AD

"-" INTRINSIC AND THERMAL STRESS MODELING

FOR THIN-FILM MULTILAYERS

TECHNICAL REPORT

A. M. Ledger and R. C. Bastien

The Perkin-Elmer Corporation

Norwalk, Connecticut 06856

Contract No. DA-25-76-C-'010

June 1977 -

DEFENSE ADVANCED RESEARCH PROJECTS AGENCY1400 WILSON BOULEVARD

ARLINGTON, VIRGINIA 22209

>u- Distribution of this document is unlimited

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's , ,/ INTRINSIC AND THERMAL "STRESS MODELING /FOR THIN-FILM MIULTIILaYERS

STECHNICAL REPORT- -.

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A.M. /Ledger / R. C. lastienA- -. /eder- . C/Bat

The Perkin-Elmer Corporation

N alcoknnecticrit 06856 ..

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Contr.w't No, PAA!-ý -?'-76-C-P414

Juno, 1977

DE•'ENSE ADVANCED RESEARCH PROJECTS AGENCY1400 WILSON BOULEVARD

ARLINGTON, VIRGINqA 22209

Distribution of this document is unlimited _,' c

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The findings in this report are not to b-e construed as an officialDppartw~ent of the Army positionunless so designated by otherauthorized documents.

ii

TABLE OF CONTENTS

Section Title Page

INTRODUCTION

2 STRESS MEASUREMENTS IN THIN FILMS 3

2.1 Stress Measurement Techniques 32.2 Stress Measurements - System Requirements 42.3 Stress Interferometer - Cat's Eye Design 5

2.3.1 Interferometer Configuration for VariableVapor-Incidence Angles 9

2.3.2 Data Acquisition and Data Recording System 92.4 Stress-Measurement System - Operational

Characteristics 132.5 Fringe Direction Sensing Using a Siugle Detector 132.6 Film Stress Data Reduction 162.7 Evaluation of Stress Measuring System -

Experimental Tests 21

S3 STRESS ADDITION AND TEMPERATURE EFFECTS IN THINFILM MULTILAYERS 24

3.1 Analytical Model Formulation 243.2 Derlection of Circular Plates Due to a Single

Stressed Film 263.3 Unit Stress Curve Fitting 293.4 Stress Relief Effects 313.5 Thermally Induced Stress 353.6 Stress Addition in Multilayer Films 36

4 INTRINSIC STRESS MEASUREMENTS 38

4.1 Material Selection 384.2 Deposition Conditions - Experimental 384.3 Intrinsic Stress in Thorium Tetrafluoride Films 38

4.3.1 Deposition Rate Dependence 384.3.2 Substrate Temperature Dependence 404.3.3 Dependence of Stress Upon Incidence Angle 404.3.4 Nonuniform Stress Distribution in 71F 4 Films 404.3.5 Stiess Coefficients for ThF 4 Films 40

4.4 Intrinsic Stress in Zinc Selenide Films 404.4.1 Stress Coefficients for ZnSe Films 454.4.2 Nonuniform Stress Distribution in ZnSe FiiLmt 45

4.5 Intrinsic Stress in Thallium Iodide and CeriumFluoride Films 45

iii

TABLE OF CONTENTS (Continued)

Section Title Page

5 MECHANICAL PROPERTY MEASUREMENTS 50

5.1 Expansion Coefficient and Young's ModulusDetermination for Thin-Film Materials 50

5.2 Experimental Results 52

6 SUMMARY AND CONCLUSIONS 55

REFERENCES 56

Appendix A WAVEFORM ASYMMETRY FOR CA'S-EYE INTERFERMETER 57

F

iv

Jt

LIST OF ILLUSTRATIONS

Figure Title Page

1 Cat's-Eye Interferometer b

2 Stress Interferometer 8

3 Variable Vapor-Incidence Angle Configuration 10

4 Stress Interferometer Array 11

5 Data Acquisition and Data Recording System 12

6 Fringe Pattern at Output of Stress-Measuring Interferometer 14

7 Intensity Variations 15

8 Fringe Count for a 0.5-un Thick Cer-Vit Disk DuringDeposition of MgF 2 15

9 Computer Waveform, Asyimmetry for Cat's Eye Interferometer 174 '10 Data Recording for Four Simultaneous Stress Measurementsfor ThF4 Deposited onto Cer-Vit Disks of Varying Thick-nesses at 200 0 C 18

11 Stress Datz Reduction of Data in Figure 10, ThF 4 -6Deposited onto Substrates of Various Thicknesses at 200%C 20

12 Instantaneous Stress Levels Computed for ThF 4 Depositedonto Cer-Vit Fused Silica and KCI under IdenticalConditions 23

13 Deflection of Disk due to a Single Stressed Film 28

14 Tensile Stress Produced in Thorium Fluoride Film MaterialDeposited at 37/s at 200 0 C 32

15 Compressive Stress Produced0 in Zinc Selenide Thin FilmMaterial Deposited au 4.4A/s at 150'C 33

16 Stress Relief Effects 34

17 Dependence of intrinsic Striss in ThF1 F s on Thickness 39

18 Intrinsic Stress Dependence of ThF 4 Films Qn substrateTemperature 41

19 Variation of Intrinsic Stress vith Incidtmce Angle forThF 4 Films Deposited at 150 0 C 42

20 Variation of Intrinsic Stress with Incidence Angle forThF 4 Films Deposited at 2000 C 43

21 Fringe Patterns Produced for Cracked Films Depositedonto KCi 44

S22 Variation of Intrinsic Stress in Zinc Selenide withDeposition Rate (Source Controlled). Stress measure-ments made using 0.25-= Cer-Vit disks at a substrate

* temperature of 200°C6

v

LIST OF ILLUSTRATIONS (Continued)

Figure Title Pag

23 Variation of Intrinsic Stress ir Zinc Selenide Filmswith Deposition Rate (Source Controlled). Stressmeasurements made using 0.25-mm Cer-Vit Disks at atemperature of 150*C. 47

24 Variation of Intrinsic Stress in Zinc Selenide Filmswith Deposition Rate (Source Controlled). StressMeasurements made using 0.25-mm Cer-Vit Disks at aSubstrate Temperature of 100%C 48

25 Intrinsic Stress in Cerium Fluoride Film Deposited at

230*C by Electron Beam Gun 49

26 Intrinsic and Thermally Induced Stresses in ThF FilmsDeposited onto Cer-Vit and KCI Substrates at 0°C 51

27 Fringe Changes for X/4 Film of ThF 4 Deposited onto KCIand Cer-Vit during Heating, Deposition, and Heat Cycling 53

vi

SECTION 1

INTRODUCTION

Multilayer dielectric coatings fabricated by thermal evaporation existin a stressed condition due to intrinsic stress buildup during deposition,combined with temperature-induced stress changes established during post-deposition cooling. The intrinsic stress levels found in thin films dependprimarily upon film thickness but are also influenced for some materials bythe evaporation rate and substrate temperature during deposition. After thefilm is formed in a vacuum at a given temperature, a reversible stress changecan occur due to differential contraction of film and substrate during cool-ing, and in some cases an irreversible stress change occurs when the film isvented to air. These stress levels greatly influence the durability of thinfilm structures when utilized under extreme thermal conditions such as inhigh energy laser systems.

Although stress levels in growing film structures have been measured andwidely reported during recent decades, little progress has been made 'n es-tablishing a quantitative link between induced stress and coating reliabilityfor multilayer dielectric coatings. The measurement of stress in thin filmstructures is only one important aspect of the dursbility problem; the otheris the adhesion between film and substrate and between individual films in qmultilayer stack. For instance, certain films can be deposited in a highlystressed condition and show good durability, a good example being chromiumwhich shows an intrinsic stress (_- 10,000 kg/cm2 ) two or three times greaterthan most materials. Evaporated deposits of chromium adhere so strongly thatthe glass substrate undergoes surface rupture as the film thickness approachesi-jim thickness.

£he 1 resent program was initiated to develop stress and adhesion modelsfor multilaer dielectric coatings in an attempt to predict the reliabilityand durability of thin film coatings. In particular, stress models of anti-reflection coatings for high expansion window materials such as potassiumchloride and calcium fiuoride were studied, since such materials producelarge thermally induced stress changes in the antireilection coating materialswhen subjected to high-power laser beams.

This report describes a stres- measurement system, stress models for thinfilms, and stress and material property measurements of thorium tetrafluoride,zinc selenide and thallium iodide films for use as materials for antiref1ec-tion coatings cn potassium chloride at 10.6 hm.

A new stress interferometer that measures both the magnitude and sign ofthe intrinsic stress in a coating during deposition was developed during theprogram and is described in Section 2. A system of four such stress inter-ferometers equipped with an automatic data recording system was utilized inconjunction with a 36-inch box coating facility to characterize the stress

profiles of several antireflection coating materials.

Stress models for multilayer coatings were also reviewed during the pro-gram and a computer code was completed to enable thermal stress modeling ofmultilayer coatings to be carried out. This theoretical phase is describedin Section 3.

The intrinsic stress behavior of two infrared coating materials, thoriumtetrafluoride and zinc selenide, was investigated in detail together with thestress properties of thallium iodide and cerium fluoride (Section 4).

Section 5 discusses a new method of measurement of the expansion coef-ficient and Young's modulus for thin film m~terials using the stress inter-ferometer system,

2

SECTION 2

STRESS MEASUREMENTS IN THIN FILMS

2. 1 STRESS MEASUREMENT TECHNIQUES

Thin films used for antireflection coatings in the 10-Vim region are de-posited n thicknesses of I to 2 km depending upon refractive index, andstress data has not previously been measured for such "thick" film structures.Previous measurement methods and experimental results for the stress proper-ties of metal and dielectric films have been comprehensively reviewed byHoffman (Refs. 1,2) and Kinosita (Ref. 3).

The intrinsic stresses developed in metal films have been measured bymany authors to develop theories of film nucleation and growth; however,stresses developed in dielectric films have not been inr.:&est.gated as thor-oughly. The two most comprehensive investigations of stress buildup in di-electric films were carried out by Campbell (Ref. 4) and Ennos (Ref. 5). The

A; stress behavior of various fluorides, bromides and iodides (LiF, NaF, NaCI,NaBr, KBr, KI) have been measured by Campbell using a capacitance bridgemrethod, whereas Ennos used a laser interferometer to measure intrinsic stressin a large variety of coating materials (ZnS, MgF2, ThOF2, PbF2, cryolite,chiolite, CaF 2 , CaF 3 , SiO, PbCl 2 , TICI, TlI, Ce, Te, CdTe) as a function oftheir deposition conditions. Many different measuremient techniques can beutilized for the measurement of intrinsic stress, most of which depend upondetecting the minute deflections of a thin glass beam or disk upon which thefilm is being deposited. Optical interference methods provide a very sensi-tive method of measuring such small deflections although capacitatIve andele-ctro-mechanical methods can also provide comparable sensitivities. Themeasurement of stress using electron diffraction as carried out by Halliday(Ref. 6) and X-ray diffraction ttchniques reported by Kinabara (Ref. 7) can

-* - also be used, but such techniques are not '• easily implemented as are thebec.dinv beam- and disk methods.

