Transparent Tissues and Porous Thin Films: a Brillouin Light Scattering Study

Transparent Tissues and Porous Thin Films: A Brillouin Light Scattering Study

DISSERTATION

Presented in Partial Fulﬁllment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

By Sheldon T. Bailey, M.S.,B.S. Graduate Program in Physics

The Ohio State University 2012

Dissertation Committee:

R. Sooryakumar, Advisor

C. Jayaprakash

Richard Hughes

DongPing Zhong © Copyright by Sheldon T. Bailey

2012 Abstract

The elastic properties of materials composed of thin laminar structures control a broad range of phenomena in diverse systems. For example, elasticity affects the response of tissues in the eye that control the focusing of light, while strains within nano-scale films and coatings in the next generation of microelectronic devices could have profound effects on their functionality. Measurement of the elastic properties of such microscale structures has however proven difficult with traditional techniques such as mechanical stretching and nanoindentation being ineffective at these spatial length scales. In this thesis, Brillouin light scattering is shown to offer an effective approach to accurately measure the elastic properties of transparent tissues within the eye as well as dielectric thin films of interest to the semiconductor industry.

As the human eye ages, focusing on a near object generally becomes diﬃcult - a condition known as presbyopia. An age related stiﬀening of lens mechanical properties has been suggested as a cause for the onset of presbyopia. High frequency (GHz) Brillouin light scattering (BLS) experiments were performed on human lenses spanning an age range from

30-70 years. The measured frequency shifts, and derived bulk moduli values were found to not change signiﬁcantly over the age span studied suggesting the human eye lens does not appreciably stiﬀen with aging. In addition, similar high frequency studies on the cornea were performed with Brillouin light scattering (BLS) and quantitative ultrasound spectroscopy

(QUS) that were complimented with low frequency (<5 Hz) dynamic mechanical analysis

(DMA). Intact bovine eye globes were also studied with BLS at low power levels, allowing the

stiﬀness of the transparent cornea and lens tissues to be mapped ex-vivo as a function of axial

depth. These ﬁndings demonstrate the potential of utilizing BLS for clinical applications.

ii Scaling down the material components used in microelectronic interconnects presents increasing challenges to technology development in the semiconductor industry. To reduce RC time delays, low dielectric constant (k) hybrid organic-inorganic carbon doped

SiO2(SiOC:H) and amorphous carbon (a-C:H) interconnect layers with controlled levels of porosity have been pursued. However, increased porosity coupled with reduced film thicknesses (<100nm) could potentially reduce device functionality. Nanoscale film thicknesses render techniques such as nano-indentation to be ineffective to characterize the mechanical properties of these highly compact and porous structures. Brillouin light scattering from localized acoustic excitations enable the independent elastic constants, and thus the mechanical properties, of dielectric films with thicknesses as low as 94 nm and porosity levels up to 45%. The frequency dispersion and associated light scattering intensities of longitudinal and transverse acoustic standing mode type excitations were observed. The Poisson’s ratio (ν) and Young’s Modulus (E)of these highly porous low-k materials were determined and compared to those of conventional SiO2 and non-porous low-k materials.

iii Dedicated to Ernie

iv Acknowledgments

I would like to thank my adviser Prof. R. Sooryakumar for providing encouragement and support throughout my research endeavours in his group as well as all my fellow Sooryaku- mar group members for lending their expertise from time to time.

I would like to thank Professors Michael Twa and Mark Bullimore for advice on tissue preparation, and speciﬁcally M. Twa for invaluable insight and discussions on the human eye and bovine cornea work. I would like to thank Intel collaborator Sean King for providing and characterizing low-k dielectric thin ﬁlms as well as numerous contributions to our papers. I would like to thank Alan Litsky, Do-Gyoon Kim, HyunJung Kwon, Sean He, and Jun Liu for collaborative work on the bovine cornea. I would also like to thank Tom Kelch, The

OSU physics machine shop staﬀ, Kris Dunlap, Brenda Mellet, JD Wear, and Brian Keller for invaluable reasearch and other assistance over my tenure as a graduate student at OSU.

Additionally, I thank my advisory committee, Prof. C. Jayaprakash, Prof. DongPing

Zhong, and Prof. Richard Hughes for serving on my thesis committee and candidacy exam.

I would like to acknowledge the support I received from physics department as a GTA and GRA, the GK-12 Teaching fellowship and support from the Institute of Materials

Research at The Ohio State University and the Semiconductor Research Corporation under contract 2012-IN-2296.

Finally, I would like to thank my family and friends for their support and tolerance throughout my degree. I should give special mention to some of the graduate students who accompanied me on this prolonged sojourn: Julia Young, James C. Davis, Gregory Vieira,

Patrick D. Smith, Rakesh Tiwari, Jeﬀ Stevens, Michael Fellinger, Kevin P. Driver, G. Ben

Dundee, Dave Gohlke, Robert Guidry, Adam Hauser, Kerry Highbarger, William Parker,

v Mike Hinton, Bill Schneider, Mehul Dixit, Chris Porter and Alex O. H. Mooney.

vi Vita

October 20, 1982 ...... Born - Erie, Pennsylvania

2005 ...... B. S., Pennsylvania State University at Erie, Erie, Pennsylvania 2005–present ...... Graduate Research and Teaching Assis- tant, Dept. of Physics, The Ohio State University, Columbus, Ohio

Publications

[1] Sheldon T. Bailey, Michael D. Twa, Jared C. Gump, Manoj Venkiteshwar, Mark A. Bullimore, and Ratnasingham Sooryakumar. “Light-Scattering Study of the Normal Human Eye Lens: Elastic Properties and Age Dependence,” IEEE Trans Biomed Eng 57, 2910-17 (2010)

[2] W. Zhou, S. Bailey, R. Sooryakumar, S. King, G. Xu, E. Mays, C. Ege, and J. Bielefeld. “Elastic properties of porous low-k dielectric nano-ﬁlms,” J. Appl. Phys. 110, 043520 (2011)

[3] S. Bailey, E. Mays, D. J. Michalak, R. Chebiam, S. King, and R. Sooryakumar. “Me- chanical properties of high porosity low-k dielectric nano-ﬁlms determined by Brillouin light scattering,” J. Phys. D: Appl. Phys. (2012)

Fields of Study

Major Field: Physics

Studies in Brillouin Light Scattering: R. Sooryakumar

vii Table of Contents

Page Abstract...... ii Dedication ...... iv Acknowledgments ...... v Vita...... vii List of Figures ...... x List of Tables ...... xv

Chapters

1 Introduction 1 1.1 Motivation ...... 1 1.2 General Background and Light Coupling Mechanisms ...... 2 1.2.1 Brillouin Light Scattering in Transparent and Opaque Materials. . . 2 1.2.2 Brillouin Light Scattering in Highly Opaque Materials...... 5 1.3 SummaryofThesisChapters ...... 8

2 Experimental Methods 9 2.1 Introduction...... 9 2.2 BrillouinLightScattering ...... 9 2.2.1 Fabry-PerotInterferometer ...... 10 2.2.2 Six Pass Fabry-Perot Interferometer ...... 12 2.2.3 ExternalOptics...... 13 2.3 Quantitative Ultrasound Spectroscopy ...... 17 2.4 DynamicMechanicalAnalysis...... 17 2.5 PicosecondLaserUltrasonics ...... 19 2.6 Nanoindentation ...... 21

3 Brillouin Light Scattering Study of the Human Eye Lens 24 3.1 Introduction-TheHumanEyeLens ...... 24 3.2 MaterialsandMethods...... 28 3.3 HumanEyeLensResults ...... 30 3.4 Discussion...... 35 3.5 Summary ...... 40

4 Bovine Corneal Elasticity and its Frequency Dependence 42

viii 4.1 Introduction...... 42 4.2 MaterialsandMethods...... 44 4.3 Results...... 47 4.3.1 BrillouinLightScattering ...... 47 4.3.2 Quantitative Ultrasound Spectroscopy ...... 50 4.3.3 DynamicMechanicalAnalysis...... 50 4.4 Discussion...... 52 4.5 Summary ...... 56

5 Mechanical Properties of Low-k Dielectric Nanoscale Thin Films De- termined by Brillouin Light Scattering 58 5.1 Introduction...... 58 5.1.1 Low-kDielectricFilms...... 59 5.2 Nonporous and Moderately Porous Low-k Nano-Films ...... 61 5.2.1 Experiment ...... 61 5.2.2 BrillouinLightScatteringResults ...... 64 5.2.3 Discussion...... 72 5.2.4 Summary ...... 78 5.3 HighlyPorousLow-kNano-Films ...... 81 5.3.1 Experiment ...... 81 5.3.2 Results ...... 83 5.3.3 Discussion...... 88 5.3.4 Summary ...... 93

6 Conclusions and Future Work 95

Bibliography 97

ix List of Figures

Figure Page

1.1 An example Brillouin spectrum showing the elastically scattered Rayleigh peak and the inelastically scattered Stokes and anti-Stokes frequency shifted peaks. At the top of the ﬁgure is a cartoon showing the arrangement of incident ki and scattered ks photon wavevector for BLS in backscattering geometry k = k k = q...... 4 i − s 1.2 Depiction of a surface acoustic wave (SAW) as it travels along the surface. Note that the amplitude decays exponentially with depth into the material. 5 1.3 Brillouin light scattering geometry from a point on the surface of a thin ﬁlm fromComins2001[5]...... 7

2.1 Plots of two Airy function orders. Note as Finesse (F ) is increased, signal to noise, contrast (C), improves and the linewidth FWHM, represented here as δλ,decreases.FromComins2001[5] ...... 11 2.2 The two interferometers FP1 and FP2, have slightly different plate spacings as described in the text, producing two slightly offset Airy functions shown as the first and second curves from the top of the figure. The multiplication of these two functions is given as the curve at the bottom of the figure. Referring back to Equation 2.2 suppression of the transmission of neighboring interfence orders is evident allowing the FSR to be increased. Figure from Sandercock manual[9]...... 14 2.3 Top view of the six pass tandem Fabry-Perot interferometer. One plate from each FP is placed on single translation stage to assure equal movement of each plate. The distances d1 and d2 in the text are refered to as L1 and L2 in the figure. Figure from Sandercock manual [9]...... 15 2.4 Schematic of the experimental setup showing tandem Fabry-Perot interferometer (FP), sample holder (S) and various optical components (L: Lens, M: Mirror). The sample is placed on a linear translation stage at a location where the focal spot of the incident light is confocal to the entrance pinhole P of the tandem Fabry-Perot Interferometer. The translation stage enables sampling of desired positions within the sample while maintaining theconfocalarrangement...... 16

x 2.5 Depiction of cornea positioned between two DMA jigs with surface curvatures matching that of a bovine cornea. Only the axial force mode is depicted. . . 18 2.6 Four step schematic showing how a picosecond acoustic pulse is generated, propagated and detected. In step 1, a picosecond optical laser pulse heats a micron sized area to a depth of 20 nm. For example, an aluminum film generates 10 ps, 100 GHz pancake shaped acoustic pulse which propagates ∼ ∼ through the film as shown in step 2. The acoustic pulse reflects from the film-substrate interface (step 3). In step 4, the reflected acoustic pulse travels to the surface causing a local surface expansion which is detected by an ultrashort optical probe pulse. The acoustic pulse travel time is determined via an interferometer. Figure from Hokudai 2008...... 20 2.7 Example AFM illumination mode image of a Berkovich tip indent in a 5 µmx 5µm area of a glassy metallic alloy for 60 mN maximum load to a penetration depthof720nm,fromKim2002[29]...... 23

3.1 Schematic diagram of the backscattering geometry for measurements from the eye lens placed within a holder containing 0.9% saline solution. The holder, mounted on a programmable linear translation stage, enables the lens to be translated parallel to the optic axis for consecutive measurements withhighprecision...... 29 3.2 Representative Brillouin spectra from diﬀerent sections of the right (OD) lens from a 31 year old measured along the primary optic axis showing characteristic Stokes, anti-Stokes Brillouin doublet. The modes are associated with the longitudinal acoustic phonon of the tissue. In addition to spectra from the cortex (right panel) and nucleus (left panel), modes in the vicinity of the nucleus-cortex interface are shown. As the transition is made out of the nucleus into the cortex, (curves 2.2 mm to 3.2 mm center panel), two distinct peaks are evident whose spectral weight gradually makes a transition from high frequency (nucleus) to low frequency (cortex)...... 32 3.3 Sequence of Brillouin light scattering spectra recorded from the eye lens of a 41 year old man. From bottom (anterior) to top (posterior), the Stokes/anti- Stokes doublet represent scans recorded along the primary axis in incremental steps of 0.100 mm. The modes progressively increase from 7.80 GHz in the cortex to 8.90 GHz in the nucleus and then steadily recover back to 7.80 GHz when transitioned to the posterior of the lens. The uncertainty of the frequency measurements is 0.05 GHz. Note some initial data was taken by ± former graduate student Jared Gump...... 33 3.4 Age dependence of the longitudinal acoustic phonon frequency in the cortex and nucleus of the lens.For all ages, the frequency of the acoustic mode associated in the cortex is always smaller than the corresponding mode in the nucleus. The lines correspond to the average frequency, 7.85 GHz (cortex) and 8.80 GHz (nucleus), values of the data set. The standard deviation from the average is 0.14 GHz (cortex), and 0.22 GHz (nucleus). Note some initial data was taken by former graduate student Jared Gump...... 34

xi 3.5 Age dependence of the bulk modulus in the cortex and nucleus of the lens.For all ages, the bulk modulus in the cortex was always smaller than the corresponding modulus in the nucleus. The modulus is determined from the phonon frequencies of Figure 5. The lines correspond to the average bulk modulus values 2.36 GPa (cortex) and 2.79 GPa (nucleus) of the data set. The standard deviation from the average is 0.09 GPa (cortex), and 0.14 GPa (nucleus). Note some initial data was taken by former graduate student Jared Gump...... 35

4.1 Schematic of BLS experimental setup showing intact eye globe submerged in saline contained in a quartz holder secured to a translation stage. Axial movement of the stage enables the eye globe to be spatially traversed and probed...... 45 4.2 Schematic of Quantitative ultrasound spectroscopy setup used by our collaborator J. Liu and X. He 2009 [18]. The complete eye globe is submerged in saline solution, and the ultrasound transducer is lowered just below the saline level. The reﬂected sound waves from the anterior and posterior cornea surfaces are detected by the pulser-receiver...... 46 4.3 Typical Stokes and anti-Stokes BLS spectra recorded from cornea anterior to posterior (top to bottom curve). Note frequencies increase in the central region of cornea and decrease at anterior and posterior of the tissue. . . . . 48 4.4 BLS frequencies as a function of axial depth from anterior to posterior cornea measured ex-vivo from intact bovine eye globe...... 49 4.5 QUS reﬂectance spectra from the anterior and posterior cornea from collab- orationwithX.HeandJ.Liu...... 51 4.6 Displacement response on a single ex-vivo bovine cornea under a 1 Hz sinusoidally varying force. Data collected in collaboration with H. Kwon and D. Kim...... 53 4.7 BLS frequency (measured ex-vivo) as a function of axial depth from the anterior cornea to posterior eye lens of a bovine eye globe...... 54

5.1 Representative BLS spectra recorded at different scattering angles, θ = 0◦, ◦ ◦ ◦ ◦ 20 , 30 , 50 and 60 for a 100 nm Si0.2C0.8 : H#2 film (see Table 5.2) at the threshold of porosity. Peaks observed at the lowest scattering angles are the standing longitudinal modes 1LSM and 2LSM. As θ increases additional modes, including the transverse resonance (2TSM) emerge...... 65 5.2 Dispersion of acoustic modes supported in the h=100 nm porous Si0.8C0.2 : H#2 low-k dielectric film showing variation of mode frequencies with scattering angle θ in degrees. The measured data are large solid dark dots and the small dots are fits. The group of three higher (lower) frequency lines is the LA, TA and Rayleigh modes associated with the silicon substrate (bulk film). The left panel illustrates mode displacements within the film for ex- ◦ citations near θ = 0 where the solid line is Ux and the dotted line is Uz corresponding to the standing modes TSM and LSM. Here x identifies the direction of mode propagation parallel to film surface, and z, the normal to thesurface...... 67

xii 5.3 Representative spectra recorded at different scattering angles, θ = 10◦, 30◦, 50◦ and 60◦ for a 100 nm thick SiOC : H#2 film at 12% porosity (Table ∼ 5.3). The strong peaks observed at lower scattering angles are the longitudinal standing modes 1LSM and 2LSM, whereas the weaker peaks, not resolved in this measurement, represent the transverse standing modes 2TSM and3TSM...... 68 5.4 Dispersion of acoustic modes supported in the h=100 nm porous SiOC : H#2 low-k dielectric film showing variation of mode frequencies with scattering angle θ in degrees. The data are solid dark dots and the small dots are fits. The left panel illustrates mode displacements within the film for ◦ excitations near θ = 0 where the solid line is Ux and the dotted line is Uz corresponding to the standing modes TSM and LSM respectively. Here x identifies the direction of mode propagation parallel to film surface, and z, thenormaltothesurface...... 69 5.5 Representative spectra recorded at different scattering angles, θ = 20◦, 30◦, 40◦ and 60◦ for a 150 nm thick SiOC : H#4 film at 25% porosity (Table ∼ 5.3). Peaks observed at higher scattering angles emerge from the longitudinal standing mode (1LSM) and the 2LSM, 3TSM modes whose frequencies overlap. 70 5.6 Dispersion of acoustic modes supported in the h=150 nm porous SiOC : H#4 low-k dielectric film showing variation of mode frequencies with scattering angle θ in degrees. The data are solid dark dots and the small dots are fits. The group of three higher (lower) frequency lines is the LA, TA and Rayleigh mode associated with the silicon substrate (bulk film). The left panel illustrates mode displacements within the film for excitations near θ = ◦ 0 where the solid line is Ux and the dotted line is Uz corresponding to the standing modes TSM and LSM respectively. Here x identifies the direction of mode propagation parallel to film surface, and z, the normal to the surface. 71 5.7 The calculated and measured dispersion curves for the principal and higher order modes supported in the Si0.2C0.8 : H#2 film at the threshold of porosity ( 2%) as function of the normalized thickness Kkh. The solid line iden- ≤ T tifies VSi, the velocity above which the waves have an oscillatory component inthesubstrate...... 79 5.8 The calculated and measured dispersion curves for the principal and higher order modes supported in the SiOC : H#4 film with 25% porosity as function T of the normalized thickness Kkh. The solid line identifies VSi, the velocity above which the waves have an oscillatory component in the substrate. . . . 80 5.9 Illustrative BLS Stokes and Anti-Stokes spectra for 200 nm thick, 33.5% porous SiOC:H film recorded at θ = 5◦, 15◦, 45◦, and 60◦. At low angles, the N = 2 and N = 3 LSM modes are observed. As θ increases the modes become dispersive and additional modes emerge. The calculated spectra, utilizing elastic constants derived from the frequency dispersion (Figure 5.10), are illustrated above each measured anti-Stokes spectrum...... 84

