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

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16 Thin ﬁlm growth

As discussed above, the Ehrlich–Schwoebel barrier on the Si(111) surface

at high temperatures is small and this kind of step wandering is not observed.

Here, we show step instability in a different way. We utilized the fact that

the adatom ux to atomic step is an increasing function of the terrace width,

and distorted the symmetry between the upper and lower terraces by changing

the ratio of their sizes (Finnie and Homma, 2000c). This is possible only by

using an ultra-large terrace such as shown in Fig. 1.8(c).

Figure 1.12 shows the time evolution of atomic step shape on a 100 mm

wide terrace (Homma et al., 2001). The observation was carried out using

a low Si molecular ux for nucleating only an island at the centre of the

terrace at 880°C. Each frame was observed by the quenching method after

growth duration starting from the at surface. This was to avoid any extra

nucleation due to repeated quenching. a small circular island is seen at the

centre of the terrace in image (a). This changes to the six-fold symmetry

island extending in <110> directions as seen in images (b) and (c). In this

stage, the peripheral atomic step progressing from the edge of the terrace is

smooth. after further growth, the periphery step becomes wandering as seen

in image (d). The wandering amplitude maximizes at 0.5 monolayers, and

then decreases for further growth as in image (e). The decay of wandering is

due to the stabilization of step ow when the upper terrace becomes large.

While the shape of the centre island reected the symmetry of the Si(111)

surface, the periphery step was initially smooth and became wandering

afterwards. This is exactly the result of step uctuation enhancement by the

large lower terrace.

[110]

[112

]

50 µm

(a)

(b)

(d)

(c)

(e)

1.12 SEM image sequences showing the evolution of atomic step

instability during growth at 880°C on the ultra large Si(111) terrace

(Homma et al., 2001). The images were obtained after growth of (a)

10 s, (b) 20 s, (c) 1 min, (d) 5 min and (e) 10 min.

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17Measuring nucleation and growth processes in thin ﬁlms

1.7 Conclusion and future trends

This chapter has shown that crystal growth of Si and Gaas in molecular beam

epitaxy is well described by the BCF model. That is, the surface diffusion

of adatoms is the dominant process of crystal growth and the incorporation

of adatoms into atomic steps is fast enough. on the evaporating surface, the

behaviour of advacancies is also well described by the BCF model. The key

to observe the atomic step motion of growing and evaporating Si surface at

high temperatures is the use of an ultra-large terrace created at the bottom

of a crater. Since the surface diffusion length of adatoms on a Si(111)

surface at high temperature becomes as large as 10–50 mm, a terrace width

comparable to the surface diffusion length is a prerequisite. SEM imaging

with the quenching method is useful for such a large-scale observation. In this

method, atomic steps were decorated with the 7 ¥ 7 phase domains. In order

to obtain an enhanced 7 ¥ 7 domain contrast, an oblique incidence of a 25 keV

primary electron beam was used. Recent progress in electron microscopy has

made it easier to observe atomic steps. A low energy SEM instrument with

a primary electron beam of 0.1–1 keV is commercially available these days.

Surface sensitivity is largely enhanced with the low energy beam, especially

when it is used in an ultrahigh vacuum. Low energy electron microscopy

(LEEM), which uses projection optics of reected electrons for imaging, has

realized real-time imaging of atomic steps even at elevated temperatures.

LEEM is now widely used for observation of growing surfaces of various

materials (Bauer, 1994; Meyer zu Heringdorf, 2008).

1.8 References

Bales G S and Zangwill A (1990) ‘Morphological instability of a terrace edge during

step-ow growth’, Phys. Rev. B 41, 5500–5508.

Bauer E (1994) ‘Low energy electron microscopy’, Rep. Prog. Phys. 57, 895–938.

Binnig G and Rohrer H (1983) ‘7 ¥ 7 reconstruction on Si(111) resolved in real space’,

Phys. Rev. Lett. 50, 120–123.

Burton W K, Cabrera N and Frank F C (1951) ‘The growth of crystals and the equilibrium

structure of their surface’, Phil. Trans. Roy. Soc. 243, 299–358.

Ehrlich G and Hudda F G (1966) ‘Atomic view of surface self-diffusion: tungsten on

tungsten’, J. Chem. Phys. 44, 1039–1049.

Finnie P and Homma Y (2000a) ‘Motion of atomic steps on ultraat Si(111): constructive

collisions’, J. Vac. Sci. Technol. A18, 1941–1945.

