The effects of accelerated aging on optical components : Application to vehicle camera systems

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Master Thesis 30 hp | Biomedical Engineering

Spring 2019 | LiTH-IFM-A-EX-19/3639-SE

The effects of accelerated aging on optical

components

Application to vehicle camera systems

Marina Baric

Examiner: Sergiy Valyukh

Supervisor: Roger Magnusson

Supervisor at Veoneer: Tomas Eklöv

2019-06-18

Linköpings universitet

SE-581 83 Linköping

013-28 10 00, www.liu.se

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2019-06-10 Department of Physics, Chemistry and Biology

Linköping University

URL för elektronisk version

ISBN

ISRN: LITH-IFM-A-EX--19/3639--SE

_________________________________________________________________

Serietitel och serienummer ISSN

Title of series, numbering ______________________________

Språk Language Svenska/Swedish Engelska/English ________________ Rapporttyp Report category Licentiatavhandling Examensarbete C-uppsats D-uppsats Övrig rapport _____________ Titel Title

The effects of accelerated aging on optical components

Författare

Author

Marina Baric

Nyckelord

Accelerated aging, adhesives, optical focus, tensile strength, Arrhenius, Eyring, Lawson, Peck

Sammanfattning

Abstract

Companies providing products have many requirements, both from standards and customers, that they need to comply with in order to be able to sell their product. Veoneer AB is a leading automotive machine vision supplier, providing mono, stereo, night vision and driver monitoring systems consisting of both electronic, mechanical and optical components. These systems have to withstand certain environmental tests in order to assure the lifetime of the total systems. Since the life time is usually several years accelerated tests are used that correspond to a few weeks or months. The tests used at Veoneer are specified for electronic equipment and what Veoneer does not know today is if the accelerated environmental tests stated for electronic equipment are relevant for the optical component of the vision system.

In this master thesis project two different accelerated environmental tests, dry and damp heat, have been chosen in order to investigate the effect of temperatureandrelativehumidityontheadhesiveintheopticalcomponentconnectingthe sensor and lens. The optical components where characterized by measurement of focus position and mechanical strength. Different combinations of temperature and relative humidity where chosen in order to compare the effect of different stress levels but also for the purpose of deriving parameters needed for accelerated testing models such as the Arrhenius, Eyring, Lawson and Peck model.

Amongst the results from this thesis work is the focus shift measurement which follows the same trend as seen in previous research regarding the effect of temperature and relative humidity on adhesives. With an exponential distribution being seen in different directions for the respective stresses. Pull tests show a greater degradation with higher stress levels, where one test case shows the greatest degradation. Calculations regarding activation energy and constants for models match previous research where one model, combining temperature and relative humidity, shows similar values as found in literature. Calculations also show that standard accelerated life time tests overexpose adhesives due to calculations of test times with lower activation energies.

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Companies providing products have many requirements, both from standards and customers, that they need to comply with in order to be able to sell their product. Veoneer AB is a leading automotive machine vision supplier, providing mono, stereo, night vision and driver monitoring systems consisting of both electronic, mechanical and optical components. These systems have to withstand certain environmental tests in order to assure the lifetime of the total systems. Since the lifetime is usually several years accelerated tests are used that correspond to a few weeks or months. The tests used at Veoneer are specified for elec-tronic equipment and what Veoneer does not know today is if the accelerated environmental tests stated for electronic equipment are relevant for the optical component of the vision system.

In this master thesis project two different accelerated environmental tests, dry and damp heat, have been chosen in order to investigate the effect of tempera-ture and relative humidity on the adhesive in the optical component connecting the sensor and lens. The optical components where characterized by measurement of focus position and mechanical strength. Different combinations of temperature and relative humidity where chosen in order to compare the effect of different stress levels but also for the purpose of deriving parameters needed for acceler-ated testing models such as the Arrhenius, Eyring, Lawson and Peck model.

Amongst the results from this thesis work is the focus shift measurement which follows the same trend as seen in previous research regarding the effect of tem-perature and relative humidity on adhesives. With an exponential distribution being seen in different directions for the respective stresses. Pull tests show a greater degradation with higher stress levels, where one test case shows the greatest degradation. Calculations regarding activation energy and constants for models match previous research where one model, combining temperature and relative humidity, shows similar values as found in literature. Calculations also show that standard accelerated lifetime tests overexpose adhesives due to calcu-lations of test times with lower activation energies.

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Företag som tillhandahåller produkter har många krav, både från standarder och kunder, som de måste följa för att kunna sälja sin produkt. Veoneer AB är en ledande leverantör av aktiva säkerhetssystem för bilar. Veoneer tillhandahåller olika system med både elektroniska, mekaniska och optiska komponenter. Dessa system måste klara vissa miljötester för att försäkra hela systemets livslängd. Eftersom livstiden är vanligtvis flera år används accelererade tester som motsvarar några veckor eller månader. De tester som används vid Veoneer är specificerade för elektronisk utrustning och vad Veoneer inte vet idag är om de accelererade miljötesterna som anges för elektronisk utrustning är relevanta för den optiska komponenten i deras visionsystem.

I detta examensarbete har två olika accelererade miljöprov, dra and damp heat, valts för att undersöka effekten av temperatur och relativ fuktighet på limet i den optiska komponenten som förbinder sensorn och linsen. De optiska komponen-terna har karakateriserats genom mätning av optisk fokusposition samt mekanisk styrka. Olika testfall, kombinationer av temperatur och relativ fuktighet, har utförts för att jämföra effekten av olika stressnivåer men också för att härleda parame-trar som behövs för accelererade testmodeller som Arrhenius, Eyring, Lawson och Peck.

Bland resultaten från detta projekt visar fokusskiftmätningen samma trend som föregående forskning visat angående effekten av temperatur och relativ fuktighet på lim. En exponentiell fördelning ses i olika riktningar för respektive stress. Dragprov visar en större nedbrytning med högre stressnivåer, där ett testfall visar störst nedbrytning. Beräkningar avseende aktiveringsenergi samt konstanter för modeller matchar tidigare forskning där en modell, som kombinerar temperatur och relativ fuktighet, visar liknande värden som hittades i litteraturen. Beräkningar visar också att standardiserade accelererande livstidstester överexponerar lim på grund av beräkningar av testtider med lägre aktiveringsenergier.

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I would like to thank the department of Physics, Chemistry and Biology at Linköping university and especially thanks to my examiner Sergiy Valyukh and supervisor Roger Magnusson for both help and examination of my master theis project. I would also like to thank Veoneer Sweden AB for giving me the chance of doing my master thesis project with both financial and technical support. Especially to my supervisor Tomas Eklöv for both providing me with this opportunity and sup-porting me trough all steps. A big thanks to the whole team of optics at Veoneer in Linköping for all technical support and advice given through the project.

