### 3.2.4 Essentials to Chapter 3.2 Diffusion Mechanisms

| Considering diffusion in crystals we have exactly three basic cases |  |
|  | 1. An interstitial impurity atom diffuses in the crystal=impurity diffusion. |
|  | 2. A substitutional impurity atom diffuses in the crystal=impurity diffusion. |
|  | 3. An atom of the crystal diffuses in the crystal=self-diffusion. |
| Case 2. and 3. are impossible without diffusion "vehicles", i.e. vacancies (and on occasion self-interstitials). |
| Diffusion mechanisms are the atomic mechanisms that are capable of moving atoms. The most important ones are: |  |
|  | Vacancy mechanism. Accounts for most of cases 2. and 3. from above in simple crystals, |
|  | Direct interstitial mechanisms. Accounts for almost all of case 1. |
| Some more complex mechanisms exist (and are of prime importance) in Si (and possibly other semiconductors and somewhat more complex crystals) |  |
Wait and see! And keep an open mind
|  | "Kick-out" mechanism, impurity and self-diffusion via self-interstitials, ... |
| 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
|  | Typical values are - like always, it seems - in the 1 eV (better: 0.5 eV - 3 eV) and 1 k region, respectively. |
|  | 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) |

© H. Föll (Defects - Script)