Inside the Miscibility Gap Nanostructuring and Phase Transformations in Hard Nitride Coatings

Linköping Studies in Science and Technology Dissertation No. 1472

Inside The Miscibility Gap Nanostructuring and Phase Transformations in Hard Nitride Coatings

Lars Johnson

Thin Film Physics Division Department of Physics, Chemistry, and Biology (IFM) Linköping University SE-581 83 Linköping, Sweden

Linköping 2012 © Lars Johnson Except for papers 1-3 © Elsevier B.V., used with permission. ISBN 978-91-7519-809-5 ISSN 0345-7524 Typeset using LATEX

Printed by LiU-Tryck, Linköping 2012

II ABSTRACT

This thesis is concerned with self-organization phenomena in hard and wear resistant transition-metal nitride coatings, both during growth and during post-deposition thermal annealing. The uniting physical principle in the studied systems is the immiscibility of their constituent parts, which leads, under certain conditions, to structural variations on the nanoscale. The study of such structures is challenging, and during this work atom probe tomography (apt) was developed as a viable tool for their study. Ti0.33Al0.67N was observed to undergo spinodal decomposition upon annealing to 900 °C, by the use of apt in combination with electron microscopy. The addition of C to TiSiN was found to promote and refine the feather-like microstructure common in the system, with an ensuing decrease in thermal stability. An age-hardening of 36 % was measured in arc evaporated Zr0.44Al0.56N1.20, which was a nanocomposite of cubic, hexagonal, and amorphous phases.

Magnetron sputtering of Zr0.64Al0.36N at 900 °C resulted in a self-organized and highly ordered growth of a two-dimensional two-phase labyrinthine structure of cubic ZrN and wurtzite AlN. The structure was analyzed and recovered by apt, although the ZrN phase suﬀered from severe trajectory aberrations, rendering only the Al signal useable. The initiation of the organized growth was found to occur by local nucleation at 5-8 nm from the substrate, before which random fluctuations in Al/Zr content increased steadily from the substrate. Finally, the decomposition of solid-solution TiB0.33N0.67 was found, by apt, to progress through the nucleation of TiB0.5N0.5 and

TiN, followed by the transformation of the former into hexagonal TiB2.

III

INUTILÖSLIGHETSLUCKAN nanostrukturering och fasomvandlingar i hårda nitridskikt

Populärvetenskaplig Sammanfattning

Den här doktorsavhandlingen behandlar mätningen och förståelsen av nanostrukturering och fasomvandlingar i hårda nitridskikt. Skikt, eller tunna filmer, används idag i stor omfattning, i allt från deko- rativa beläggningar på husgeråd till komplexa lager i halvledarindustrin. Vanligtvis görs tunna filmer genom kondensation av en ånga på ytan som ska beläggas, och genom att endast lägga ett tunt lager kan material med vitt skilda egenskaper från de som förekommer i tjockare former skapas. Detta gör tunna filmer viktiga, då man genom att kombinera en film med ett sub- stratmaterial kan åstadkomma egenskaper som inte går att uppå på något annat sätt. Av speciellt intresse för den här avhandlingen är nötningståliga skikt, vilka i industrin används som beläggningar på skärande verktyg för metallbearbetning. Egenskaper som hårdhet kan förbättras ytterligare om filmen har en struktur på nanometerskalan. Ett sätt att åstadkomma sådana strukturer är att belägga en yta med två material som är olösliga i varandra, t.ex. titanni- trid (TiN) och aluminiumnitrid (AlN), som då kommer att försöka separera om atomerna har tillräcklig rörlighet, d.v.s. om temperaturen är tillräckligt hög. Nanostrukturering kan ske antingen vid själva beläggningen, eller vid värmebehandling i efterhand. Det är detaljerna i sådana separationsprocesser som har studerats i det här arbetet, med sikte på atomär avbildning, där mekanismerna för fasomvandling i TiAlN och TiBN har identifierats som spinodalt sönder- fall och icke-klassisk kärnbildning och tillväxt i de respektive fallen. En två- dimensionell labyrintisk struktur i ZrAlN har upptäckts, och förklarats så- som orsakad av en balans mellan ytenergi och elastisk energi på tillväxtytan. Den viktigaste tekniken för studierna har varit Atomsondstomografi, där man mäter ett prov atom för atom, och sedan återskapar det i tre dimen- sioner. Då tillämpningen på hårda skikt är ny har det inspirerat till att en metodutveckling som också ingår i avhandlingen.

PREFACE

This thesis is the result of my doctoral studies in the Thin Film Physics Di- vision at the Department of Physics, Chemistry, and Biology at Linköping University between 2007 and 2012. The main body of the work was done under the auspices of the Vinnex Center for Functional Nanoscale Materi- als (FunMat), in collaboration with Sandvik Coromant, SECO Tools, and Ionbond Sweden. I have also been visiting the Microscopy and Microanaly- sis group at Chalmers University of Technology, and the Nanostructured Materials group at Montanuniversität Leoben. I would like to thank my supervisors Lars Hultman, Magnus Odén, Krystyna Stiller, and Mattias Thuvander; my co-authors and the members of Theme 2 of FunMat; and my friends and colleagues, especially the coﬀee club, at the department.

Lars Johnson Linköping, September 2012

VII

INCLUDEDPAPERS

I Spinodal Decomposition of Ti0.33Al0.67N Thin Films Studied by Atom Probe Tomography L.J.S. Johnson, M. Thuvander, K. Stiller, M. Odén, L. Hultman Thin Solid Films 520 (2012) 4362.

II Microstructure Evolution and Age Hardening in (Ti,Si)(C,N) Thin Films Deposited by Cathodic Arc Evaporation L.J.S. Johnson, L. Rogström, M.P. Johansson, M. Odén, L. Hultman Thin Solid Films 519 (2010) 1397.

III Age Hardening in Arc-evaporated ZrAlN Thin Films L. Rogström, L.J.S. Johnson, M.P. Johansson, M. Ahlgren, L. Hultman, M. Odén Scripta Materialia 62 (2010) 739.

IV Self-organized Labyrinthine Nanostructure in Zr0.64Al0.36N Thin Films N. Ghafoor, L.J.S Johnson, L. Hultman, M. Odén In manuscript.

V Self-organized Nanostructuring in Zr0.64Al0.36N Thin Films Studied by Atom Probe Tomography L.J.S Johnson, N. Ghafoor, M. Thuvander, K. Stiller, M. Odén, L. Hultman In manuscript.

VI Phase Transformation of Ti(B,N) into TiB2 and TiN Studied by Atom Probe Tomography L.J.S Johnson, R. Rachbauer, P.O.Å. Persson, L. Hultman, P.H. Mayrhofer In manuscript.

The Author’s Contributions

I Did all experimental work, and wrote the paper. II Did most of the experimental work, and wrote the paper. III Took part in the experimental work, and in writing the paper. IV Took part in the experimental work, and wrote the paper. V Did most of the experimental work, and wrote the paper. VI Took part in the experimental work, and wrote the paper.

IX CONTENTS

INTRODUCTION TO THE FIELD 3

1 Introduction 5

2 Materials 9 2.1 Immiscible Nitride Systems 9 2.2 Ti-Al-N 10 2.3 Zr-Al-N 11 2.4 Ti-Si-C-N 12 2.5 Ti-B-N 14

3 Deposition 19 3.1 Physical Vapour Deposition 19 3.2 Film Growth 21

4 Phase Transformations 25 4.1 Diﬀusion 26 4.2 Immiscibility 27

5 Thin Film Characterization 33 5.1 X-ray Diﬀraction 33 5.2 Transmission Electron Microscopy 34 5.3 Elastic Recoil Detection Analysis 41 5.4 Nanoindentation 41

6 Atom Probe Tomography 43 6.1 History 43 6.2 Principle of Operation 45 6.3 Tomographic Reconstruction 48 6.4 Visualization and Data Analysis 51 6.5 Sample Preparation 52 6.6 APT of Hard Coatings 53 6.7 Development of a Blind Deconvolution method for APT Mass Spectra 54

7 Contributions to the Field 67

X PAPERS 71

I Spinodal Decomposition of Ti0.33Al0.67N Thin Films Studied by Atom Probe Tomography 73 1 Introduction 75 2 Experimental Details 76 3 Data Analysis 76 4 Results 78 5 Discussion 85 6 Conclusions 89

II Microstructure Evolution and Age Hardening in (Ti,Si)(C,N) Thin Films Deposited by Cathodic Arc Evapora- tion 93 1 Introduction 95 2 Experimental Details 96 3 Results and Discussion 97 4 Conclusions 106

III Age Hardening in Arc-evaporated ZrAlN Thin Films 109

IV Self-organized Labyrinthine Nanostructure in Zr0.64Al0.36N Thin Films 117

V Self-organized Nanostructuring in Zr0.64Al0.36N Thin Films Stud- ied by Atom Probe Tomography 127 1 Introduction 129 2 Experimental Details 130 3 Results and Discussion 130 4 Conclusions 138

VI Phase Transformation of Ti(B,N) into TiB2 and TiN Studied by Atom Probe Tomography 141 1 Introduction 143 2 Experimental Details 143 3 Results 144 4 Discussion 150 5 Conclusions 152

XI ACRONYMS

apt atom probe tomography

cbed convergent-beam electron diﬀraction

ctf contrast transfer function

cvd chemical vapour deposition

ed electron diﬀraction

edx energy-dispersive X-ray spectroscopy

eels electron energy loss spectroscopy

erda elastic recoil detection analysis

fcc face centered cubic

fib focussed ion beam microscopy

fim field ion microscopy

fwhm full-width at half maximum

haadf high angle annular dark field stem

hcp hexagonal close packed

hrtem high-resolution tem

icf image compression factor

leap local-electrode atom probe

pvd physical vapour deposition

rbs rutherford backscattering spectroscopy

rdf radial distribution function

saed selected area electron diﬀraction

sem scanning electron microscopy

stem scanning transmission electron microscopy

XII szm structure zone model tem transmission electron microscopy tof time-of-flight uhv ultra-high vacuum xps X-ray photoelectron spectroscopy xrd X-ray diﬀractometry

XIII

The Tao that can be told is not the eternal Tao; The name that can be named is not the eternal name. The nameless is the beginning of heaven and earth. The named is the mother of ten thousand things.

Ever desireless, one can see the mystery. Ever desiring, one can see the manifestations. These two spring from the same source but diﬀer in name; This appears as darkness.

Darkness within darkness. The gate to all mystery. Tao Te Ching, Gia-Fu Feng & Jane English transl.

Skulle jag sörja då wore jag tokot Fast än thet ginge mig aldrig så slätt Lyckan min kan fulla synas gå krokot Wackta på Tijden hon lär full gå rätt; All Werlden älskar Ju hwad som är brokot Mången mått liwa som eij äter skrätt. Lasse Lucidor

PARTI

INTRODUCTION TOTHEFIELD

INTRODUCTION 1

This thesis is concerned with the measurement and understanding of various phenomena of nanostructuring and phase transformations in hard nitride coatings. Coatings, or thin films, are used today in a wide range of applications, from decorative coatings on household items, to highly complex layers in the microelectronics industry. Thin films are most commonly created by the con- densation of a vapour on the surface to be coated, and through deposition as a thin layer, materials with widely diﬀerent properties than those achievable in bulk phases are possible. This is the reason for the popularity of thin film processes, as the combination of substrate and film enables properties that would be impossible to achieve with one component alone. Common properties to which thin films provide an improvement or specialization are electrical, magnetic, optical, and most importantly for the work herein, hardness, wear resistance, and thermal stability. Hard and wear resistant coatings have been an important part in the production of metal cutting tools since the 1970s. A cutting tool must be tough enough to withstand the shocks of metal cutting, and this limits the choice of tool materials; the solution is to coat the softer tool with a hard ceramic coating. The requirements of increased productivity, tougher workpiece materials, and reduced environmental impact form a powerful driving force for the development of new and better wear resistant coatings. The first hard coatings were TiC and TiN, and TiN is the base for a large part of the materials systems in use today. In perfect single-crystal form, TiN has a hardness of around 20 GPa (a hard steel is around 5 GPa, for comparison), and TiN deposited by cathodic arc evaporation can reach over 30 GPa, due to defect and strain hardening. Further improvements were achieved by alloying; the first example is TiCN, where TiC and TiN are miscible, and form a stable solid solution with improved properties compared to TiN. TiAlN is another ternary system that improved upon pure TiN, but here AlN is immiscible in TiN, which leads to a driving force for separation and phase transformation into TiN and AlN. During its early stages, this transformation produces a structural variation on the scale of a few nanometres–nanostructuring–and with this follows an increase in hardness [1]. Nanostructuring can also occur directly during film growth; the classic example is the nanocomposite TiN/SiNz system, in which nanocrystalline (nm-sized) grains of TiN are embedded in a matrix of amorphous SiNz[2].

5 INTRODUCTION

The segregated growth occurs because of the immiscibility of TiN and Si3N4. The understanding and control of such immiscibility are now technologically important in hard coatings, both to achieve the desired microstructure during growth, and to direct any transformations during metal cutting. Currently, the field is moving more and more towards complex ternary and quaternary compounds; examples include TiSiAlCN, HfAlN, ZrAlN, and TiCrAlN [3–8]. As it will always be easier to synthesize coatings in a new materials system than to characterize them, the understanding of the structures and processes that lead to them will lag behind their application. Instead, the study of simpler systems guides development of more complex, but often related systems. Here interest has been divided between TiAlN, ZrAlN, TiBN, and TiSiCN, as they all supply diﬀerent structures and mechanisms of nanostructuring. This movement towards the use and study of nanostructures also leads to interesting challenges in their characterization, and one enabling factor in their development is the continuous and rapid development of the instruments used for the characterization. Of central interest in this thesis is the technique of atom probe tomography (apt), which enables atomic chemical and positional information to be extracted from a sample. While the technique was invented in 1968 [9], it was not until the mid 2000s [10] that the instrumentation had progressed enough to enable the analysis of hard ceramic coatings. The technique is still maturing in this field, but it is already able to supply measurements that are not possible today with any other kind of instrument. While the atom probe excels at local compositional measurements, it can only resolve the crystal lattice in a few special cases, which makes a pairing with electron microscopy techniques particularly powerful. Global compositional measuring techniques are also complementary, as they provide a check on the composition given by the atom probe.

•

This thesis is composed of two parts. The first serves as an introduction to the field and background to the research made. The second part of the thesis contains the results of the work in the form of scientific papers.

