Atomic dynamics model for nanoscale ductile mode cutting of silicon wafers

ATOMISTIC MODEL FOR NANOSCALE DUCTILE MODE CUTTING OF SILICON WAFERS HE TAO NATIONAL UNIVERITY OF SINGAPORE 2004... ATOMISTIC MODEL FOR NANOSCALE DUCTILE MODE CUTTING OF SILICON WAFER

ATOMISTIC MODEL FOR NANOSCALE DUCTILE

MODE CUTTING OF SILICON WAFERS

HE TAO

NATIONAL UNIVERITY OF SINGAPORE

2004

ATOMISTIC MODEL FOR NANOSCALE DUCTILE MODE

CUTTING OF SILICON WAFERS

HE TAO

(B.Eng, WUT)

A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERITY OF SINGAPORE

2004

Acknowledgement

First of all, I would like to express my sincere thanks to my supervisors, Associate Professor Li Xiaoping and Associate Professor Mustafizur Rahman Enlightenment and guidance from them has made it possible for me to go through the pleasant period

of research and study in National University of Singapore I would also like to thank National University of Singapore for offering research scholarship to support my study

in Singapore

Besides, I am indebted to many people for instructive discussions and hands-on guidance; among them I want to mention particularly Dr Liu Kui The lab officers and technicians at Advanced Manufacturing Laboratory, Workshop 2, and Nano Biomechanics Laboratory have contributed a lot to the completion of my graduate study Their sense of responsibility is very much appreciated by me Many thanks are sincerely brought to my dear friends Xu Xingjian couple, Dr Zhao Zhenjie, Dr Zhu Jianhang, Dr Lin Qi couple, and Ms Li Lingling

Most of all, I want to thank my wife, Liu Wei, for her love and devotion which will be invaluable treasure in my whole life; my father, mother, elder sisters and younger brother, for encouragement and understanding; my father-in-law and mother-in-law, for patience and assistance

Last but not least important, I am greatly impressed and touched by many kind and hardworking citizens in this beautiful and unique country Specially, I want to give my thanks to the house owner couple for their parental care

Table of Contents

Acknowledgement………i

Table of Contents………ii

Summary……… vi

Nomenclature……… viii

List of Figures……… xiv

List of Tables……… xvii

Chapter 1 Introduction……… 1

1.1 Significance of the study ……… 1

1.2 Background and previous work ………3

1.2.1 Ductile-regime machining of brittle materials……….3

1.2.2 Ductile material removal mechanism……… 4

1.3 Subject formulation and scope……… 8

1.4 Thesis outline……… 10

Chapter 2 Literature Review……… 13

2.1 Properties of some wafer materials……… 13

2.2 Configuration of group-IV semiconductors……… 14

2.2.1 Crystal structure……… 14

2.2.2 Covalent bonding and interatomic spacing……… 15

2.3 Ductile behavior of silicon solids……… 16

2.3.1 Dislocations in covalent crystals……… 16

2.3.2 Slip, resolved shear stress and Schimid law……… 17

2.3.3 Peierls stress……… 19

2.3.4 Theoretical shear stress……… 20

2.3.5 Indentation test……… 21

2.4 Fracture of brittle solids……… 22

2.5 Molecular dynamics and simulation……… 24

Chapter 3 Model Development….……… 27

3.1 Nanoscale chip formation zone……… 27

3.1.1 Nanoscale ductile mode cutting of silicon wafers………… 27

3.1.2 Proposed model for crack shielding zone……… 30

3.2 Atomistic model……… 31

3.2.1 Stress state analysis……… 31

3.2.2 Two dimensional (2D) atomistic model………… 34

3.2.3 Critical boundary conditions……… 37

3.3 Concluding remarks.……….38

Chapter 4 Experimental Apparatus and Procedure……….40

4.1 Objectives of experiments ……… 40

4.2 Experimental setup……… 41

4.3 Specimen preparation… ……… 41

4.4 Cutting tool……… 42

4.5 Cutting conditions……… 43

4.6 Equipment used……… ……… 44

Chapter 5 Results and Discussions.……….46

5.1 Machined surface……….46

5.2 Produced chips……… 48

5.3 Surface roughness and tool wear……… 51

5.4 Model verification………55

Chapter 6 Tool Wear Effects……… 63

6.1 Introduction……… 63

6.2 Experimental apparatus and setup……… 64

6.2.1 Experimental setup and specimen preparation……… 64

6.2.2 Cutting tool………65

6.2.3 Cutting conditions……… 65

6.2.4 Equipment used……… ……… 66

6.3 Results and discussions……… 66

6.3.1 Some characteristics of tool wear……… 66

6.3.2 Tool wear effect on cutting edge geometry.……… 67

6.3.3 Microgroove and tool failure……… 68

6.4 Concluding remarks……… … 74

Chapter 7 Cutting Force in Micro/Nano Machining….……… 76

7.1 Diamond cutting of ductile materials……… 76

7.2 Nanoscale ductile cutting……… 78

7.2.1 Cutting force characteristics……… 78

7.2.2 Effect of tool cutting geometry……… 80

Chapter 8 Conclusions and Recommendations.……….83

8.1 Conclusions……… 83

8.2 Recommendation for future work………86

List of Publications from Study……… 91

References……….92

Summary

Silicon wafers serve as dominant substrates for fabricating large and ultra-large integrated circuits With the rapid increase in circuit density, silicon wafers of diameter greater than 300 mm and of flatness less than 0.1 µm in a surface area of 20 × 20 mm2are required In the mean time, one finished wafer substrate should possess a mirror-like and free-of-crack surface As a brittle material, silicon material is not amenable to conventional machining operations Currently, a silicon wafer is finished by grinding, lapping, and then polishing Conventional manufacturing in wafer preparation and dicing process is characterized by heavy and complicated subsequent polishing

