Hydrogen Diffusion Duringc Amorphous Silicon Growth and Its Consequences for the Transition to Nanocrystalline Growth
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HYDROGEN DIFFUSION DURING AMORPHOUS SILICON GROWTH AND ITS CONSEQUENCES FOR THE TRANSITION TO NANOCRYSTALLINE GROWTH Richard S. Crandall11 and Jack Thiesen2 1
National Renewable Energy Laboratory, Golden, CO 80401
2
Technology Applications, Boulder, CO 80301
ABSTRACT Using a closed-form, time-dependent solution to the partial differential equation representing hydrogen diffusion in the frame of a growing silicon film we obtain considerable insight into processes controlled by mobile H in silicon. We apply this insight to quantitatively explain the limiting thickness for Si homoepitaxy and explain by analogy the incubation thickness before the transition from amorphous to nanocrystalline silicon growth. INTRODUCTION Matter is often transported across a boundary that is moving with respect to time. An example of this is thin-film growth in an ambient from which hydrogen can diffuse through the surface of the growing layer and into the bulk. Knowledge of the concentration of diffusing species is critical to prevent an undesired phase transition and/or to control film properties. Consider thin-film Si growth from a silane precursor. Examples are the diffusion of H in both amorphous silicon (a-Si) and low-temperature epitaxial Si grown by chemical vapor deposition, CVD. In the case of silane based CVD, SiH4 is decomposed via chemical or thermal reactions with significant amounts of atomic H as a byproduct. The excess hydrogen can affect the breakdown of Si homoepitaxy [1]; the electronic properties of amorphous-silicon, where H is crucial for the passivation of dangling bonds; and the transition of a-Si to nanocrystalline Si growth. In these examples a detailed knowledge of the H concentration, which is dependent on the hydrogen flux as well as the diffusion process, is critical to predicting the properties of the as-grown layer including its phase. PROBLEM AND ANALYSIS Figure 1 is a schematic of H impinging on a growing film and diffusing through it. FH is the rate per square centimeter at which impinging atoms strike the film surface. Those particles that pass through the surface, which are not bound as isolated Si-H bonds, form the subset of diffusing H that we consider. The film surface is fixed at the coordinate x=0 and the film/substrate interface is located at the point x=VGt, where VG is the growth velocity and t the time. The substrate extends to x=,QJHQHUDOWKLVPRYLQJERXQGDU\GLIIXVLRQSUREOHPLV A27.2.1
difficult to solve. However, if we assume that the diffusion coefficient (D) is the same in film and substrate, a closed form solution is possible. We adopt this coordinate system growing for ease of solving the diffusion equation. film substrate FH The situation described above approximates many physical situations of interest. The diffusion of gas phase H atoms into a thin homo-epitaxial Si layer growing on a very thick substrate is to first order such a problem[1]. For this analysis we omit all chemical reactions involved in the x=0 x=VGt growth process, since we are interested in tracking the
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