Finnie P and Homma Y (2000b) ‘Nucleation and step ow on ultraat silicon’, Phys.

Rev. B 62, 8313–8317.

Finnie P and Homma Y (2000c) ‘Stability–instability transitions in silicon crystal growth’,

Phys. Rev. Lett. 85, 3237–3240.

Florio J V and Robertson W D (1970) ‘Phase transformations of the Si(111) surface’,

Surf. Sci. 22, 459–464.

Hibino H, Sumitomo K, Fukuda T, Homma Y and Ogino T (1998) ‘Disordering of Si(111)

at high temperatures’, Phys. Rev. B 58, 12587–12589.

ThinFilm-Zexian-01.indd 17 7/1/11 9:39:15 AM

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18 Thin ﬁlm growth

Homma Y and Finnie P (2002) ‘Step dynamics on growing silicon surfaces observed

by ultrahigh vacuum scanning electron microscopy’, J. Cryst. Growth 237–239,

28–34.

Homma Y, Tomita M and Hayashi T (1991) ‘Secondary electron imaging of monolayer

steps on a clean Si(111) surface’, Surf. Sci. 258, 147–152.

Homma Y, Suzuki M and Tomita M (1993a) ‘Atomic conguration dependent secondary

electron emission from reconstructed silicon surfaces’, Appl. Phys. Lett. 62, 3276–

3278.

Homma Y, Tomita M and Hayashi T (1993b) ‘Atomic step imaging on silicon surfaces

by scanning electron microscopy’, Ultramicroscopy 52, 187–192.

Homma Y, Osaka J and Inoue N (1994) ‘In-situ observation of monolayer steps during

molecular beam epitaxy of gallium arsenide by scanning electron microscopy’, Jpn.

J. Appl. Phys. 33, L563–L566.

Homma Y, Osaka J and Inoue N (1995) ‘In situ observation of surface morphology

evolution corresponding to reection high energy electron diffraction’, Jpn. J. Appl.

Phys. 34, L1187–L1190.

Homma Y, Hibino H, Ogino T and Aizawa N (1997) ‘Sublimation of Si(111) surface in

ultrahigh vacuum’, Phys. Rev. B 55, R10237–R10240.

Homma Y, Hibino H, Ogino T and Aizawa N (1998) ‘Sublimation of a heavily boron-

doped Si(111) surface’, Phys. Rev. B 58, 13146–13150.

Homma Y, Finnie P and Uwaha M (2001) ‘Morphological instability of atomic steps

observed on Si(111) surfaces’, Surf. Sci. 492, 125–136.

Meyer zu Heringdorf F-J (2008) ‘The application of low energy electron microscopy and

photoemission electron microscopy to organic thin lms’, J. Phys.: Condens. Matter

20, 184007-1–184007-12.

Osaka J, Inoue N and Homma Y (1995) ‘Delayed and continuous nucleation of islands

in Gaas molecular beam epitaxy revealed by in situ scanning electron microscopy’,

Appl. Phys. Lett. 66, 2110–2112.

Osakabe N, Tanishiro Y, Yagi K and Honjo G (1980) ‘Reection electron microscopy

of clean and gold deposited (111) silicon surfaces’, Surf. Sci. 97, 393–408.

Pimpinelli A and Villain J (1994) ‘What does an evaporating surface look like?’, Physica

A 204, 521–524.

Schwoebel R L and Shipsey E J (1966) ‘Step motion on crystal surfaces’, J. Appl. Phys.

37, 3682–3686.

Swartzentruber B S (1996) ‘Direct measurement of surface diffusion using atom-tracking

scanning tunneling microscopy’, Phys. Rev. Lett. 76, 459–462.

Yamaguchi H and Homma Y (1998) ‘Imaging of layer by layer growth processes

during molecular beam epitaxy of Gaas on (111)a substrates by scanning electron

microscopy’, Appl. Phys. Lett. 73, 3079–3081.

1.9 Appendix

1.9.1 Extension of the Burton, Cabrera & Frank (BCF)

model for evaporating surface

This appendix discusses the behaviour of adatoms and advacancies on an

evaporating surface following the work by Pimpinelli and Villain (1994).

at high temperatures not far from the melting point, advacancies as well

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19Measuring nucleation and growth processes in thin ﬁ lms

as adatoms exist on the surface. We need to take advacancies into account

when we discuss the problems relating to evaporation on the surface. The

concentration of advacancy s(x) on the terrace has a minimum at the centre

of the terrace opposite to the concentration distribution of adatoms. When

the concentration of advacancy exceeds a certain value, a macro-vacancy,

one monolayer deep hole, is created.