xiii 5.10 Variation of mode frequencies with scattering angle θ for the 200 nm thick, 33.5% porous SiOC : H film. The BLS data are represented as solid dark circles and the calculated fits by the small dots. The mode amplitude illustrated on the left reveal the standing mode character for the N= 2, 3 LSM and N = 2, 3, 4 TSM modes at low θ. Ux (solid) and Uz (dashed) curves correspond to TSM and LSM amplitudes respectively. Here x identifies the direction of mode propagation parallel to film surface, and z, the normal to thesurface...... 85 5.11 Illustrative BLS Stokes and Anti-Stokes spectra for 94 nm thick, 45% porous SiOC:H film recorded at θ = 5◦, 30◦, 40◦, 45◦, and 60◦. At low angles, the N = 1 and N = 2 LSM modes are observed. As θ increases the modes become dispersive and additional modes emerge. The calculated spectra, utilizing elastic constants derived from the frequency dispersion (Figure 5.12), are illustrated above each measured anti-Stokes spectrum...... 86 5.12 Dispersion of mode frequencies with scattering angle θ for the 94 nm thick 45% porous SiOC : H film. The BLS data are represented by solid dark circles and the calculated fit, the small dots. The mode amplitude plots shown on the left reveal the standing mode character for the N = 1, 2 LSM and N = 2, 3 TSM modes at low θ. Ux (solid) and Uz (dashed) curves correspond to the TSM and LSM amplitudes respectively. Here x identifies the direction of mode propagation parallel to film surface, and z, the normal tothesurface...... 87 5.13 Representative spectra recorded at different scattering angles, θ = 10◦, 40◦, 50◦ and 60◦ for a 200 nm thick SOD SiOC : H film at 35% porosity. The ∼ peak observed at lower scattering angles is the longitudinal standing modes 2LSM with the 1LSM at a frequency too low to be measured with our BLS system...... 91 5.14 Dispersion of acoustic modes supported in the h=200 nm 35% porous SOD SiOC : H low-k dielectric film (Table 5.5) showing variation of mode frequencies with scattering angle θ. The data are solid dark dots and the small dots are fits. The left panel illustrates mode displacements within the film ◦ for excitations near θ = 0 where the solid line is Ux and the dotted line is Uz corresponding to the standing mode TSM and LSM...... 92

xiv List of Tables

Table Page

4.1 Thickness, density, and bulk modulus as determined by ex-vivo BLS and QUS on corneas from the nine bovine eye globes...... 50 4.2 Summary of average bulk/Young’s modulus results from the three diﬀerent techniquesutilized...... 57

5.1 Process conditions used for deposition of the porous thin film samples investigated. ∗FromLink2006[4]...... 61 5.2 General material properties of the low-k thin films investigated. ∗From pre- viousstudyinLink2006[4],ND=NonDetect...... 62 5.3 Summary of measured sample elastic properties, note E is the Young’s modulus. Relationship between Cijs and Poisson’s ratio, Young’s modulus are providedasequations5.4and5.5...... 66 5.4 NM = Not Measured. Samples burned under pump laser. Note: The reported uncertainties for NI-E and PLU-E represent one standard deviaton of >10 measurements. E is the Young’s modulus. ∗From previous study Link 2006 [4]...... 76 5.5 Description of materials and measured properties for the porous low-k dielectrics investigated in this study, where Dep. is the deposition technique, h is the film thickness, k the dieletric constant and n the refractive index for 400nmlight...... 83 5.6 Measured sample elastic constants and determined Poisson’s ratio and Young’s modulus...... 89

xv Chapter 1 Introduction

1.1 Motivation

The elastic properties of microscopic materials with laminar structure are central to studies

ranging from the determination of the cause of presbyopia to novel semiconductor nanoscale

ﬁlms to be used in the next generation of microelectronics [1, 2]. However experimentally

measuring these properties has proven diﬃcult. For example, study of the tissues of the eye

demands a technique which can probe these properties non-invasively without destruction

of the tissue. Tissue destructive methods can potentially yield innaccurate results as cutting

into the cellular structure of a lens or cornea can disrupt intercellular interdigitations which

play a signiﬁcant role in the tissue’s overall mechanical properties. The non-destrucitve and

non-invasive nature of Brillouin light scattering circumvents these issues, demonstrating

potential suitability for adaptation to a clinical setting with the possibility to detect early

onset of common ocular diseases as well as elucidate the mechanisms behind presbyopia [3].

The beneﬁts of Brillouin light scattering are also applicable to conventional semiconductor systems. As the semiconductor industry strives to reduce the size of microelectronic structures, novel materials with high levels of porosity have emerged. However, concerns pertaining to degradation and reduced mechanical strength of these materials have risen.

Accurate measurement of the elastic properties by traditional techniques is however hin- dered by the extreme thinness of these porous ﬁlms. For example, nanoindentation measurements are skewed due to tip substrate interactions, and the light intensites used in picosecond laser ultrasonics can damage the ﬁlms. The low light intensities used in Bril-

1 louin light scattering as well as the ability to accurately determine the Young’s modulus and Poisson’s ratio in laminar ﬁlms make this optical technique an invaluable tool to the researcher [4].

1.2 General Background and Light Coupling Mechanisms

First predicted by Leon Brillouin in the early 20th century, Brillouin Light Scattering(BLS) is a form of inelastic light scattering resulting from time dependent changes in the material due to acoustic (phonons), magnetic (magnons) or thermal eﬀects. Relevant to this study are long wavelength acoustic phonons which give rise to local density changes. These Brillouin excitation (phonon) freqencies are approximately ﬁve orders of magnitude smaller than visible light frequencies [5–7].

In any material at room temperature, a frequency continuum of phonons is present.

Phonons from the optical branch have been measured with great success over the years by Raman scattering. Acoustic phonons however have proven more diﬃcult to measure, as their lower freqencies make their detection diﬃcult [8]. However with the advent of the multi-pass interferometer and later the multipass dual interferometer as detailed in Chapter

2 [9], measurement of these thermally induced acoustic phonons with frequencies 150 GHz ≤ is possible.

Brillouin light scattering (BLS) arises from two mechanisms: elasto-optic (EO) and rip-

ple (RI). In the case of highly transparent materials, the elasto-optic mechanism dominates,

whereas in highly opaque materials, the scattered light originates primarily from the ma-

terial surface (being heavily absorbed with depth) where the ripple mechanism dominates.

In the following sections, we discuss the EO and RI mechanisms as well as the eﬀect of

boundaries such as the surface-air interface.

1.2.1 Brillouin Light Scattering in Transparent and Opaque Materials.

In any Brillouin light scattering event, a photon with wavevector ki enters a material in- teracting with an electron creating an exciton. This state can either lose (Stokes) or gain

2 (Anti-Stokes) energy from a thermal phonon, producing a scattered photon of wavevector k frequency shifted by f. This frequency shift produces a Brillouin spectrum as shown in s ± ﬁgure 1.1, with symmetric Stokes and Anti-Stokes frequency shifted peaks and is measured

by a six-pass tandem Fabry-Perot interferomenter as detailed in Chapter 2.

The presence of thermal phonons in a solid creates a ﬂuctuating strain ﬁeld throughout

the material. The following equations from [5] elucidate how the strain ﬁeld aﬀects the

electric ﬁeld of the scattered light leading to the phonon wavevector (q) conservation law.

The strain ﬁeld is related, through the elasto-optic coeﬃcients Pjklm, to the dielectric tensor

κjk through

κjk = Pjklmǫlm (1.1)

where, ǫlm are the ﬂuctuating strains, with j,k,l,m as indicies. For an isotropic solid, the

electric ﬁeld of the scattered light Es

E κ e−i(ks−ki)·x)d3x. (1.2) s ∝ jk VZ

If κ is linear in strains (κ e(iq·x)), and the scattering volume is large (>> 1/q3), then jk jk ∝ the electric ﬁeld integral produces the delta function δ(k k q), resulting in phonon s − i ± wavevector conservation

q = (k k ). (1.3) ± i − s In the case of opaque materials with small optical penetration depth ξ (high optical absorp-

tion), the phonon wavevector conservation becomes

q = (k k ), (1.4) || i|| − s||

with only the wavevector components parallel to the surface conserved. The lack of conser-

vation of the perpendicular wavevector with increasing opacity (ξ), results in broadening of the BLS peaks for highly opaque materials. In this case the EO mechanism no longer plays a signiﬁcant role, and the RI mechanism dominates. To calculate BLS spectra as well as the dispersion and mode amplitudes, we follow the surface elastodynamic Green’s function method introduced in [5, 10].

3 Figure 1.1: An example Brillouin spectrum showing the elastically scattered Rayleigh peak and the inelastically scattered Stokes and anti-Stokes frequency shifted peaks. At the top of the ﬁgure is a cartoon showing the arrangement of incident ki and scattered ks photon wavevector for BLS in backscattering geometry k = k k = q. i − s

4 Figure 1.2: Depiction of a surface acoustic wave (SAW) as it travels along the surface. Note that the amplitude decays exponentially with depth into the material.

1.2.2 Brillouin Light Scattering in Highly Opaque Materials

Whereas thermal phonons in transparent materials and their associated EO mechanism enable detection of these modes by BLS, the low optical penetration depth of opaque materials render these excitations within the bulk diﬃcult to measure by BLS. The phonons that are detected by BLS in opaque materials create ripples on the surface very much like a shallow, travelling diﬀraction grating. These ripples or Surface Acoustic Waves (SAWs) for example give rise to the well known Rayleigh acoustic wave (Figure 1.2).

5 To determine the inplane phonon wavevector qk, we consider a point on the sample surface as depicted in ﬁgure 1.3 as discussed by Comins [5]. Deﬁning scattering angle φ =

180 ϕ (see Figure 1.3), we note that q has two components: q = k sinθ +k sinθ cosφ and − k 1 i i s s q2 = kssinθssinφ. Since the phonon frequency is much smaller than the photon frequency,

we assume ks = ki giving

2 2 qk = ki sin θi + 2sinθisinθscosφ + sin θs. (1.5) p Furthermore if we let φ = 0 and θs = θi,

qk = 2kisinθi (1.6)

where the phonon velocity V = ω/qk, with ω being the phonon angular frequency [5, 11]. To use the experimentally measured phonon frequency shift to determine the elastic constants, the opaque material’s surface dynamics are calculated using the Fourier domain surface dynamic Green’s function Gij(qk, ω) [5, 12]. The scattering cross section of surface phonons with wavevector qk and angular frequency ω is related to the normal displacements of the surface u3(0) by d2σ u (0) 2 . (1.7) dΩdω ∝ h| 3 | i where u (0) 2 is h| 3 | i T u (0) 2 Im[G (q ,x = 0, ω + i0)] (1.8) h| 3 | i∝ ω 33 k 3 where T is temperature, and G33 the elastodynamic Green’s function evaluated at the sample surface. Using the method of partial waves with the appropriate boundary conditions, surface tractions and displacements, we can express G33 as

6 i ah j(B)(n) G (q , ω)= 3 U (n) (1.9) 33 k ω B 3 n=1 X | | (n) where Bl incorporates the elastic tensor C3lpq as

(n) (n) (n) Bl = C3lpqUp qq /ω. (1.10) pq X In the case of thin soft supported ﬁlms on a hard substrate, knowledge of density and

6 Figure 1.3: Brillouin light scattering geometry from a point on the surface of a thin ﬁlm from Comins 2001 [5].

thickness, with appropriate choice of elastic constants, enables us to calculate BLS spectra, frequency dispersion, and mode amplitudes as a function of ﬁlm depth that also reveal modes analogous to organ pipe modes. These features are discussed in Chapter 5 [5, 12].

7 1.3 Summary of Thesis Chapters

Chapter 1 gives a brief overview of this thesis as well as a theoretical background for Brillouin

Light Scattering.

Chapter 2 summarizes the experimental techniques Brillouin Light Scattering(BLS),

Quantitative Ultrasound Spectroscopy(QUS), Dynamic Mechanical Analysis (DMA), Pi-

cosecond Laser Ultrasonics(PLU) and Nanoindentation(NI). Comparison between these

methods and their suitability for use on very thin ﬁlms is discussed.

Chapter 3 presents results on human eye lenses and intact bovine eye globes. The

measured BLS frequencies yield the bulk modulus. Its variations with depth and as a

function of age are presented. The potential suitability of the technique for in-vivo studies

in a clinical setting on intact specimens is demonstrated for the bovine eye globe.

Chapter 4 presents ﬁndings on the mechanical properties of the bovine cornea with BLS.

The results are compared to those from QUS and DMA, techniques that are characterized

by vastly diﬀerent probe frequencies.

Chapter 5 highlights results on determining the elastic constants of porous nanoscale thin

ﬁlms through measurement of BLS frequencies as well as the techniques Picosecond Laser

Ultrasonics (PLU) and Nanoindentation (NI). The evaluation of the mechanical properties

of ﬁlms with varying porosity levels and thickenss as determined from the BLS data is

presented.

Chapter 6 summarizes the overall results in this thesis and discusses possible paths for

future work.

8 Chapter 2 Experimental Methods

2.1 Introduction

This chapter provides an overview of experimental techniques used for the various mechanical property measurements utilized in this thesis. We begin with the primary technique,

Brillouin Light Scattering(BLS) based on a tandem six pass Fabry-Perot interferometer.

Four additional techniques Nanoindentation (NI), Picosecond Laser Ultrasonics (PLU),

Quantitative Ultrasound Spectroscopy (QUS), and Dynamical Mechanical Analysis (DMA), are also discussed.

2.2 Brillouin Light Scattering

As previously noted Brillouin Light Scattering (BLS) is a noninvasive experimental technique which has been used widely to analyze acoustic phonon and magnetic spin (magnons) waves of various materials [13]. Raman and Brillouin scattering share the same general underlying mechanism. However, Raman scattering emerges from optical excitations with frequencies in the hundreds of GHz, Brillouin scattering occurs for long wavelength excitations with frequencies (f) on the order of 10 - 100 GHz ∼ C f = ij /λ (2.1) s ρ where Cij are the sample elastic constants, ρ the sample density, and λ the phonon wavelength. The low frequency makes experimental observation of Brillouin frequencies more

9 diﬃcult than the higher frequency Raman counterpart to observe. Typically, a Fabry-Perot interferometer is used to measure the weak and small frequencies associated with BLS; we

ﬁrst discuss the principles of the Fabry-Perot Interferometer.

2.2.1 Fabry-Perot Interferometer

At the heart of the BLS system is the Fabry-Perot Interferometer (FP) used to disperse the weak inelastically scattered light from thermal phonons. A FP is simply comprised of two parallel optical flats spaced a distance (d) apart, whose inner surfaces have a highly reflective coating optimized for a particular optical wavelength. This allows multiple reflections for maximal optical dispersion of the light. The transmitted light intensity (It) through a FP is given by

T 2 1 T 2 I = [( ) ]m = [( )A(ψ)]m, (2.2) t (1 R)2 (1 + [4R/(1 R)2]sin2(ψ/2)) (1 R)2 − − − where T is the transmittance, R the reﬂectance, ψ the phase, A(ψ) the Airy function, and m the number of passes through the FP [9]. Figure 2.1 shows the Airy function fringe pattern of the transmitted intensity through the FP, where the spacing between adjacent peaks is deﬁned as the free spectral range (F SR).

Furthermore, the full width at half maximum (FWHM) of the fringes is related to the reﬂectivity by 2(1 R) FWHM = − , (2.3) √R [9]. A lower FWHM allows adjacent peaks to be resolved more easily. Relating the

FWHM to the F SR allows us to deﬁne the ﬁnesse (F ) of the interferometer as

π√R F = , (2.4) 1 R − [9], or in the cases of multiple passes m,

π√R F = ( )/ 21/m 1, (2.5) m 1 R − − p [9]. Referring to ﬁgure 2.1, it is evident that increasing the ﬁnesse not only decreases the

10 Figure 2.1: Plots of two Airy function orders. Note as Finesse (F ) is increased, signal to noise, contrast (C), improves and the linewidth FWHM, represented here as δλ, decreases. From Comins 2001 [5]

11 FWHM but also increasese the contrast (C) deﬁned by

I max C = t , (2.6) Itmin which, in turn, can be related to the ﬁnesse by

4F 2 C =1+ . (2.7) π2

Here Itmax and Itmin are the maximum and minimum transmitted intensity respectively [9, 14] . The maximal contrast of a single FP is typically of the order 103. However since

the contrast of the elastically scattered signal is 106 - 1010 times stronger than that of the

inelastically scattered signal, a single pass FP is not suﬃcient to resolve the inelastically

scattered light. Since It scales as the power m, a greater number of passes of the inelastically

scattered light through the interferometer will improve the ﬁnesse (Fm) as well as the

m contrast since the multiple pass contrast(Cm) is given by Cm = (C1pass) [9]. In the case of six passes, C 1018, a value suﬃcient to resolve the inelastic Brillouin peaks. 6 ∼

2.2.2 Six Pass Fabry-Perot Interferometer

Brillouin light scattering received little experimental attention until the innovation of a

two, and later a six, pass Fabry-Perot Interferometer pioneered by J. R. Sandercock in the

1970’s [15, 16]. A typical Fabry-Perot Interferometer (FP) consists of glass optical ﬂats with

a reﬂective coating on the inner surfaces optimized for a particular wavelength of light, 514.5

nm for this study. The frequencies (ω) of thermal phonons that are able to be resolved are

on the order of 2-100 GHz. The required large FSR is accomplished by supressing adjacent

orders in the transmitted Airy function of Figure 2.1 by having the two FPs with slightly

diﬀerent plate separations d1 and d2.