Linköping, June 2019 Marina Baric

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1 Introduction 1 1.1 Background . . . 1 1.2 Problem . . . 1 1.2.1 Scope . . . 2 1.2.2 Problem formulation . . . 2 2 Theory 4 2.1 Standards . . . 4 2.1.1 IEC . . . 4 2.1.2 ISO . . . 7

2.2 Accelerated lifetime testing . . . 9

2.2.1 Test environments . . . 9

2.2.2 Arrhenius model . . . 10

2.2.3 Eyring model . . . 13

2.2.4 Lawson model . . . 14

2.2.5 Peck model . . . 14

2.2.6 Activation energies for materials in optical systems . . . 15

2.3 Optical systems . . . 16

2.4 Properties & faults of optics . . . 17

2.4.1 Optical focus . . . 18

2.4.2 Resolution . . . 20

2.5 Optical aberrations . . . 22

2.5.1 Monochromatic aberrations . . . 23

2.5.2 Chromatic aberration . . . 24

2.6 Physical aging of materials due to T and RH . . . 24

2.6.1 Glassy materials . . . 24

2.6.2 Adhesives . . . 25

2.6.3 Metals . . . 29

2.7 Surface energy & Surface tension . . . 30

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3.2.1 List of materials . . . 35

3.2.2 List of used Software . . . 36

3.3 Reset of OCs . . . 36

3.4 Characterization . . . 36

3.4.1 Through Focus . . . 36

3.4.2 Pull force test . . . 37

3.5 Variation of Camera Modules . . . 38

3.6 Accuracy of TF set up . . . 39

3.7 Accelerated environmental tests . . . 40

3.7.1 Dry heat . . . 40

3.7.2 Damp heat . . . 41

3.7.3 References . . . 42

3.7.4 STD for each TF measurement for each case . . . 42

3.8 Activation Energy, Acceleration factor & Service time . . . 42

3.8.1 Activation energy for T . . . 43

3.8.2 Constants for RH . . . 43

3.8.3 Acceleration factor & Time of service . . . 44

3.9 Activation energy, constants for RH, acceleration factors and ser-vice time with previous values . . . 44

4 Results 46 4.1 Focus Shift over time . . . 46

4.2 Curve fitting . . . 47

4.2.1 Temperature . . . 47

4.2.2 Relative Humidity . . . 49

4.3 Arrhenius, Eyring, Lawson and Peck plot. . . 49

4.4 Activation Energy, constant for RH, Acceleration factor & Service time . . . 52

4.4.1 Activation energy . . . 52

4.5 Acceleration Factor & Time of service . . . 52

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5 Discussion 56

5.1 Problem formulation . . . 56

5.1.1 How does aging related to temperature and humidity affect optical systems and its components theoretically? . . . 56

5.1.2 How does the optical focus position and mechanical strength for an optical system shift during accelerated environmental lifetime tests? . . . 57

5.1.3 Is there a correlation between the effect on the optical fo-cus and pulling force needed and theory regarding aging of optical systems? . . . 57

5.1.4 What numbers can be derived for activation energy, relative humidity constants, acceleration factor, and test time in the experiment? . . . 58

5.1.5 Are the standards and models used for accelerated lifetime testing relevant compared to achieved results? . . . 59

5.2 Test set up . . . 60

5.3 Pull test . . . 61

5.4 Optical parameters . . . 61

6 Conclusions & Future work 63 6.1 Future work . . . 63

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1 Representative figure of the optical component used in this master

thesis project. . . 2

2 Arrhenius plot derived from three different points at different tem-peratures. . . 11

3 Arrhenius plot with two different slopes representing two different activation energies. . . 12

4 Two optical systems. An optical component with a sensor and an eye. . . 17

5 Ray tracing from an object through an optical system creating an image [19]. . . 18

6 MTF curve over spatial frequency with three different curves [19]. . 22

7 Atomic structure for metals, glass and polymers [23]. . . 25

8 Plot of volume change over temperature for adhesives including physical aging at a temperature Ta[33][27][28]. . . 27

9 Plot of volume change over time with the effect of temperature and relative humidity [36] [29] [37] [34]. . . 28

10 Steps performed for every TF measurement. . . 34

11 Values at foi plotted over focus position in order to derive focus shift. 37 12 Plot of focus position from initial characterisation over all OCs in order to find larger deviations from mean. . . 39

13 Plot of focus position for one OC measured 20 times in order to find STD. . . 40

14 Plot of average focus shift over time for all tests. . . 46

15 Plot of average focus shift over time in test 1. . . 47

16 Plot of average focus shift over time in test 2. . . 47

17 Plot of average focus shift over time in test 3. . . 48

18 Plot of average focus shift over time in test 3 without first TF mea-surement. . . 48

19 Plot of average focus shift over time in test 4. . . 49

20 Plot of average focus shift over time in test 5. . . 49

21 Arrhenius plot in order to find activation energy. . . 50

22 Logarithmic plot with Eyring model in order to constant B. . . 51

23 Logarithmic plot with Lawson model in order to find constant b. . . 51

24 Logarithmic plot with Peck model in order to find constant n. . . 52

25 Plot of average pull force for test 1,2,3 and 6. . . 54

26 Plot of average pull force for test 4,5 and 6. . . 54

List of Tables

1 IEC standard for electronic systems and environmental test with dry heat. . . 5

2 IEC standard for electronic systems and environmental test with damp heat. . . 6

3 "Principal effects of single environmental parameters" stated in IEC 60068-1. . . 7

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5 ISO standard for optics and photonics and environmental test with

dry and damp heat. . . 8

6 Values for activation energy and constant for the different models [17] . . . 15

7 Values for activation energy and constants for the different models [15] . . . 15

8 Values for different failure mechanisms and their activation energy [10] . . . 16

9 Values for different failure mechanisms and their activation energy [18]. . . 16

10 Approximate surface energy of different solid materials [41][39][42][43]. 31 11 Test set up for accelerated lifetime tests. . . 33

12 Procedure performed in order to restore physical properties. . . 36

13 Procedure during dry heat test. . . 40

14 Procedure during damp heat test for test 4. . . 41

15 Procedure during damp heat test for test 5. . . 41

16 Values for acceleration factor and service time with activation en-ergies of 0.4, 0.6 and 0.8 eV and service time of 56 days. . . 45

17 Values for acceleration factor and service time with previously pre-sented values for activation energy, B, b and n from table 6 and service time of 56 days. . . 45

18 Values of tests 1 - 3 in order to find activation energy Ea. . . 50

19 Values of tests 4 and 5 in order to find constant for RH. . . 50

20 Activation energy and contants derived for the different models. . . 52

21 Acceleration factor and time of service at ambient T. . . 53

22 Acceleration factor and time of service at ambient T and RH. . . . 53

23 Calculated test time for a service time of 15 years for the different models for each test environment. . . 53

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• a.u. - arbitrary unit

• ESD - Electrostatic Discharge • foi - frequency of interest

• IEC - International Electrotechnical Commission • ISO - International Organization for Standardization • MTF - Modulation Transfer Function

• OC - Optical Component • PBC - Printed Curcuit Board • STD - Standard Deviation • TF - Through Focus • UV - Ultra Violet

Glossary

• Activation energy - Energy needed for a chemical reaction to happen • Corrosion - A electrochemical reaction where a material in an unstable state

reacts with the surroundings in order to reach a more stable state • Dry heat test - Test including just High Temperature, without humidity • Damp heat test - Test including the both temperature and relative humidity • Equilibrium - A energetically favourable state at which a material is in

bal-ance

• Glass transition temperature (Tg) - The temperature at which amorphous

materials go trough a gradual transition from a glassy state to a rubbery state

• Hydroxyl group (OH−) - A functional group that provides binding sites for hydrogen bonding

• Optical aberration - A property of a optical system or lens that make light rays deviate from their normal behaviour

