Intrinsic stress effects on the growth of planar SiO 2 films
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Intrinsic stress effects on the growth of planar SiO2 films T.J. Delph and M-T. Lin Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania 18015 (Received 18 June 1999; accepted 27 August 1999)
We report here on the results of a numerical study on the effects of intrinsic stress on the growth of SiO2 thin films. In accordance with a widely accepted model of stress effects upon silicon oxidation, we assume that the intrinsic stress affects only the oxidant diffusion rate. We examine several different models of stress-assisted diffusion. In the first of these models, the diffusivity is taken to be an exponential function of the stress, whereas in the second, the stress gradient appears as an additional term in the standard diffusion equation. Intrinsic stress effects result in deviations of up to 18% in expected layer thickness, depending upon the mode of oxidation and the diffusion model adopted. The implications of these results for the measurement of diffusion coefficients in SiO2 films are discussed. I. INTRODUCTION
There exists a convincing amount of evidence, both direct and indirect, that mechanical stress has a substantial effect on the oxidation behavior of silicon.1–3 This stress arises from the fact that the thermal oxidation of silicon to form vitreous silica involves a large relative expansion in volume by approximately a factor of 2.3. When restraints to this expansion are present, as they typically are in semiconductor applications, mechanical stresses on the order of hundreds of megapascals can arise. Due to the fact that almost all of the volume expansion involved in the oxidation process takes place normal to the plane of oxidation, the prevalent belief among workers in this area is that stress effects are of interest only in the oxidation of nonplanar substrates. Hence planar oxidation is considered as a sort of stress-free, reference configuration against which nonplanar oxidation effects may be measured. It has been clear for some time, however, that this belief is incorrect. Experiments in which oxide has either been added to or removed from a single side of a silicon wafer have resulted in marked wafer curvature,4,5 indicating the existence of fairly large compressive stresses in the SiO2 film. Recently, Delph6 has examined the hypothesis that these stresses are due to a small component of expansion strain ⑀* parallel to the oxidation front, called the intrinsic strain. Delph reanalyzed the experimental results or Kobeda and Irene5 in this light, and obtained a value of ⑀* ≈ 0.002. The presence of this intrinsic strain leads to what are commonly called intrinsic stresses. Here we examine the effects of the intrinsic stress upon the growth of planar SiO2 films. As a prototypical situation, we focus upon the case of a silicon wafer oxidized simultaneously on both sides. This is identical to 4508
http://journals.cambridge.org
J. Mater. Res., Vol. 14, No. 12, Dec 1999 Downloaded: 16 Mar 2015
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