Mismatch between films and substrate

In epitaxial films on the substrate, which is usually much thicker than the film, the internal mechanical strains originate from mismatch between film and substrate lattice constants and their thermal expansion coefficients. The technological defects and imperfections can also be the sources of internal strains. The mechanical strains U can be either compressive or tensile, their values are around 1 GPa [6] and their relaxation occurs via misfit dislocations creation. However, there exists certain critical thickness he, such that these dislocations appear Sith>hc only. The calculations had shown [7] that he 1/1/ and for PbTiOs films on MgO or SrTiOs substrates he — 0.5 nm or 8.3 nm respectively. 

Thermal cycling Cracked resistors Various film defects Excess bonding time Thermal coefficient of expansion mismatch between film and substrate Open or out of tolerance... 

The residual thermal stresses in a substrate-coating combination are due to the interfacial forces arising from the thermal expansion coefficient mismatch between coating and substrate and from the presence of a ending moment [1]. The former are uniformly distributed over the film thickness while the latJe - arises from the requirement to balance the external bending moment induced by the interfacial force in a coating-substrate combination and varies across the film thickness [2]. 

It is important to determine stresses in thin films in relation to mechanical stability as a result of the deposition process and the temperatures involved. The stress developed in a film is made up of three components. The first component is intrinsic, which is the result of factors such as deposition, structure, and mode of growth the second is the result of the mismatch in thermal expansion between film and substrate and the third is related to externally applied stresses (Lepienski et al., 2004). Once the values of intrinsic stress ( thermal stress ( (thermal)), and externally applied stress ((T(extemal)) are determined, the stress developed within a film can be calculated using the following equation ... 

Epitaxial growth of thin films usually involves the formation of strained material as a result of mismatch between the film and substrate and because of the large surface to volume ratio in the film. Surface stress can be a major factor, even when the lattice constants of film and substrate are perfectly matched. Although it appears to be difficult to eliminate the stress totally, it is important to be able to control it and even use it to produce desired qualities. 

To all these intrinsic reasons, one would have to add the expected modifications in the electronic structure of the growing film as it thickens, due to the decreasing influence of the substrate. This can be better judged for a system that is not pseudomorphic, such as Ag/Cu(lll). The large (12%) mismatch between Ag and Cu would provoke such a tremendous compressive stress for a pseudomorphic layer that the Ag layers keep their own lattice parameter from the first monolayer on. For 1 ML of Ag/Cu(lll), the surface state has been found to be 120 meV lower in energy than for bulk Ag(lll) [79], and shifts with increasing Ag coverage to the bulk value. 

The growth of 3C-SiC on porous Si using the cold-wall LPCVD method resulted in a slightly better film quality compared with that on standard Si, as determined by LTPL. Further improvement in film quality was obtained by growing on a stabilized porous Si substrate. The epitaxial films did contain TBs and APBs at the interface, which is common due to the 20 % lattice mismatch between Si and SiC. 

Heteroepitaxial growth of GaN is usually performed on sapphire or SiC (13 % and 3.4% lattice mismatch, respectively, with GaN). Such a lattice mismatch between GaN and these substrates results in a high dislocation density in the epitaxial films. A variety of techniques have been employed in the past to reduce this high dislocation density and one of the common methods has been to engineer the substrate surface to control, and thus inhibit, the formation of threading dislocations. 

Chapters 5-8 discuss uses of porous SiC, and porous intermediate layers of other materials, as substrates for GaN epitaxy. The lattice mismatch between GaN and SiC leads to dislocations in GaN films, and use of a porous template offers a mechanism for reducing the dislocation density. 

Similar to the case of semiconductor thin films and quantum well structures, there is a need to deposit buffer layers prior to deposition of the superconducting thin-film, see Fig. 14.6. The role of a buffer layer is to prevent detrimental interactions between the film and substrate and to diminish the effect of surface defects on the film growth. In addition, there are examples of film/substrate combinations where the mismatch in thermal expansion coefficients is severe enough to cause cracking in the thin films [14.16, 14.17]. A suitably chosen intermediate buffer layer can reduce the stress caused by such a mismatch. 

The YBCO films are deposited at relatively high temperatures, i.e. about 700 °C, and are subsequently cooled to room temperature. The Tc of YBCO is about 90 K depending on the quality of the thin-film, and fihn devices are therefore cycled between room temperature and temperatures below 90 K during use. It is thus essential to have a good match in thermal expansion coefficient between the film and substrate. The magnitude of the strain due to thermal expansion mismatch increases with deviation from the deposition temperature. Other mechanisms relieving the strain may be activated as the temperature decreases, since the formation probability and mobility of a misfit dislocation decrease with temperature. 

Closely related substrate-fluid-soid films can also exhibit undulation growth of the top solid layer. This is thought to occur due to the buckling of the top layer in response to a thermal expansion mismatch between solid and fluid layers [7] and van der Waals forces are not thought to play a significant role [8, 9]. This may seem curious to the reader, because we have just explained how van der Waals forces can play such a significant role in the trilayer films we are interested in. It should first be noted that in the trilayer films in which we are interested, the van der Waals forces are always attractive, due to the symmetry of the problem, while this is not necessarily the case for the substrate-fluid-solid films. However,... 

In thin films, the picture of the film thickness influence on lattice constants is more complex than that in the powders and/or ceramics. First of all, this is related to the influence of mismatch between the film and substrate parameters, which leads to appearance of compressive or tensile mechanical strain normal to the film surface, similarly to the discussion in Sect. 2.1. This means, that parameter of a film tetragonality c/a l even in cubic phase. Moreover, the substrates, which induce large enough compressive strain, essentially impede thickness induced phase transition from ferroelectric to paraelectric phase, so that ferroelectricity can be conserved even in ultrathin films deposited on such substrates. As an example of such behavior, we show on Fig. 2.5 the ratio c/a measured for PbTiOs film on SrTi03 Nb substrate at r= 300 K [20]. It is seen, that similarly to the powders and ceramics, c/a ratio diminishes with the size (film thickness) decrease. However, up to the thickness 4 nm the ferroelectricity is retained and c/a remains to be more than the value 1.3, corresponding to the disappearance of ferroelectricity with respect to mechanical strain. 

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