6 REFERENCES

References

1. P. H. Mayrhofer et al. Self-organized nanostructures in the Ti–Al–N system. Applied Physics Letters 83 (2003) 2049. 2. S. Vepřek, S. Reiprich, and L. Shizhi. Superhard nanocrystalline composite materials: The TiN/SiN system. Applied Physics Letters 66 (1995) 2640. 3. H. Lind et al. Improving thermal stability of hard coating films via a concept of multicomponent alloying. Applied Physics Letters 99 (2011) 091903. 4. B. Howe et al. Real-time control of AlN incorporation in epitaxial

Hf1-xAlxN using high-flux, low-energy (10-40 eV) ion bombardment during reactive magnetron sputter deposition from a Hf0.7Al0.3 alloy target. Acta Materialia 59 (2011) 421–428. 5. M. Stüber et al. Magnetron sputtered nanocrystalline metastable (V,Al)(C,N) hard coatings. Surface & Coatings Technology 206 (2011) 610–616. 6. A. Pogrebnyak et al. Eﬀect of deposition parameters on the superhardness and stoichiometry of nanostructured Ti-Hf-Si-N films. Russian Physics Jour- nal 54 (2012) 1218–1225. 7. V. Beresnev et al. Triboengineering properties of nanocomposite coatings Ti-Zr-Si-N deposited by ion plasma method. Journal of Friction and Wear 33 (2012) 167–173. 8. D. V. Shtansky et al. High thermal stability of TiAlSiCN coatings with “comb” like nanocomposite structure. Surface and Coatings Technology 206 (2012) 4840–4849. 9. E. W. Müller, J. A. Panitz, and S. B. McLane. The atom-probe field ion microscope. Review of Scientific Instruments 39 (1968) 83–86. 10. T. Kelly and D. Larson. The second revolution in atom probe tomography. MRS Bulletin 37 (2012) 150–158.

MATERIALS 2

Transition metal nitrides (especially those of group IV elements, Ti, Zr, and Hf) have several properties that make them technologically important. The first one is their high hardnesses: single-crystal TiN has a hardness of 20 GPa [1], and TiN deposited by cathodic arc evaporation can reach over 30 GPa due to defect and strain hardening [2]. The second is their high melting points [3], around 3000 °C, and stability against reactions. For example, TiN oxidizes at around 500-600 °C. The group IV nitrides share a common crystal structure in the cubic NaCl, or B1, structure. This consists of two face centered cubic (fcc) lattices oﬀset by one-half of the lattice parameter, where the metal element atoms occupy one lattice and the nitrogen atoms the other. Another way of visualizing the lattice is to surround each metal atom with eight nitrogen atoms arranged in a regular octahedron. This structure can tolerate a wide range of compositions; the N fraction (z in TiNz) has been observed to vary from z 0 7 to z 1 2 [4, 5]. Due to its wide availability≈ TiN. is the≈ most. important of these materials for applications today, and it appears as precipitates in steels, as a component in certain cemented carbides, as diﬀusion and thermal barriers, and in semiconductor stacks, amongst others. Most important for this thesis is its use as a wear resistant coating for metal cutting applications, although it is often alloyed to further control and enhance its properties. In addition to its wide applicability, TiN has proven to be a good model system for basic materials science, and it has been extensively studied since the 1970s for thin film growth [4, 6], and for alloying [7, 8].

2.1 Immiscible Nitride Systems

During experimentation to produce film materials with even better properties than the base binary nitrides, it was discovered that there exist a number of other nitride materials with low or essentially no solubility in

TiN. AlN and SiNz [7, 9] are the most well-known and used materials in this class today. By growing such alloys far from equilibrium, complex and interesting nanostructures can form, either directly or during heat treatment. The details of such transformations vary greatly with the constituent elements of a system and with their composition. Each system that is treated below exhibits diﬀerent behaviour from the others, both in terms of growth and subsequent heat treatment.

9 MATERIALS

N figure 2.1 The Ti-Al-N isother- 900 °C mal phase diagram at 10 90 900 °C, after [10]. 20 80

30 70

40 60 at. %

at. % 50 50 AlN TiN 60 40 Ti2N 70 30

Ti2AlN 80 Ti AlN 20 3 Ti 90 10

TiAl TiAl TiAl Ti 8070605040302010 90 Al 3 Al Ti

3 2 at. %

2.2 Ti-Al-N

Ti-Al-N was the first metastable alloy to be used by industry as a coating for cutting tools. Aluminium was first added with the intention to improve the oxidation resistance of TiN, as cutting tools may reach over 1000 °C during operation [2]. It is possible to retain the B1 TiN phase with an Al content up to 70 atomic % of the total metal content [9]. The miscibility gap of the TiN-AlN pseudobinary system is significant, with essentially no mutual solubilities of either AlN in TiN or TiN in AlN [11]. Furthermore, the stable phase of AlN at normal conditions is the hexagonal wurtzite phase, while there is a cubic phase which is only stable at pressures over 14 GPa [12]. Hörling et al. [13] were the first to connect age hardening in metastable TiAlN thin films to decomposition into TiN and AlN. Hörling found that the TiAlN film would first decompose into TiN and B1 AlN, and only upon further annealing would the cubic AlN transform into the thermodynamically stable wurtzite phase. The nature of this first decomposition has been the subject of much interest. It was suggested early on [13] that an iso-structural spinodal decomposition mechanism was possible, and calculations [11] found support for a spinodal region in the miscibility gap. The question

1 0 Z r - A l - N

N figure 2.2 1000 °C The Zr-Al-N isother- 10 90 mal phase diagram at 1000 °C, after [25]. 20 80

30 70

40 60 at. %

at. % 50 50 AlN ZrN 60 40

70 30

80 Zr3AlN 20

90 10

Zr5Al3N Al 8070605040302010 90 Zr at. % was settled by a number of works using both direct and reciprocal space techniques to study the phase transformation, which all concluded that the transformation was indeed spinodal [14–18]. Even so, there are still unsolved questions in the system, which is reflected by the recent literature [19–24].

2.3 Zr-Al-N

Moving one row down in the periodic table from Ti you arrive at Zr, and the idea of Zr-Al-N follows directly. ZrN is similar to TiN; the crystal structure is the same B1 structure, and with a similar electronic structure, but ZrN has a larger lattice parameter (a 4 58 Å[26]) than TiN (a 4 24 Å[27]. This makes the mismatch between= ZrN. and AlN bigger as well,= as. AlN will assume a lattice parameter of 4 05 Å[28] if forced into the B1 structure. Just as AlN is immiscible in TiN,∼ it. is immiscible in ZrN, and experiments indicate that the driving force for segregation is larger in the case of Zr-Al-N. Rogström et al. investigated the possibility of forming solid solutions of

Zr1 xAlxN over the whole pseudobinary composition range, and found that− it was only possible to grow cubic solutions with x up to 0 4 and hexagonal solutions for x over 0 7, with composition in between∼ yielding. a highly distorted nanocrystalline∼ . mixture of cubic, hexagonal, and amorphous phases [29]. There are just a few more industrially-inclined papers dealing with Zr-Al-N [30–33], most likely due to the expensiveness of Zr.

1 1 MATERIALS

figure 2.3 N The Ti-Si-N isother- 1000 °C mal phase diagram at 10 90 1000 °C, after [34]. 20 80

30 70

40 60 at. % Si3N4 at. % 50 50 TiN 60 40

70 30

80 20

90 10

TiSi Ti Si 8070605040302010 90 Ti 5 Si

2 at. % 3

2.4 Ti-Si-C-N

The alloying of Si in TiN is another way to improve properties for certain cutting applications. Like TiAlN, the system has a considerable miscibility gap, and about 5 at. % of Si appears to be the limit of solubility, when synthesized by cathodic arc evaporation [35]. The alloy Ti-Si-N has gath- ered a lot of attention as it was reported that TiN crystallites (≤ 10 nm in

diameter) surrounded by one to a few monolayers of SiNz(1 ≤ z ≤ 1.33), usually referred to as the nc-TiN/a-SiNz nanocomposite, exhibited an ex- traordinary hardness of over 50 GPa [36–38]. The Ti-Si-N nanocomposite was first synthesized by CVD, but films deposited by magnetron sputtering will typically also have this microstructure. When TiSiN is synthesized by arc evaporation it grows columnar, but with increasing Si content, the grain size becomes smaller, as Si acts as a strong grain refiner, and it also causes the grains to tilt slightly, causing a feather-like appearance in TEM images, which is also termed “comb-like” in TiAlSiN films [39]. A typical example is shown in Fig. 2.4. Solid solution TiSiN films undergo decomposition when heat treated [35],

by segregation and transformation into TiN and SiNz. The segregation of Si is diﬀerent from the TiAlN case, as the microstructure and chemistry

1 2 T i - S i - C - N

figure 2.4 A typical TiSiCN film, from Paper II.

0.5 μm of TiSiN films is typically diﬀerent. The segregation of Si in this case was shown by Flink to proceed to the grain boundaries, and then, upon further annealing, Si was found to leave the film entirely [40]. Another common method of enhancing some properties of TiN for cutting tools is the addition of C, which substitutionally replaces N. TiCN films are stable and do not decompose upon annealing [2]. Ti-Si-C-N deposited by CVD is very similar in properties and structure to nc-TiN/a-SiN [41, 42]. N 1000 °C figure 2.5 10 90 The Ti-B-N isothermal phase diagram at 1000 20 80 °C, after [34]. 30 70

40 60 at. %

at. % BN 50 50 TiN 60 40 Ti N 70 230

80 20

90 10

TiB TiB B 8070605040302010 90 Ti 2 at. %

1 3 MATERIALS

2.5 Ti-B-N

The Ti-B-N is seemingly similar to the previous systems, especially to Ti-Si- N, yet diﬀerent. The similarity is due to the existence of a miscibility gap, and there are no ternary compounds in the system. Like Ti-Si-N it can form a

structure of nanocrystalline grains (of TiN and TiB2) embedded in an amorphous (BN) matrix [43–46]. This structure forms in the three-phase-field in the ternary phase diagram (see Fig 2.5). It is also possible to synthesize solid solution films in the cubic phase with a B content up to approximately 17 at. %[47]. The diﬀerence from the previous systems becomes apparent here, as the insolubility is between the N and B elements, leading to a separation

into TiN and TiB2 upon annealing. TiBN coatings also provide good wear resistance [48, 49].

References

1. H. Ljungcrantz et al. Nanoindentation studies of single-crystal (001)-, (011)-, and (111)-oriented TiN layers on MgO. J. Appl. Phys. 80 (1996) 6725. 2. L. Karlsson. Arc Evaporated Titanium Carbonitride Coatings. Linköping Stud- ies in Science and Technology, Dissertation No. 565. Linköping University, 1999. 3. L. E. Toth. Transition Metal Carbides and Nitrides. New York: Academic Press, 1971. 4. J. E. Sundgren. Structure and Properties of TiN Coatings. Thin Solid Films 128 (1985) 21–44. 5. A. J. Perry. On the existance of point-defects in vapor-deposited films of TiN, ZrN, and HfN. J Vac Sci Technol A 6 (1988) 2140–2148. 6. L. Hultman. Thermal stability of nitride thin films. Vacuum 57 (2000) 1–30. 7. G. Beenshmarchwicka, L. Krolstepniewska, and W. Posadowski. Structure of Thin-Films Prepared by the Cosputtering of Titanium and Aluminum or Titanium and Silicon. Thin Solid Films 82 (1981) 313–320. 8. W. Münz. Titanium aluminum nitride films: A new alternative to TiN coatings. J. Vac. Sci. Technol. A 4 (1986) 2717–2725. 9. U. Wahlström et al. Crystal-Growth and Microstructure of Polycrystalline

Ti1 X AlxN Alloy-Films Deposited by Ultra-High-Vacuum Dual-Target Mag- netron− Sputtering. Thin Solid Films 235 (1993) 62–70. 10. Q. Chen and B. Sundman. Thermodynamic assessment of the Ti-Al-N system. Journal of Phase Equilibria 19 (1998) 146–160.

11. B. Alling et al. Mixing and decomposition thermodynamics of c-Ti1 xAlxN from first-principles calculations. Physical Review B 75 (2007) 45123.−

1 4 REFERENCES

12. Q. Xia, H. Xia, and A. Ruoﬀ. Pressure-induced rocksalt phase of aluminum nitride: A metastable structure at ambient condition. J Appl. Phys. 73 (1993) 8198–8200.

13. A. Hörling et al. Mechanical properties and machining performance of Ti1 x − AlxN-coated cutting tools. Surf. Coat. Technol. 191 (2005) 384. 14. M. Odén et al. In situ small-angle x-ray scattering study of nanostructure evolution during decomposition of arc evaporated TiAlN coatings. Applied Physics Letters 94 (2009) 053114. 15. A. Knutsson et al. Thermal decomposition products in arc evaporated TiAlN/ TiN multilayers. Appl Phys Lett 93 (2008) 143110. 16. P. H. Mayrhofer et al. Self-organized nanostructures in the Ti–Al–N system. Applied Physics Letters 83 (2003) 2049. 17. R. Rachbauer et al. Decomposition pathways in age hardening of Ti-Al-N films. Journal of Applied Physics 110 (2011) 023515.

18. L. J. S. Johnson et al. Spinodal decomposition of Ti0.33Al0.67N thin films studied by atom probe tomography. Thin Solid Films 520 (2012) 4362–4368. 19. D. Holec et al. Phase stability and alloy-related trends in Ti–Al–N, Zr–Al–N and Hf–Al–N systems from first principles. Surface & Coatings Technology 206 (2011) 1698–1704. 20. M. Baben et al. Origin of the nitrogen over- and understoichiometry in Ti 0.5Al 0.5N thin films. Journal of Physics Condensed Matter 24 (2012) 155401. 21. R. Rachbauer et al. Eﬀect of Hf on structure and age hardening of Ti–Al-N thin films. Surface & Coatings Technology 206 (2012) 2667–2672. 22. R. Rachbauer et al. Temperature driven evolution of thermal, electrical, and optical properties of Ti-Al-N coatings. Acta Materialia 60 (2012) 2091–2096. 23. G. Greczynski et al. Role of Tin+ and Aln+ ion irradiation (n=1, 2) during

Ti1 xAlxN alloy film growth in a hybrid HIPIMS/magnetron mode. Surface & Coatings− Technology 206 (2012) 4202–4211. 24. L. Rogström et al. Strain evolution during spinodal decomposition of TiAlN thin films. Thin Solid Films 520 (2012) 5542–5549. 25. Y. Khan et al. Phase equilibria in the Zr-Al-N system at 1273 K. Russian Metallurgy (Metally) 2004 (2004) 452–459. 26. PDF-card No. 30-0753. JCPDS - International Centre for Diffraction Data, 1998. 27. PDF-card No. 38-1420. JCPDS - International Centre for Diffraction Data, 1998. 28. PDF-card No. 46-1200. JCPDS - International Centre for Diffraction Data, 1998.

