Metal film stress dependence on composition and growth conditions

In the page overview page on stress measurement you can find links to studies made at DTU Nanolab about specific deposition results with our own sputter and e-beam evaporation systems. This page aims to give more general information about the origin of stress in thin films. It appears that the following is a good rule of thumb:

Tensile stress is associated with low atomic mobility and generally increases when the deposition rate is increased.
Compressive stress is associated with high atomic mobility and generally increases when the deposition rate is decreased.

This general rule is described, e.g., in Abermann's 1990 article, Measurements of the intrinsic stress in thin metal films. The article describes how thin film stress depends both on inherent material properties and on deposition conditions, as one would probably also expect intuitively.

Materials that tend to exhibit tensile stress were called Type I materials by Abermann. They have comparatively low atomic mobility and high melting points and include Cr, Ni, and Pt.

Materials that tend to exhibit compressive stress were called Type II materials by Abermann. They have comparatively high atomic mobility and low melting point and include Au, Cu, Al, and Ag.

The melting point does not predict the stress behavior of a material all that well, however. Abermann's own data show that Au (mp 1065 °C) has more compressive stress than Al (mp 660 °C) despite a higher melting point, and internal Nanolab data show that Ti (mp 1660 °C) has more compressive stress than Au. So other factors are at play, as has been described by other authors. For instance, all other things being equal the tensile stress decreases or the compressive stress increases with smaller grain size, according to E. Chason and collaborators (see references below). Since large grains gives more tensile stress and the grain size tends to increase for thicker layers, the tensile stress will tend to increase when a thicker layer is grown. This is apparently especially true for the many metals with low mobility that tend to form columnar grains during thin film growth.

You can read more about the model of thin film stress developed by E. Chason and collaborators at Brown university in their many publications including this tutorial.

Notice that you can increase the atomic mobility (and reduce the tensile stress) by increasing the temperature. This trend is clearly shown in e.g., Abermann's data. In sputtering you can also increase the mobility of the atoms in the growing films by decreasing the pressure and adding a bias to accelerate the sputtered atoms towards the growing film. In evaporation you can in some cases also add mobility to the growing film by ion bombardment during the deposition.

Another way to summarize in general – based on tutorial articles by E Chason and coauthors:

Very thin films exhibit tensile stress (island coalescence)
Thicker films can be tensile or compressive

Tensile tends to occur in low-mobility materials
More tensile with fast deposition at low temperature
Examples Ni, Cr

Compressive stress tends to be in high-mobility materials
More compressive with slower deposition at higher temperature
Can become less compressive as temp drops at end of deposition
Examples Au, Ag, Cu

Models of thin film growth and stress

According to the Abermann article, the tutorial mentioned above, and this review, the explanation for the origin of tensile stress in thin films is that most films start growing as islands rather than as a continuous atomic layer. The surface energy of these islands is reduced when islands unite into a layer, which makes up for the energy needed to exhibit tensile stress (initially when there is no film but only small islands, there is no stress).

The origin of the compressive stress is apparently more controversial (according to the group at Brown) but presumably has to do with the energetics of grain growth and densification of the film, especially in columnar growth of materials that are capped by an oxide layer.

An interesting observation also seen here at Nanolab is that stress in thin films can change significantly over time after the end of the deposition. In some materials this occurs over the course of days not just minutes - apparently this can, e.g., take place in nickel and in gold, see, e.g., articles about TiPtAu and TiPt contacts on III-V materials (references coming soon!).

To learn more generally about stress in thin films, we recommend the classical article by John A. Thornton and D. W. Hoffman from 1979, Stress-related effects in thin films, and other articles by the same authors. The tutorial by E. Chason refers back to the model of thin film growth developed in that paper.

Note this page is in progress - comments are very welcome.