ABSTRACT
Fick’s first law of diffusion states that the flux of a diffusing species is proportional to the concentration gradient of that species. J = –D ddCx (10.4)where J is the flux in atoms/cm2/sec, D is a constant under fixed conditions, and dC/dx is the concentration gradient. The diffusivity or the diffusion coefficient, D, depends upon the mechanism, temperature and crystal or material structure (including presence of defects, dislocations, etc.). The diffusion constant is particularly strongly dependent upon temperature and has the form described in Section 10.1 (Eq. 10.3):
D = D0 exp -ÊËÁ ˆ¯˜EkT (10.5) 10.2.1 Basic Mechanisms
Diffusion is a result of atomic fluctuations and wandering of lattice atoms or impurities that cause a net movement of material atoms down a concentration gradient. There are two basic mechanisms and a few complicated mechanisms that are prevalent is semiconductor or metal material systems. 10.2.1.1 Interstitial mechanism
The first one is the interstitial mechanism, shown in Fig. 10.2a. Here an interstitial atom can move into a neighboring interstitial site and
keep moving by repeating the process without needing any vacancies or substitutional sites. In the zinc-blende face-centered cubic (fcc) structure, the interstitial sites are in a tetrahedral arrangement (see Fig. 1.3) between Si atoms in a silicon lattice or between Ga and As atoms for GaAs. An interstitial atom has to overcome the energy barrier to jump to an adjacent interstitial. The atomic fluctuation magnitude has to be large enough to accomplish this. Therefore the jump frequency vi is proportional to exp(–Em/kT).