1 5 MATERIALS

29. L. Rogström et al. Influence of chemical composition and deposition conditions on microstructure evolution during annealing of arc evaporated ZrAlN thin films. J Vac Sci A 30 (2012) 031504. 30. R. Franz et al. Oxidation behaviour and tribological properties of arc evaporated ZrAlN hard coatings. Surface & Coatings Technology 206 (2012) 2337– 2345. 31. W.Z. Li, M. Evaristo, and A. Cavaleiro. Influence of Al on the microstructure and mechanical properties of Cr–Zr–(Al–)N coatings with low and high Zr content. Surface & Coatings Technology 206 (2012) 3764–3771. 32. L. Rogström et al. Phase transformations in nanocomposite ZrAlN thin films during annealing. Journal of Materials Research (2012) 1–9. 33. L. Rogström et al. Auto-organizing ZrAlN/ZrAlTiN/TiN multilayers. Thin Solid Films 520 (2012) 6451–6454. 34. P. Rogl and J. C. Schuster. Phase Diagrams Ternary Boron Nitride Sili- con Nitride Systems. In: ASM Int., 1992. Chap. Ti-Si-N (Titanium-Silicon- Nitrogen), 198–202.

35. A. Flink et al. The location and eﬀects of Si in (Ti1-xSix)Ny thin films. Journal of Materials Research 24 (2009) 2483–2498. 36. L. Shizhi, S. Yulong, and P. Hongrui. Ti-Si-N films prepared by plasma- enhanced chemical vapor deposition. Plasma Chemistry and Plasma Process- ing 12 (1992) 287–297. 37. S. Vepřek, S. Reiprich, and L. Shizhi. Superhard nanocrystalline composite materials: The TiN/SiN system. Applied Physics Letters 66 (1995) 2640. 38. A. C. Fischer-Cripps, S. J. Bull, and N. Schwarzer. Critical review of claims for ultra-hardness in nanocomposite coatings. Philosophical Magazine (2012) 1. 39. D. V. Shtansky et al. High thermal stability of TiAlSiCN coatings with “comb” like nanocomposite structure. Surface and Coatings Technology 206 (2012) 4840–4849. 40. A. Flink. Growth and Characterization of Ti-Si-N Thin Films. PhD thesis. Linköping University, 2008. 41. D. Shtansky et al. Synthesis and characterization of Ti-Si-C-N films. Metall Mater Trans A 30 (1999) 2439–2447. 42. D. Kuo and K. Huang. A new class of Ti-Si-C-N coatings obtained by chemical vapor deposition. Thin Solid Films 394 (2001) 72–80. 43. P. H. Mayrhofer et al. Thermally induced self-hardening of nanocrystalline Ti–B–N thin films. J Appl. Phys. 100 (2006) 044301. 44. J. Neidhardt et al. Structure-property-performance relations of high-rate reactive arc-evaporated Ti-B-N nanocomposite coatings. Surface and Coatings Technology 201 (2006) 2553–2559.

1 6 REFERENCES

45. P. H. Mayrhofer and M. Stoiber. Thermal stability of superhard Ti-B-N coatings. Surface and Coatings Technology 201 (2007) 6148–6153. 46. R. Zhang, S. Sheng, and S. Vepřek. Stability of Ti-BN solid solutions and the formation of nc-TiN/a-BN nanocomposites studied by combined ab initio and thermodynamic calculations. Acta Materialia 56 (2008) 4440–4449. 47. P.H. Mayrhofer, M. Stoiber, and C. Mitterer. Age hardening of PACVD TiBN thin films. Scripta Materialia 53 (2005) 241–245. 48. J. Neidhardt et al. Wear-resistant Ti–B–N nanocomposite coatings synthesized by reactive cathodic arc evaporation. International Journal of Refractory Metals and Hard Materials 28 (2010) 23–31. 49. I. Dreiling et al. Temperature dependent tribooxidation of Ti–B–N coatings studied by Raman spectroscopy. Wear 288 (2012) 62–71.

1 7

DEPOSITION 3

The act of creating a thin film is called deposition, recalling both the creation of the whole film and the placement of individual atoms in it. There are many diﬀerent ways of depositing a thin film; the most common ones are based on deposition from a vapour of some sort (as opposed to wet chemical methods, for example). These techniques may be further subdivided into physical vapour deposition (pvd) and chemical vapour deposition (cvd) [1]. The diﬀerence is in the vapour: in pvd the vapour is composed of atoms and molecules that simply condense on the substrate, whereas in cvd the vapour undergoes a chemical reaction on the substrate, the product of which forms the film. This work is solely focused on pvd methods.

3.1 Physical Vapour Deposition

The perhaps simplest pvd method is thermal evaporation, in which the source material is evaporated (or sublimated) in one end of an evacuated chamber and deposited on the substrate at the other, colder, end of the chamber. This captures the basic process of pvd; first a vapour is produced, then it is transported to a substrate and made to deposit there. What separates the diﬀerent techniques is the method of vapour production, its dependent properties, and the level of control available over the deposition. The production and transport of the vapour will, in general, take place under vacuum, and hence such deposition requires technology and equip- ment to produce and maintain the low pressures that are needed. The usage of vacuum stems from the desire to enable and control both the process of deposition itself and the level of impurities (typically oxygen and carbon) in the as-grown film. This thesis treats films grown by two pvd techniques: magnetron sputtering and cathodic arc evaporation, both of which are introduced here.

3.1.1 magnetron sputtering

Magnetron sputtering is perhaps the most common and popular of the pvd methods available today. As an umbrella of techniques it is highly versatile, and it can be adapted to suit everything from small lab-scale systems to large industrial systems with dimensions measured in meters. It is possible to grow everything from simple metal layers to semiconductor structures, nanowires and other complex geometrical structures.

1 9 DEPOSITION

The vapour of the depositing species is produced when energetic ions hit the source material, called the target, and atoms are ejected from the target due to the energetic collision cascade. This ejection by collisions is termed sputtering. To provide the sputtering ions, the deposition chamber is first evacuated to a low pressure regime (typically around 1 mPa or better),

called high vacuum, and then filled with the process gas, often N2 for growth of nitrides, or Ar due to its chemical inertness. A plasma is then ignited in the gas by the application of a high electric field between the target and the chamber walls. Free electrons in the gas are accelerated, and occasionally one of these impacts a gas atom, ionizing it by knocking off an electron. Under the right conditions, this will trigger a cascade of collisions and electron emission, which reaches a steady state where the gas in the chamber is partially ionized, forming a plasma [2]. The positive ions are accelerated towards the negatively biased target, inducing sputtering. The plasma is usually confined magnetically to a region in front of the target by a fixture of strong magnets, a magnetron, to enhance the efficiency of the process. When growing certain compounds, such as TiN, a metallic target and a reactive gas can be used instead of sputtering directly from a target of the desired compound material. The reactive gas interacts with the depositing metal atoms on the growing surface, forming the desired structure. Sputter- ing from a metallic target is most often easier than sputtering from a ceramic one (if it is at all possible), and the partial pressure of the reactive gas is an additional process parameter that can be tuned. At high process pressures the reactive gas also interacts with the target surface, forming compounds that are difficult to sputter, thus reducing the deposition rate, a phenomenon that is called poisoning due to its generally undesirable nature. The growth conditions on the substrate side are controlled by the substrate temperature, and the fluxes and energies of the incoming species from the vapour phase. The energy of incoming ions can be affected by electri- cally biasing the substrate, and the flux of process gas ions impinging on the substrate can be enhanced by changing the magnetic field from the target to extend down towards the substrate. The combination of these parameters provides a large configurational space for growing films, and this is the source of the versatility of magnetron sputtering.

3.1.2 cathodic arc evaporation

Cathodic arc evaporation is a technique that is widely utilized in the coating industry, especially in the cutting-tool industry, as it is a superior method of producing hard adherent coatings. The technique also has drawbacks, in

2 0 FILMGROWTH

that the films tend to be in a compressive stress state, which needs to be carefully controlled, and so-called macro-particles from the target cathode produced by the evaporation are embedded in the film. As the name implies, the source material is evaporated by an intense cathodic arc, produced by negatively biasing the target and triggering a dielectric breakthrough by striking the target – or cathode – with a sharp pin. The spot on the cathode where the arc hits is locally melted, and atoms are ejected away from the surface in an almost completely ionized state (typically greater than 95 %) and with high kinetic energies (20-200 eV dependent on material [3]. Along with the ionized flux, macro-particles are also ejected; these are particles of molten and semi-molten target material that are produced by the pressure of the arc spot on the molten zone in the cathode. Arc evaporation may also be run reactively, to deposit a nitride thin film, for example; then it is common to combine the arc evaporation with a glow discharge to help crack the gas molecules. Due to the high currents needed to sustain the arcing, the cathode material must be conductive. A further practical limitation is given by the melting point of the cathode material; the higher the melting point the harder it will be to arc evaporate. Therefore, deposition of hard coatings is done in the reactive mode, where the process gas reacts with the emitted vapour, producing the desired compound, such as TiN. Thin films produced by cathodic arc evaporation are typically dense, in a compressive stress state and very defect rich. This is due to the high kinetic energies of the incident ions, which produce collision cascades in the growing film that tend to create lattice point defects. The adhesion of arc evaporated films is often better than that of comparable films from other pvd methods, and this is again due to the energetic ions, which produce a mixed interface by implantation in the substrate. By applying a high bias to the substrate, the eﬀect of implantation may be enhanced, either for implantation treatments or for etching of the substrate at higher voltages.

3.2 Film Growth

The two deciding factors of how a film grows are the substrate temperature and the flux and energy distribution of the incident species. These parameters determine the kinetics of the growth. As a rule of thumb, the more energy that is available during growth, the closer the structure will be to thermal equilibrium. The two properties of the growing film that are of interest are its phase and microstructure.

2 1 DEPOSITION

3.2.1 phase

The phase of a thin film—even for a constant composition—can vary widely with deposition conditions. In the case of kinetically limited depositions, it is not uncommon for the films to be amorphous, as the incident atoms just quench directly on their site of arrival with minimal diffusion or relaxation. Provided with more energy, the arriving atoms will diffuse and form crystalline clusters. The nature of the phases that form is determined by the thermodynamically stable phases at the growth conditions, but is also influenced by the surface energies of the substrate and vacuum interfaces. The stability can also be affected by the bombardment of incident species, given high enough energies per atom.

3.2.2 microstructure

The microstructure of a film depends on the processing parameters. At low surface diﬀusivities adatoms will nucleate at many points on the substrate, and these nucleation sites will grow into individual columnar grains. At higher diﬀusivities the adatoms will be able to travel greater distances, which produces fewer and bigger grains. At even higher temperatures the film may recrystallize during growth, transforming the growing columns to an equiaxed grain structure. These possibilities are often summarized in a structure zone model (szm) diagram [4], and one suitable for pvd is given in

figure 3.1 The structure zone model of pvd film growth, after Barna et al. [4]

Deposition temperature

2 2 REFERENCES

Fig. 3.1. Films deposited by arc evaporation typically fall into the mid zone of this diagram, with a dense columnar microstructure. Columns frequently grow in competition with each other, where the growth rate often depends on the crystallographic orientation of the column [5]. The orientation of the grains may vary or be templated from the substrate, but it is often the case that different orientations of grains will grow with different speeds due to differences in surface diffusivity. If this is the case a film may almost completely consist of columns with a certain orientation even though the grains originally nucleated with a variety of orientations. This is known as competitive growth. At high enough mobilities it is possible to grow a single crystal layer on a single crystal substrate, in a process which is known as epitaxy. This requires a suitable crystallographic relationship between substrate and film. Easiest is to grow a film of the same phase as the substrate, with the lattice continuing coherently into the film. If the film and substrate differs in their lattices, the growing film is strained to match the substrate interface; typically the film relaxes by introduction of misfit dislocations when the strain energy becomes too large.

3.2.3 growth in immiscible systems

There are a few possible results when growing a film with a composition that is in the miscibility gap of the system in question. Solid solutions are obtained for low mobilities, as the mean diﬀusion length of an ad-atom before incorporation is too short to allow for demixing. Solid solutions can also be synthesized by forceful mixing by energetic ion bombardment, termed recoil mixing, and which is common in cathodic arc evaporation. Here the outmost layers are continually bombarded and thus mixed during growth.

This is for example how solid solution0.33 Ti Al0.67N is grown industrially. If the driving force for segregation and the mobility are high enough, compositional fluctuations will develop, as the system seeks to minimize its free energy by separating the immiscible species. Given enough mobility this separation will cause phase separation, The classic example is the

nc-TiN/SiNx growth mentioned earlier.

References

1. M. Ohring. Materials Science of Thin Films. San Diego: Academic Press, 2002. 2. M. A. Lieberman and A. J. Lichtenberg. Principles of Plasma Discharges and Materials Processing. Hoboken: Wiley-Interscience, 2005.

2 3 DEPOSITION

3. A. Anders. Energetic Deposition Using Filtered Cathodic Arc Plasmas. Vac- uum 67 (2002) 673–686. 4. P. B. Barna and M. Adamik. Fundamental structure forming phenomena of polycrystalline films and the structure zone models. Thin Solid Films 317 (1998) 27–33. 5. I. Petrov et al. Microstructural Evolution during Film Growth. J Vac Sci Technol A 21 (2003) 117–128.

2 4 PHASETRANSFORMATIONS 4

Phase transformations are processes in which atoms reorganize themselves, and they are most often viewed through the lens of thermodynamics. A basic result from thermodynamics is that a system is in equilibrium (with a reservoir of some kind, with which it exchanges energy, particles, volume, etc.) when its Gibbs free energy (or Helmholtz in the case of constant volume instead of constant pressure) is at a minimum. For a binary mixture of elements A and B, with molar quantities XA and XB, the total free energy is:

G XAGA XBGB ΔGmix XA XB (4.1) = + + ( , ), where ΔGmix is the deviation from the energy of two fully separate blocks of elements A and B. ΔGmix can be further divided into enthalpy and entropy terms:

ΔGmix ΔHmix TΔSmix (4.2) = − . The enthalpy of mixing describes the change in binding and volume energy due to the exchange of some A-A and B-B bonds into A-B bonds, and the entropy of mixing is due to the increased number of possible ways to arrange the atoms in the system, within the external constraints, e.g., pressure. The sign of the free energy of mixing describes the two fundamental possibilities for mixing elements. Mixing is energetically favourable when it is negative, and unfavourable for positive values. Both the enthalpy and entropy of mixing are currently calculable by density functional theory and derived methods [1]. Equilibrium between two phases is defined by equality between the chemical potentials of the phases:

1 G1 G2 2 μA 휕 휕 μA (4.3) = XA = XA = , 휕 휕 which is easily visualizable in graph form as the common tangent rule (Fig.4.2), with the relative phase fraction defined by the average compo- ΔGbarrier sition of the system. When a system is not in its lowest energy state, there is a thermodynamic ΔGdrive driving force towards the equilibrium state, which is proportional to the diﬀerence in free energy between the states. The transition pathway, however, figure 4.1 Free energy barrier may entail an increase in free energy; a barrier. The height of the barrier and driving force for a determines how probable a transition is given a certain temperature, or in transformation. other words: how large thermal fluctuations are needed to overcome the

2 5 PHASETRANSFORMATIONS

figure 4.2 Equilibrium of two G phases by the tangent G1 2 rule construction.