The allowed transmitted phonton wavelengths (λ0) in a FP with plate separation (d) are given by 1 d = nλ , (2.8) 2 0 where n is an integer. In the case of two interferometers with diﬀering plate separations we

12 obtain the condition 2d1 2d2 = = λ0. (2.9) n1 n2 In Figure 2.2, it is evident that the eﬀect of diﬀerent plate spacings is to eliminate the

transmission of neighboring peak orders, thereby extending the free spectral range of the

instrument. However in practice, the tandem FP plates are scanned by a very small dis-

placements δd1 and δd2 given by

δd d δλ 1 = 1 = 0 . (2.10) δd2 d2 λ0

Here δd1 and δd2 are the displacements of the plate spacing in FP1 and FP2 respectively, usually on the order of angstroms. To ensure these small displacements are synchronized,

both FPs are arranged such that one plate from FP1 and FP2 is on the same translation

stage which is scanned via Sandercock’s novel deformable parallelogram construction [9].

The corresponding FP plate separations are d1 and d2 = cosθ, where θ is the angle between the optical axes of the FPs as shown in Figure 2.3.

2.2.3 External Optics

Figure 2.4 shows the main optics, both inside the interferometer box (JRS six pass tandem

Fabry-Perot interferometer), and outside. The external optics direct the laser light onto

the sample (S), where a lens (L) collects the scattered light which is transmitted through a

smaller lens (L2) to the entrance pinhole (P) on the exterior of the box. Since S is mounted on a translation stage (horizontal movement in the ﬁgure) and the focus is confocal with

the pinhole P, collection of scattered light from speciﬁc depths of S is accomplished. As

will be evident, in the case of thick transparent materials, such as the eye-lens, this allows

collection of BLS data, and thus information on mechanical properties, as a function of

depth within the tissue.

13 Figure 2.2: The two interferometers FP1 and FP2, have slightly different plate spacings as described in the text, producing two slightly offset Airy functions shown as the first and second curves from the top of the figure. The multiplication of these two functions is given as the curve at the bottom of the figure. Referring back to Equation 2.2 suppression of the transmission of neighboring interfence orders is evident allowing the FSR to be increased. Figure from Sandercock manual [9].

14 Figure 2.3: Top view of the six pass tandem Fabry-Perot interferometer. One plate from each FP is placed on single translation stage to assure equal movement of each plate. The distances d1 and d2 in the text are refered to as L1 and L2 in the ﬁgure. Figure from Sandercock manual [9].

15 Figure 2.4: Schematic of the experimental setup showing tandem Fabry-Perot interferometer (FP), sample holder (S) and various optical components (L: Lens, M: Mirror). The sample is placed on a linear translation stage at a location where the focal spot of the incident light is confocal to the entrance pinhole P of the tandem Fabry-Perot Interferometer. The translation stage enables sampling of desired positions within the sample while maintaining the confocal arrangement.

16 2.3 Quantitative Ultrasound Spectroscopy

Quantitative Ultrasound Spectroscopy (QUS) is a non-invasive, non-destructive technique to measure the mechanical properties of a wide range of materials, including biological specimens such as the cornea and bone [17–20]. In this variant of acoustic spectroscopy as developed by Liu and He [21], a low energy (several mw/cm2) acoustic pulse created by a transducer is strongly coupled to the sample. As the pulse propagates though the tissue, microscopic deformations are created, leading to attenuation of the acoustic pulse, as well as reﬂections at boundary layers. The travel time of the reﬂected pulse is measured at a rate of 500 MHz enabling the sound velocity of the medium to be determined as well as providing information on spatial information of the layers. In this study, this technique is applied to the cornea as detailed in Chapter 4. These measurements were carried out with the help of Professor Jun Liu and graduate student Sean He in the Department of

Biomedical Engineering at The Ohio State University.

2.4 Dynamic Mechanical Analysis

Dynamic Mechanical Analysis (DMA) is used to characterize the low frequency acoustic properties of materials. In general, there are two types of DMA measurements axial and torsional [22]. In this study only axial measurements are considered (Figure 2.5), and was done in collaboration with Professor Do-Gyoon Kim and postdoctoral researcher HyunJung

Kwon in the College of Dentistry at The Ohio State University. In a typical axial measurement the sample is placed between two jigs with user deﬁned surface geometry where the bottom jig is mounted on a force transducer, and the sample is compressed under a sinusoidal oscillation. The oscillation can be run in either stress (force) or strain (displacement) control mode. Under force/displacement control, the force/displacement is held constant with the displacement/force measured [22]. When force vs displacement is evaluated in terms of stress vs strain, mechanical properties such as Young’s modulus can be extracted from the measurement.

17 Figure 2.5: Depiction of cornea positioned between two DMA jigs with surface curvatures matching that of a bovine cornea. Only the axial force mode is depicted.

18 2.5 Picosecond Laser Ultrasonics

First pioneered by the Humphrey Maris group in the 1980’s [23], Picosecond Laser Ultrason- ics (PLU) has become a predominant method for measuring thin ﬁlm properties (including thickness, elastic constants and sound velocities) for the semiconductor industry [23–25].

This non-invasive method uses a picosecond optical pump pulse which is absorbed by the upper layer of the film creating a thermal stress near the film surface. The resulting thermal stress produces an elastic strain pulse (longitudinal acoustic phonon pulse) which propogates through the film, reflects off the film-substrate interface and is detected on the return as shown in Figure 2.6. Shear waves can also be produced from anisotropic materials [25, 26].

19 Figure 2.6: Four step schematic showing how a picosecond acoustic pulse is generated, propagated and detected. In step 1, a picosecond optical laser pulse heats a micron sized area to a depth of 20 nm. For example, an aluminum film generates 10 ps, 100 GHz ∼ ∼ pancake shaped acoustic pulse which propagates through the film as shown in step 2. The acoustic pulse reflects from the film-substrate interface (step 3). In step 4, the reflected acoustic pulse travels to the surface causing a local surface expansion which is detected by an ultrashort optical probe pulse. The acoustic pulse travel time is determined via an interferometer. Figure from Hokudai 2008.

20 2.6 Nanoindentation

Indentation measurements have been performed since the beginning of the 20th century as a means of quantifying material mechanical properties [27]. In traditional indentation an indenter tip of a speciﬁed size and geometry is pressed into a bulk material until a predetermined maximum load (Pmax) is reached. The tip is then removed and the area of the indent (A) is measured, typically with an optical microscope, to determine the material hardness (H) given by P H = max . (2.11) A However, these traditional measurements are limited by the need of precisely knowing the indenter tip dimensions as well as resolution issues associated with optical microscopic imaging. [28].

With the advent of instruments able to continuously measure loads and displacements on the scale of nanonewtons and nanometers, it was realized in the 1970’s that elastic moduli could be determined through load-diplacement curves. Nanoindentation (NI) has become a common technique [27]. It uses small tip areas on the order of square nanometers making determination of the indent area diﬃcult. A solution to this diﬃculty is to use an indenter tip with precisely known geometrical dimensions, typically a 3 sided pyramid known as a

Berkovich tip. During a measurement, the indent area is determined by measuring the depth of indentation with previous knowledge of the tip area and geometry. Figure 2.7 shows an

Atomic Force Microscope (AFM) image of a typical Berkovich indent [29]. Load (P ) vs penetration depth (h), known as a load-displacement curve, is recorded, allowing properties such as Young’s modulus (E) to be determined. With knowledge of the stiﬀness (S) of the contact extracted from the slope of the P vs h curve and the projected area of indentation

(Ap) at contact depth (hc), the reduced Young’s modulus (ER) can be calculated by

1 √π S Er = , (2.12) β 2 Ap(hc) p where β is a geometrical constant, and Ap(hc) is approximated by ﬁtting a polynomial for the Berkovich tip [27]. Furthermore Young’s modulus (E) is determined from the reduced

21 Young’s modulus (Er) through the relationship

E E E = r i (1 ν2), (2.13) E E (1 ν 2) − i − r − i

where Ei and νi are the Young’s modulus and Poisson’s ratio of the indenter tip material, and ν is Poisson’s ratio of the bulk material under measurement.

NI results are accurate in the case of thick ﬁlms on a subtrate. However, as the material thickness falls below 1000 nm, indenter-substrate interactions become important and introduce errors into the NI measurements. For example, in the case of ﬁlms <200 nm

highlighted in Chapter 5, E values determined through such indententation approaches will

be skewed higher due to interaction with the harder substrate.

22 Figure 2.7: Example AFM illumination mode image of a Berkovich tip indent in a 5 µm x 5µm area of a glassy metallic alloy for 60 mN maximum load to a penetration depth of 720 nm, from Kim 2002 [29].

23 Chapter 3 Brillouin Light Scattering Study of the Human Eye Lens

3.1 Introduction-The Human Eye Lens

The young human eye can adjust its focal power so that images of both distant and near objects can be focused on the retina a process known as accommodation. During accommodation, changes in the focal power of the lens result from changes in the shape of the crystalline lens [30]. The material properties of the lens are an important factor that determines the responsiveness of this tissue to the external forces that reshape the lens during lenticular accommodation.

Understanding the material properties of the lens, their correspondence with the known anatomical structure and how these material properties change with age is critical for understanding the forces required to alter the shape of the lens, the mechanism of accommodation and its age-related decline. The objectives of the current study were to evaluate regional diﬀerences in the material properties of the human lens ex-vivo using a non-destructive test method Brillouin light scattering (BLS) and to determine if there are any measure- able age dependent changes using this technique. The lens is a biconvex spheroidal tissue encapsulated within an elastic collagenous outer membrane of varying thickness [31, 32].

During accommodation, external forces are translated to the internal mass of the lens tissue through the lens capsule. This causes the lens to thicken in its anterior-posterior dimension and asymmetrically steepens the curvature of the external surfaces.

24 Lens tissue is formed by lens fiber cells, which are highly differentiated epithelial cells containing few organelles, no cell nucleus and a relatively high proportion of specialized cytoplasmic proteins ( 65% water and 35% protein) [33]. Because of its high water ∼ ∼ content, Poisson’s ratio ν, of the lens is 0.5 [34]. The body of the lens is comprised of ∼ several structurally distinct regions that may be generally divided into an inner nucleus and outer cortex. Lens fibers continue to grow throughout life, adding volume to the lens cortex [35]. The nucleus is developmentally older than the cortex and, although it is formed by the same lens epithelial fibers, the nucleus lacks the visibly distinct lamellar organization of lens fibers seen in the cortex [36] and it does not increase in thickness with age [35]. These morphological and ultrastructural differences may confer different material properties to each region of this tissue that may also differ by age [36]. With increasing age, the ability to accommodate to near targets gradually diminishes resulting in the need for reading glasses or bifocals by the age of 45 years - a condition known as presbyopia. The mechanisms underlying presbyopia are equivocal. Helmholtzs theory states that a stiffening of the crystalline lens is responsible, although differences between the central nucleus and outer cortex of the lens and their separate roles in relation to presbyopia have not yet been fully addressed. A non-invasive technique capable of probing the elastic properties of different segments of the lens would be especially valuable in identifying contributions to the lens deformations and their evolution with age.

Here we report on the application of Brillouin scattering to probe the axial spatial variation (or gradient) of the lens mechanical properties. Brillouin light scattering (BLS) is the inelastic scattering of light waves caused by interactions of the electric ﬁeld of the light with acoustic modes of materials. The expansions and contractions created in the material by propagating acoustic waves result in spatial and temporal modulations of the material density. The resulting time dependent changes in the electromagnetic characteristics, such as the refractive index of the material, underlie the coupling of the light to the acoustic modes. Conversely, the electric ﬁeld of an incident light wave can induce spatially varying and temporally periodic elastic strains and initiate acoustic waves in materials. The corresponding loss of energy from the light wave to the material results in a down shift of the

25 photon frequency (Stokes scattering), while the transfer of energy from existing acoustic waves in a material to the incident light wave results in a light frequency upshift (anti-

Stokes scattering). These transfers of energy result in modulations of the scattered light wave with discrete sum (anti-Stokes) and diﬀerence (Stokes) frequencies impressed upon the frequency of the incident light wave, leading to the characteristic Brillouin doublets evident in the spectra presented below. The downward and upward shifts in the light frequencies correspond to the creation and annihilation of discrete acoustic vibrations (phonons) with resulting Brillouin scattering conforming to the conservation of total energy and momentum.

Since, for well deﬁned acoustic waves to propagate, there must exist appreciable coupling of neighboring atoms and/or other structural elements (i.e. mechanical properties) of the material, detection of these acoustic waves by a technique such as BLS, provides direct access to its elastic properties.

The low energies of acoustic vibrations in materials, compared to light waves, are related to their relative propagation speeds. This ratio is typically 10−5. Since the 514.5 nm laser light utilized in this study has a frequency of about 1014 Hz (100 THz), the frequency shifts of the incident light produced by the photon-acoustic wave interactions is of the order of 109 Hz (GHz). Such small frequency shifts from the incident light, requires a means to isolate and analyze the Brillouin scattered signal against a strong background of elastically scattered laser light. This requires a high-resolution dispersive unit such as

Fabry-Perot interferometers with high light throughput and superior extinction (contrast) characteristics. The multi-pass tandem interferometer system utilized in this study provides these features with a contrast ratio of over 1010.

Brillouin scattering is distinct from other types of light scattering phenomena. In Ra- man scattering, while formally identical to Brillouin scattering, the energy transfer between the light and the material often involve vibrational modes (optic phonons) of the material.

These are excitations that lie in the terahertz range, and are distinct from their acoustic mode counterparts. In contrast, photoacoustic spectroscopy requires a laser source that thermally excites acoustic waves in the material which are subsequently detected by a sensitive acoustic transducer. Fluorescence spectroscopy involves the interchange of energy

26 between light and electronic energy levels of the material. There are numerous advantages of Brillouin scattering, especially from biological tissues. Since the acoustic waves in a BLS measurement are induced at ambient temperature without the need for external transducers, this non-contact, non-destructive confocal technique is especially suited to investigate the biomechanical properties of the lens. In addition to not requiring any special tissue preparation, strong Brillouin spectral features are acquired within seconds and with low laser power levels that when reﬁned, may be suitable for use in vivo. Most previously reported methods of measuring the elastic properties of the lens are either destructive [2, 33, 37] or at least disruptive [38] of the normal lens structure. Thus the BLS technique has numerous advantages over other techniques for determining the regional material properties of the lens.

The Brillouin light scattering technique has been applied to many conventional con- densed matter systems [39]], heterostructures [40] and to monitor the pressure dependence of compressional acoustic modes supported in solutions [41]. The high precision of the method is evident in its application to supported ﬁlms [42] and free standing, 100 nm thick, membranes [43] to non-destructively measure the sound velocity, and hence the elastic properties of these ultrathin systems. It has also been successfully applied to completely characterize the elastic properties of highly anisotropic laminar structures [44].

In general, the propagation speed U of a longitudinal acoustic wave in a viscoelastic 4 2 K+ 3 G medium of density ρ is given by U = ρ where the medium is determined by a combination of the bulk modulus (K) and shear modulus (G). In the case of the eye lens, G is

much smaller than K, and thus the variation of the bulk modulus with depth is determined by the expression K = U 2. In Brillouin scattering, the speed of the acoustic wave is given

by U = λf/2n where λ = 514.5 nm is the illumination laser wavelength, f is the average

of the backscattered Stokes and Anti-Stokes Brillouin frequency shifts, and n the refractive

index of the lens. Thus the spatial variation of the bulk modulus K = ρλ2f 2/4n2 is directly

obtained from the measured Brillouin shift f, and knowledge of n and as the incident laser

beam probes diﬀerent positions within the lens.

The precision and accuracy with which Brillouin scattering has been successfully applied

27 to determine all of the independent elastic constants of highly anisotropic [44] materials can, in general, be also applicable to biological tissues. In the case of the eye lens however, the very low values for its shear modulus that arise from its large water content, would make a complete characterization of the elastic properties by this method difficult. For instance a G = 102 kPa, would yield Brillouin frequencies of the order of megahertz which is below the range accessible with our interferometer system. Instead the method offers excellent opportunities to fully characterize the compressional moduli, and thus to evaluate their role in reshaping the lens during accommodation. This study takes advantage of the high spatial resolution, non-invasive and non-destructive features offered by Brillouin scattering to probe the spatial gradients of the longitudinal bulk modulus within the lens and its age dependence.

3.2 Materials and Methods

Figure 3.1 illustrates schematically the backscattering geometry and the holder for the eye lens under study. Fresh and otherwise healthy human crystalline lenses were provided by the Ohio Lions Eye Bank, Columbus, Ohio already placed in a storage media consisting of a balanced salt solution with an osmolarity similar to that of the aqueous humor (290 millimoles) of the following composition (in g/L): NaCl 8.0, KCl 0.4, Na2HPO4 0.1, glucose 1.0, Hepes 2.38, and buﬀered with 8 ml of 0.5 M NaOH to a pH of 7.4. The lenses were obtained at most 3 days postmortem, and stored in solution at a temperature below

60◦F. A total of 29 lenses from 22 subjects spanning an age range of 30 70 years were − used. The lenses evaluated had intact capsules, were not diseased, and the lens tissue from these eyes had no clinically visible signs of cataract. No lenses within intact enucleated eyes were studied.

The Brillouin measurements were performed along the central axis through the geometric center of the lens, with the reﬂected laser beam traveling along the backscattered path that overlapped with the incident beam as illustrated in Figure 3.1. Spectra were recorded with

2 10 mW of λ = 514.5 nm laser radiation focused to spot of about 35 to 50 microns in −

28 Figure 3.1: Schematic diagram of the backscattering geometry for measurements from the eye lens placed within a holder containing 0.9% saline solution. The holder, mounted on a programmable linear translation stage, enables the lens to be translated parallel to the optic axis for consecutive measurements with high precision.

diameter. The lenses were placed in a custom made square holder containing 0.9% saline solution. In order to conveniently maintain normal incidence of the incoming laser light to the lens tissue, no measurements were made along the lateral dimension as that would be sensitive to the equatorial curvature of the lens.

Spectra were measured as a function of depth within the lens in 25 1µm step sizes, ± starting from the anterior surface, proceeding through the lens tissue, and ending at the posterior surface. As schematically illustrated in Figure 2.4, the scattered radiation was dispersed by a 6-pass tandem Fabry-Perot interferometer (JRS Scientiﬁc Tandem Fabry-

Perot Interferometer TFP-1) with 450µm entrance pinhole that determines the axial spatial resolution of the measurement. Further reduction of the pinhole size to 150µm did not improve the axial spatial resolution that we estimated as 100m. For a lateral spot size of 35 to 50µm in diameter, we had a total probe volume between 4 to 8 x 10−4 mm3 for

our measurements. The lower limit for the frequency measurement for our interferometer

system was 1 GHz. A baseline measurement was ﬁrst recorded with saline in the holder

29 prior to recording spectra from the lens. Each scan was integrated for 20 - 100 seconds depending upon the depth of the probe region within the lens, for an average total time of 35 minutes. Data acquisition times as low as five seconds were possible, without overly compromising the accuracy of the results. On average approximately 60 scans were taken with each lens to characterize a single complete depth profile starting from the anterior and moving toward the posterior pole of the lens. Often the measurements were repeated from the same lens to ensure reproducibility of the Brillouin data, with no significant differences observed between the different sets of measurements. The Brillouin doublets for each scan were fitted by Gaussian profiles and the average of the two peak frequencies were taken.

