Chapter 5 Epitaxial Growth. The Problem of the Interface

128 CHAPTER

5

EPITAXIAL GROWTH. THE PROBLEM OF THE INTERFACE

This chapter cannot,

within the framework of the present book,

be an exhaustive

treatment of epitaxy. In the space allot ed, it should provide the keys to an understanding of the formation mechanisms of the oriented growth of one crystalline structure on another. The reader should refer also to the crystallographic descriptions of 20 structures (chapter 4) as well as to the thermodynamic section on the existence and formation of adsorbed layers (chapter 3). The general idea to be developed is that whatever the growth mechanism predicted by thermodynamics, the relative orientation of one crystal growing on another is not readily predictable. The 20-30 transition takes place via a compact plane with minimum surface energy in the case of a so-called "discontinuous" interface. For a so-called "monomolecular" interface, characteristic of gas-solid interactions, we shall suggest a three-step mechanism : formation of a 2D stage having intrinsic structure; simultaneous existence of a 3D nucleus which rests on the compact intermediate plane; growth in thickness with or without pseudomorphism. In the case of a diffuse interface we will consider continuous passage from the substrate to the alloy via a succession of compact planes. The processes of diffusion and exchange which are basic to the mechanisms described are not dealt with here in any way. 5-1. THE GENERAL PROBLEM OF EPITAXIAL GROWTH The oriented growth of two phases A and B attracted the attention of crystallographers very soon after the introduction of X-ray diffraction by Laiie in 1911.

In 1928

Royer introduced the term "epitaxy" and put forward explanatory laws on a purely geometrical basis. Only within the last decades, with the appearance of sophisticated methods of surface analysis, have theoretical models and experimental criteria worked together to permit a universal classification. The interface The determination of the energy associated with the interface between two crystalline phases is an extremely complex problem, because of the variety of crystal structures and their relative orientations.

It is,

however,

possible to delineate some general criteria

based on two intimately related formalisms, namely: j) the theory of heterogeneous nucleation, which deals with the formation of a critical

nucleus from adsorbed atoms; ii) the formation of an adsorbed layer from the vapour phase.

AII,T YA . +AA .YAB ,+AB YB, +BB

NUCLEATION

VA! ,. ~

..... \to

YAB

•

ff\Lltn' ,., 01'\

611>0

>~

• I

INTERFACES epitax y related minima of YAB

A-

B [

YAB =fltJ

MODELS DISC O NTI NUOUS INTERFACE

+

A B

I

AII
monolayer

\

./

"'AB< "'BB

"

.1

"'AB >+BB

compact or high symmetr y model

Bolid solution

/ ordered

ADSORPTION

CONDENSATION Fig. 5.1

alloy

I _ A I

A - B

A ABA "A""BBA

[ TRANSITION B

MONOLAYER

B[

ABAB

ABAB - B

DIFFUSE INTERFACE

EPITAXY

Schematic diagram of mechanisms in epitaxial growth.

130 These two mechanisms allow us to envisage the interface as : a) a discontinuous transition from a pure deposit to a pure substrate, i,e, A-+ B or b) a monomolecular region of a transitional "compound" with a discontinuity between

"A"