X X X A A avg A B XA

barrier. Even if a barrier is low, the transition may still not occur if there is insuﬃcient thermal energy for diﬀusion to take place.

4.1 Diﬀusion

Diffusion describes the effect of the mean movement of atoms. There are two basic kinds of diffusion in crystals: substitutional and interstitial diffusion. Substitutional diffusion is the movement of an atom on the lattice, and is normally mediated by the diffusion of vacancies, while interstitial diffusion takes place in empty interstitial sites in the lattice. While each jump an atom makes is a random process, any inhomogeneity will introduce a difference in the chemical potential, and thus a driving force for the elimination of the inhomogeneity. It should be noted that the direction of the mean diffusion flow does not necessarily have to be from high concentrations towards lower concentrations: a positive energy of mixing can cause the most favourable direction to be the direct demixing of two components. The typical example of this is spinodal decomposition (see below). There is a dearth of data for diffusion constants in transition metal nitrides, most likely due to the difficulty of measuring diffusion in thin films. Two summaries of the available data are found in refs. [2, 3]. A good rule of thumb for these materials is that temperatures of 800-900 °C are required for the activation of bulk diffusion of the metal atoms, while N and other light elements are easier to activate.

2 6 IMMISCIBILITY

4.2 Immiscibility

4.2.1 nucleation and growth

One way a system can overcome an energy barrier is a localized fluctuation that is strong enough to take that part of the system over the barrier, allowing the region to then smoothly grow by following the transition path down to the new state. Such local fluctuations are called nucleation, and this is the dominant process of phase transformations. The fluctuation is often in composition, but it can also be a change in the crystal structure. The barrier for nucleation (the change of a small region into a diﬀerent configuration) has its origin, from a classical thermodynamics perspective, in the surface energy created by the new interface between the matrix and the precipitate. As the free energy reduction due to the nucleus scales with its volume, and the surface energy with the surface area, the change in free energy will eventually become favourable for the precipitate as it grows, leading to stability. If, instead of being situated on a perfect lattice, the nucleation event happens on a defect, such as a grain boundary or a dislocation, the barrier is generally lower, as there is some energy bound up in the defect which can be used to overcome the barrier. This is called heterogeneous nucleation, in contrast with homogeneous nucleation on perfect sites. In some cases the nucleation barrier for the equilibrium phase may be considerable, making a direct transformation unlikely. Instead, if there are intermediate phases which, while not being of the lowest free energy, have a lower barrier to nucleation, the transformation can progress through these intermediate phases before arriving at the equilibrium phase. As the lower barrier comes from better coherence with the matrix lattice (a lower surface figure 4.3 energy), the shape of the precipitates will depend on the level of coherence Free energy of a sys- possible. For complete coherence the tendency will be for spherical precip- tem with gp zones. itates, but if, for example, one crystallographic orientation is energetically unfavourable, shapes such as plates are common. This behaviour was first observed by Guinier and Preston as the precipitation of Cu-platelets from an Ag- Cu solid solution; consequently they are called Guinier-Preston (gp) zones.

4.2.2 non-classical nucleation

The classical theory of nucleation discussed above, as first formulated by Gibbs [4], does not describe all possible local fluctuations leading to nucleation. Cahn and Hilliard, building on work by Hillert [5–9], showed that the

2 7 PHASETRANSFORMATIONS

ΔG > 0 G ∂ 2G < 0 ∂ X2

ΔG < 0

A B figure 4.4 X Free energy curve with A a spinodal, and an illustration of stability depending on the critical nucleus does not necessarily have to be of constant composition of curvature of the free the equilibrium, precipitating phase: a fluctuation of a lower compositional energy. amplitude and with a extended diﬀuse interfacial region can also form a critical nucleus, capable of growing [7, 10, 11]. This eﬀect is particularly strong as the limit of metastability is approached (see spinodal decomposition, below), where extended fluctuations of low compositional amplitude will be the dominant nucleation mechanism. On the other end of the spectrum, the classical theory is asymptotically recovered as the binodal line is approached.

4.2.3 spinodal decomposition

The other fundamental type of fluctuation that Gibbs considered was one of low compositional amplitude, but extensive in space [4]. This idea was then further developed by Hillert, and Cahn and Hilliard [5, 8, 12–14]. Normally, a system will be stable against such small fluctuations, as they lead to increases in the free energy if the free energy curvature is positive, as 2G is the typical case. If, on the other hand, the curvature is negative, 휕X2 0, any fluctuations that change the composition will lower the free energy휕 < of the system, as visually shown in Fig. 4.4. This implies the absence of any barrier to this kind of transformation, and the system is unstable; hence the only limiting factor will the the kinetics of diﬀusion. The dynamics of the transformation can be modeled by a partial diﬀer- ential equation, as was first developed by Cahn [12]. The free energy of a

2 8 IMMISCIBILITY

solid can be written as an integral of the molar free energies over the volume:

F f c κ c 2 dV (4.4) = ∫V ( ) + (∇ ) + … . The change in F due to a small fluctuation in the composition field c, δc is:

f κ 2 2 δF 휕 휕 c κ c δcdV (4.5) = ∫V ( c + c (∇ ) − ∇ ) , 휕 휕 κ which gives the molar change in free energy, assuming 휕c 0: 휕 = F f 2 휕 휕 κ c μ (4.6) c = c − ∇ = , 휕 휕 which is the chemical potential. This, together with the conservation equation for a flow J in field c, gives: c 휕 J M μ t = −∇ ⋅ = −∇ ⋅ (− ∇ ) 휕 f 2 M 휕 κ c (4.7) = ∇ ⋅ ∇ ( c − ∇ ) . 휕 This is the Cahn-Hilliard equation, and while it can be solved numerically today [15], some insights can be derived from finding approximate solutions. Linearizing the previous equation and transforming it to reciprocal space gives: C k t 2f ⏐k2 2κk4 C (4.8) 휕 ( , ) 휕 2 ⏐ t = ⎛ c ⏐ − ⎞ , 휕 휕 ⏐c c0 ⏐ = which by inspection has the solution:⎝ ⎠

2 f 2 4 ⏐k 2κk t figure 4.5 ⎛휕c2 ⏐ ⎞ ⏐ − A schematic R k 휕 ⏐c c0 C k t C k 0 e ⏐ = ( ) ( , ) = ( , ) ⎝ ⎠ amplification curve. C k 0 eR k t (4.9) = ( , ) ( ) . The R k term is called the amplification factor, and it determines to which extent( compositional) waves will be amplified or dampened. A typical R k curve is plotted in Fig. 4.5, where two features are important: firstly, it has( ) a maximum for a certain wavelength, and secondly, it is negative for all wavelengths shorter than a critical wavelength. As the amplification is exponential in nature, the fastest growing wavelength will soon outgrow all others, defining the typical microstructure

2 9 PHASETRANSFORMATIONS

figure 4.6 Spinodal decomposition in one dimension by the solution of the Cahn-Hiliard equa- c tion. t

of a spinodally decomposed material: a regular variation in composition with broad and diﬀuse interfaces. The negative amplification for small wavelengths causes dampening, so short-length fluctuations will disappear, even though they contribute to the initiation of the decomposition. The last equations above are the results of a number of simplifications, all valid for the very initial state of the decomposition with small compositional fluctuations, which become progressively less applicable as the decomposition progresses. For example, the exponential growth cannot continue indefinitely, as the composition field is bounded on 0 1 . Including higher order terms in the equations will first introduce harmonics( , ) of the fundamental decomposition sinewave, which serves to limit the exponential growth and introduce asymmetry in the decomposition if it is shifted from the symmetric position in the free energy diagram [14].

4.2.4 age hardening

Systems that undergo phase decomposition during annealing may also show a consequent increase in their hardness. This is termed age hardening, and is a direct result of the changes in nanostructure due to the decomposition. Hardness is, by definition, the degree to which a material is able to resist plastic deformation, i.e. resistance to the generation and movement of dislocations and other defects. In particular, the movement of dislocations is hindered by the creation of precipitates or composition fluctuations in the matrix, as this will generally introduce strain. Dislocations may be arrested, cut through, or bow around precipitates, and each mode is more diﬃcult than passage through a homogeneous lattice. If the annealing is continued

3 0 REFERENCES

for too long the system will transform into its equilibrium phases and any hardening eﬀects will be lost. A convincing example of age hardening in thin films is found in solid solution TiAlN [16]. As mentioned in the previous chapter, c-TiAlN will decompose upon annealing, first to TiN and c-AlN parts (800-900 °C), followed by a transformation into h-AlN at higher temperatures (1100 °C). The age hardening is in eﬀect during the segregation into cubic phases, but is generally lost upon formation of the hexagonal AlN phase.

References

1. A. Ruban and I. Abrikosov. Configurational thermodynamics of alloys from first principles: Effective cluster interactions. Reports on Progress in Physics 71 (2008). 2. L. Hultman. Thermal Stability of Nitride Thin Films. Vacuum 57 (2000) 1– 30. 3. H. Matzke and V. V. Rondinella. Diffusion in nitrides. In: ed. by D. L. Beke. Vol. Diffusion in Non-Metallic Solids. Landolt-Börnstein - Group III: Con- densed Matter. Springer-Verlag, 1999. 4. J. W. Gibbs. Collected Works. In: vol. 1. New Haven, Connecticut: Yale University Press, 1948, 105–115, 252–258. 5. M. Hillert. A Theory of Nucleation for Solid Metallic Solutions. Massachusetts Institute of Technology (1956). 6. J. Cahn and J. Hilliard. Free energy of a nonuniform system. I. Interfacial free energy. The Journal of Chemical Physics 28 (1958) 258–267. 7. J. Cahn and J. Hilliard. Free energy of a nonuniform system. III. Nucleation in a two-component incompressible fluid. The Journal of Chemical Physics 31 (1959) 688–699. 8. M. Hillert. A solid-solution model for inhomogeneous systems. Acta Metal- lurgica 9 (1961) 525–535. 9. J. Cahn. Coherent fluctuations and nucleation in isotropic solids. Acta Met- allurgica 10 (1962) 907–913. 10. T. Philippe and D. Blavette. Nucleation pathway in coherent precipitation. Philosophical Magazine 91 (2011) 4606–4622. 11. T. Philippe and D. Blavette. Minimum free-energy pathway of nucleation. Journal of Chemical Physics 135 (2011) 134508. 12. J. Cahn. On Spinodal Decomposition. Acta Metallurgica 9 (1961) 795–801. 13. J. W. Cahn. On spinodal decomposition in cubic crystals. Acta Metallurgica 10 (1962) 179–183.

3 1 PHASETRANSFORMATIONS

14. J. W.Cahn. The Later Stages of Spinodal Decomposition and the Beginnings of Particle Coarsening. Acta Metallurgica 14 (1966) 1685–1692. 15. J. Ullbrand. Phase field modelling of spinodal decomposition in TiAlN. Linköping Studies in Science and Technology, Licentiate Thesis No. 1545. Linköping University, 2012.

16. A. Hörling et al. Mechanical properties and machining performance of Ti1 x − AlxN-coated cutting tools. Surf. Coat. Technol. 191 (2005) 384.

3 2 THINFILMCHARACTERIZATION 5

To study thin films, and processes in thin films such as age hardening, we must know the state that the film is in. We need to know the phase(s), the composition (on diﬀerent scales), the microstructure, eventual nanostructure, and so on. This understanding is gleaned from the combination of several characterization techniques, as a single technique seldom gives the whole picture. In this chapter, the main characterization techniques used in the thesis are presented, except for apt, which is treated in the next chapter.

5.1 X-ray Diﬀraction

Due to the periodic ordered structure of a crystal, X-ray waves scattering against the atoms in a crystal will produce interference reflexes in certain directions, which are tied to the crystal structure and the specific orientation of the incident wave. This effect is utilized in the various techniques of X-ray diffractometry (xrd) to investigate the crystal structure of a sample, as well as structural properties such as grain size, texture, and the thickness of a thin film [1]. The basic principle of xrd is most easily understood as positive interference of waves scattered against adjacent planes in the crystal, which gives rise to Bragg’s law. A more useful description is due to von Laue, who described diffraction in reciprocal space with the diffraction condition:

ki kf Δk G, where k1 and kf are the wave vectors of the incident and− scattered= waves,= respectively, and G is a reciprocal lattice vector. This formulation leads directly to the interpretation of the shape of a reflection as that of the shape of the respective reciprocal lattice point, which in turn is due to deviations from the theoretical infinite periodic crystal lattice. The most basic xrd method is the θ-2θ scan (sometimes referred to as the Bragg-Brentano geometry) in which the incidence and exit angles are varied symmetrically. This limits the diﬀerence in wave vectors for the incident and scattered beams to being parallel to the surface normal of the sample. By assigning the observed peaks in a scan to a crystal structure, the lattice parameter may be measured from the position of the reflections. Care must be taken, however, as the lattice parameter may be significantly shifted by strain in the samples – due to film-substrate strain or strain from atom peening during deposition in thin films, for example. The width of a peak is dependent on the average size of a coherently scattering region – most often taken as the grain size – and any local variations in the lattice due to defects, as well as the limitations posed by the instrument used.

3 3 THINFILMCHARACTERIZATION

figure 5.1 The Ewald’s sphere construction for diﬀraction in reciprocal space.

ki G

A view of any texture of the sample is given by the relation of the various peak intensities and how they deviate from theoretical values. The view is partial, as only scattering regions with planes parallel to the surface are probed in the method. For a fuller analysis of texture, complementary techniques are required, such as pole figure analysis, where a certain reflection is selected and then mapped by rotating the sample. To measure the strain in a thin film the sin2 ψ is a commonly used method. The change in peak position is measured( ) as the sample is tilted away from the symmetric θ-2θ geometry, thus probing the change in lattice parameter as a function of angle to the surface normal. Assuming a biaxial stress state, the stress may then be derived from elastic theory. This biaxial stress state is the typical situation for hard coatings, as they are typically strained compressively against their substrates.