• Pull force - Force required to pull until breaking

• Refraction - Change of a direction of a wave, for example light, passing from one material to another

• Relative Humidity - Amount of water vapour, humidity, present in air relative the saturation point at a given temperature

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Physics Constants

T Absolute Temperature K

RH Relative Humidity %RH

Tservice Service Temperature °C

RHservice Service Relative Humidity %RH

Ttest Test Temperature °C

RHtest Test Relative Humidity %RH

tservice Time of service years

ttest Time of test days

tf Time to failure days

AT Acceleration Factor (for T)

AT /RH Acceleration Factor (for T and RH)

Ea Activation energy eV

kb Boltzmans Constant eV/K

A Pre-exponential Factor (frequency factor) s−1

k Rate Constant s−1

Tg Glass Transition Temperature °C

Tm Melting Temperature °C

Ta Aging Temperature °C

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1

Introduction

Veoneer AB is a leading automotive machine vision supplier within the realm of active safety, providing mono, stereo, night vision and driver monitoring systems. A system within active safety is a system that helps avoid accidents where as passive systems help to reduce the effect of the accident such as seat belts. Their products contain electrical, mechanical and optical components. In this master thesis project the effect of accelerated aging on the adhesive used in the optomechanical component is investigated and analyzed.

1.1

Background

In the optics team at Veoneer Sweden AB in Linköping, they develop an optical system of a vision system working with both design and test. According to an article by NBC news from 2006, the average car lifespan is around 8 years or 150,000 miles and a well-built 21st century cars lifetime is approximated to 15

years and 300 000 miles [1]. In order to qualify the durability of the systems to withstand 15 years in a vehicle accelerated lifetime tests are performed, specified by standards and sometimes extended by the customer. In order to shorten the test time in comparison with the actual expected life span of the product, accel-erated lifetime tests are used to estimate the life span for products where lifetime data is unavailable. There are several different types of accelerated lifetime tests: high temperature, fast temperature ramps, vibration, high temperature + high hu-midity, sun radiation, salt spray and mechanical shock. By performing accelerated life testing, the test time is shortened down from the wanted test span to months or days.

1.2

Problem

The optics team at Veoneer Sweden AB has seen that there are unwanted sys-tem effects after performing accelerated life tests. This could be due to the fact that the developed vision system contains electrical, mechanical and optical com-ponents. The problem with the stated accelerated lifetime tests is that the tests

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are originally specified for electrical systems. Since optical and electrical sys-tems consist of different materials having different properties, the tests performed might not be optimal and might therefore cause unwanted system effects. If the tests underestimate the lifetime of units, there is a risk of field returns and if the tests overestimate the lifetime of units the system might be over specified causing unnecessary testing time and resources. Customers of Veoneer Sweden AB pro-vide specified accelerated lifetime tests, originally from IEC and ISO standards, in order to qualify the vision system. Today it is not known if there is a correla-tion between the accelerated lifetime tests and optical lifetime performance which might be the cause for damages and focus drift observed.

1.2.1 Scope

The area of testing optical systems is quite broad and therefore specific tests are chosen according to areas of interest from the optics team at Veoneer Sweden AB and academic background of the student involved. The main focus chosen for this master thesis project is to investigate the effect of the accelerated lifetime tests performingdry heat and damp heat in steady state on the adhesive used in the optical system. The chosen system effects that have been characterized are the focus shift and mechanical failure. Figure 1 represents the optical component used in this project.

Figure 1: Representative figure of the optical component used in this master thesis project.

1.2.2 Problem formulation

This project will be performed in order to answer the following questions:

1. How does aging related to temperature and humidity affect optical systems and its components according to the previous research?

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2. How does the optical focus position and mechanical strength for an optical system shift during accelerated environmental lifetime tests?

3. Is there a correlation between the effect on the optical focus position and mechanical strength observed in the experiment and the theory regarding aging of optical systems?

4. What numbers can be derived for activation energy, relative humidity con-stants, acceleration factor, and test time in the experiment?

5. Are the standards and models used for accelerated lifetime testing relevant in comparison to achieved results?

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2

Theory

In the theoretical part of this master thesis project, the standards stating environ-mental accelerated lifetime test will be represented as well with tests often used in industry. This will be followed with the theory regarding different models used for accelerated tests. Parameters used in the models will be taken from the lit-erature. The part regarding the accelerated lifetime tests will be followed by the theory of optical systems, with focus on optical focus and image resolution, as well as the theoretical aspects related to materials science, with consideration adhesives, and the effect of temperature and humidity.

2.1

Standards

The standards stated in this master thesis deal with accelerated lifetime tests and specifically dry heat and damp heat tests. All tests are performed at con-stant/steady state environment. If there is no separation between the cells in the tables there is no specific determined combination of temperature, relative hu-midity and duration of the test. The standards are not always specified when it comes to choosing a severity for a specific product instead this is often specified by a company. Though there are some general severity’s used, these are stated in section 2.2.

2.1.1 IEC

IEC 60068 is a standard defining environmental testing of electrical, electrome-chanical and electronic equipment and devices, their sub-assemblies and con-stituent parts and components. IEC 60068 is stated only for electrical equipment and there is nothing about optics or mechanics. It is also mentioned that the standard reference ambiance is T=20 °C with the wide range of relative humidity being 60 to 70 %RH [2]. Tables 1 and 2 show the defined test conditions for dry heat [3] and damp heat [4].

The severity of a dry heat test can be chosen by different means, stated by IEC 60068-2-2 it can be: [3]:

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• chosen from the values given in table 1

• "derived from the known environment if this gives significantly different val-ues or"

• "derived from other known sources of relevant data (for example IEC 60721)" Table 1: IEC standard for electronic systems and environmental test with dry heat.

Standard Environment T (°C) RH (%RH) Duration (h)

60068-2-2 Dry heat +30 +125 +35 +155 +40 +175 +45 +200 +50 +250 +55 +315 +60 +400 +65 +500 +70 +630 +85 +800 +100 +1000 - 2 22222222222222 1622222222222222 72 22222222222222 96 22222222222222 168 222222222222 240 22222222222222 336 22222222222 1000

When choosing the severity for a damp heat test the IEC 60068-2-78 states "Un-less otherwise specified in the relevant specification, temperature and relative humidity severities may be selected from the following" [4].

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Table 2: IEC standard for electronic systems and environmental test with damp heat.

Standard Environment T (°C) RH (%RH) Duration

(h or days) 60068-2-78 Damp heat 30 ± 2 85 ± 3 22 93 ± 3 12h 2222 16h 2222 24h 2222 2days 4days 10days 21days 56days 60068-2-78 Damp heat 40 ± 2 85 ± 3 22 93 ± 3 12h 2222 16h 2222 24h 2222 2days 4days 10days 21days 56days

In appendix A of the Environmental Engineering Handbook published by SEES, Swedish environmental engineering society it is stated that the duration of a test is not specific in standards such as IEC 600721, that is referenced to in IEC 60068. It is also stated that the standards should mainly be used as aid when choosing the environments [5].

IEC 60068-1 includes a list of "Principal effects of single environmental parame-ters" that states some principal effects and typical failure resulting from a certain environmental parameter. Table 3 states the effects for high and low temperature and high and low relative humidity [2].

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Table 3: "Principal effects of single environmental parameters" stated in IEC 60068-1.