the pure substrate and the pure deposit, i.e, A -+ B

-+B

or c) a continuous transition, across a diffusion zone, in which the composition of the alloy or solid solution varies from pure A to pure B, i,e, A -+

~~~~ -+

B.

These conclusions, which permit an understanding of the scientific approach, are set out in Fig. 5.1. We present below the broad outlines of the theory of heterogeneous nucleation (without engaging in polemics on the "liquid" or "solid" nature of the critical nucleus), and we shall distinguish the macroscopic thermodynamic quantities involved in the

process of

epitaxial growth, Le. the specific surface and interfacial energies, temperature and supersaturation. In the case of condensation under conditions of under-saturation these quantities are replaced by the deposit-support bond energy and the energies of

cohesion of the

deposit and of the substrate. We use the following nomenclature:

y

= surface

8

= coverage

a

energy

wetting angle geometrical function of a azimuth of disorientation = interaction energy = supersaturation (= kT In piPe)

free energy of 3D nucleus formation

n.

number of nuclei of i atoms per unit area

1

D T

= surface diffusion coefficient

s

temperature of the surface

wAB

work of adhesion between A and B

Po

= density of nuclei

r

= radius of critical nucleus

p

= vapour

Pe

= equilibrium vapour pressure.

5-11.

pressure

THERMODYNAMIC APPROACH

5-11.1. Heterogeneous nucleation. Conditions of equilibrium. Implications. 5-II.l A Work of formation of a critical nucleus (3D) The free energy of formation

of a condensed phase A from a supersaturated gas

phase is generally written as the sum of two terms:

.6G. = .6G . +.6G f 1 supersaturation sur ace where in the process of formation of a nucleus of size i, consisting of i atoms, the excess

131

free energy,

due to supersaturation of the gas phase,

is lost in the form of the work

necessary for the creation of a new surface. Assuming for simplicity a hemispherical nucleus, we can write L'lG supersaturation with

s: ,,_ v

RT ln (E)

V

Pe

where V is the molar volume, 2 t:,Gsurface = 411 r where YA is the nucleus-vapour interfacial free energy of the new phase, and

YAB and

'(B are the energies corresponding to the nucleus-substrate interface and to the substrate itself. YA' YB and YAB are positive quantities related by Young's equation [lJ Y = Y + YACOS a AB s LG can thus be written: 3 i CP3(o)+ Y 11r2 CP3 (0) t:,q= t:,G 11; v A CJl ' cP 2 and cP 3 are geometric functions of a j in l)articular l 2 -3<;:05('/+ cos a CP3 (a) = Lj is represented in Fig. 5.2.

1 r----r-------,-----,--=--~

'S

~

(")

S-

1

2

a

O"---....-:::~..L---_=:_+_-----'----~

Fig. 5.2 Variation of CP3 (a) versus a. Ifo; = 0, wetting is perfect and t:,G'* is negative, which favours adsorption. !f a = 11, wetting does not occur; this is the limiting case of homogeneous nucleation which

neglects the substrate as a trigger for nucleation. The variation of t:, G as a function of r is shown in Fig. 5.3. i When the vapour is undersaturated p< p , so that RT In e.
132

o

i +Ve

a -Ve

Fig. 5.3 Variation of the free energy of formation of a 3D nucleus (OGi) versus radius of the nucleus (r), occur only if the vapour phase is supersaturated. 5-11.1 B Conditions of equilibrium. Implications.

wAB = O. homogeneous nucleation

I

,

/~

< -,

f

\

wAB > 2y A' \

20 growth

" \

I

" .... --",'

Fig. 5.1+ Wetting angles of a liquid droplet in equilibrium with a substrate. From Winterbottomlj]

133 Combining Young's equation with Dupre's equation adhesion of A on B

W AB

YA + YB - YAB

we obtain

W

Y

AB

A

[2] which defines the work of

(1 +cosa)

1t is obvious that discussion of the equilibrium condition depends on the inequality Y AB -

YB

>< YA

The different cases are summarized in Fig. 5.4.

In the case of 2D nucleation, Le, for

wAB > 2YA' it is more reasonable to use atomic quantities, since the macroscopic quantities yare no longer meaningful. A discussion of the effects of adsorption on equilibrium conditions is presented in the next chapter and also in the work of Hirth and Pound [4]. 5-11.2 Condensation at undersaturation 2D thermodynamic approach As Mutaftschiev [5] has pointed out the thermodynamic equilibrium between a monomolecular adsorbed layer and a dilute phase of the same substance can be expressed by the general isotherm :

k T In _8_ 1-6

="'l'ad - "'1'0

+ f',

)1