Although stress data exist lor many of the materials utilized for anti-reflection coatings for KC! windows, the mwasuremtents only provide the in-trinsic stress up to film thicknesses of several thousand angstrons. The useof new materials, higher deposýtion temp;eratures and deposition rates togetherwith improved v~catn systems necessitated r,-asuret-nt of thin film stressesfor such thick fi lms during the present program.

1. hiofman., Physics of TVi24 Films. Vol. 3, ý. 211 (1966).2 2. R.W. iloff •n, Thin Solid FiVlm, Vol. 34, p. 185ý (1976).3. k. KXncstta, Thon Solid Fillms, Vol. 17, p. 17 (1972).4. R.S. Carpenter aid D.S. Campbell, J. Matl. Ski., Vol. 2, p. 173 (1967).5. A.F. Fnnos, Applied Optirci. Vol. 5, No. 1, p. 51, (1966).6. J.S. Halihday, T.B. RymLr, and K.Hi.R. Foyght, Pr•. Poy. S'c. Londcn

A225, 548 (1954).7. A. kinabara, H. Harabi, J. Appl. PHYs., (Ja •¢n), Vol. 4. p. 243 (1965).I

Laser interferometry was chosen as the most useful technique, and asystem of four interferometers together with an automatic data recording sys-tem was designed and fabricated for use with a 36-inch metal box coating unit.This system enables stress measurements to be made rapidly and reproduciblyfor a variety of substrate configurations and deposition conditions and isdescribed in detail in this section.

2.2 STRESS MEASUREMENTS - SYSTEM REQUIREMENTS

The principal problem occurring in any cf the stress-measurement tech-niques mentioned previously is a thermal one. The amount of bending detectedin a beam or disk is due to both the buildup of intrinsic stress in the de-positing film and any nonuniform temperature existing radially or across thethickness of the disk. Calculations of the deflections expected for typicalstress levels in a thin film (100C-3000 kg/cm2 ) show that they are comparableto thermally induced distortions caused by front to back or radial gradientsin the thin substrate. Since deposition usually occurs at a fixed substratetemperature, such gradients can be initially minimized; however, thermalenergy from the source, heaters, and shutters can provide disturbing thermalfluxes and extreme care must be exercised to understand and compensate forthese factors if reproducible measurements are to be made.

The use of large disks or beams of extremely small cross section (50 to100 pm) increases the stress measurement sensitivity since the disk deflec-tion is proportional to the square of the aspect ratio (D/d). Unfortunately,thin disks are also increasingly susceptible to temperature effects and therelease of built-in stresses caused by polishing. Since stress data are pri-marily required for thick films (_ X/4 at 10.0 pm) for the present study, onecan utilize thick substrates in the 0.25- to l.0-rmm range. Accurate stressmeasurements can be made using thick substrates if deflections are recordedat a rapid rate on paper tape during deposition. The use of thick substratesnot only minimizes vibration problems and thermal effects but also allows manyother different materials, such as ZnSe, ZnS, Ge, KCI. to be used to form thedeformable substrate. It is nlot usually possible to polish such materials tothicknesses of 50 to 100 L1m without suffering a ver; low polishing yield andthe use of suth thin disks or beams becoas impractical for experi=ental pur-poses.

At the oitset of the program, a list of required -easuremen• capabilirieswas established to enable stress measure-ments to be made for both single andmultilayer films deposited under the kinds of conditiqns found in practice infabricating l0.6-%,m antireflection coatings. These capabilities inclued theuse of:

* Multiple stress interfe-rometers to enable stress measure.ents to bemade for different f l- I-aterials on both flexible and rigid sub-strates during s*=e evaporation cycle by the use of remote shutters

* Accurate deposition rate control by the use of a crystal fil, thick-nevs -ronitor that controls the input power t-' the source (electron gun)

* Variable vapor-incidence angles possible 2t each Interfercmeter

-4

i!I

* Rigid substrates (KCI) at equivalent deposition positions and inci-dence angles

* Both electron-gun sources and resistance sources

& Accurate optical film-thickness monitoring using a white-light sourceand spectral filter or monochromator

* Enclosed heater assembly to maintain the interferometers, opticalmonitor, and rigid substrates at elevated temperatures up to 2500C

* A semiautomatic data acquisition system to enable substrate deflec-tion data and optical film thickness to be recorded on paper tapefor subsequent computer data reduction

Four individual interferometers were designed and fabricated and mountedon a 36-inch stainless-steel box coater to enable the stress behavior of dif-ferent combinations of t•wo or more thin-film materials to be investigatedduring a single pumpdown. By the use of remote shutters and four interferom-

a• eters, stress data can be obtained for materials A and B alone as well as formaterials B on A and A on B on four different flexible and rigid substrates.

The details of the interferometer design, coating chamber configuration, anddata processing equipment are briefly described in the following paragraphs.

2.3 STRESS INTERFEROMETER - CAT'S EYE DESIGN

A previous laser interfermeter system used at Perkin-Elmer by Ennos(Ref. 5) consisted of a Michelson interferometer that detected changes in de-flection of a thin fused silica beam supported at both ends by ceramic knifeedges. The deflecting substrate forms one mirror of the interferometer andthe output fringe pattern consists of line fringes that move past a fixed dŽ-tector as the substrate deflects.

In practice, this type of interfetomet-r configuration was found to besensitive to vibration, and distortion of the interfero,,eter occurred at hightemperatures. Recently, a high temperature Nichelson interfcrotetLer designedfor UH3V applications has been described by Roll aM-d Roffman (Ref. 8). Ilhe-maldistortions are minimizcd in this design by obtaining an ititerferogram of thefull aperture of the bending uisk amJ by deducing the deflection from succes-sive photographs of the fringe psttern. Tilts and axial diltplacements of thesubstrate can be removed by computation but the "xthod requires substantialdata reduction time for each successive fringe pattern taken during deposition.

Thermal distortions and angular tilts between the two interfero,.eter mir-rors can be virt,;ally eliminated if the distancc between the two reflectingsurfaces is made very small and if the interferometer is arranged ;n the !ormof a cat's eye as show-n i., Figure 1.

The interfercneter consists simply of a glass element whose front surfaceis polished to focus the incident laser bea= onto two reflecting surfaces

8. K. Roll and Ii. Hoffman, Rev. Sci. 1ist., Vol. 47, No. 9 (1976).

5

6328A 50%, Reflecting Dielectric StackCollimated Laser Beam 50% Reflecting

Suprasil II Cat's-Eye Lens

lexible Substrate(Cer-Vit, Fused Silica,KCl)

jKai

~Figure I (, C!t'-q-LYc Tflterfer6meter

6

formed by the base of the cat's eye lens and the substrate upon which thefilm is being deposited. The base of the lens is coated with a hard dielec-tric reflector to reflect -50% of the incident beam at 6328 A and the de-formable substrate is coated on its top surface with a partially reflectingmetal coating. In most experiments a gold coating was used for this purposesince, when cold-deposited, gold has a low stress and has such poor adhesionto the substrate that it can be easily wiped from the surface. In addition,gold films can withstand high temperature baking without the occurrence ofexcessive recrystallization.

This interferometer configuration acts in a manner similar to a retro-reflecting mirror, and alignment is a simple task; however, the reflectedlight consists of a set of circular interference fringes that either expandor contract from the center as the substrate is deformed depending upon the

tensile or compressive nature of the film stress. A single silicon detectormounted in the center of the return fringe pattern enables not only the amountof deflection to be measured but also allows the direction of motion to bedetermined automatically from the fringe change recording.

Since the separation of the base of the cat's-eye lens and the deformingsubstrate is limited in practice to a few hundred micrometers, thermal expan-sion of the lens and substrate mount do not introduce serious fringe counterrors. For small separations between the two mirror surfaces the effect ofan angular change (AG) of the substrate is extremely small amounting to achange in optical path between the two apparent point sources of OPDD(Ae) 2 /2, where D is the separation between mirror surfaces. This insensi-tivity to angular tilts can be visualized if the distance between the mirrorsis made negligibly small; when this occurs the two spherical waves reflectedfrom both mirror surfaces slide inside one another and produce lateral shear-ing but no change in fringe patterns. In a similar manner, small changes inincident angles of the laser beam cause only a minute shearing of the compo-nent wavefronts that form the output fringe pattern.

The cat's-eye interferometer lenses used during the program were fabri-cated0 from Suprasil II and antireflection coated on the convex surface for6328 A. The flexible substrates of various thicknesses utilized during theprogram were fabricated from Cer-Vit, fused silica, KCI, germanium, zincsulphide and zinc selenide. Thicknesses of 0.25, 0.5, 0.75 and 1.0 nm were

used for the Cer-Vit and fused silica substrates, whereas 1.0-mm thick disksof the other materials were used because of the difficulty of polishing thinsections of these materials. Various spacers were fabricated for these dif-ferent thicknesses to maintain a constant separation between the two reflect-ing surfaces and thus provide an output fringe pattern of uniform size at thedetector.

The interferometer is illuminated with a 4-mm diameter collimated laserbeam (6328 A) produced by the interferometer laser source illustrated inFigure 2. The polarized beam from a 2-mW He-Ne laser is chopped by a synchro-nous chopper wheel and expanded to 4-mm diameter by a beam expander and spa-tial filter. A polarizing beamsplitter reflects approximately 1 percent ofthe "p" polarized laser beam to a silicon synchronous reference detector and

7

Spatial /Vewing ScreenSynchronou /Fringe De~tector

Synchronouschrnou

(2~ ~~~( XWle-eX4 lt

Polarized)g

(a) Stress Interferometer Configuration

(b) L~aser Interferomnter Source

Figure 2. Stress TnLerf.,roineter

transmits the remaining energy to the cat's-eye interferometer. A quarter-iwave plate located between the polarizing beamsplitter and interferometerrotates the polarization from "p" to 'Is" after two passes, and the returnfringe pattera is reflected by the polarizing beamsplitter to a fringe-countcdXtec*or and display screen. The polarizing beamsplitter/quarter-wave platesystem is used only to maximize the amount of light on the viewing screen andLs not fundamental to the operation of the interferometer system.

2.3.1 Interferomoter Configuration for Variable Vapor-Incidence Angles

Since stress levels in deposited films of certain materials are known tochange with vapor-incidence angle, it is desirable to configure the inter-fezomutei:s inside the chamber such that four different vapor-incidence anglescan be accommodated with minimal interferometer realignment. The additionof two small fold mirrors to the interferometer mount, together with an offsetin angle of the cat's-eye interferometer such that its axis passes through thevapor source, allows -ncidnce angles to be easily changed. Figure 3(a) illus-trates this conf.gur-tion and Figure 3(b) shows a photograpb of an interferom-eter head.

The vapor-incidence rigles attainable with either an electron-gun or re-sistance source 1 oci-ted in the center of the chamber are variable at each in-Lerferometer between 00 and 420 with the existing tooling. The four positionsallocated for rigid substrates are posi.ioned on the same radius as the inter-ferometer heads, a.id the vapor-ircidence angles of the rigid substrate canalso be set to any angle betueen 0' and 42'.

An optical-thickness monitor is located on the centerline of the chamber,and optical film thicknesses are monitored at any desired wavelength up to1.0 pim by suitable choice of line filters. Optical thicknesses of the compos-ite films of multilayers are individually monitored using fresh glass micro-scope slides for -oaiponent films during an raporation cycle.

