The complex issues and behaviour associated with stress, fatigue cracks and dislocation in solid films and its modelling has been addressed by a number of researchers [3.74-3.80]. Total film stress (σfilm) is given by.
a combination of intrinsic stress (σintrinsic) and extrinsic stress (σextrinsic).
Stresses in polycrystalline thin films can be intrinsic as a result of growth stress or extrinsic due to thermal expansion mismatch between film and substrate. Extrinsic or thermal stress (σthermal) is defined as:
where E, α, and ν represent the elastic modulus, thermal expansion coefficient, and Poisson’s ratio, respectively. Some typical values for the thermal expansion coefficients of substrate and thin film materials are given in appendix 1.
Stress is introduced into the crystal lattice of the film during cooling after the annealing (crystallisation) process. For BZT of ferroelectric composition, this occurs when transitions from cubic to other phases are encountered below the Curie temperature. Induced stress in thin ferroelectric films affects the dielectric and ferroelectric properties of the material. Lu et al. discuss phase transition related stress in ferroelectric thin films [3.74]. Contributing factors that give rise to stress include: thermal expansion and lattice parameter mismatch between film and substrate [3.76]; structural phase transformation (e.g., paraelectric to ferroelectric) of films when cooled from high temperature to room temperature; and formation and disappearance of grain boundary during film growth. All of this can result in an uneven distribution of stress through the film. The stress can take the form of either compressive or tensile and influences the Curie temperature (Tc) by increasing Tc for compressive stress and decreasing Tc for tensile stress. Film stress is force per unit area in Pa units for which positive values are assigned to tensile and negative values to compressive stresses. Stress can therefore vary from large tensile through zero to large compressive values dependent on the deposition method, materials and conditions chosen. Film stress can be a real issue reducing the dielectric constant, increasing the dielectric loss and limiting the tunability. As a consequence of stress in piezoelectric material used in actuators, a study of fracture behaviour is essential to address performance and reliability issues. On the other hand, stress in films can be a positive attribute as in the operation of the cantilever.
Defects in sol-gel deposited films can arise at the spin coating stage with the formation of striations and ‘comets’ similar to the defects observed in photoresist when spin coated. Striations are the result of inhomogeneities of the film thickness and can be reduced by using high spin speeds. The comet shaped regions are thinly coated areas which start from particles on the substrate or from air bubbles in the sol. Air bubbles can arise when dispensing the sol. Particulate contamination of the substrate surface is the most likely cause of defects due to inadequate substrate cleaning prior to spin coating. Oxides that are porous can absorb water which tends to make films compressive, whereas oxide films devoid of water are tensile.
Virtually all vacuum deposited coatings including metallic and inorganic compound films are in a state of stress. The total film stress is composed of a thermal or extrinsic stress and intrinsic stress. The thermal stress is due to the difference in the thermal expansion coefficients of the film and the substrate material. Defects such as holes and hillocks form in films as a result of diffusion processes arising from temperature changes during deposition and annealing. Thornton et al. showed that intrinsic stress is due to crystallographic flaws that are built into the film during deposition [3.81]. Intrinsic stresses in thin films can be a real issue since tensile or compressive stresses can lead to film cracking or buckling. The origin of intrinsic stresses in evaporated and sputtered films is discussed in a paper by d’Heurle et al. [3.82].
In sputtering processes, both tensile and compressive stresses are possible depending upon the deposition conditions. Sputtering power and gas pressure both influence the sputter rate which has an effect on film stress. Chinmulgund
et al. showed that for sputtered Ti there is a thickness dependency of stress.
Below a film thickness of ~300 nm the as-deposited Ti is compressive and for films >300 nm the Ti is tensile [3.83]. After annealing the Ti film at 400oC for 1 hour, the room temperature stress became more tensile due to the increased densification of the Ti film. At low argon pressure (<2 mTorr) sputtered metal films tend to yield compressive stress. As the pressure is increased the stress changes from compressive to tensile. Also, tensile stress is increased with film
thickness but decreased with power. Tokura et al. showed that sputtered Pt films have compressive stress due to bombardment of the growing film by energetic argon atoms and inclusion of argon gas in the film [3.84]. Compressive stress is generated when energetic particles (atoms and ions) from the sputtering plasma hit the metal surface in accordance with the atomic peening model. The peening effect is when surface atoms are knocked into voids and grain boundaries within the film.