To treat both advacancies and adatoms, we need to consider their pair

creation and pair annihilation. The annihilation rate of an adatom-advacancy

pair is proportional to the product of their concentrations, rs. The pair

creation rate at equilibrium is proportional to their equilibrium concentration,

. These values satisfy the coupled equations

= Dr≤ – r/t

+ D r

– D rs + F

= L s≤ + D r

– D rs

where D and L are the diffusion coef cients of adatoms and advacancies,

respectively, and ∆ is the proportional constant. To linearize the equations,

we introduce dr = r – r

and ds = s – s

, and suppose these are small (near

equilibrium). Also, we neglect the external  ux F. Then, we get

ª Ddr≤ – dr/t

– r

– D r

ds – D drs

ª Lds≤ – D r

ds – D drs

Since the step motion is much slower than the diffusion of adatoms and

advacancies, dr

= 0 and ds

= 0. Under the boundary conditions, r(± l/2) =

, s(± l/2) = s

, we get

()

cosh

()

cosh

)

– 1

()x()

(2l(2

(2/(2

[a1.1]

()

1 –

cosh

()

cosh

()x()

(/l(/

where

In general, since adatoms diffuse much faster than advacancies, Dr

>> Ls

then, 1/k

ª Dt

= l

The step velocity for equidistant parallel steps is given by

–

dl(2dl

)

(

D( D

(

dl(/dl

(2/(2

000

)

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20 Thin ﬁ lm growth

1.9.2 Macro-vacancy formation

at high temperatures, the density of advacancies increases, resulting in the

formation of macro-scale vacancies of monolayer deep. The edge of the

macro-vacancy is an additional step. The formation of macro-vacancies is

described by nucleation theory. The free energy of a macro-vacancy with

radius R is expressed as

F(R) = 2pRg – pR

where g is the step stiffness, and dm is the chemical potential. The  rst term is

the energy increase due to step formation and the second term is the chemical

potential decrease due to formation of advacancy cluster. Since the density

of macro-vacancy is proportional to the Boltzmann factor, exp[–F(R)/k

T],

the clusters larger than the critical value R, which gives maximum of F(R),

expand, while those smaller than the critical value shrink. The maximum

of F(R) occurs at R

= g/dm,

F(R

) = pg

/dm

The condition for the formation of at least one macro-vacancy on the terrace

within the area of l ¥ l is

exp[–F(R

)/k

T] = l

exp[– pg

/dmk

T] ≥ 1 [A1.2]

Since r ~ r

r(x) = r

exp(–dm/k

T) [a1.3]

On the other hand, from Eq. A1.1,

()

cosh

()

cosh

)

()

()x()

(2l(2

(2/(2

[A1.4]

By comparing these two equations, A1.3 and A1.4, we get

()

= – ln

cosh

()

cosh

)

1 –

cosh

(

()xk()

/ xk/

/ T/

()x()

()

(2l(2

(2/(2

kkk

)

cosh

l(2l

)

(2/(2

at at

= 0,

8 =

(

)

(

( D(

lll

Then, inserting this result into Eq. A1.2, we get

exp

–8

()

lk()lk

T()T

()

≥ 1

()

≤ 2 ln

()lk()

()T()

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21Measuring nucleation and growth processes in thin ﬁlms

Using typical step spacing l ~10

– 10

g/k

T ≤ lk.

Since g is the order of k

T, we obtain the condition for macro-vacancy

nucleation,

l ≥ 1/k.

Using 1/k

ª Dt

= l

l ≥ l.

That is, a macro-vacancy is formed when the terrace size is comparable or

larger than the adatom diffusion length.

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Quantum electronic stability of atomically

uniform films

T. Miller and T.-C. Chiang, University of illinois at

Urbana-Champaign, USa

Abstract: The valence electronic states in thin lms are quantized by the

lms’ boundaries. This represents a substantial modication of the band

structure of the system which inuences all physical properties. Dramatic

variations in thermal stability are observed in thin metallic lms on an

atomic layer-by-layer basis. This chapter describes measurements of

morphology, stability, and electronic structure of thin metallic lms using

angle-resolved photoemission spectroscopy, and discusses theoretical

models that can predict stability based on the quantization of states. Further

measurements using x-ray diffraction extend these results to structures more

complex than uniform lms.

