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  • Quality And Reliability OF Electronic ComponentsC.A. IgnatiousDD, VSSC (SR)

  • Definitions

    Reliability - The ability of an item to perform its required function under defined conditions for a stated period of time.

    Failure The termination of the ability of an item to perform its required function.

  • Degrees of FailureFailures may be SUDDEN (non-predictable) or GRADUAL (predictable). They may also be PARTIAL or COMPLETE.

    A Catastrophic failure is both sudden and complete.

    A Degradation failure is both gradual and partial.

  • Causes of FailureMisuse failures attributable to the application of stresses beyond the stated capabilities of the item.

    Inherent Weakness failures attributable to weakness inherent in the item itself when subjected to stresses within the stated capabilities of the item.

  • Cost-Reliability Functions

  • MTBF & MTTFMean Time Between Failures Applies to repairable items.

    Mean Time To Failure Applies to non-repairable items.

    Both of these terms indicate the average time an item is expected to function before failure.

  • Failure Rate vs TimeEarly Failures substandard components, manufacturing faults.Random Failures this is the useful lifetime of the item. Reliability is predictable in this region.End-of-Life Failures items reaching the end of their useful life. Also called the wear-out period. Because of the characteristic shape, this is commonly known as the Bathtub Curve.

  • Useful LifetimeReliability is predictable.R = reliability.t = time for which equipment is run.m = MTBFNote that R has no units. The prediction yields a number
  • ExamplesIf an item of equipment has MTBF of 500hrs, then the reliability for 100hrs operation is :-= 0.8187 (81.87% probability of survival)and if the equipment is operated for 1000hrs, the reliability will be :-=0.1353 (13.53% probability of survival)

  • Failure RateFailure unit = 1 FIT = 1 failure/1000000000 (9 zeroes) device hrsExample: System with 100,000 discrete parts, has one failure per month, then the failure ratel = 1 failure / 100,000/(30x24 hrs) = 14 E -9 = 14 FITSummary:FIT Failures/month # devices failing in 10 years10 0.7 0.1%100 7.0 1.0%1000 70 10%A failure rate of about 10 FIT is needed. At 1000 FIT there are about 2 failures/day and the entire system will be replaced over its life time

  • Testing Time to ReliabilityTesting and Proving Reliability is very Expensive as Illustrated in These Tables

    Table 1: For 100 devices on test FIT Test Time for 1 failure (Years) 10 114 100 11 1000 1

  • Accelerated TestingStresses are used to accelerate failure. For example temperature cycling is used to accelerate mechanical failure.

    Temperature Acceleration Voltage Acceleration Current Acceleration Humidity Acceleration

    Different failure mechanisms may be accelerated by different amounts for the same stress.

  • Accelerated LifeThe bathtub curve predicts a high early failure rate.

    Elevated temperatures are used to accelerate component aging and ensure that products move from the Early Failure area and into the Useful Lifetime area.

    The technique is used to pre-screen early failures during manufacturing.High temperatures accelerate all known chemical reactions. Almost all failure mechanisms associated with semiconductor devices are the result of a chemical reaction

  • Arrhenius Equation = Rate of the chemical reaction. = A constant.e = Activation energy in electron volts (eV) that is associated with the chemical reaction.K = Boltzmans constant. T = Absolute temperature.

  • Acceleration Factoris the elevated temperature.

    is the temperature for which the new reaction rate is calculated.

    Is the reaction rate at the elevated temperature.

    Is the reaction rate at The constant, , is the same for both temperatures and has been cancelled out of the equation

  • Acceleration FctorAcceleration Factor and Time Equivalent to 40 YearsTime Equivalent toAcceleration Factor 40 years in Hours Temp (C) Ea = 1.0 eV Ea=1.0 eV

    300 2.2e6 0.2 250 3.2e5 1.1 200 3.1e4 11 150 1700 200 125 300 1,200 85 11.5 30,000Temp Ambient = 60 C

  • Failure MechanismsElectrostatic DischargeAlpha-Particle-Induced Soft ErrorsRadiation Hard DevicesMetal ElectromigrationSodium Metal Migration in Gate OxideHot ElectronsOxide BreakdownLatch Up in CMOS CircuitsMetallisation Corrosion

  • Design & Manufacture

    Pre-Production Design Control of Production Working Tolerances Material Quality Component Quality Component StressInstallation & EnvironmentalTemperatureHumidityVibrationChemical AttackInterconnectionsFactors Affecting Reliability

  • Factors Affecting ReliabilityInstallation & Environmental

  • TemperatureGenerally, Operation at higher temperatures degrades reliability performance. Internally generated heat must be removed by mechanisms such as cooling fins or forced-air.

