Venables J. Introduction to Surface and Thin Film Processes
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ESR: electron spin resonance [8.1.3]
FEM, FES: field emission microscopy, spectroscopy [6.2.3]
FET: field effect transistor [8.4.2]
FIM: field ion microscopy [3.1.3, 5.4.2]
GGA: generalized gradient approximation [6.1.1]
GMR: giant magneto-resistance [8.3.3]
GSMBE: gas source MBE [2.5.3]
HAS: helium atom scattering [4.4.4, 5.4.3]
HEMT: high electron mobility transistor [8.2.4]
HREELS: high resolution electron energy loss spectroscopy [3.3.1]
HOLZ: higher-order Laue zone [3.2.2]
IA-IR: incommensurate aligned- incommensurate rotated (phase or transition) [4.4.2]
IBAD: ion beam assisted deposition [2.5.4]
IBSD: ion beam sputter deposition [2.5.4]
IC: integrated circuit [9.1]
ICB: ionized cluster beam [2.5.4]
ICISS: impact collision ion scattering spectroscopy [3.1.2]
I–V: current (I)–voltage (V), as in LEED I–V curves [3.2.1]
KKR: Korringa–Kohn–Rostoker (band structure method) [6.1.2]
KMC: kinetic Monte Carlo simulations [5.2]
KPZ: Kardar, Parisi & Zhang; an equation used in crystal growth modelling [7.3.4]
KTHNY: papers by Kosterlitz, Thouless, Halperin, Nelson & Young [4.4.2]
L: Langmuir (unit of gas dose) [4.5.4]
LDA: local density approximation [6.1.1]
LDOS: local density of states [4.5.2]
LEED: low energy electron diffraction [1.4, 3.2]
LEEM: low energy electron microscopy [3.1.3, 3.2]
LEP: large electron positron (ring) at CERN [2.3.2]
LPCVD: low pressure CVD [2.5.5]
LSD: local spin density [6.3.4]
MBE: molecular beam epitaxy [2.5.3]
MC: Monte Carlo (simulation method) [1.3]
MCD: magnetic circular dichroism [6.3.3]
MD: molecular dynamics (simulation method) [1.4.3, 4.5.2]
MFM: magnetic force microscopy [6.3.3]
MIDAS: a microscope for imaging, diffraction and analysis of surfaces [3.5.3, 6.3.3]
MIGS: metal induced gap states [8.2.1]
ML: monolayer [2.1.4] (do not confuse with mega (M) Langmuir (L))
MOKE: magneto-optical Kerr effect [6.3.3]; SMOKE is MOKE applied to surfaces.
MOMBE: metal-organic MBE [2.5.3]
MOS: metal-oxide-semiconductor (device) [8.1, 9.1]
MQW: multiple quantum well [7.3.2, 8.2.3]
MTP: multiply twinned particle [4.5.4]
NEA: negative electron affinity [1.5.5, 6.3.3]
List of acronyms 307
OMVPE: organo-metallic vapor phase epitaxy [2.5.5]
OPW: Orthogonalized plane waves (band structure method) [6.1.2]
PBN: pyrolytic boron nitride [2.5.2]
PEEM: photo-electron emission microscopy [3.1.3]
PECVD: plasma enhanced CVD [2.5.5]
PLD: pulsed laser deposition [2.5.2]
PTFE: poly-tetrafluor ethylene [2.4.4, Appendix H]
QMS: quadrupole mass spectrometer [2.3.5]
RBS: Rutherford backscattering spectrometry [3.4.2]
REM: reflection electron microscopy [3.1.3]
RGA: residual gas analyzer [2.3.5]
RHEED: reflection high energy electron diffraction [2.5.3, 3.1.3, 3.2.2]
SAM: scanning Auger microscopy [3.5.1]; self-assembled monolayer [8.4.2]
SDW: static distortion wave [4.4.2]
SEM: scanning electron microscopy [3.1.3, 3.5.1]
SEMPA: scanning electron microscopy with polarization analysis [6.3.3]
SI: système internationale (of units) [2.1.1, Appendix C]
SIMS: secondary ion mass spectrometry [8.1.3]