3.3 Human Eye Lens Results

Figure 3.2 illustrates the scattering conﬁguration in relation to the lens and representative

Brillouin spectra recorded from different segments of the lens. The right panel shows typical Brillouin modes in the outer (cortex) section of a 31 year old lens at 7.8 GHz. This mode is identified as the longitudinal acoustic phonon of the local region being studied; the corresponding transverse mode is not evident due to the low value of the shear modulus. Also, the thickness of the lens as determined from the Brillouin data at the front and posterior of the lens is in agreement with the value of 3.5 mm obtained from direct measurement, where the lens was viewed against a ruler scale after the Brillouin measurements were made further confirming that the source of the Brillouin scattering was coincident with the anatomical boundaries of the lens. From the work of Brown and others the anterior to posterior thickness of the lens for a 29 year old is apporoximately 3.75 mm [45–47]. Our observations for the maximum Brillouin frequency at 9.0 GHz (2.2 mm deep to the anterior lens surface), agree with estimates of Brown for the location of the lens nucleus (0.68 mm to 3.28 mm deep) to the anterior pole of the lens, left panel Figure 3.2). Upon moving the focus of the probe laser further within the lens (3.3 mm), the spectra demonstrate a shift that corresponds well with Browns expected location of the transition from the nucleus to the posterior cortex. The spectra shown in Figure 3.2 were typical for the lenses evaluated.

30 The axial location of the spectral shift between the nucleus and cortex diﬀered between samples and the thickness of the anatomical regions corresponded with age of the sample.

Of particular interest as discussed in detail below, are the distinct frequencies in the cortex and nucleus as well as the doublet structure evident in the cortex-nucleus transition region

(center panel Figure 3.2).

The mode frequencies, which are directly dependent on the elastic properties of the lens, provide a map of the bulk modulus of the lens. A compilation of a sequence of Brillouin spectra from a 41 year old lens is illustrated in Figure 3.3 and shows the transformations of the mode within the lens. Figure 3.4 summarizes the Brillouin frequencies for the cortex and nucleus for the entire age range of lenses investigated. Two features are clearly evident.

First, the frequency of the longitudinal acoustic phonon within the cortex is lower than the corresponding mode in the nucleus for all age groups. The average frequency of 7.85 GHz

(cortex) and 8.80 GHz (nucleus) over the entire age range had standard deviations of 0.14

GHz and 0.22 GHz respectively. This variation within the nucleus and cortex may be attributed to real variations observed within the population studied, e.g. biological variability, as well as experimental sources of error. Despite our eﬀorts to control them, the precision of axial and lateral alignment, the possible degeneration of tissue condition between the time of collection and our experiments, and other factors may also have contributed to our observations. Second, there is little variation in the magnitude of each frequency over the entire age range, a behavior consistent with the absence of change in the bulk modulus of the cortex and nucleus of the lenses over an age span of four decades. The observed frequency shift in the lens cortex was unrelated to age (slope = 0.005 GHz/year, 95% CI =

0.012 to +0.002; P = 0.18). Likewise, the observed frequency shift in the lens nucleus was unrelated to age (slope = 0.001 GHz/year; 95% CI = 0.006 to +0.004; P = 0.62).

The variation of the bulk modulus (K) within the nucleus and cortex may be calculated from the dependence of the frequency shift on the probe spot within the lens. The refractive index for human lenses was taken as n = 1.42 for the nucleus, and 1.37 for the cortex [48].

Bulk moduli were calculated from the mode frequency f, where the density for the lens was taken to be approximately 1,085 kg/m3. The results are presented in Figure 3.5.For all

31 Figure 3.2: Representative Brillouin spectra from diﬀerent sections of the right (OD) lens from a 31 year old measured along the primary optic axis showing characteristic Stokes, anti-Stokes Brillouin doublet. The modes are associated with the longitudinal acoustic phonon of the tissue. In addition to spectra from the cortex (right panel) and nucleus (left panel), modes in the vicinity of the nucleus-cortex interface are shown. As the transition is made out of the nucleus into the cortex, (curves 2.2 mm to 3.2 mm center panel), two distinct peaks are evident whose spectral weight gradually makes a transition from high frequency (nucleus) to low frequency (cortex).

32 Figure 3.3: Sequence of Brillouin light scattering spectra recorded from the eye lens of a 41 year old man. From bottom (anterior) to top (posterior), the Stokes/anti-Stokes doublet represent scans recorded along the primary axis in incremental steps of 0.100 mm. The modes progressively increase from 7.80 GHz in the cortex to 8.90 GHz in the nucleus and then steadily recover back to 7.80 GHz when transitioned to the posterior of the lens. The uncertainty of the frequency measurements is 0.05 GHz. Note some initial data was taken ± by former graduate student Jared Gump.

33 Figure 3.4: Age dependence of the longitudinal acoustic phonon frequency in the cortex and nucleus of the lens.For all ages, the frequency of the acoustic mode associated in the cortex is always smaller than the corresponding mode in the nucleus. The lines correspond to the average frequency, 7.85 GHz (cortex) and 8.80 GHz (nucleus), values of the data set. The standard deviation from the average is 0.14 GHz (cortex), and 0.22 GHz (nucleus). Note some initial data was taken by former graduate student Jared Gump.

34 Figure 3.5: Age dependence of the bulk modulus in the cortex and nucleus of the lens.For all ages, the bulk modulus in the cortex was always smaller than the corresponding modulus in the nucleus. The modulus is determined from the phonon frequencies of Figure 5. The lines correspond to the average bulk modulus values 2.36 GPa (cortex) and 2.79 GPa (nucleus) of the data set. The standard deviation from the average is 0.09 GPa (cortex), and 0.14 GPa (nucleus). Note some initial data was taken by former graduate student Jared Gump.

ages, the bulk modulus in the cortex is always smaller than the corresponding modulus in the nucleus. The average bulk modulus is 2.36 GPa (cortex) and 2.79 GPa (nucleus) with standard deviations of 0.09 GPa and 0.14 GPa respectively.

3.4 Discussion

Our results demonstrate a depth dependent regional variation in the bulk modulus of the ocular lens tissue with an average value for the cortex lying below that of the nucleus. These results agree with the bulk moduli calculated from the data of Vaughan and Randall [3],

35 who were the ﬁrst to use BLS to deduce the longitudinal bulk modulus of the crystalline lens, but did not evaluate the age or depth dependent spatial variation of these moduli. The regional variation in the bulk modulus that we found are consistent with what others have reportedthat the cortex modulus is less than the nucleus modulus [49–51]. In a re-analysis of Fishers original estimates [33] of the Elastic moduli for the lens cortex and nucleus,

Burd and colleagues [50] argue that the original analysis of data collected by Fisher was

ﬂawed and that the correct interpretation of this data suggests a greater Youngs modulus

(E) for the lens nucleus than the outer cortex, which is in agreement with our results.

We also ﬁnd no age dependence for the bulk modulus in either the cortex or nuclear lens

tissues. Hence our ﬁndings are consistent with the hypothesis that the underlying cause

for presbyopia is not due to changes in the bulk modulus of the lens with age. Beers and

van der Heijde evaluated the velocity of ultrasound propagation in lens tissue. This tissue

velocity is governed by the same principles as BLS and is dependent upon Youngs modulus

and material density. As in our results, they found no age dependent change in ultrasound

velocity in healthy lens tissues [52]. Our ﬁndings on the diﬀerences between the cortex and

nuclear bulk modulus lend additional support to the work of others who have used diﬀerent

techniques to show that the lens and its material properties cannot be accurately modeled

as a simple or homogenous structural entity [31, 38, 50, 52, 53].

Irrespective of these results, understanding the age-related decline in accommodation

may be more complicated than simply knowing the mechanical properties of the lens tissues.

For example, some have argued that hardening of the lens nucleus can explain presbyopia

[53]. Koopmans and colleagues have demonstrated that replacement of lens tissues with

softer deformable gel materials results in a decreased amplitude of accommodation in ado-

lescent monkeys, in-vivo. Others have suggested that a decline in the elasticity of the lens

capsule or that reduced zonular tension with age-related increased lens mass may contribute

to presbyopia. It is possible that several of these factors may conspire to reduce accom-

modation in middle age. For instance, in spite of the lack of changes to the bulk modulus

with age, changes to the shear modulus of the lens that we were unable to measure through

Brillouin light scattering could contribute to presbyopia.

36 The Brillouin light scattering technique oﬀers a number of advantages over previously employed indentation and micro bubble techniques [2, 37, 42], which are destructive or at least disruptive to the anatomical structure of the lens tissue. BLS is a non-destructive probe of the elastic properties of the crystalline lens over a microscopic volume (4 to 8 x 10−4 mm3, a scale over which the properties of these tissues are thought to vary [49].

By comparison the micro-indentation techniques of Heys and colleagues used a 0.5 mm cylindrical indenter that probed the lens tissue at a depth of 0.5 mm and therefore had a sample volume of approximately 0.4 mm3, nearly 1000 times the sample volume of our method. The BLS technique has also recently been successfully used to evaluate the lens of the mouse eye [54]. Additional work is needed to evaluate the shear modulus of the lens, the role of visco-elastic properties of the biological tissue and the biomechanical characteristics of the lens capsule by BLS. Further development and refinements of this technique may permit the evaluation of biomechanical characteristics of these and other ocular tissues in vivo. − The recent work of Weeber et al. [2] and Heys et al. [37], shows a massive increase in lens shear modulus with age, from frozen, non-fresh tissue samples. These mechanical probes reveal a shear modulus gradient across the lens. Weeber et al. found shear moduli values in the 1 100 kPa range with the shear modulus of both the center (nucleus) and − periphery (cortex) increasing by a factor of 104 and 102 respectively over the measured age range. These results reveal a cross-over around 45 50 years where the youngest lenses − had a minimum central shear modulus, to older lenses having a maximum [2]. It is noted that the consequence of freezing the specimen and subsequent sectioning on the measured moduli remain unknown [55]. Studies using differing techniques have yielded mixed results ranging from only limited increases in lens stiffness before the age where accommodation is lost [56–59], to a massive increase in nuclear stiffness [2, 37].

It is diﬃcult to compare published experimental results because of the wide variety

of experimental approaches: some were not conducted on human eyes, were performed

on donor tissues, or were based on assumptions of mathematical modeling. The increase

in lens stiﬀness as a function of age reported by some studies is exponential, contrary to

37 the linear age-related decline of accommodation that is observed clinically. Likewise, the major increases in lens stiﬀness occur beyond the age of 50 years, long after the majority of accommodative function is lost [34].

We note that the term stiffness has been widely used in the context of the eye lens and subject to broad interpretation. It is therefore important that measured parameters are precisely identified within the framework of terminology of elasticity theory such as stiffness, hardness, as well as shear (G), bulk (K) and Youngs (E) modulus used to characterize tissue mechanics. Moreover, elastic modulus and elasticity are often utilized inappropriately for the Youngs modulus E. The various moduli can, in principle, be compared through

relations amongst the diﬀerent elastic constants. For instance in an isotropic system, the

bulk modulus K is related to the shear modulus G and Poisson’s ratio ν through the 2G(1+ν) equation, K = 3(1−2ν) . In the case of a highly hydrated tissue which can be characterized as incompressible (i.e. ν 0.5), it follows that the bulk modulus can be very large while ∼ the shear modulus (G) remains small. It is thus not unusual for the human eye lens to have shear modulus values G 102 103 Pa, while bulk moduli are in the giga-pascal (i.e. ∼ − K 109 Pa) range, as found in this study. The term stiffness has often been identified with ∼ the shear modulus. For instance, in the study of Heys et al. [37], the local stiffness of the lens was related to G based on an assumed a linear relationship between the applied force and shear modulus.

In light of a growing body of evidence the loss of elasticity of the surrounding capsule and the lens matrix must be considered as a, if not the, major factor in the loss of accommodation. Fisher indicates that the ability of the capsule to mould the lens wanes as we get older [60]. Thus, depending on the compliancy of the lens matrix to the moulding pressure of the capsule, the decline in near focusing ability with age could be associated with the decline in the ability of the lens system to both apply moulding pressure and to respond to this pressure. As noted above, as in the case of water, supporting no shear with a ﬁnite

(2.2 GPa) bulk modulus, a hydrated tissue like the lens nucleus with 64% water by weight and cortex (69%) [61] could have widely diﬀering shear and compressive moduli. The high protein content of the lens tissue leads, as observed in our study, to a substantial shift of

38 the longitudinal acoustic phonon frequency from that of water. This behavior is consistent with a lens structure of concentric layers of closely apposed fiber cells that forms a complex protein gel with an overall protein content that is about one-third of the lens mass. Light and electron microscopy studies of the lens structure [62] reveal numerous interdigitations between lens fibers that presumably stabilize the lens mass, resist deformation during accommodation and help account for the low shear modulus that would be consistent with our study. Our approach yields a description of the local constitutive compressional properties of the lens fibers.

One approach to the analysis of the biomechanical characteristics of the lens is the use of

ﬁnite element modeling [2, 63]. The success of this approach depends largely upon accurate estimates of the elemental properties of the lens material as well as correct characterization of how the gross structure of the lens is derived from organization and interaction of these individual elements. Our results not only provide an estimate of the elemental physical characteristics of the lens material, but suggest a plausible explanation for how these observed physical characteristics may be reconciled with the known anatomical structure of the lens.

Our results show that on a microscopic level, the lens material is relatively incompressible, a hydraulic characteristic that is desirable for translating forces eﬃciently and eﬀectively.

This further suggests an important role for the interaction of the individual lens ﬁbers and the shear forces generated between them during accommodation. Characterization of these forces will require a diﬀerent approach.

As described above, our computation of the bulk modulus of the lens depends directly upon the sample density and inversely upon the index of refraction. By this expression, either a decrease in tissue density or an increase in the index of refraction of the sample would lead to a corresponding decrease in the calculated bulk modulus (K). Our current methods do not account for the effects of viscoelasticity or the influence of anisotropic structure, which is known to exist in biological tissues. Age associated lens changes such as an increase in insoluble protein fraction or a change in the index gradient [64–67], would lead to offsetting effects on our calculated bulk modulus that would proportionally favor the influence of an increasing index of refraction and thus a lower calculated bulk modulus of

39 older eyes. However, a recent study concluded that age dependence of the central refractive index, showed no statistical significance [68]. It should be emphasized that all of the lenses evaluated in this study were from normal eyes that showed no evidence of clinically defined cataracts. Additional experiments with lenses from older eyes and from eyes with cataracts are needed to understand how our observations would differ with the onset of age associated nuclear sclerosis or disruption of the normal lens morphology that occurs with cataracts.

At present we are witnessing development of additional treatments for presbyopia. For example, the lens capsule could be reﬁlled with biocompatible and optically suitable clear gel creating a new physiological lens in situ [69]. The arrest or reversal of age related hardening of the lens cortex is a theory being pursued aggressively by a number of groups [70].

An alternative approach is to pharmacologically manipulate lens elasticity [71, 72]. While such surgical or pharmacological alterations of lens elasticity can be assessed by measuring a patients amplitude of accommodation, a non-invasive objective measurement of lens elasticity would be beneficial. When suitably modified, the light scattering approach presented here, could offer a means of quantifying the age-associated biomechanical properties of the lens.

3.5 Summary

In conclusion, Brillouin light scattering studies were conducted to determine the variation of the bulk modulus within the human crystalline lens and to determine if this variation depended on age. Spectra recorded from the anterior through the posterior of the lens revealed that the nucleus was characterized by a higher longitudinal acoustic phonon frequency, and thus bulk modulus, than the surrounding cortex for all ages. Moreover, there was little variation in these longitudinal elastic properties over four decades. These ﬁndings contrast recent results based on dynamic mechanical probes that reveal the shear modulus of frozen lens specimens to increase exponentially with age. Our results are consistent with the hypothesis that an age-dependent change in the bulk modulus of lens tissues does not fully account for the natural decline of accommodation. The non-invasive feature of the

40 BLS technique has the potential to provide a detailed in-vivo measure of the bulk modulus of the lens measured through the cornea and aqueous humor.

41 Chapter 4 Bovine Corneal Elasticity and its Frequency Dependence

4.1 Introduction

The cornea is the transparent front tissue of the eye providing two thirds of the eyes optical power. It is an anisotropic and viscoelastic material formed from layers of collagen arranged in a pattern of lamellae sheets. Transparency is maintained through an active control mechanism (via micropumps) controlling the osmotic and ﬂuid forces within the tissue

[73, 74]. The collagen ﬁbers within each sheet are oriented parallel, providing resistance to longitudinal deformation. The collagen ﬁbers in adjacent layers progress in a twisted fashion providing three-dimensional resistance to the longitudinal deformation of the cornea.

However separation of the individual collagen lamellae sheets can occur with relative ease, especially in the deepest cornea layers where the collagen ﬁbers have less interconnects between the layers. The result of this complex collagen ﬁber organization is a structure that is resistant to longitudinal forces, but far less resistant to shear forces leading to easier separation of the layers along the optical axis of the cornea[74].

The cornea is central to the focusing ability of the eye, and is often modiﬁed to improve

vision, for example as in Laser-Assisted in Situ Keratomileusis (LASIK). Knowledge of the

corneal elastic properties prior to any surgical procedure is valuable as they are often relevant

to the cause, detection, and treatment of many ocular diseases. In the case of glaucoma, for

example, the intraocular pressure (IOP) is measured to diagnose and manage treatment of

42 the disease. IOP is measured by the indentation technique of applanation tonometry. The elastic properties of the cornea are directly responsible for how the cornea deforms, and knowledge of them would greatly enhance the accuracy of clinical determinations of IOP.

Moreover, the elastic properties of the cornea aﬀect its response to refractive surgery, the healing process of the patient, and the ability to identify patients who may respond poorly to treatment [75]. An in-vivo non-destructive technique to measure these elastic properties is needed, as well as understanding the eﬀect these elastic properties have on the cornea after surgery are of value [75, 76].