Environmental parameters

Principal effects Typical failure resulting

High 222222

temperature

Thermal ageing: oxidation,

cracking, chemical reactions. Softening, melting, sublimation. Viscosity reduction, evapora-tion. Expansion

Insulation failure, mechanical failure, increased mechanical stress, increased wear on mov-ing parts due to expansion or loss of lubricant properties

Low 222222

temperature

embrittlement. Ice formation. Increased viscosity and

solidi-fication. Loss of mechanical

strength. Physical contraction

Insulation failure, cracking, me-chanical failure, increased wear on moving parts due to con-traction or loss of mechanical strength and to loss of lubricant properties, seal and gasket fail-ure.

High 222222

relative 222222

humidity

Moisture absorption or

adsorp-tion. Swelling. Loss of

me-chanical strength. Chemical re-actions: corrosion, electrolysis. Increased conductivity of insu-lators

Physical breakdown, insulation failure, mechanical failure

Low 222222

relative 222222

humidity

Desiccation. Embrittlement.

Loss of mechanical strength.

Shrinkage. Increase of

abra-sion between moving contacts

Mechanical failure, cracking

2.1.2 ISO

ISO 16750-4 is a standard for road vehicles defining environmental conditions and testing of electronic equipment for climatic loads. The 16750 standard does either not mention anything about optics or mechanics. ISO 16750-4 refers to IEC 60068-2-2 for dry heat and to IEC 60068-2-78 for damp heat. Table 4 shows the specific standards for dry heat and damp heat. In this case there is only one severity [6].

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Table 4: ISO standard for electronic systems and environmental test with con-stant high temperature and damp heat.

Standard Environment T (°C) RH (%RH) Duration

(h or days)

16750-4 High-temperature 85 - 48h

16750-4 Damp heat 40 ± 2 85 ± 3 21days

ISO 9022-2 is a standard for optics and photonics defining environmental test methods and conditions for cold, heat and humidity. According to ISO 9022-1, "Optics and photonics - Environmental test methods - Part 1: Definitions, ex-tent of testing" an optical instrument is defined as: ”instrument whose function is mainly based on optical phenomena, consisting of several assemblies and/or components, illumination systems, instruments with light condition and instru-ments which, apart from optical units, contains assemblies and/or omponents from other fields” [7]. Table 5 below shows the specific standards for dry heat and damp heat including stated severities [8].

Table 5: ISO standard for optics and photonics and environmental test with dry and damp heat.

Standard Environment T (°C) RH (%RH) Duration

(h or days) 9022-2 Dry heat 10 ± 2 <40 16h 40 ± 2 <40 16h 55 ± 2 <40 16h 63 ± 2 <40 16h 70 ± 2 <40 6h 85 ± 2 <40 6h 70 ± 2 <40 2h 85 ± 2 <40 2h 9022-2 Damp heat 40 ± 2 90-95 24h 40 ± 2 90-95 4days 40 ± 2 90-95 10days 40 ± 2 90-95 21days 40 ± 2 90-95 56days 55 ± 2 90-95 6h 55 ± 2 90-95 16h

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2.2

Accelerated lifetime testing

Accelerated lifetime tests are performed in order to shorten the test time for a product. Since a cars lifetime is expected to be around 8-15 years it would not be reasonable for a company to test the product for the same amount of time. Due to this accelerated lifetime tests are performed by increasing different stress levels and decreasing the time. The test times are derived through different equations stated in this section.

2.2.1 Test environments

Accelerated lifetime tests are performed according to the standards that are usu-ally not specific. As a rule, customers usuusu-ally have their own specifications where they state more specifically the stress levels for the tests performed at and they usually refer back to the standards. There are some regularly used levels for both dry heat and damp heat tests. These stress levels are usually much higher than measured in real life but are used since they decrease the testing time to a great extent. When it comes to temperature, different standards state different levels but most often the stress level for temperature is stated according to the maximum temperature that the product can withstand without breaking. There is also a de-pendency on the application when choosing the test time. For example a PCB, printed circuit board, used in a mobile phone needs a shorter lifetime span than the PCB in a car. The temperature load can also depend on where the product is placed in a car: the hood, the passenger compartment or at the front windshield. A product in the hood demands a better reliability since there a bigger heat de-mand. For damp heat tests there is one test often used. In the book of Applied Reliability Engineering, written by Marvin L. Rush and Willie M. Webb they dis-cuss reliability of electronics. In chapter 9.3.1, Traditional Temperature/Humidity Test, they state that the most frequently employed accelerated lifetime test is the the 85/85 or 85°C/85%RH test. It was produced by Western Electric in the 1960s and is usually performed for 1000 to 2000 hours. The test will allow penetration of humidity into the encapsulation and show corrosion effects [9]. The 85/85 test is also mentioned in other articles regarding reliability of electronics [10].

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In the automotive industry there are some regularly used temperatures and du-ration’s used within accelerated lifetime tests and dry and damp heat. 85/85 is the most common regarding damp heat tests and can be seen at various compa-nies such as Panasonic, Bosch, Toshiba and Ericsson. They all use a duration of 1000 h according to found specifications [11][12][13][14]. The dry heat tests are different for the four companies. Panasonics dry heat test is performed at 150 °C for 1000 h [11], Bosch use 125 °C for 2000 h [12] and Ericsson also use 125 °C but for 1000 h [14]. Toshiba also has a duration of 1000 h but does not state its maximum temperature [13].

There are several models that can account for how long a test should be per-formed. Such tests are usually an extension of the regularly used model, the Arrhenius equation. The tests are often used but there are doubts since the tests are often in steady state and different environments are tested separately which is not the case in real life. Following sections describe some models often used in industry related to the types of materials or components tested. There are more models then described in this project for relative humidity but the chosen bring different ways of accounting for the stress level. According to the book "Failure Modes and Mechanisms in Electronic Packages" by Puli-gandla Viswanadham and Pratap Singh models used for constant stress all have a exponential distribu-tion [15].

2.2.2 Arrhenius model

The Arrhenius model is used when calculating the rate of a chemical reaction, such as corrosion, with the effect of temperature. The model is stated as:

k = Ae−EakbT (1)

Where k is the reaction rate or the rate until failure, A is the pre-exponential factor, a constant, Eais the activation energy which tells us the amount of energy needed

for the chemical reaction to happen, kb is boltzmans constant (8.617 * 10−5 ev/K)

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loga-rithm of equation 1 one can get the activation energy, Ea, and the constant A by

creating an Arrhenius plot.

ln(k) = −Ea kb

(1

T) + ln(A) (2)

Where ln(k) on the y axis, (1/T) on the x axis, ln(A) represents the intercept with 0 and -Ea/Kb represents the slope. In figure 2 an example of an Arrhenius plot is

shown with inserted values of three different points, failure times, over T [16].

Figure 2: Arrhenius plot derived from three different points at different tempera-tures.

In the Arrhenius equation one can have the reaction rate k or the inverse of the time to failure tf on the left hand side since they both become a rate of s−1. When

performing accelerated lifetime tests one can calculated the test time, ttest, by

dividing the time of service, tservice for a system with the acceleration factor. The

acceleration factor tells at which rate we test our product compared to the service time depending on at which temperature one performs the test. So if the Tservice

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factor will be 1. AT = tservice ttest = e(−Eakb (( 1 Ttest+273.15)−( 1 Tservice+273.15)) (3)

Where AT is the acceleration factor. By using equation 3 one can use

tempera-tures used for test and get the testing time needed in order to match the service time [10].