SK: Stranski-Krastanov (growth mode) [5.1.3, 5.4.1]
SMOKE: surface magneto-optical Kerr effect [6.3.3]
SMP: small metal particle [2.4.4, 4.5.4]
SNOM: scanning near-field optical microscopy [3.1.3]
SNR: signal to noise ratio [3.1.3, problem 3.3]
SOS: solid on solid (model) [1.3.2]
SPA: spot profile analysis, as in SPA-LEED [3.2.1] or SPA-RHEED [3.2.2]
SPLEEM: spin-polarized low energy electron microscopy [6.3.3]
STEM: scanning transmission electron microscopy [3.1.3]
STM: scanning tunneling microscopy [1.4.5, 3.1.3]
TDS: thermal desorption spectroscopy [4.4.4]
TEA: triethylaluminum [2.5.3]
TEG: triethylgallium [2.5.3]
TEM: transmission electron microscopy [3.1.3]
TFE: thermal field emisison [6.2.3]
THEED: transmission high energy electron diffraction [1.4.5, 3.1.3]
TLK: terrace ledge kink (model) [1.2]
TSP: titanium sublimation pump [2.3.3]
TXRF: total reflection X-ray fluorescence [8.1.3]
UHV: ultra high vacuum [2]
UK: United Kingdom [2.1]
UPS: ultra-violet photoelectron spectroscopy [3.3.1]
VBO: valence band offset [8.2.3]
VdW: Van der Waals (interactions or forces) [4.1, 5.3.2]
XPS: X-ray photoelectron spectroscopy [3.3.1]
ZOLZ: zero-order Laue zone [3.2.2]
308 Appendix B
Appendix C
Units and conversion factors
To convert a quantity expressed in the units listed in the first column to those listed in
the third column, multiply by the number given in the second column. The SI unit is
given in brackets for each quantity. The values with (61
s
) error bars are taken or
deduced from the CODATA 1986 report (Cohen & Taylor 1987, 1998) as recom-
mended by NIST in the USA and NPL in the UK. Note that it is not required to keep
the full accuracy of these data to do the typical calculations encountered in this book,
but it is helpful to have the extra decimal places were one to need them.
Mutiplication factors
The standard prefix is used for multiples and sub-multiples of units. These are shown
in Table C1 below.
Table C1
Factor by which
unit is multiplied Prefix Symbol
10
12
tera T
10
9
giga G
10
6
mega M
10
3
kilo k
10
22
centi c
10
23
milli m
10
26
micro m
10
29
nano n
10
212
pico p
Length (m)
m10
10
Å
Å 0.1 nm
kX (Cu K
a
1
X-ray unit) 1.00207789 (670) Å
a.u. (Bohr radius a
0
) 0.529177249 (624) Å
inch 2.54 cm
309
Mass (kg)
m (electron mass) 9.1093897 (654)310
231
kg
u (atomic mass unit) 1.6605402 (610)310
227
kg
lb (pound) 0.45359237 kg
Time (s)
min 60 s
h 3600 s
day (mean solar) 86400 s
yr (sidereal) 3.1558310
7
s
Angle (deg
5
60 min
5
3600 s of arc)
rad 57.295779 deg
rad 3437.7468 min
rad 206264.81 s
Force (N) and pressure (pascal (Pa)
5
N·m
2
2
)
dyne 10
25
N
mbar 100 Pa (N·m
22
)
bar 10
6
dynes·cm
22
Atm. 1.01325 bar
torr (mm Hg) 1.33322 mbar
pound weight (or force) 4.4822 N
ditto/square inch, i.e. (p.s.i) 68.9476 mbar
Energy (J)
erg 10
27
J
cal 4.18400 J
litre-atm. 101.328 J
eV 1.60217733 ( 649)310
219
J
a.u. (Hartrees) 4.3597482 ( 626)310
218
J
a.u. (Hartrees) 27.2113961 ( 681) eV
Energy related units
Energies are expressed in different units in different disciplines, and we also often need
energies expressed in energies per unit area, per mole or per molecule.
