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Considering diffusion in crystals we have exactly three basic cases |
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1. An interstitial impurity atom diffuses in the crystal=impurity diffusion. |
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2. A substitutional impurity atom diffuses in the crystal=impurity diffusion. |
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3. An atom of the crystal diffuses in the crystal=self-diffusion. |
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Case 2. and 3. are impossible without diffusion "vehicles",
i.e. vacancies (and on occasion self-interstitials). | |
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Diffusion mechanisms are the atomic mechanisms that are capable of moving atoms.
The most important ones are: | |
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Vacancy mechanism. Accounts for most of cases 2. and 3. from above in simple
crystals, | |
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Direct interstitial mechanisms. Accounts for almost all of case 1. |
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Some more complex mechanisms exist (and are of prime importance) in Si
(and possibly other semiconductors and somewhat more complex crystals) |
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Wait and see! And keep an open mind |
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"Kick-out" mechanism, impurity and self-diffusion via self-interstitials, ... |
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In any case we need the migration enthalpy Hm and entropy
Sm of the "jumping" entities to obtain the diffusion coefficient D of the
process | |
Ddir | = |
g · a2 · n
0 · exp | S k |
· exp – |
Hm kT |
DSD | = |
cV · Dv |
| = |
D* · exp – |
Hm + HF kT |
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Typical values are - like always, it seems - in the 1 eV (better: 0.5 eV - 3 eV)
and 1 k region, respectively. | |
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Question to ponder: How long does it take for all atoms of crystal to be somewhere else; i.e.
not at the original position? (Exercise 3.2-1) |
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© H. Föll (Defects - Script)