The entire assembly of interferometers, rigid substrate holders, andoptical monitor slides a enclosed in stafnless-steel shields and can beheated to 250%C by a Calrod heater lczated at the top of the vacuum chamber(Figures 4(a) and (b)). Temperature control is ob*ained using an SCR propor-tional controller end thermistor mounted 'ose to the interterometer housings.

2.3.2 Datv Acquisition and pata Recordin Eystem

Stress changes in the films dtrin, deposition cause the bull's-eye fritagepatterns at the frir.ne-count detector to expand or contract depending upon thenature of the stress 'tensile or compressive). Ch-nges in in~ensity of Lhecentral tringe are detected by PIN diodes ane are fed to lock-in amplifiersthat synchronously demodulate the chopped signals using a reference signalfrom a second silicon diode in the laser so'rue housing.

The outputs of the optical monitor and stre.s interferometers are recordedon a six-channel chart recorder and are als• applied to the input of a data-logger/punched tape recorder. Fiure 5(a) and (b) illustrates the functionand form of the data recording system.

.. " .

incident

Laser Beam

Aluminized

Fold Mirrors

OpticalMonitor

Vapor Source

4 ,~I~nterferometer Housing v'nd oFold Mirror Rotatable Thru1800 Around Vertical Axis ForVapor-Incidence Angles Fromo to 26

(a) Conf-.guration

(b) Stress Interferotneter Head with Variable Vapor-Incidence

Angle Fold Mirrors

Figure 3. Variable Vapor-Incidence Angle Configuration

10

0OpticalzMonitor

VacuUmnGxlWindowMoir

StressI Interferonieters

41/

Vapor

Source

(a) Interferometer and Optical Monitor Configuration in a Vacuum System

.IM(b) 'ýLrcsi-4-lnt~erferometcr Arrayv inHie fleaid rnc losure

F. ror'c 4.Stres -. nterfet netei

(a),.':;:. ['•. ") e D a AI

St(b) S.-; Innre2oPrSsmDataloggDtr Rapern

Ste sInt. 03t

(a) Interferometer Data Acquisition and Recording System

(b) Stress-1easuring Interferometer System withData Recording Instrumentation

Figure 5. Dzita Acquisition and Data.-Recording System

12

The recording system data logger can be arranged to scan the five inputchannels at two fixed speeds of two channels/second or seven channels/second,the first channel always being the elapsed time. These two speeds in combi-nation with the use of different glass thicknesses for the flexible substrateallow sufficient sampled data points to be recorded per fringe over a widerange of stress levels.

2.4 STRESS-MEASUREMENT SYSTEM - OPERATIONAL CH,'- ICTERISTICS

i Initial tests of a single stress interferometer mounted to the vacuumsystem showed that:

* Stable bull's-eye fringes were formed at the display screen andfringe-count detector, and pump vibration was not a disturbing factor.

* High contrast interference fringes are projected onto the detector,and changes in the fringes are recorded with great fidelity.

. *• Although heating the vacuum system to 250 0 C causes the fringe count2 to change because of nonuniform heating of the glass disk, the fringe

system is reproducible and stable and of high contrast when the sys-tem reaches thermal equilibrium.

Figure 6 shows a typical fringe pattern (overexposed) produced at thedetector (PIN-10 diode) and display screen; the detector's sensitive area isaligned with the center of the fringe pattern and detects intensity changesas fringes move away from or toward the center of the fringe pattern. Fig-ure 7 shows the change in intensity or fringe count for a thin glass disk0.25 mm thick at 200%C being coated with thorium fluoride evaporated from anelectron-gun source. The frirtge change contains an amplitude modulation dueto material being deposited onto the second surface of the flexible disk.

TThe use of a gold semitransparent film to provide a reflectivity of 507- at6328 A on the upper surface of the flexible disk, together with the 50% ref-erence reflector, forms a three-mirror cavity and leads to amplitude modula-tion in the reflected fringes because of the deposited film thickness. Al-though this could be used to measure the deposited film thickness, it is notused in practice since the fringe counts obtained for thicker glass slidesare generally of longer period than the optical thickness changes.

2.5 FRINGE DIRECTION SENSING USING A SINGLE DETECTOR

Sensing the direction of fringe motion during film deposition determinesthe sign of the stress, i.e., compressive or tensile. This information canbe obtained either by observing the direction of fringe change during deposi-tion or by the use of two detectors displaced laterally in the fringe pattern.

During initial testing of the cat's-eye interferometer. it was noted thatthe waveform generated by the detector as the fringes were either contractingor expanding possessed an asymmetry that occurred each cycle and dependedupon the direction of fringe motion. This effect has since proven to be ex-tremely useful since both the direction and magnitude of the stress are re-corded automatically during deposition. Figure 8 illustrates this behavior

F 13

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1 4°i,, " ° I--,,'!!.,

S• • • •' '•,I

Detector Area

F'igure 6. Fringe P~atrern .it Outpust ot St ress-Xezuiringlutect'erometer

Deflection of Cer-Vit2 Diuc

Reflectivity ModulationDue to Increased Reflectivity Of

2nd Surface of Flexible Disk During Deposition

IFringe Ch•.nges Recorded by Stress -Measuring Interferometer

Figure 7. Intensity Variations (Fringe Count Due to ThF4 Film BeingDeposited onto a 0.25-un Cer-Vit Disk)

Film Disruption Point

T 1:

.* V�o� f"~1I~lope

> -ve going slopleFrtngef, expwiading -v or •t~

out from center < -re goa slr)p¢Frinse contract-ing Into center

"after film rupture

""Figure 8. Fringe Count for a 0.5-nn Thick Cer-VIt Disk Duriv,,

Deposition of MA4gF2 (Note ,aveform. asyun.etry indicating

direction of fringe motion before and after film cracking)

115

... -. -:, . . . 1.., , - - p.---.-. ,-... ..

for a film of magnesium fluoride deposited onto Cer-Vit at room temperature.As the film thickness increases from zero, the positive-going slope is greaterthan the negative-going slope, corresponding both to fringes moving outwardsfromn the center of the fringe pattern and to a tensile stress. At the pointindicated, the film breaks and the deflection reverses in sign; the fringesc-oilapse into the center of the pattern; and stress-relief occurs correspond-ing to a stress reduction in the film. After 'ium rupture, the positive-goingslope is less than the negative-going slope, anu this slope change with fringedirection can be utilized during data reduction to obtain the nature (sign) ofthe stress in the depositing film.

The asymmetry of the output waveform is not due to angular alignment er-rors in the fringe pattern and detector system but is quite reproducible andis a basic property of the interferometer configuration. The asymmetricalbehavior arises from the interference of multiply reflected Gaussian beamswhich undergo radial shearing as the mirror separation alters. The fringeformation process was investigated theoretically for this intetferometer (seeAppendix A) by sunning the first ten multiple reflections that occur betweenthe two mirror surfaces. Gaussian intensity profiles were assumed for thereflected laser beams and the integrated energy falling on a deteý:-or of agiven diameter was evaluated numerically as a function of the mirror separa-tion. Figure 9 shows the computed detector signal as the mirror spacing isaltered for two cases:

(1) A small detector diameter -0.01mm corresponding to operation ofthe interferometer in collimated light

(2) A detector area comparable to the beam size at the exit plane ofthe interferometer

The curve~s 3how the waveforms for a mirror separation change of 1/2 when thetwo r,ýflectors are spaced 100 and 400 kim apart. The asymmetry is much morepronounced for large separations corresponding to reduced overlap of the re-"flected wavefronts. In practice, the mirror separation is of the order o)400 -m ani the amount of asymmetry present in a recording of the fringechanges maL-hes that predicted by analysis.

2.6 FILM S11RESS DATA REDUCTIaN

Initial tsts of the four-channel interferometer system showed that astable and repioducible fringe co_ ., is obtained when the intcrferometers aremounted on the vacuum system. Vibration is not a problem and, although fringechanges occur during heati:ig and "ooling of the system, the change.e in fringecount at constant high temperatu:es are small coripared with the deflectioncaused by film stress. 'emra-t drifts at constant temperz.ture when the systemhas reached equilibrium produce apparent stress errors of the order of 20 to50 kg/cm2 compared with expected m=terial stresses of up to 5000 kg/cm2 . Fig-ure 10 shows the chart recording obtained for a ty;ical stress measurementexperiment in which thorirn fluo-ide was deposited onto Cer-Vit disks of var-ious thicknesses zt 200C. The fringc changes cal.sed by film stress are re-corded on channels 1, 3, 4 and 5, while channel 2 contains a recording fromthe optical monitor located in the center of the charmber. All these waveformsare recorded on paper tape via a data-logging system and the sampled data areprocessed using an II-M 370 after the deposition is completed.

16

CL. 0

0. 4, 14,

+ '44

a. 0 4

cu V

-4 -4

C 44

C4.4

V >4L

LI '*-. i-

-41 N~

17L

.... ... ... ....

0,25

Ce v - V i ' t 1)isý-

I bic . A nEýlo 0 , W

j : 1 7:i :i. : -7

7 7M.7 Mi

I: it . .... .. .. .... ... ... ... ...... .... .... ..

Citzijim-1 2rT-

);)ticýd Thickness t U; t:::777 ... .. .... .... .... .... ....\l(mito" ()Iltl)ut .. .... ....... .... .... .. ..... ....

(111c. Anjijk- -0.0')

.. .... .... .-1:;;: :::: 1:: it.... .. . 0& rh ii ib r4

.. .... ....

C I I I :i... .... .... ...

-tr: -ýt 7Tý r"T r ý" ý;". _"" ""

F villpfe Climige 7777

.. .... .... .Tý0.5 -!:11'n '7 1H .... .... ...'er T". T..T-Vit Dist,

(inc. An_,'Ic, =0. Oo)

.. .... .... 7: 1;... ... .... .... . . ..

BRUSH AC

.... .. ... . .. . .. .... .... ..

-inýre Cli;tnge .. ...... ... .... ;ki TTT! "T- T". r"! !"T

M, M:F(or 0.75-nifn;tit

CeI.-Vit Disl, :TIOnc. Angle -0.0')

:iii T: Mi '.TP

tit

C-liinn.t-1 -5

j!t ititit

t f.1 . . - , , . i ! ill: :;Ii iii.! !IliF(w 1 .0-111111 'HI

Cer-Vit Disk itlit !. i I ill * l`1W iT (I tit! I::A tiv le 0, 0 1 if ýIi mi

f 04 ;4IN 4.1 4 !:I-1', if1: it _4

Figure 10., Data Recording for Four Simultaneous Streqs Measurements for ThF4Deposited onto Cer-Vit Disks of Varying Thicknesses at 2000C

* - w r-- -

The total number of sampled data points per channel is nominally 250(data rate of two channels/second) for the entire deposition run, but thiscan be varied by changing the recording speed and/or the glass disk thick-ness. This number of data points is typical for the deposition of k/4 filmsat 10.6 pm, although a data rate of seven channels per second is availablefrom the data-logger/tape-punch unit.

