Cao Z. (Ed.) Thin Film Growth: Physics, materials science and applications

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Editor and Chapter 8

Z. Cao

Institute of Physics

Chinese Academy of Sciences

P.O. Box 603

100190 Beijing

P. R. China

E-mail: zxcao@aphy.iphy.ac.cn

Chapter 1

Y. Homma

Department of Physics

Tokyo University of Science

1-3 Kagurazaka, Shinjuku

Tokyo 162-8601

Japan

E-mail: homma@rs.kagu.tus.ac.jp

Chapter 2

T. Miller*

c/o Synchrotron Radiation Center

3731 Schneider Drive

Stoughton, WI 53589-USA

E-mail: tamille1@wisc.edu

Contributor contact details

T.-C. Chiang

Loomis Laboratory of Physics

University of Illinois at Urbana-

Champaign

1110 West Green Street

Urbana, IL 61801-3080

USA

E-mail: tcchiang@illinois.edu

Chapter 3

Professor A. Voigt

Institute for Scientic Computing

Technische Universität Dresden

01062 Dresden

Germany

E-mail: axel.voigt@tu-dresden.de

Chapter 4

Y. Kajikawa

Graduate School of Engineering

The University of Tokyo

2-11-16 Yayoi Bunkyo-ku

Tokyo 113-8656

Japan

E-mail: kaji@ipr-ctr.t.u-tokyo.ac.jp

(* = main contact)

ThinFilm-Zexian-Pre.indd 11 7/1/11 9:38:48 AM

Chapter 5

S. Kowarik*

Institut für Physik

Humboldt-Universität zu Berlin

Newtonstr. 15

D-12489 Berlin

Germany

E-mail: stefan.kowarik@physik.hu-

berlin.de

A. Hinderhofer, A. Gerlach and

F. Schreiber

Institut für Angewandte Physik

Universität Tübingen

Auf der Morgenstelle 10

D-72076 Tübingen

Germany

Chapter 6

D. Ye*

Department of Physics

Virginia Commonwealth University

Richmond, VA 23284

USA

E-mail: dye2@vcu.edu

T.-M. Lu

Department of Physics

Applied Physics and Astronomy

Rensselaer Polytechnic Institute

110 8th Street

Troy, NY 12180

USA

Chapter 7

F. Ramiro-Manzano, E. Bonet,

I. Rodríguez and F. Meseguer*

Centro de Tecnologías Físicas

Unidad Asociada ICMM-CSIC/

UPV

Universidad Politécnica de

Valencia

Avda. Naranjos. Acceso J

Edicio 8B, entrada K, 1 piso

46022 – Valencia

Spain

E-mail: fmese@s.upv.es

Chapter 9

B. H. Hong*

Department of Chemistry

Sungkyunkwan University

Suwon 440-746

S. Korea

E-mail: byunghee@skku.edu

and

SKKU Advanced Institute of

Nanotechnology (SAINT) and

Center for Human Interface

Nanotechnology (HINT)

