Table Of ContentCRYSTAL CHEMISTRY AND SEMICONDUCTION
in Transition Metal Binary Compounds
J. P. SUCHET
Centre National de la Recherche Scientifique, Paris
1971
A C A D E M IC PRESS New York and London
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Preface
Several generations of semiconductor materials can be distinguished:
(1) The elements Ge and Si, which brought about a scientific and industrial
revolution in the fifties.
(2) The "classic" binary, ternary, etc. compounds. Some of these are
already being used industrially (InSb, GaAs), and many are fairly familiar
(III V, IIVI). Research undoubtedly will continue for many years because of
their very large number. Although original devices have been constructed
from these materials, their impact has not been revolutionary.
(3) The "special" compounds: transition metal or rare earth compounds,
organic semiconductors, vitreous or liquid substances, etc. Here we are faced
with different^ semiconduction mechanisms which are still obscure, and
combinations of possibly unexpected properties.
The presently emerging generation of semiconductor crystals containing
magnetic atoms can be traced to research on oxides of mixed valency and the
development of magnetic ferrites in the immediate post-war years. Since these
crystals combine high permeability with transparency to electromagnetic
waves, they have recently been used in hyperfrequency devices. Such uses, in
fact, constitute the first practical application of magnetic semiconductors.
This book covers more generally the substances whose transport properties
are not typically metallic, and in which atomic magnetic moments exist. It
will be shown, in fact, that it is impossible to draw such neat boundaries
ix
X Preface
between semiconductor compounds and metallic alloys of transition elements
as for compounds of alkaline or alkaline-earth elements. In addition, there
is scarcely any difference between the effect of a ferromagnetic order and
that of an antiferromagnetic order on the transport properties. What is
more, this order always ends at a certain temperature, and it is very difficult
to ignore phenomena occurring at higher temperature (i.e., in the para-
magnetic region).
Oxide materials with a high energy gap have been studied fairly systematic-
ally, although recent discoveries, such as that of the ferroelectric material
Ni B 0 I, may be opening up further fields for research. In contrast, little
3 7 13
is known about antimonides, selenides, and tellurides. Their chemical proper-
ties and crystallographic structure are usually obvious, and in many cases,
their magnetism is defined. However, there is still lively controversy about
their transport properties, and the very definition of the semiconductor seems
to be far less precise. The wide range of phase homogeneity and the effect of
the stoichiometric ratio in all these substances give them a versatility not
inherent in conventional materials. However, scientists are handicapped in
dealing with these substances because of the absence of any book combining,
in a comprehensible form, the essential chemical and physical information
and a detailed analysis of existing experimental results. One of my aims has
been to fill this gap.
In Part Two all the experimental work on the electrical conductibility of
compounds of transition metals, rare earths, or actinides published since the
war is analyzed and summarized. I have tried to provide those embarking on
scientific research with a guide that may make it easier for them to approach
a body of writing that can sometimes be heavy going.
Part Three deals briefly with some areas in which applications may be
expected. It would be premature to devote any greater space to this. The
theoretical concepts needed for the construction of approximate models to
estimate the properties of new compounds are given in a condensed and
fairly original form in Part One.
To make clear the spirit in which this book has been written, I shall
briefly review the three separate activities that ensure the advancement of
science: understanding (for the research scientist), application (for the
engineer), and teaching (for the teacher). The research scientist gathers
experimental data, correlates them, deduces partial laws, and tries to construct
a working model. These procedures involve a certain amount of trial-and-
error work, and frequent backward steps. It is, therefore, pioneering work.
Tough industrial competition forces the engineer to apply the results of
research immediately, without awaiting their verification. The teacher, in more
basic courses, cannot run the risk of presenting concepts that may be subject
to radical modification. The scientific instruction that he provides for most of
Preface xi
his pupils is therefore based on research conducted 5 to 10 years earlier. In
this very rough scheme, this book is concerned with in the first stage—
understanding. It is intended primarily for young research workers wishing to
enter into this field, and secondarily for research engineers, who are investi-
gating the construction of new devices. Finally, this book will be of use to
teachers, who will themselves assess what they can include in their courses
without too much risk.
Solid state chemistry is a new branch of science, which came into existence
a few years ago in the United States as a result of the need to solve the
numerous practical problems connected with the synthesis and crystallization
of pure substances. Its rapid expansion has been due to close contact between
pure and applied research. It also involves a certain reaction against the
esoteric tendencies that often appear in solid state physics and nuclear
physics. One of the most enthralling aspects is the hope that one day it may be
possible to carry out, to order, the synthesis of compounds with the properties
required for a given application. However, this goal implies significant
advances in some fields of inorganic chemistry, and wider training of
theoreticians.
Acknowledgments
I should like to express my gratitude to my colleague, Francis Bailly, Charge de
Recherche at the C.N.R.S., for his active collaboration in the preparation of Part
One of this book.
I should like also to thank Dr. J. B. Goodenough, Group Leader in the Lincoln
Laboratory of M.I.T., Cambridge, Massachusetts, and Professor A. Wold of Brown
University, Providence, Rhode Island, for the comments they were kind enough to
make about the manuscript.