Nanoscale ductile cutting of silicon wafer materials, by which good surface integrity as well as high shape accuracy can be obtained without requirement for subsequent polishing, tends to be an alternative advancement in semiconductor industry By selecting the right ratio of undeformed chip thickness and cutting edge radius and controlling the undeformed chip thickness at the nanometric level, ductile mode cutting of single crystal silicon can be achieved This emerging technology is important because of the decrease in production time, which has many manufacturing and economic advantages

In this study, an atomistic model for this state-of-the-art technology is presented A crack shielding zone is defined, within which crack propagation is screened by large compressive stress that plastic deformation rather than brittle fracture is dominant process An atomistic model is then constructed to quantitatively describe such a ductile chip formation process This atomistic model not only maintains crystalline

features in silicon single crystals but also considers accelerated movement of all the atoms involved Furthermore, a two-dimensional model is developed for the prediction

of critical chip thickness by introducing two parameters, namely elasticity coefficient and stress gradient Geometrical relationship between the predicted value and the actual thickness of produced chips allows the proposed model to be verified by carrying out machining experiments The key factors affecting the discrepancy between predicted and measured chip thickness include some neglects in the course of mathematical calculation as well as the errors resulting from experiments

Tool cutting geometry and cutting force involved in the theoretical model are extensively analyzed based on experimental study Tool wear effects and influence on cutting behavior is experimentally investigated in terms of cutting edge radius, micro-cutting force and chip formation mode It is found that the flattening process of the tool cutting edge increases the cutting edge radius but leaves the cutting edge geometry unchanged This process can be accelerated by the progressive flank wear until catastrophic tool failure occurs Moreover, the fluctuation of cutting force, especially the thrust force component, with tool cutting geometry has negative effect on accurate sampling and accordingly the final outcome Therefore, all these effects have to be considered in developing the atomistic model

In the end, further work is suggested on using molecular dynamics and simulation to study the chip formation mechanism in nanoscale ductile cutting of brittle materials