Figure 3: Arrhenius plot with two different slopes representing two different acti-vation energies.

Higher temperature gives a higher acceleration and therefore a shorter test time. Same goes for the activation energy. 15 years for a reaction with higher activa-tion energy will represent a shorter test time than the reacactiva-tion with low activaactiva-tion energy. This can be seen in a Arrhenius plot with more than one line. Figure 3 shows two different linear distributions representing two different activation ener-gies. The reaction with higher activation energy, Ea1, is more sensitive to

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then for the reaction with lower activation energy, Ea2. A reaction with lower

acti-vation energy is less dependant of temperature and will more likely occur [16].

2.2.3 Eyring model

The Eyring model is an extension of the Arrhenius model, combining tempera-ture and another thermomechanical stress, such as voltage or relative humidity. It is often used for electronic systems and an example where it is used is the standard MIL-HDBK-217. MIL-HDBK-217, by the Department of Defence in the U.S., provides tests for reliability of electronic equipment by the use of the Eyring model when accounting for temperature and other stress factors [10]. In the book of Bo Carlsson regarding Lifetime Technology and chemical stress, published by the Swedish Environmental Engineering Society, the Eyring model is stated as a model for describing the effect of temperature and relative humidity. Specifically it is recommended when describing the initial corrosion of metals in the interval of 60-95 %RH [5].

k = Ae−EakbT− B

RH (4)

Everything in the Eyring model is the same as for the Arrhenius equation but with the addition of the relative humidity level. B is an constant describing the effect of relative humidity. And the acceleration factor can be calculated as for the Arrhenius equation. AT /RH = tservice ttest = e(−Eakb (( 1 Ttest+273.15)−( 1 Tservice+273.15))−B(( 1 RHtest)−( 1 RHservice))) (5)

Where AT /RH is the acceleration factor including both temperature and relative

humidity, RHtest is the relative humidity used in test, RHservice is the ambient

rel-ative humidity and other factors are the same is in for the Arrhenius equation. If performing at least two tests at the same temperature but at different levels of relative humidity an Arrhenius plot can be made as in figure 2 and the x axis will be −Ea

kbT +

B

RH instead where the temperature part becomes a constant and the

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2.2.4 Lawson model

The Lawson model is also an extension of the Arrhenius model as it combines both temperature and relative humidity but here the relative humidity varies non linearly. The model is also used for reliability of electronics [10].

k = Ae−EakbT+b(RH 2) (6) AT /RH = tservice ttest = e(−Eakb (( 1 Ttest+273.15)−( 1 Tservice+273.15))+b(RH 2 test−RH2service)) (7)

All factors are the same as for the Eyring model except for the difference in vari-ation of relative humidity and a small b is used instead of B since the constant for relative humidity is not the same in the two models. If performing at least two tests at the same temperature but at different levels of relative humidity an Arrhenius plot can be made as in figure 2 and the x axis will be −Ea

kbT + b(RH)

2instead where

the temperature part becomes a constant and the relative humidity is known.

2.2.5 Peck model

The Peck model is also an extension of the Arrhenius model combining both temperature and relative humidity. The Peck model was derived by Örjan Hallberg and D. Stewart Peck in 1991 in order to calculate the effect of relative humidity on epoxy moulded encapsulations for semiconductor devices [17]. This model is different as it is not specified for electronics but electronic encapsulations.

k = A(RH)ne−EakbT (8) AT /RH = tservice ttest = ( RHtest RHservice )ne−Eakb (( 1 Ttest+273.15)−( 1 Tservice+273.15)) (9)

For the Peck model all the variables and constants are the same as for the other models except for the variable n and how the relative humidity is varied [17].If performing at least two tests at the same temperature but at different levels of relative humidity an Arrhenius plot can be made as in figure 2 and the x axis will be −Ea

kbT + nln(RH) instead where the temperature part becomes a constant and the relative humidity is known.

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2.2.6 Activation energies for materials in optical systems

Within electronic equipment there are several known activation energies for dif-ferent failure mechanisms used for calculations. In the article "Recent Humid-ity accelerations, a base for testing standards" written by Örjan Hallberg och D. Stwwart Peck they compare the Peck Model to models such as the Eyring and Lawson model. Table 6 shows the values that are used for the models in the article [17]:

Table 6: Values for activation energy and constant for the different models [17]

Model Activation Energy, Ea(eV) Constant for RH (B,b,n)

Eyring 0.65 304

Lawson 0.6 -0.00044

Peck 0.9 -3.0

In the book "Failure Modes and Mechanisms in Electronic Packages" by Puli-gandla Viswanadham and Pratap Singh they also discuss the field of reliability within electronics and in chapter 7 they present several failure models including Arrhenius, Eyring, Peck and Lawson. They also represent a table with values for activation energy and constants for relative humidity [15].

Table 7: Values for activation energy and constants for the different models [15] Model Activation Energy, Ea(eV) Constants for RH (B,b,n)

Eyring 0.65, 0.71, 0.30, 0.20, 0.60 304, 528, 296, 61, 304

Lawson 0.6 -0.00044

Peck 0.54, 0.60 -4.55

There are differences in the signs of the values for the different models depending on how the acceleration factor is calculated and if the test factor is subtracted with the ambient factor or the other way around.

For the Arrhenius equation the website EDN Network, an electronics community for engineers, provides the values in table 8 for different failure mechanisms for semiconductor devices, the activation energy Ea for the temperature and for the

relative humidity: Eyring Model: B = 296, Peck Model: n = -4.5, Lawson model: b = 5.57 * 10−4[10].

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Table 8: Values for different failure mechanisms and their activation energy [10] .

Failure Mechanism Activation Energy, Ea (eV)

Oxide defects 0.3 - 0.5

Bulk silicon defects 0.3 - 0.5

Corrosion 0.45

Assembly defects 0.5 - 0.7

Electromigration 0.6 (Aluminium line) 0.9 (Contact)

Mask or photoresist defect 0.7

Contamination 1.0

Charge injection 1.3

The book "Reliability Improvement with Design of Experiments" by Lloyd W. Con-dra discusses reliability and mentions different models for accelerated testing, The book also mentions values for the activation energy and constants for rela-tive humidity for semiconductor devices. Table 9 shows values for different failure mechanisms for Ea[18]:

Table 9: Values for different failure mechanisms and their activation energy [18].

Failure Mechanism Activation Energy, Ea (eV)

Metal Migration 1.8

Charge injection 1.3

Ionic contamination 1.0 - 1.1

Gold-aluminium intermetallic growth 1.0

Corrosion in humidity 0.8 - 1.0

Electromigration in aluminium 0.5

Electromigration of silicon in aluminium 0.9

Time dependent dielectric breakdown 0.3 - 0.6

Electrolytic corrosion 0.3 - 0.6

Gate oxide defects 0.3

2.3

Optical systems

The most common optical system of all is the eye. It is the human bodies own vision system providing a visual picture of our surroundings. Similar to an optical system an eye consists of a lens and also a retina which is the sensor of the eye where the viewed object is depict. Other optical systems with only one lens are magnifying glasses and eye glasses. Cameras, microscopes and telescopes are examples of optical systems including several lenses. All of the mentioned

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systems are lens systems belonging to dioptrics, the study of light refraction. Light refraction, changed direction of light, happens when a light passes from one material to another with different material properties. For example when passing from air to a glass lens. The refraction can be measured by knowing the refractive index, n, where a material with a higher refractive index is more dense. Other then dioptrics there is catoptrics, mirror systems, studying the reflection of light [19].

