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This subchapter means to show that
even the seemingly most simple defects - vacancies and interstitials - can get
pretty complex in real crystals. This is already true for the most
simple real crystal, the fcc lattice with one atom as a base, and very
true for fcc lattices with two identical atoms as a base, i.e. Si or
diamond. In really complicated crystals we
have at least as many types of vacancies and interstitials as there are
different atoms - it's easy to lose perspective. |
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To give just two examples of real life with
point defects: In the seventies and eighties a bitter war was fought concerning
the precise nature of the self-interstitial in elemental fcc crystals.
The main opponents where two large German research institutes - the dispute was
never really settled. |
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Since about 1975 we have a world-wide
dispute still going on concerning the nature of the intrinsic point defects in
Si (and pretty much all other important semiconductors). We learn from
this that even point defects are not easy to understand. |
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You may consider this sub-chapter as
an overture to the point defect part of course: Some themes touched upon here
will be be taken up in full splendor there. Now lets look at some phenomena
related to point defects |
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We start with a simple
vacancy or
interstitial in (fcc)
crystals which exists in thermal
equilibrium and ask a few questions (which are mostly easily extended to
other types of crystals): |
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What is the atomic structure of point defects? This seems to
be an easy question for vacancies - just remove an atom! |
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But how "big", how
extended is the vacancy?
After all, the neighboring atoms may be involved too. Nothing requires you to
have only simple thoughts - lets think in a complicated way and make a vacancy
by removing 11 atoms and filling the void with 10 atoms -
somehow. You have a vacancy. What is the structure now? |
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How about interstitials? Lets not be
unsophisticated either. Here we could fill our 11-atom-hole with
12 atoms. We now have some kind of "extended" interstitial? Does this happen? (Who knows, its possibly true in
Si). How can we discriminate between "localized" and
"extended" point defects? |
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With interstitials you have several possibilities
to put them in a lattice. You may choose the
dumbbell configuration,
i.e. you put two atoms in the space of one with some symmetry conserved, or you
may put it in the octahedra or
tetrahedra interstitial
position. Perhaps surprisingly, there is still one more possibility: |
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The
"crowdion", which is supposed to
exist as a metastable form of interstitials at low temperatures and which was
the subject of the "war" mentioned above. |
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Then we have the
extended interstitial made following
the general recipe given above, and which is believed by some (including me) to
exist at high temperatures in Si. Lets see what this looks like: |
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Next, we may have to consider
the charge state of the point defects
(important in semiconductors and ionic crystals). |
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Point defects in ionic crystals, in general,
must be charged for reasons of charge neutrality. You cannot, e.g. form
Na-vacancies by removing Na+ ions without either
giving the resulting vacancy a positive charge or depositing some positive
charges somewhere else. |
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In semiconductors the charge state is coupled to
the energy levels introduced by a point defects, its position in the
bandgap and the prevalent
Fermi energy. If the Fermi energy changes, so does, perhaps, the charge state.
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Now we might have a
coupling between charge state and
structure. And this may lead to an athermal diffusion mechanisms;
something really strange (after Bourgoin). |
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Just an arbitrary example to illustrate this: The
neutral interstitial sits in the octahedra
site, the positively charged one in the
tetrahedra site (see below). Whenever the charge states changes (e.g. because
its energy level is close to the Fermi energy or because you irradiate the
specimen with electrons), it will jump to one of the nearest equivalent
positions - in other word it diffuses independently of
the temperature. |
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These examples should convince you
that even the most simplest of defects - point defects - are not so simple
after all. And, so far, we have (implicitly) only considered the simple case of
thermal equilibrium! This leads us to the
next paragraph: |
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The list above gives an idea what could happen. But what, actually, does happen in an ideal crystal in thermal equilibrium? |
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While we believe that for common fcc metal this
question can be answered, it is still open for many important materials,
including Silicon. You may even ask: Is there thermal
equilibrium at all? |
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Consider: Right after a new portion of a growing
crystal crystallized from the melt, the concentration of point defects may have
been controlled by the growth kinetics and not by equilibrium. If the system
now tries to reach equilibrium, it needs sources and sinks for point defects to
generate or dump what is required. Extremely perfect Si crystals,
however, do not have the common sources and sinks, i.e. dislocations and grain
boundaries. So what happens? Not totally clear yet. There are more open
questions concerning Si; activate the
link for a sample. |
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Well, while there may be some doubt
as to the existence of thermal equilibrium now and then, there is no doubt that
there are many occasions where we definitely do not have thermal equilibrium.
