Stress Distribution In Thin Films Research Articles

Determining local residual stresses from high resolution wafer geometry measurements

Multiple thin film deposition steps are central to most semiconductor device fabrication processes. The residual stresses in these thin films can induce both in-plane and out-of-plane distortions to the wafer. These residual stresses can vary spatially across the wafer, and the residual stress distributions can change between lithography steps. This can result in noncorrectable overlay errors in the lithography processes. In order to develop strategies for minimizing overlay errors due to residual stress-induced distortion, there is a critical need for techniques that allow the distributions of residual stresses in deposited thin films to be characterized with high spatial resolution. In this paper, the application of established analytical methods for extracting local residual stress from wafer geometry measurements (shape) is investigated. Three-dimensional finite-element models were used to generate simulated wafer shapes resulting from nonuniform residual stress distributions in thin-films. The results of these finite element simulations were used to assess the effectiveness of established analytical techniques. Furthermore, the results demonstrated that local mean curvature of the wafer shape is a simple metric that can be used to qualitatively describe local residual stress variation across the wafer. The simulations also demonstrated that when residual stresses varied over scales of tens of millimeters that high spatial resolution (<1 mm) shape measurements were required in order to accurately predict local residual stress.

Spatially resolved residual stress assessments of GaN film on sapphire substrate by cathodoluminescence piezospectroscopy

Two cathodoluminescence piezospectroscopic (CL/PS) approaches for measuring the residual stress distribution in thin films are critically examined and compared using an intrinsic GaN film sample (2.5μm in thickness) grown on a (0001)-oriented sapphire substrate. The first approach invokes an analytical model to fit experimental stress distributions as retrieved in both film and substrate at the edge of an artificially created cross section of the sample. Such an edge-stress distribution takes into account both the thermal expansion mismatch between the film and substrate and the mechanistics of film growth process. In the second approach, we directly and nondestructively measure the bulk residual stress field from the sample top surface on the film side using an increase in electron beam voltage (maintaining a constant beam power) as a means for screening the film subsurface. In this latter case, the combined effects of self-absorption and misfit dislocations on the GaN spectrum severely affect the CL/PS assessments; therefore, they need to be analyzed separately from the effect of stress. After spectral deconvolution of the obtained stress profiles, according to either in-plane or in-depth response functions of the electron probe for both film and substrate, cross-section and top-surface stress data were compared and discussed in an effort to substantiate the feasibility of spatially resolved CL/PS approach for the examination of residual stress distributions in film structures.

Governing equation for the measurement of nonuniform stress distributions in thin films using a substrate deformation technique

Determination of stress in thin films deposited on substrates is a basic and essential requirement in micronanotechnology. Most often local measurements of the induced substrate curvature are related to local stress using the Stoney equation. However, it is well known that this method gives incorrect results if the stress distribution is nonuniform. Here a general governing equation for the evaluation of nonuniform stress distributions in thin films is derived, which has the new feature of being able to treat the cases of anisotropic stress and also the effect on substrate deformation of a large in-plane thin film tension.

A General Solution for Two-Dimensional Stress Distributions in Thin Films

We present closed-form solutions for stresses in a thin film resulting from a purely dilatational stress-free strain that can vary arbitrarily within the film. The solutions are specific to a two-dimensional thin film on a thick substrate geometry and are presented for both a welded and a perfectly slipping film/substrate interface. Variation of the stress-free strain through the thickness of the film is considered to be either arbitrary or represented by a Fourier integral, and solutions are presented in the form of a Fourier series in the lateral dimension x. The Fourier coefficients can be calculated rapidly using Fast Fourier Transforms. The method is applied to determine the stresses in the film and substrate for three cases: (a) where the stress-free strain is a sinusoidal modulation in x, (b) where the stress-free strain varies only through the thickness, and (c) where a rectangular inclusion is embedded within the film, and the calculated stresses match accurately with the exact solutions for these cases.

Inhomogeneous Deformation in Thin Films

Residual stresses are a major factor in the reliable operation of multi-layer thin film structures. These stresses may form due to defect incorporation during deposition, recrystallization, second-phase precipitation, thermal coefficient of expansion (TCE) mismatch, etc., as well as local plastic flow, delamination or cracking. In the literature, residual stresses are usually assumed to be constant in the plane of the film. This assumption is sometimes implicitly made, as in the cases where only two psi-tilts are used in the stress determination with the sin2Ψ analysis.In this paper, we will review the possible causes of heterogeneous stress distributions in thin films and discuss their impact on x-ray stress determination techniques using some new data from W films.