Key words: quantum electronic stability, metallic quantum wells, thermal

stability, atomically uniform lms, angle-resolved photoemission.

2.1 Introduction

The valence electronic states in a solid-state system of nanoscale dimensions

are modied relative to their bulk counterparts by the presence of the system’s

boundaries. These modications, referred to generally as ‘quantum size

effects’ (QSEs), inuence all physical properties of the system. Of particular

interest here is the thermal stability of a thin lm. The rst section of this

chapter deals with the related idea of ‘electronic growth’ – the concept that

the growth mode of a lm can be governed to a large degree by the quantum

effects on the valence bands. Here we are considering metallic lms in which

the electronic states are most amenable to a relatively simple treatment and

competing effects are minimized. Next, angle-resolved photoemission (ARPES)

will be described as it is applied to thin lm studies. This is an important tool

for studies of these phenomena because, as applied to atomically uniform

lms, it can reveal the electronic structure of the system while at the same

time serving to precisely measure a lm’s thickness to an exact number of

monolayers. The growth and characterization of atomically uniform lms by

ARPES follows. Such lms may be of value for technological applications

because their unusual uniformity supports quantum states with a high degree of

coherence, and certainly they are important for scientic studies of quantum-

size effects because of their relative simplicity and ease of characterization.

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23Quantum electronic stability of atomically uniform ﬁlms

Next, measurements of quantum stability of some thin lm systems will be

presented. This will lead into a discussion of the general principles of thin

lm stability and their application to nanostructure development. Mostly this

is based on a simple picture of electronic quantization akin to the ‘particle-

in-a-box’ problem of elementary quantum mechanics. However, a section is

devoted to systems where the basic quantization conditions are modied by,

for example, specic substrate physical and electronic structures. Finally,

we speculate on what directions future research might be expected to take.

2.2 Electronic growth

Valence electrons are responsible for the bonding of the atoms or molecules

that make up a crystalline solid. In the case of a covalently bonded solid, it

is intuitive that the nature of the valence states would exert a dominant role

in the growth of a thin lm just as they do in the formation of a molecule,

via directional bonds and the lling of chemical orbitals, starting right from

bonding with the substrate. For a metallic overlayer, however, of all the

myriad factors inuencing lm growth, the valence electronic states of the

overlayer would perhaps seem to be at most a minor factor. Considering the

delocalized states of the metallic bond gives rise to a picture of lm growth

where kinetics, such as the lm/substrate lattice match and efciency of

packing, and bulk thermodynamic properties, such as surface tension and

melting point, are the driving forces shaping lm morphology. Electronic

effects due to the quantization of states by the boundaries of a smooth lm

have been discussed for some time, but their impact on lm properties, if

any, would be mitigated by a variety of effects, including loss of coherence

due to lattice mismatch and defects, and in any event would eventually

become irrelevant for lms thicker than a few monolayers (Feibelman

1983, Feibelman and Hamann 1984). Experiment has shown, however,

that this is not the case for well-ordered thin lms of nanoscale thickness,

where electronic effects can have a dramatic impact on thin lm properties

including surface reactivity (Danese, Curti et al. 2004, Zhang, Zhang et al.

2008), work function (Paggel, Wei et al. 2002), superconductivity (Guo,

Zhang et al. 2004), and surface energy and thermal stability (Czoschke,

hong et al. 2005). Coherent electronic behavior has also been observed in

lms thicker than 100 monolayers and even across a mismatched substrate/

lm boundary (Paggel, Miller et al. 1999b, Speer, Tang et al. 2006). It

is so that quantum-electronic inuences on metallic lm growth would

be expected to diminish with increasing thickness, but they are of direct

importance for practical applications as thicknesses of interest continue to

shrink, and indirectly for all deposited lms inasmuch as they start off as

nanolms where quantum effects should be considered in the establishment

of the initial growth modes.

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24 Thin ﬁlm growth

Of course, these quantum-mechanical effects are in competition with

kinetic constraints and, depending on one’s viewpoint, there are also different

aspects of electronic structure, such as charge spillage, Friedel oscillations

from either the substrate or the vacuum boundary, energy associated with

connement, etc., all of which may be in competition with each other in

determining the morphology of a growing lm (Zhang, Niu et al. 1998). Also,

the quantum effects being considered here arise from the overall geometry of

the system, and the growing lm may never have the opportunity to take a

suitable form for them to develop if kinetic constraints prevent it from doing

so from the initial stages of growth. The term ‘electronic growth’ has been

applied to deposition and annealing methods that permit quantum effects to

be expressed.