where¢ ad is the differential enthalpy of adsorption (per molecule) at the degree of coverage8, and ¢o is the enthalpy of evaporation of the infinite condensed phase of the adsorbate. The supersaturation f',)1 is the difference between the chemical potential )1 of the vapour in equilibrium with the adsorbed layer, and the potential )10 of the infinite condensed phase of the adsorbate at the same temperature. The above equation takes account of approximations concerning the entropy factors of the adsorbed layer and of the infinite condensed phase. If we suppose that the adsorbed layer is isomorphous with a lattice plane of the crys; talline phase of the adsorbate, and if we consider only interactions between nearest neighbours, we can write, with nand m being the number of neighbours in the plane and out of the plane respectively: and

¢0 =

1

'2 m 'jJAA

+

1

2"

n'I'AA

'I'A and'!'AB being the energies per bond between two molecules of the adsorbate and between a molecule of the adsorbate and a molecule of the support respectively. Substituting ¢ad and ¢o' we write: kTln

b

= - in'l'AA (I - 28) +

i

m ('I'AB -'I'AA) + lI)1

It is well known that the Frumkin-Fowler isotherm shows a region of instability, corresponding to a first-order transition of the condensed layer, if 'I'AA>4kT. In this case the theoretical curve 8 = f«',)1) is S-shaped. The real curve has a step of infinite slope. It cuts the theoretical curve at the point of inflection for 8 = 1/2. The supersaturation f',\lm corresponding to the layer is thus given by f',)1m

I = '2 ('l'AA -'I'AB)

134

Given that a two-dimensional condensed layer can exist only under conditions which preclude a three-dimensional state of the a dsorbate, it is clear that a step can appear only when the saturation L\iJ m <0, i.e, YAB > 'fAA' It is thus possible, as proposed by Bauer in 1958 and in 1972, to classify different

modes of growth from a knowledge of the macroscopic quantities Y, or from the quantities 'f , which amounts to the same thing.

5-Ill.

DIFFERENT MODES OF GROWTH

Bauer

[6J

showed by a thermodynamic approach that it was possible to distinguish

the "two-dimensionality" or "three-dimensionality" of the initial nucleus

of a phase A

growing on B, simply by means of the surface free energies YA' Y Band YAB'

respect-

ively the surface free energies of the deposit, the substrate and the interface. We recall the conclusions : L) YB = YA + YAB' Nucleation and growth occur by formation of successive monolayers,

2) YB > Y A + Y AB' A monatomic layer is formed initially. 3) YB < YA + Y AB' 3D growth exists from the start. The continuous film is obtained by coalescence of discrete nuclei. Later Bauer (1972) took up these mechanisms again and designated them by the names of the pioneers who first studied them: for conclusion

0,

the Frank-van der Merwe mechanism [7J

for conclusion 2), the Stranski-Krastanov mechanism for conclusion 3), the Volmer-Weber mechanism

[8J

[9J.

Two other conclusions reached by Bauer are relevant to our problem of epitaxial order, namely: of all the possible orientations of the nucleus on the surface, epitaxy is that which corresponds to the minimum free energy of the system. For such an eventuality it is necessary that the supersaturation be small enough that the system

can reach a

minimum configurational energy, and that the free energy show pronounced minima as a function of the mutual orientations of the nuclei and the support. (We shall discuss this point in more detail in section 5-V). Finally, Bauer emphasizes that his thermodynamic treatment is obviously not capable of predicting a specific orientation or preferred orientations. While adopting Bauer's classification, we prefer to base our approach on the nature of the interface, which leads us to propose the following classification, already discussed by van der Merwe

[10 J ,

-- the discontinuous interface; -- the "monomolecular" interface; -- the diffuse interface. These three cases will be treated in detail using specific examples.

This analysis will

permit us to discuss a fact which is often neglected, namely the 2D-3D transition. We propose the hypothesis that the transition from deposit (3D) to support occurs in

135 the majority of cases via a compact (simple) plane, corresponding to a minimum surface energy of the 3D substance. From this point of view, the Volmer and Frank-van der Merwe cases will be grouped together. We introduce on the other hand the supplementary case of the ordered alloy, which will be discussed using the example of AuPb

2• The examples which we have chosen differ also in the analytical methods proposed for