310 Appendix C
Surface energy (J·m
2
2
)
eV·nm
22
0.160217733 ( 649) J·m
22
eV·Å
22
100 eV·nm
22
Energy to temperature
Via E5kT, where Boltzmann’s constant k51.380658 (612)310
223
J·K
21
. This con-
version is useful for energy values in eV which occur in Arrhenius expressions
exp(2E/kT).
eV 1.160444 (610)310
4
K
K 1.380658 (612)310
223
J
Energy to frequency
Via E5h
n
, where Planck’s constant h56.6260755 (640)310
234
J·s. This conversion
is needed in discussing (lattice) vibrations.
eV 2.4179884 (67)310
14
Hz
meV 0.24179884 (67) THz
Energy to wavenumber
Via E5hc/
l
, where the velocity of light c52.99792458310
8
m·s
21
exactly. This con-
version is often needed in (infrared) spectroscopy.
eV 0.80655411 (624)310
6
m
21
meV 8.0655411 (624) cm
21
Energy per mole, or per molecule (kJ·kmol
2
1
)
Energies of molecules (or atoms) can be expressed in units such as kJ·kmol
21
, J·mol
21
,
kcal·mol
21
, K/molecule, ergs/molecule, eV/molecule etc. These are all related via the
energy conversion table above and N
A
k5R58.314510 (670) J·mol
21
·K
21
, where
Avogadro’s number N
A
56.0221367 (636)310
23
mol
21
. Note: using kmol
21
means the
exponent is 26 rather than 23 in this expression, but the value of R stays the same if we
use both kJ and kmol
21
.
E (kJ·kmol
21
)1 E (J·mol
21
)
E/R (K·mol
21
)1 E (K/molecule)
E/k (K/molecule) 8.314510 (670) E (J·mol
21
)
E/k (K/molecule) 1.98722 (62) E (cal·mol
21
)
E (eV/molecule) 23.060 E (kcal·mol
21
)
E (eV/molecule) 96.485 E (kJ·mol
21
)
Units and conversion factors 311
Appendix D
Resources on the web or CD-ROM
Many resources are available on the World Wide Web (web for short) and some selected
resources are available on CD-ROM. The advantages of the latter are immediate local
availability and hence speed of access, but they lack the flexibility of the web, and typ-
ically cost real money. However, the disadvantage of referring to materials on the web
is that they are not under one’s own control; hence information may be out of date, and
there can be no guarantee of accuracy. A partial solution to this problem is to con-
struct one’s own web page in the form of a ‘portal’ to relevant web sites, and only to
link to those sites which have been created by colleagues whose work one trusts/
admires. I plan to keep my site active for the immediate future, at the address http://ven-
ables.asu.edu/grad/appweb1.html which is accessible from my home page http://ven-
ables.asu.edu/index.html as Web-based resources. The initial appearance of this page is
shown in figure D.1 below. The web-teaching experiences which lead to the construc-
tion of such pages are described by Venables (1998).
Potentially relevant resources on CD-ROM include the following:
(1) The NIST Surface structure database. Details are accessible via my page on data
bases at http://venables.asu.edu/grad/appdat1.html
(2) The Matter project. This CD-ROM consists of a series of modules for teaching
Materials Science to undergraduates, produced by P.J. Goodhew and co-workers,
and available from Chapman and Hall as version 2.1 (1998). Many of these
modules are useful as self-study materials for graduate students in other disciplines
who need to know what materials science is about. The crystallography modules
are described in print by Goodhew & Fretwell (1998).
