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The basic idea behind these
techniques is simple: if you have more
point defects than what you would have in thermal equilibrium, it should be
easier to detect them. There are several methods, the most important one being
quenching from high
temperatures. Lets look at this technique in its extreme form: |
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A wire of
the material to be investigated is heated in liquid and superfluid He II (i.e. a liquid with a
"∞" large heat conduction) to
the desired temperature (by passing current through it). Astonishingly, this is
easily possible because the He-vapor produced acts as a very efficient
thermal shield and keeps the liquid He from exploding because too much
heat is transferred. |
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After turning off the heating current, the
specimen will cool extremely fast to He II temperature (» 1K). There is not much time for the point
defects being present at the high temperature in thermal equilibrium to
disappear via diffusion; they are to a large percentage "frozen-in". The frozen-in
concentration can now be determined by e.g. measuring the
residual
resistivity ρres of the
wire. |
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The residual resistivity is simply the
resistivity found around 0 K. It is essentially dominated by defects
because scattering of electrons at phonons is negligible. |
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There are, however, many problems with the quenching technique. |
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The quenching
speed ( » 104
oC/s with the He II technique) may still be too small to
definitely rule out agglomeration off point defects (look at exercise 4.2-1). The cure for this problem is to repeat
the experiments at different quenching speeds and to extrapolate to infinite
quenching speed. What you will see may look like the schematic representation
below. |
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Recorded is the residual resistivities after a
quenched sample was annealed for some specified time at the temperature
T. This can bedone in-situ; after the anneal the specimen is
cooled down again and ρres is
measured |
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Plastic
deformation is the next big problem. |
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The unavoidable large temperature gradients
introduced by quenching produce large mechanical stress which may cause severe
plastic deformation or even fracture of the specimen. Plastic deformation, in
turn, may severley distort the concentrations of point defects and fracture of
a sample simply terminates an experiment. |
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Finally, impurities, always there, may influence the
results. |
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Since impurities may drastically influence the
residual resistance, measurements with "dirty" specimens are always
open to doubt. In addition, it is not generally easy to avoid in-diffusion of
impurity atoms at the high temperatures needed for the experiment. |
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Quenching experiments with Si, for
example, did not so far give useful data. If any "good" curves were
obtained, it was invariably shown (later) that the results were due to impurity
in-diffusion (usually Fe). |
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The illustration in the link gives an
example for the processes
occurring during quenching for Au obtained by calculations and
demonstrates the difficulties in extracting data from raw measurements. |
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If all else
fails: try to find agglomerates of point
defects looking at your specimen with the
transmission electron
microscope (TEM), with X-ray
methods or with any other method that is applicable. |
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Accept
local equilibrium:
Don't cool too fast, allow time for agglomerates to form. Conclude from the
type of agglomerate, from their density and size, and whatever additional
information you can gather, what kind of point defect with what concentration
was prevalent. |
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This is rather indirect and qualitative, but: |
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It gives plenty of information. There
are many examples where TEM contributed vital information to point
defect research. Especially, it was TEM that gave the first clear
indication that self-interstitials play a role in thermal equilibrium in
Si and some rough numbers for formation energies and migration energies
(Föll and Kolbesen
1978). |
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In the link an example of the
agglomerates of
self-interstitials as detected by TEM is given. The major
experimental problem in this case was to find the agglomerates. Their density
is very low and at the required magnification huge areas had to be
searched. |
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A very new way of looking at point
defects is to use the scanning
tunneling microscope (STM) and to look at the atoms
on the surface of the sample. This idea is not new; before the advent of the
STM field ion microscopy was
used with the same intention, but experiments were (and are) very difficult to
do and severely limited. |
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One idea is to investigate the surface after fracturing the
quenched sample in-situ under ultra-high vacuum (UHV) conditions. This would give the
density of vacancies on the fracture plane from which the bulk value could be
deduced. |
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An interesting set of STM images of
point defects in GaAs
from recent research is given in the link. |
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Vacancies can be seen, but there are many problems: The image
changes with time - the density of point defects goes up! Why - who knows? |
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The interpretation of what you see is also difficult. In the
example, several kinds of contrasts resulting from vacancies can be seen,
probably because they are differently charged or at different depth in the
sample (STM also "sees" defects one or two layers below the
top layer). It needs detailed work to interprete the images as shown in the
link. |
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More recent
pictures show the surface of Si or Pt, including point
defects, in astonishing clarity. But we still will have to wait a few more
years to see what contributions STM will be able to make towards the
understanding of point defects. |
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© H. Föll