Figure 4: Two optical systems. An optical component with a sensor and an eye.

Figure 4 is a representation of a camera and an eye. The camera consists of a sensor attached to a PCB and the PCB is attached to a body of lenses through an adhesive. The sensor is made out of pixels that by collecting light intensity can create an image. There are several lenses in the body that are combined in order to increase the performance of the camera. The distance between the lenses, often mentioned as one lens system or lens, and the sensor is a crucial factor when wanting to depict an object in the best way. The same goes for the distance between the lens and the retina in the eye [19].

2.4

Properties & faults of optics

Optical systems consist of different parts and different materials but the one thing they all have in common is that the lenses have to be placed and combined in order to get the wanted performance and avoid unwanted faults.

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2.4.1 Optical focus

As mentioned before the distance between a sensor and the lens system of a camera is a crucial factor to get the best image. Figure 5 shows a ray tracing from an object through an optical system. Rays of light will spread from an object in a spherical manner and some of these rays might reach an optical system of some kind, for example an eye. The rays from the object will cross the lens of the eye and refract. The refracted rays will eventually cross each other and the point at which these rays cross is where the image of the object will be formed. The point where the rays cross is called the focus position.

Figure 5 shows an optical system that has created an image of an object. The rays in the figure represents the rays of light from the object and the image is created through these rays. The optical axis of a optical system is a line vertical to the system and rays that cross the lens at the optical axis will not refract. Ray 2 shows this path. Every lens has focal length, f and f’. Rays parallel to the optical axis will pass through the focal point on either side of the system. Rays 1 and 3 show these paths. If an object is at infinite distance the rays will eventually be almost parallel which means that all the rays will focus at the focal point of the system and therefore the eye can see at infinite distance, for example the stars [19].

Figure 5: Ray tracing from an object through an optical system creating an image [19].

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the lens, one can use the thin lens equation: 1 f = 1 o + 1 i (10)

Where f is the focal point, i is the distance from the lens to the image and o is the distance from the lens to the object. When creating an optical system with a sensor the sensor should be placed at the wanted focus position in order to get the best image. For example if the object is at an infinite distance one would want to place the sensor at the focal length of the lens since the rays will be parallel to the optical axis when crossing the lens. The lens of the eye has a focal length as well but this focal length can change due to muscles in the eye. When the eye is relaxed the lens has one shape and can therefore get a focused image of infinite objects while a contracted eye muscle is better at focusing on objects near by. By contracting and relaxing the muscle in the eye the eye lens can have several focal lengths and this is why we can focus on objects at different distances. The human eye can focus on objects that are infinite when the eye is relaxed but it can only contract to a certain point which means that we have near point that states how close an object can be for us to be able to create a focused image. For a middle aged person this is roughly 28 to 40 cm [19].

Some people are near or far sighted which means that their eyes are not good at focusing on objects far away or near to the eye respectively and the eye has a focus shift. If a person is near sighted it means that the distance between the eye lens and the retina is increased compared to a regular eye and if a person is far sighted it means that the distance is decreased. This can be corrected by wearing eye glasses. By wearing eye glasses one puts a new lens in front of the eye which can then refract the light before it crosses the eye lens. Depending on near- or farsightedness one will want to refract the light at in different man-ners, converging or diverging the rays. Converging meaning the rays will refract to the optical axis and diverging being the opposite. If one is far sighted the eye is shorter and therefore the focus point will be after the retina. This can be cor-rected by using eye glasses with converging lenses which means that the rays will be refracted towards the optical axis forcing them to reach a focus point earlier,

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at the retina. The optical system in figure 5 consists of a converging lens. A near sighted persons eyes are longer and therefore the focus position is in front of the retina. By using eye glasses with diverging lenses the rays will refract from the optical axis and be forced to reach their focus position later than initially, at the retina. By knowing the focal lengths of all lenses involved and using equation 10 the focus position can be calculated and by adding lenses to the system one can correct for faults [19].

When creating a camera the distance to the photographed object has to be fig-ured out in relation to lenses and the sensor has to be placed correctly in order to get an image that is focused at the sensor. If one wants to depict objects at an infinite distance, creating parallel rays, a optical system consisting of an con-verging lens and a sensor at the focal point of the lens will often be enough to create an image. Though it is not often not that simple. Light rays are affected by other things and all light does not refract in the same way. Therefor optical systems often consist of several lenses. With several lenses the calculations are more advanced since the focal length of the lens closest to the object does not often have the same focal length as the lens closest to the sensor. Therefor the distance between the object to the lens system and the distance between the lens system to the sensor does not have to be the same. An object with larger distance from the camera than the focal point will create an image focused in front of the sensor. An object closer to the camera than the focal point creates an image that is focused beyond the sensor. All rays can be imaged on the sensor but there will be a difference in how good the images are compared to the object [19].

2.4.2 Resolution

A camera or an optical system has several critical properties. One important issue is the resolution. The resolution of a camera defines how good it can separate two different objects at a certain distance. The resolution can be measured through measuring contrast or also called modulation. A specific measurement is MTF, modulation transfer function, is defined by:

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M odulation = Imax− Imin Imax+ Imin

(11) Where I is the intensity measured. Imax and Imin are the maximum and minimum

value of a sinusoidal curve representing the intensity of the image over space, for example pixels, where white light is the maximum of 1 and black is the minimum of 0. The calculated modulation represents how well the camera depicts the ob-ject. Figure 6 below shows the MTF curve for three different positions or lenses inspired by Eugene Hechts book on Optics [19]. The three different curves rep-resents three different cameras or three different positions of an object with the same camera. In figure 6 the green curve gives the best image with the best focus and the other two curves, red and blue, represents two other positions of the object providing lower MTF. The spatial frequency on the x axis can be seen as every other black and white line that increase in frequency to the right. And therefore the MTF is in the range of 0 to 1. For just an optical system the line would be decreasingly linear but by combining an optical system with a sensor, the performance decreases [19]. When working with a sensor with several pixels the intensity over the pixels will be detected. Since the edge between black and white cannot be ideally imaged there will be a gray area as well. By taking the derivative of the intensity over pixels one can therefore get the pixel position with the largest intensity. By taking the Fourier Transform of the derivative we are able to get modulation, or intensity, over spatial frequency which is the MTF. [20].

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Figure 6: MTF curve over spatial frequency with three different curves [19].

The cut-off frequency in the figure is the frequency where a system cannot longer resolve the data [19]. The foi, frequency of interest, is chosen in order to derive the quality of the camera. Depending on what the objective for a camera is dif-ferent spatial frequencies can be chosen and the MTF at the chosen foi will be used. For example the human eye has the best focus in the range of 3 to 12 lp/mm at stated standard distances. The points on each curve crossing the foi line are points at a specific foi, frequency of interest, for a system that are cho-sen according to the the best resolution. In stead of choosing a specific foi the frequency where the MTF is 0.5, MTF50, can be found, represented by the pink dotted line in the figure. This is a common way of measuring the quality and is often a measure of comparison between cameras [21].