The recorded data is processed to yield the stress in the film depositedonto each disk, and the data reduction calculates the average stress KSifor the ith disk according to

2

i 3 (1-v) &D,)1 i mW

where

thE. = Young's modulus of i disk

th= Poisson's ratio of i disk

1.'th_4 h. = Thickness of i disk (u)

thD. = Diameter of i disk (an)

S= Deflection due to stress Si) of ith disk (pm)

St = Mechanical thickness of film deposited on monitor slidem

. = Distribution factor for i t slide (ratio of thickness on the ith!;slide to thickness of film on the optical monitor)

The deflections (,±.) are obtained from the sample data by the followingalgor itlun:

(I) Normalize all channels to the maximum recording occucring duringdeposiLion.

(2) Locate zero crossing points.

(3) Normalize individual cycles to unity.

(4) Calculate mechanical deflections.

(5) Differentiate deflections and s= absolute values.

The mechanical thickness of the film deposited onto the optical moniter isalso calculated in a similar manner and, together with the dxstributionfactors (6i) and the optical deflections (,!,j), is used to calculate the aver-age stress -,Si for each point recorded. The data computed in this =annerare interpolated to provide stress level as a fu-nction cf the mechanical film

•7 thtckness deposited onto each substrcte. Figure 11 shows the data reduction

. ,,19

SRfI-:SS; DAT4 AIAI.Y IP:UN :mJ 1 IfIiC 22 IilF4 )(y ' , 0 ,O ., I t Cl f l2ld/:LC

F' "',AL 111 ,I NPUI' DATA 1.1 ' S2

CIAlI,.. 1. I C;IA.!I',L 2 C2IIA1 1,1 1. J ,I.:l 3!:I. . CIIA:.3I.2 5,* Il VIl. I A .' O) .;+'.1 .. rl0.3 3 Pe.e.l;"I+. V!.+ 1 + i\'.I 0 7. 0. ("1.0 ', 0..''.L 0.1 J 0.f

CI IA.NINl. I C1 A,!. 2 C;IA;.hI, L 3 CIA.,lilI:L 4 CHA;..ILL 5I a'I.T ((;I S) 0.-24 0.616 O. t13 I

I I0.2L1! 0.4116 0.1"17, 1 .0221)1b, (.0 1") F,',fU. 0,3J 0.693 0.712 0.161

* Fit.:: t1El~E SI'.) = 20 U.tUA L'Ei ;AVES 01' INDEX I.4d AT O.bG4 'ICI/)II .w*.

SU'ST AI'F D L"L' [tIHi1:1 ('.tClao;S)(C:':,!.;;FL 2 is U;IH'ICAL" nt .'ll ')

CIIA;I;L I CIIA;I':.I. 2 ClIWI--L 3 ClA .. l 4 CHA.IfIh[. 50.309. 0.000 ).G0 I0/0. 122 0. lil 5 0.014 0..0530.'.30 0.239 0.10 ().0 / 17 .1. 053G.V49 0.334 0.234 0.100 C.07/1.424 0.025 0.33H 0.131 0.2021 .04n3 0.562 0.432 0.174 0. 422.277 0.63'.) 0../•I 0.221 0.2002. 750 0.132 0.66 9 0.269 0.2303.1A4 0.t49 0.'//1 0. 329 () . 2 513.63v O.Y63 O.vOt) C. 3'j %.26/4.01 1 .065 2.004 0.424 1).4.527 1.159 1.119 0.464 0.3144.9165 1.294 1.245 0.50d $ 0.3335.401 1 .43; .335 0.566 0.3695.0d6 I. 51y .411 0.62d 0.40086.326 1.61P 1.5"19 0.6Y2 0.4396.771 1./89 1.677 0.734 0.4727.211 I .)6-2 .- II 0 0.16v 0.4997.6421 1. Vl-9 1.yl O.R09 0.52H8.113 2.113 2.008 0.864 0.075R.543 2.201 2.1c2 0.927 0..C G69.012 2..3106 2.25)0 0.91)7 0.631V.A50 2.3P9 2.351 2.042 0. (1499.9(%3 2.500 2.4V6 1 .03 0. 67n

10.366 2.56.4 2.1309 1 .124 r. M220. 794 2.726 2.700 1 .169 0. 12YI1.2"14 2. ;'65 2. 0:36 3 .22 0. 6/53

1 .701 3.047 2.vJd 2 .2•6 . 1.5412. ItfI 3.162 31%6r 1.34d O. 0 ;,(612.616 3.3n5 3. /M I .3ý)3 0.o4413.06,2 3. A I t 3.2t60 1.434 0.1,6613.52/ 3.Ady 3.422 I..db' 0. 3r1l

TOIJAL NO OF.

1.

Mt' A,;,' 1 .III11/A Hy 43 22 6L), .511l=on(INATh (A/!;', C) 33.29.4 45.120 31.29v 32. 12t 34.J41

] i CA A1; 1),. \1 1' L

.229... ... 1 /.. 1' 3. .1I.0'6.1I ' 0.l"'0 10,40.+ P4I .1.'I 1..+ ,

2302C'.029 .1. C '0}.; 2-;/:,."l'. . 22 .4• '/ 13 ,: I I. L"."" 0 . e" ( 1o :)• J01".3.)• 1,16.• 't v ). ',

""(. 2. 1 el.. l IJ -,I., t.. 1I204. -'MI .* 20 I 0".)j ' A I I .. /1;3 I 1 ":..';

0 .62 l'ty 0. : I ( (t , I.D 1,.1 ) +1 "4. ."21) I '+ "'-,)'. (, .jI1119. A14 Or/,y.; 1 1 . 4 1 I.11~ +. e-.- 1 . 2. !0';II1 .%1 .1 . nt:) iO 4.p;ýA 1 1 .) +2 1.1 i

II1 .1 o . 1.2rn 1 309Y. P.t I 1,-W. /41 1 -.124. .1 2tI,. 1 1. , ':1.,,, 12 1.3.2. /9 1 123/...

II * .I I .s. 22.1 .I (" .1 t',, : I IVO. P) ,I IC .I1 41 2 ,t'1 I V:" 2,.?. C., II. ,..

Figure 11. Stress Data Reduction of Data in Figure 10, ThF"4-.6 Deposited ontoSubstrates of Various Thicknesses at 2000C

20

BEST AVAILABLE COPY

for the curves shown in Figure 10 for a thorium fluoride film deposited ontoCer-Vit disks of various thicknesses. Evaporation rates are automaticallycalculated for each channel together with the number of fringes calculated bythe data-reduction program and serve as a check on the experimental conditions.The optical monitor input from the Balzer monitor is an extremely noisy signalresulting in double maxima and minima when depositing ThF4 on 1.5 index moni-

T tor slides and, consequently, the fringe count for channel 2 is computed incor-rectly as are the variations of thickness with time. Since the noise is uni-

form throughout the recording and since the optical film thickness is depositedT ~as an exact number of quarter-waves at some preselected monitor wavelength,-• the thickness data is linearly scaled to the correct thickness. This source

of error was subsequently eliminated by depositing ThF 4 films onto high-indexmonitor slides.

The entire interferometer system was used for a series of preliminaryexperiments designed to check out the entire system under operational condi-tions, and thorium fluoride (ThF4 ) was selected as the thin-film material be-cause ef its wide use in laser coatings in the 1 0 -kim region.

2.7 EVALUATION OF STRESS MEASURING SYSTEM - EXPERIMENTAL TESTS

The calculation of stress utilizing equation (1) assumes that:

(1I) The deposited film thicknesses are small compared to the flexible* 'substrate thicknessWe,__t

(2) The measurement is independent of the substrate material chosen

(3) The measurement is independent of the substrate thickness

(4) No stress relief occurs in the substrate/film combination and noslippage occurs at che film/substrate boundary.

The first condition is satisfied for X/4 films in the 10-pm region (t 1 to2 km) as described here since the flexible glass substrates used range from250 to 1000 pm in thickness. The dependence, if any, of the stress measure-ment upon the thickness and type of substrate material used can be checkedusing the present four-channel interferometer system. The final condition ismore difficult to verify experimentally, but calculaLions given in Section 3sho,, that the effects of stress relief are small for thick films. Since the

4\ Interferometer system can measure the stress on four different thicknesses ofmaterials or on difierent substrates in the same vacuum deposition, the sec-ond and third conditions can be checked experimentally.

The data Phown in Figures 10 and II give the stress levels for ThF4 filmsdeposited onto Cer-Vit disks of different thicknesses of known weight anddensity and show that indeed the equilibrium stress is independent of theglass substrate thickness. A similar experiment was carried out utilizingthin flexible disks of fused silica, Cer-Vit and potassium chloride to deter-mine the effect of different substrate materials. The disk thicknesses wereobtained by weighing the disks, and the elastic constants or each -materlalused in the data reduction are shown in Table I.

21

TABLE 1. MECHANICAL PROPERTIES OF FLEXIBLE SUBSTRATES

Material Young's Modulus (E) Density Poisson's Ratio (v)Cer-Vit 9.23 x 0 kg/cm2 2.5 g/cm3 0.25

Fused 5 2 0Silica 7.00 x 10 kg/cm 2.2 g/cm

KCI (Ref. 9) 3.02 x 105 kg/cm2 1.98 g/cm3 0.11

Owens-Illinois Data

Corning Glass Works Data

, The stress data measured for ThF 4 using two KCl substrates (1.0 mm thick),

a 0.5-mm thick fused silica substrate and a 0.5-mm thick Cer-Vit substrate areshown in Figure 12.

These intrinsic stress levels measured for ThF4 agree within 10% for dif-ferent substrate materials although subsequent measurements of ZnSe films onvarious substrates showed wide discrepancies for Cer-Vit and KCI substrates.Whether the intrinsic stress is truly dependent upon the substrate materialor whether the high expansion substrate (KCI) in combination with a film ofhigh index cause enhanced thermal deflections is not known.

9. L.S. Combes, S.S. Ballard, and K.A. McCarthy, J. Opt. Soc. Amer., _41_1215 (1951).

22

1500

1250 ThF4 on Cer-Vit at 200'C(

(0.5 mm x 25.0 mm Disk)

1' 1000

ThE on Fused Silica at 200'C

750 Th 4 onKCl at 200 0C (0.5 mm x 25. 0 mm Disk)4)4

(1. 0 mm x 25 mm Disk)

U2

SThF - 7S500

Deposition Rate = 31.5 ±. 5A/sSubstrate Temp 200°CVapor IncidenceAngle = 0. 00

Substrate = Cer-Vit 0. 5 mm

250

"0.5 1.0 1.5 2.0 2.5

Mechanical Film Thickness (IL in)Figure 12. Instantaneous Stress Levels Computed for ThF4 Deosited onto

Cer-Vit Fused Silica and XCl under Iden'ical Conditions.

23

4 SECTION 3

STRESS ADDITION AND TEMPERATURE EFFECTS IN THIN FILM MULTILAYERS

3.1 ANALYTICAL MODEL FORMULATION

An analytical task was undertaken as part of this program to model thestress behavior of multilayer film stacks in order to identify modes of fail-ure when exposed to intense laser beams.

Such a model requires at the very least experimentally measured data of4. intrinsic film stresses, thin-film thermal and mechanical properties, dis-

ruptive film thicknesses, adhesion and film breaking stresses. A knowledgeof such properties for the component materials of a thin-film stack should inprinciple enable the spatial stress distribution within each film to be com-puted when the coating is placed in a spatially nonuniform high energy laserbeam. Predicting the stress levels at which a film system fails involvesmeasurement of both film adhesion and the breaking stress level; and suchmeasurements have always proven difficult since models of film adhesion arevirtually non-existent.

