Venables J. Introduction to Surface and Thin Film Processes

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metastable 231 structure which is produced by cleaving, there are three domains.

This 23 1 structure, and its electronic structure, are described by Lüth (1993/5),

with the p-bonded chain model ﬁnding favor. There is also the possibility of anti-

phase boundaries, between domains which are in the same orientation, but which

are not registered identically to the underlying bulk structure.

boundary structures have been made, as set out brieﬂy by Chadi (1989, 1994).

Several writers have discussed the physical reasons behind such reconstructions.

We pursue this topic in chapter 7.

1.4.5 The famous 7

7 structure of Si(111)

This structure is described in many places and you cannot leave a course on surfaces, or

put down a book, without having realized what this amazing structure is. The question

of why nature chooses such a complex arrangement is absolutely fascinating, and we

will look at how people have thought about this in chapter 7. It was determined by a

combination of LEED, scanning tunneling microscopy (STM) and transmission high

energy electron diﬀraction (THEED) (Takayanagi et al. 1985). It has three structural

1.4 Introduction to surface and adsorbate reconstructions 27

Figure 1.19. Models of the Si(001) 231 structure: (a) dimer model after Chadi (1979), with

the dimerized atoms C and D as in the (132) cell in ﬁgure 1.18, but with a shifted origin.

Higher order, e.g. c(432) structures are formed if C and D are diﬀerent heights, and are

ordered alternately; (b) vacancy model after Poppendieck et al. (1978), with surface vacancies

in the two highest levels at V. Their c(432) structure also contained distortions in the third

layer; (c) conjugated chain model after Jona et al. (1977), with atoms E and F forming the

chain in a horizontal 冓110冔 direction, and considerable implied distortions between the two

highest levels.

VVV

–1/4

(a) (b) (c)

zero

+1/4

Level

units, dimers, adatoms and stacking faults, and is hence known as a DAS model. The 7

37 is just one possible structure of this type, all of which have odd numbers of multi-

ples between the surface and bulk meshes. The LEED or THEED patterns of the 737

structure contains 49 superstructure spots (or beams) of diﬀerent intensity, which

needed to be analyzed to solve the structure in detail.

1.4.6 Various ‘root-three’ structures

These structures arise in connection with metals and semi-metals (B, Cu, Ag, Au, In,

Sb, Pb, etc.) on the (111) face of semiconductors, and adsorption of gases on hexag-

onal layer compounds such as graphite. Here again we have three domains, but

they are positional, as well as sometimes orientational, in nature. One can put the

atoms in three positions on the substrate, but if you put them on one lattice (A),

the other two (B and C) are excluded, in the case of rare gases on graphite because

of the large size of the adatoms, as indicated earlier in ﬁgure 1.16. Studies of such

structures have a long history in statistical mechanics, as in the ‘three-state Potts

model’, where the three equivalent positions leads to a degenerate ground state, and

interesting higher temperature properties. Adsorption is discussed here in more detail

in chapter 4.

Figure 1.20 shows the reported structure of Ag adsorbed on Si or Ge(111), which

has been determined by surface X-ray diﬀraction (Howes et al. 1993), with the surface

and bulk lattices indicated. The interesting point in the present context about this Ag-

induced structure is to realize how much has to happen at the surface, to produce these

structures. Deposition of metal atoms alone is not nearly enough to produce it start-

ing from Si(111)737 or Ge(111)238. Substantial diﬀusion of both metal and semi-

conductor is required. The same consideration applies to producing Si(111) surfaces

by cleavage, which results in the 231 structure. This p-bonded structure, which does

not require any long range atomic motion is, however, metastable. Heating to around

250°C causes it to transform irreversibly into the 737, which is the equilibrium struc-

ture below the reversible 737 to ‘131’ transformation at 830°C; these transformations

involve major movement of atoms at the surface.