There are several estimates for the elastic properties of the cornea. Unfortunately, most measurement techniques are usually destructive and therefore unsuitable for in-vivo studies

[76, 77]. The cornea is often cut into pieces interrupting the complex collagen fibril structure, and possibly modifying the elastic properties [77]. Adequate characterization of anisotropic materials such as the cornea requires measurement of the shear and longitudinal responses to stress. Given the lamellar structure of the cornea, this shear (kPa), tensile (GPa) and compressive (GPa) elastic properties, not surprisingly, differ greatly [3, 76–78]. Further, these elastic properties are likely affected by parameters such as tissue hydration, IOP, and external factors including surgery.

In this chapter, two non-invasive techniques, confocal Brillouin light scattering (BLS) with GHz frequencies and Quantitative ultrasound spectroscopy (QUS) at MHz freqencies, are used to measure the sound velocities from identical regions of the same cornea specimen to determine the high frequency bulk/Young’s modulus. The BLS technique is, in principle, suitable for measuring the elastic response in three dimensions, although only data along the optical axis of the eye is reported in this study. BLS probed the spatial variation (to within 25 micron resolution) of the longitudinal acoustic (LA) phonon mode axially through the thickness of the cornea. The frequency was found to steadily increase from the anterior to a depth of 0.25 mm, remain constant within the central 0.5 mm section, and decrease through the posterior of the cornea. An overall frequency increase ranging between 5 - 8% was observed between the central stroma and outer corneal layers. For constant density and refractive index these ﬁndings suggest that the corneal modulus determined from BLS

43 and QUS from the same tissues agree excellently. They lie in the GPa range, despite the probe frequencies of the two technique being diﬀerent by three orders of magnitude. We demonstrate both techniques on intact eye globes ex-vivo showing the techniques to be valuable laboratory research tools, and with the potential to emerge as a clinical tool to measure physical properties in-vivo. A Dynamic Mechanical Analysis (DMA) measurement at lower frequencies (Hz) was also made for comparison to similar measurements found in the literature with modulus values in the MPa range.

4.2 Materials and Methods

The speed of sound, U, in an elastic material is given by U 2 = (K + 4G/3)/ρ, where ρ is

the density of the material, K the bulk modulus and G the shear modulus of the material.

For the case of the cornea, G is much smaller than K giving K = U 2ρ, or

2 2 2 K = ρλ0f /4n , (4.1)

where λ0 is the laser wavelength, f is the Brillouin frequency shift in backscattering, and n is the refractive index of the medium. For this study a value of n = 1.38 was used for the

cornea index of refraction [75].

As discussed in Chapters 2 and 3, confocal BLS is a non-invasive inelastic light scattering

technique well suited to measure acoustic mode frequencies f of the cornea [3]. In our

study conducted at ambient temperatures, density ﬂuctuations caused by acoustic phonons

inherent to the scattering medium, shift the frequency of the incident light by 10 GHz for ∼ 14 excitation laser frequency f0 = 5.8 x 10 Hz (wavelength λ0 = 514.5 nm). The frequency shift of the resulting Stokes, anti-Stokes doublet in the scattered light was measured in a

backscattering geometry with a tandem, six-pass Fabry-Perot interferometer (JRS Scientiﬁc

Tandem Fabry-Perot Interferometer TFP-1) Figure 4.1. The entrance pinhole diameter was

set to 450 µm. The axial spatial resolution of the measurement was estimated to be 100 µm

by measuring spectra for a set time while moving a thin layer of water( 10µm) through ∼ the focal region until the intensities of the water Brillouin peaks dropped to 25% of their

44 Figure 4.1: Schematic of BLS experimental setup showing intact eye globe submerged in saline contained in a quartz holder secured to a translation stage. Axial movement of the stage enables the eye globe to be spatially traversed and probed.

maximum value. Decreasing the size of the entrance pinhole by a factor of three did not improve axial spatial resolution. The incident laser light was focused to a 35 - 50 µm

diameter spot on the sample resulting in a sampling volume ranging between (4 - 8) x 10−4

mm3. The incident laser power of 2 - 10 mW resulted in strong scattered signals enabling

spectra to be recorded in less than 30 seconds per scan.

Brillouin frequencies f, were measured along the optical axis of intact fresh bovine eye

globes. The Stokes and anti-Stokes Brillouin frequencies were ﬁt with Gaussian proﬁles and

averaged. The spatial variation of the bulk modulus K was calculated from the measured

Brillouin frequencies according to Equation 4.1. The eye globes were obtained 2 hrs post ∼ mortem and measurements made up to 8 hrs later. The globes were placed in a custom made

cubic quartz holder containing a 0.9% saline solution to prevent dehydration of the outer

cornea during the measurement. The entire BLS measurement of 60 scans for a complete

cornea lasted approximately 1 hr, during which no corneal hydration eﬀects, speciﬁcally

45 Figure 4.2: Schematic of Quantitative ultrasound spectroscopy setup used by our collaborator J. Liu and X. He 2009 [18]. The complete eye globe is submerged in saline solution, and the ultrasound transducer is lowered just below the saline level. The reﬂected sound waves from the anterior and posterior cornea surfaces are detected by the pulser-receiver.

swelling and loss of clarity, were noticed. The quartz holder was securely attached to a linear translation stage with a 25 1 µm step resolution. ± Quantitative ultrasound spectroscopy (QUS) has been previously used to measure elastic properties of bone and other tissues including corneas [19–21, 79]. It is also a non-invasive, non-destructive technique with the potential for in-vivo applications. Done in collaboration with Professor Liu at The Ohio State University, the eye globe was submerged in saline, cornea facing up, and an ultrasound transducer lowered into the solution to ensure eﬃcient coupling of the sound waves to the tissue (Figure 4.2). The ultrasound energy from the transducer (<3mW/cm2) was transferred into the cornea leading to microscopic deformations of the tissue. Attenuation of the signal was determined from the reﬂected signal from anterior and posterior of the cornea and recorded at a rate of 500 MHz enabling the sound velocity of the medium to be determined.

46 In contrast to the high frequency BLS(GHz) and QUS(MHz) measurements, low frequency dynamic mechanical analysis (DMA) studies were used to measure the elastic properties of a bovine cornea ex-vivo in collaboration with Professor Do-Gyoon Kim in the

College of Dentistry at The Ohio State University. The DMA measurements utilized an

ElectroForce 3230 dynamic mechanical analyzer. The cornea was surgically removed from the globe ( 2 hrs postmortem) and placed on a holder with similar curvature. A probe ∼ with a concave surface area 330 mm2 was lowered onto the cornea until a small speciﬁed

force was reached indicating probe-material contact. The probe was oscillated sinusoidally

with constant displacement (of 10 µm) while the force on the cornea was measured. The

entire measurement for one scan took 60 seconds. ∼

4.3 Results

4.3.1 Brillouin Light Scattering

A typical set of Stokes and anti-Stokes shifted Brillouin spectra as a function of depth

through the cornea is shown in Figure 4.3. The frequency increases 7% (from 7.7 GHz to

8.3 GHz) as the probe beam is traversed through the cornea with the maximum frequency

occurring in the central 0.5 mm of the tissue. The bovine corneal thickness of 1 mm ∼ determined from Figure 4.4 is in agreement with both the published values [80] and direct

measurements on the corneal specimens (Table 4.1). Frequencies from the central 0.5 mm

section of the cornea were used in calculation of the BLS cornea bulk modulus (Table 4.1).

Frequency shifts were measured ex-vivo from nine bovine corneas, producing depth proﬁles

similar to that illustrated in Figure 4.4. Corneal densities ranged from 1.05-1.12 g/cm3

as determined during the QUS measurements performed by Sean He. The calculated bulk

modulus along the optical axis of the central cornea from BLS ranges between 2.50 GPa -

2.68 GPa.

47 Figure 4.3: Typical Stokes and anti-Stokes BLS spectra recorded from cornea anterior to posterior (top to bottom curve). Note frequencies increase in the central region of cornea and decrease at anterior and posterior of the tissue.

48 Figure 4.4: BLS frequencies as a function of axial depth from anterior to posterior cornea measured ex-vivo from intact bovine eye globe.

49 Sample# Thickness (mm) Density (g/cm3) Bulk Modulus Bulk Modulus ( 0.02) ( 0.02) (BLS) GPa (QUS) GPa ± ± ( 0.03) ( 0.03) ± ± 1 0.90 1.12 2.50 2.65 2 0.98 1.11 2.64 2.69 3 1.03 1.11 2.66 2.67 4 1.02 1.10 2.67 2.70 5 1.05 1.11 2.64 2.68 6 0.91 1.10 2.68 2.60 7 0.96 1.08 2.62 2.61 8 1.00 1.07 2.61 2.58 9 1.02 1.05 2.60 2.50

Table 4.1: Thickness, density, and bulk modulus as determined by ex-vivo BLS and QUS on corneas from the nine bovine eye globes.

4.3.2 Quantitative Ultrasound Spectroscopy

In the arrangement shown in Figure 4.2 acoustic waves generated from a transducer are re-

flected from both the anterior and posterior of the cornea since the acoustical impedance of the tissue differs from that of the saline or aqueous humor. These reflections are measured by the transducer producing a typical QUS reflectance spectra as shown in Figure 4.5. A mathematical model developed by Liu etal [19] which simulates elastic wave propogation through the in-vivo cornea submerged in saline by solving the appropriate stress and deformation continuity equations at the anterior and posterior surfaces, is used to calculate the reflectance spectra. The inputs including corneal thickness, bulk modulus and density are varied until a match to the experimentally measured reflectance spectra is achieved [21].

For the nine bovine corneas studied, the QUS thickness, density and bulk modulus values were found to range from 0.90 - 1.05 mm, 1.05 - 1.12 g/cm3 and 2.50 - 2.70 GPa respectively

(see Table 4.1).

4.3.3 Dynamic Mechanical Analysis

Figure 4.6 shows a set of sinusoidal displacement and force data from an axial DMA measurement on an ex-vivo bovine cornea. As previously described, the DMA probe was lowered 50 Figure 4.5: QUS reﬂectance spectra from the anterior and posterior cornea from collaboration with X. He and J. Liu.

51 onto the detached cornea speciman until a load of 0.5 Newtons was recorded. The probe was oscillated sinusoidally at frequencies 5 Hz with a displacement amplitude of 0.01 mm. ≤ The displacement/force data from the linear-like portions of the sine curves was converted to stress/strain. The slope of the linear region of the stress-strain plot provides the Young’s modulus (E). Averaged over several of the linear regions, a value of 3-10 MPa was obtained and agrees with previous results [80].

The BLS technique is highly suitable for in-vivo studies of not only the cornea, but other clear tissues of the eye globe, such as the lens, as a function of axial depth. As shown in Figure 4.7, the BLS frequencies were measured axially from the anterior of the cornea, through the aqueous humor, crystalline lens, and into the vitreous humor and reveal the elastic properties change through these bovine tissues. As illustrated in Figure

4.7, approximately 3.5 mm from the posterior of the cornea, the BLS frequency increases as the crystalline lens is detected enabling the bulk modulus of the lens to be mapped as achieved for the cornea.

4.4 Discussion

The cornea provides two thirds of the refracting power of the eye and can be modified by refractive surgical techniques such as LASIK. These types of surgical techniques involve physical modification of the cornea and their success is likely affected by the elastic properties of the cornea. Understanding how the underlying cellular structure contributes to the overall elasticity of the cornea is necessary to ensure positive surgical outcomes. Corneal elasticity has been measured with destructive cutting methods [77, 80] as well as with the use of indenters [76]. Indentation techniques also have large variability between measurements with published shear and Young’s modulus values from these techniques for human corneas ranging from 10-30kPa, and 1-5 MPa respectively [76, 81, 82]. However, a stretching technique indicates a Young’s modulus in the GPa range[77]. This variation highlights a need for a better understanding of the role of viscoelasticity as the bulk modulus is probed through the frequency range. BLS or QUS offer clarification on cornea elastic properties at

52 Figure 4.6: Displacement response on a single ex-vivo bovine cornea under a 1 Hz sinusoidally varying force. Data collected in collaboration with H. Kwon and D. Kim.

53 Figure 4.7: BLS frequency (measured ex-vivo) as a function of axial depth from the anterior cornea to posterior eye lens of a bovine eye globe.

54 high frequencies where viscoelastic eﬀects are negligible.

BLS was ﬁrst used to measure the bulk modulus K of the cornea by Vaughan and

Randall, with the result of 2.56 GPa which agrees with the results reported in this thesis[3].

The cornea is comprised of a thick, stiﬀ inner layer known as the stroma, and bound on each side by thin epithelial layers [79]. As expected, referencing Equation 4.1, the bulk modulus scales as f 2, the square of the BLS frequency. Hence changes in f as the cornea is

traversed axially from anterior to posterior (Figure 4.4), reﬂect changes in the bulk modulus

assuming constant ρ and n. We observed the highest BLS frequency in the central cornea.

With input from our collaborator Professor M. Twa from the University of Houston, the

outer epithelial layers of the tissue investigated are estimated to be typically 10 µm which

is below the spatial resolution of our BLS measurements. As shown in Figure 4.4, BLS

correctly measures the corneal thickness of 1 mm. While an abrupt transition from the ∼ saline into the anterior surface of the cornea would be expected, a smooth increase in mode

frequency was found upon entering into the anterior of the cornea. A similar decrease

in frequency was detected upon emerging out of the posterior cornea(Figure 4.4). This

smooth transition likely arises from tissue hydration. A previous study has shown BLS

frequencies in low macromolecular content aqueous gels are close to the frequencies of water

[83]. As the macromolecular concentration is increased the BLS frequencies also increase.

Hence, locations where water can hydrate the cornea should result in the BLS frequency

decreasing from its unhydrated state. Since water is continuously exchanged between the

posterior cornea and the aqueous humor, one would expect an increasing hydration from

anterior to posterior, leading to the diﬀering slopes observed in Figure 4.4 at the outer edges

of the cornea [84].

As shown in Equation 4.1, the bulk modulus K scales linearly with density and inversely

with index of refraction. If ρ is lowered or n increases, K would decrease. Thus diﬀering

density or refractive index gradients between the anterior and posterior cornea could also

explain the diﬀerence in slopes at these regions of the cornea evident in Figure 4.4.

Finally, in BLS the photons have a frequency of approximately 1015 Hz at a wavelength

which is smaller than the repeat distance of the collagen ﬁbrils. In QUS the probe frequency

55 is on the megahertz scale at a wavelength of several microns, that is larger than the repeat distance. Since both techniques result in similar values for the bulk modulus, each is probing the pure storage bulk modulus of the cornea tissue. Contributions from viscoelastic loss modulus are negligible in these cases.

BLS and QUS are both high frequency techniques with phonon frequencies on the order of GHz and MHz respectively. At these high frequencies the associated time scales (µs, ns) the material does not have time to respond viscoelastically to the probe displacement resulting in a measure of its compressive properties. However at lower frequencies (Hz), the material does have time to respond (less damping), resulting in a lower value for the storage elastic modulus, and the loss modulus now has nonzero values [85, 86]. The DMA measurement we report results in a Young’s modulus that lies in the MPa range, in agreement with published results both for a bovine cornea and human corneas [76, 80]. In contrast both BLS and QUS resulted in bulk modulus values in the GPa range lending creedence that loss modulus plays a far less signiﬁcant role at the MHz and higher frequency regime.

4.5 Summary

A non-invasive, non destructive, potentially in-vivo technique to measure the elastic properties of the cornea is needed. Both BLS and QUS have been shown to meet these criteria and have been demonstrated as an eﬀective method to determine the average bulk modulus of the cornea. BLS has been shown to have the spatial resolution to additionally map the bulk modulus as a function of axial depth through the cornea as well as the lens within an intact eye globe. BLS also provides a reliable non-invasive measure of the thickness of the cornea, the lens, as well as the relative spacing between these two tissues inside the eye globe. These measured spatial dimensions agree well with published values. The average bulk modulus of the nine corneas used in this study, as determined by both BLS and, in- dependently, by QUS is 2.6 GPa, while Young’s modulus determined from DMA lies in the

3-10 MPa range (Table 4.2). These vastly diﬀerent values demonstrate the time dependent eﬀects for the frequency regime of BLS and QUS. The non-invasive, non destructive, low

56 power natures of BLS and QUS show them to be promising techniques for determination of potential in-vivo corneal elasticity a clinical setting.

Technique Modulus BLS Bulk modulus = 2.62 0.03 (GPa) ± QUS Bulk modulus = 2.63 0.03 (GPa) ± DMA Young’s modulus = 6.5 3.0 (MPa) ±

Table 4.2: Summary of average bulk/Young’s modulus results from the three diﬀerent techniques utilized.

57 Chapter 5 Mechanical Properties of Low-k Dielectric Nanoscale Thin Films Determined by Brillouin Light Scattering

5.1 Introduction

Low-k dielectrics have predominantly replaced silicon dioxide as the interlayer dielectric for interconnects in state of the art integrated circuits. To further reduce interconnect

RC delays, additional reductions in dielectric constant (k) for these low-k materials are being pursued by integrating nanometer sized pores into hybrid organic-inorganic interconnect layers, which will sustain the continued scale down of micro-electronic devices. While increasing pore volume of the layers achieves the desirable lowering of k, it also has the potential to reduce mechanical and thermal stability and degrade device functionality. In this chapter we use the well established technique of Brillouin Light Scattering (BLS) to accurately determine the mechanical properties of these films at thicknesses below 200 nm and porosity levels up to 45%, amongst the highest porosity levels in the industry. Longitudinal and transverse standing wave acoustic resonances and their transformation into traveling waves with finite in-plane wave vectors are observed providing for a direct, non-destructive measure of the principal independent elastic constants that completely characterize the mechanical properties of these porous nano-scale films. The mode dispersions were utilized to determine Poissons ratio (ν) and Young’s modulus (E) of these films with comparisons to

58 SiO and amorphous carbon (a C : H) made. 2 −

5.1.1 Low-k Dielectric Films

As the semiconductor industry strives to keep pace and sustain Moores law and decrase

RC time delays by lowering the resistance (R) and the capacitance (C) of traditional metal

/ SiO2 dielectric interconnects [87], new materials are increasingly being introduced into micro/nano-electronic products. Among these material innovations are dielectric materials

with a dielectric constant (k) less than or greater than that of SiO2 so called low-k and high-k dielectrics. Both high and low-k dielectrics are currently utilized in high volume

manufacturing of transistors and interconnect structures for advanced microprocessors. For

example, Intel Corporation introduced a low-k SiOC : H interlayer dielectric (ILD) with

its 90 nm interconnect technology[88], and a high-k Hf based gate dielectric in its 45 nm

transistor technology [89]. As stated in the 2009 International Technology Roadmap for

Semiconductors (ITRS) [1, 90] dielectric materials with still higher and lower dielectric

constants will be needed for future 22 and 16 nm technologies.