The present effort is aimed principally at providing a better under-standing of antireflection coatings deposited onto window materials that havelarge thermal expansion coefficients. Window materials such as potassiumchloride, calcium fluoride and strontium fluoride are extensively utilizedfor C02 lasers and chemical lasers, and all possess much higher expansion co-efficients than most materials traditionally utilized for antireflection coat-ings in the infrared region.

As a starting point for this topic it is instructive to describe the be-havior of a thin disk upon which a stressed film is being deposited at hightemperatures. Since film stress is obtained indirectly by measuring the de-flection of a thin disk, such an analysis also quantifies sources of error inthe measurement technique.

The substrates utilized for stress measurements consist of a thin glassdisk whose upper surface is coated with a partially reflecting metal film,which itself can cause a deflertion of the disk w6 due to its own internalfilm stress. When this disk is placed in the Interferxneter and heated by ex-ternal sources (Calrod heaters, quartz iodine lamps, etc.), the disk distortsprimarily because of the existence of radial and front to back temperaturegradients producing deflections WRI and WpgB1, respectively. After equilib-riun is esLablished in the vacuum system, opening of shutters and exposure toa hot vapor source can introduce short-term temperature gradients that producea deflection -S at the start of evaporation. Such thermal deflections occurwhen film stress is low s;ince films appear to approach zero stress at zerothickness, and this effect can introduce large errors in the measured stress.A continuous deflection occurs during deposition, the rate of deposition beingproportional to the stress if the film thickness increases linearly. This de-flection wf(t) is used to calculate the intrinsic film stress of the film

24

material knowing the elastic properties of the substrate. As the coated diskis cooled to room temperature after the film is deposited, deflections arecaused by radial and front to back gradients WR2 and WkTB2 as during heatingtogether with a deflection 'DTE caused by any mismatch in thermal expansionof the film and substrate. The amount of deflection 0 DTE depends on both the

expansion coefficient mismatch and the elastic properties of the film andsubstrate. A further deflection WAIR can occur when the substrate is exposedto air.

The deflection of the disk during these processes is the sum of all these

effects, i.e.,

W = wG + WRI + WFTBI + S + wf(t) + WR2 + WFTB2 + %DTE + WAIR (2)

and the experimental conditions must deduce the deflection due to film stress4 Wf(t) from the total deflection w. The above expression pertains to a single

film being deposited onto a flexible substrate. When multiple films are de-posited at the same temperature, the deflection caused by the ith film pro-duces small stress changes in all the preceding films, a phenomenon we de-

scribe as stress relief. Fortunately, we will show that the stress changescaused by additional deformation of the substrate are exceedingly small andcan be neglected when the total film thickness is much less than the substratethickness. The deflection obtained for multiple films can be represented asa sum of the deflections due to the individual films, the intrinsic stress ofall preceding films being unaffected by the addition of the ith film at con-

stant temperature.

Since the intrinsic stress for most film materials varies with thicknessit is important to understand the relationship between unit stress a(t) andthy stress calculated from the disk deflection equations (S(t)) . The value

S(t)) is calculated from the total deflection of the disk W at a particularfilm thickness and, as such, is a weighted average of the unit stresses a(t)of all the infinitesimally thin layers of thickness dt that form the growingfilm. When the unit stress in the material is constant, then a(t) = KS(t))but this is not the case for thin films since the measured stress tends towardzero at zero thicknesses. All of the experimental methods for stress measure-ment provide the weighted stress (S(t_)) ; however, the unit stress c(t) is amore fundamental quantity for modeling the behavior of multilaver films andthis function can be derived from the experimentally measured values of KS(t))as will be shown.

The total deflection of the thin disk during film growth at a cqnstaqptemperature is therefore the sum of the first five terms in equation (2), i.e.,

U WG +URl +WFTBI +4S +wf(t)

In the experinents carried out during this program, the deflection due to thepartially transparent gold film on the top surface of the substrate is assumedto be small and of constant value during film deposition. Similarly, sincethe thin disks are allowed to reach thermal equilibrium over a long timeperiod) the deflections caused by radial and front to back gradients LRI and

25

-4L

wrFTB, are assumed constant and small. This assumption is valid duringmeasurement since the change in fringe intensity due t) such gradients ismonitored during the heating cycle until the changes become negligibl, small,of the order of one or two fringes per hour.

The time dependent disk deflection at constant temperature during deposi-tion is therefore

w(t) WS(t) + Wf(t)

where W (t) is the deflection caused by opening or closing the shutters lo-cated beneath the substrate and by exposing the disk surface to the hot vaporsource either by opening a source shutter or by heating the evaporant material.

The contribution from the opening and closing of substrate shutters can

be extremely large, especially if a film has been previously deposited ontothe disk; however, these transients can be allowed to die away before filmdeposition is started. Thermal fluxes from the hot source material cannot beso conveniently minimized and can contribute large errors at the start of

film deposition, where the intrinsic stress is changing most rapidly duringthe nucleation and island growth phase. A mathematical description of thebehavior of an absorbing disk coated with a second surface gold reflector il-luminated by a hot source was attempted during the program in order to esti-mate the amount of deflection expected for various sources and substrate ma-terials. The resulting second-order inhomogeneous differential equation thatis obtained must be evaluated numerically to obtain the temperature gradientsin the disk and the corresponding time-dependent deflections. This analysiswas not pursued since experimental measurements for uncoated thick disksutilized during the measurement program showed that such effects were small,amounting to an error of 100 kg/cm2 at most for the various substrate materi-

* l als used. A rigorous thermal analysis is still required for the case of acoated disk since thermal stresses due to expansion mismatch may produce largeapparent stresses. These source-induced deflections were minimized by pre-heating the evaporant with the source shutter open, and evaporation was ini-tiated by increasing the power to the electron beam gun.

Expressions are derived in the following paragraph for the various de-flection contributions described above for a thin disk together with the re-lationship between the measured stress (S(t)b and the more fundamental unitstress a(t). The effect of stress relief is calculated and the influence ofthermally induced stress due to expansion coefficient mismatch and thermalgradients are derived for a single film. The results are then utilized todescribe the behavior of a multilayer coating under conditions of changingtemperature.

3.2 DEFLECTION OF CIRCULAR PLATES DUE TO A SINGLE STRESSED FILM

Although the equation for the deflection of a thin disk due to a stressedcoating has been derived by many authors, we include the derivation here forthe sake of completeness. The equation for stress and deflection derived inthe following discussion assumes that:

26

',,

(1) The film properties are uniform; i.e., unit stress is uniform ina plane perpendicular to the direction of film growth

(2) The disk is stress-free and no twisting moments exist within the

material or are induced in the disk by the deposition of a thinfilm of material; i.e., stress is isotropic

(3) Deflections are small compared with the substrate thickness

A (4) No slippage occurs at the film substrate boundary.

If the circular plate has a thickness h and a diameter D, the initiallyunstressed disk is bent to a sphere by the film and the neutral surface ofthe disk assumes a sphericity r, as shown in Figure 13. The film shown inFigure 13 is under tensile stress, and the deflection, w, of the neutralsurface due to the film stress is for small deflections.

2v D (3)

The bending moment, M, and the disk radius, r, are related by (Ref. 10)

I M2r A (1+,v)

where

Eh 3

12 (1-v2)

and

•: ~hl2+ t,4 = a(z)zdz (6)

h/2

Here the material parameters are

E = Young's modulus of elasticity

SPoisson's ratio

a Unit stress in the film (i.e., stress in a thin layer dz at distancez from the neutral surface)

*•Combining equations (3), (4), and (5), the deflection (L) in terms of the in-duced bending moment, M, of equation (6) becomes

* 23• (IL M (7)

10. S. Timoshenko, Theory of Plates and Shells 2nd ed. (McGraw-Hill, New York,1959) p. 43.

27

Y Axis

Neutral Surface

Film

ILI

t I Element of Growin 1ilm of Vnit Stress a(7)mat a Thickness of z

Substrate

Figure 13. Deflection of Disk due to a Single Stressed Film

28

The stress measured during an experiment is the average stress, (S) , and thisvalue is a function of film thickness since the unit stress depends upon filmthickness. The relationship between experimentally measured stress (s) andthe unit stress a(z) can be obtained by considering the origin of the bendingmoment due to a film of thickness t at a distance h/2 from the neutral surfaceproducing a deflection that is equivalent to the existence of an average

C stress (S> in the film a distance h/2 from the neutral surface, i.e.

AM = J'(t) (h/2 +t)dt =h (s) t/2 (8)

The unit stress at any thickness can therefore be obtained from measured data* as

* which for the case where tc<<h/2 reduces to the form

• I a(t) = (s) + t Ks> (1)

Equation (7) can now be written as

3 1v 2• h/2+t

2 J X3 )f (t)(k+t dth hI2

2

so that the average film stress measured at some thickness t is

() 4E (10\2 ((13)!~ ~ ~ ~ S \,s (-)kD) t-7(3

If this function is continuously calculated during film deposition, the unit

stress at any point in the film can be obtained from equation (10).

3.3 UNIT STRESS CURVE FITTING

A knowledge of the unit stress function for a given coatirg materialcompletely describes its stress behavior and is utilized for calculating thedeflection of a disk when coated with multiple films.

During the early portion of the program, the stress behavior of thoriumfluoride was measured for different substrate temperature disposition ratesand angles of incidence for film thicknesses up to 1.5 .m (see Section 4) andshowed that the stress always approached a constant value as the film thick-ness increased. These equilibrium values were slightly different for the

29

S!F. .. .. . *.. .. -. . -. * . .. -

various deposition conditions but the functional form of the stress variationswere similar. Later measurements for zinc selenide and cerium fluoride showeda similar behavior v.ith increasing film thickness although the rate at whichthe equilibrium value is reached is greatly different for each material undercomparable evaporation conditions.

In order to characterize the materials in a convenient mathematical form,data points for the average stress were fitted to a polynomial by least squares

.methodsn k

(s) = a kk (14)k=l

This procedure gives a good fit to the average stress curve for n rangingfrom 4 to Iu; however, when the unit stress is computed from the fitted curve,the existence of local maxima and minima between data points results in wildly

1" oscillating values of unit stress.

An alternative data fitting process was investigated whereby a mathemat-1ical exprestion is assumed for the shape of the unit stress curve based uponthe functions that have been used to describe nucleation phenomena in thinfilms. The nuw.mber of clusters per unit area above critical size in a growingfilm after an evaporation time t can be written (Maissel and Glang (Ref. 11))as

(t) 1 ep(-I*DTa t) (15)

ra

where D is the surfacx, diffusion coefficient and 1* is the nucleation fre-quency. If we assume that the unit stress in a thin film is proportional tothe number of clusters, N/(t), then the unit stress function can be written asa function of film thickaess x as

cr(x) - a (16)NW

where Nm is the saturation number of n--clei on the substrate. Consequently,

•(x) ailexp(bx)?(17)

and the measured stress becomes

KSt (X- exp (i-bx)(s (x)) a - 41x(~J(15)

bX

The stress behavior of thin films of ThF4 for large thicknesses also shows adecrease in the equilibritmr stress value, which can be thought of as a stressrelief effect to the growing number of defects (cracking) as the .ixlm th-ckness

1L. L1. Maissel, R. Clang, Handbook of Thin Film Technolcgy,(McCraw-ilill,14"kNew York, 1970) p. 8-15.