5.2 Transmission Electron Microscopy

Transmission electron microscopy (tem) is one of the most versatile techniques available for analysis of thin film samples. In diﬀerent configurations, information on the crystal structure, microstructure, local chemical composition, and bindings, as well as interfacial relations and defects, may be gained [2]. The main drawback of the technique is the extensive sample preparation necessary, potentially introducing artifacts, as well as the small volume probed.

3 4 TRANSMISSIONELECTRONMICROSCOPY

figure 5.2 A typical cross sectional tem micrograph of a TiSiN thin film.

0.5 μm

The basic principle of a tem is that a beam of electrons is shone through a thin foil and the scattered electrons are focused by an electromagnetic lens into an image which is collected as intensities on a view screen or ccd-camera. While the actual details of a tem are far more complex, this is still a fair description of the bright-field mode of tem (so named after the light microscopy technique it mimics). Here, contrast in the image is formed either through mass-thickness contrast or diffraction contrast phenomena. Mass-thickness contrast is due to denser or thicker regions scattering or absorbing more of the electron beam, respectively. Diffraction contrast is due to the blocking of diffracted beams, so that they are not projected back onto the image of their origin by the objective lens. This means that grains oriented such that they are in a strong diffracting condition will appear darker than other grains. Diffraction contrast may also appear locally due to strain in the foil, from bending of the sample or the strain field around a dislocation, for example, which allows the imaging of individual dislocations. The dark-field mode is closely related to the bright-field mode and has again gained its name from light microscopy. By selecting one (or more) diffracted beams and eliminating the transmitted beam, instead of filter- ing out all diffracted beams as in the BF-mode, an image is formed with crystallographic information from the selected reciprocal lattice point.

3 5 THINFILMCHARACTERIZATION

figure 5.3 A plan-view electron diffraction (ed) pat- 5.2.1 electron diffraction tern of a ZrAlN film from Paper IV. As alluded to in the section above, electron waves that interact with a crystal undergo diffraction scattering in the same general way as X-rays do. There are differences – electrons interact with the crystal potential from the atomic nu- clei while X-rays scatter against the tightly bound core electrons in the crystal – but these are in most cases of lesser importance when analyzing thin films. As transmission electron microscopy is fundamentally an imaging technique, the common view of diffraction is the diffraction pattern, which is essentially the result of testing all possible scattering vectors perpendicu- lar to the incident beam. A consequence of the control over the incident electron beam afforded by the illumination part of a tem is that there are two fundamental modes of diffraction in the tem, called selected area electron diffraction (saed) and convergent-beam electron diffraction (cbed). In saed the illumination is kept as parallel as possible – ideally projecting reciprocal lattice points to points on the diffractogram – and the name stems from the fact that one most often limits the area contributing to the pattern on the sample by an aperture in the image plane of the aperture. An example saed pattern is given in Fig. 5.3, which shows a complex pattern from three crystallographic phases. cbed, on the other hand, uses a convergent beam, with the beam at its largest convergence angle, and as such, points in reciprocal space are projected as disks, the diameters of which are inversely proportional to the convergence angle. Here, information is gained from a limited part of the sample (unlike when using saed). For thicker samples, cbed patterns may also contain information from dynamical diffraction effects, which show up as variations in intensity inside the diffraction disks.

3 6 TRANSMISSIONELECTRONMICROSCOPY

Electron diffraction is an easy way to look for any possible texture in thin films, as a fully random ordering will produce rings in the diffraction pattern spaced according to the plane spacings for all orientations of the sample, whereas the pattern of a sample with a texture will–-for some orientations–show gaps in the rings. Compared to to X-ray diffraction the various electron diffraction techniques are less powerful or precise for determining accurate plane spacings or peak shapes, due to the nature of the tem. To reach the screen, the diffracted beams are magnified by electromagnetic lenses which introduce uncertainty, and even if that is eliminated – for example, by using a standard sample as reference – the recording of the pattern on either film or ccd is not as precise as the dedicated instrumentation of an xrd instrument. Hence, electron diffraction is best used to discern patterns and symmetries. On the other hand, ed has one advantage over xrd, namely the substantially lower wavelength of high energy electrons as compared to X-rays. A typical X-ray radiation used in xrd is from the CuKα emission line at 1.54 Å, to be compared with the 2.5 pm relativistic de Broglie wavelength of an electron at 200 keV. This allows smaller scattering regions to be imaged without excessive peak broadening that limits xrd analysis of regions smaller than 10-20 nm. Finally, electron diffraction is used to precisely align samples for other imaging techniques in the tem specifically for high-resolution tem (hrtem).

5.2.2 high-resolution tem

In electron microscopy the term high resolution has a special significance, in that it implies the direct imaging of the crystal lattice. Resolving the lattice planes – or even individual atom columns – allows the microscopist to image structural configurations on the nanoscale, such as grain boundaries, dislocations, nanoscaled grains themselves, interfaces such as substrate-film or multilayer relationships, and of course the crystal structure itself. An hrtem image from Paper IV is given in Fig. 5.4, which shows a two-phase coherent nanostructure. The contrast mechanism in hrtem is phase contrast, that is, contrast due to interference of electron waves producing variations in intensity which we observe in the microscope. The electron wave incident on the sample is diﬀracted against the lattice planes, and these waves will interfere with the unscattered beam and each other (a more correct and complex view is that the electron wave-function interferes with itself). This produces an exit wave that the objective lens then transforms to an image which is projected on the viewscreen in the microscope. Due to the electromagnetic nature of the

3 7 THINFILMCHARACTERIZATION

figure 5.4 A cross-sectional hrtem image of a ZrAlN film from Paper IV, showing a two-phase coherent structure.

3 nm

objective lens it is limited in how it transfers information; this is described by the contrast transfer function (ctf) of the lens is which most often used in frequency space: CTF u E u sin χ u (5.1) ( ) = ( ) ( ( )). Here E u is an envelope function that dampens the transfer of high-frequency signals( and) so limits the available resolution, and χ u depends on the lens aberrations, which are dominated by the spherical aberration( ) for an ordinary EM-lens. The control and eﬀective elimination of this aberration has become possible with the latest generation of microscopes, and as such they are often

called aberration corrected microscopes (or Cs-corrected microscopes, as Cs is the name given to the spherical aberration).

5.2.3 scanning tem

A radically different way of producing an image in a tem is the Scanning tem mode, in which the electron beam is condensed down to as fine a point as possible, which is then rastered across the sample. Contrast is then formed by recording the intensity of the scattered beam and assigning that value to the raster position. Most commonly, a high angle annular dark field stem (haadf) is used as the detector, recording the intensity scattered far out in the diffraction image from the sample. This will then detect differences in average atomic scattering factors, whose dependence on Z-value becomes larger for larger scattering angles. Today scanning transmission electron microscopy (stem) is often cou- pled with spectroscopic methods – the two main ones being energy-dispersive X-ray spectroscopy (edx) and electron energy loss spectroscopy (eels) – to

3 8 TRANSMISSIONELECTRONMICROSCOPY

figure 5.5 Zero loss peak Eels spectrum from a TiSiCN coating, showing zero-loss, plasmon and core-loss peaks. 300x Counts

C Ti Plasmon peak

0 50 100 150 200 250 300 350 400 450 500 Energy loss (eV)

access the local chemical composition of the sample. For each point in the stem raster, one or several spectra are recorded; these spectra may then be analyzed and images of variations of features (integrated peak height of an X-ray emission line, for example) produced.

5.2.4 electron energy loss spectroscopy

As the name implies, in eels the signal of interest is the energy loss of the electrons that have been transmitted through the sample. These electrons have a certain probability of interacting with the electrons present in the sample; in these interactions they lose energy that is characteristic of the actual interaction. The two main interactions that are present in an eels spectrum are interaction with the valence electrons to excite plasmons (called plasmon loss) and interaction with the core electrons, which are then ejected from their shells (core loss). A typical spectrum plotted as energy loss versus intensity is dominated by the zero-loss peak, as most electrons do not undergo any losses at all when passing through a thin sample. The second largest feature will be the plasmon peak(s), situated in the region of 10-100 eV. Core loss peaks are found on the tail of the plasmon peak, at the corresponding binding energy of the core electron ejected in the interaction. A typical spectrum showing these two regions is shown in Fig. 5.5.

3 9 THINFILMCHARACTERIZATION

When a core electron is ejected from its shell it must be excited to a vacant quantum state above the Fermi level, and hence the core loss peak (or edge) will have the shape of the electron density of states above the Fermi level multiplied with the transition probability. The core loss peaks are much weaker in intensity than the plasmon peaks due to a smaller cross-section, and because of this, background subtraction is essential to their analysis. As a sample gets thicker the probability of multiple scattering increases, and this is the fundamental limiting factor of eels analysis of samples. Each additional scattering will convolute the original signal with the second scattering event, and as plasmon scattering is most likely this will dominate and broaden peaks until they are no longer detectable.

5.2.5 energy-dispersive x-ray spectroscopy

The electrons in the beam may interact with atoms in the sample, and while eels deals with the measurement of that interaction’s effect on the beam, X-ray spectroscopy may be used to detect the effect on the sample itself. As core electrons are removed from their shells, the atom is no longer in its ground state and will hence relax. This is achieved by the filling of the hole by an electron from a higher shell according to quantum transition principles. The excess energy is then released either as a photon (most often in the X-ray part of the spectrum) or an Auger electron. Due to the limited possibilities for de-excitation, the spectrum of the emitted X-rays acts as a fingerprint for the elements. Energy-dispersive X-ray spectroscopy is a technique for measuring the emitted X-rays. The term energy-dispersive relates to the detection of the X-rays, and stands in contrast to wavelength-dispersive spectrometers. The term comes from the use of a solid state Si-Li detector in which electron-hole pairs are generated by the incident X-ray photons. The number of pairs are dependent on the energy of the photon, which may then be derived by counting the pairs created. The counting mechanism is the fundamental limitation of the energy- dispersive spectrometer, as a certain time is needed to count the pairs, and the precision depends on the time spent. To avoid miscounting two photons as one, the counting time must be sufficiently small in relation to the flux of photons to avoid miscounting, and this limits the energy-resolution. Another issue is the detection of light elements. This is often problematic, as the window between the detector and the microscope’s column will tend to absorb the characteristic X-rays of light elements, greatly lowering their detection rate. Notably, this applies to the detection of carbon and nitrogen.

4 0 ELASTICRECOILDETECTIONANALYSIS

5.3 Elastic Recoil Detection Analysis

Elastic recoil detection analysis (erda) is a technique for compositional analysis, in which high energy ions (typically in the MeV range) of a heavy element are directed at an angle onto the sample of interest. Elements lighter than the incident ions will then be emitted from the sample due to elastic collisions. By detection of both ion mass and energy, compositional depth profiles may be constructed from the data. The technique is able to detect all elements that are lighter than the incident ion at depths approaching 1 μm.

5.4 Nanoindentation

Nanoindentation is a technique to determine mechanical properties (pri- marily hardness) of a sample. A sharp, hard tip (most often of diamond) is pushed into the sample as the depth and load required are recorded. This forms an indentation curve from which it is possible to extract, for example, the hardness by fitting parts of the curve to a model [3]. The most widely used model is due to Oliver & Pharr [4], where, by contact mechanics, the elastic modulus is determined as a function of the slope of the start of the unloading curve, the elastic modulus of the diamond indenter and Poisson’s ratios of both sample and tip. Due to the method’s dependence on the geometry of the indenting tip, any divergence from the ideal shape must be recorded and used to correct the projected areas. As the projected areas are extracted from the indentation depth, any errors in this will also affect the measurement. Besides surface roughness, two commonly occurring behaviours are sink-in and pile-up. In sink-in the real area of contact is reduced because the surface bends in instead of forming an edge at the indenter edge. In pile-up the actual area of contact is increased as the indented material flows and buckles up around the indenter. These behaviours are not directly detectable from the load-displacement curves and must be verified by microscopy. Measuring the hardness of a thin film poses extra difficulties in that care must be taken to measure only the film and not the substrate. In practice this means reducing the load and indentation depth so as not to affect the substrate; a typical test is to do a range of maximum loads from low to high which should give two plateaus representing the film and substrate with a transition region in between. The sharpness of the tip and the stability of the instrument determine how thin samples may be analyzed. A common rule of thumb is to have a maximum penetration depth less than 10 % of the film thickness, and for ease of measurement, a film thickness of 1 μm is often desirable.

4 1 THINFILMCHARACTERIZATION

References

1. M. Birkholz. Thin Film Analysis by X-Ray Scattering. Weinheim: Wiley-VCH, 2006. 2. D. B. Williams and C. B. Carter. Transmission Electron Microscopy. New York: Springer-Verlag, 1996. 3. A. C. Fischer-Cripps. Nanoindentation. New York: Springer-Verlag, 2004. 4. W. C. Oliver and G. M. Pharr. An Improved Technique for Determining Hardness and Elastic-Modulus Using Load and Displacement Sensing In- dentation Experiments. Journal of Materials Research 7 (1992) 1564–1583.

4 2 ATOMPROBETOMOGRAPHY 6

Atom probe characterization has long been a highly esoteric technique; impressive in its power of imaging, but limited in its applicability. This is rapidly changing today, as advances in the instrumentation have allowed the technique to be applied to a much wider range of materials [1]. At its core, an atom probe works by sequentially field-evaporating a sample shaped into a sharp tip, atom by atom. The atoms, which become ionized during the evaporation, are accelerated towards an area detector at which both the position and the time of flight are measured. A three-dimensional model of the sample is reconstructed from this data, essentially by back-projection in both space and time. Thus, the atom probe is not a true microscope, and it is not an imaging technique, but rather a destructive tomographic technique which can provide up to atomic lattice resolution space and the chemical identity of individual atoms [2, 3]. The technique is presented in some depth, as it is central to the thesis, and its application to hard coatings is still emerging. The history and theory of apt is given in section 6.1-6.5, followed by some notes on the application to hard ceramic thin films, and finally an original method for deconvolution of mass spectra is presented.