(3) The VIMS CD-ROM. This CD-ROM (Visualization in Materials Science) has
been produced by J.C. Russ and co-workers since 1995, and is published by PWS
Publishing. It is widely used for undergraduate teaching in materials science.
(4) Advanced Computing in Electron Microscopy. CD-ROMs are marketed with spe-
cialist books on occasion, as in this text by Kirkland (1998), giving actual programs
for simulating high resolution electron microscope images.
312
Resources on the web or CD-ROM 313
Figure D.1. Web-based resources available from my home page at
http://venables.asu.edu/grad/appweb1.html
Appendix E
Useful thermodynamic
relationships
This book assumes a familiarity with thermodynamics and statistical mechanics at the
level of an undergraduate course in Physics, Chemistry, Materials Science or a related
discipline. However, for many readers these topics may not reside in foreground memory.
This appendix is divided by chapter, indicating outline arguments, and giving references
to places where one can brush up on topics which are needed to understand the text.
E.1 Thermodynamic laws and potentials (chapter 1)
The three laws of thermodynamics encompass: the conservation of energy, the rela-
tionship between heat and work, and the zero of entropy at the absolute zero of tem-
perature. Conservation of energy (the first law) is written as
DU5Q1DW, (E.1)
where the change in internal energy of the system DU comprises the heat added to it Q
plus the work done on it DW. The partition of DU into Q and DW is not unique, but
depends on the way the system changes, e.g. from one temperature or volume to
another, i.e. it depends on the path, and is not a ‘function of state’. However, in a rever-
sible, or quasi-static, change these quantities are well determined, and we can define an
infinitesimal change in entropy, dS such that dU5TdS and dW52pdV, where p and
T are the pressure and temperature respectively.
Inserting these quantities into (E.1) leads to the equation for dU, which incorporates
the second law into the first as
dU5TdS2pdV. (E.2)
This is the first equation involving a thermodynamic potential U, and can be used to
derive thermodynamic quantities at constant volume or constant entropy. For
example, the specific heat at constant volume C
V
is by definition
C
V
5(U/T)
V
5T(S/
T)
V
(E.3)
or the bulk modulus at constant entropy B
S
is
314
B
S
52V(p/V)
S
51V(
2
U/V
2
)
S
. (E.4)
The relations obtained via different second partial derivatives involve consistency
checks known as the four Maxwell relations; the one which follows from (E.2) is
(T/V)
S
52(p/S)
V
.
The above considerations apply to constant numbers of particles, N, but if N is itself
a variable, then there is an extra term in (E.2)1
m
dN, where
m
is known as the chemi-
cal potential. This is the internal energy at which the particle is added to the system.
When we are considering isolated systems at constant volume V and particle number
N, the thermodynamic potential U is constant, and
dU5TdS2pdV1
m
dN. (E.5)
This is what is meant by the entropy being maximized (dS50) in an isolated system at
equilibrium, the second law of thermodynamics having shown that dS$dQ/T. The
corresponding microscopic distribution is the micro-canonical ensemble of statistical
mechanics. Consideration of constant pressure processes leads to definition of the
enthalpy, H5U1pV, so that
dH5TdS1Vdp1
m
dN; (E.6)
the enthalpy is useful in describing thermally isolated constant pressure processes.
Often these correspond to (irreversible) flow processes, such as the flow of air over a
wing or through a nozzle valve. Analogous to (E.3) we can now define the specific heat
at constant pressure C
p
as
C
p
5(H/T)
p
5T(S/T)
p
. (E.7)
The Maxwell relation which follows from (E.6) is (T/p)
S
52(V/S)
p
.