Nomenclature

A cross-sectional area

cross-sectional area of the uncut chip

A, B, M, N constants

A f cross-section area of the fracture

D cohesion energy

E Young’s Modulus

Tersoff potential for a covalent system

E f energy required for fracture

E i site energy

E p energy required to plastically deform a specified volume

Peierls engery

F applied force

F B (y) force-separation function

FEM finite element method

F N normal force resolved on one atom on the tool cutting edge

F S tangential force resolved on one atom on the tool cutting edge

F Th critical localized load at the crack tip

F c measured cutting force component

F crit localized loading on the boundary of the crack shielding zone

F c,j cutting force resolved on each atom in the uncut area

F c,jk cutting force resolved on each atom on the tool cutting edge

F i resultant force to the ith atom

F i,1 , F i,2 interactive force resulting from relative replacement

F t measured thrust force component

F t.j thrust force resolved on each atom in the uncut area

F t,jk thrust force resolved on each atom on the tool cutting edge

F 0ij force between two atoms when undeformed

F 1,F 2 , …, F i local loading on atoms in the primary chain

F(r ij) force between two atoms

G Griffith crack propagation parameter

MDS molecular dynamics simulation

N A , N B numbers of atoms in each side

P external pressure applied

P c critical load on the diamond indenter

ideal surface roughness

R c cutting edge radius

R max maximum peak to valley height of roughness evaluation length

S area of interface plane

U(r) bonding energy

V i velocity of the ith atom

Zeff location of the ductile-to-brittle transition

a spacing of the rows of atoms

radius of semi-cylindrical or hemispherical core

elastic modulus

a, b, m, n constants

a ave actual chip thickness

a c undeformed chip thickness

a 0 lattice constant

a02 interfacial area of the bond

b spacing between atoms in a close-packed direction

b, c semi-axes length of an elliptical cavity

b ij bond order term

b 0 equilibrium interatomic spacing

d depth of cut

d c critical depth of cut

critical indentation depth

e elasticity coefficient

f tool feed

fBAB attractive pair potential

fBCB smooth cut-off function

fBRB repulsive pair potential

fBijB interatomic force between atoms

h integration time

i, j, k atoms of the system

j number of atoms in the uncut area

k number of atoms on the contact length

m Schimid factor

atomic mass

mBi,1B, mBi,2B mass of nearest neighboring atoms of the ith atomB

mB1B, mB2B, …, mBiB mass of atoms at each lattice site on the cutting edge

n number of atoms in primary chain within crack shielding zone

pBThB theoretical cohesive strength of the solid

pBiB momentum of the ith atom

r center-to-center spacing between atoms

ratio of thrust force component to cutting force component

rBijB length of the ij bond

distance between two atoms

rBwB workpiece radius

rB0B atomic distance at equilibrium

t predicted chip thickness

tBcB critical depth of penetration

tBminB minimum chip thickness

uBij B bond energy

u(rBijB) potential between two atoms

ω width of the dislocation core in the slip plane

x shear translation away from low energy equilibrium position

xB1B, xB2B, …, xBiB relative replacement of each atomB

yBcB the subsurface damage depth

β angle at one lattice site on the cutting edge

γBBB intrinsic surface energy

δ percentage of difference

δ’ ‘range’ parameter for the bond

θ angle at the intersection of the tool rake face and cutting edge

θBijkB bond angle between the bonds ij and ik

λ angle between the loading and the slip direction,

decreasing gradient

ξBijB number of other bonds to atom i besides the ij bond

ρ density

radius of crack curvature

σ normal stress activated on the tool cutting edge

σBFB critical applied stress

σBcB critical tensile stress

σBcleaveB cleavagestress for crack initiation

σBcompB compressive stress at a crack tip

σBslipB resolved tensile stress normal to the cleavage plane

σB y B yield stress

τ shear stress activated on the tool cutting edge

applied resolved shear stress

τBcB critical shear stress

τBpB Peierls Stress

τBslipB resolved shear stress in the slip direction on the slip plane

τBthB theoretical critical shear stress

υ Poisson’s Ratio

φ angle between the loading and the normal to the slip plane

List of Figures

Figure 1.1 Project of the tool-workpiece interface in feeding direction…………5 Figure 1.2 A model of chip removal with a size effect in terms of

defects distribution.……… 6 Figure 2.1 Diamond cubic structure of single crystal silicon……… 14 Figure 2.2 Attractive and repulsive forces versus interatomic spacing……… 16

Figure 2.3 ( )01 projection of the diamond-cubic lattice showing stacking 1 sequence of the (111) planes, and the shuffle and glide planes…… 17 Figure 2.4 Illustration of the geometry of slip in crystalline materials Note

that (φ +λ)≠90°in general……… 19

Figure 2.5 Schematic illustration used to estimate the theoretical critical

shear stress for slip in a perfect crystal……… 21 Figure 2.6 Typical stress-strain curves for two crystals……… 21 Figure 2.7 Graphs of fracture failure modes I, II, and III……… …… 23 Figure 2.8 Intrinsic interatomic force in Orowan-Gilman approximation…… 24 Figure 3.1 Model of elastic-plastic indentation……… 28 Figure 3.2 Illustration of nanoscale ductile mode chip formation……… 31 Figure 3.3 Shear stress and normal stress on the tool cutting edge in a plane

PBneB perpendicular to the cutting edge Note that FBcB<FBtB in the

ductile mode cutting……… 32 Figure 3.4 Schematic diagram of 2D atomistic model ……… 35 Figure 4.1 Illustration of experimental setup and cutting force

Figure 4.2 A typical single crystal diamond cutting insert observed using

miscroscope and SEM, respectively……… 43 Figure 4.3 Experimental setup of ductile mode cutting for silicon wafers…… 44 Figure 5.1 Nomarski micrograph and SEM photograph of the ductile surface machined at a cutting speed 2.355 m/s, feed rate 100 nm/rev,

depth of cut 2.0 µm, undeformed chip thickness

dBmaxB = 8.925 nm and dry cutting ……… 46 Figure 5.2 SEM photographs of the surfaces corresponding to different stages during ductile cutting at a cutting speed 2.355 m/s, feed rate

100 nm/rev, depth of cut 2.5 µm, and undeformed chip

thickness dBmaxB = 9.978 nm ……… ……… 47 Figure 5.3 SEM photographs of the brittle surfaces at a cutting speed

2.355 m/s, feed rate 100 nm/rev, depth of cut 5.0 µm, and

undeformed chip thickness dBmaxB = 42.232 nm.……… 48

Figure 5.4 SEM photographs of the cutting chips at a cutting speed

2.355 m/s, feed rate 100 nm/rev, depth of cut (a) 1.5 µm, (b) 2.0 µm and (c) 6.0 µm ……… 49 Figure 5.5 TEM photographs of the continuous chip layers at a cutting speed 2.355 m/s, feed rate 100 nm/rev, depth of cut 5.0 µm,

and undeformed chip thickness dBmaxB = 8.925 nm ……… 50 Figure 5.6 Illustration of ideal surface roughness machined using a rounded

corner cutting tool……… 51 Figure 5.7 Nomarski micrograph and profile of the surfaces machined at

a cutting speed 2.355 m/s, feed rate 100 nm/ rev, depth of

cut (a) 2.0 and (b) 6.0 µm, and undeformed chip thickness

dBmaxB = 8.925 nm and 15.436 nm, respectively.……… 52

Figure 5.8 Nomarski micrograph of the flank wear with cutting distance

1.4 km at a maximum undeformed chip thickness 15.436 nm…… 54

Figure 5.9 SEM photograph of the flank wear at the same cutting

conditions as that in Figure 5.8……… 54 Figure 5.10 Relationship between input and output under the critical

boundary conditions for 2D atomistic model……… 55

Figure 5.11 Programming of flowchart for calculating critical CSZ thickness… 56

Figure 5.12 Normal and shear stress distribution on the tool cutting edge versus included angle (π/2-θ) (0º < π/2-θ < π/2) with undeformed chip

thickness dBmaxB (a) 7.730 nm, (b) 8.925 nm, (c) 9.978 nm,

(d) 12.614 nm, and (e) 15.436 nm, respectively……… 58 Figure 5.13 Minimum normal stress on the cutting edge versus undeformed

chip thickness in nanoscale ductile cutting of silicon wafer ……… 59 Figure 6.1 SEM photographs of the rake face and flank face after ductile

mode cutting for 1.42 km at a cutting speed 2.355 m/s, and

undeformed chip thickness dBmaxB = 9.987 nm ……… 66

Figure 6.2 Graphs of flank wear, tool cutting edge on Tool A, and micrographs

of machined workpiece surface versus cutting distance………… 69 Figure 6.3 Graphs of flank wear, tool cutting edge on Tool B, and micrographs

of machined workpiece surface versus cutting distance.………… 70 Figure 6.4 Close-up of micro-grooves at the same cutting condition

as Figure 6.1……… 71 Figure 6.5 Section analysis of AFM images along the main cutting edge on