1.4.7 Polar semiconductors, such as GaAs(111)

When lower symmetry structures are combined with the lower symmetry of the

surface, various curious and interesting phenomena can occur. For example, GaAs

and related III–V semiconductors are cubic, but low symmetry (4

3m point group).

Looked at along the [111] direction, the atomic sequence is asymmetric, as in (Ga, As,

space) versus (As, Ga, space). This results in ‘polar faces’, with (111) being diﬀerent

from (1

). These are the A and B faces, and can have diﬀerent compositions and

charges on them. Atomic composition and surface reconstruction interact to cancel

out long range electric ﬁelds. For ‘non-polar’ faces, e.g. GaAs (110), this composi-

tion/charge imbalance does not occur, and these tend to have (131) surfaces. This

28 1 Introduction to surface processes

1.4 Introduction to surface and adsorbate reconstructions 29

Figure 1.20. (a) Top and (b) side views of the Ag/Ge(111) root-three structure, as determined

by surface X-ray diﬀraction, showing the spacings normal to the surface which have been

determined (after Howes et al. 1993, reproduced with permission).

(a)

(b)

again is a specialist topic, combining surface structure with surface electronics, that

we consider in chapter 7.

1.4.8 Ionic crystal structures, such as NaCl, CaF

, MgO or alumina

Here we have to consider the movement of the two diﬀerent charged ions, likely to be

in opposite directions, and the resulting charge balance in the presence of the dielec-

tric substrate. However, this ‘rumpling’ is often found to be remarkably small, typically

a few percent of the interplanar spacing; a ﬁrst point for a search of what is known

experimentally and theoretically is the book by Henrich & Cox (1996). A recent devel-

opment is to combine structural experiments (e.g. LEED) on ultra-thin ﬁlms grown on

conducting substrates, to avoid problems of charging, with ab initio calculation. Some

of these methods and results can be found in the atlas of Watson et al. (1996), review

chapters in King & Woodruﬀ (1997) and a 1999 conference proceedings on The Surface

Science of Metal Oxides published as Faraday Disc. Chem. Soc. 114. Grazing incidence

X-ray scattering is also helping to determine structures (Renaud 1998). A notable

exception to the general rule is alumina (A1

), where the surface oxygen ion relaxa-

tions have been calculated to reach around 50% of the layer spacing on the hexagonal

(0001) face (Verdozzi et al. 1999). But are we getting ahead of ourselves: you can see

how soon we need to read the original literature, but we do need some more back-

ground ﬁrst!

1.5 Introduction to surface electronics

Here we are concerned only to deﬁne and understand a few terms which will be used

in a general context. The terms which we will need include the following.

1.5.1 Work function,

The work function is the energy, typically a few electronvolts, required to move an elec-

tron from the Fermi Level, E

, to the vacuum level,E

, as shown in ﬁgure 1.21(a). The

work function depends on the crystal face {hkl} and rough surfaces typically have

lower

, as discussed later in section 6.1.

1.5.2 Electron afﬁnity,

, and ionization potential

Both of these would be the same for a metal, and equal to

. But for a semiconductor

or insulator, they are diﬀerent. The electron aﬃnity

is the diﬀerence between the

vacuum level E

, and the bottom of the conduction band E

, as shown in ﬁgure 1.21(b).

The ionization potential

is E

, where E

is the top of the valence band. These

terms are not speciﬁc to surfaces: they are also used for atoms and molecules generally,

as the energy level which (a) the next electron goes into, and (b) the last electron comes

from.

30 1 Introduction to surface processes

1.5.3 Surface states and related ideas

A surface state is a state localized at the surface, which decays exponentially into the

bulk, but which may travel along the surface. The wave function is typically of the form

⬇ u(r)exp (2i k

⬜

|z|) exp (i k

r), (1.18)

where, for a state in the band gap, k

⬜

is complex, decaying away from the surface on

both sides, as shown in ﬁgure 1.22(a). Such a state is called a resonance if it overlaps

with a bulk band, as then it may have an increased amplitude at the surface, but evolves

continuously into a bulk state. A surface plasmon is a collective excitation located at the

surface, with frequency typically

/冑2, where

is the frequency of a bulk plasmon.