6.1 History

For an understanding of the instrument and the field, the history of the technique is helpful. A condensed version is given here, mainly drawing on the review by Kelly and Larson [1], and the apt primer by Seidman and Stiller [4]. The history starts with Erwin Müller, who had been tasked with building a field emission microscope by his supervisor Gustav Hertz at the Technical University of Berlin. The idea was to produce the high electric field predicted necessary for field emission of electrons by using a curved surface, a sharp tip, as the electric field around a hemisphere scales as the inverse of its radius. The microscope Müller developed consisted of a sharp tip in front of a fluorescent screen, inside a vacuum chamber. When experimenting with reversing the polarity, with the idea of clean- ing the emitting tip from adsorbed species, it was discovered that a steady stream of positively charged particles was emitted from the tip. Müller pub- lished the first papers on field ion microscopy (fim) in 1951 [5], but it was

4 3 ATOMPROBETOMOGRAPHY

only in 1955 that atomic resolution was achieved by Bahadur and Müller [6, 7], after a fortuitous combination of cryogenic temperatures and an ex- tremely sharp tip made field evaporation possible, providing a clean surface for imaging. This was the first time an image of atoms was produced. The fim works by the continuous adsorption of an imaging gas on the tip, followed by field ionization, causing the ions to be accelerated towards the screen, with the near spherical apex leading to a point projection of the surface. The next evolution was the introduction of the first atom probe by Panitz, Müller, MacLane, and Fowler [8]. It worked by embedding a time-of-flight (tof) spectrometer inside a fim, with a small aperture in the screen leading to the spectrometer; this kind of instrument is called an atom probe field ion microscope. This allowed the measurement of compositional profiles from a small part of a sample. The tof was measured by pulsing the voltage applied to the specimen, causing field evaporation at a well-defined start time, and measuring the drift time to the detector, which is proportional to the square of the mass of the incident ion (see below). Panitz improved the design in 1972 [9], constructing the imaging atom probe. By replacing the fluorescent screen with a spherical microchannel plate, which were gated to a selected tof, maps of the distribution of a single ion species versus depth could be recorded. Even though the instrument saw limited spread, it provided the conceptual framework for later instruments. Kellogg and Tsong developed the first laser atom probe, where the voltage pulse is replaced by a thermal pulse caused by an incident laser pulse [10], with similar ideas also being pursued by the group of Block [11]. The reason for changing the pulse trigger is that voltage pulsing requires a moderately conductive specimen. While working in a laboratory environment, the state of laser technology made the technique impractical, and laser pulsing was not pursued generally for almost 30 years. The imaging atom probe was parallelized in the mid-late 1980’s, allowing for the first time true tomographic measurements on specimens. The first instrument was constructed by Cerezo, Godfrey, and Smith [12], and named the PoSAP, for position sensitive atom probe. The final piece of a modern atom probe is the local electrode, invented by Nishikawa in 1993 [13]. Traditionally, atom probes utilized a counter electrode a few millimeters away from the tip to apply the electric field. By moving the electrode closer to the surface Nishikawa localized the field to sharp features on a sample, making a scanning atom probe. The close proximity of the electrode also allowed a decrease in voltage to reach the necessary field strength for evaporation. This allowed Kelly and Larson to

4 4 PRINCIPLEOFOPERATION

figure 6.1 Fim image of a W specimen. Courtesy of Prof. K. Stiller.

design the local-electrode atom probe (leap) with a drastic increase in pulse repetition rate, and a much increased field of vision (from 20 nm to 250 nm) [1]. The simultaneous development of pulsed lasers fast and stable enough for use in a atom probe and the adoption of focused ion beam microscopy (fib) sample preparation techniques [14, 15] from the tem world, now allowed the analysis of essentially all inorganic materials.

6.2 Principle of Operation

A modern atom probe consists of a few key parts. The basis is an ultra-high vacuum (uhv) chamber, in which the sample stage, the local electrode and the detector are mounted. The detector type used today consists of a chevron multi-channel plate backed by crossed delay lines [2], that measures the delay between the ion hitting the channel plate and the signal reaching the ends of the delay lines, which is then transformed into a position on the detector. This allows for fast operation (up to 1 MHz) and separation of most

4 5 ATOMPROBETOMOGRAPHY

figure 6.2 The basic set-up of an ħω apt measurement.

counter electrode V detector

multiple events. The local electrode is a hollow cone with an opening of 40 μm, placed at approximately the same distance from the specimen apex.∼ A static electric field is applied between the sample and the local electrode, with the applied voltage in the range of 3-15 kV and resulting fields at the tip of 10-50 V nm3. Field evaporation of the specimen is then induced by pulsing either the/ voltage by 15-25 % or by locally heating the tip with a focused laser pulse. The standing voltage is then regulated to achieve a mean evaporation rate of 0.002-0.05 atoms/pulse. The actual data recorded by the detector is an x,y-position (after processing of the delay line signals) and a tof. Some instruments are equipped with a reflectron, which sits in the flight path to compensate for energy deficits that cause a spread in the tof. The tof is then converted to a mass- charge ratio, m/q, (most often given as a mass-charge-state ratio, m/z) by the assumption of essentially instantaneous acceleration to the full field potential: mv2 qE m 2Et2 ⎫ 2 = 2 (6.1) ⇒ q = L , L vt ⎬ = ⎭ where V is the potential, L the flight length, t the tof, q the charge, and m the mass of the ion. Today, second-order corrections are applied to correct for variations of flight path with position on the detector.

6.2.1 field evaporation

Field evaporation is the process in which an electric field causes the evaporation and ionization of surface atoms. For temperatures above 20 K the process is thermally activated, and is well described by an Arrhenius rela-

4 6 PRINCIPLEOFOPERATION

figure 6.3 Potential energy curve for an atom during field evaporation. The atomic binding unionized binding curve is shown as the dashed line for reference.

Potential energy Potential barrier charge draining

Distance from surface

tion, whereas tunneling becomes increasingly important at lower temperatures [16]. The probability of evaporation can thus be written as a trial

frequency, f0, and a Boltzmann factor: Q t ( ) kBT t P t f0e− (6.2) ( ) = ( ) , with a barrier Q, and temperature T. The barrier depends on the applied field; a classical formula is given by Forbes [16]:

2 Fe Q Q0 1 (6.3) = ( F − ) , where the main point of interest is that the barrier goes to zero as the applied

field, F, approaches the evaporation field, Fe. The actual barrier depends directly on the electronic structure of the surface atoms, and it is quite diﬃcult to calculate. It is possible to calculate it using ab-initio methods [17], but such calculations are far from routine. The eﬀect of the electric field can be understood as pushing the electron cloud of the surface atom down towards the surface, partially ionizing it, and the further it travels from the surface in its potential well, the more ionized it becomes. Eventually the atom passes over the barrier, where the potential energy from the electric field overcomes the binding potential; it gets captured by the field and accelerated away from the surface. A sketch of the binding potential in the presence of a field is shown in Fig. 6.3. After the initial ionization, while the ion is still close to the surface, there is a chance of it being further ionized by electron tunneling. This process

4 7 ATOMPROBETOMOGRAPHY

is termed post-ionization, and its strength depends on the applied field. Kingham [18] calculated the charge state distributions as a function of field strength for a number of elements. Such curves are useful for estimating experimental fields from apt mass spectra. The introduction of reliable laser pulsing has made analysis of previously difficult-to-impossible materials feasible and routine. Brittle materials or those with low conductivity are typical examples, such as TiC [19, 20], and various oxides [21]. The effect of the laser pulses is to momentarily increase the temperature of the tip, and thus increase the probability of field evaporation [22]. To get the fastest cooling possible, control over spot size [22] and polarization [23] are important factors. The laser power must also be controlled, as too high powers can cause ablation and the destruction of the sample. Higher powers also usually cause undesirable evaporation behaviour (see below). How changing wavelengths affect the evaporation is currently not fully understood; especially for semiconductors, uv lasers generally outperform those with longer wavelengths [21].

6.3 Tomographic Reconstruction

To transform the measured data back into an estimate of the original specimen, a reconstruction algorithm is used. The basic algorithm was developed by Bas et al. [24], with later refinements made by Gault, Geiser et al. [25, 26].

6.3.1 the bas protocol

The task of the reconstruction algorithm is to transform the data consisting

of position, mass and arrival number, xD yD m i, to the set x y z m in the sample space. The Bas protocol achieves this, by, treating, the system, , , as a point projection microscope; the emitter is modeled as a truncated cone with a hemispherical cap. This gives the transformation:

xD xM L = M (6.4) yD yM ; = ξR , = where M is the magnification, L the tip-detector distance, R the sample end radius, and ξ the image compression factor (icf), due to the electro- static coupling of the field to the chamber. Fig. 6.4 shows the projection geometrically. As the detector cannot record the z (depth) information this coordinate must be calculated from the other available information: ion arrival number

4 8 TOMOGRAPHICRECONSTRUCTION

ξR x

L R

figure 6.4 A visualization of the Bas tomographic and position on detector. Each new ion will (in the mean) be slightly below reconstruction algo- the last, giving an increment in z of Δz: rithm. Ω Δz (6.5) = Saη, where Ω is the volume per ion in the sample, Sa the observed surface area of the sample in the field of view, and η the detection eﬃciency. Transforming from the detector area: 2 Ω 2 Ω L Δz M 2 2 (6.6) = SDη = SDη ξ R . The depth position is then moved from the flat specimen plane by correcting for the specimen curvature, ΔzR x y , which is cumbersome to reproduce here [25]: ( , )

z Δ zi ΔzR x y (6.7) = �i ( ) + ( , ). The radius is finally deduced in one of two possible ways; either by calculating it from a shank angle [26], or by estimating it from the applied standing voltage through the evaporation field: V R (6.8) = kf Fe , where Fe is the applied field and kf the field factor, which accommodates for geometrical shape of the specimen. The product kf Fe can be estimated by measurement of the end radius of the specimen after an apt run.

4 9 ATOMPROBETOMOGRAPHY

6.3.2 reconstruction artifacts

Artifacts in the reconstruction are introduced when the real field evaporation of the sample does not match the assumptions of the reconstruction. However, at this point it should be mentioned that the reconstruction is close to exact for some materials, typically pure metals such as Al and W, where recovery of the lattice is routine today [27]. There are several causes of non-ideal evaporation. On the atomic scale, the tip surface will be faceted on the major crystallographic poles, which will be reconstructed as under-dense as evaporation is most likely at the enhanced field at the step edges, which projects the ions away from the poles. This will be visible on the desorption map on the detector as a pattern similar to a stereographic projection of the poles. The mean endform of the tip can also deviate from the perfect hemisphere of the reconstruction assumption [28], as the system works towards an equal evaporation probability over the surface, and not towards any particular geometry. This effect tends to worsen as one moves from the center of the detector outwards. If the sample is not homogeneous, but consists of multiple regions with differing evaporation behaviour, local changes in the projection of ions onto the detector will develop, which are termed local magnification effects. As the field necessary for evaporation varies, the sample will adapt the local curvature to equilibrate the evaporation probability, and it is these local changes that cause the difference in the projection. Depend- ing on whether the field of the inclusion is higher or lower than the matrix phase, the region will either be magnified or reduced in size. Precipitates, for example, may be magnified and the constituent atoms ejected out into the matrix region, or the matrix atoms close to the precipitate may be projected out into the region of the precipitate; both cases lead to a confusion of the size and composition of the precipitate. Another common configuration when this effect is active is the case of layers with different evaporation fields, which causes problems with reconstructing the interfaces as flat and dense. Presently, these problems are unsolved, but there is extensive work towards solutions [25, 28–34]. Besides the artifacts related to trajectory effects, even the evaporation itself can be non-ideal. The Bas protocol assumes that the evaporation of each ion is not correlated with any other evaporation event. This is, however, not always true; the removal of one atom distorts the local lattice, increasing the probability of another atom (or more) following the first. The effect is called correlated evaporation, and is generally undesirable, but sometimes unavoidable. It appears to be common in compound ceramics [35].

5 0 VISUALIZATIONANDDATAANALYSIS

The problem for the reconstruction algorithm stems from the way the z-coordinate is calculated, as the only incremental increase for each arriving ion leads to bunching of the correlated ions, which appears as curved streaks in the reconstruction. It also poses a problem for the detectors, as the delay line construction makes it diﬃcult to distinguish two events that are close both in space and time [20].

6.4 Visualization and Data Analysis

There are many ways to visualize apt data, and as the data is intrinsically in four dimensions (spatial and mass), it often needs to be projected to lower dimensions for the visualizations to be of any value for understanding it. Here the most common means of visualization are briefly presented. The basic graph is the mass spectrum, as it shows counts of the detected ions, and is needed to identify the ions present in the analysis. Today, compositions are derived from mass spectra by assigning ranges of masses to individual ions; a more sophisticated method is presented in section 6.7. Most of the problems with ranging stem from the thermal tails present in most spectra, as overlaps cause errors of classification and thus composition. Atom maps are the simplest representation of a tomographic data set. Atoms are displayed as points in 3d space, often with false colours according to their species. Atom maps are most useful when the region of interest contains several regions with good variation between them, or when a detailed view of the reconstruction is needed. They are more diﬃcult to interpret for gradual changes in composition. Composition fields (or maps) process the raw point data and estimate a composition for the sample divided into a regular grid of voxels. They are most useful when plotting a chemically interesting variable, such as the composition of the metal sublattice in a TiAlN data set, rather than direct concentrations. For data analysis, the raw count data for each volume is desirable, but for qualitative images a smoothed data set is generally preferable. The standard way is to represent each ion with a 3d Gaussian function, and calculate the concentration of a voxel as the integral over the sum of all Gaussians extending into it:

cA r G ri r dV (6.9) ( ) = ∫V �i A ( − )" . ∀ ∶ The smoothing depends on the choice of the width of the Gaussians, and a balance between smoothing out noise and blurring features needs to be struck.

5 1 ATOMPROBETOMOGRAPHY

figure 6.5 Steps for fib preparation of apt samples. First a wedge of the material to be investi- From a composition field isoconcentration surfaces are easily derived. gated is cut loose, then They are useful for both visualizing 3d relationships, e.g., between precipi- wedges are welded tates, and for further processing of data, such as sectioning. to a supporting post, and finally they are Concentration profiles are useful when the feature of interest can be shaped into cones by described by a linear profile. The choice of the width for which the profile is annular milling. After calculated needs to take the lateral variation of the feature into account, as Thompson et al. [15]. overly broad lines will distort the profile. In the case where the feature of interest is not planar in some direction, proxigrams [36] can be helpful. The name is a shortening of proximity histogram; they are constructed by taking a reference surface (often an isoconcentration surface), and calculating the shortest distance to it for all ions, which are then binned according to this distance in a histogram. This works well if the reference surface is smooth enough in relation to the compositional variation of the features of interest.