Sungkyunkwan University

Suwon 440-746

S. Korea

H. R. Jeon

Department of Chemistry

Sungkyunkwan University

Suwon 440-746

S. Korea

xii Contributor contact details

ThinFilm-Zexian-Pre.indd 12 7/1/11 9:38:48 AM

Chapter 10

Johann Coraux*

Institut Néel

CNRS-UJF

25 rue des Martyrs

38042 Grenoble

CEDEX 9

France

E-mail: johann.coraux@grenoble.cnrs.fr

A. T. N’Diaye, C. Busse and

T. Michely

II. Physikalisches Institut

Universität zu Köln

Zülpicher Strasse 77

Köln

Germany

Chapter 11

N. Nilius

Fritz-Haber-Institut der MPG

D-14195 Berlin

Germany

E-mail: nilius@fhi-berlin.mpg.de

Chapter 12

X. Q. Wang

State Key Laboratory of Articial

Microstructure and Mesoscopic

Physics

School of Physics

Peking University

Yiheyuan Road 5

Beijing 100871

P. R. China

xiiiContributor contact details

A. Yoshikawa*

Graduate School of Electrical and

Electronic Engineering

Chiba University

1-33 Yayoi-cho

Inage-ku

Chiba 263-8522

Japan

E-mail: yoshi@cute.te.chiba-u.ac.jp

Chapter 13

F. Foucher*

Centre de Biophysique Moléculaire

UPR CNRS 4301

rue Charles Sadron

45071 Orléans

CEDEX 2

France

E-mail: frederic.foucher@cnrs-orleans.fr

C. Coupeau,

J. Colin,

A. Cimetière

and J. Grilhé

Institut P’

UPR CNRS 3346

Laboratoire de Physique des

Matériaux

Université de Poitiers – UFR

Sciences

SP2MI, Boulevard Marie et Pierre

Curie

BP 30179

86 962 Futuroscope

Chasseneuil CEDEX

France

E-mail: christophe.coupeau@univ-

poitiers.fr

jerome.colin@univ-poitiers.fr

alain.cimetiere@univ-poitiers.fr

jean.grilhe@univ-poitiers.fr

ThinFilm-Zexian-Pre.indd 13 7/1/11 9:38:48 AM

Chapter 14

J. Song*

Department of Mechanical and

Aerospace Engineering

University of Miami

Coral Gables, FL 33146

USA

E-mail: jsong8@miami.edu

J. Wu and Y. Huang

Department of Mechanical and

Department of Civil and

Environmental Engineering

Northwestern University

Evanston, IL 60208

USA

Chapter 15

S.-G. Lu and Q. M. Zhang*

Materials Research Institute

and Department of Electric

Engineering

The Pennsylvania State University

University Park, PA 16802

USA

E-mail: qxz1@psu.edu

Z. Kutnjak

Jozef Stefan Institute

1000 Ljubljana

Slovenia

Chapter 16

H. Guclu*

Department of Biostatistics

University of Pittsburgh

Pittsburgh, PA 15261

USA

E-mail: guclu@pitt.edu

T. Karabacak

Department of Applied Science

University of Arkansas at Little

Rock

Little Rock, AR 72204

USA

M. Yuksel

Department of Computer Science

& Engineering

University of Nevada – Reno

Reno, NV 89557

USA

xiv Contributor contact details

ThinFilm-Zexian-Pre.indd 14 7/1/11 9:38:48 AM

It is well known to researchers who work on thin lms that there are currently

more than 200 books published that deal with various aspects of thin lm

science and technology, but this fact does not exclude the necessity for new

volumes in this eld. None of the existing books has tried to be exhaustive

and, more importantly, the eld itself keeps marching forward at an elevated

pace and in more diversied directions. The latter point is quite understandable

since thin lms provide the most efcient, exible and thoughtful uses of solid

materials; they offer a uniquely versatile material base for the development

of novel technologies. In fact, industries based on the utilization of thin-lm

devices constitute the strongest driving force for our economy. The attempt

to meet the requirements of making more advanced thin-lm devices in turn

has led to the innovation or invention of deposition techniques and of tools

for the characterization of growth processes, and along with this technical

progress the understanding of the fundamental physics behind the seemingly

endless spectrum of phenomena concerning thin-lm growth is also becoming

increasingly clear. The publication of a new book on thin-lm growth is

justied by the fast development of this enterprise alone.

With the current book we intended to summarize the most recent

advancements in the eld of thin-lm growth, focusing on the introduction

of new growth and characterization methods, the application-oriented

developments and, more importantly, the understanding of the physics

relevant to the growth of some particular lms, which are at the forefront

of thin-lm science today. The chapters included in the book aim to present

highlights on those topics that have attracted the special attention of the

authors and the editor. We hope they can be useful to an interdisciplinary

and varied audience including science and engineering graduate students

working on thin lms, researchers and working professionals who want to

have an overview of the eld in the recent years or have a strong interest in

the new growth and characterization techniques.