Tool A as (a) fresh and sharp cutting edge, and

(b) 2.83 km cutting……… 71 Figure 6.6 Section analysis of AFM images along the main cutting edge on

Tool B nose corner as (a) fresh and sharp cutting edge, and (b) 2.83 km cutting, respectively……… 72

Figure 6.7 Section analysis of AFM images after cutting 2.83 km for

(a) Tool A and (b) Tool B, respectively……… 72

Figure 6.8 3D AFM image of tool cutting geometry of (a) Tool A and

(b)Tool B, respectively, after cutting 2.83 km……… 74 Figure 7.1 Effect of depth of cut on cutting forces measured in orthogonal

fly cutting with cutting speed 1380 m/min……….77 Figure 7.2 Cutting force versus cutting distance in mirror finishing by a

curved cutting edge (nose radius: 2 mm)……… 78 Figure 7.3 Cutting force components vs cutting time at a cutting speed

2.355 m/s, feed rate 100 nm/rev, and undeformed chip

thickness (a) 7.730 nm and (b) 9.978 nm….……… 79 Figure 7.4 Variations in cutting force components and force ratio with

undeformed chip thickness at a cutting speed 2.355 m/s, and feed rate 100 nm/rev……… 80

Figure 7.5 Cutting force versus cutting time at a cutting speed 2.355 m/s,

feed rate 100 nm/rev, and undeformed chip

thickness 9.978 nm……….80

Figure 7.6 Variations in cutting forces with cutting distance for

(a) Tool A and (b) Tool B……… 81 Figure 8.1 MD model of nanoscale cutting for silicon wafer materials……… 87

List of Tables

Table 2.1 Property parameters of single crystal silicon……… 13

Table 2.2 Some important properties of Si and other materials

at 25ºC……… 13 Table 2.3 Parameters of Tersoff potential function……… 26 Table 4.1 Cutting conditions for model verification tests……… 44 Table 5.1 Main property parameters of silicon <111> single crystal………… 60 Table 5.2 Change in cutting force and chip thickness with undeformed

chip thicknes……… 60 Table 6.1 Cutting conditions for tool wear effect tests……… 65 Table 6.2 Actual cutting edge radius versus cutting distance for

Tool A and Tool B……… 68

Chapter 1: Introduction

Chapter 1 Introduction

1.1 Significance of the study

Silicon crystals have sustained the explosive growth of semiconductor technology since their inception Several types of crystals are used as base materials for building semiconductor devices Nevertheless, silicon wafers, with either a <111> or <100> crystal orientation, by far serve as dominant substrates for fabricating large and ultra-large integrated circuits Surface roughness (mirror-like) and surface integrity (free-of-fracture) are the key issues to evaluate one finished wafer substrate surface With the rapid increase in circuit density, silicon wafers of diameter greater than 300 mm and of flatness less than 0.1 µm in a surface area of 20 × 20 mm2 are required The productivity of wafer fabrication, to a great extent, relies upon the acquisition of such a high quality surface

Currently, a silicon wafer is finished by grinding, lapping, and polishing Typical wafer pre- and post- processes break down into wafer slicing, lapping, polishing, edge profiling, thinning, and wafer dicing As the initial step, the silicon ingot is precisely cross-cut into thin “wafers” that are processed until perfectly flat One side is then lapped, etched, and polished in the following sequences: first, the sliced wafers are mechanically lapped to flatten the wafer surfaces, make them parallel, and reduce mechanical defects like saw markings Second, wafer surface etching is performed to remove microscopic cracks or surface damage caused by previous mechanical lapping steps In the end, final wafer polishing, an actual combination of chemical and

Chapter 1: Introduction mechanical polishing process (CMP), is performed Then, the qualified wafers are ready to start on their journey in a wafer fab After integrated circuit fabrication and before chip packaging, the wafer goes through a dicing process, a post-procedure in which the wafer is cut by a precision diamond blade into hundreds of “dies” Generally speaking, almost all these mechanical operations involved are grinding in nature Brittle fracture and severe subsurface damage are thus inevitable due to occurrence of such random and uncontrolled material removal processes Conventional manufacturing technology in wafer preparation and dicing is characterized by so heavy and complicated subsequent polishing tasks that it increases the machining cost and impedes the timely delivery