Mostly we are concerned with systems at a given temperature, or in more technical
terms ‘in contact with a heat bath at temperature T’. For these the Helmholtz free
energy F5U 2TS and the Gibbs free energy G5U2TS1pV have been devised. These
are particularly useful for discussing processes at constant volume and constant pres-
sure respectively. Correspondingly we have
and dF52SdT2pdV1
m
dN, (E.8)
and dG5– SdT1Vdp1
m
dN. (E.9)
In particular, F is minimum at constant (T, V and N) and G is minimum at constant
(T, p and N), and the corresponding microscopic distribution is the Canonical ensem-
ble. Section 1.1 is concerned with discussing the additional terms which arise when the
area A of a surface is an additional thermodynamic variable.
The third law is concerned with establishing the zero of entropy for systems in equi-
librium at the absolute zero of temperature (0 K). Since physical effects result only
from differences in entropy and absolute zero cannot be reached, this may appear a
bit academic. However, it has a certain fascination in the context of phase changes,
especially since kinetics compete with thermodynamics, and can become very sluggish
at low temperature. An example would be the entropy difference between solid N
2
and
Useful thermodynamic relationships 315
solid CO, which have the same crystal structure, Pa3. At absolute zero, CO should
undergo head to tail ordering, whereas N
2
molecules, with identical ends, should not.
However, the barriers to rotational ordering become completely unsurmountable at
low temperatures, which leaves solid CO with non-zero entropy at 0 K. This argument
can get quite complex if we consider nuclear ordering as well, e.g. in a system of
14
N–
15
N molecules.
There are many, many books on thermodynamics and statistical mechanics, and it
is perhaps unwise to single out particular ones. All of them will contain the above
material, but may have slightly different notation. For example E may be used for inter-
nal energy instead of U, and upper (P) or lower (p) case for pressure. Books I have
found useful include Hill (1960) and Mandl (1988); for a modern introduction, see
Baierlein (1999). For a detailed list of thermodynamic quantities, and evaluation of
properties which use the statistical mechanics of lattice vibrations in various models,
see Klein & Venables (1976, 1977) especially chapters 6 (M.L. Klein & T.R. Koehler),
11 (R.K. Crawford), 12 (P. Korpiun & E. Lüscher) and 13 (C.A. Swenson).
E.2 Phase equilibria and phase transitions (chapter 4)
Two phases (subscripts 1 and 2) in equilibrium are described by the condition
m
1
5
m
2
. In addition, adsorbed layers in equilibrium with the vapor phase have
m
1
5
m
2
5
m
v
; the spreading pressures also have to be equal:
F
1
5
F
2
. Thus a phase transition
line on a diagram such as figure 4.10 is defined thermodynamically by d
m
1
5d
m
2
5
d
m
v
. Using
m
x
5h
x
2Ts
x
for the phases x51, 2 and
m
v
5h
v
2T
s
1kTln(p), we can
obtain via (4.8)
d(
m
x
/T)5h
x
d(1/T)2 (1/Tn
x
)d
F
(E.10a)
and
d(
m
v
/T)5h
v
d(1/T)1kd(ln p), (E.10b)
in terms of the enthalpy per atom or molecule h, and the areal density of phase x, n
x
5N
x
/A. It follows that we can express ln p for transition lines as a function of 1/T
involving differences as
ln p5 (E.11)
and hence
kd(ln p)/d(1/T)52h
v
1 . (E.12)
The isosteric heat of adsorption, which is the slope of the lines of constant coverage
within a given phase, was discussed in section 4.3.1. It can be cast in a similar form to
(E.12) as
2q
st
5k[d(ln p)/d(1/T)]
N
52h
v
1[(nu)/n]
A,T,V
(E.13)
n
2
u
2
2 n
1
u
1
(n
2
2 n
1
)
冤
2 n
2
(h
v
2 h
2
) 1 n
1
(h
v
2 h
1
)
(n
2
2 n
1
)kT
冥
1
冤
n
2
(
s
2 s
2
) 1 n
1
(
s
2 s
1
)
(n
2
2 n
1
)k
冥
316 Appendix E