The book contains 16 chapters grouped into two parts. Part I comprises

ve contributions introducing the theory of thin-lm growth, including

measuring nucleation and growth processes in thin lms (Homma), quantum

Preface

ThinFilm-Zexian-Pre.indd 15 7/1/11 9:38:48 AM

electronic stability of atomically uniform lms (Miller and Chiang), phase-

eld modelling of thin lm growth (Voigt), analysis of surface roughness

evolution (Kajikawa), and modelling of deposition processes based on

real-time observation (Kowarik et al.). The 11 chapters in Part II deal with

the advancement of techniques for thin-lm growth and relevant device

fabrication procedures, including silicon nanostructured lms grown on

templated surfaces by oblique angle deposition (Ye and Lu), study of phase

transitions in colloidal crystal thin lms (Ramiro-Manzano et al.), growth for

thermally unstable noble-metal nitrides by reactive magnetron sputtering (Cao),

growth of graphene layers for thin lms (Hong and Jeon), epitaxial growth

of graphene on single-crystal metal surfaces (Coraux et al.), determination

of electronic properties and adsorption behaviour of polar lms (Nilius),

polarity control and growth on polar substrates (Wang and Yoshikawa),

understanding of buckling (Foucher et al.) and controlled buckling of

thin lms on compliant substrates for stretchable electronics (Song et al.),

electrocaloric effect in ferroelectric polymer lms (Lu et al.), and network

behaviour in thin lms and nanostructure growth dynamics (Guclu et al.).

From the very beginning we cherished the hope that these chapters can

serve as a guide to the advancement of thin-lm science and that graduate

students and specialists in both academic and industrial institutions may

nd the book a valuable reference. As editor I gratefully acknowledge the

contributing authors of these chapters, who are all renowned experts in the

corresponding subeld of thin-lm science. I thank them all for having spent

considerable time and effort in compiling these high-level contributions.

Lastly, I am profoundly grateful to the editorial staff of Woodhead

Publishing, including Dr Cliff Elwell (commissioning editor), Ms Laura

Pugh (commissioning editor) and Miss Nell Holden (project editor), for their

sustained support during the two-year preparation of this volume.

Zexian Cao

Beijing

xvi Preface

ThinFilm-Zexian-Pre.indd 16 7/1/11 9:38:48 AM

Measuring nucleation and growth

processes in thin films

Y. Homma, Tokyo University of Science, Japan

Abstract: This chapter focuses on the observation of crystal growth

processes by tracking the motion of atomic steps, which are the growth front

of the crystal. after reviewing the theoretical model for atomic step motion,

the chapter discusses atomic step imaging by scanning electron microscopy,

and reveals basic growth modes using this technique: two-dimensional-

island nucleation and step-ow modes both in growth and evaporation, and

morphological instability of atomic steps between these two modes.

Key words: atomic steps, scanning electron microscopy, molecular beam

epitaxy, step ow, island nucleation.

1.1 Introduction

Recent progress in surface observation techniques has enabled crystal surfaces

to be observed at the atomic scale. In particular, with scanning tunnelling

microscopy (STm) (Binnig and Rohrer, 1983), the motion of individual

atoms on the surface can be tracked (Swartzentruber, 1996). However, at high

temperatures where crystal growth takes place, atoms diffuse on the surface

so fast that any existing methods cannot catch up with their movements. In

vapour phase growth, those diffusing atoms, termed adatoms, nally evaporate

or meet an atomic step where they are incorporated into the crystal. By

the incorporation of adatoms, the motion of atomic steps takes place. The

motion of atomic steps is much slower than that of adatoms. Furthermore,

atomic resolution is not necessary for the observation of atomic steps which

have a one-dimensional structure on the surface. Therefore, we are able to

observe the crystal growth processes by tracking the motion of atomic steps

which constitute the growth front of the crystal. For this purpose, electron

microscopy techniques with a high sensitivity to atomic steps are useful:

these include reection electron microscopy (REM) (Osakabe et al., 1980)

and low energy electron microscopy (LEEM) (Bauer, 1994). These two

techniques utilize electron diffraction from the surface, and thus are sensitive

to the surface morphology at atomic steps.