For low-k dielectrics, the use of Cu has enabled R to be minimized while reductions in

C have been achieved by introducing interlayer dielectric (ILD) materials with increasingly

lower dielectric constants [1, 88–91]. The principle means for reducing the dielectric constant

has been through the introduction of various organic constituents into a SiO2 matrix to make a carbon doped oxide or SiOC : H material. The organic component in the SiOC : H

material is typically present in the form of terminal methyl (CH3) groups which disrupt

the connectedness of the SiO2 network. This altered the connectedness of the SiO2 matrix increases the free volume / nano-porosity present in the dielectric material and results in

lowered density (ρ) [92]. The lower density leads to a lower dielectric constant due to the

reduced electronic and ionic contributions to the dielectric function of the material [93, 94].

A rich array of hybrid inorganic-organic low-k materials have been produced in this manner

with the resulting dielectric constants spanning that of SiO2 (kSiO2 = 3.9) down to k values as low as 2.5 [95]. However, further reductions in interconnect RC delays will require

ILD materials with k 2.5 and eventually k 2.0 [1]. At these k values, the diameter ≤ ≤ 59 of the free volume starts to approach 1-2 nm and the resulting pores become increasingly interconnected [96]. Low-k materials with no interconnected porosity are typically referred

to as dense low-k ILDs, and materials with interconnected porosity as porous low-k ILDs.

However, the lower density achieved by decreased network interconnectedness also leads

to reduced mechanical properties such as Young’s modulus, Hardness, and fracture tough-

ness [92, 97–100]. Low-k dielectric materials also exhibit intrinsic tensile stresses and in-

creased coeﬃcient of thermal expansion relative to SiO2 [92, 98]. For these reasons, thin ﬁlm cracking and adhesion are serious thermal-mechanical reliability issues for low-k dielec-

tric materials [101, 102]. Porous low-k dielectrics (PLKs) are expected to have mechanical

properties still further reduced relative to their non-porous counterparts and increased re-

liability concerns due to the presence of porosity [98, 103, 104]. For these reasons, accurate

measurements of the mechanical properties such as the elastic constants (Cij), Young’s modulus(E), and Poisson’s ratio (ν), are needed for PLK materials.

The most common method for measuring Young’s modulus of a thin ﬁlm is nano-

indentation [105]. This technique, however, typically requires relatively thick ﬁlms (1-2

microns) to avoid substrate-indenter interactions [106]. As the semiconductor industry

moves to 22 nm and beyond technologies, the low-k ILD thickness in interconnects will

approach 100 nm or less and the suitability of nano-indentation techniques on porous ma-

terials is not apparent. Therefore, non-destructive techniques capable of measuring the

elastic constants of materials of thickness 150 nm are needed. Further, thermal mechan- ∼ ical modeling of low-k interconnects also requires knowledge of Poisson’s ratio. Poisson’s

ratio is typically assumed to be 0.25-0.33 for most dielectric materials. However, the value of

Poisson’s ratio for a nano-porous dielectric material is not intuitively obvious and has been

assumed to be anywhere from 0-0.2 [107, 108]. Negative values have also been reported for

some porous auxetic materials [109]. Therefore, accurate determination of Poisson’s ratio

for PLKs of interest to the semiconductor industry is needed.

60 5.2 Nonporous and Moderately Porous Low-k Nano-Films

5.2.1 Experiment

All thin ﬁlm materials investigated in this study were provided by our collaborators at

Intel. They were deposited on (001) silicon wafers by Plasma Enhanced Chemical Vapor

Deposition (PECVD) using various combinations of silane, organosilanes, hydrogen, helium,

oxidizers, and porogens [101]. Deposition temperatures were on the order of 250 400 ◦C. − Some ﬁlms received a post deposition e-beam or UV cure to enhance the network connec-

tivity and mechanical properties [110]. The ﬁlm thicknesses (h) ranged between 100-200 nm and densities from 1.10 1.35g/cm3. Table 5.1 summarizes the general process conditions − used to deposit the ﬁlms in this study.

Sample# Precursors/Gases Cure Si0.2C0.8 : H#1 H2/He/HpSi(CqHr)1−p No Si0.2C0.8 : H#2 H2/He/HpSi(CqHr)1−p No Si0.2C0.8 : H#3 H2/He/HpSi(CH3)1−p & Porogen Ebeam SiOC : H#1 H2/He/Oxidizer/HpSiO(CqHr)1−p UV SiOC : H#2 H2/He/Oxidizer/HpSiO(CH3)1−p & Porogen UV SiOC : H#3 H2/He/Oxidizer/HpSiO(CH3)1−p & Porogen Ebeam SiOC : H#4 H2/He/Oxidizer/HpSiO(CH3)1−p & Porogen Ebeam ∗ CDO H2/He/Oxidizer/HpSiO(CqHr)1−p No

Table 5.1: Process conditions used for deposition of the porous thin ﬁlm samples investigated. ∗From Link 2006 [4].

Table 5.2 summarizes some of the general material properties for the ﬁlms investigated.

They include: nominal ﬁlm thickness (h), dielectric constant (k), refractive index (n), mass

density (ρ), porosity, pore diameter, and ﬁlm composition. These parameters were measured

and provided by collaborators at Intel. Film thickness and refractive index were measured

using a J. A. Woollam VASE Spectroscopic Ellipsometer. Refractive index values in Table

5.2 are reported at a wavelength of 673 nm. The low frequency dielectric constant of these

61 materials was measured using a Solid State Measurements Inc. Hg probe at 100 kHz.

The porosity and the pore diameter were determined using spectroscopic ellipsometry and toluene as the solvent as described[111].

Sample# h k n ρ Porosity Pore XPS (nm) (g/cm3) (%) Dia. Composition (A˚) (% Si, C, O) Si0.2C0.8 : H#1 100 3.20 1.678 1.15 < 2 ND 15.7%, 77.8%, 6.7% Si0.2C0.8 : H#2 100 3.20 1.679 1.15 < 2 ND 15.2%, 77.9%, 7.1% Si0.2C0.8 : H#3 200 2.85 1.584 1.15 8-12 4-6 14.7%, 78.2%, 7.2% SiOC : H#1 100 2.55 1.558 1.10 < 2 ND 33%, 46%, 21% SiOC : H#2 100 2.60 1.482 1.10 12 < 10 34%, 52%, 14% SiOC : H#3 200 2.50 1.340 1.25 25 15-20 29%, 18%, 53% ≤ SiOC : H#4 150 2.50 1.340 1.25 25 15-20 29%, 18%, 53% ≤ CDO∗ 100 3.10 1.430 1.35 ND ND 33%, 29%, 39%

Table 5.2: General material properties of the low-k thin ﬁlms investigated. ∗From previous study in Link 2006 [4], ND = Non Detect.

Elemental ﬁlm composition was determined by x-ray photoelectron spectroscopy (XPS).

All XPS data was collected using a VG Theta 300 XPS system equipped with a hemi- spherical analyzer and a monochromated Al anode x-ray source (1486.6 eV). The emitted photoelectrons were detected using a pass energy of 20 eV for high resolution scans of the

Si 2p, C 1s, and O 1s core levels. XPS depth proﬁling was performed by using a 5 keV Ar+ ion sputtering beam[101].

The mass density for all films was determined via x-ray reflectivity (XRR). The XRR spectra were collected using both a Bede Fab200 Plus (employing a Cu microbeam source and an asymmetric cut Ge crystal), and a Siemens D5000 (employing a Cu line source and graphite monochromator)[112]. The data was collected in the range of 0 to 9000-15000 arcseconds with approximately 20 arcsecond steps. Spectra were acquired from 100 nm films and fitted using the REFSTM software package (version 4.0, Bede). The XRR spectra were

ﬁtted by adjusting ﬁlm thickness, mass density, and surface/interface roughness.

62 The BLS measurements were performed in a backscattering geometry at room temperature with a tandem Fabry-Perot interferometer operated in a sequential six-pass conﬁguration[113].

Approximately 70 mW of p-polarized λo = 514.5 nm laser radiation focused to a spot diameter of 35-50 µm was used to record the unpolarized (p + s) spectra; a typical measurement time for each spectrum ranged from 0.5 to 2 hours. The BLS laser peak power per unit area was approximately six orders of magnitude less than the corresponding value thin the picosecond ultrasonic measurement[114]. The standing wave excitations with discrete wave vector components perpendicular to the ﬁlm (K⊥) were most clearly observed at small scattering angles θ, where θ is the deviation of the backscattered beam from the ﬁlm normal

(z-axis). Measurements were also recorded when θ increased from 0◦ to 60◦ thereby ∼ monitoring the transformation of longitudinal and transverse standing wave modes into traveling modes with progressively larger in-plane wave vector Kk [= (4π/λθ)sinθ] along the x-direction. The velocity of the traveling modes is thus given by V = fλθ/(2sinθ) where f is the measured frequency of the mode. The elastic properties of seven samples with varying degrees of porosity and compositions were investigated.

For comparison to the BLS results, Young’s modulus for these ﬁlms was also determined using both Nano-indentation (NI) and Picosecond Laser Ultrasonics (PLU) by our collaborators. The details of these measurements have been described in prior publications[115, 116].

Brieﬂy, the indentation experiments were performed using a Hysitron Triboindentor and a

Berkovich diamond tip with a load range up to 30 mN. Samples were loaded in a partial unloading mode up to 2 mN in this study. The modulus was calculated using a shallow contact depth range below 10% of film thickness to avoid substrate interaction effects, which can be pronounced for very low-k films[106]. PLU measurements were performed using an optical pump and probe technique. An ultrafast laser is utilized to expose the film surface to an optical pulse of less than a picosecond in duration. The laser light is absorbed by the thin film surface and generates a strain pulse which propagates into the bulk of the

film. A portion of that strain pulse propagates down to the film/substrate interface and reflects back to the surface where it is detected using a second time-delayed probe laser as a change in the reflectivity of the surface. The transit time of the reflected strain pulse is

63 proportional to the longitudinal sound velocity from which Young’s modulus can also be computed by assuming elastic isotropy and pre-existing knowledge of the mass density and

Poisson’s ratio for the ﬁlm of interest[114].

5.2.2 Brillouin Light Scattering Results

To illustrate the main features of our study we present spectra and analysis from two samples, one lying at the threshold of porosity ( 2%) and the other at a relatively large ≤ porosity (25%). Figure 5.1 displays BLS spectra as a function of scattering angles θ from 0◦

◦ ◦ to 60 , for Si0.2C0.8 : H#2 (h=100nm, < 2% porosity). At small θ (< 5 ), the peaks at 5.8

GHz and 18.5 GHz are excitations with vanishing Kk and are identiﬁed[42], respectively, as the N=1 and N=2 longitudinal standing modes (1LSM and 2LSM). In addition, the weak

mode at 9.8 GHz occurring at θ = 5◦ emerges from the N = 2 transverse standing mode

2TSM. Calculations revealed the 3TSM to occur at 16.3 GHz for θ < 20◦ which was not resolved in the BLS measurements. For increasing θ, the modes become dispersive and additional excitations are evident in the spectra.

Mode frequencies, determined by fitting a Gaussian profile to each peak and averaging the Stokes and anti-Stokes shifted frequencies, are shown in Figure 5.2. Fits to the dispersion are calculated by finding resonances in the elastodynamic Greens tensor following the method of Every et.al.[12] In the present case of the thin film supported on a substrate, this approach consists of solving the wave equation in each medium subject to the presence of a delta force acting on the free surface and the usual boundary conditions related to continuity of stress and displacement at the interface. The best fit to the data in Figure

5.2 were obtained using C11 = 6.5 GPa, C12 = 2.8 GPa, and C44 = 1.9 GPa (Table 5.3). Consistent with the weaker mechanical properties of the porous ﬁlm, these elastic constants

Si Si are much smaller than those for the silicon substrate C11 = 165.6 GPa, C12 = 63.9 GPa, Si and C44 = 79.5 GPa. The three higher slope solid lines in Figure 5.2 identify the LA, TA, and Rayleigh modes of bulk silicon, while the lower three lines are the corresponding modes calculated for the bulk low-k ﬁlm. The mode amplitudes parallel to propagation direction

◦ (Ux) and normal (Uz) to the ﬁlm were calculated at low θ (= 5 ) and illustrated in the left

64 Figure 5.1: Representative BLS spectra recorded at diﬀerent scattering angles, θ = 0◦, ◦ ◦ ◦ ◦ 20 , 30 , 50 and 60 for a 100 nm Si0.2C0.8 : H#2 ﬁlm (see Table 5.2) at the threshold of porosity. Peaks observed at the lowest scattering angles are the standing longitudinal modes 1LSM and 2LSM. As θ increases additional modes, including the transverse resonance (2TSM) emerge.

65 panel of Figure 5.2. The standing wave feature is well deﬁned and conﬁrms the principally longitudinal (LSM) or transverse (TSM) character of the modes.

Material Porosity (%) C11 (GPa) C44 (GPa) Poisson’s Ratio E (GPa) Si C : H#1 < 2 6.5 0.3 1.3 0.2 0.38 0.01 3.5 0.4 0.2 0.8 ± ± ± ± Si C : H#2 < 2 6.5 0.4 1.9 0.2 0.30 0.01 4.8 0.7 0.2 0.8 ± ± ± ± Si C : H#3 8-12 10.0 0.3 2.6 0.2 0.33 0.01 6.8 0.9 0.2 0.8 ± ± ± ± SiOC : H#1 < 2 7.1 0.4 2.4 0.2 0.25 0.01 5.9 1.1 ± ± ± ± SiOC : H#2 12 6.5 0.2 2.4 0.1 0.22 0.01 5.7 1.1 ± ± ± ± SiOC : H#3 25 9.0 0.4 3.5 0.2 0.18 0.01 8.3 1.6 ≤ ± ± ± ± SiOC : H#4 25 10.0 0.4 3.6 0.2 0.22 0.01 8.7 1.5 ≤ ± ± ± ±

Table 5.3: Summary of measured sample elastic properties, note E is the Young’s modulus. Relationship between Cijs and Poisson’s ratio, Young’s modulus are provided as equations 5.4 and 5.5.

Spectra from the h = 100 nm SiOC : H#2 sample with 12% porosity are displayed in

Figure 5.3. The 1LSM and 2TSM modes at occur at 6.0, 10.9 GHz respectively while the

2LSM and 3TSM modes overlap at 18.2 GHz for small θ. The calculated dispersion curves

for this ﬁlm (Figure 5.4) yields C11 = 6.5 GPa, C12 = 1.8 GPa, and C44 = 2.9 GPa. Representative spectra from the h = 150 nm SiOC : H#4 sample with 25% porosity are displayed in Figure 5.5. The BLS intensity associated with the longitudinal modes are generally strongest at low angles, with additional modes appearing with increasing θ.

Calculations reveal distinct 1LSM and 2TSM modes at 4.5, 8.4 GHz respectively while the 2LSM and 3TSM modes overlap near 14.1 GHz for θ 0◦. As in Figure 5.2, the ∼ calculated dispersion curves for this ﬁlm (Figure 5.6) yields C11 = 10.0 GPa, C12 = 2.9

GPa, and C44 = 3.6 GPa. Similar spectra were measured from the other ﬁlms and the elastic properties of the PLK thin ﬁlm samples evaluated in this study are summarized in

Table 5.3.

66 Figure 5.2: Dispersion of acoustic modes supported in the h=100 nm porous Si0.8C0.2 : H#2 low-k dielectric film showing variation of mode frequencies with scattering angle θ in degrees. The measured data are large solid dark dots and the small dots are fits. The group of three higher (lower) frequency lines is the LA, TA and Rayleigh modes associated with the silicon substrate (bulk film). The left panel illustrates mode displacements within the film for ◦ excitations near θ = 0 where the solid line is Ux and the dotted line is Uz corresponding to the standing modes TSM and LSM. Here x identifies the direction of mode propagation parallel to film surface, and z, the normal to the surface.

67 Figure 5.3: Representative spectra recorded at diﬀerent scattering angles, θ = 10◦, 30◦, 50◦ and 60◦ for a 100 nm thick SiOC : H#2 ﬁlm at 12% porosity (Table 5.3). The strong ∼ peaks observed at lower scattering angles are the longitudinal standing modes 1LSM and 2LSM, whereas the weaker peaks, not resolved in this measurement, represent the transverse standing modes 2TSM and 3TSM.

68 Figure 5.4: Dispersion of acoustic modes supported in the h=100 nm porous SiOC : H#2 low-k dielectric film showing variation of mode frequencies with scattering angle θ in degrees. The data are solid dark dots and the small dots are fits. The left panel illustrates mode ◦ displacements within the film for excitations near θ = 0 where the solid line is Ux and the dotted line is Uz corresponding to the standing modes TSM and LSM respectively. Here x identifies the direction of mode propagation parallel to film surface, and z, the normal to the surface.

69 Figure 5.5: Representative spectra recorded at diﬀerent scattering angles, θ = 20◦, 30◦, 40◦ and 60◦ for a 150 nm thick SiOC : H#4 ﬁlm at 25% porosity (Table 5.3). Peaks observed ∼ at higher scattering angles emerge from the longitudinal standing mode (1LSM) and the 2LSM, 3TSM modes whose frequencies overlap.

70 Figure 5.6: Dispersion of acoustic modes supported in the h=150 nm porous SiOC : H#4 low-k dielectric film showing variation of mode frequencies with scattering angle θ in degrees. The data are solid dark dots and the small dots are fits. The group of three higher (lower) frequency lines is the LA, TA and Rayleigh mode associated with the silicon substrate (bulk film). The left panel illustrates mode displacements within the film for excitations near θ = ◦ 0 where the solid line is Ux and the dotted line is Uz corresponding to the standing modes TSM and LSM respectively. Here x identifies the direction of mode propagation parallel to film surface, and z, the normal to the surface.

