3.3 Sharp interface shift

3.3.1 Computer simulations

To investigate the interface kinetics and morphology we used basically two types of models: continuum (2) and discrete (atomistic) (2.6). The advantage of the continuum models over atomistic ones is that stress effects can easily be included. However the validity of the continuum models is limited on the nanoscale, especially if the diffusion coefficient ($D$ ) is composition dependent (2.5). The range of the validity of the continuum model shifts strongly with increasing $m'$ and, in many real thin- or multilayer systems with typical characteristic length of few nanometers, it may break down.

However, both from the discrete and continuum models, we obtained that the development of the composition profiles is quite symmetrical for composition independent $D$ , whereas, for strong composition dependent $D$ (strong diffusion asymmetry), the composition profiles are very asymmetric. The interface between the $A$ and $B$ matrixes remains abrupt and shifts until the component in which the diffusion is slower is no longer consumed. It can be seen in Fig. 3.2 that the Si atoms diffuse very fast into the Ge matrix and are distributed homogeneously, whereas the Ge atoms practically cannot penetrate into the Si matrix, since the diffusion is more than $4$ orders of magnitude faster in the Ge than in the Si [2].

Figure 3.2: Concentration distributions of Si in a Si/Ge multilayer (only half bilayers are shown for symmetry reasons) at different times for the continuum model. (a) composition independent $D$ , i.e. $m'=0$ (b) composition dependent $D$ , where $m'=4$ . The arrows show the initial position of the interface.

3.3.2 Experiments

Amorphous Si/Ge multilayers with nearly equal thickness of sublayers were prepared by dc magnetron sputtering. The nominal thickness of the Si and Ge sublayers was $18$  nm, the total thickness of the multilayer was $180$  nm. The asymmetric development of the composition profile was shown by measurement of the time evolution of the composition profile by the Auger depth profiling technique. It was shown that, during annealing, the Si atoms diffuse into the Ge and are homogenised there. As a consequence, the interface shifts towards the Si resulting the thinning of the Si layer and thickening of the initial Ge layer, within which, the Si content increases (Fig. 3.3) [16].

Figure 3.3: One period of the composition profiles of the as-received and heat treated amorphous Si/Ge multilayers obtained by Auger depth profiling.