1.1.5 Oxidation

  The isolation of semiconductor devices fabricated on the same substrate is essential for IC technology. For the electrical isolation on silicon substrates two common methods are known: (1) junction isolation, where p-n junctions and space charge regions avoid current flows between devices, and (2) the thermal oxidation of silicon. Due to the high affinity of silicon for oxygen, an oxide layer with dielectric properties is rapidly formed by applying an oxidizing ambient to the silicon surface. Also the mechanical properties, like the sticking coefficient between oxide and the underlying silicon, are quite sufficient for permanent adhesion. Oxide layers are not only used for dielectric isolations, they can also operate as padding oxide for ion implantation to avoid channeling or as diffusion barrier for dopants to protect the underlying material. Oxide is also used as isolation material between multi-level metalization systems. In this case it is not fabricated by thermal oxidation. For this application chemical vapor deposition of oxide is uniquely suitable. With the shrinking design rules this method becomes of vital importance to fabricate thin oxide layers within the range. With nowadays technology it is possible to fabricate oxides of the thickness of a few atomic layers. Besides this thin layer applications the knowledge of the oxidation process and its physical reliability is essential.

From the process modeling point of view Deal and Grove published their famous oxidation model in the mid sixties [Dea65]. Despite of the physical basis of their model, it has proven its capability for reproducing experimental data for both dry and wet oxidation conditions. It incorporates the transport of oxidized species from the ambient to the silicon dioxide surface, the diffusion of the oxygen through the oxide and the interface conditions at the silicon-oxide material interface. The main weakness of this model is the lack of precision in the initial thin regime for dry oxidation ( ). Thereby an anomalously high oxidation rate is predicted by this model. Various models and modifications of the Deal-Grove model have been proposed in the past [Chi82] [Ire83] [Far83]. As oxidation of silicon is a multi-dimensional problem, the local oxide flow has to be incorporated. This phenomenon may be modeled by the Navier-Stokes equation [Chi83] [Pen90] or by viscoelastic behavior [Mat85] [Pon85]. Analytical solutions have been widely used for fitting oxide profiles to reproduce a variety of isolation structures [Gui87]. These techniques have the advantage of less CPU time consumption compared to other methods, but the final oxide shapes must be known prior to the simulation. Therefore, it is impossible to predict profiles for new technologies with this technique.

The quality of an oxidation model is directly associated with the incorporation of the complex oxidation mechanism at the silicon/silicon dioxide interface. At this point it is not clear whether charged or uncharged species are transported through a silicon-oxide interface. Investigations by various authors have shown that also interstitials can overcome the silicon-oxide diffusion barrier [Tsa95]. The most common modeling approach is given by [Til80] and treats the interface as a transition area, where movement of this interface requires vacancies from the silicon side and delivers interstitials to the bulk. Thereby a local supersaturation of interstitials occurs nearby the interface, which is consistent with the oxidation enhanced diffusion (OED) phenomenon observed for interstitialcy diffusers. Besides this injection mechanism there is dopant segregation occurring, where the dopant exhibits a preference for migration to one of the interface materials, eg. boron segregates into oxide and phosphorus into the silicon under oxidation conditions. Additional mechanisms associated with the volume expansion during oxidation like stress effects and higher stacking fault formation rates within the silicon bulk are still evident.

The major problems arising with oxidation simulation are related with the movement of the discretization domain due to the growth process. After each solution of the viscous or viscoelastic oxide fluid flow, the simulation domain has to be updated. This means new discretization grids have to be generated or the old ones have to be modified and interface boundaries have to be recalculated. Therefore, it is necessary to have special gridding services and new concepts to manage this enormous data update [Law95]. From the numerical point of view the finite element method (FEM) is favored for oxidation applications, because it imposes less restrictions on the grid quality compared to the box discretization method (BM).

As the design trend is moving towards the usage of nonrectangular devices [Tak91], there is an extraordinary need of three-dimensional oxidation simulators to model the arbitrary device structures and isolation lines. In three dimensions, the performance decreases rapidly due to larger system matrices. Further work is required on improved solving techniques. While Gaussian solvers suffer from time and memory consumption, iterative solving techniques seem to be the best choice for mixed diffusion and mechanical problems. Also investigations on multigrid methods for solving oxidation problems including strain/stress equations are promising for three-dimensional process simulation [Lei95].