30

-.": -•

increases. Such an effect is modeled by assuming a unit stress function ofthe form

a(t) a aexp (-bt) {l -expE(b-c)tJ} (19)

where the term exp(-bt) modifies the stress for large thicknLsses.

The average measured stress can be rep~resented by

( 5(t)) = (t)dr (20)Sit0

for t << h/2 and, consequently, the form of this function from equation(19) is

(s(t)) = l-exp(-bt) - t - exp(-ct)] (21)

The constants a, b, a•ad c are calculated from a set of average stress datapoints KSi(ti)> such that the expression

nI (s~(t)) -St b [l-exp(-bti)3+-c-[l-exp(-cti)1Ji(22)

(S 1 (2

is minimized.

The fitted average stress curves are shown in Figures 14 and 15 forthorium fluoride and zinc selenide thin fitms. These curves are generatedf-oa experimental data using the above curvi fitting codes, and this procedureenables the data to be reduced to three constants for each type of film. Theseconstants vary with deposition conditions as described in Section 4 but pro-vide a convenient input to a computer model of stress addition in multilayorstruc tures.

3.4 STRESS RELIEF EFFECTS

When a stressed thin film is deposited onto an uncoated disk, the deflec-tion of the disk causes a small amount of stress relief to occur in the film

material. Alternatively, if an extenial force is applied to the center of theplate such that the deflection produced by the film is removed, the film iselongated and the true value of film stress is larger than if the plate wereallowed to bend freely. Such stress relief effects also occur when films areadded to an existing ilctilayer structure since a deflection of the plateelongates or contracts the previously deposited film stack.

Fortunately, the magnitude o[ this effect !.s very small and such consid-eration can be neglected for stress addition in vultilavcr films. The amountof stress relief can be calculated from the unit elongation, , (Figure 16)which occurs when the curved plate is flattened, i.e..

31

EXPONENTIRL MODEL:R= 1057.10B= 0.000000050C= 12.49699STO. DEV.= 4411.202

00

0

o

'U

03

, "" . Unit Stress

0-

iAverage Stress (Best Fit)

-o

(D

t3

SUnit Stress a(t) SA exp (-Bt)[ 1 exp(-Ct)]

C)" t in ýLm• **A = 1057. 1 (kg/ )

B = 5x10-8oC = 12."5

o

1b .00 0. 30 0.60 0.90 1.20 1.50 1 . f0 2.10 2.40

THlICKNESS (M ICRO[NS)

Figure 14. Tensile Stress Produced in Thorium. Fluoride FilmMaterial Deposited at 37 ,X/s at 200°¢. Stressmeasured from the deflection of 0.5-mm-thiekCer-Vit substrate.

S:32

EXPONENTIAL MODEL:= -3300.00

= 0199999680C 8~8b.00000STD. OEV.= 83.205

00 0.08 0.16 0.24 0.32 0.40 0.48 0.1G 0. 6,THICKNESS MICRONS)

-400

-800

-1200

(.2 -1600

• .k -2000

: Average Stress (lest Fit)

-2400o Sampled IDat.,

-2800 , .. €",. /" t....

" ~-32002 bUnit Strcss cr(t) A exp (-B0In 1 - xp(-C't0

-3600 t III l1mA - -3300.0 (kg `cm,h 0.199.

c -- 0. 0-. 000

Figitre 15. Coprersive Stress Produced in Zinc ScI'nidcTbin Film matcrial tkpositcd at .& J,;b/ at150'C. Stress meastured frmr, deflectit-r of0.25-••-thick Cor-ViL .substrate.

33

I2,

Neutral Surface

Figure 16. Stress Relief Effects

34

I

* S-So rcr(r-h/2)p h

E S (r-h/2) T2r--h---h0

Since the radius of the plate, r, is much greater than its thickness, thise elongation can be written

h 8wh (4-2r 2 (24)2D

The initial radius of the plate is related to the plate deflection as given inequation (3) and, consequently, the unit elongation can be written

Sh(25)

D

From the definition of Young's modulus for the film material, the inducedstress is

4E fWh

V f -(26)D2A D

The corrected value of film stress including the stress relief term is thus

/S" 4Es h2 )\(/ + 4E f wh

"S) total 3(1-v) D -/jt 2

or, alternatively,

4Es E f 3 ('-v) th (28)•; <(S)tctal- 3(I-V) \D it E -3Iv hJ

The correction term can be seen to be small, involving the ratio of film thick-ness to substrate thickness, t/h, assuming that Young's modulus for the film,Ff, and the substrate, Es, are of comparable size. Consequently, stress re-lief effects are no, included in the data reduction codes for film stress.

The expressions derived thus far relate to deflections of a thin diskcaused by the unit stress function and stress relief as the film is being de-posited at constant temperature. When the film/substrate combination is cooledin vacuum after deposition, the disk undergoes detlections caused by thermalgradients and differences in expansion coefficient of film and substrate ("bi-metallic effects").

3.5 THERMALLY INDUCED STRESS

Since thin films are usually deposited onto hot substrates, the measuredvalues of intrinsic stress pertain to the deposition temperature, aad largechanges in intrinsic film stress can occur when the ooated substrate is cooled

Safter film deposition. During cooling, differential contraction of the film

35

and substrate due to an expansion coefficient mismatch produces stress changesin the film a6suming that no slippage occurs at the film/substrate boundary.

If the film/substrate system undergoes a uniform temperature change AT,the unit elongation of film and substrate is Cf and Cs respectively, i.e.,

E cfATf a = AT

s s

where af and a are the thermal coefficients of expansion of the film andsubstrate material.

Since the film is assumed to adhere to the substrate, it cannot physicallyelongate more than the substrate elongates; hence, the excess elongation of thefilm (Ef- (s) can only be prevented by the presence of a compressive stress

af =E (a -a )AT (29)

The values of the expansion coefficient and the Young's modulus for thin filmsare usually unknown and bulk values are normally utilized for calculation pur-poses. Since the thermal stress changes can easily exceed the intrinsic stressestablished during deposition when films are deposited onto high expansion sub-strates, a method of measuring both quantities was developed using the stressinterferometer and is described in Section 5.

3.6 STRESS ADDITION IN MULTILAYER FILMS

"Using the expressions derived above, the stress in the ith film of anmultilayer stack deposited at a temperature Ti can be written as

i(t) = Ai exp(-B i t)[l - exp(-C i t)I + Eii-Qs)(Tr-T ) (30)

where T is the final temperature of the multilayer stack. The above expres-o

sion neglects stress relief effects and assumes that the thermally inducedstresses are reversible, i.e., no phase changes or film interdiffusion occursduring formation of the multilayer stack. The constants Ai, Bi, Ci arc themeasured atress coefficients that can depeud upon the deposition conditions.

If each film has a thickness ti, the total bending moment after depositionat some equilibrium temperature TO is given by

h/2 + t

MSTACK 2 [a [(z) +E U( -s)(T 1 -T) zdz

1,/2 + t 1 + t2

+ jF2(z)+E 2 (C -a)(To-To)] zdz+... (31)

h/2 + tj

36

or in terms of the stress coefficients

kh/2+ E

j=lm eM ( Ai exp(-Biz)[l -exp(-Ciz)]

MSTACK

k-Ih/2 + E

j=l

+ Ei(ai-as)(Ti-To)]zdzo.. (32)

This expression is a measure of the force acting at the substrate/stack bound-ary tending to separate the films from the substrate.

The corresponding deflection of the substrate is obtained by substituting

the above expression for M into equation (7), i.e.

•< 2

'T-OT V) N ( T) (33)• fOAL 2 h STA)

Ss

If a multilayer stack is formed of materials having opposite stress char-acteristics it is sometimes possible to arrange for the net bending moment toapproach zero after the film substrate combination is cooled to room tempera-ture. Such a film system is usually incorrectly referred to as a zero stresssystem; however, failure can still occur within the film stack if the sum ofthe intrinsic and thermal stress is allowed to exceed the breaking stress inany layer. Similarly, the bending moment at intermediate boundaries can ex-ceed the boundary adhesive forces resulting in delamination.

As an aid to describing the stress behavior of thin film systems, a coan-puter code was completed during the program to determine the stress level inthe component films of multilayer film stacks. The model utilizes the meas-ured values of the stress coefficients, Ak, Bk, anc! Ck, together with measureddata for thin film expansion coefficients and Young's modulus. This enablesstress changes to be determined in each film in the stack at various uniformtemperatures. In addition, the total bending moment is calculated for thesubstrate/film boundary.

The prime motivation for measuring film stresses is to discover methodsof changing the intrinsic stress by altering deposition conditions, by utiliz-ing mixtures or by investigating the influence of radiation (UV, visible) uponfilm formation. The intrinsic stress of ThF 4 films has been found to be rela-tively insensitive to deposition conditions, whereas ZnSe films show largechanges in intrinsic stress with changes in rate and temperature.

37

A.9.

SECTION 4

INTRINSIC STRESS MEASUREMENTS

4. 1 MATERIAL SELECTION

During the present program two widely utilized infrared materials, tho-rium tetrafluoride and zinc selenide were investigated in detail and severalmeasurements were made using thallium iodide and cerium fluoride material.Thallium iodide was investigated late in the program because of its increas-ing importance in the fabrication of IR window antireflection coatings andREL metal dielectric mirrors (Ref. 12). Cerium fluoride was also character-ized to some extent since it is used extensively as a protective overcoat forFLIR windows.

4.2 DEPOSITION CONDITIONS - EXPERIMENTAL

During the present investigation, deposition of ThF 4, ZnSe, TlI, and CeF 3were carried out using an electron beam source. Changes in vapor incidenceangle for a single deposition were obtained by rotating the interferometerto Drovide incidence angles of 0', 20', 30° and 40° resulting in slightlylower vapor deposition rates and higher spatial nonuniformity in film thick-ness at higher incidence angles. Changes in deposition rate for the variousmaterials were obtained by altering the input power to the electron beam gunsource. During a single evaporation, the entire interferometer system wasenclosed in a stainless-steel housing and heated by a large spiral Calrodheater at the top of the chamber. Deposition could 1-e made at temperaturesup to 250 0 C, and the temperature of the substrates was measured using a singlethermocouple attached to one of the interferometer housings.

4.3 INTRINSIC STRESS IN THORIUM TETRAFLUORIDE FILMS

Variations in intrinsic stress as a function of film thickness weremeasured for thorium fluoride films up to 2.0 pm in thickness. Stress meas-urements were made primarily utilizing Cer-Vit disks since previous measure-ments (Figure 12) showed that the calculated stress values were relatively in-dependent of the substrate material. Unfortunately, later measurements forZnSe films showed large stress differences for films deposited onto Cer-Vitand KCI.

4.3.1 Deposition Rate Dependence

The intrinsic stress in ThF 4 materials (Figure 17) shows a small depend-ence upon deposition rate, low rates (15 -20 A/s) producing a tensile stressof -1400 kg/cm2 while higher rates of 75 A/s produce lower tensile stressesof +11O0 kg/cm2.