Early experimental work on electronic growth showed that atomically

at lms of Ag could be obtained on GaAs substrates by rst depositing

at low temperature and subsequently annealing to room temperature (RT)

(Smith, Chao et al. 1996). By starting at low temperature, kinetic effects

could be suppressed until enough material was deposited so that quantum

electronic effects could stabilize the formation of a at lm upon annealing

(Miyazaki and Hirayama 2008). More studies of low-temperature deposition

using reection high-energy electron diffraction with spot prole analysis

(RHEED-SPA) on Pb lms on Si(111) substrates revealed a preference

of island step heights of seven monolayers (Budde, Abram et al. 2000).

RHEED-SPA data contain information from a large area of the sample in

which there may be many small islands of different dimensions; later work

by the same group using scanning tunneling microscopy (STM) conrmed

these results and found also a preference for bilayer steps, and the authors

suggested a connection to quantum electronic effects (Hupalo, Kremmer

et al. 2001). Generally, these Pb lms consisted of islands with a distribution

of sizes sitting on top of a continuous wetting layer. With lower growth

temperatures, atomically uniform lms are possible in this material system

(Upton, Miller et al. 2004). For STM studies, a distribution of island sizes

may be a desirable feature, as the spectrum of preferred heights can be

directly measured on a single sample prepared at one time. However, in

islands, lateral connement occurs and the full three-dimensional structure

should be considered for theoretical treatment.

For fundamental studies of quantum electronic effects, a uniform thin

lm gives a simple interpretation in terms of one-dimensional quantum-well

states, leading to a more intuitive picture of the physics. Angle-resolved

photoemission is well suited for studies of uniform lms, and at the present

time a wealth of information is available from many photoemission studies

on quantum-well states in a variety of thin lm systems (Chiang 2000,

aballe, rogero et al. 2001, 2002, Bian, Miller et al. 2009, evans, alonso

et al. 1993, Liu, Paggel et al. 2008, Patthey and Schneider 1994). Even for

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25Quantum electronic stability of atomically uniform ﬁlms

these systems of relatively simple geometry, interactions between the lm

and substrate can give rise to quantized electronic structures of substantial

complexity (Liu, Speer et al. 2008).

2.3 Angle-resolved photoemission spectroscopy

ARPES is an experimental technique well suited for the measurement of the

electronic structure of solids. A monochromatic photon beam of sufcient

energy to overcome the sample’s work function is used to eject electrons

from the sample. The light source can be a laboratory one such as a resonance

lamp or a laser, or synchrotron radiation using a vacuum monochromator.

Synchrotron radiation is most versatile as the photon energy can be changed

over a continuous range. The electrons are collected by an analyser which

measures their angle of emission relative to the sample surface and their

kinetic energies. Since the photon is annihilated in the photoexcitation event,

energy conservation gives

kin

= hv – E

– W

where E

kin

is the measured kinetic energy, hv is the impinging photon

energy, E

is the binding energy of the electron inside the solid relative to

the Fermi level (E

) before excitation, and W is the work function. This

makes it possible to relate the measured energy spectra to the spectrum of

initial states inside the crystal (Hüfner 1995).

The energy states form a set of energy bands, each characterized by a

dispersion relation E

(k), where E is the energy, i is a band index, and k is

a wave vector referred to (somewhat loosely) as the ‘crystal momentum’.

Crystal momentum is analogous to momentum in free space, but takes into

account the fact that electrons in a crystal are diffracted by the xed lattice

and so are in states of mixed momentum. It is customary to label states

by the ‘reduced crystal momentum’ k which is the lowest value that could

be obtained by a hypothetical individual measurement of the electron’s

momentum, other values being possible from the same state by additions

from the discrete set of reciprocal lattice vectors. The set of all such k’s lls

the rst Brillouin zone of k-space (Ashcroft and Mermin 1976). An example

of crystal electronic structure is shown in Fig. 2.1, which shows calculated

bands of Ag along various directions within the rst Brillouin zone (Moruzzi,

Janak et al. 1978, Papaconstantopoulos 1986, Smith and Mattheiss 1974).

Knowledge of the emission angle and energy equates to knowing the

electron momentum after it has been emitted from the sample. Passing

through the surface, the translational symmetry of the lattice is preserved

in the surface plane, but not perpendicular to it, and likewise with the

crystal momentum. So, photoemission can characterize electronic states in

a crystal almost completely – the energy and the two in-plane components

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