    In high ambient temperatures, the process of removing excess heat becomes more difficult.

    Equipment operating in low ambient temperatures will need to be designed using components which can tolerate this environment.

  • HumidityMoisture can cause oxidation and corrosion and reduce insulation effectiveness. Particularly vulnerable are solder joints and connectors. Equipment designed for use in areas of high humidity will use components and materials which are selected for their resistance to damage by moisture.

    Vulnerable components, such as circuit boards, can be protected by encapsulation e.g. in resin. Individual components may be hermetically sealed.

  • VibrationVehicles (cars, ships, aircraft etc) are particularly prone to vibration damage.

    Vulnerable equipment can use flexible mountings.

    Components on a PCB can be made less susceptible to vibration by the use of encapsulation.

    Vibration effects on electronic components has been minimised by the process of miniaturisation.

  • InterconnectionsInterconnections are liable to degradation by vibration, humidity and chemical factors. They are one of the most vulnerable components in an electronic system.

  • Factors Affecting ReliabilityDesign & Manufacture

  • Component ReliabilityTypical Failure Rates of Electronic Components

    ComponentTypeFailure Rate (%/1000h)CapacitorsCeramic0.001Paper0.005Tantalum0.01Electrolytic0.01DiodesSilicon0.001

    ResistorsCarbon0.001Wirewound0.001Film0.001

    TransistorsDiscrete Silicon0.01

    ConnectionsSoldered0.001

    ConnectorsPer Pin0.005

  • Operating Stresses Weighting Factors for Electronic Components

    ComponentOperating ConditionWeighting FactorResistors 0.1 of max. rating 1.0Transistors 0.5 of max. rating 1.5Diodes 1.0 of max. rating 2.0

    Capacitors 0.1 of wkg voltage 1.0 0.5 of wkg voltage 3.0 max wkg voltage 6.0}System Failure Rate = [(Component Failure Rate) x (Quantity) x (Weighting Factor)]Mil std 217 gives very detailed system failure rate prediction based on component failure rate and end use

  • IC Fabrication An Introduction

  • Integrated circuit showing memory blocks, logic and input/output pads around the periphery

  • Front-End Processing (Wafer fabrication) Back-End Processing (Assembly and Testing)

    Semiconductor Fabrication Processes

  • A logic circuit diagram is drawn to determine the electronic circuit required for the requested function. Once the logic circuit diagram is complete, simulations are performed multiple times to test the circuits operation. Logic Circuit Design / Layout Design

  • Photomask CreationThe photomask is a copy of the circuit pattern, drawn on a glass plate coated with a metallic film.The glass plate lets light pass, but the metallic film does not. Due to increasingly high integration and miniaturization of the pattern, the size of the photomask is usually magnified four to ten times the actual size.

  • The photomask of a RF IC Chip

  • Wafer Fabrication

    A high-purity, single-crystal silicon called "99.999999999% (eleven-nine)" is grown from a seed to an ingot.The wafers are generally available in diameters of 150 mm, 200 mm, or 300 mm, and are mirror-polished and rinsed before shipment from the wafer manufacturer.

  • Deposition

    the wafer is placed in a high-temperature furnace to make the silicon react with oxygen or water vapor, and to develop oxide films on the wafer surface (thermal oxidation).To develop nitride films and polysilicon films, the chemical vapor deposition (CVD) method is used, in which a gaseous reactant is introduced to the silicon substrate, and chemical reaction produce the deposited layer material. The metallic layers used in the wiring of the circuit are also formed by CVD, spattering (PVD: physical vapor deposition)

  • Photoresist Coating

    A resin called "photoresist" is coated over the entire wafer. (~1m thick coating.)Photoresist is a special resin similar in behavior to photography films that changes properties when exposed to light.

  • Masking/ExposurePlaced over the photoresist-coated wafer, which is then irradiated to have the circuit diagram transcribed onto it. An irradiation device called the "stepper" is used to irradiate the wafer through the mask with ultraviolet (UV) light.

  • Lithography area in clean room

  • Etching"Etching" refers to the physical or chemical etching of oxide films and metallic films using the resist pattern as a mask. Etching with liquid chemicals is called "wet etching" and etching with gas is called "dry etching".