12. M.C. Ohmer, Private Cotsunication, Air Force Materials Laboratory, Wright-Patterson AFB, Ohio.

38

"I'" ': :.. " ' :.," '•i ! s , 'i" r -- ¢•" ' ? , • " "• '' ": • "! • •" :•. . -" • : ' . .. . .."• .. ..: • • • :" )' 2 ' " i '7" -, : ' •:2• "-•: ! ' ..::•• ' ,' - 't-:-'

1500

'•- .~

, " • I000 o

33A/s . 75A/s (ThF 10)bD 4

~14

Substrate Temp 2000C

Incidence Angle = 0. 0

Substrates - 0. 5rm Cer-Vit

0.5 1.0 1.5 2.0 2.5

Film Thiclness (4 II)

Figure 17. Dependence of Intrinsic Stress in ThF4 Films on Thickness.

Stress Measured using 0.5 mm Thick Cer-Vit Disks and Elec-tron Beam Gun Deposition at 200*C.

39

,... <"

4.3.2 Substrate Temperature Dependence

Variation in substrate temperature between 1000C and 23V C has littleeffect upon the intrinsic stress at large thicknesses (Fig,!re 18); however,the quasi-equilibrium value is reached for smaller film thirknesses as thesubstrate temperature is reduced. A previous mnasurement o' ThOF 2 depositionat ambient temperature is included in Figure 18 for comparison.

4.3.3 Dependence of Stress Upon Incidence Angle

Figures 19 and 20 show the variation of stress wit.i incidence angle fortwo different substrate temperatures. At extreme angles (>40°) the stress

I levels at large thicknesses exhibit a large decrease "or the 150%C deposition,whereas deposition at 200C produces a well-defined minimum stress level be-tween 1.0 and 1.7 pm mechanical thickness. These changes are relatively un-important since large vapor incidence angles are avoided if possible in mostthin-film depositions.

4.3.4 Nonuniform Stress Distribution in ThF4 Films

A The experimentally measured values of intrinsic stress for ThF4 show

little dependence upon incidence angle or substrate temperature and a mild de-pendence upon deposition rate. All measuremerts indicate a variation of unitstress with thickness with a maximum stress uczurrirg at a thickness in the0.25-pm range. The effect of such a stress 'ariation of unit stress withthickness can be seen when cracked films of ThF 4 are viewed through an inter-ference microscope as shown in Figure 21(a). The cracked film was producedby depositing ThF 4 (%/4 at 10.6 pm) onto KCl at ICOC and heating to 2500 C invacuum after deposition. The flakes shiow circular fringes itdicative of aslow variation of unit stress with filn thickness.

4.3.5 Stress Coefficients for ThF4 Films

Stress coefficients were measured for a ThF4 film \/2 at 10.0 Pm usingbest fit routines. Thin film was deposited ct 200'C. The unit stress beinggiven by three coefficients:

A = 1057 kg/cm2B = 5 x 10-8C - 12.5

4.4 INTRINSIC STRESS IN ZINC SELENIDE FILIMS

Intrinsic streis measurements for ZnSe films show a much larger depend-ence upon deposition conditions than do measurements obtained for ThF 4 films.Measurements were made for films up to 2.4 pm thick (-X,/2 at l0.0im) atdeposition temperatures of 200%c, 150"C, and 200'C for three rates of deposi-tion, the highest and lowest deposititni rates being limited by the vaporsource characteristics and the chamber configuration.

40

St...;..

1500

/ 0

ThOF 2 24A/s at Ambient

Temperature (Ref. 5)

C~1000O•1500C (ThF4-12)

U 100'C (ThF 4-13)!'•2000C (h 4-9)4j4

0•0

Deposition Rate 33A/s

Incidence Angle = 0. 00

500 Substrates - 0. 5mm Cer-Vit

1i 1

0.5 1.0 1.5 2.0 2.5

Film Thickness (1inm)

Figure 18. Intrinsic Stress Dependence of ThF4 Filns on Substrate T-mper-ature. Stress measured using 0.5-t= Cer-Vit disks and electronbeam deposition at -33A/s.

41

1500

• o 300°(30A/s)

0

S200 (33A/s)

_• 400(25A/s)

4--

S500C Substrate Temp = 1500 C

Deposition Rate ;:25-34A/s)

Substrates - 0. 5-imm Cer-Vit

S11 I .. . .

0.5 1.0 1.5 2.0 2.5

Film Thickness (4m)

Figure 19. Variation of Intrinsic Stress with Incidence Angle for ThF4Films Deposited at 150 0 C. Stress rmeasured using 0.5-mmCer-Vit disks; electron beam gun deposition 34A/s.

42

-i.~

15001

1 /

: 4 •"400°(15A /s)°

50 Substrate Temp 2C0°C

Deposition Rate = 15 - 19A/s)

Substrates - 0.5-mm Cer-\-it

0.5 1.0 1.5 2.0 2.5

Filin Thickness (-k m)

Figure 20. Variation of Intrinsic Stress with Incidence Angle for ThF 4Films Deposited at 200*C. Stress measured using 0.5-rnCer-Vit disks and electron beam gun deposittion at 34 1/s.

43

_ _"

a -

(a) Cracked ThF4 Film on KCl. Fringe CurvatureIndicates Intrinsic Stress Variation With FilmThickness

to40 50Q

(b) Cracked ZnSe Film on KCl. Pattern Showsj Predominantly Straight Fringe&

FigureŽ 21. Fringe Patterns Produced for Cracked FilmsDeposited onto K(71

.44.

The dependence of intrinsic stress for ZnSe is shown in Figures 22, 23,and 24 and indicates that a large amount of stress control can be obtained byvarying the source rate. Low deposition rates of 2 to 4 X/s produce highcompressive stresses in the 2800 to 3200 kg/cm. range wh-reas the highest ratesof deposition, 20 to 25 A/s, produce compressive stresses in the 1i00 to1800 kg/cm2 range.

This reduction in stress is offset to some extent by an increase in in-trinsic stress with substrate temperature.

4.4.1 Stress Coefficients for ZnSe Films

Stress coefficients for various rates and temperatures for zinc selenidefilms (X/2 at 10.6 pm) are given in Table 2.

42: TABLE 2. STRESS COEFFICIENTS FOR ZnSe FILMS

"Temperature Rate

(X/s) A B C

100 2.6 -5150 2.05 25.0

100 18 -2100 u.95 56.0

100 18 -1866 0.58 60.0

150 4.4 -3300 0.20 80.0

150 20.0 -2200 0.94 68.2

150 24.0 -2384 0.9 74.3

200 3.o -4640 1 x 10- 9 9.0

200 19.0 -3800 0.01 21.5

200 24,0 -3020 0.44 82.5

4.4.2 Nonuniform Stress Distribution in ZnSe Films

In general, the rate of rise of stress with increased film thickness forZnSe films is much faster than for ThF4 films and is followed by a steady de-crease with an increase in thickness. Observation of flakes of zinc selenidefilms (Figure 21(b)) tend to confirm this thickness-dependent stress behav-ior showing predominantly straight line fringes for most of the crackedsamples observed.

4.5 INRINSIC STRESS IN THALLILN IODIDE AND CERIU! FLUORIDE FILMS

De osition of thallitza iodide films (\/2 at 10.6 j.m) at rates of 4 A/sand 20^/s shows that the stress in this material is extremely low. Usingthe thinnest fused silica slides available (0.18 n thick x 19 -n diameter)the maximum fringe count obtained corresponded to a stress of less than50 kg/cm 2. This compares vith previeos values measured for thinner films byEnnos (Ref. 5) of 200 kg/cm2 .

45

-100C

Substrate Temperature =2000C

Incidenm \ngle = 0. 0°

Substrates - 0. 5 -mm Ce'-Vit

c' . -200G'IU 24A

•W

ft U

"Film 1likis 9A4 111

12.

i i2

-400Q _________ ________L ___o. 5 1. U I. 5 2. 02 .

Figure 22. Va.riation of Intrinsic Stress in Zinc Selenide with DepositionRate (Source Control lO'). Stress m asurerzwnts made using 0. 25-=-Cer-Vit disks at a substrate temperaLure of 200'C.

46

. . - --- .-}- ~ K .4~l-"~.

Substr~ate Temperature 150'C

A -1000

(2.AL

CU)

0. 1 0!. .o 2

1-47

Subst-rate Temp 100'C

Incidence Angle =0. 0'

Substrates -0. 5 -mm Cer-Vit

- 1000

2.GA/s

00

-400 __________________________________

0.-2000 0

Fligue2.draino nrni tesi icSlnd

-4048

Cerium fluoride films were also evaluated and show highly tensile be-havior together with a small disruptive film thickness. The variation of

4 tensile stress for this material is given in Figure 25.

All 2000

Sobstrate Temp,= 2300C

Incidence Angle =0. 00

1500- Substrate - 0.5-mmn Cer-Vit

Z. Deposition Rate -5A/s

wI 1000

5001

0.1 0.2 0.3 (.4

-'ilni Thiclkness (G' m)Figure 25. intrinsic Strees in Ceriu~m NFLuridt' Film Deposited at 230 0C

by Electron Beam Gun. Stress measur-ed using Cer-12it 0.5 mm,Thick.

49

SECTION 5

MECHANICAL PROPERTY MEASUREMENTS

5. 1 EXPANSION COEFFICIENT AND YOUNG S MODULUS DETERMINATION FOR THIN-FILMMATERIALS

Experimental values of the thermal expansion coefficient (af) and Young'smodulus (Ef) for a thin film can be obtained using the four-channel interferom-eter system by observing the total deflection caused by thermally inducedstress. Figure 26 shows the output from two interferometer channels duringdeposition of a film of ThF4 (X/4 at 10.6 im) and during subsequent cooldown.This film is deposited onto Cer-Vit and KCI disks and the thermally inducedstress contribution is sufficient to produce a large tensile stress (+3400kg/cm2 ) for ThF 4 on Cer-Vit and a large compressive stress (-1400 kg/cm2 ) fcrThF4 deposited onto KC1. When zinc selenide films are deposited onto KCl inthis manner the large initial intrinsic stress -(1500-3000) kg/cm2 togetherwith a thermally induced stress of _2400 kg/cm2 is usually sufficient to crackthe films by compressive film failure at the -4000 to -5000 kg/cm2 stresslevel.

Initial experiments using uncoated disks of various materials showed thatsubstantial fringe changes occurred upon heating and cooling presumably dueto temperature gradients (radial and front to back) existing in the flexibledisks. Experimental measurements were therefore made using all four inter-ferometers and coated and uncoated disks of each substrate maerial. Fringechanges were utilized on cooldown since this results in a much lower coolingrate than during the heatup cycle.

The values of expansion coefficient and Young's modulus can be obtainedfrom the expressions for the thermally induced deflection of a thin disk, i.e.,

3 (1 -vS t /D2W 4E • f(a f- U ) (T i-To)

where (T, -TO) is the total temperature change, .s, vs, and E. being the ex-pansion coefficient, Poisson's ratio, and Young's modulus, respectively, ofthe substrate.