1.5 Introduction to surface electronics 31

Figure 1.21. Schematic diagrams of (a) the work function,

; (b) the electron aﬃnity,

and

ionization potential

, both in relation to the vacuum level E

, the Fermi energy E

, and

conduction and valence band edges E

and E

(a) (b)

Figure 1.22. Schematic diagrams of: (a) a surface state deﬁned by wave vector k

, and

⬜

; (b) the surface Brillouin zone and 2D reciprocal lattice vector G

for the 冑33冑3R30°

structure, plotted in the same orientation as the real (xenon) lattice of ﬁgure 1.16.

1.5.4 Surface Brillouin zone

A surface state takes the form of a Bloch wave in the two dimensions of the surface, in

which there can be energy dispersion as a function of the k

vector. For electrons cross-

ing the surface barrier, k

is conserved, k

⬜

is not. The k

conservation is to within a 2D

reciprocal lattice vector, i.e. 6 G

. This is the theoretical basis of (electron and other)

diﬀraction from surfaces. For electrons there are two states contained in the surface

Brillouin zone, which is illustrated for the hexagonal lattice of the 冑33冑3R30° struc-

ture in ﬁgure 1.22(b).

1.5.5 Band bending, due to surface states

In a semiconductor, the bands can be bent near the surface due to surface states. Under

zero bias, the Fermi level has to be ‘level’, and this level typically goes through the

surface states which lie in the band gap. Thus one can convince oneself that a p-type

semiconductor has bands that are bent downwards as the surface is approached from

inside the material, as shown in ﬁgure 1.23(a). This leads to a reduction in the electron

aﬃnity. Some materials (e.g. Cs/p-type GaAs) can even be activated to negative elec-

tron aﬃnity, and such NEA materials form a potent source of electrons, which can also

be spin-polarized as a result of the band structure.

1.5.6 The image force

You will recall from elementary electrostatics that a charge outside a conducting plane

has a ﬁeld on it equivalent to that produced by a ﬁctitious image charge, as sketched in

ﬁgure 1.23(b). The corresponding potential felt by the electron, V(z)52e/4z. For a die-

lectric, with permitivity «, there is also a (reduced) potential V(z)52(e/4z) («21)/ («1

1). It is often useful to think of metals as the limit «→`, and vacuum as «→1. Typical

semiconductors have «⬃10, with «511.7 for Si and 16 for Ge; so semiconductors and

metals are fairly similar as far as dielectric response is concerned, even though they are

not at all similar in respect of electrical conductivity.

32 1 Introduction to surface processes

Figure 1.23. Schematic diagrams of: (a) band bending due to a surface state on a p-type

semiconductor; (b) the E-ﬁeld between an electron at position z and a metal surface is the

same as that produced by a positive image charge at 2z.

(a)

(b)

–

= 0

1.5.7 Screening

The above description emphasizes the importance of screening, in general, and also in

connection with surfaces. We can also notice the very diﬀerent length scales involved

in screening, from atomic dimensions in metals, (2k

)

, increasing through narrow

and wide band gap semiconductors to insulators, and vacuum; there is no screening (at

our type of energies!), unless many ions and electrons are present ( i.e. in a plasma). In

general, nature tries very hard to remove long range (electric and magnetic) ﬁelds,

which contribute unwanted macroscopic energies. We will come back to this point,

which runs throughout the physics of defects; in this sense, the surface is simply

another defect with a planar geometry.

Further reading for chapter 1

Adamson, A.W. (1990) Physical Chemistry of Surfaces (Wiley, 5th Edn) chapters 2

and 3.

Blakely, J.W. (1973) Introduction to the Properties of Crystal Surfaces (Pergamon) chap-

ters 1 and 3.