their study. It is not our intention to describe in detail these different techniques, but to show that there exist techniques which are more appropriate and more specific for each of the different systems of growth. 5-IV. THE INTERFACE We have shown above that two complementary formalisms permit us to describe the different mechanisms of growth of a substance A on a substance B, but we have to recognize that neither of these can help us in the description of the AB interface.

Before

attempting an approach to the problem, with specific experimental examples, we should mention what can be done by a priori

studies.

There are two opposing points of view. The first is a purely "visual" approach to the interface which thus relies on geometric concepts to describe it. From the time of Bragg [11 J to that of Bollman [12 J the description of a surface was based on the theory

of

coincidence lattices, which permits us to account for the geometry of the interface. To be sure, in order to succeed in such studies, it is necessary to suppose that A and Brest one on the other via compact planes of A and B, and that the interface is planar.

It

follows that the greater the number of points of coincidence existing in the interface, the greater is the work of adhesion between the deposit and the support, and thus the smaller is the interfacial energy. Thus in terms of the Dupre equation the epitaxial orientation is that for which wAB is a maximum. Moire imagery can account for these orientations (see section 5-V.3). The coincidence conditions represent local minima in the surface energies. An exhaustive study of this approach has been made by Bollman [12J. A different standpoint is adopted by Fletcher [13J • Given two compact planes of A and B, and knowing the values of the bulk elastic moduli of A and B and

a pair-wise

interaction potential, is it possible to minimize YAB? Fletcher has shown that the two parameters, the parametric misfit (b/a) and the disorientation angle ¢ of A on B imply minima in the interfacial energy YAB' By way of example, Fig. 5.5 gives the curve relating the variation of the parameter b/a to the interfacial energy for two angles of disorientation. A third parameter introduced by Reiss

r14J,

in addition to those considered by the

coincidence model, permits minimization of the energy. This approach will be described in the following section, in connection with the study of Volmer-Weber growth, to which it has been applied, but we can state here that Reiss concludes that a 3D nucleus can more easily find some epitaxial orientation the smaller it is and the farther away its original

136 6

N

0

......

(;

4

~

cjl:

c

:>

c

2

I

/

O~

cr

/'

/'

cjl:45°

>-

~ c Ql Ql

0

Ql

u

~

sc

2 /

06

0

~

o8

10

lattice

1.2

parameter

14

ratio

I 6

18

20

b/o

Fig. 5.5 Variation of interface energy versus lattice parameter ratio tsle; From Fletcher [131 orientation is from a deep minimum in the energy of binding to the periodic substrate. In what follows we have always assumed that epitaxy is a phenomenon connected with the nucleation phase. Results obtained in recent years show that in the case of a weak interaction(Au deposited on alkali halides), nucleation does not necessarily lead to epitaxy and epitaxy does not necessarily occur during nucleation.

Epitaxy is a post-nucleation

phenomenon. (This idea will be developed in 5-V.n. We conclude this section by saying that it is possible to describe the oriented growth of A on B on condition that the mechanism is known (important parameters: T, Y n)' but above all that a theoretical approach is possible only if the interface is discontinuous via compact planes. The examples which follow have been chosen with this in mind. 5-V. DISCONTINUOUS INTERFACE This is the type of interface that will be encountered in the Volmer-Weber growth mechanism, a typical example of which is the condensation of a metallic vapour on insulating substrates such as the alkali halides. This growth mechanism lends itself particularly well to study by microscopy and electron diffraction. Growth occurs directly by formation of three-dimensional nuclei from a population of adsorbed atoms, as was indicated in 5-II.I.

137

The most important results may be summarized as follows: J) It is possible to verify the laws of heterogeneous nucleation by determining the