What does that mean with respect to point defects? |
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Global equilibrium, defined by the absolute minimum of the free enthalpy of the system
is often unattainable; the second best solution, local equilibrium where some local minimum of the
free enthalpy must suffice. You always get non-equilibrium, or just a local
equilibrium, if, starting from some equilibrium, you change the temperature.
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Reaching a new local equilibrium of any kind
needs kinetic processes where point defects must move, are generated, or
annihilated. A typical picture illustrating this shows a potential curve with
various minima and maxima. A state caught in a local minima can only change to
a better minima by overcoming an energy barrier. If the temperature
T does not supply sufficient thermal energy kT,
global equilibrium (the deepest minimum) will be reached slowly or - for all
practical purposes - never. |
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One reaction helpful for reaching a minima in
cases where both vacancies and interstitials exist in non-equilibrium
concentrations (e.g. after lowering the temperature or during irradiation
experiments) could be the mutual annihilation of vacancies and interstitials by
recombination. The potential barrier that must be overcome seems to be only the
migration enthalpy (at least one species must be mobile so that the defects can
meet). |
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There might be unexpected new effects, however,
with extended defects. If an localized interstitial meets an extended vacancy,
how is it supposed to recombine? There is no local empty space, just a thinned
out part of the lattice. Recombination is not easy then. The barrier to
recombination, however, in a kinetic description, is now an entropy barrier and not the common energy
barrier. |
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Things get really messy if the
generation if point defects, too, is a non-equilibrium process - if you produce
them by crude force. There are many ways to do this: |
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Crystal
Growth As mentioned above, the incorporation of point defects in
a growing interface does not have to produce the equilibrium concentration of
point defects. An "easy to read" paper to this subject (in German) is
available in the Link |
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Quenching, i.e.
rapid cooling. The point
defects become immobile very quickly - a lot of sinks are needed if they are to
disappear under these conditions - a rather unrealistic situation. |
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Plastic
deformation, especially by dislocation climb, is a
non-equilibrium source (or sink) for point defects. It was (and to some extent
still is) the main reason for the degradation of Laser diodes. |
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Irradiation with electrons (mainly for
scientific reasons), ions (as in ion implantation; a key process for
microelectronics), neutrons (in any reactor, but also used for neutron transmutation doping of
Si), a-particles (in reactors, but
also in satellites) produces copious quantities of point defects under
"perfect" non-equilibrium conditions. |
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Oxidation of Si injects Si
interstitials into the crystal. |
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Nitridation of Si injects vacancies
into the crystal. |
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Reactive
Interfaces (as in the two examples above), quite generally, may
inject point defects into the participating crystals. |
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Precipitation phenomena (always requiring a
moving interface) thus may produce point defects as is indeed the case:
(SiO2-precipitation generates,
SiC-precipitation uses up Si-interstitials. |
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Diffusion
of impurity atoms may produce or consume point defects beyond
needing them as diffusion vehicles. |
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And all of this may critically
influence your product. The Si crystal growth industry, grossing some
8 billion $ a year, continuously runs into severe problems caused by
point defects that are not in equilibrium. |
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So-called
swirl-defects,
sub-distinguished into A-defects and B-defects caused quite some
excitement around 1980 and led the way to the acceptance of the
existence of interstitials in Si. |
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Presently,
D-defects are the
hot topics, and it is pretty safe to predict that we will hear of
E-defects yet. |
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Now, most of the examples of possible
complications mentioned here are from pretty recent research and will not be
covered in detail in what follows. |
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And implicitely, we only discussed defects in
monoatomic crystals - metals, simple semiconductors. In more complicated
crystals with two or more different atoms in the base, things can get really
messy - look at chapters 2.4 to get an idea. |
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Anyway, you should have the feeling now that
acquiring some knowledge about defects is not wasted time. Materials Scientists
and Engineers will have to understand, use, and battle defects for many more
years to come. Not only will they not go away - they are needed for many
products and one of the major "buttons" to fiddle with when designing
new materials |
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© H. Föll (Defects - Script)