  • Photoresist StrippingThe photoresist remaining on the wafer surface is no longer necessary after etching is complete. Ashing by oxygen plasma or the likes is performed to remove the residual photoresist.

  • Device Insulation Layer (Field-Oxide Film) Formation

    After the oxide film and nitride film are developed, a resist pattern is formed on the regions that will become the device insulation layer. Ion implantation is performed on the wafer, forming a p-type diffusion layer. Next, the oxide film and nitride film on the diffusion layer are etched. Using the nitride film pattern as the mask, the oxide film that will become the device insulation layer is developed.

  • Transistor Formation An insulation layer called "gate oxide" is first formed on the wafer surface. A polysilicon film is deposited onto the gate oxide, and a polysilicon gate for controlling the flow of electrons between the source region and the drain region is formed by lithography and etching. After the polysilicon gate is formed, an n-type diffusion layer consisting of both the source and the drain regions is formed by implantation of impurities

  • Polysilicon Gate Cross-Section Image

  • MetallizationInterconnecting the devices, such as transistors, formed on the silicon wafer completes the circuit. the wafer is first covered with a thick and flat interlayer insulation film (oxide film). Next, contact holes are drilled by lithograph and etching, through the interlayer insulation film, above the devices to be connected. Nine-layer Copper Interconnect Architecture

  • Wafer InspectionEach IC on the completed wafer is electronically tested by the tester. After this inspection, the front-end processing is complete.

  • DicingIn back end processing, a wafer completed in front end processing is cut into individual IC chips and encapsulated into packages.

  • MountingAfter the IC chips are cut apart, they are sealed into packages. The IC chips must first be attached to a platform called the "lead frame.

  • Wire bondingThe mounted IC chips are connected to the lead frames.

  • EncapsulationThe IC chips and the lead frame islands are encapsulated with molding resin for protection.

  • Characteristic SelectionThe packaged IC chips are tested and selected.

  • Printing and Lead FinishThe final step of IC chip manufacturing is the printing onto the package surface and the finishing of leads. After this step, the IC chips are complete.

  • Types and Causes of DefectsResistive open due to unfilled via [R. Madge et al., IEEE D&T, 2003]Particle embedded between layers

  • Process and Operational VariationsEven if there isnt a complete short or open, resistance and capacitance variations can lead to troubleChip temperature map

  • Yield and Its Associated Costs

  • The dramatic decrease in yield with larger dies

    Effect of Die Size on YieldShown are some random defects; there are also bulk or clustered defects that affect a large region

  • Effects of Yield on Testing and Part ReliabilityAssume a die yield of 50%

    Out of 2,000,000 dies manufactured, 1,000,000 are defective

    To achieve the goal of 100 defects per million (DPM) in parts shipped, we must catch 999,900 of the 1,000,000 defective parts

    Therefore, we need a test coverage of 99.99%Testing is imperfect: missed defects/faults (coverage), false positivesGoing from a coverage of 99.9% to 99.99% involves a significant investment in test development and application times

  • High-rel PartsSpace Grade parts Class S/JAN SMil grade parts ClassB/JANTX/JTXVQualified & Certified Production LineDevices produced as per Qualified ProcessProducts Qualified to Mil/Space level100 % Screening as per Mil Std/883 or Mil Std 750LAT/ Certificate for every batchStandard electrical/environmental Specification

    Very low failure rate

  • Mil Standards for Avionics Parts

  • QML PartsMIL-PRF-38535: "General Specification for microcircuits (IC) Manufacturing" - Supersedes MIL-M-38510Microcircuits manufactured, assembled, and tested according to MIL-PRF-38535 bear the "QML certification markClass Q: Hermetic products. Military level covered by MIL-PRF-38535 main body + appendixes C, D, E, F, G, H, J. Class V: Space level: class Q + appendix B requirements. Class M: covered by MIL-PRF-38535 appendix A. Require a vendor self certification. DSCC performs verification audit onlyClass N: plastic parts.