distribution P of the nuclei on the surface. o 2) Nucleation is neither a necessary nor a sufficient condition for oriented growth. 3) A study of the variation with time of a spatial distribution of crystallites and of their relative orientations has shown that epitaxy can be a post-nucleation phenomenon. 4) It is possible to put forward models of interfaces. We will illustrate one of the results directly related to the discontinuous nature of the interface, namely the dynamic and progressive approach to epitaxy, starting from a discontinuous distribution of crystallites with random orientations on a surface. 5-V.1. Epitaxy - a

post~nucleation

phenomenon

We shall not give any experimental details; the reader may refer to the review articles (Masson

et al.,

[l5J).

It is possible, as Zanghi has done [16 J , to study the collective behaviour of a distribution of gold crystallites on a (lOO) KC I surface, cleaved under ultrahigh vacuum, by following the time and temperature dependence of the radial distribution function of the particles. Taking one crystallite as origin, the average number of nuclei

situated at a

distance between rand r + dr, for an average density of nuclei Po can be written P P(r)21Trdr o where Ptr) is the radial distribution function for the nuclei. The result can be seen in Fig. 5.6a, which shows an increase in the number of nuclei at a distance r = 100A. Such a result can be interpreted only in terms of an intrinsic mobility of the crystallites, for which the general histogram is invariant (Fig. 5.6b). The transition between the curves (I) and (2) shows the existence of a critical temperature Tc' above which the function P(r) gives a graph with two peaks. mobility of the crystallites.

This indicates

Electron diffraction photographs taken of the distributions 0) and (2) show simply Debye-Scherrer types of pattern, confirming that there is no preferential azimuthal orientation (fibre pattern). At a given temperature it is possible to follow from the diffraction pattern the gradual orientation of the crystallites as a function of time. It is thus reasonable to speak of the progressive establishment of epitaxy by rotation and translation of the crystallites. Various experiments performed by Masson

et: al.,

lead to the same

et al , have demonstrated these phenomena electron microscopy on the Au-MgO system [17 J • conclusions. Finally, Metois

directly by

5- V.2. Interface model It is

a priori

difficult to win acceptance in the field of epitaxy for the idea that

crystalline entities can have intrinsic mobility. However, as early as 1968 Reiss proposed an interface model capable of accounting for its theoretical feasibility.

PI

I

I

.slrl·'·..

i

i

i

"0

EXPERIMENTAL DllA

6

I

T/I-I,X

,1

@!

.1~

'~l

~.

.50

•

n

1

I

~

h ... I••• II.

..

>

Ill:

~

~

~~ 1O

:: ~

:IE

c c

... Ill:

1'.

•

1

~

)".

~ F'.

~ ~

I",,,·..;bm.,

tf

10

,~

"

~ ,:~ c

c

t,

_. )'

1[;1;1,

1

,:.:, ..I\h

X ) II f 11-UJ1H:I:f:l:!+H t1 y': ~:

I/~) 1

-I·!

"

U ::::l

z ~--l5 >~

;;; ~ c

JUY

o

, VI

I

I

100

~o

I

I 200

I~

IJ

2~0

22

r(A)

)1

61

7li

DIAMETER (A)

a

b

dial distribution function of Au nuclei evaporated on NaCl (100) cleaved in vacuum. From Zanghi et al; [[6 ]. Room temperature. (2) 150°C.

139

Consider a two dimensional square lattice of fixed atoms resting on a substrate of the same symmetry, azimuthally disoriented by an angle ¢ . Suppose N is the total number of atoms in an island. Reiss showed that the calculation of the interfacial energy (E) gives minima for specific values of the angle ¢ , namely I 2 ¢ = (zn + J)/2N /

E is shown as a function of

e=

n (integer}; 0

21TN ¢ in Fig. 5.7.

f I

:--1r·B·, :.;

I

: _.. t., .

.,.--~"'"



, I

Fig. 5.7. Variation of interfacial energy versus angle of disorientation. From Reiss [14], Although the model does not allow any relaxation of the atoms ("frozen model"), which no doubt reduces the height of the activation energy barriers for migration, it has the merit of making plausible the rotation and translation of the islands, without the necessity of energies significantly greater than for the migration of isolated atoms. Finally, a crystallite is more readily able to undergo migration the smaller and more highly disoriented it is. 5-V.3. Physical image There is another approach to interface models, which, inspired by the "island model" of Mott U8], consists in describing the interface using a coincidence lattice model. This permits the interface to be visualized as shown in Figs. 5.8 and 5.9.

140