For two different substrate materials each coated w.th a film of thick-ness t the thermally induced deflections are

3(1-v ) 2(' 1 E,-, - " (T -To)

S4E (

I Ih-. 1iIJ E(Cl ( -~2( T)

50

4000Stress I Stress Changes Due to

3800 - Buildup During I Differential Contraction

3600 - Coating Between Film and

34 Deposition I SubstrateS3400 -[

n 3200

S3000 -

,, 2800

S2600 IU2I

n 2400 I&•2200

i 2000

-' 1800 ThF 4 Cer-VitDeposited Onto o• T

S1600 -Cer-Vit (0.5 mmI1400 - at 2000 C 4

1200Increase in Tensile Stress

1000 i of ThF During Cooling4

800

600

400 Onto4KClon Temp. k**C)200 (l.0Omm) at ITm.(C

2 00°C2 00 100 01 1. . . .1 . 1 1 1 1

0.5 1.0 1.5 2.0C4 200 -Mech. Filhn KCI

400 - 'ihickness (L)

U - 600. ~Conpressive

c'* 800 tress

. t1 DevelopedS1000 -4

P 1200 Film DuringE100S10Cooling1400

Figure 26. Intrinsic and Thermalil Induced Stresses in Th-F4 FilmsDeposited Onto Cer-Vit and KCM Substrates at 200C

51

Consequently, the values of the film constants af and Ef are given by

cz2wl 1A 2 - a•W 2 A 1

f W1A 2- w2A 1

E w2Ef = A 2 (Uf -a 2) t (T-TO)

where

221 4-E (i~7 and A 2 - 4EAl• 4EEh

characterize the substrate properties.

In all experimental determinations the deflections Wl and WL2 correspondto the differences in deflection between the coated and uncoated substrates,

S~i.e.,

W1 (w2) - (W ,l)uc

*c uc

5.2 EXPERIMENTAL RESULTS

"The typical changes that occur during heating, cooling, and reheating of* coated and uncoated disks of different materials are shown in Figure 27. Here,

disks of Cer-Vit and KCI are coated with ThF 4 material, and the fringe changesas a function of temperature are used to compute the expansion coefficient andYoung's modulus of the thin-film material as shown above.

Measurements were made of thin films of ThF4 , ZnSe, TII in this manner andthe results are summarized in Table 3.

Emphasis was placed on obtaining values of tif for thorium tetrafluoridesince measurements of this material in single crystal form by Van UiterL (Ref.13) show that the expansion coefficient is small and negative in the regionfrom 0 to 200 0 C. The experimental values for thin films consistently showeda large positive value both for measurements mad^- during cooldown and Inmme-diately after the film was deposited and during subsequent reheating cycles.Different pairs of substrates (KCI + Cer-Vit and KCI . ZnSe) were also used

for these experiments and gave similar results.

The expansion coefficient of thallium iodide material was so closelymatched to that of the KCl substrate that discernible difference in thefringe changes could be seen for the coated and uncoated subsL. ats.

13. L. Van Uitert, et al., Mat. Res. Bull. 11, 669 (1976).

52

Cd

414

V 4 0

00u

v f-4C

0c

Ch

0 C

C C 0 0 CC\3 C\ (

53

TABLE 3. EXPANSION COEFFICIENT AND YOUNG'S MODULUS DETEMI0NATION

Substrates Film Film Expansion Young'sUtilized Material Coefficient (czf) Modulus (Ef)

-6 5 2KCU, Cer-Vit ThF 4 13.3 x 10 "/C 4.3 x 10 kg/cm

KCI, Cer-Vit ThF4 11.1 x 10-6/-c 3.9 x 105 kg/cm2

KC1, ZnSe ThF4 18.1 x I0"6/QC 6.8 x 105 kg/cm2

KCI, ZnSe ThF4 15.1 x 10-6/°c 4.3 x 105 kg/cm2

KC1, ZnSe TlI 36.0 x 10-6/*C 2.3 x 105 kg/cm2

KC1, Cer-Vit ZnSe 8.1 x 106/°C 4.2 x 10 kg/cm2

54

il.

SECTION 6

SUMMARY AND CONCLUSIONS

The work performed during the present program has resulted in

e Fabrication of a four-channel stress interferometer system that iscapable of measuring stress levels in films as they are being de-posited in the form of single layers or as part of multilayer films.

* A new experimental technique has been established whereby the thermalexpansion coefficient and Young's modulus of thin-film materials canbe measured interferometrically.

o A computer code has been developed that utilizes the experimentallymeasured values of intrinsic stress, expansion coefficient, andYoung's modulus to model the stress levels in multilayer coatings"when subjected to a changing uniform temperature environment.

5

V

Ii

J 55

REFERENCES

1. R.W. Hoffman, Physics of Thin Films, Vol. 3, p. 211 (1966).

2. R.W. Hoffman, Thin Solid Films. Vol. 34, p. 185 (1976).

3. K. Kinosita, Thin Solid Films Vol. 17, p. 17 (1972).

4. R.S. Carpenter and D.S. Campbell, J. Matl. Sci., Vol. 2, p. 173 (1967).

5. A.E. Ennos, Appl. Opt., Vol. 5, No. 1, p. 51 (1966).

6. J.S. Halliday, T.B. Rymer, and K.H.R. Wright, Proc. Roy. Soc. (London)A225, p. 548 (1954).

7. A. Kinabara, H. Harabi, J. Appl. Phys. (Japan), Vol. 4, p. 243 (1965).

8. K. Roll and H. Hoffman, Rev. Sci. Inst., Vol. 47, No. 9 (1976).

9. L.S. Combes, S.S. Ballard, and K.A. McCarthy, J. Opt. Soc. Am.. Vol. 41,p. 215 (1951).

10. S. Timoshenko, Theory of Plates and Shells, 2nd ed. (McGraw-Hill,New York, 1959) p. 43.

11. L.I. Maissel and R. Clang, Handbook of Thin Film Technology, (McGraw-Hill,New York, 1970), p. 8 - 15.

12. M.C. Ohmer, Private Conmmunication, Air Force Materials Laboratory,Wright-Patterson AFB, Ohio.

13. L. Van Uitert, et al., Matl. Res. Bull, Vol. 11, p. 669 (1976).

i5

APPENDIX A

WAVEFORM ASYMMETRY FOR CAT 'S-EYE INTERFEROMETER

The waveform asymmetry obtained from a cat's-eye interferometer can bemodeled by using the field equations for Gaussian beams given by Kogelnik andLi (Ref. A-i). Figure A-i shows the multiple reflections arising from appar-ent beam waists at distances 26, 46, 66, etc., due to a mirror separation 6.These spherical waves having Gaussian amplitude profiles are all described at

* a point z along the axis by a radial electric field given by

E(r,z) ( L- expL(kz - er) ex (A-1)

where•;;'!: "" F2%2-I

Rz 21+ (A-2)

/ 22

2 (A-3)

(Z) tan= - (A-4)

Here t.,o is the beam waist at the first mirror and z is the distance to thesuammation point of the apparent beam waists.

The radial intensity wi. (12 U0J3 1 etc., at a point z1 is therefore obtainedas a coherent sumaation of all the spherical waves reflected by the mirrorsurfaces whose individual amplitude reflectivities are given by RI and R2 . Theradial intensity can be written as

IP. rr2 21 2 PP 2(r,-z) -2 exp -J(kz _-)2) -L-- +I- I r _ ex J(kz -$ - -

(A-5)

A-I. H. Kogelnik, T. Li, Proc. IEE, Vol. 54, No. 10, p. 1312 (Oct. 1966).

57

4i

where the individual reflection coefficients, Pi, are given by

P =R

2P2 = (i- R)R 2

22 n-i

P = (I-R)2 (R2 )nl (R)n-2n2 1

The values of Vi, Oi and Ri are obtained from equations (A-2), (A-3), and(A-4) by substituting for the various axial distances, i.e.,

z =z + 2(n-1)6n 1

• ,where 6 is the displacement of the second mirror surface due to the film being

deposited.

The expression for the radial intensity was obtained by minimal calcula-tion of the first 10 terms of the series, and these values were numericallyintegrated over a given detector area to obtain the shape of the detectoroutput as the mirror spacing was altered.

The computed waveform asynmietry becomes large as the mirror separationis increased, and the shape of the waveform asymmetry matches that obtainedin practice.

-a ;U~ssiall Intenusity

4/ I- -ofi IC

/

Hadi.all, Shea red Reflectevd Wavefronts

Figure A- I

58

UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE I Yoin Date Entered)____________________

REPOT DCUMNTATON AGEREAD INSTRUCTIONSREPOR DOCMENTTIONPAGEBEFORE COMPL.ETING FORMI. REPORT NU*MBER 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER

4. TITLE (and Subtitle) S. TYPE OF REPORT & PERIOD COVERED

Final Technical ReportINTRINSIC AND THERMAL STRESS MODELING FOR May 1976 - May 1977

THIN-FILM MULTILAYERS G. PERFORMING ORG. REPORTNUMBER

13396 17. A;UTHOR(s) S. CONTRACT OR GRANT NUMBERW#

A.M. Ledger 1~\A?-7,-;-v1R.C. Bastien

9. PERFORMING ORGAiNIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASKAREA 6 WORK UNIT NUMBERS

_0 The Perkin-Elmer CorporationNorwalk, Connecticut 06856 f ARPA Work Order No. 3220

1 1. CONTROLLING OFFICE NAME AND ADDRESS 112. AEPORT DATE

Defense Advanced Research Projects Agency 15 June 19771400 Wilson Boulevard1.NUeROPAE

RArlington, Virginia 22209 514 MONITORING AGENCY NAME 6 ADDRESS(it different tram Controlling 0111 ci) IS. SECURITY CLASS. (01 this report)

UNCLASSIFIED

IS.. DECLASSIFICATION 'DOWNGRAOINGSCHEDULE

16. DISTRIBUTION STATEMENT (of this Report)

Distribution of this document is unlimited.

17 DISTRIEPUTION STATEMENT (Qft

tA.batrctI entered A 816ek 20.Itdteetfo er)

I4 SUPPLCMENTAPY NOTES

'eiti~tincoiig Optical cotinrsHiph-energy lasers Op mat ~1cria.q~Infraired windows l1tIasniir- chloridelnterfcrometers St re-.5e5Materiail I.ctc__________ ____

The mesure-ment of intrinsic aind ther-mal lv indticed stresses in nmslt ilaverdieectic oatngswasinvstigated to improve reliability and du:rabil'tv

predictions of thin'-filn coatirFrs, Particularly, those coatiny.% th.-t will heutitlized under exitreme [her-mal conditions (e.g.. in high-energy laser syste-ms).l'rincipailly, the investigation %;-s conducted using thorium tetrailtioride,zinc selenide. And thalli-m iodide films As antireflection coatings on

j54 c' 1473 f D-1%o mvT s 9,L

SIECURITY CLASS4rICAT1ON Or THIS PAQC fUhea B~et Urse~ee

UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAOE(I9.hen Date Entered)

20. •ABSTRACT (Continued)

potassium chloride at 10.6 micrometers. A foar-channel stress interferom-eter system that measures stress levels in single or multilayer films asthey are heing deposited was fabricated and tested. A new experimentaltechnique was established whereby the stress interferometer system canalso be used to compute Young's modulus and the coefficient of thermalexpansion for the thin film matetials. A computer code was developed thatutilizes the experimentally measured values of intrinsic stress, expansioncoefficient. and Young's modulus to model stress levels in multilayercoatings when subjected to a changing uniform environment.

1-,

NC IASS IF lED

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