I must also thank Denis Mahaffey for his help in translating the original French
manuscript.
xiii
Symbols, Abbreviations, and Physical Constants
AB antibonding level
AO atomic orbital
A actinide element
B bonding level
c speed of light, 2.998 x 1010 cm sec-1; number of Lewis pairs formed by one
atom; height of the elementary cell (NiAs structure)
Cu C2, C, C normation coefficients
3 4
d electron with azimuthal quantum number 2
D electronic density; Madelung constant
e electron charge, 1.602 x 10"20 cgs or 10"19 C
e, e height of forbidden band gap (extrinsic excitation mechanism)
d a
e fused d,*-^ and d2 MOs
g z
E activation energy (transfer mechanism)
A
E Fermi level energy
F
E height of forbidden band gap (intrinsic excitation mechanism)
G
EPR electronic paramagnetic resonance
f electron with azimuthal quantum number 3
G Avogadro's number, 6.02 x 1023
h Planck's constant, 4.14 x 10"15 eV sec = 6.62 x 10~27 erg sec or 10"34 J sec
H hyperfine field (Mossbauer effect)
h
/ magnetization intensity
/ exchange integral of two electrons
e
k Boltzmann's constant, 8.62 x 10"5 eV °K"1 = 1.38 x 10"16 erg °K"1 or 10"23 J
o -i
K
k wave vector with module 2/r/A
XY
xvi Symbols, Abbreviations, and Physical Constants
K electron with principal quantum number 1
L electron with principal quantum number 2
L rare earth element (Sc, Y, or Ln)
LCOA linear combination of atomic orbitals
Ln lanthanide element (rare earth)
m mass of the electron "at rest," 9.109 x 10" 28 gm; covalent "charge" of the atom
m*/m effective mass of a carrier
M symbol for a metal
M electron with principal quantum number 3
MO molecular orbital method
n principal quantum number; ionic charge
N number of electrons per cubic centimeter
N electron with principal quantum number 4
NMR nuclear magnetic resonance
p electron with azimuthal quantum number 1
p any integer
p number of positive holes per cubic centimeter; oxygen pressure; electric
polarization
q effective charge of the atom "at rest"
r polar coordinate (radial); ionic radius
R Hall coefficient
H
R ordinary Hall coefficient
0
R extraordinary Hall coefficient
t
s electron with azimuthal quantum number 0
S atomic component of spin quantum numbers
t fused d, d, and d MOs
2g xy yz zx
T symbol for a transition metal
T temperature
v velocity of a particle
VB valence bond method
x trirectangular coordinate; fraction of crystallographic sites
X symbol for a metalloid
y trirectangular coordinate
z trirectangular coordinate
4> polar coordinate (geographical longitude)
a Seebeck coefficient
a, spin functions
a, /?, y, S, e phases of a diagram
S asphericity of the electronic distribution; isomeric shift (Mossbauer effect)
A energy difference between the d sublevels
e dielectric constant; quadrupolar interaction (Mossbauer effect)
(p amplitude of an AO wave function
A wavelength; ionicity parameter
A equilibrium ionicity of a bond
0
H Hall mobility of carriers
ju Bohr magneton
B
Symbols, Abbreviations, and Physical Constants xvii
p drift mobility of carriers
D
v frequency of an electromagnetic wave or associated wave; hopping frequency
(transfer mechanism)
7T, 7i types of bond with a symmetry plane (MO approach)
g u
p electrical resistivity
a electrical conductivity, 1 \p
tfg> o\i types of bond with a symmetry axis (MO approach)
0 polar coordinate (geographical latitude); Curie-Weiss parameter
\j/ amplitude of an MO wave function
y/+,y/- bonding and antibonding functions
/ magnetic susceptibility
I, II, III, etc. elements in the corresponding columns of the periodic table
1 eV = 8068 cm"1 = 23.063 kcal = 1.602 x 10~19 J or 10"12 erg
Chapter I From the Atom to the Molecule
1.1. ATOMIC ORBITAL FUNCTIONS
To avoid overburdening this book unnecessarily, it is assumed that the
reader is familiar with the basic principles of chemistry, i.e., the structure of the
atom and the periodic table. Those who need some reminder of these points
should refer to the classic works on the subject, such as the one by Moore [1.1].
Beginners might use the extremely simple and straightforward little book
written by Seel [1.2].
It is known that a particle (photon) has to be associated with an electro-
magnetic wave. The momentum (mv) attributed to a photon of energy E is,
according to Maxwell, (mv) = E/c = hv/c (where c is the speed of light,
h Planck's constant, and v the frequency). This gives us an expression for the
wavelength
X = h/(mv) (1.1)
In 1924, de Broglie proposed a generalization of this equation for electro-
magnetism, postulating that it also defined a wave of a new type associated with
any material particle of momentum mv (m mass and v velocity). Three years
later, experiments in electronic diffraction confirmed this bold concept.
The stationary state of a system vibrating in one dimension, such as a
vibrating cord, is described by a wave with an amplitude (p(x) a wavelength A,
9
and is a solution to the differential equation
(d2(p/dx2) + (4tt2/A2) = 0 (1.2)
If one accepts that this differential equation, well known in conventional
mechanics, applies to the associated wave imagined by de Broglie (Schrodinger's
3