2.5

Optical aberrations

Geometrical optics is often not idealized and undesirable faults occur due to faults in design. A optical system often consists of more than one lens and the number

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of lenses in the system are placed in an order to avoid these undesirable faults which in the field of optics are called aberrations. Aberrations can be split in to two groups, chromatic and monochromatic aberrations where chromatic aberrations happen due to different light having different properties and wavelengths while monochromatic is faults with one specific light with a certain wave length. [19]

2.5.1 Monochromatic aberrations

Spherical aberration is an effect that is a result of a lens being spherical. As mentioned before all light rays parallel to the optical axis that strike a lens will be refracted towards and focused at the focal point of the lens. This is the case for an ideal lens, but lenses are not often ideal and therefore the parallel rays striking the lens further away from the optical axis will have a stronger refraction and focus at a point closer to the lens than at the focal point. This will result in the image not being as resolved since all rays will not hit the sensor at the wanted point [19].

Coma is a aberrations similar to spherical aberrations and is also a fault that refracts the light rays in a way deviating from an ideal optical system. The differ-ence to spherical aberrations is that it does not refract the rays in an symmetric way. So instead of the focused rays providing one bright image spot the image will be blurry and it will look as if the image has a tail [19].

Astigmatism means that a optical system does not refract rays in different per-pendicular planes the same way, they do not focus at the same point. So vertical and horizontal lines will not be sharp at the same point [19].

Field curvature aberration is when the image provided is not planar but instead rays that are not parallel to the optical axis will focus before the focal point and be projected in a curved manner relative the focal point providing a curved image [19].

Distortion is an aberration where the image is magnified more or less in dif-ferent parts. An image with a grid will provide a certain radius from the middle

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out to the corner edge, this radius will be increased or decreased in a distorted image. An image with decreased radius has Barrel distortion while a image with increased radius has Pincushion distortion whit magnified inner parts and outer parts respectively [19].

2.5.2 Chromatic aberration

Since lens equations are dependant of wavelengths different colour lights, with different wavelengths, provide different focus positions with the same lens. Using visible light, approximately 390 - 780 nm, the refractive index n will decrease with increasing wavelength λ and therefore the focal point will increase. This means that each wavelength provides a specific focal point [19].

2.6

Physical aging of materials due to T and RH

Since materials degrade with environment and time it is important to know their life span. When studying the aging of materials there is both chemical and physi-cal aging where chemiphysi-cal aging permanently changes the structure of the mate-rial where as physical aging is an effect on the configuration. Physical aging is the aging of materials in different environments such as temperature and compared to chemical aging, is not an structurally permanent changing effect and is there-fore reversible. During aging many physical properties of an material will change. [22].

2.6.1 Glassy materials

Glass and polymers both belong to the group of amorphous materials, glassy materials. Amorphous materials are different from for example metals in the their atomic structure which gives them other properties as well. While metals have a ordered 3D-structure amorphous solids have a broad range of atomic structures. Some amorphous solids such as glass, silica glass, have a more ordered atomic structure and therefore some of its properties are similar to metals while polymers have a more random ordered structure. Figure 7 shows a representation of the atomic structures of metals, glass and polymers [23].

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Figure 7: Atomic structure for metals, glass and polymers [23].

Amorphous materials such as silica and polymers might have different structure but they follow the same volume change over temperature since all amorphous materials have a glass transition temperature, Tg and at a higher temperature

they also have a melting temperature, Tm, while metals only have a Tm.

Optical lenses can be made of both polymers and glass. The two materials both belong to the group of amorphous materials but due to their different atomic structure they posses different properties such as the Tg. Regular soda-lime-silica

glass, used for example jars, has a Tg of approximate 600 °C [23] while a standard

polymers Tg is below 150 °C [24]. All amorphous materials will act similar over

time but since glass has a much more stable atomic structure it is less affected by the environment than polymers [23] though it can be affected by corrosion since it has a high surface energy which is explained in section 2.7.

2.6.2 Adhesives

When it comes to electronic systems, thermoset polymer adhesives are the most commonly used adhesive [25]. These types of adhesives can be cured by heat, moisture and also by curing with different methods such as UV and microwave [26]. Thermoset adhesives create a three dimensional network, cross-links, that are strong due to covalent bonds [27][28]. Thermoset adhesives are affected by temperature and will soften with increasing heat exposure but the process is reversible and the chemical nature of the polymer does not change. The most common type of thermoset adhesive is the Epoxy adhesive which is used for encapsulation, as glue, to make PCB laminates and for microelectronic system

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attachment [25] and due to the extensive use there is also a lot of research re-garding physical aging of epoxy adhesives [25][27][28][29][30] [31][32]. Epoxy adhesives can have a Tg up to more than 200 °C [24].

Figure 8 shows volume over temperature for thermoset adhesives where the area within the dashed lines represents the free volume inside the adhesive and the dotted line at Tarepresents the physical aging at a constant Ta[33][27][28].

Phys-ical aging is a process at which a material is exposed to an constant T, Ta, below

Tg, at a specific amount of time. This process occurs as the materials want to

reach the crystal equilibrium line. [27]. The free volume decreases with physical aging and makes the material more dense and brittle. The physical aging in-creases the Tg with some degree depending on the additives in the adhesive [29]

since the mobility within the adhesive is decreased [30]. Additives such as fillers, stabilizers and other agents used for property changes [25]. Due to cross-linking bonds within the adhesive the region of no free volume is rarely reached and the pink dotted line represents the volume that is reached with physical aging at Ta

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Figure 8: Plot of volume change over temperature for adhesives including physical aging at a temperature Ta[33][27][28].

Due to physical aging the adhesives mechanical properties change as well and overall the mechanical strength will increase [29] but since the material becomes more dense due to physical aging the material also becomes more brittle and therefore potential microcracking can occur and the tensile strength decreases [28] [27]. These properties can recover if the material is exposed to temperatures above Tg, this process is called rejuvenation [33].

Epoxy adhesives are hydrophilic due to the fact that they contain hydroxyl groups which can form hydrogen bonds with water molecules. Because of this the ma-terial is susceptible to moisture and will swell when in contact [34]. At ambient temperature and high moisture levels the process of water molecules entering the adhesive will follow Fickian diffusion which means that there will be a mois-ture uptake at a specific rate until reaching a saturation point which depends on the adhesive and its additives [29]. Fickian diffusion follows a exponential

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dis-tribution which is represented in figure 9 but Fickian diffusion does not account for volume decrease due to aging so a curve representing ideal Fickian diffusion would follow the saturation line to infinity [35]. Some adhesives will deviate from the process of Fickian difussion due to additives or other effects such as other stresses [29]. The moisture uptake is also effected by the temperature. When exposing a material to different levels of moisture at the same temperature it can be seen that saturation level increases with increasing relative humidity [36][34]. When increasing the temperature at the same level of moisture, absolute humid-ity, an increase in the rate of diffusion will be seen with increasing temperatures. [37] The combination of temperature and relative humidity for aging will initially mean diffusion of water molecules which will bring swelling of the adhesive and eventually the effect of aging with temperature will take over and an increase in the density will be seen. The increase in density will mean that the initial swelling will decrease [29].

Figure 9: Plot of volume change over time with the effect of temperature and relative humidity [36] [29] [37] [34].