.................• .................. .............••... .........•.••..... ...........•...... ...........•.....• ..............•.•• .........••....••. ........•....••... ....•...•....••... ..........•••....• ........••........ ..........••.....• ...•...•...••..... .................. •...•...•••..••.•. •..••..•...•..•.•. •••....•...•.•..•. (100)

.......•. .........••• .•.•••.....•. •......•..•• .......•..•.....• . .......••.••... ...........•••••••

................ .........•.•.•.• . ........•••..•. ......•••• .........••• .....•••• . . (111)

••••••••••••••••••• .... .... •••••••••••••••••••

i:~:i

~i~i~, ["0]_., ••••••••••••••••••• .... .....•....••••..... ['00],(1 ................•••

."

Fig. 5.8 Moire pattern approach to the crystal surface interface. From Masson et at. [15].

crystallite

Fig. 5.9 "Island Model" of the substrate-crystallite interface From Masson et at. [15J. 5-VI THE "MONOMOLECULAR" INTERFACE This type of interface, occuring typically in the Stranski-Krastanov growth mechanism, is characterized by the establishment of a two-dimensional layer whose structure is totally different from that of the 3D compound subsequently obtained,

and it is distinguished

141 from the Frank-van der Merwe case in which the structure of the layer is similar to that of the 3D compound (pseudomorphism with variation of the lattice parameter). 5- VI.l. The nickel-oxygen system: calibration The interaction of oxygen with nickel gives a particularly interesting system, in that the cubic NiO phase formed is stable over a wide range of temperatures. Many authors have been interested in this system, using LEED or AES techniques [I9J. We will discuss the experiments of Mitchell, Sewell and Cohen [20J , who used high-energy electron diffraction at grazing incidence (RHEED), in conjunction with X-ray fluorescence. It is possible, using standards, to make the latter analytical technique quantitative. The O(Ka) signal of oxygen obeys the law R = Roo (I _ e- a x) where R = signal/noise ratio for a film of thickness x Roo = signal/noise ratio for bulk NiO a

2

= coefficient of absorption in cm Jlg-

l

-2

x = oxygen content of the phase in Jlg cm • (The detection limit is 0.002 ug cm-2 for a counting time of 20 seconds). 2) 15 a monolayer of oxygen corFor a (100) plane of nickel (density 1.6 x 10 at.cmresponds to 0.428 Jlg cm -2 •

Such very thin films correspond to the linear parts of the plots shown in Fig. 5.10.

Alz0 3 0

Fe~04

NiO

4

A

NbzO• •

TQzo.

D

o

ou---

/y

/0 • if .-=====-~-_., /a..-,...-..: _.--~::.:-~---------:=;:==, ·a--:::---~%l------g'./ .z;rr-./

/

D

~

lO

15

FILM WEIGHT (p.o/cm2 )

25

Fig. 5.10 Calibration curve for X-ray fluorescence. From Mitchell et al; [20J.

142 The experimental values found on the different faces of nickel are given in the table 5.1. TABLE

5.1

Thickness of layers of oxygen deposited on single crystals of Ni (a

= 3.24A) and NiO (a

(100) Ni

Plane

Wt, of Oxygen

No. of

('!1g cm -2)

layers

I

o

o

0.5

0.0214

1

0.0428

0

o

= 4.177A)

(11l) NiO

(l00) NiO Thickness 0

(A)

2.09

Wt, of Oxygen (1Jg cm -2)

0.076

Thickness 0

(A)

Wt. of Oxygen ~g cm- 2)

2.41

0.035

2

4.18

0.0612

4.82

0.0702

3

6.27

0.0918

7.23

0.1053

5-VI.2 Kinetics and structure It is possible to follow the kinetics and the structures which produce a protective

layer of oxide in three stages. 1) A chemisorption step (non-activated), associated with two-dimensional structures. 2) The presence of this chemisorbed layer prevents the non-activated process from occuring, but at "non-specific" locations on the surface (defects), nuclei of NiO are formed. The nuclei grow laterally, by interaction with adsorbed oxygen, to cover the surface with a monomolecular film of NiO. There are several epitaxial orientations, which are destroyed by heating. 3) A logarithmic growth in thickness. This classical scheme of gas-solid interaction is interesting in that it raises the problem of the continuous 20-30 transition, and of the different relative (30) orientations with the support. It poses the problem of the simultaneous presence on the surface of nuclei of NiO and of an intermediate (20) structure, in this case, c(2x2) on Ni (100) and c(2x4) on Ni (110), while there are nuclei of NiO in epitaxial relation with the support, with orientations NiO (00l) NiO (1[0)

II Ni uro) II Ni ur»

As Bauer has already noted [21J , a double diffraction phenomenon occurs between NiO and the nickel support, while there are never double diffraction spots between the c(2x2) structure and the nickel oxide crystals. This indicates that the c(2x2) structure exists side by side with the NiO crystals and it is not a transition layer between NiO and Ni, This kind of interpretation seems to be general for this kind of growth mechanism.