In evaporated high melting point metals (e.g. Cr) stresses are tensile since films usually exhibit a porous structure, whereas in low melting point metals (e.g. Au) comparatively small tensile as well as compressive stresses are built up due to increased densification of films. Abermann showed that stress correlates with growth mechanisms (columnar grain growth or island growth) caused by differences in the material mobility [3.85]. Thin film growth of gold by the generation of charged clusters during thermal evaporation is discussed by Barnes et al. [3.86]. They showed that the evaporated film quality is dependent on evaporation rate which affects the charging behaviour. Higher evaporation rates result in smooth, dense, good quality films due to the generation of larger, more easily charged clusters. By comparison, low evaporation rates generate small, neutral clusters that tend to result in a rough film of poor quality. Stress related effects in thin films are discussed by Thornton et al. and showed that electroplated films tend to produce tensile intrinsic-type stresses similar to those seen in evaporated coatings [3.81]. Porous structures also yield tensile stress. Buehler et al. reported on the study of grain boundary diffusion and associated dislocation mechanisms in polycrystalline thin films on substrates [3.77]. Stresses in the film are relaxed by inelastic deformation mechanisms when material is transported from the surface into the grain boundary. The material defect called a diffusion wedge is formed as material accumulates in the grain boundary. This promotes dislocation activity within the grains.
Figure 3.12 shows the stages relating to the formation of a diffusion wedge along a grain boundary as a result of mass diffusion from the surface. This
stress in the vicinity of the film-substrate interface. This then gives rise to inelastic deformation and the formation of crack-like dislocations parallel to the plane of the film which subsequently causes the stress to be relaxed. Buehler et
al. developed a model (atomistic simulation) to study deformation mechanisms
in sub-micron polycrystalline thin films. A similar study was undertaken by Gao
et al. that looked at diffusional deformation (i.e. grain boundary diffusion
wedges) in thin metal films [3.78].
Figure 3.12 Formation of a diffusion wedge. Step 1 shows material being transported from the surface into the grain boundary. Step 2 displays formation of the diffusion wedge due to material accumulating in the grain boundary. Step 3 shows the stress concentration at the film-substrate interface causing dislocations parallel to the plane of the film [3.77].
Materials that develop stresses in grain boundaries can spontaneously crack depending on the size of the grains. Fatigue crack growth in ferroelectric material is exacerbated under mechanical and electrical loads [3.79]. It was pointed out that non-uniform domain switching in ferroelectrics can also produce internal stresses, that if sufficiently high, can result in crack growth.
Understanding deformation mechanisms in polycrystalline thin films and other ultrathin material layers are essential for the development of material systems and the miniaturisation of devices in areas such as integrated microelectronics, optoelectronics, nanotechnology and biotechnology (e.g. lab-on-a-chip).
Several authors have reported on the thermal stability of Pt, titanium diffusion and the stress dependence of platinum hillock formation; they also discuss ways of alleviating these problems [3.87-3.98]. Metal electrodes such as platinum play a significant role in determining the material and device properties and performance. Stress in Pt/Ti bottom electrode can be varied from tensile to compressive by modifying the sputtering conditions. Deformation of the Pt electrode due to the formation of defects (hillocks) can cause stress cracks to appear in the film and at worst lead to capacitor shorts. The problem arises during both sample preparation and post-annealing, and manifests itself when the Ti used as an adhesion layer diffuses into the Pt along the Pt grain boundaries. Hillocks form on the surface of the Pt film to relieve the compressive stress generated by the Ti diffusion and oxidation [3.87]. Although hillocks can affect leakage current, they can also serve as nucleation sites for growth of thin film. Cha et al. investigated the effects of Ti thickness on the orientation, stability, and electrical characteristics of Pt bottom electrodes and found that problems such as interdiffusion and surface roughness could be improved when Ti layers 3-5 nm thick were used [3.97]. To stabilise the Pt electrode others suggest using TiOx in place of Ti as the adhesion layer [3.90, 3.91, 3.94].