    QML Q = 883 Class B (Mil) ; QML V = 883 Class S (Space)

  • MIL-PRF-19500: General Specification for Semiconductor Devices

    Supersedes MIL-S-19500 ; Refers to MIL -STD-750 test methodsQuality levels: classes JAN, JANTX, JANTXV, JANJ, JANS Class JAN: Military level QCI OnlyClass JANTX: Screening and QCI without Visual inspectionClass JANTXV: JANTX with Visual inspectionClass JANJ: Space level product as defined in the specification sheet that can pass test and inspections in Appendix E for JANTXV as a minimum. Not available for all semiconductor devices.Class JANS: Highest Space level product

  • Standards for Hybrids

    MIL-PRF-38534/MIL-STD-883 are the controlling specifications for hybrids.

    Hybrids are made to class H or class K.

    Class H requirements form the baseline.

    The K level parts involve extra pre-build inspections of components, post-build inspections and testing

  • Passive Parts : Established ReliabilityThe reliability rating are established on the basis of life tests for various Failure Rates

    Exponential distribution with 60% confidence level and 10-percent producer's riskM : 1.0 % per 1000 hoursP : 0.1 % per 1000 hoursR: 0.01 % per 1000 hoursS : 0.001% per 1000 hours

    Weibull distribution with 90% confidence level B: 0.1 % per 1000 hoursC: 0.01 % per 1000 hoursD : 0.001% per 1000 hours

  • Capacitors (Established Reliability)

    Style and Type Reference SpecificationFixed Ceramic DielectricCKR/CKS>1uF, use CKS onlyMIL- PRF-39014Fixed Mica DielectricCMRMIL-PRF-39001Fixed Tantalum Solid ElectrolyticCSRMIL-PRF-39003Fixed Ceramic ChipCDRMIL-PRF-55681Fixed Tantalum Chip Solid ElectrolyticCWRMIL-PRF-55365Fixed Tantalum-Non Solid ElectrolyticCLRMIL-PRF-39006

  • Resistors (Established Reliability)

    Fixed Carbon Composition(Insulated)RCRMIL-R-39008Fixed Metal Film RLRMIL-PRF-39017Fixed Wire WoundRWRMIL-PRF-39007Fixed Wire Wound Power TypeRERMIL-PRF-39009Variable - Film/Foil RJRMIL-PRF-39035Variable Wire WoundRTRMIL-PRF-39015Fixed ,Film NetworksMIL-R 83401ThermistorRTHMIL-PRF-23648

  • Magnetic elements

    Power Inductors/ TransformersMIL-PRF-27MIL-PRF-21308RF fixed colisMIL-PRF-39010Chip inductors MIL-PRF-83446Variable inductorsMIL-PRF-15305

  • Connectors

    Style and Type Reference SpecificationCircularMIL-DTL-38999,MIL-C-26482D Sub miniature-Rectangular crimp type-Flat typeMIL-DTL-24308MicrominiatureMIL-DTL-83513Printed CircuitAngled spillsMIL-DTL-55302,MIL-C-24308Coaxial(RF connectors)MIL-PRF-39012MIL-STD-1553 Data BusMIL-PRF-49142Push pull connectors MIL-C-81703

  • Switches, fuses, wires and cables

    Push switchesMIL-PRF-8805FusesMIL-PRF-23419Coaxial cableMIL-C-17PTFE / Spec 55 insulated wiresMIL-DTL-22759/86MIL-W-16878MIL-W-22789

  • Quality level for launch vehicles

    MicrocircuitsParts listed in QML class Q/B Parts listed in ESCC/DSCC/ JAXA QPL including non-SDiscrete parts Jan TX/JTXVHybridsClass H/ Indigenous Class B/SPassive PartsEstablished Reliability level S / RRF and MicrowaveHigh REL parts (eg : HL grade)

  • Quality level for satellite applications

    MicrocircuitsParts listed in DSCC QML Class V/S or equivalent in QPL of ESCC /JAXA/ DSCC Discrete parts Jan SHybridsClass K/ Indigenous Class SPassive PartsEstablished Reliability level S / RRF and MicrowaveHigh REL parts (eg : SHL grade)

  • Parts to be avoided in new designsParts not qualified to MIL/ESA specParts that are obsolete and not availableParts listed in MIL/ ESA/ NASA/ ISRO alert system for quality issueParts having export license issueParts for which criticality and / or quality issues were faced in ISRO applications in the past (eg. LT1086)

  • The Preferred Parts ListComponents listed in the VSSC Preferred Parts List (PPL) only are used for launch vehicle applications. Part A : Parts listed in Part A are qualified as per MIL/ESA-SCC/ISRO GSS/BS9000 (Hi-rel MIL specifications) and are available as standard MIL parts from manufacturers.