Nanoscale ductile cutting of silicon wafer materials, by which good surface integrity as well as high shape accuracy can be obtained without requirement for subsequent polishing, tends to be an alternative approach for technological advancement in semiconductor industry Since the 1980s, ultra-precision machining technology has been highly developed in the manufacturing of optical, mechanical and electronic components for industrial purpose For many advanced technology systems, higher fabrication precision is complicated by the use of brittle and hard materials with superior quality Recently, diamond turning on an ultra-precision lathe has been reported as a kind of tool-based technology for producing optical quality surfaces on brittle materials such as quartz crystal, silicon, and germanium Moreover, it has been well recognized that ductile machining of silicon single crystals can be achieved when depth of cut is down to several tens of nanometers On the other hand, many attempts have been made to systematically understand the ductile behavior of brittle materials and the machining mechanism of this state-of-the-art technology This emerging

Chapter 1: Introduction technology is important because of the decrease in production time, which has many manufacturing and economic advantages

1.2 Background and previous work

1.2.1 Ductile-regime machining of brittle materials

A basic hypothesis for ductile-regime machining rests with such observations, namely, that plastic deformation can be actually achieved within a small controlled volume in brittle and hard materials before fracture occurs As previously shown (Van Groenou and Veldkamp, 1982; Tow and McPherson, 1986; Moore and King, 1980), observations of a small amount of plastic deformation in ceramics and glasses have been reported in wear or abrasive machining studies Earlier investigations have indicated that glasses do not always behave as nominally brittle materials, which was manifested by the indentation tests at external loads of the order of grams and at tip-depths of the order of micrometers Furthermore, when the indenter was moved laterally at constant loading, it was observed by Taylor (1949), Ishida and Ogawa (1962), and Marsh (1964) that, rather than causing brittle chipping, material piled up

on both sides of the groove edges A large body of data on indentation hardness has also been available from those notable tests conducted by Lawn and Wilshaw (1975), Marshall and Brown (1984), and Lawn et al (1980) The various radial and lateral crack fracture systems associated with indentation deformation have been clearly identified All these studies consistently demonstrate the fact that a limited amount of plastic deformation precedes the development of brittle fracture for localized-contact deformation underneath the sharp indenters The energy of plastic deformation

Chapter 1: Introduction becomes energetically favorable as the scale of deformation decreases, and there is a threshold volume below which a material will deform but not fracture (Kendall, 1978)

Diamond turning of certain brittle materials is now a viable option for producing superior quality optical surfaces without requiring any post-machining polishing The need to machine brittle materials arose as the need for both infrared and reflective optics escalated Non-ferrous metals, such as aluminium and copper, were the first to

be diamond turned However, brittle materials such as ceramics and glasses are not normally amenable to machining operations because of their low fracture toughness During the last decades, enormous work has been done on ductile machining of brittle and hard solids so as to make them more widely applicable in industry There are two distinct research subjects addressing ductile regime machining: ductile grinding and ductile cutting The development of ultraprecision, high-stiffness machine tools based

on air-hydrostatic bearings allows extremely precise control of deformation volume, which is indispensable to achieving ductile-regime machining

1.2.2 Ductile material removal mechanism

It has been a reproducible finding that ductile cutting of brittle materials can be achieved when depth of cut is extremely small, down to several tens of nanometers for wafer materials using diamond tools (Leung et al.,1998; Sreejith and Ngoi, 2001; Yan

et al., 2000; Yan et al., 2002) Systematical study on its machining mechanism and the technology is of theoretical significance and practical value Many research workers have been delving into understanding the phenomena of brittle-ductile transition and revealing the mechanism underlying continuous chip formation in ductile-regime machining Some initial work is noteworthy and briefly described here

Chapter 1: Introduction Blackley and Scattergood (1991) developed a new machining model for single point diamond turning of brittle materials The original research leading to this model was done by Blake (1988) Figure 1.1 is the phenomenolocial model of the machining process which was verified by interrupted tests According to the energy balance concept, fracture damage will initiate at the effective cutting depth and will propagate

to an average depth But as long as the damage does not replicate beyond the cut surface plane, ductile regime conditions are achieved The model uses two parameters,

the critical depth of cut dBcB and the subsurface damage depth yBcB, to characterize the ductile-regime material removal process The following equation was derived so that

both dBcB and yBcB could be obtained using the known machining parameters, namely, tool

radius R and tool feed f, and location of the ductile-to-brittle transition, ZBeff

2

(1.1)

Diamond tool

Critical chip thickness

Figure 1.1 Projection of the tool-workpiece interface in feeding direction

Nakasuji et al (1990) and Shimada et al (1995) proposed a possible material removal mechanism, which can fall into two modes when machining brittle materials One is

Chapter 1: Introduction the process due to plastic deformation in the slip direction on the characteristic slip plane(s) and the other is due to cleavage fracture on the characteristic cleavage plane(s)

When the resolved shear stress τBslipB in the slip direction on the slip plane exceeds a

certain critical value τBcB inherent to the workpiece material, a plastic deformation occurs

in a small stressed field in the cutting region of a specified scale, which may correspond to the depth of cut, for example On the other hand, a cleavage occurs when

the resolved tensile stress normal to the cleavage plane σBslipB exceeds a certain critical

value σBcB Material removal mode, therefore, depends on the stress state under a particular machining condition as well as the material properties

Critical stress field

Tool

Defect

(a) Small depth of cut (b) Large depth of cut

Figure 1.2 A model of chip removal with a size effect in terms of defects distribution

They further argued that the critical magnitude of cleavage and plastic deformation are affected by the density of defects and/or dislocations enclosed in the workpiece material Figure 1.2 shows a model of chip removal with a size effect in terms of defects distribution When uncut chip thickness is small, as shown in Figure 1.2(a), the

