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«A thesis presented by Yong Xiang to The Division of Engineering and Applied Sciences in partial fulfillment of the requirements for the degree of ...»

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Plasticity in Cu thin films: an experimental

investigation of the effect of microstructure

A thesis presented

by

Yong Xiang

to

The Division of Engineering and Applied Sciences

in partial fulfillment of the requirements

for the degree of

Doctor of Philosophy

in the subject of

Engineering Sciences

Harvard University

Cambridge, Massachusetts

October, 2005

© 2005 - Yong Xiang

All rights reserved.

Thesis advisor Author Joost J. Vlassak Yong Xiang

Plasticity in Cu thin films:

an experimental investigation of the effect of microstructure Abstract The mechanical behavior of freestanding Cu thin films is investigated using the plane-strain bulge test. Finite element analysis of the bulge test technique confirms that the measurement is highly accurate and reliable. A versatile specimen fabrication process using Si micromachining is developed and an automated bulge test apparatus with high displacement and pressure measurement resolutions is constructed. The elastic-plastic behavior of Cu films is studied with emphasis on the effects of microstructure, film thickness, and surface passivation on the plastic response of the films. For that purpose, Cu films with a range of thickness and microstructure and with different surface passivation conditions are prepared by electroplating or sputtering. The microstructure is carefully characterized and the stress–strain curves are measured. The mechanical properties are determined as a function of film thickness and microstructure for films both with and without surface passivation. The stiffness of the Cu films varies with film thickness because of changes in the crystallographic texture of the films and the elastic anisotropy of Cu. No modulus deficit is observed. The yield stress of unpassivated films varies mainly with the average grain size, while film thickness and texture have a iv Abstract negligible effect. The yield stress follows the classical Hall-Petch relation with a coefficient close to that for bulk Cu. The results indicate that grain boundary strengthening is the main strengthening mechanism for unpassivated Cu films. Passivated films exhibit increased yield stress and work-hardening rate, as well as a distinct Bauschinger effect with the reverse plastic flow already occurring on unloading.

Moreover, the yield stress increases with decreasing film thickness. Comparison of the experimental results with strain-gradient plasticity and discrete dislocation simulations suggests that the presence of any film-passivation interface restricts dislocation motion and results in the formation of a boundary layer with high dislocation density near the interface, which leads to a back stress field that superimposes on the applied stress field in the film. The directionality of the back stress leads to plastic flow asymmetry: it increases the flow stress on loading but assists reverse plastic flow on unloading. The boundary layer does not scale with the film thickness; hence the influence of the back stress increases with decreasing film thickness.

Table of Contents

Title Page ··························································································································i

Abstract···························································································································iii

Table of Contents ············································································································ v

List of Figures················································································································· ix

List of Tables ················································································································· xv

Acknowledgements······································································································· xvi

Dedication ···················································································································xviii

Introduction ····························································································· 1

Chapter 1

1.1 Background: Thin films and their applications ·········································· 2





1.2 Mechanical behavior of thin films: Motivation·········································· 4 1.2.1 Technological driving force: Mechanical behavior

and materials reliability·································································· 4

1.2.2 Scientific driving force: Size effects ·············································· 7

1.2.3 Materials system ············································································ 9

vi Table of Contents

1.3 The goal and outline of the thesis ···························································· 11

Chapter 2 Microstructure and mechanics of thin films:

Background information ······································································· 13

2.1 Thin film growth······················································································ 14

2.1.1 Evaporation and sputtering ·························································· 14

2.1.2 Electroplating··············································································· 16

2.2 Thin-film microstructures ········································································ 17

2.3 Mechanical characterization techniques··················································· 20 2.3.1 Techniques for films on substrate ················································ 20 2.3.2 Techniques for freestanding films ················································ 24

2.4 Advances in thin film mechanics ····························································· 26 The plane-strain bulge test technique for thin films···························· 31 Chapter 3

3.1 A brief review of the bulge test technique ··············································· 32

3.2 Finite element analysis············································································· 35

3.3 Sample preparation ·················································································· 44

3.4 Experimental setup ·················································································· 47

3.5 Results and discussion ············································································· 48

3.6 Summary ································································································· 51

Chapter 4 The mechanical properties of freestanding electroplated

Cu thin films··························································································· 53

4.1 Objective and overview ··········································································· 53

4.2 Experimental···························································································· 54

4.3 Results ····································································································· 55

4.3.1 Microstructural characterization··················································· 55 4.3.2 Mechanical properties ·································································· 64

4.4 Discussion ······························································································· 67

4.4.1 Elastic modulus············································································ 67

4.4.2 Stress–strain curves and residual stresses····································· 70

4.4.3 Yield stress··················································································· 71

vii Table of Contents

4.5 Summary ································································································· 75

Length-scale effect in freestanding Cu thin films ································ 77 Chapter 5

5.1 Objective and overview ··········································································· 78

5.2 Experiments····························································································· 79

5.3 Experimental results ················································································ 82

5.3.1 Microstructure·············································································· 82

5.3.2 Stress–strain curves······································································ 87

5.3.3 Yield stress··················································································· 91

5.4 Strain-gradient plasticity calculations ······················································ 94 5.4.1 The strain-gradient plasticity························································ 95

5.4.2 Problem formulation ···································································· 96

5.4.3 Numerical results ······································································· 100

5.5 Discrete dislocation dynamics simulations ············································ 103

5.5.1 Modeling···················································································· 103

5.5.2 Numerical results ······································································· 105



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