71 5.2.3 Discussion

As evident in the mode amplitudes of Figures 5.2 and 5.6, the acoustic excitations observed at θ < 5◦ (K 0) in general separate into highly polarized longitudinal or transverse ex- k ∼ citations. Their underlying physics stems from a simple physical analog of acoustic modes

associated with an organ pipe where vibrations at the ﬁlm surface and ﬁlm-substrate in-

terface are akin to those at the open and closed ends of the organ pipe[42]. The LSM and

TSM excitations are, respectively, most sensitive to the C11 and C44 (C12) elastic constants of the elastically isotropic low-k ﬁlms. In this case the standing wave mode frequencies are

provided by V f = (2m + 1) (5.1) 4h where m is an integer, h the ﬁlm thickness and

C V ij (5.2) ∼ s ρ the mode velocity. The frequency f and spacing

V ∆f = (5.3) 2h between neighboring longitudinal or transverse resonances at small θ thus provide a sensitive measure of the principal elastic constants of the ﬁlm. As expected, C11 is mainly determined from the LSM modes at low θ (< 10◦). For example, in the case of the ﬁlm with 25% porosity,

C can lie in a range of 7% and still provide a ﬁt to the LSM mode frequency to within 11 ± 5%. Likewise, the TSM branch is most sensitive to the C44 (and C12) constants that are determined to within an 11% error. The more complete mode dispersion as illustrated in

Figures 5.2 and 5.6 provides further constraints on the ﬁlm elastic constants, thickness and density as summarized in Table 5.3.

The deduced Cij values illustrate the value of Brillouin light scattering as a viable approach to non-destructively determine the elastic constants, Young’s (E) and Poisson’s

72 ratio (ν) of the porous nano-ﬁlms through the relationships,

C ν = 12 (5.4) C11 + C12 and (1 + ν)(1 2ν) E = − C . (5.5) ν 12 The Young’s modulus for the seven samples investigated in this study is found to range

between 3.5 and 8.7 GPa. The largest contribution to the uncertainty in E comes from the diﬃculty in resolving the TSM for low θ resulting in an error margin of 2.4 GPa (SiO0.2C0.8 :

H#3) associated with the determination of C44. These values are consistent with NI Young’s modulus measurements reported for non-porous and porous low-k dielectric materials with

similar dielectric constants. Typical reported NI values are 9 - 18 GPa for non-porous

materials[98, 100, 104, 106, 107, 117, 118] and 3.5-9 GPa for porous materials[98, 104, 107,

117–120]. For further comparison, the lower values of Young’s modulus are comparable to

those of nylon (2-4 GPa)[121], and polystyrene (3-3.5 GPa)[122]. As another comparison,

Young’s modulus for aero/xerogel materials which are extremely porous, SiO2 matrix low-k dielectrics (k < 2, ρ < 0.6g/cm3, porosity 50-90%) ranges from 0.0005 to 0.005 GPa[123–

126].

Within this sample set, which spans the SiOxCy : H phase diagram for the region of 0-25% porosity, x = 0.4-1.8 and y = 0.6-5.0, there is an interesting variation in Young’s

modulus. The lowest modulus ﬁlm is Si0.2C0.8 : H#1 with a Young’s modulus of 3.5 GPa.

Interestingly, this ﬁlm has a lower modulus than Si0.2C0.8 : H#3 which has approximately the same composition but signiﬁcant levels of porosity. The higher elastic modulus for

Si0.2C0.8 : H#3 is believed to be partially a result of the additional electron beam cure this ﬁlm received. Electron beam cures are well established for increasing the network

connectivity of low density materials and accordingly increasing the elastic modulus of the

dielectric ﬁlm[127]. The higher modulus may also be a result of using a lower carbon content

organosilane that enables better Si C network bond formation and connectivity. It should − also be noted that while no oxygen containing gases were used during the deposition of this

73 film, 7 atomic % oxygen was detected in this film by XPS (as well as for Si0.2C0.8 : H#1&2). The presence of oxygen is believed to be the result of the low density of this film and the

ability of ambient moisture to diﬀuse into and react with weak chemical bonds within the

ﬁlm[128]. Depending on how the oxygen is incorporated, this could also result in small

variations in Young’s modulus for ﬁlms with similar Si/C ratios.

The highest elastic modulus ﬁlms in this study are also the highest porosity ﬁlms.

SiOC : H#3&4 both have porosity levels approaching 25% with Young’s moduli of 8.3-8.7

GPa. In addition to receiving an electron beam cure, these films also have the highest oxygen content as determined by XPS. In contrast, SiOC : H#1&2 (Figures 5.3 and 5.4)have lower porosity levels but also lower Young’s moduli relative to SiOC : H#3&4. This is in contrast to most theories for the elastic properties of porous materials which predict E to decrease with increasing porosity[108, 129]. A possible explanation for this anomalous behavior likely lies with either the higher carbon content for these films and/or the fact that these films received a UV cure instead of an electron beam cure. The higher carbon content for SiOC : H#1&2 is predominantly in the form of terminal (CHx)y groups. The introduction of such a large number of terminal organic groups will significantly lower the average Si O network connectivity of the matrix material relative to the matrix material − for SiOC : H#3&4. As predicted by percolation theory, this will result in a significant loss of rigidity in the material despite having a lower overall porosity[130–132]. Interestingly, the precursors for SiOC : H#3&4 are identical to those for Si0.2C0.8 : H#3 minus the oxidizing gas. This illustrates how the incorporation of small amounts of oxygen into the network structure of Si C : H#1 3 can have a significant stiffening effect on the 0.2 0.8 − Young’s modulus for these materials.

Additional interesting differences between the films in this sample set are also observed for Poisson’s ratio. As evident from Table 5.3, ν is found to range from 0.18 to 0.38. The high value of ν = 0.38 for Si0.2C0.8 : H#1 is comparable to that of typical polymeric materials such polyethylene and polytetrafluoroethylene (Teflon) where ν is reported to range from

0.3 - 0.4[133–135]. The values of ν = 0.30 - 0.38 for Si C : H#1 3 thus suggest the 0.2 0.8 − possibility for observing signiﬁcant plasticity during the fracture of these materials. In this

74 regard, we note that preliminary dual cantilever beam tests on these same materials have indicated signiﬁcant plasticity for Si0.2C0.8 : H#3 [136]. The lowest Poisson’s ratio value of 0.18 was observed for SiOC : H#3 which has the

highest porosity of the ﬁlms investigated. This value is comparable and consistent with the

values of Poisson’s ratio for aerogel materials which have been reported to be in the range of

0.15-0.26[124, 125]. For these materials, ν decreases from 0.26 for < 10% porosity to 0.16 ≤ for > 90% porosity. Aerogels with porosities of 20 - 40% typically have ν = 0.18-0.22[125]

which is in excellent agreement with our results for SiOC : H#2 4. The value of ν = 0.25 − for SiOC : H#1 is consistent with our previous report of 0.26 [4] for a non-porous carbon

doped oxide (k=3.1), and the upper bound on ν observed for aerogel materials[125]. The

Poisson’s ratio values for SiOC : H#1 4 are also consistent with two independent BLS − measurements where ν was reported to be 0.15 0.02 for a non porous SiOC : H thin ﬁlm ± dielectric (k=3.0, ρ = 1.5g/cm3)[137] and 0.26 0.1 for a low porosity SiOC : H dielectric ± (ρ = 1.18g/cm3, porosity = 16%)[138].

In Table 5.4, we compare the Young’s moduli determined by BLS, NI, and PLU. The

NI and PLU measurements were both performed by other researchers at outside locations,

independent of the BLS results and assume a Poisson’s ratio of 0.25. As can be seen, the

values from all techniques agree with one another to within 4 GPa. For most of the ± ﬁlms, the NI Young’s moduli are slightly higher than those determined by both the BLS

and PLU techniques. This is consistent with our previous report[4] and those by others

[139, 140] where acoustic techniques are observed to indicate lower elastic moduli than NI.

The higher values determined by NI are generally attributed to convolution of the load versus

indentation depth response with the composite stiﬀness of the ﬁlm and substrate[4, 106].

However for a few cases, BLS actually indicates Young’s moduli equal to or slightly higher

than those determined by NI. This may be a result of assuming ν = 0.25 in the indentation

measurements, but correcting the indentation measurements for the ν determined in BLS

would change the measured modulus by only a small percentage of the diﬀerence between

the two techniques. Instead for Si0.2C0.8 : H#3, we attribute the BLS-NI difference to the observed plasticity for this film which may have affected the measured load-indentation

75 depth response.

Sample# BLS-E (GPa) NI-E (GPa) PLU-E (GPa) Si C : H#1 3.5 0.4 4.9 0.2 4 0.4 0.2 0.8 ± ± ± Si C : H#2 4.8 0.7 6.3 0.2 4 0.4 0.2 0.8 ± ± ± Si C : H#3 6.8 0.9 5.6 0.4 4.3 0.4 0.2 0.8 ± ± ± SiOC : H#1 5.9 1.1 7.5 0.4 NM ± ± SiOC : H#2 5.7 1.1 9.7 0.4 NM ± ± SiOC : H#3 8.3 1.6 8.3 0.4 5.9 0.6 ± ± ± SiOC : H#4 8.7 1.5 8.1 0.4 5.9 0.6 ± ± ± CDO∗ 8.4 6.1 11.8 8.9 0.9 ± ±

Table 5.4: NM = Not Measured. Samples burned under pump laser. Note: The reported uncertainties for NI-E and PLU-E represent one standard deviaton of >10 measurements. E is the Young’s modulus. ∗From previous study Link 2006 [4].

In comparing BLS vs. PLU, we observe that the Young’s moduli are comparable but

the PLU technique yields slightly lower numbers. This is in contrast to the previous report

for non-porous CDO[4] and somewhat surprising given that PLU measures the velocity

of longitudinal sound waves which are directly analogous to the longitudinal organ pipe

modes detected in BLS. As with NI, the diﬀerence between BLS and PLU are too large

to be attributed solely to the assumption of ν = 0.25 in PLU. Interestingly though, the

ﬁlms for which there is the biggest diﬀerence in E measured by the two techniques are

SiOC : H#3&4 and Si0.2C0.8 : H#3 and are the highest porosity films. The agreement between BLS and PLU for Si0.2C0.8 : H#1&2 which have very low porosity is better. While this difference in E could be simply a porosity effect, it could also be a laser heating affect as well. For Si C : H#1 3, significant burning of these films under the PLU probe laser 0.2 0.8 − was observed. In fact, our collaborators were not able to achieve any PLU measurements for SiOC : H#1&2 for this same reason. While no visible laser heating was observed under

PLU conditions for SiOC : H#3&4, it cannot be completely ruled out. At the much lower power levels utilized for the BLS study no damage to the ﬁlms was evident.

Together with the precision for determining the elastic constants of the porous nano-

76 films, the BLS approach offers several advantages over nanoindentation which is the most prevalent method for obtaining the stiffness of thin films. As noted, the reliability of nanoindentation data from supported films less than a micron thick is of concern, especially for low modulus, low-k porous dielectrics. The stiffness derived from indentation is a combination of the two elastic parameters E and ν. In general, the value of Poisson’s ratio is assumed,

and the Young’s modulus is computed from the measured indentation proﬁle. A detailed

analysis shows that the interaction of the indenter tip with the substrate can in fact make

the measured stiffness of the thin film appear significantly greater, especially for films less

than a micron in thickness[141]. For low-k dielectric materials, which can have values of

E from 2 GPa to 15 GPa, this eﬀect can skew the measured E upwards as much as 20%.

This limitation of nanoindentation is a signiﬁcant concern as, with each new generation

of interlayer dielectrics, the ﬁlms are required to be much thinner than 200 nm and their

properties will begin to diﬀer from those of thicker ﬁlms.

Alternatively, there are two laser-based non-contact techniques available to non-destructively

measure the elastic moduli of thin ﬁlms-BLS[4, 6, 43, 138, 142], and PLU[4, 116]. Both are

ideally suited for investigations of ultrathin ﬁlms, since there are no special sample prepa-

ration requirements. As mentioned previously, PLU detects longitudinal acoustic waves

created through picosecond laser pulses[143, 144]. Several assumptions related to elastic

isotropy, Poisson’s ratio and ﬁlm density are required for interpreting the laser ultrasonics

data and extracting Young’s modulus. For BLS, density is also a requirement, however,

simultaneous detection of longitudinal and transverse acoustic waves allows for the deter-

mination of both Young’s modulus (E) and Poisson’s ratio (ν). In addition, Brillouin light

scattering has been in particular shown capable of measuring E for ﬁlms down to and below

100 nm thickness in supported and free-standing structures[43, 142].

For the two laser acoustic methods described above, the detected acoustic signals can be

isolated to the ﬁlm of interest which implies that the substrate has a minimal eﬀect on the

values of the moduli deduced. This strong evanescent character of the guided modes within

the Si substrate is consistent with the large acoustic mismatch between the low elastic

moduli of the porous ﬁlm and values of the Si substrate. These two acoustic methods have

77 each been used to measure the elastic modulus of a low-k dielectric film with precision on the order of 5%[4]. It has been shown that Brillouin scattering is capable of determining ± the dispersion relations of the modified Rayleigh wave of other thin films and their elastic properties down to a few nanometers in thickness[145, 145].

Figures 5.7 and 5.8 summarize for both the low ( 2%) and high (25%) porosity ﬁlms the ≤ phase velocities V (= fλ/(2sinθ)) of the modes and their variation with Kkh, the normalized thickness. In the limit K h 0, the lowest mode velocity approaches 4.6 km/sec, the k → non-dispersive Rayleigh wave velocity on an isotropic unlayered Si halfspace, while in the opposite limit when Kkh tends to large values, this branch tends towards the Rayleigh mode appropriate to a free surface of the bulk low-k material. In the present case, it is evident

that the porous ﬁlm loads the substrate and the phase velocity of the Rayleigh-like mode

decreases with increasing Kkh. If the phase velocity of the film-related modes lies above the T bulk transverse velocity, VSi, of the substrate, the acoustic modes do not localize in the film. Instead at least one of the partial waves describing these leaky modes has an oscillatory component normal to the interface. The solid line in Figures 5.7 and 5.8 identify this cutoff velocity associated with the Si substrate. When the film shear velocity is substantially

T smaller than VSi, the higher order modes asymptotically approach the layer shear velocity for large Kkh. Consistent with their localized, non-leaky character, modes below the shear velocity of Si are observed as strong peaks in the BLS spectra illustrated in Figures 5.1, 5.5.

The transition from guided to leaky modes is however not as abrupt as shown by the solid line in Figures 5.7 and 5.8. Rather the transformation into leaky character occurs while the modes retain relatively large amplitude within the ﬁlm or interface region while radiating some power into propagating bulk waves. This behavior is consistent with the BLS peaks of such excitations lying well above this threshold, being generally weak and characterized by less distinct frequencies in comparison to the guided modes.

5.2.4 Summary

We have observed several longitudinal and transverse standing acoustic resonances in ultra thin (< 200 nm) dense and moderately porous low-k dielectric ﬁlms supported on Si. In

78 Figure 5.7: The calculated and measured dispersion curves for the principal and higher order modes supported in the Si0.2C0.8 : H#2 ﬁlm at the threshold of porosity ( 2%) as T ≤ function of the normalized thickness Kkh. The solid line identiﬁes VSi, the velocity above which the waves have an oscillatory component in the substrate.

79 Figure 5.8: The calculated and measured dispersion curves for the principal and higher order modes supported in the SiOC : H#4 ﬁlm with 25% porosity as function of the normalized T thickness Kkh. The solid line identiﬁes VSi, the velocity above which the waves have an oscillatory component in the substrate.

80 addition, the transformation of these low lying LSM and TSM modes to acoustic excitations with ﬁnite Kk are well accounted for by the projected local density of phonon states and provide for the principal elastic constants of the isotropic porous ﬁlms. These calculations,

based on the associated elastodynamic Greens tensor to ﬁt the measured mode dispersions,

conﬁrm modiﬁcations in the Young’s modulus (8.7-3.5 GPa) and Poisson’s ratio (0.38-

0.18) that accompany the introduction of porosity and ensuing reductions in the dielectric

constant k. These ﬁndings also illustrate the advantage of the non-invasive approach of BLS

measurements over nano-indentation methods for determining the mechanical properties of

low modulus nano-ﬁlms being developed as the semiconductor industry moves to the next

generation of interlayer dielectrics for emerging large scale integrated technology.

5.3 Highly Porous Low-k Nano-Films

In this section, we discuss BLS measurements on even higher porosity (levels up to 45%)

isotropic thin ﬁlms deposited on silicon wafers as well as a moderate porosity carbon ﬁlm.

Fabrication and ﬁlm property measurement methods are similar to those used on the dense

and moderately porous samples discussed in the previous section but with slight diﬀerences

as detailed below.

5.3.1 Experiment

As in the other low-k materials all ﬁlms studied in this section were produced by collab-

orators at Intel. The highly porous thin ﬁlms investigated were all deposited on 300 mm

diameter (100) Si wafers by Plasma Enhanced Chemical Vapor Deposition (PECVD) or

spin-on deposition (SOD). PECVD ﬁlms were deposited at temperatures on the order of

250◦C using various combinations of organosilanes, alkoxysilanes, oxidizers, helium and ∼ sacriﬁcial pore-generating porogens [146]. These sample characteristics are summarized in

Table 5.5. The solution for the SOD SiOC : H ﬁlm consisted of a mixture of industry stan-

dard solvents, inorganic-organic oligomers, and sacriﬁcial organic porogens [91, 95]. The

SOD polymeric a C : H ﬁlm utilized a self assembling chemistry without any sacriﬁcial −

81 porogens and has been previously described [147] The SOD oligomer solutions were spin coated onto the silicon wafers in a dynamic dispense mode and then given a soft bake at temperatures on the order of 200◦C before final curing at > 300◦C. Post deposition, all ∼ PECVD and some SOD films utilizing sacrificial porogens were given either a UV or electron beam cure at 400◦C. The UV/electron beam cure removes the second phase porogen ma- ∼ terial used to create increased porosity while also increasing the connectivity and mechanical properties of the resulting films [127]. To facilitate more efficient removal of the sacrificial porogen and generate increased porosity and lower k, the 45% porous PECVD film (#94) was cured in the downstream afterglow of a remote H2/He plasma prior to UV/electron beam curing as before. Atomic hydrogen from a remote H2/He plasma has been previously shown to selectively remove the sacrificial organic porogen without significantly attacking terminal Si CH groups and the SiO network [120]. The resulting porous SiOC : H − 3 2 and a C : H films were assumed to be amorphous and spatially isotropic. − Film thicknesses, ranging from 94-200 nm, were obtained from a J. A. Woollam variable angle spectroscopic ellipsometer (VASE). The percent porosity for the films investigated was determined by ellipsometric porosimetry [111] using a vacuum system equipped with a separate spectroscopic ellipsometer to measure changes in the optical properties of the porous materials upon exposure to the vapor of various different solvents. The mass densities for the porous films were determined by x-ray reflectivity (XRR) and ranged from 0.7 to

0.9g/cm3 [112]. Table 5.5 provides a summary of these and other material properties.

