF( T RH ) = exp[ α ( ln( RHo) ln( RH ))] exp α, 2 RH è ( ) AF α T, RH = exp α 2 RHo To T To T with α = 2 p and α = Ea Kb

16 λ Physical ( X ) = λo. AF( X ). Πinduced Based on: physics of failures (JEDEC Failure Mechanisms and Models for Semiconductor Devices - JEP 22G, nov 20) and Accelerated stress tests (Mechanical, Humidity, temperature cycling) were done over 6 boards to validate assumptions taken in FIDES on physics of failures. Acceleration factor estimation 99,00 Use Level Probability Weibull 90,00 50,00 Cumulative density function 0,00 5,00,00 Beta=2,4494, a=8,9462e+6, n=0, , ,00 Time

17 Integrated Circuit Acceleration factor for Thermal Stress Arrhenius law Reciprocal of the Boltzmann s constant. In an operating phase Π Thermal = e ( T + 273) j component Activation energy Ea is adapted to each type of component. 0.7 ev is for active components [3] (semiconductors). This value has been chosen after an analysis that shows that this was -for current technologies- the only acceptable value. An identified alternative was to make the activation energy variable with temperature, Ea = f(t ); this was a bit too complicated to calibrate (to improve in the future). In a non-operating phase: Π Thermal = 0 In non operating phases, this factor is zero. The total failure rate will not be zero because of additive part of the model (the other contributors). The Pi_thermal is especially complemented by the Pi_RH (humidity) for non operating phases.

18 Integrated Circuit Acceleration factor for Thermal cycling Norris Landzberg Π Tcy for soldier joints : Effect of constraints relaxation Effect of temperature amplitude Effect of maximum temperature ,2 2 Nannual-cy min(θ cy,2) ΔTcycling 33 ( Tmax cycling + 273) e t annual 2 20,9 Conversion cycles to failure rate 33K is to compare to the maximum temperature in the cycle. As the "reference cycle" chosen for FIDES is of 20 C and the reference ambient temperature of 20 C, this make a reference maximum cycle temperature of =33K. Π Tcy for case : 604 0,2 2 Nannual-cy ΔTcycling 33 ( Tma x cycling + 273) e tannual 20 4

19 Inverse Power Law Integrated Circuit Acceleration factor for Vibration The value of.5 is at the bottom of the range of values usually encountered in Basquin's law uses. This is because the failure mechanisms accelerated by vibrations are numerous and not restricted to fatigue (for example: move of particles). And even only for fatigue, the materials to cover are also numerous. This leads to this low exponent. The value of.5 is relevant for reliability prediction, not to accelerate testing. There is a specific warning on this topic in the FIDES guide 2009 page 43 Π Mech = G RMS 0.5.5

20 Integrated Circuit Acceleration factor for Humidity Peck Law Indeed the most common values seen for this exponent in Peck's law are between 2.7 and 3, but several trials have shown that a power of 4.4 is more realistic for non-operating conditions. As this law is mainly used for non-operating phases in FIDES, the value of 4.4 has been taken. 4, RH Π RH = ambient ( T + ) board-ambient e Effect of humidity Effect of temperature The reference relative humidity is taken at 70% (average world humidity). It is true that in a building the RH is lower is often lower because of heating or air-conditioning (see also the FIDES Guide page 40-42) In some way, the humidity factor replaces the thermo-electric factor for non-operating phases.

21 λ Physical ( X ) = λo. AF( X ). Πinduced Acceleration factor determination Tests results are globally matching FIDES parameters and validate its approach. Tests results include bonding and solder joints failures. Discrepancies between FIDES and tests results due to the fact that tests were done on supplied boards (Π RH not null)

22 λ Physical ( X ) = λo. AF( X ). Πinduced Induced factor estimation Reliability tests cannot reveal all possible failures: Tests are not done in the final environment and cannot reflect the complexity of the whole system e.g. interaction between equipments. Experience from field returns shows that main failures are catalectic and due to EOS, humans errors, Those failures cannot always be recreated during the tests. Those types of failures cannot have a Cox representation because there is no physics of failure behind them. Therefore, an audit with qualitative questions is done. The result is a coefficient between to 00. Because of the additive form of the failure rate, these modelisations cannot be put directly in equation because the audit result is not a failure rate. => A multiplicative form has been chosen

23 TERMINOLOGY AGAN : As Good As New COTS : Component On The Shelf DFR : Design For Reliability GLL : General Log Linear HASS : Highly Accelerated Step Stress HAT : Highly Accelerated Test HPP : Homogeneous Poisson Process MTBF : Mean Time Between Failure PLP : Power Law Process

24 Document reference [REF0] : Statistical Methods for the reliability of repairable systems Steven E.RIGDON & Asit P.BASU Wiley 2000 [REF02] : Modeling & Analysis for Multiple Stress-Type Accelerated Life Data Adamantios METTAS 2000 PROCEEDINGS Annual RELIABILITY and MAINTAINABILITY Symposium [REF03] : «The failure law of complex equipment» R.F.DRENICK J.Soc.Indust.Appl.Math.960 Vol 8 N 4 [REF04] : The effect of assuming a HPP when the true process is a PLP Steven E.RIGDON & Asit P.BASU Journal of Quality technology 990 [REF05] : JEDEC Standards JEP22G [REF06] : FIDES Guide 2009 [REF07] : «Über die Reaktion-geschwindigkeit bei der Inversion vor Rhorzücker durch Sauren S.ARRHENIUS Z. Phys.-Ch., 889.