PHYSICAL REVIEW B VOLUME 51, NUMBER 8 15 FEBRUARY 1995-II Fractal aspects related to the Si oxidation process I uca Verdi and Antonio Miotello Dipartimento di Fisica dell Universita di Trento and Istituto Nazionale per la Fisica della Materia, I-88050 Pavo, Trento, Italy (Received 11 October 1994) We propose a model for the silicon oxidation process in dry atmosphere, where the growing oxide is seen not as a continuous random lattice but instead as a granular random lattice through which oxygen diffusion occurs. A reactive layer connects the oxide with the Si bulk at the SiO&/Si interface. The model is applied to a representative set of experimental results, obtained at diferent temperatures and oxygen pressures, leading to a consistent picture of the oxidation process n terms of a fractal geometry with a definite correlation length ( = 4 nm, and random-walk dimension d = 3. 25. During the past 30 years much research activity has been devoted to establishing the mechanisms leading to silicon oxidation; a process having a central role in the manufacturing of microelectronics components. How- ever, people contributing to establishing the fundamen- tals of a theory for Si oxidation agree that new efforts must be made before concluding that the Si oxidation process is definitely understood. In this paper we try to give an original contribution to clarify some aspects involved in oxygen difFusion through a growing Si oxide film in dry oxygen atmosphere. In par- ticular we will see that the oxide growth may be consis- tently described by making use of concepts appropriate to a &actal geometry. In general the Si oxide growth in dry atmosphere is described by considering diffusion of the oxidizing species through the growing oxide and chemical reaction of that species at the Si02/Si interface. Several models have been proposed to explain the experimental Si oxide growth data which depart &om a simple linear- parabolic kinetics ' which is easily justified in terms of a normal diffusivity of the oxidizing species. The linear- parabolic kinetics involves a standard diffusion equation while attributing the linear oxide growth regime (thin oxide films, ( 30 nm) to the relevance of boundary con- ditions. These models generally propose empirical equa- tions and suggest many different mechanisms such as ox- ide stress, space charge effects in transport of ionized species, and finally more complicated chemical reactions where the 02 ++ 20 reaction is connected to parallel re- actions involving other species. The starting point of establishing a scheme for the analysis of the oxygen diffusion process which leads to the oxide formation is again the observation that a sim- ple linear-parabolic mode14 cannot account for the ex- perimental oxide growth results and also that it does not provide an explanation for the observed external pressure dependence of the oxidation process. Structural properties of the growing oxide are particu- larly relevant when considering transport properties: the presence of an altered reactive layer at the Si02/Si inter- face is both well established &om an experimental point of view and necessary in order to explain phenomena involving isotopic exchange. ' Moreover, recently pub- ::-. :: DRY OXYGEN ATMOSPHERE --'-:-----:SURFACE (~— LLI Q X O Z', O (/) REACTIVE LAYER S) SUBSTRATE FIG. 1. Schematic representation of the a-Si02 structure as seen in the sense of a percolationlike system. The sys- tem is fractal within length scales f everywhere, i.e. , it is a homogeneous fractal just as the percolation cluster is. lished experimental results, and related models, indicate that bulk a-Si02 is most probably not a continuous ran- dom network, but rather it includes granularities ' and inhomogeneities. In addition, neutron scattering exper- iments, in a-Si02, show that at low frequency (~ ( 50 cm i) and in the temperature range 1 — 10 K, the density of the vibrational states (and the related specific heat) departs &om the Debye law: this fact again may be at- tributed to a noncontinuous random lattice since quan- tum tunneling effects are irrelevant in this temperature range. These structural features of the a-Si02 should be con- 0163-1829/95/51(8)/5469(4)/$06. 00 5469 1995 The American Physical Society