Chapter 1: Introduction size of the critical stress field is small enough to avoid cleavage initiated at the crack tip Consequently, the transition of chip removal process from brittle to ductile may take place, dependent upon the uncut chip thickness In order to obtain the chip removal by a plastic deformation rather than brittle fracture, therefore, the stress state and the defects distribution have to be accounted for

Bifano et al (1991) investigated ductile-regime grinding and established a depth-of-cut model They discussed the transition from brittle to ductile material-removal at smaller cutting depths purely from viewpoints of material-removal energy Consideration of this energy argument leads to a generalization that is named the

critical-“Ductile-regime Grinding Hypothesis.” This hypothesis states that for brittle solids, if the dimensional scale of material removal is made small enough, material removal will

be dominated by the mechanism of plastic flow rather than crack propagation The

yield stress σB y Bis defined as one of the material properties characterizing resistance to

plastic flow The energy (EBpB) required to plastically deform a specified volume of

material (VBpB) can be written as

The Griffith crack propagation parameter, G, denotes the material property

characterizing resistance to fracture The energy (EBfB) required for fracture is

Chapter 1: Introduction

d E

E Energy

Fracture

Energy Flow

material-1.3 Subject formulation and scope

Although much has been done on micro/nano machining, the chip formation mechanism, especially for nanomachining of wafer materials such as silicon and germanium, is not well established from atomistic viewpoints yet Continuum mechanics cannot be applied to the analysis of nanoscale solids or liquids where plastic flow and/or brittle fracture is inherently atomistic behavior rather than continuous one (Maekawa and Itoh, 1995; Luo et al., 2000) Since the effective stress area includes only a few tens of atomic layers and the nature of bonding also has a direct impact on the material removal process, the mechanism in nanometric cutting for silicon wafer materials must be explained from interactive and dynamic movement of individual atoms within this area Molecular dynamics (MD) or statics (MS) has been employed

to study and visualize chip removal processes, surface finish, tool wear and even thermal field in ultraprecision cutting (Shimada et al., 1992; Shimada et al., 1994; Inamura et al., 1994; Nozaki et al., 1998) Monocrystalline aluminium or copper crystals have been used as sample materials and diamond crystals as cutting tools for this study Some researchers (Cheng et al., 2003) have also carried out MD simulation

to study the tool wear mechanism in the nanometric cutting of a single crystal silicon plate with the diamond tip of an atomic force microscope (AFM) MD simulation,

Chapter 1: Introduction functioned as ‘computational microscope’, becomes a thrusting force in this investigation in conjunction with the application of statistical mechanics theory and the use of powerful computers

Besides, a fracture mechanics model in terms of machining conditions (rake angle, coolant, etc) should be provided It is well established that crack initiation and propagation are the essential elements for the normal failure of brittle substances The dynamic nanoscale cutting for brittle materials definitely makes the situation and stress state in the cutting region much more complex Accordingly, the failure mode and material removal mechanism in machining brittle materials are very complex The machining forces play an important role in this regard As magnitude and direction of the cutting force components change with machining conditions, the configuration of the elastic-plastic zone formed at the tool tip will change Fracture initiation can be related to the size of the plastic zone (Blake and Scattergood, 1990)

In this study, modeling at atomic level for nanoscale ductile mode cutting of silicon wafer materials is highlighted, in hope of better understanding the underlying chip formation mechanism Much effort would be directed at the development of such a model and the objectives as such are:

• An atomistic model for nanoscale chip formation zone will be built for the analysis of the material removal mechanism in nanoscale ductile mode cutting

A two dimensional model will be developed for the prediction of critical chip thickness so that the atomistic model can be verified This model is based upon two aspects:

• Nanoscale ductile chip formation zone

Chapter 1: Introduction

• Crystal structure of single crystal silicon

• Machining experiments will be conducted, allowing the model to be verified Characteristics of the cutting force, the machined surface and tool wear will also be observed and studied

• What is anticipated from this study is that it will serve as a solid foundation of further investigation A theoretical model using the molecular dynamics approach will be developed so that the movement of individual atoms and stress state in ductile cutting can be tracked and simulated

1.4 Thesis outline

The layout of the thesis follows the progressive development from building an atomistic model for nanoscale ductile cutting of wafer materials at one end to experimental verification at the other The background and previous work regarding ductile regime machining as well as ductile behavior of brittle solids, is covered in this chapter Significance and objectives of the study are presented together with the literature survey Basic and conceptual foundations are laid in chapter 2, with a view of atomistic configuration of crystal structure and dislocations in covalent crystals Besides, the computational approach now applied in analyzing micro/nano cutting from atomistic point of view is described in detail

Chapter 3 focuses on the construction of a two dimensional atomistic model Firstly, nanoscale chip formation zone, i.e so-called crack shielding zone, is methodically defined from atomic interaction in terms of loading gradient Secondly, the account of stress state on the tool cutting edge is accomplished by making some assumptions

Chapter 1: Introduction Thirdly, the critical boundary conditions are established for the occurrence of plastic deformation rather than brittle fracture in ductile mode cutting of brittle substances These are followed by introduction of two physical parameters so that critical thickness of the above mentioned zone can be predicted