The essential features of the lateral growth mechanism are based on a model proposed

143 by Orr (see ref. [19]), of which Fig. 5.11 shows the fundamental steps.

IMPINGEMENT

DESORPTION CHEMISORBED OXYGEN LAYER

NICKEL SUBSTRATE

Fig. 5.11 Model of nickel oxide growth. [19]. From Hudson et: at. The subsequent logarithmic growth can be conceived of only in terms of nickel-oxygen exchange, the latter diffusing to the interior of the bulk nickel, as suggested

by the

mechanism of Fehlner and Mott (1970) [22] for oxidation at low temperatures. (At high temperatures experimental observations of lateral growth of oxide particles have been made by Benard et: at.

[23] and a model for the surface diffusion process, including

effects of Ostwald ripening, has been described [24]). Measurements of the RHEED patterns from the oxidized nickel surfaces give about

° for the parameter of the oxide lattice in the surface plane at an oxygen coverage 1.41A

° is reached at an equivalent thickness of about 4 of 1 monolayer. The bulk value of 1.476A rnonolayers, Thus a layer slightly contracted by about 5 percent is first formed and the

lattice parameter varies with thickness until it reaches the bulk value. A study of the oxidation of nickel at 295°C by Norton et: at.

125] using UPS and

XPS completely confirms this mechanism. The study of the Ni

and 01 photoernission 2P3!2 s spectra shows the following changes for e up to 3 monolayers (Fig. 5.12). For e'" 0.5 (region of

rapid chemisorption), which corresponds in RHEED to the c(2x2)

saturation, there is no change in intensity in the Ni

structure at

spectrum, and the binding energy

2P3!2 is 852.8eV. Simultaneously the 0ls spectrum decreases in width and shifts to lower energy. For

e

between 0.6 and 0.8, the 0ls binding energy reaches its saturation value of 529.7eV

at ambient temperature. The spectrum of the d band of nickel (obtained with He II radiation) shows no change up to

e = 0.5.

Continued exposure to oxygen beyond

e = 0.6

shows an overall narrowing of the 0ls band by 1.8eV, while the Ni2P line broadens and 3!2

144

01s

8 ~ 3.0

>-

8 ~ 2.0

0::
\ S:

co 0::
~I

W

f
",~4

f-

Z

8 ~ 06

~

o

u

CLEAN

849

853

857

861

CLEAN

865 526

BINDING

528

ENERGY

530 (eV)

532

534

536

Fig. 5.12 XPS spectra from oxygen adsorbed on a Ni (100) surface. From Norton et al , [25J. shows a shoulder at 854.4eV, the binding energy of N/+ and NiO. All these results are consistent with nucleation and growth of NiO for 8> 0.6,

for

which the corresponding 0ls binding energy at 529.7eV, obtained for a single crystal, is characteristic of the formation of a thin layer of NiO. 5-VlI

THE "DlFFUSE INTERFACE"

The formation and growth of the alloy AuPb gold was studied in detail by Perdereau

on the (100) (110) and (111) faces of 2 et al , [26J using LEED and AES. The variation

of the peak-to-peak heights of the Auger signals of gold and lead as a function of the time of deposition permitted these authors to characterize a layer-by-layer type of growth The first changes of slope or "knees" in such curves are interpreted by the authors as corresponding to complete formation of a first layer (Fig. 5.13). We follow here,

for the 000) face,

Biberian's approach [26b J which attempts

to

account for the formation of the first layer of adsorbed lead, and then for the epitaxy of AuPb A possible mechanism for the formation of the alloy by diffusion of atoms of gold 2• across the layer of Pb was given by Oudar and Huber [27].

145 IAuger

lead A

2\

gold T

Fig. 5.13 Variation of the Pb and Au Auger signals versus time. From Biberian [26b] • See also [29]. 5-VII.I. The monolayer of lead Biberian and Huber [28] give a description of the intermediate

structures

c(2x2),

d7l2xv1) R 45° and c(3l2x >,2) R 45° observed by LEED, before the c(6x2) structure is obtained at saturation. The interpretation is based on a high-symmetry model. This model assumes a c2mm two-dimensional group symmetry for the rectangular coincidence cell, all the atoms being in sites of quaternary symmetry (Fig. 5.14a).

Fig. 5.14a

c2mm symmetry of coincidence cell. From Biberian [26b].

In fact, without displacing the atoms situated on the A axis and keeping the c2mm 2

146 symmetry, but taking into account the steric effect of the lead atoms, slight displacements lead to the model shown in Fig. 5.14b.

T

r

