The stresses in periodic Mo/Si, W/Si, and Mo/C multilayer films were determined from wafer-curvature measurements. The layer thickness of each material was varied systematically, and parametric stress contours were generated, showing contours of constant stress in the two-dimensional layer thickness parameter space. These results illustrate that the net stress in a periodic multilayer is not an intrinsic property of the film (for specific deposition conditions) but, rather, depends strongly on the individual layer thicknesses. X-ray diffraction measurements show (a) how the lattice spacing in the W and Mo crystallites varies with layer thickness, and (b) in the case of the W/Si films, how the phase composition of the polycrystalline W layers vary with W layer thickness. In the case of the W/Si and Mo/Si multilayers, irreversible stress changes were observed after the samples were stored in air at room temperature for a period of several months. Stress–temperature measurements made on the as-deposited W/Si...

Stress, microstructure, and stability of Mo/Si, W/Si, and Mo/C multilayer films

By measuring stress and strain that build up in thin films during hydrogen absorption, the elastic constants of the films can be determined, if a one-dimensional elastic behavior occurs only. This will be demonstrated for hydrogen absorption in Nb films. The in-plane stress is determined from the substrate curvature that is measured by using a two-beam laser setup. The out-of-plane strain is measured via x-ray diffraction. Furthermore, this method allows us to distinguish whether the film is plastically or elastically deformed by checking the reversibility of the stress–strain curve. In the case of a 250-nm-thick Nb film, the elastic constants obtained are similar to that of bulk Nb.

Determination of elastic constants in thin films using hydrogen loading

In this paper, the mechanism of growth strain is discussed based on the irreversible evolving equations by considering the coupling effects of stress and chemical reaction during isothermal oxidation, and a simple model relating the growth strain and the oxide thickness is developed. If the effect of the stress on the chemical reaction is not taken into account, the model reduces to the Clarke assumption. The expression of Dox is exhibited, and its value can be determined by experiments. The stress evolving equations are derived, where the viscoplastic strain of the oxide and metal and the growth strain of the oxide are considered. Numerical results are given and compared with results from experiments and the existing model. There is good agreement between the proposed model and the experimental data.

General approach on chemistry and stress coupling effects during oxidation

The as‐deposited stress in sputtered, 75‐A‐period Mo/Si multilayers was measured to be approximately −350 MPa (compressive), and relaxed to approximately −150 MPa after thermal cycling to 200 °C. The multilayer period was found to decrease by 0.25 A as a result of thermal cycling, with only a slight decrease in peak soft‐x‐ray reflectance. The stress‐temperature behavior of individual Mo and Si films was also measured, and correlated with the multilayer behavior: stress relaxation in the multilayer is attributed to viscous flow associated with defect annihilation, occurring predominantly in the amorphous Si layers.

Stress relaxation in Mo/Si multilayer structures

The elastic constants and thermal expansion coefficient of C49 TiSi2 thin films have been investigated by in situ curvature measurement during heat treatment and ex situ x‐ray diffraction measurements. The C49 TiSi2 compound was formed from Ti‐Si multilayers deposited on monocrystalline silicon and sapphire substrates. The films were polycrystalline without any evident texture. Young’s modulus (142 GPa), Poisson’s ratio (0.27), and the thermal expansion coefficient (10.9×10−6 K−1) have been determined. Note that these values are averages over random crystal orientations. Directly after formation C49 TiSi2 films exhibit tensile stress. This stress relaxes considerably above 375 °C. Below this temperature the thermal expansion is found to be independent of the state of relaxation of the C49 TiSi2 film.

Elastic constants and thermal expansion coefficient of metastable C49 TiSi2

A model is given for the stress change in a thin film on a thick substrate during annealing. It takes into account temperature changes, volume changes, viscous flow, and anelastic relaxation occurring in the film. The stress change in amorphous Mo/Si multilayer films deposited on Si single-crystal substrates was obtained from in situ wafer-curvature measurements during annealing at temperatures below the glass temperature. The thickness change and the interdiffusion coefficient were obtained from the position and the intensity of the first-order multilayer x-ray reflection. The unconstrained volume change was derived from the measured stress and thickness changes. The free-volume model for amorphous solids has been used to interpret the interdiffusion in and the volume change of the amorphous Mo/Si multilayers. The stress change as it occurred during isothermal annealing was explained by free-volume annihilation, viscous flow, and anelastic relaxation. If anisotropy of the volume change is accepted, the stress change could also be described with free-volume annihilation and viscous flow alone. The product of the experimentally observed viscosity and diffusion coefficient for amorphous Mo/Si multilayers was compared to the value expected from the free-volume-model-based equivalent of the Stokes-Einstein relation.

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E.R. van Snek

Papers

Model for stress and volume changes of a thin film on a substrate upon annealing: Application to amorphous Mo/Si multilayers