6.5 Sample Preparation

There are two main methods of preparing samples for apt analysis. For bulk materials, the easiest way is electropolishing, where a thin rod of the material is etched in the middle; this forms a neck which eventually breaks, leaving two separate sharp tips. For thin films, or when a site specific analysis is required, a lift-out fib is used [14, 15]. After deposition of a protective Pt-strip, a wedge is cut loose, and then repeatedly attached to a needle-shaped support, usually a microfabricated post on a Si wafer), and cut oﬀ. The wedges are then annularly milled into cones, leaving the protective Pt cap on the end, and then finished by low energy (2-5 kV) milling, which forms the final tip shape. This process is shown schematically in Fig. 6.5. For good thermal transport, which is desirable as it limits thermal tails during laser apt, the tip should not be too thin, as the transport depends on the cross-sectional area; the shank angle should likewise not be too low. The low energy milling serves to reduce the depth of the Ga implantation, usually limiting it to the very apex of the tip [37, 38].

5 2 APTOFHARDCOATINGS

70 1050

60 900 Multiple events 50 750 FWHM 40 600 FWHM

Multiple events 30 450 300

60 Ti figure 6.6

50 Dependence of frac- at.

tion of multiple events N 40 and chemical com- 30 position on laser energy/pulse for TiN. 20

Composition 10 O 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 Laser energy pulse nJ

Reconstruction artifacts from analyzing across interfaces can be checked in two ways. If the feature remains after turning the sample upside down and analyzing across the interface from the other direction, it is likely a true feature of the sample. Another trick is to analyze the interface edge-on, which has been found to improve both data quality and specimen yield.

6.6 APT of Hard Coatings

In this thesis apt has been used to analyze tm-nitrides, which all proved to share essentially the same evaporation behaviour. Data for TiN is given here to briefly exemplify this behaviour. The fraction of multiple events per pulse is a sensitive function of the applied laser energy per pulse, as is illustrated in Fig. 6.6. As the laser power decreases the multiple events fraction rises, and at typical analysis conditions is close to 50 %. The fraction is also sensitive to the applied field, and as such it is a useful gauge whether the evaporation conditions have reached the steady state, for example when manually running the turn-on procedure, or

5 3 ATOMPROBETOMOGRAPHY

figure 6.7 42

40 Variation of the evaporation field 38 nm of TiN with laser en- V

ergy/pulse, determined 36 by Kingham analysis 34 of Ti-ions. 32 Field 30 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 Laser energy pulse nJ

as a sanity check that the evaporation is indeed from the sample material, and nothing else. The large fraction of multiple events is due to the correlated evaporation and gives rise to streaks in the reconstructions, as discussed in the section on artifacts above. The fields during evaporation for a range of laser powers are given in Fig. 6.7, estimated from charge-state distributions of Ti ions from Kingham curves [18]. The evaporation field of TiN is thus 40 V/nm. Fig 6.8 shows TiN apt spectra for two laser powers.∼ There are two major changes visible when going from low to high power. Firstly, the charge state distribution changes towards fewer ions with high charge states, and secondly, multiple complex ions appear in the spectra. The derived compositions are shown in Fig. 6.6, and it is apparent that higher laser powers degrade the compositional determination.

6.7 Development of a Blind Deconvolution method for APT Mass Spectra

The compositional data of apt are derived from analysis of the time-of- flight mass spectra inherent in the technique, which are composed of peaks corresponding to the mass over charge state (m/z) of the detected ions where the width of the peaks is determined by the physics of evaporation during the experiment. Traditionally, ion identities are assigned to all ions falling inside a certain range in the mass spectrum (“ranging”), and this method works as long as all peaks are well separated with negligible tail overlaps. This is not always the case, however, as the observed peaks of diﬀerent ions may overlap, and in these cases such overlaps are one of the limiting factors of the accuracy of the compositional measurements. Such overlaps may be minimized by careful experimental control, but may be unavoidable as the

5 4 BLINDDECONVOLUTIONOFAPTSPECTRA

8 10 2.4 nJ/pulse

106 log. scale 104 0.3 nJ/pulse counts 100

1 20 40 60 80 100 mass charge state Da figure 6.8 Mass spectra of ion masses are fixed by nature. For example, in laser apt experiments on TiN for 0.3 and 2.4 nJ/pulse. ceramics with low thermal conductivity, tails may be severe [39–43]. As the mass-charge state ratios are determined by the masses and charges of the individual ions that are detected, the real peaks have well-defined values, and all observed broadening is due to the experiment itself. This broadening is most often a nuisance parameter, without interest to the materials science questions most apt experiments are meant to answer. However, if the experimental peak broadening is known, resolving most peak overlaps becomes almost trivial; a simple matter of ordinary curve fitting, which is already well-developed in various fields. Here, a method for the simultaneous determination of the peak profile and ion counts in an apt mass spectrum, solely from knowledge of the ion species present in the spectrum, is presented. This is essentially an instance of blind deconvolution, as the system function is not known beforehand, though specific features of apt spectra are leveraged to arrive at a solution.

6.7.1 method

The method follows from one consideration and one assumption. Firstly, all broadening is due to the experiment, and secondly, it is assumed (for now, at least), that all peaks under consideration have the same shape in the time domain. That is, the evaporation probability against time from the triggering pulse is equal for all ions in the spectrum. Working in the fictitious time domain of τ m z, the mass spectrum can be written s τ = √ / ( )

5 5 ATOMPROBETOMOGRAPHY

as a convolution of the system peak shape p τ and Dirac distributions with ( ) a prefactor ci and positions τi for ion i:

s τ p τ ciδ τ τi (6.10) ( ) = �i ( ) ∗ ( − ). This equation can be discretized and put into matrix form as a spectrum s with N channels, and a peak shape p with M channels, or a compositional vector c: s C p P c (6.11) = = where C is an N M matrix, which is diagonally striped according to the × ion position τi:

ci k l 1 τi ckl , − ( − ) = (6.12) = {0 otherwise , , . or P is a matrix with elements pkl:

pl m k τl pkl , = + (6.13) = {0 otherwise . , . The pair of vectors, p and c, is then the solution to the deconvolution problem, under the constraint that the sum of the component of p equals unity, as it describes the probability of evaporation during the pulse:

pm 1 (6.14) �m = . For goodness of fit, let us take the sum of the square of the normalized residuals, or χ2: obs 2 2 sk C p k χ ( − (2 ) ) (6.15) = �k σk . Given that the detection of each ion in an apt measurement is a Bernoulli trial with a probability of success equal to the detection eﬃciency of the instrument, each channel in sobs will be binomially distributed according to

Bin sk* η , where sk* is the true amount of evaporated ions in channel k, and η the( detection, ) eﬃciency. Therefore, the estimate for the variance of each channel is given by the implicit Gaussian approximation of Eq. 6.15:

2 obs σk sk*η 1 η sk (6.16) ̂ = ( − ) ∝ . Even though we have now reduced the problem significantly, it is generally still quite diﬃcult, as the free-form shape of the peak needs to be estimated. A practical method for solving such problems is the Maximum

5 6 BLINDDECONVOLUTIONOFAPTSPECTRA

4 1 10 Data Fit True kernel 0.1 1000 Fit 0.01 100 Counts 0.001 Probabilty 10 10 4 1 10 5 0 100 200 300 400 500 600 700 0 10 20 30 40 50 60 70 m z channels Peak broadening m z

figure 6.9 Entropy (MaxEnt) method [44], where an informational entropy term is (a) Synthetically constructed atom introduced into the optimization target function to regularize it. With the probe spectrum with entropy, S, defined as: uniform Poisson background noise and pk binomially sampled S pk mk pk log (6.17) ion counts together = �k ( − − mk ) , with the estimated where mk, is the measure, which describes our prior assumptions of the spectrum from appli- shape of the peak, the optimization problem then becomes: cation of the blind deconvolution method, max S αχ2 (6.18) and (b) original and c p , − , estimated peak forms. where α determines the weight placed on the goodness-of-fit versus the entropy, and is varied in steps from zero upwards until the desired convergence is achieved, moving from the initial assumptions of the peak shape, m, towards a shape taking the data into account.

6.7.2 examples

The deconvolution method was applied to two separate sources of data: first synthetically generated spectra were analyzed to test the accuracy of the method, and then an experimentally obtained Fe-Cr spectrum was analyzed to show the applicability to real data. A synthetic mass spectrum, along with the estimated spectrum from the deconvolution, is shown in Fig. 6.9 a. Visually, the spectrum is well described by the model, and most importantly the peak overlaps are reproduced well. Fig. 6.9 b shows the extracted peak shape along with the original, which agrees almost perfectly for the initial part, where the magnitude is large, and only diverging in the very tail due to the worsening signal-to-noise ratio in the spectrum, and truncation of the recovered peak shape. Fig. 6.10 shows the distribution of errors per peak over 100 randomly generated and automatically analyzed spectra. The analysis was performed

5 7 ATOM PROBE TOMOGRAPHY

0.25 figure 6.10 Distribution of observed error per peak 0.20 from the blind deconvolution of 100 0.15 randomly generated spectra consisting of 10 peaks each. Fraction 0.10

0.05

0.00 1.0 0.5 0.0 0.5 1.0 Error per peak at.

using the known peak positions from the creation of the spectra, but with no 17 user intervention. The mean error per peak is eﬀectively zero at 9 10− at. %, with a standard deviation of 0.33 at. %. The distribution itself− shows∗ more structure than a Gaussian distribution, with most of the weight centered close to the mean, but with a small satellite bump on the lower side. The distribution of the recovered peak shape versus the original is shown in Fig. 6.11 with iso-probability lines taken at 10, 60, and 80 % of the probability mass centered around the mean. There is a slight deviation at the initial point, as the true kernel is identically zero there, while the estimated kernel is left 5 at 10− , but following this the peak shape shows basically no variation for∼ up to around half the width, after which the variation in the recovered peak tails exposes an uncertainty as to the exact form. Still, the mean agrees wellwiththecorrectvalueupto 15 channels from the end. The deconvolution of an experimentally∼ obtained apt spectrum from a Fe-Cr alloy sample is given in Fig. 6.12,wherethetopgraphshowsthe measured spectrum along with the estimated spectrum, and the lower graph shows the individual components as estimated by the deconvolution algorithm. The spectrum consists of Fe, Cr, Mn, and V, all in the 2 charge state. Thebackgroundnoise,asseenjusttotheleft of the first table 6.1 + Composition of the Cr peak, is low (less than 10 counts per channel, at a channel width of Fe-Cr alloy sample as measured by normal ranging, blind Cr (at.%) Fe (at.%) V (at.%) Mn (at.%) deconvolution, and Blind deconv. 37.5 62.4 0.023 0.083 themeansamplecom- Std. ranging 38.4 61.5 0.032 0.094 position from X-ray fluorescence (XRF). XRF 37.8 62.1 0 0.089

58 BLIND DECONVOLUTION OF APT SPECTRA

0.1 figure 6.11 Data Fit Peak shape used to 0.01 generate the test spectra, drawn as solid 0.001 line, and sample dis-

Probabilty tribution of recovered 4 10 peak shapes, plotted 2.0 for intervals of 10, 0 10 20 30 40 50 60 70 60,and80%ofthe probability mass. 1.5 Peak proadening m z 1.0

0.5 Estimated deviation 0 10 20 30 40 50 60 70 Peak broadening m z

Δ m z 0 001 0 01 Da in Δ m z ). Themainpartsofthepeaksare mostly√ / well= separated,. ≈ . with the exception( / ) of 54Cr and 54Fe, which overlap almost perfectly; the tails, on the other hand, extend over multiple peaks for the largest peaks, adding to the background noise. The agreement between the experimental spectrum and the estimated one is again good: all peaks are well fitted by the mean estimated peak shape, including the shoulder visible on the left side of the peaks that are large enough, as well as the significant tails. There is a small hump (made more pronounced in the log-scale of Fig. 6.12) appearing just before the long and straight tail in the peak shape. This is most likely a remnant of the nonlinear fitting, as a number of peaks appear with the same spacing, giving a local minimum where some of the satellite peak intensity is ascribed to the main peak. Thetailsaremostlywelldefined and quite constant, with noise becoming significant at distances of more than 2 Da. The complete overlap of 54Cr and 54Fe was resolved via constraints introduced in the nonlinear solver, constraining the overlapping peaks to be close to isotopic distributions with regard to the other peaks in the spectrum, helping the nonlinear solver. The derived composition is given in Table 6.1, where it is compared with the standard ranging done by hand, as well as the global composition measured by X-ray fluorescence (xrf). The composition from the present method is accurate to less than one-half atomic percent of the bulk composition, while the standard ranging overestimates the Cr content by nearly 1 at. %. The ranging by hand was done by disregarding

59 ATOM PROBE TOMOGRAPHY

105 Data 10 4 10 Fit 10 1000 1000

Counts 100 100 10 10 1 1 5 Cr Fe 10 25 26 Fe 27 28 29 30 10 4 Cr Cr 10 Cr Fe 10 1000 m z DaMn Fe 1000 V Counts 100 100 10 10 1 1 25 26 27 28 29 30 m z Da figure 6.12 apt spectrum from a Fe-Cr alloy and thefulloverlapof54Cr and 54Fe, and compensating afterwards with isotope its resolution into components by blind abundance ratios. This overlap is most likely the main source of error in the deconvolution, (a) ob- overestimation of Cr. served and estimated spectra, and (b) esti- 6.7.3 discussion mated components of the experimental spectrum. The performance of the method, as illustrated above, shows its applicability to spectrum analysis, with a special import for those cases where larger peaks interfere with smaller-sized peaks. In such cases neither of the tails are negligible, making standard ranging difficult. The lack of assumptions regarding the peak shape is another strength, which allows for the analysis of situations where analytical models [42, 45]wouldbedifficult to apply; for example, when the tails of peaks have bumps or other structures [40]. The limiting factors for the compositional accuracy in the present examples are all related to noise; background noise is of course always present, even if simple models can account for most of it [46]. But more importantly, the sampling noise introduced by the instrument due to the detection efficiency being less than unity can be significant. The standard deviation for a binomial sampling process is approximately the square root of the detected counts, which is the cause for the noise present in the tails of peaks in apt spectra. It was possibly this condition that led Hudson et al. to conclude that the less of a tail that was used for compositional ranging, the better the estimate. The noise problem is also seen in the increasing uncertainty in the recovered peak shape further out in the tails (e.g. Figs. 6.11 and 6.12). At the same time, it is essential to extract the full tail shape if overlaps are to be solved. Thus, a tension exists between the noise in the tails and the general fit of the spectrum, and as in most cases of data analysis, the best solution is simply more data.