Chapter 4 and chapter 5 extend the 2D atomistic model into machining verification In chapter 4 experimental setup, machine tool, and analysis instruments are dealt with The preparation of workpiece, cutting tool and specified cutting conditions are also clearly introduced These all contribute to the final accomplishment of nanometric ductile cutting for single crystal silicon On the basis of the achievement in the deliberate tests, the results and discussion section is complied into chapter 5 Chip thickness is predicted from the atomistic model and then experimentally verified by comparing with actual thickness of produced chips Finally, the theoretical and experimental effects leading to the errors between the actual thickness and predicted thickness of produced chip are analyzed

Tool wear characteristics and influence in nanoscale ductile mode cutting of silicon wafer materials are presented in chapters 6 and 7 Experimental setup and cutting conditions are illustrated in chapter 6 The rest part of chapter 6 consists of observation

on tool wear characteristics and tool wear effects on cutting behavior Chapter 7 describes cutting force in micro/nano machining, with an emphasis on cutting force characteristics in nanoscale ductile cutting

Conclusions are given in chapter 8, regarding the following aspects in nanoscale ductile cutting of single crystal silicon:

Chapter 1: Introduction

• Tool cutting edge effects

• Material removal mechanism

• Atomistic model

• Tool wear characteristics and influence

• Cutting force characteristics

Chapter 2: Literature Review

Chapter 2 Literature Review

2.1 Properties of some wafer materials

The two silicon crystal orientations commonly used in semiconductor industry are the

<100> and <111> planes These two orientations satisfy almost all requirements

Table 2.1 Property parameters of single crystal silicon Property Parameter Single Crystal Silicon Crystal Structure Diamond cubic

Primary Slip System {111}<110>

Number of Slip Systems 6

Number of Independent Slip Systems 2

Young’s Modulus E (GPa) 168

Vickner’s Hardness HB v B (GPa) 10.0

-3/2

) 0.6 Peierls Stress (GPa) 2.8-4.6 (0 K)

Table 2.2 Some important properties of Si and other materials at 25°C

Properties Si GaAs SiOB 2 B Crystal Diamond Zncblende Amorphous

Lattice constant 5.4307 5.6532 N/A

(Å)

Melting Temperature 1412 1237 1700 (°C)

Thermal Conductivity 1.5 0.455 0.015 (W/cmK)

-2

) (110) Bond Density 1.9189×10P

15 (cmP

-2

) Koop hardness 850 750 820 (N/mP

Chapter 2: Literature Review Table 2.1 and Table 2.2 list mechanical and physical properties of single crystal silicon

(Leung et al., 1998; Kelly and Macmillan, 1986; Cressler and Niu, 2003) and some

important properties of Si and other semiconductor materials at 25°C (Gsele and Tong,

1999), respectively

2.2 Configuration of group-IV semiconductors

2.2.1 Crystal structure

Silicon atoms crystallize in the cubic diamond lattice (Giacovazzo, 1992), as shown in

Figure 2.1 Shaded circles and bold lines represent Si atoms and covalent bonds

between atoms, respectively

1/2

3/4 1/4

3/4 1/4

0,1

Si atom

(a) Spatial illustration with covalent bonding (b) Projection view on base plane

Figure 2.1 Diamond cubic structure of single crystal silicon

The spatial representation of the diamond lattice can be seen in part a) of Figure 2.1

The covalent bonding structure between the atoms can be clearly recognized The

projection view of its spatial structure on the basic plane is illustrated in part b) of

Figure 2.1 The symmetry of atoms located on the body diagonals can be identified

The position of the lattice point measured from the base plane of the cube is denoted by

Chapter 2: Literature Review the number beside of each atom at the lattice points, with the value of the lattice parameter taken as a unit value

2.2.2 Covalent bonding and interatomic spacing

The bond between nearest neighboring atoms in Si and Ge is covalent, electron pair bond (Balkanski and Wallis, 2000) The bonding between atoms in covalent crystals is specific and directional, involving the exchange of electron charge between pairs of electrons When they are stressed to a sufficient extent, covalent crystals exhibit brittle fracture due to breaking of electron pair bonds without subsequent bonding reformation The equilibrium spacing between atoms is determined by a balance between attractive and repulsive forces no matter what type of bond is involved (Murray, 1993) The bonding force between atoms may be approximately by the general equation

)(N M r

where r is the center-to-center spacing between atoms and A, B, M, and N are constants

How these forces and bonding energy vary with distance can be examined by referring

to Figure 2.2 In this graph, the solid line, dash line and center line denote net force, attractive force and repulsive force, respectively The bonding energy is found by integrating the force equation Eq (2.1) as follows

r

b r

a

r

U =− m + n > (2.2)

where a and b are constants related to A and B, m = M, and n = N – 1

Since force can be related to stress, and change in distance can be related to strain within any material, the slope of the net force curve (Figure 2.2) is related to the

Chapter 2: Literature Review modulus of elasticity The slope of this curve is a continuous function and does not vary significantly within the first one or two percent strain on either side of the equilibrium distance (Van Vlack, 1970)

Born repulsive force

Figure 2.2 Attractive and repulsive forces versus interatomic spacing

2.3 Ductile behavior of silicon solids

As a brittle material, silicon is not amenable to conventional machining operations Its fracture toughness is lower than its yield strength When silicon is deformed at room temperature in tension or bending, it fractures before any permanent measurable plastic deformation occurs due to the difficulty of moving dislocations in silicon at room temperature