    Part B : Parts which are not qualified to Hi-rel MIL specifications. These are non-MIL devices based on experience in usage and qualification tests conducted by VSSC.

    Part C : Parts which are not qualified to Hi-rel MIL specifications. These are non-MIL devices. based on experience in usage and qualification tests conducted by VSSC. Recommended only for Non-critical applications.

  • Parts quality- NASA experienceOne study Reviewed DODs satellite and missile systems and NASA systemsParts quality problems affected all 21 programs reviewedThey caused cost over runs and schedule delays. ($250M and 2 year delay in one case) More problems were associated with electronic parts (65%) than mechanical (15%) parts or materials (20%). Explained by presence of more electrical components than mechanical devices.US government recommends action for preventing, detecting, and mitigating parts quality problems

  • Parts Quality Assurance Requirements

    Assurance of procurement from qualified sources or their authorized distributors Quality Conformance Inspection (QCI) to ensure that each lot meets the specReceiving inspection to verify compliance with the controlling specificationsScreening to remove defective parts DPA to be performed when part is not QML /QPL and procured from traceable source

  • Application Criteria Requirements.

    Derating guidelines shall be met by the design

    Operating Environment requirement including temperature, humidity, shock, and vibration should be met by the part spec.For most space applications, military qualified parts will satisfy these requirements except for radiation

    Effects of the projected ionizing radiation on each part shall be determined. Failure mitigation or a design margin shall be established by the project

  • Manufacturing and handling requirementsESD control in accordance with MIL-STD-1686Environmental controls such as temperature and humidity during parts handling, packaging, and storage.Rescreening if a maximum period has elapsed since screeningProcured quantities should allow for nominal fallout of parts in screening.Parts should be ordered from a single date code for effectiveness of qualification Ensure part compatibility with planned manufacturing processes. Parts affected by ALERTS shall not be used in manufacturing Traceability : identifying which package contains specific part lots

  • Pure Tin finish on IC leadsPure tin (Sn) coatings mandated by regulations on leads and other surfaces of parts.Pure tin electroplates develop tin whiskers.May result in a visible "electrical shortThe short may result in fusing of the whisker, but the device would have damaged aleady.

  • Reliability analysis

    Failure mode effects and criticality analysisAnalyses the effect of each part failure modeRanks each failure mode based on criticality of the result and the probability of occurrenceWorst case analysis Verifies the circuit operation at all combinations of input conditions and part parametersCarried out by dividing to smaller blocksPart Stress AnalysisFailure rates increase exponentially with stress on part (voltage, current and power dissipation )Analysis ensures that stresses are below the maximum rating of the partSingle Event Effects Analysis

  • Failure rate of components - The bath tub curve

  • Nature of failures during life cycleInitial failures result from contaminations and process variations Such devices are removed by high voltage stress tests at wafer probing or by burn-in tests on packaged deviceRandom failures are triggered by electrical noise, electrostatic discharge and electrical overstress and enhanced by minor defectsWear out failures result from electro-migration, hot carrier effect, time dependent dielectric break down etc

  • Causes of field failure- EOS and ESDAn EOS event can be a momentary event lasting only milliseconds or can last indefinitely.EOS can be the result of a single g event or the result of ongoing periodic or non-periodic events.EOS is a lower voltage (10A) event that occurs over longer time frame (generally >1ms).ESD is a very high voltage (generally >500V) and moderate peak current (~1A to 10A) event that occurs in a short time frame (generally
  • Possible causes of EOS

    Uncontrolled voltage surge on the power supply.Voltage spikes due to internal PCB switching.Voltage spikes due to an external connectioncapacitive charge on an external cable, antenna pick-up of external switching noise, inductive loads.Poor grounding resulting in excessive noise.Overshoot or undershoot during IO switching.EMI due to poor shielding ESD events that weaken the device.Latch-up events

  • Non mil grade parts Availability of military standard electronic parts diminishing

    State of the art parts available only in commercial and industrial grades

    Devices in small foot print packages available Initial (acquisition ) cost is less.

    Wider operating temperature range (-55C to 125C) than standard industrial parts (-40C to 85C) available in some cases

  • Concerns with non mil partsTime to obsolescence in some cases is as low as one to two years; Re-procurement may not be possible. No alternate manufacturer for most partsA manufacturer uses a number of fabs, packaging houses, test houses etc. Reliability can vary from lot to lot. Traceability is poor. Many devices do not have even date code informationFailure analysis and DPA are difficult

  • Concerns with Non mil grade parts (contd..)Design compromises like reduced metallization and oxide layer thickness reduce reliability.

