We present a computational study of spontaneous polarization and piezoelectricity in Sc(x)Al(1-x)N alloys in the compositional range from x = 0 to x = 0.5, obtained in the context of density functional theory and the Berry-phase theory of electric polarization using large periodic supercells. We report composition-dependent values of piezoelectric coefficients e(ij), piezoelectric moduli d(ij) and elastic constants C(ij). The theoretical findings are complemented with experimental measurement of e33 for a series of sputtered ScAlN films carried out with a piezoelectric resonator. The rapid increase with Sc content of the piezoelectric response reported in previous studies is confirmed for the available data. A detailed description of the full methodology required to calculate the piezoelectric properties of ScAlN, with application to other complex alloys, is presented. In particular, we find that the large amount of internal strain present in ScAlN and its intricate relation with electric polarization make configurational sampling and the use of large supercells at different compositions necessary in order to accurately derive the piezoelectric response of the material.

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The reaction mechanisms in the Si/Ta/Cu metallization system and their relation to the microstructure of thin films are discussed on the basis of experimental results and the assessment of the ternary Si-Ta-Cu phase diagram at 700°C. With the help of sheet resistance measurements, Rutherford backscattering spectroscopy, x-ray diffraction, a scanning electron microscope, and a transmission electron microscope, the Ta barrier layer was observed to fail at temperatures above 650°C due to the formation of TaSi 2 , the diffusion of Cu through the silicide layer, and the resulting formation of Cu 3 Si precipitates. However, in order for the TaSi 2 phase to form first, the Ta diffusion barrier layer must be thick enough ͑e.g., 50-100 nm͒ to prevent Cu diffusion into the Si substrate up to the temperature of TaSi 2 formation ͑ϳ650°C͒. Independent of the Ta layer thickness, Cu 3 Si was present as large nodules, whereas the TaSi 2 existed as a uniform layer. The resulting reaction structure was found to be in local equilibrium on the basis of the assessed Si-Ta-Cu phase diagram at 700°C, and therefore no further reactions were expected. The role of oxygen was also found to be important in the reactions and it seems to have a strong effect on the thermal stability of the barrier layer.

The reaction mechanisms and related microstructures in the Si/TaC/Cu metallization system have been studied experimentally and theoretically by utilizing ternary Si-Ta-C and Ta-C-Cu phase diagrams as well as activity diagrams calculated at 800°C. With the help of sheet resistance measurements, Rutherford backscattering spectrometry, x-ray diffraction, scanning electron microscopy, and transmission electron microscopy, the metallization structure with the 70 nm thick TaC barrier layer was observed to fail completely at temperatures above 725°C because of the formation of large Cu 3 Si protrusions. However, the formation of amorphous Ta layer containing significant amounts of carbon and oxygen was already observed at the TaC/Cu interface at 600°C. This layer also constituted an additional barrier layer for Cu diffusion, which occurred only after the crystallization of the amorphous layer. The formation of Ta 2 O 5 was observed at 725°C with x-ray diffraction, indicating that the oxygen rich amorphous layer had started to crystallize. The formation of SiC and TaSi 2 occurred almost simultaneously at 800°C. The observed reaction structure was consistent with the thermodynamics of the ternary system. The metallization structures with 7 nm and 35 nm TaC barrier layers failed above 550°C and 650°C, respectively, similarly because of the formation of Cu 3 Si. The high formation temperature of TaSi 2 and SiC implies high stability of Si/TaC interface, thus making TaC layer a potential candidate to be used as a diffusion barrier for Cu metallization.