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=Stress dependence on film and growth characteristics=
=Metal film stress dependence on composition and growth conditions=




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*Tensile stress is associated with '''low atomic mobility''' and increases when the deposition rate is increased.
*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 will increase when the deposition rate is decreased.
*Compressive stress is associated with '''high atomic mobility''' and generally increases when the deposition rate is decreased.
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This general rule is based on from Abermann's 1990 article, [https://www-sciencedirect-com.proxy.findit.cvt.dk/science/article/pii/0042207X9093933A Measurements of the intrinsic stress in thin metal films]. It means the stress depends both on inherent material properties and on deposition conditions, as one would probably also expect intuitively.  
This general rule is described, e.g., in Abermann's 1990 article, [https://www-sciencedirect-com.proxy.findit.cvt.dk/science/article/pii/0042207X9093933A 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 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.  
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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.  
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. 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.  
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  [https://pubs.aip.org/aip/jap/article/119/19/191101/1032395/Tutorial-Understanding-residual-stress-in this tutorial].  
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  [https://pubs.aip.org/aip/jap/article/119/19/191101/1032395/Tutorial-Understanding-residual-stress-in 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.
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==
==Models of thin film growth and stress==