60 BLINDDECONVOLUTIONOFAPTSPECTRA

As mentioned in the method description, there are two main assumptions underlying the derivation of the algorithm, which both call for further discussion. Of the two, the assumed knowledge of peak positions has the firmest physical basis; however, this may not be perfectly true in practice, as there will always be uncertainties in any calibration of the mass spectrum. Even so, most reasonable guesses of the peak positions can be used initially to extract a rough first estimate of the peak shape, which in turn may be used to optimize the peak positions so as best to describe the spectrum. It also follows that care must be taken not to coarsely bin the dataset, which would make the placement of peaks with sufficient accuracy impossible. This leads to the second assumption, namely the description of all peaks as a convolution of a single peak profile with a Dirac function, as in Eq. 6.10. If the peak positions are wrong, by definition this will never hold, but even if it is fulfilled, it may or may not hold, depending on the particular details of the sample under analysis. Simple, one-phase samples consisting of elements of similar bindings, such as the Fe-Cr alloy in section 6.7.2, will most likely be well described under this assumption, whereas more complex samples (multi-phase etc.) will instead likely deviate from the model due to differences in evaporation physics [47]. A model describing this situation must therefore contain several peak profiles to fit the observed spectrum sufficiently well. The present method may be generalized, and the single peak shape restriction loosened, by changing Eq. 6.11 into a sum over linear terms:

s Ppcp (6.19) = �p , where p indexes different peak shapes. The cost of this extension, besides an increase in computational difficulty, is a reduction in the available number of peaks of each shape, leading to worse statistics and more uncertainty. The feasibility of this generalization will therefore again depend on the particulars of the mass spectrum under analysis. In writing Eq. 6.15, an implicit Gaussian approximation of the true binomial distribution of the counts in a channel was made. This should not pose any problems in general, as the difference between the binomial and Gaussian distributions decreases with increasing counts, and for the high counts in apt spectra this will typically be well fulfilled. For the estimation of very dilute components, however, it might prove necessary to forgo the Gaussian approximation and use the full binomial sample distribution for calculating the target function, for some additional complexity and computational costs. In connection to this the necessity of a proper approximation

6 1 ATOMPROBETOMOGRAPHY

for the variance in each channel, here given in Eq. 6.16, must be emphasized, as it changes by several orders of magnitude in a single spectrum. Another potential computational issue is the possibility of the target function being multimodal, that is having multiple local minima, as was seen for Fe-Cr (Fig. 6.12). In that case the diﬃculty arises due to the (almost) constant interval between peaks. As the algorithm is intrinsically free-form, such problems are an unfortunate side eﬀect of solving the inverse problem. To remedy such situations, and arrive at a proper and physically realistic solution, the non-linear solver can be helped by the use of a starting point that is close to the shape expected by the operator. If solutions are found that are clearly unphysical, constraints can also be introduced into the nonlinear solver to forbid such solutions, which is equivalent to assigning zero probability to those solutions. Related to this is the fact that the MaxEnt method does not define a clear stopping condition [44], especially in the case of a multimodal problem, so care must be taken by the operator not to force convergence where only noise is fitted. Finally, it should be noted that the method does not give built in error estimates. To achieve this a more advanced method of estimation is needed, such as the Bayesian method of nested sampling [48], where a random walk samples the configuration space of all possible solutions, iteratively moving closer to the region of maximum probability.

References

1. T. Kelly and D. Larson. The second revolution in atom probe tomography. MRS Bulletin 37 (2012) 150–158. 2. T. F. Kelly and M. Miller. Invited Review Article: Atom probe tomography. Review of Scientific Instruments 78 (2007) 31101. 3. M. K. Miller and R. G. Forbes. Atom Probe Tomography. Materials Charac- terization 60 (2009) 461–469. 4. D. Seidman and K. Stiller. An Atom-Probe Tomography Primer. MRS Bul- letin 34 (2009) 717. 5. E. W. Müller. Das Feldionenmikroskop. Zeitschrift für Physik 131 (1951) 136. 6. E. W.Müller and K. Bahadur. Field ionization of gases at a metal surface and the resolution of the field Ion microscope. Physical Review 102 (1956) 624. 7. E. W. Müller. Resolution of the atomic structure of a metal surface by the field ion microscope. Journal of Applied Physics 27 (1956) 474–476. 8. E. W. Müller, J. A. Panitz, and S. B. McLane. The atom-probe field ion microscope. Review of Scientific Instruments 39 (1968) 83–86.

6 2 REFERENCES

9. J. Panitz. The 10 cm atom probe. Review of Scientific Instruments 44 (1973) 1034. 10. G. Kellogg and T. Tsong. Pulsed-laser atom-probe field-ion microscopy. Journal of Applied Physics 51 (1980) 1184–1193. 11. W. Drachsel, S. Nishigaki, and J. H. Block. Photon-induced field ionization mass spectroscopy. International Journal of Mass Spectrometry and Ion Physics 32 (1980) 333–343. 12. A. Cerezo, T. Godfrey, and G. Smith. Application of a position-sensitive detector to atom probe microanalysis. Review of Scientific Instruments 59 (1988) 862–866. 13. O. Nishikawa and M. Kimoto. Toward a scanning atom probe - computer simulation of electric field -. Applied Surface Science 76-77 (1994) 424–430. 14. D. Larson et al. Focused ion-beam milling for field-ion specimen preparation:-preliminary investigations. Ultramicroscopy 75 (1998) 147–159. 15. K. Thompson et al. In situ site-specific specimen preparation for atom probe tomography. Ultramicroscopy 107 (2007) 131–139. 16. R. Forbes. Field evaporation theory: a review of basic ideas. Applied Surface Science 87 (1995) 1–11. 17. H. Kreuzer, L. Wang, and N. Lang. Self-consistent calculation of atomic adsorption on metals in high electric fields. Physical Review B 45 (1992) 12050– 12055. 18. D. Kingham. The post-ionization of field evaporated ions: A theoretical explanation of multiple charge states. Surf Sci 116 (1982) 273–301. 19. J. Angseryd et al. Quantitative APT analysis of Ti(C,N). Ultramicroscopy 111 (2011) 609–614. 20. M. Thuvander, K. Stiller, and H.-O. Andrén. Quantitative atom probe analysis of carbides. Ultramicroscopy 111 (2011) 604–608. 21. Y. Chen, T. Ohkubo, and K. Hono. Laser assisted field evaporation of oxides in atom probe analysis. Ultramicroscopy 111 (2011) 562–566. 22. J. H. Bunton et al. Advances in Pulsed-Laser Atom Probe: Instrument and Specimen Design for Optimum Performance. Microscopy and Microanalysis 13 (2007) 1. 23. J. Houard et al. Conditions to cancel the laser polarization dependence of tip field enhancement. 2011 Conference on Lasers and Electro-Optics Europe and 12th European Quantum Electronics Conference, CLEO EUROPE/EQEC 2011 (2011) 5943601. 24. P. Bas et al. A general protocol for the reconstruction of 3D atom probe data. Applied Surface Science 87 (1995) 298–304. 25. B. Gault et al. Advances in the reconstruction of atom probe tomography data. Ultramicroscopy 111 (2011) 448–457.

6 3 ATOMPROBETOMOGRAPHY

26. B. Geiser et al. Wide-field-of-view atom probe reconstruction. Microscopy and Microanalysis 15 (2009) 292–293. 27. B. Gault et al. Origin of the spatial resolution in atom probe microscopy. Applied Physics Letters 95 (2009) 034103. 28. E. A. Marquis et al. Evolution of tip shape during field evaporation of complex multilayer structures. Journal of Microscopy 241 (2010) 225–233. 29. D. Larson et al. Eﬀect of analysis direction on the measurement of interfacial mixing in thin metal layers with atom probe tomography. Ultramicroscopy 111 (2011) 506–511. 30. D. Larson et al. Improvements in planar feature reconstructions in atom probe tomography. Journal of Microscopy 243 (2011) 15–30. 31. E. A. Marquis and F. Vurpillot. Chromatic Aberrations in the Field Evap- oration Behavior of Small Precipitates. Microscopy and Microanalysis 14 (2008) 561. 32. M. P. Moody et al. Qualification of the tomographic reconstruction in atom probe by advanced spatial distribution map techniques. Ultramicroscopy 109 (2009) 815. 33. F. Vurpillot, L. Renaud, and D. Blavette. A new step towards the lattice reconstruction in 3DAP. Ultramicroscopy 95 (2003) 223–230. 34. F. Vurpillot, A. Bostel, and D. Blavette. Trajectory overlaps and local magnification in three-dimensional atom probe. Applied Physics Letters 76 (2000) 3127. 35. M. Müller et al. Some aspects of the field evaporation behaviour of GaSb. Ultramicroscopy 111 (2011) 487. 36. O. Hellman et al. Analysis of three-dimensional atom-probe data by the proximity histogram. Microscopy and Microanalysis 6 (2002) 437–444. 37. M. K. Miller, K. F. Russell, and G. B. Thompson. Strategies for fabricat- ing atom probe specimens with a dual beam FIB. Ultramicroscopy 102 (2005) 287–298. 38. M. K. Miller et al. Review of Atom Probe FIB-Based Specimen Preparation Methods. Microscopy and Microanalysis 13 (2007) 1–9. 39. Y. M. Chen, T. Ohkubo, and K. Hono. Laser assisted field evaporation of oxides in atom probe analysis. Ultramicroscopy 111 (2011) 562–566. 40. B. Mazumder et al. Evaporation mechanisms of MgO in laser assisted atom probe tomography. Ultramicroscopy 111 (2011) 571–575. 41. M. Müller et al. Some aspects of the field evaporation behaviour of GaSb. Ultramicroscopy 111 (2011) 487–492. 42. A. Vella et al. Field evaporation mechanism of bulk oxides under ultra fast laser illumination. J. Appl. Phys. 110 (2011) 044321.

43. L. J. S. Johnson et al. Spinodal decomposition of Ti0 33Al0 67N thin films studied by atom probe tomography. Thin Solid Films 520. (2012). 4362–4368.

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44. D. S. Sivia and J. Skilling. Data Analysis, A Bayesian Tutorial. Oxford: Oxford University Press, 2006. 45. J. Bunton et al. Advances in Pulsed-Laser Atom Probe: Instrument and Spec- imen Design for Optimum Performance. Microsc. Microanal. 13 (2007) 1. 46. E. Oltman, R. M. Ulfig, and D. Larson. Background removal methods applied to atom probe data. Microsc. Microanal. 15 (2009) 256–257. 47. R. Forbes. Field evaporation theory: a review of basic ideas. Appl. Surf. Sci. 87 (1995) 1–11. 48. J. Skilling. Nested sampling’s convergence. AIP Conf. Proc. 1193 (2009) 277.

6 5

CONTRIBUTIONSTOTHEFIELD 7

Taken together this work contributes to the understanding of self organized nanostructuring phenomena in hard nitride coatings, both during growth and during subsequent annealing. A few advancements in apt for the studies of such coatings are also included. The main specific contributions to the fields of materials science, nanotechnology, and advanced surface engineer- ing are given in some detail below.

•

The decomposition mechanism of supersaturated solid solution Ti0.33Al0.67N was observed to be spinodal decomposition, by direct observation of a spinodal wavelength in heat treated samples, using apt and and statistical processing by autocorrelation of the composition on the metal sublattice. The as-deposited state was shown to have larger spatial fluctuations of the metal content than expected from a homogeneous solid solution, indicating an already incipient decomposition during growth. The N content was also found to have larger fluctuations than expected; in the as-deposited sample the variations were of random nature, while in the annealed state a variation correlated with the metal-sublattice decomposition was observed. This correlated variation was attributed to the energetics of N vacancies, indi- cated by theoretical calculations [1], and a possible Kirkendall effect, due to differences in the diffusivity of Al and Ti atoms.

•

The effect of adding C to cathodic arc evaporated TiSiN was the enhancement and refinement of the original featherlike nanocomposite structure previously found to depend on the Si content in the material [2]. This addition also lead to an increase in hardness up to 40 GPa, and an increased age hardening effect (up to 10 %). The refinement of the structure, however, caused the thermal stability to worsen, especially for the high Si content films, where Si out-diffusion and interdiffusion of Co and W from the substrate was observed. The temperature of over-aging was consequently reduced from 1000 to 700 °C.

•

In a ZrAlN nanocomposite, composed of cubic, wurtzite, and amorphous phases, and deposited by cathodic arc evaporation, an age hardening of 36 %

6 7 CONTRIBUTIONSTOTHEFIELD

was observed after annealing to 1100 °C. Growth of the cubic ZrN-like phase was the dominating factor during the annealing up to 1100 °C, while the w-ZrAlN only underwent minor recovery. At 1200 °C w-AlN nucleated and lead to a significant drop in hardness, by almost 50 %. An ordered nanocomposite of cubic ZrN and hexagonal AlN was ob-

served to grow in Zr0.64Al0.36N, when deposited on MgO(001) substrates at high mobility conditions. The nanostructure was a 2d labyrinthine structure composed of ZrN and AlN lamellae. The growth occurred directly into the observed phases, with the ZrN being in cube-on-cube epitaxy with the

substrate, and the AlN having an orientation of (0001)AlN (001)ZrN in the growth direction and <1120> <110> in the growth plane.‖ The order- ̄ AlN ZrN ing was attributed to a competition‖ between interfacial and elastic surface relaxation energies. This organized growth resulted from local nucleation at 5-8 nm from the substrate, before which random fluctuations in the Al content increased with each layer. The growth was unstable to perturbations by the renucleation of ZrN, which caused inverted pyramidal regions to grow in the film, and which were composed nanocrystalline grains of either pure ZrN or a random mixture of ZrN and AlN with large compositional variations.

•

The transformation of supersaturated solid solution TiBN into the ther-

modynamically stable components TiN and TiB2 was shown to occur through nucleation of TiN and TiB0.5N0.5, the latter due to a GP-zone behaviour, where it, after having grown suﬃciently in size, transformed into TiB2.

•

Apt has been shown to be applicable, and of great help, in understanding the complex nanostructures that form in immiscible transition metal nitrides. Spinodal decomposition, nucleation and growth, and self organization during growth have been successfully imaged and differentiated between, even though reconstruction artifacts are common and unavoidable with current algorithms. Apt has also been shown to provide local measurements of the N stoichiometry in such nanostructures, a quantity which is otherwise difficult to observe, but which may, for example, be expected to mitigate coherency strains between TiN and AlN domains in decomposed TiAlN and thus affect the decomposition.

6 8 REFERENCES

References

1. B. Alling et al. First-principles study of the eﬀect of nitrogen vacancies on

the decomposition decomposition pattern in cubic Ti1−xAlxN1−y. Applied Physics Letters 92 (2008) 71903.

2. A. Flink et al. The location and eﬀects of Si in (Ti1-xSix)Ny thin films. Journal of Materials Research 24 (2009) 2483–2498.

6 9