    Design for a life of less than 5 years is normalProcess changes incorporated by manufacturer are unknown to customers and may have negative impacts for space applications.

    Device may not have sufficient EOS/ESD protection built in to its designLack of characterization data for space environmentRadiation performance Insufficient environmental/ mechanical/ electrical testing

    Not following Design For Test practices result in low fault coverage

  • Additional Concerns with PEMSParts in plastic packages absorbs moisture leading to corrosion Popcorn effect due to absorbed moistureThermal cycling induced cracking, delamination, die detachment or damage to metal conductors Recommended to use metal clad PCBsTraces of radio active materials in molding compound lead to soft errors.

  • Failure rate comparison : mil and non-milFailure rate of PEMs from reputed manufacturers like Analog Devices,Texas etc. are comparable to Mil std parts.

    However, humidity and thermal cycling performance tend to be inferior.

  • NASA policy on usage of PEMsUse of PEMs is permitted on NASA spaceflight applications, providedEach use is thoroughly evaluated for thermal, mechanical, and radiation implications of the specific application and if found to meet mission requirements.PEMs shall be selected for their functional advantage and availability, not for cost savingThe steps necessary to ensure reliability usually negate any initial apparent cost advantage.A PEM shall not be substituted for a form, fit and functional equivalent, high reliability, hermetic device in space flight applications.

  • VSSC policy for induction of Industrial grade partsRecommended for Telemetry applications onlyIndustrial grade parts of higher reliability or temperature range (-55 C to 125 C) are preferredQMB approves the usage after consideringCriticality of the parameter for which the particular part has been selectedManufacturer assessmentDestructive Part Analysis ResultQualification test resultVSSC PPL lists industrial grade parts in a separate section.

  • Use of non mil parts in NGC applicationsMore stringent control needed in procurement, storage, qualification and screening for critical applications.

    Procurement should be only from reputed manufacturers

    Storage and ESD conditions prior to procurement should be known

    Procurement should be made in as few date code codes as possible and each lot should subjected to sample DPA and qualification.

    Screening flow to incorporate C-SAM test, which is found to be very effective in detecting cracks, debonds and delaminations.

  • Non-ER versus ER parts : Example of Multi-layer Ceramic Capacitors :

    AttributeNon-ERMIL-ERSmallest Chip Sizes0201 01005 (new to market)0805Lowest Voltage Ratings6.3 V50 VNo. of sourcesNumerousFewDelivery timeDays to weeksWeeks to MonthsProcurement CostsSmalllargeVendor Design RulesVariable & AggressiveStable & ConservativeQualification BasisNon StandardStandardProcess Material ChangeMore frequent, without notice to user Less frequent, needs re qualificationReliability Not knownPublished Failure rates

  • Technological Differences ER capacitors uses Precious Metal Electrodes (PME) like Palladium Silver; use of Base Metal Electrodes (BME) like nickel is prohibitedCommercial caps can make use of BME for cost saving. The firing process used with BME affects the insulating properties of barium titanate dielectricIn ER type MLCC, maximum value available is 1F.Values larger than 1F are available with COTSAchieved using thin dielectric(0.2mil) compared with mil for ER types (1.0 mil minimum)Process variations may induce voids and cracks in Commercial caps using thin dielectricCan result in short circuit failures

  • Structure of an MLCC

  • Use of non-ER parts

    Non-ER parts should be avoided as far as possibleIf essential,non ER parts should be selected from a Hi- Rel line. Use manufacturer- suggested Hi-Rel versions KEMET : GR900 series, High Rel COTSVISHAY : VJ High RelSYFER : S05,S02A seriesQualification should be carried out for each lot

  • Thank You

    ******Ciciani, B., Manufacturing Yield Evaluation of VLSI/WSI Systems, IEEE Computer Society Press, 1995. *Note that the product of defect density and die area is the expected number d of defects per die. If this expected number is very small, then, (1 + d/a)^(a) =approx 1/(1 + d) =approx 1 d. So, if we expect an average of 0.01 defects per die, say, the yield will be 0.99. For larger values of d, however, nonlinearity kicks in and yield is substantially reduced.**