I.

!

L

r

i

,

I

I

1

I

Fig.5.14b Pseudo-hexagonal (Ill) plane of lead. From Biberian [26bJ. The layer of lead is very similar (lattice parameter within 10 percent)

to a (I I j)

plane of bulk lead. This is a case where both the high-symmetry coincidence lattice approach and the model of a compact monolayer similar to a bulk plane lead to identical structures (see chapter 4). 5-VII.2. AuPb epitaxy 2 The alloy identified by X-ray and electron diffraction is the inter metallic compound AuPb

whose (110) plane, parallel in each case to the face of gold, has a rectangular cell 2 of sides 5.65A and 10.36A. If we compare this with the square cell of the (100) plane of gold, we note that there is a multiple cell for epitaxy, equal to 18x2 that of gold (100). It is thus possible to show the analogy between three c(6x2) cells of the (111) pseudoplane of Pb and 5 cells of AuPb

as seen in Fig. 5.15.

2,

, !

, ,

,

,

1 I

r

, I

,

,

,

,

l7'" ,

r

../

,

T

11

,

,

,

Fig. 5.15 Analogy between three c(6x2) cells of the (Ill) pseudoplane of Pb and 5 cells of AuPb From Biberian [26b], 2• In this model the c(6x2) structure of lead forms an integral part of the alloy. On the basis of such a model Biberian suggests that it is possible to describe the growth of the alloy in terms of the variations of the Auger intensities [26bJ. However, other authors claim that it is not possible to make a reliable analysis from the Auger data and raise the question of quantitative AES beyond the monolayer range -where there may occur cornpli-

147 eating effects of Auger electron diffraction and scattering [29J • According to Biberian the transition from 2D growth to 3D growth occurs via stacking of double layers, as shown in Fig. 5.16.

L1

n

L2

n-l

--------

-

11

3

12

2

L1

Au /1001

Fig. 5.16 Schematic growth mechanism of Pb on Au. From Biberian [26bJ. It is worth emphasising that in this particular system, a priori

knowledge of the

structure of the adsorption compound AuPb

in contact by its (110) face with each of the 2 three faces of gold, in conjunction with the LEED and AES techniques, permits us to give

a complete description at each stage of epitaxy : first the formation of a compact monolayer of Pb, then growth in thickness of AuPb in Au and of Au in Pb,

2

with the simultaneous diffusion of Pb

5-VIIl CONCLUSION THE 2D-3D TRANSITION If it were possible to predict

a priori the growth mode following the scheme of

Bauer, knowing the interfacial energies, it would still be necessary to deal with the following difficult problem: how does the 2D-3D transition take place in the cases of layerby-layer growth, layer followed by crystallite growth, and alloy growth? We have attempted to answer this question in the preceding section by means of specific examples. Anticipating the conclusion, we can say that if growth occurs by a compact layer on a compact layer, the so-called Frank-van der Merwe mode,

the problem

depends simply on a greater or lesser variation of the matching parameter of A on B, with or without pseudomorphism. But in all cases a continuous compact layer transition is maintained.

148

In the case of an alloy the example of AuPb

suggests that growth occurs by compact 2 layers on compact layers, in such a way that the 2D interface always resembles the compact plane of the support. For the intermediate case, an adsorbed layer followed by growth of a 3D compound, we adopt the following idea: there is in general an incompatibility of structure or superstructure between the adsorption compound and the three-dimensional compound. A typical example is given by the study of Le Lay et al , on Ag/Si [30]. More characteristic examples occur in the series of studies of compounds from metal-gas interactions (sulphur and oxygen) described in other chapters. The mechanism can be summarized as follows a) formation of the 2D adsorbed layer; b) nucleation of the 3D compound on the defects of the adsorbed layer; c) disappearance of the adsorbed layer in favour of the 3D compound; d) possible pseudomorphism of the 3D compound (several layers) before reaching the 3D structure. We can speak of epitaxy when there is a transition between the compact plane of the substrate and a compact plane of a bulk crystal with a well

defined interface

in the

Fletcher or van cler Merwe sense, even if this interface includes several planes of both materials. REFERENCES I 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26a 26b

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