BLS measurements were again accomplished in backscattering geometry as described in the previous section and used to determine the two independent elastic constants C11 and C (C ) through the relation C = (C C )/2. The measured BLS mode frequencies are 44 12 44 11− 12 ﬁt to a calculation of mode dispersion based on a Greens function formalism to determine

C11 and C44 [12, 148]. The same formalism provides for the mode displacements and the Brillouin scattering intensities [4].

82 Sample# Dep. h k n Porosity ρ XPS Composition − Material (nm) (%) (g/cm3) (% Si, C, O 5%) ± 22 C : H SOD 110 2.25 1.47 17 0.7 0.05 0, 100, 0 − ± 625 SiOC : H PECVD 200 2.2 1.34 32.6 0.9 0.05 37.3, 20.4, 42.3 − ± 186 SiOC : H PECVD 200 2.25 1.33 33.5 0.9 0.05 37.4, 19.5, 43.1 − ± 322 SiOC : H SOD 200 2.2 1.3 35.0 0.9 0.05 35.9, 36.3, 27.8 − ± 94 SiOC : H PECVD 110 2.0 1.26 45 0.7 0.05 39.3, 9.9, 50.8 − ±

Table 5.5: Description of materials and measured properties for the porous low-k dielectrics investigated in this study, where Dep. is the deposition technique, h is the ﬁlm thickness, k the dieletric constant and n the refractive index for 400 nm light.

5.3.2 Results

The ﬁve samples investigated range in porosity from 17%-45% (Table 5.5). To highlight our main results, we illustrate results from two SiOC : H samples: (i) 200 nm thick with 33.5% porosity and (ii) 94 nm thick with 45% porosity. Representative BLS spectra showing the

Stokes and anti-Stokes shifted peaks at several scattering angles from the 200 nm ﬁlm are illustrated in Figure 5.9. Observing the Stokes and Anti-Stokes shifted peak pairs ruled out the possibility of spectral artifacts with the mode frequencies determined by their average.

Multiple modes are observed and the variation of their frequencies with scattering angle is summarized in Figure 5.10. At small θ where longitudinal type modes dominate, N= 2 and N = 3 LSM harmonics are evident at 6.6 GHz and 11.6 GHz, respectively, while N=

2, N = 3, and N = 4 TSM modes occur 4.2 GHz, 6.6 GHz, and 9.7 GHz respectively .

Similarly, Figure 5.11 displays BLS spectra for the highest porosity (45%) ﬁlm, a 94 nm thick SiOC : H layer. In this case, at low θ, the N=1, 2 LSM modes are observed at 4.3

and 12.9 GHz, and the N = 2, 3 TSM modes at 7.8 and 12.9 GHz respectively. Again,

the strongest BLS peaks (4.3 and 12.9 GHz) in the low θ (< 10◦) spectra corresponded to

the LSM mode, with the weaker peak corresponding to the N = 1 TSM mode not being

resolved in the measurement. Figure 5.12 summarizes the mode dispersions with relation

to the scattering angle θ for the 94 nm thick ﬁlm.

83 Figure 5.9: Illustrative BLS Stokes and Anti-Stokes spectra for 200 nm thick, 33.5% porous SiOC:H ﬁlm recorded at θ = 5◦, 15◦, 45◦, and 60◦. At low angles, the N = 2 and N = 3 LSM modes are observed. As θ increases the modes become dispersive and additional modes emerge. The calculated spectra, utilizing elastic constants derived from the frequency dispersion (Figure 5.10), are illustrated above each measured anti-Stokes spectrum.

84 Figure 5.10: Variation of mode frequencies with scattering angle θ for the 200 nm thick, 33.5% porous SiOC : H film. The BLS data are represented as solid dark circles and the calculated fits by the small dots. The mode amplitude illustrated on the left reveal the standing mode character for the N= 2, 3 LSM and N = 2, 3, 4 TSM modes at low θ. Ux (solid) and Uz (dashed) curves correspond to TSM and LSM amplitudes respectively. Here x identifies the direction of mode propagation parallel to film surface, and z, the normal to the surface.

85 Figure 5.11: Illustrative BLS Stokes and Anti-Stokes spectra for 94 nm thick, 45% porous SiOC:H ﬁlm recorded at θ = 5◦, 30◦, 40◦, 45◦, and 60◦. At low angles, the N = 1 and N = 2 LSM modes are observed. As θ increases the modes become dispersive and additional modes emerge. The calculated spectra, utilizing elastic constants derived from the frequency dispersion (Figure 5.12), are illustrated above each measured anti-Stokes spectrum.

86 Figure 5.12: Dispersion of mode frequencies with scattering angle θ for the 94 nm thick 45% porous SiOC : H film. The BLS data are represented by solid dark circles and the calculated fit, the small dots. The mode amplitude plots shown on the left reveal the standing mode character for the N = 1, 2 LSM and N = 2, 3 TSM modes at low θ. Ux (solid) and Uz (dashed) curves correspond to the TSM and LSM amplitudes respectively. Here x identifies the direction of mode propagation parallel to film surface, and z, the normal to the surface.

87 5.3.3 Discussion

As noted, for low θ (< 10◦), the standing wave type excitations in the thin ﬁlms can be

described as acoustic modes similar to those in an organ pipe, where the open end corre-

sponds to the ﬁlm surface and the closed end to the ﬁlm/substrate interface [42]. The LSM

(TSM) excitations whose mode amplitudes at θ 5◦ are shown in insets to Figures 5.10 ∼ and 5.12, are largely controlled by C11 (C44), which can lie within the error range quoted in Table 5.6 and still provide a fit to the LSM (TSM) mode within 5%. The character of the modes is evident from the calculated mode amplitudes, with Uz denoting LSM amplitudes as a function of film depth, and Ux the corresponding TSM amplitudes. As θ increases, these modes progress into traveling waves with increasing wave vector components parallel to the film surface. Further confirmation of the mode assignment and of the elastic constants Cij is found in the measured BLS peak intensities (Figures 5.9 and 5.11). For instance in Figure 5.9 at low angle (θ = 10◦), the stronger peaks observed at 6.6 GHz and

11.6 GHz correspond to 2 LSM and 3 LSM which is consistent mode displacement profiles dominated by Uz (and thus C11) leading to enhancement of the associated surface ripple mediated light scattering[149]. On the other hand, at this low angle, the weakness of the peak at 9.7 GHz (4 TSM) is consistent with its dominant Ux character that does not contribute to the surface ripple. At higher scattering angles the transverse components of the mode displacements do contribute to surface undulations Uz and to ripple-based scattering [149]. The corresponding BLS peak frequencies and intensities are thus most sensitive to C44 at high θ. In these cases, due to the small scattering volume within the ultrathin films, elasto-optic mediated scattering is weak [150]. The calculated BLS peak intensities illustrated above each measured spectrum in Figures 5.9 and 5.11 were calculated using the ripple mechanism. Evaluated by matching electromagnetic boundary conditions across the rippled surface and interface, the BLS scattering intensities are sensitive to the extent of the undulations and thus to the individual Cijs. As illustrated in Figures 5.9 and 5.11, the measured peak profiles are fairly well described by the intensity calculations. For instance several features: (a) transformation of the overlapping peaks (Figure 5.11) in the 4-5 GHz

88 range at 40◦ and their evolution to distinct modes as θ increases to 60◦, (b) the broad asymmetric mode (Figure 5.9) evident at θ = 15◦ and its progression with increasing scattering angle are in reasonable agreement with the measured spectra. When taken in conjunction, the calculated BLS peak intensities (Figures 5.9 and 5.11) and the dependence of the mode frequencies with θ (Figures 5.10 and 5.12), provide tight constraints on the measured elastic constants for the corresponding low-k layers. The fact that only two independent elastic constants - C11 and C44 - are suﬃcient to describe the dispersion and BLS peak intensities, is additional evidence for the isotropy of the ﬁlms on a scale of the wavelength of the acoustic waves probed.

Sample# C C C Poisson’s BLS NI Young’s − 11 12 44 Material (GPa) (GPa) (GPa) Ratio Young’s Modulus Modulus (GPa) (GPa) 22 C : H 2.7 0.3 0.6 0.2 1.1 0.2 0.18 0.08 2.5 0.3 4.5 0.5 − ± ± ± ± ± ± 625 SiOC : H 2.7 0.3 0.4 0.2 1.2 0.2 0.13 0.06 2.6 0.3 4.5 0.5 − ± ± ± ± ± ± 186 SiOC : H 3.0 0.3 0.9 0.2 1.1 0.2 0.22 0.04 2.6 0.4 5.1 0.5 − ± ± ± ± ± ± 322 SiOC : H 5.0 0.3 2.0 0.3 1.5 0.2 0.29 0.03 3.9 0.5 5.4 0.5 − ± ± ± ± ± ± 94 SiOC : H 2.0 0.3 0.5 0.2 0.8 0.2 0.20 0.10 1.8 0.3 4.4 0.5 − ± ± ± ± ± ±

Table 5.6: Measured sample elastic constants and determined Poisson’s ratio and Young’s modulus.

The fits illustrated in Figure 5.10 for the mode frequencies and corresponding BLS intensity profiles for the 200 nm thick 33.5% porous film yield C11 = 3.0, C12 = 0.9, and

C44 = 1.1 GPa respectively. Similarly, the fits illustrated in Figure 5.12 for the mode frequencies and corresponding BLS intensity profiles for the 94 nm thick 45% porous film

yield C11 = 2.0, C12 = 0.5, and C44 = 0.8 GPa respectively. These elastic constants lie

well below those of SiO2 (C11 = 75 GPa and C44 = 22.5 GPa) and of a less porous (25%)

SiOC : H thin ﬁlm whose elastic constants C11 = 10.0 GPa, C12 = 2.9 GPa, C44 = 3.6 GPa were previously determined through BLS [151].

89 The Young’s modulus calculated for the ﬁve samples studied range between 1.8 and 3.9

GPa (see Table 5.6). These values are consistent with separate nano-indentation Young’s modulus measurements on identical but slightly thicker ﬁlms (200-500 nm) [151]. As shown in Table 5.6, the values of Young’s modulus determined by nano-indentation ranged from 4-6

GPa. These values are 2-3 GPa higher than those determined by BLS. This is consistent with previous studies where Young’s modulus determined from BLS measurements was observed to be slightly lower than those determined by nano-indentation. This oﬀset between BLS and nano-indentation was attributed to parasitic substrate eﬀects in the nano-indentation measurements [4, 151, 152]. Due to the low values of Young’s modulus for the porous

ﬁlms investigated in this study, the 2-3 GPa oﬀset represents an almost 2x overestimate in the elastic properties determined by nano-indentation. This result highlights the need for alternative techniques for measuring the mechanical properties of ultra-thin (< 100 nm),

low-k / low modulus materials and the risks associated with utilizing mechanical properties

determined by nano-indentation in modeling thermo-mechanical reliability.

Of the samples investigated, the 45% porous ﬁlm (#94) with the lowest dielectric con-

stant (2.0) also has the lowest Young’s modulus (1.8 GPa). This is consistent with this

material also having the highest porosity and lowest density. The porous material with

the highest Young’s modulus (3.9 GPa) was the SOD SiOC : H ﬁlm. Figures 5.13 and

5.14 show representative spectra and dispersions curves for this material. As the density and porosity for this film is not significantly different from those of the other two PECVD

SiOC : H ﬁlms, the higher Young’s modulus must be due to subtle diﬀerences in the com-

position and network structure of this material. This was partially conﬁrmed by separate

x-ray photoelectron spectroscopy measurements carried out by collaborators (Table 5.5)

that show this material has nearly twice the carbon content of the PECVD SiOC : H

materials. This is in contrast to a previous investigation (see section 5.2.3) where we ob-

served that non-porous SiOC : H dielectrics with high carbon content had lower Young’s

modulus values relative to porous SiOC : H dielectrics with low carbon content [151]. The

diﬀerences in the role of carbon content in determining Young’s modulus presented in the

current and previous sections indicate that subtle diﬀerences in how carbon is incorporated

90 Figure 5.13: Representative spectra recorded at diﬀerent scattering angles, θ = 10◦, 40◦, 50◦ and 60◦ for a 200 nm thick SOD SiOC : H ﬁlm at 35% porosity. The peak observed ∼ at lower scattering angles is the longitudinal standing modes 2LSM with the 1LSM at a frequency too low to be measured with our BLS system

into the low-k material (i.e. terminal Si CH vs. network Si C Si) likely play a − 3 − − determining role in the resulting mechanical properties. This is further supported by the

results from the SOD polymeric a C : H ﬁlm that is comparatively 100% carbon, yet − shows similar mechanical properties to the other PECVD SiOC : H dielectrics.

The corresponding Poisson’s ratios for these porous materials lie between 0.13 and 0.29

(Table 5.6). These are comparable to the Poisson’s ratios for aerogel materials that have

been reported to lie in this range [124, 125]. Speciﬁcally, Poisson’s ratios of 0.18 to 0.22

have been reported for aerogels with porosities of 20% to 40% [125]. It is interesting to note

91 Figure 5.14: Dispersion of acoustic modes supported in the h=200 nm 35% porous SOD SiOC : H low-k dielectric film (Table 5.5) showing variation of mode frequencies with scattering angle θ. The data are solid dark dots and the small dots are fits. The left panel illustrates mode displacements within the film for excitations near θ = 0◦ where the solid line is Ux and the dotted line is Uz corresponding to the standing mode TSM and LSM.

92 that the SOD SiOC : H dielectric with the highest Young’s modulus also has the highest

Poisson’s ratio (Figures 5.13 and 5.14). In contrast, the SOD polymeric a C : H ﬁlm has − a smaller Poisson’s ratio of 0.18 that is uncharacteristic of other polymer materials [151].

Theories on the elastic properties of random porous media depend on the properties of

the solid matrix, the solid volume fraction and the microstructure. Depending on the shape

and volume fraction of the pores, a variety of eﬀective medium and rigorous approximations

provide predictions on the linear elastic response [153]. Moreover, a number of theoretical

formulae relevant to macroscopically interconnected or interpenetrating pore phases and

bi-continuous structures have also been proposed [154–156]. A ﬁnite element approach to

study the elastic properties of random three-dimensional porous materials with highly in-

terconnected pores show that Young’s modulus is practically independent of Poisson’s ratio

of the solid phase (νs) over the entire solid fraction range [153]. Moreover, it is found that

Poisson’s ratio of the porous layer ν becomes independent of νs as the percolation threshold is approached [153]. To verify a particular theory, not only should it correctly provide for the Young’s modulus, but the subtleties of the Poisson’s ratio behavior provides for an eﬀec- tive method for revealing diﬀerences between the theories and demonstrating their range of validities [153]. Results such as those presented here should thus be useful in discriminating the merits of various theoretical approaches that describe the elastic properties of random three-dimensional porous materials.

5.3.4 Summary

Longitudinal and transverse standing acoustic modes have been observed from thin, highly porous, low-k dielectric ﬁlms deposited on silicon substrates. BLS has been used to non-

destructively measure the frequency dispersion as a function of phonon wave vector for

ﬁve ultra-thin (< 200 nm) samples. In addition to ﬁtting the variation of the mode fre-

quency with scattering angle, the calculated peak intensities place additional independent

constraints on the values of the measured elastic constants from which Poisson’s ratio and

Young’s modulus are determined. Values of Poisson’s ratio (Young’s modulus) are found to

vary from 0.13 - 0.29 (1.8 GPa 3.9 GPa) indicating that the mechanical properties of the

93 nano-ﬁlms investigated in this study are strongly inﬂuenced by porosity levels and growth parameters.

94 Chapter 6 Conclusions and Future Work

Brillouin light scattering is a valuable experimental tool which can be applied to a wide range

materials and systems. This approach has been shown to be eﬀective in the determination

of elastic properties of both biological tissues including the eye lens and cornea as well as

low-k solid state materials. The non-invasive and non destructive nature of the techniques

shows promise for potential use in a clinical and industrial setting.

In Chapter 3 BLS was used to study the lenses from human eyes provided by the eye

bank. In an eﬀort to determine if the human lens becomes stiﬀer with age as a possible

explanation for presbyopia, BLS frequencies from lenses over a range of ages were collected,

allowing calculation of their bulk modulus. No increase of signiﬁcance in bulk modulus

for either the cortex or nucleus regions of the lens was found over ages spanning 30-70

years, rendering the possibility of age related stiﬃng of the lens as the cause for presbyopia

unlikely. Additionally, due to the confocal arrangement of the BLS system, axial dimensions

and variation of the Brillouin frequencies of a bovine cornea and lens inside an intact eye

were measured. In chapter 4, we presented results from intact bovine corneas using both

BLS (GHz) and QUS (MHz) probe frequencies. Both techniques produced similar values

of bulk moduli, lending further creedance to our BLS results, both to those of the cornea

and those in the human lens study.

In the studies presented, only measurements along the central, axial direction through the lens and cornea were performed. It is known in both of these ocular tissues, the cellular arrangement changes dramatically as the outer limits of the tissue is reached. BLS studies

95 of these regions have the potential to illuminate how this altered structure aﬀects the tissue elastic properties. It would also be of use to modify the system such that a BLS frequency shift (bulk modulus) 3-D map of these tissues could be measured in a time eﬃcient manner.

Such a measurement has the potential to more clearly euclidate any changes, should they exist, throughout the entirety of the lens as a function of age. Such a non-invasive and non-destructive in-vivo system would also have application in a clinical setting perhaps as a diagnosic of early onset of ocular related diseases.

Highly porous low-k films were studied, demonstrating the advantage of the BLS technique over NI for film thicknesses 100-200 nm. Porosity values ranged from non-porous to 45%, the highest in the industry. Determination of the elastic constants of the films, revealed only modest degration in their mechanical properties (Young’s modulus and Pois- son’s ratio) despite the large range of porosities studied. The organ pipe character of specific phonon modes confined to the film was also observed arising from their thin nature.

Further work for extension of this technique, would be the ability to focus on a microscopic region of the sample. In the case of eye tissues, it would be beneficial to collect BLS data from individual fibrils, potentially revealing how internal structure of cells, as well as their interconnections, affect the macroscopic mechanical properties. Also, the semiconductor industry has moved towards patterning the high porosity low-k thin films creating designed structures to be utilized in real devices. The effect of this architecture on film mechanical properties could be measured by BLS at microscopic spatial dimensions.

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