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Figure 9 shows four different lines representing the volume change over time for different levels of both temperature and relative humidity [36] [29] [37] [34]. There are four different combinations of temperature and relative humidity by the use two different levels of temperatures, T1 and T2, and four different levels of relative

humidity, RH1−4. The pink lines represent the saturation region at each level of

relative humidity. The same color represents the same level of absolute humidity while the same type of line represents the same level of temperature. The line does not follow the saturation over time due to the physical aging overtaking and decreasing the volume. The diffusion of water into the Epoxy can be both a re-versible and irrere-versible effect. If there is a high chemical interaction the effect is not physical and permanent changes will occur [35].

Research also shows that the tensile strength and the Tg of the material

de-creases with increasing moisture content [29]. The Tg decreases due to the

in-creased mobility within the adhesive caused by hydrogen bonding between the water molecules and the adhesive [36].

There are several different epoxy adhesives on the market and their activation energy are in a broad range from approximate 0.5 to 1.0 eV depending on addi-tives used [37].

2.6.3 Metals

Metals also degrade over time and show the same effects as for glassy materials but since they have a more stable atomic structure the bulk will not be as easily effected by relative humidity. Physical aging with temperature generally shows an increase in strength of the material but decrease in fracture toughness making the material more brittle and creating micro cracks. Regions that are mostly effected by environmental changes are interfaces and grain-boundary regions such as cracks. At these sites the metal will, due to its high surface energy, react with the surroundings and this will lead to corrosion which one of the greatest problems with degradation of metals [38].

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2.7

Surface energy & Surface tension

Optical systems often consists of more then one type of material and there is more then one interface to account for. In an optical system such as an OC there is an interface between the lenses and the lens holder and also the interfaces to the adhesive. This is an important factor to address when discussing the reliabil-ity of the product with the effect of environmental stresses such as temperature and relative humidity.

Solid materials have a property called surface energy which tells us how much an material attracts other materials to its surface. Liquid material have a prop-erty with the same unit called the surface tension which tells us how strongly the material can hold together as in a droplet. The both properties come from a non-symmetric bonding of the molecules or atoms at the surface creating charged sites which opens up for an acceptor and donor bonding between two materi-als. A liquid will spread out on a solid material, substrate if its surface tension is lower than the surface energy of the substrate which means that the molecules of the liquid have a weaker interaction than the one between the substrate and the liquid. This is due to the fact that high surface energy substrates want to lower their energy [39]. To get the strongest possible adhesion between an adhesive and a substrate the substrate should have as high surface energy as possible. A stronger adhesion is also related to Tm of materials and it is seen that higher

Tm provides higher surface energy [40]. Table 10 shows the approximate

sur-face energy of some solid materials including metals, polymers and adhesives [41][39][42][43]:

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Table 10: Approximate surface energy of different solid materials [41][39][42][43].

Material Surface energy, γ (mJ/m2)

Epoxy adhesive 45 Water 73 Polymers 10 - 50 Glass 250-1200 Platinum 2500 Silver 1000 Copper 1000 Aluminium 500 Stainless steel 700-1100

An Epoxy adhesive has a surface energy of approximately 45 mJ/m2which means

that for a strong adhesion the substrate should have the same or higher surface energy than that. The surface of an substrate can be processed in order to get a higher surface energy by different techniques. To get greater adhesion roughen-ing of the surface is often performed by techniques such as: by usroughen-ing emery pa-per, grit blasting and etching. Surface activation can be performed as well which instead of removing material as with adhesion roughening uses techniques that activates the surface for a certain time creating a time slot at which the adhesion will be the best. Surface activation techniques include: plasma activation, UV, X-ray electron or ion radiation [39].

The surface energy and adhesion of materials is also effected by aging with tem-perature and relative humidity. Research has been performed to investigate if mechanical fracture most often occurs within the adhesive or if it is at interfaces to the other materials. Test performed with temperature and relative humidity be-tween metals and epoxy adhesives show a three step degradation, both cohesive and adhesive. The three steps are stated as: [44].

1. First days of exposure shows a cohesive degradation within the adhesive and a loss of adhesion due to modification in the highly stressed zones of the surface of the adhesive

2. After further exposure a loss in adhesion happens due to initiation of corro-sion

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3. Even greater loss in adhesion due to spread of surface corrosion

Another important factor is if the surfaces are clean. If there are unwanted parti-cles or dirt the adhesion will not be as good as wanted. This can cause unwanted degradation’s of the adhesive joint and breaks. Over all the adhesion between metals and polymers show a greater strength than the cohesive strength within in the adhesive which is a effect of the high surface energy of the metallic substrate which if processed correctly has great bonding sites [45].

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3

Method

The method section will describe the different measurement and characteriza-tion methods used and also how standard deviacharacteriza-tion is derived. Equacharacteriza-tions used for calculations for the different models for accelerated lifetime tests will also be provided. This will also include calculations with values for activation energy and constants provided in theory in order to make comparisons further on.

3.1

Test set up

Table 11 shows the six different accelerated environmental tests, cases, chosen for the experiment. Two dry heat and two damp heat test were chosen in order to see if the results match the theory about epoxy adhesives for different levels of stress. With two temperatures and two relative humidity levels a comparison can be made of the results as well. A third temperature was added to be able to see the relevance of the Arrhenius equation. By making a plot from two points one can see if the third temperature and rate matches. Test 6 was held as a reference group containing the OCs, optical components, with large deviation and also some random good OCs. Figure 11 shows the 6 different tests with environment and number of OCs.

Table 11: Test set up for accelerated lifetime tests.

AT Test T (°C) RH (%RH) Number of OCs

Dry heat 1 115 low 15

Dry heat 2 100 low 15

Dry heat 3 85 low 15

Damp heat 4 85 60 15

Damp Heat 5 85 85 15

Reference 6 Lab Environment Lab Environment 20

The three different dry heat tests are at high temperature to achieve high acceler-ation due to time constraints. With low temperatures the adhesive may not react fast and no effects of aging would be seen. Restrictions for the system are also considered when choosing the temperatures. Test 3 with 85 °C was also chosen in order to make a comparison with test 6 between adding relative humidity and

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without. Test 5 is a common environment for damp heat tests with electronics and was therefore chosen from start. The relative humidity level of test 4 was chosen lower than for test 5 due to restrictions defined in the Eyring model and also since it is often stated as a ambient level of relative humidity.

During the experimental phase the OCs have been in accelerated test cham-bers for both dry heat and damp heat and before TF measurement they have been cooled down and then taken out and measured so the OCs have not been measured continuously and have not been in the chambers continuously either. After measurement they have been inserted in the chambers again. After placed in chambers the data from the TF measurements have been collected. Figure 10 shows the 4 steps performed for each test case for every TF measurement.

Exact relative humidity is not stated for cases 1-3 since ambient relative humidity showed an approximate relative humidity of 20 %RH in normal lab temperature. Since the water vapour saturation value in g/m3increase with increasing

tempera-tures it means that 20%RH at 21°C gives a much lower relative humidity at higher temperatures. Due to this the relative humidity for cases 1-3 can be disregarded.

Figure 10: Steps performed for every TF measurement.

The OCs where exposed to a total test time of approximate 8 weeks to match test times stated in the stated standards from IEC and ISO where the maximum test time presented is 56 days which is 1344 h.

Figure

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