In this chapter, however, we use a different electron microscopy, scanning

electron microscopy (SEM), to observe the motion of atomic steps. As the

growth method, we focus on the molecular beam epitaxy (MBE), where the

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

4 Thin ﬁ lm growth

crystal surface in a vacuum is exposed to a molecular  ux of evaporated

source material. Before explaining the principle of atomic step imaging

by SEM, we review the theoretical description of atomic step motion. The

theoretical model was established in 1951 by Burton, Cabrera and Frank

(BCF model) (Burton et al., 1951). Interestingly, this is far earlier than the

establishment of MBE and surface characterization techniques.

1.2 Basic theory of epitaxial growth

We consider step- ow growth on a vicinal surface with parallel atomic steps.

We take the x-axis perpendicular to the atomic steps as shown in Fig. 1.1(a).

atoms supplied from a molecular beam are adsorbed and migrate freely

on the surface (adatoms). The time evolution of adatom density, r(x,t), is

described by the following diffusion equation:

∂

)

(

–

)

(,xt(,

)xt )

∂x∂

(xt (

, xt,

(,xt(,

)xt )

)

[1.1]

where D

is the diffusion coef cient of adatoms, F is the  ux of impinging

atoms, 1/t

is the evaporation probability of an adatom. The  rst term on the

right-hand side in Eq. 1.1 represents the diffusion of adatoms, the second

term represents the loss by evaporation, and the third term is the increment

due to deposition. F is expressed by using the partial pressure, p, of the

molecule composed of h atoms usable for growth:

Atomic step

Terrace

l ’

(a)

(b)

1.1 Models of crystal surfaces with (a) parallel atomic steps and (b)

circular atomic steps.

ThinFilm-Zexian-01.indd 4 7/1/11 9:39:11 AM



5Measuring nucleation and growth processes in thin ﬁ lms

where k

is the Boltzmann constant, m is the mass of the molecule, and T

is the absolute temperature.

To solve Eq. 1.1, we assume that the rate of attachment and detachment

of adatoms at the steps is much faster than that of diffusion. That is, the

adatom density at the step becomes an equilibrium value r

. When the

surface diffusion is much faster than the motion of steps,



= 0

. Then, for

an isolated step at x = 0, the boundary conditions are r(0) = r

, r(•) = Ft

These give the following solution

()

+ (

)

1 – exp

–

()

||x||

˙˙˙

where l

= D

, and l

is the surface diffusion length of adatoms. The step

velocity v is determined by the adatom  ux at the step

jD(0jD

)

jD) jD

jD= jD

)

For an isolated step, assuming the  uxes from upper and lower terraces are

equal (symmetric),

•

= 2(

)

= (

–

)

[1.2]

where n

= a

–2

is the density of lattice (lattice constant a) on the surface.

The step velocity is proportional to 2l

. This means that only atoms

impinging within l

from the step contribute to the step motion, and other

atoms evaporate before reaching the step. This growth mode occurs when

the diffusion length is much smaller than the step spacing. For the opposite

case, when the diffusion length is much larger than the step spacing:

ll +ll

•

[1.3]

where l and l¢ are the widths of upper and lower terraces, respectively.

For circular steps, we need to solve the diffusion equation in the cylindrical

coordinates. The general solution is expressed as

r(r) = Ft

+ A(r

– Ft

) I

( r/l

) + B(r

– Ft

(r/l

)

where K

and I

are the modi ed Bessel functions of order zero, and A and B

are the proportional constants. For the circular step between an inner terrace

of radius R on a larger terrace of radius S as shown in Fig. 1.1(b),

ThinFilm-Zexian-01.indd 5 7/1/11 9:39:12 AM