2.3.1 Dislocations in covalent crystals

Dislocations in these semiconductors affect both mechanical and electrical properties According to the review of Alexander and Hassen (1968), the dislocation slip in the deformation of diamond cubic crystals occurs on the closest-packed {111} planes in the closest-packed <110> direction The covalent bond formed by two atoms sharing electrons is strongly localized and directional, and this feature is important in determining the characteristics of dislocations (Hull and Bacon, 2001) Each atom is

Chapter 2: Literature Review tetrahedrally bonded to four nearest-neighbors, and the shortest lattice vector

110

2

1

links a second-neighbor pair The close-packed {111} planes have a six-fold

stacking sequence AaBbCcAaBb… as illustrated in Figure 2.3 Shaded circles represent

atoms in a covalent crystal The intrinsic fault and the extrinsic fault have stacking

sequence AaBbAaBbCc… and AaBbAaCcAaBb…, respectively Stacking faults formed

between adjacent layers of the same letter do not restore tetrahedral bonding and have

high energy Perfect dislocations, having Burgers vector 110

2

1

and slip on {111}

planes, usually lie along 110 directions at 0° or 60° to the Burgers vector The

dislocations produced fall into either the glide set or the shuffle set, as denoted in Figure

2.3 Climb, in which point defect absorption or emission is involved, transforms shuffle-set dislocations to glide-set dislocations, and vice versa

Figure 2.3 ( )01 projection of the diamond-cubic lattice showing the stacking 1

sequence of the (111) planes, and the shuffle and glide planes

2.3.2 Slip, resolved shear stress and Schimid Law

A characteristic shear stress on the slip plane in the slip direction is required for slip

The crystal illustrated in Figure 2.4 is being strained in tension by an applied force F

Chapter 2: Literature Review along the axis of the cylindrical crystal (Dieter, 1988; Hosford, 1993) The shear stress

τ, resolved on the slip plane in the slip direction, is

λφ

A

F

= (2.3)

where A is the cross-sectional area, λ is the angle between the loading and the slip

direction, and φ is the angle between the loading and the normal to the slip plane If the

yield stress σB y B is the tensile stress required for the onset of slip, the corresponding value

of the shear stress τBcB is called the critical shear stress for slip The Schimid factor is defined as

to grain The grain boundaries, being regions of considerable atomic misfit, act as strong barriers to dislocations A grain in a polycrystal is not free to deform plastically

as though it were a single crystal, for it must remain in contact with, and accommodate the shape changes of, its neighboring grains Under the circumstances, Schmid Law for polycrystals in which grains have random orientations may be generalized to

Chapter 2: Literature Review

λ

direction Slip plane

F

F Figure 2.4 Illustration of the geometry of slip in crystalline materials

Note that (φ+λ)≠90°in general

2.3.3 Peierls stress

Peierls (or Peierls-Nabarro) stress arises as a direct consequence of the periodic structure of the crystal lattice and depends sensitively on the form of the force-distance relation between individual atoms, i.e on the nature of the interatomic bonding Peierls stress is a function of the core structure The core disregistry imparts upon a dislocation

a core energy and resistance to dislocation motion which are functions of the forces between atoms in the core region Peierls (1940) and Nabarro (1947) derived the

following two equations to calculate Peierls energy EBp Band Peierls stress τBpB,B Brespectively

1

2

(2.8)

where G, ν, ω, and b are shear modulus, Poisson’s ratio, the width of the dislocation

core in the slip plane and spacing between atoms in a close-packed direction, respectively The covalent bonds resist any material deformation which will alter their electron configuration For this reason, dislocations in silicon have a high Peierls stress

Chapter 2: Literature Review

of about 2.8 – 4.6 GPa at 0 K However fracture occurs normally at much lower levels

of tensile stress before such high magnitude of stress is attained

2.3.4 Theoretical shear stress

In a perfect crystal, i.e in the absence of dislocations, the sliding of one plane over an adjacent plane would have to be a rigid co-operative movement of all the atoms from one position of perfect registry to another The theoretical shear stress required for this process was first calculated by Frenkel in 1926 The ideal situation is illustrated in

Figure 2.5, where τ is the applied shear stress, b the spacing between atoms in the direction of the shear stress and a the spacing of the rows of atoms It is assumed that

there is a periodic shearing force required to move the top row of atoms across the bottom row, which is given by the sinusoidal relation

b

x a

Chapter 2: Literature Review stress-strain curves are shown in Figure 2.6 The curve in Figure 2.6(a) represents a brittle material which exhibits little plasticity In tests on single crystals, it is usual to resolve the stress and strain onto the plane and direction for which slip occurs first The resulting stress-strain curve often has the form shown in Figure 2.6(b)

Shear stress

b

a

Figure 2.5 Schematic illustration used to estimate the theoretical

critical shear stress for slip in a perfect crystal

Figure 2.6 Typical stress-strain curves for two crystals

2.3.5 Indentation test

Although chip formation in diamond turning differs from the deformation produced using quasi-static hardness indentation dynamically and geometrically, there are some similarities in the two processes The indentaion test can be extensively used as a series

of tests, to demonstrate the extent of plastic deformation that precedes the development

of brittle fracture under a diamond tip For example, in the Hertizan fracture test (Wilshaw, 1971), three important surface properties of strong solids and consequently their strength were measured These are fracture toughness, surface crack size densities