Clarke, L.J. (1985) Surface Crystallography: an Introduction to Low Energy Electron

Diﬀraction (John Wiley) chapters 1, 2 and 7.

Desjonquères, M.C. & D. Spanjaard (1996) Concepts in Surface Physics (Springer)

chapter 1.

Gibbs, J.W. (1928, 1948, 1957) Collected Works, vol. 1 (Yale Univerity Press, New

Haven); reproduced as (1961) The Scientiﬁc Papers, vol. 1 (Dover Reprint Series,

New York).

Henrich, V.E. & P.A. Cox (1996) The Surface Science of Metal Oxides (Cambridge

University Press) chapters 1, 2.

Hudson, J.B. (1992) Surface Science: an Introduction (Butterworth-Heinemann) chap-

ters 1, 3–5, 17.

Kelly, A. & G.W. Groves (1970) Crystallography and Crystal Defects (Longman) chap-

ters 1–3.

Lüth, H. (1993/5) Surfaces and Interfaces of Solid Surfaces (3rd Edn, Springer) chap-

ters 3, 6.1, 6.2.

Prutton, M. (1994) Introduction to Surface Physics (Oxford University Press) chapters

3 and 4.

Sutton, A.P. & R.W. Balluﬃ (1995) Interfaces in Crystalline Materials (Oxford

University Press) chapter 5.

Problems for chapter 1

These problems test ideas of bond counting, elementary statistical mechanics,

diﬀusion and surface structure. When set in conjunction with a course, they have typ-

ically not been done ‘cold’, but have been used to open a discussion on topics which

are best attempted through problem solving rather than by lecturing. Note that there

Problems for chapter 1 33

are further problems of a similar type in Desjonquères & Spanjaard (1996, chapters 2

and 3).

Problem 1.1. Bond counting and surface (internal) energies of a static

lattice

Consider the (012) face on a Kossel (simple cubic) crystal with six nearest neighbor

bonds.

(a) Use the analysis of section 1.2 to consider the surface energy of this crystal in terms

of the sublimation energy L and the lattice parameter a. Find the ratio of the

surface energy of the (012) and the (001) face.

(b) Repeat this exercise for the (012) face of a f.c.c. crystal with 12 nearest neighbor

bonds. Compare your result with ﬁgures 1.6 and 1.8, and comment on the relative

values.

Note: this problem can be done most readily by drawing the structure and counting

bonds. There is a more general vector-based approach by MacKenzie et al. (1962), but

this is not simple for a ﬁrst try, or for complex structures. If the stereograms (ﬁgure 1.8)

are not familiar, see Kelly & Groves (1970) or another crystallography book, or obtain

web-based information via Appendix D.

Problem 1.2. Local equilibrium at the surface of a crystal at

temperature T

Consider the (001) face of an f.c.c. crystal with 12 nearest neighbor bonds, and (small

concentrations of) adatoms and vacancies at this surface. The sublimation energy is

3eV and the frequency factor is 10 THz. Use the appropriate formulations of section

1.3 to do the following.

(a) Construct a diﬀerential equation to describe the processes of arrival of atoms from,

the and re-evaporation into the vapor, to ﬁnd the equilibrium concentration of

adatoms in monolayer (ML) units. Find the adatom concentration at T51000 K

if the arrival rate R51 ML/s.

(b) Use the chemical potential formulation to express the local equilibrium between

the bulk crystal and the surface adatoms, to obtain their equilibrium concentra-

tions at the same temperature, ignoring arrival from, or sublimation to, the vapor.

Hence decide whether the case (a) corresponds to under- or over-saturation, and

calculate the thermodynamic driving force in units of kT.

Problem 1.3. Effects of vacancies and/or lattice vibrations on the

sublimation pressure

Consider the model of the vapor pressure of a solid described in section 1.3, table 1.1

and ﬁgure 1.9. This model neglects the eﬀects of vacancies, and the model of lattice

vibrations is only a ﬁrst approximation.

