An asymptotic analysis of the kick-out diffusion mechanism

The kick-out model for impurity diffusion in semiconductors is studied. The kick-out mechanism is thought to play an important rôle in a number of applications, including the diffusion of zinc and chromium in gallium arsenide. Asymptotic solutions are derived for both one- and two-dimensional surface source problems. In the one-dimensional case, a mechanism for the destruction of self-interstitials is also incorporated. The calculated diffusion profiles have shapes which are typical of diffusion systems in which the kick-out mechanism is believed to be active. For the two-dimensional problem, contours of constant impurity concentration are calculated and some are found to have the bird's beak shape which is frequently observed in experiments.     

Asymptotic analysis of a non-linear model for substitutional diffusion in semiconductors

The simple non-Fickian model for the substitutional diffusion of an impurity in a III-V semiconductor proposed by Zahari and Tuck assumes that both the impurity and host atoms diffuse by a vacancy mechanism. Here we give an asymptotic analysis of the governing pair of coupled partial differential equations, obtaining analytical solutions for the impurity and vacancy distributions in systems for which the impurity diffusivity is much greater than that of the vacancies. Two problems are considered. The first is that in which the impurity concentration is initially zero and a prescribed concentration is given at the surface. The second problem models the diffusion of ion implanted impurity, for which initial impurity and vacancy distributions are specified and a condition of zero impurity flux is assumed at the surface. Both leading order and correction terms are obtained and in each case the solution predicts the anomalous double profiles often observed in III-V systems. The ion-implantation analysis also displays the observed phenomenon of uphill diffusion against the impurity gradient close to the surface.     

Asymptotic analysis of a model for substitutional-interstitial diffusion

A substitutional-interstitial model for impurity diffusion in semi-conductors is discussed. In particular we consider a surface-source problem and obtain asymptotic solutions in the limit of the surface concentration of impurity being much greater than the equilibrium vacancy concentration. In the absence of vacancy generation, a double error function impurity curve is obtained. These double profiles reproduce some of the qualitative features of diffusion in many III–V semiconductor systems. We also discuss how vacancy generation modifies the analysis and show that in the limit of high vacancy generation, the problem becomes one of linear diffusion with the diffusion curves then being single error function complements.