34 1 Introduction to surface processes

(a) How might you consider the eﬀects of vacancies, which are expected to have an

energy of 1 eV in Ag, and reduce the frequency of atomic vibration in the vicinity

of the neighbors of the vacancy to 80% of the value in the bulk?

(b) How might you consider the eﬀect of other lattice dynamical models, for example

the cell model, discussed in more detail in chapter 4.2?

Note: this problem is useful for a discussion of points of principle and practicality, and

could be expanded via detailed computation for a course project.

Problem 1.4. Crystal growth at steps and the condensation coefﬁcient

Consider a surface consisting of terraces of width d, separated by monatomic height

steps.

(a) Set up a one-dimensional rate-diﬀusion equation describing the diﬀusion of

adatoms to the steps in the presence of both adatom arrival and desorption.

Explain what boundary conditions you use at the steps.

(b) Show that the steady state proﬁle of adatoms between the steps depends on the

ratio cosh (x/x

)/ cosh(d/2x

), where x

is the BCF length (section 1.3). Show that

the fraction of atoms which get incorporated into the steps, the condensation

coeﬃcient, is given by (2x

/d)tanh(d/2x

). Evaluate the limits (2x

/d) ..1 and ,,1,

and give reasons why these limits are sensible.

Problem 1.5. Surface reconstructions of particular crystals

Consider a surface structure in which you are interested. In metals this could be W and

Mo(100) which have transitions below room temperature to 231, and 231-like struc-

tures, or in semiconductors the diﬀerence between 231, c432 and p 232 superstruc-

tures on Si or GaAs(100). Use your chosen system to explore the relation between the

structure, the symmetry and size of the surface unit cell, and the diﬀraction pattern,

most obviously the LEED patterns in the literature.

Problems for chapter 1 35

2 Surfaces in vacuum: ultra-high

vacuum techniques and processes

This chapter presents a practically oriented introduction to modern vacuum tech-

niques, in the context of studying surface and thin ﬁlm processes. The following sec-

tions review the science behind the technologies, and give a few worked examples,

which we refer to later. Section 2.1 reviews the kinetic theory concepts on which

vacuum systems are based; section 2.2 outlines the basic ideas involved in ultra-high

vacuum (UHV) system design. The next section 2.3 deals with vacuum system hard-

ware, in order to make sense of the large range of chambers, ﬂanges, pumps and gauges

which make up a complete system. It is assumed that the reader is already familiar with

a basic vacuum system and its components, so that only a few ﬁgures of apparatus are

needed. Section 2.4 describes the procedures used in performing experiments under

UHV conditions, and discusses some of the challenges involved in scaling these proce-

dures up to manufacturing processes. Finally, section 2.5 brieﬂy lists some of the more

commonly used thin ﬁlm deposition techniques, and describes where more information

on such processes can be found.

2.1 Kinetic theory concepts

2.1.1 Arrival rate of atoms at a surface

The arrival rate R of atoms at a surface in a vacuum chamber is related to the molec-

ular density n, the mean speed of the molecules v¯ and the pressure p, via the standard

kinetic theory formulae (Dushman & Laﬀerty 1992, Hudson 1992)

R5nv¯/4 per unit area5p/(2pmkT)

1/2

; (2.1)

you may also need n5p/kT and v¯ 5(8kT/pm)

1/2

, which are required to connect the two

versions of the above formula. The notation can be confusing: R is sometimes called

the deposition ﬂux, F, and v¯ is sometimes written v, c or c¯.

Now let us work through an example to ﬁnd the molecular density n, the mean free

path

, and the monolayer arrival time,

. We take, as a typical example, the residual

gas in a vacuum system, which is often a mixture of CO, H

and H

O; the following

calculations are for carbon monoxide, CO, which has molecular weight 28. Then the