Tunable electrons in oxides and hot phonons in silicon: Insights from theory

Computational materials science aims at studying effects or mechanisms that are hard to probe via experiments. Using numerical approaches it is possible to systematically and efficiently study materials with unmatched control and tunability. Density functional theory (DFT) has been the standard method within electronic structure calculations due to to its good balance of low computational cost and high predictability. In this thesis, I describe how I have employed DFT to study the electronic structure and transport properties of SrNbO3, but also the thermal transport in Si.

For SrNbO₃, the total energy landscape was mapped as a function of rotations of the NbO₆ octahedra. Here, the effect of biaxial strain was considered. Interestingly, SrNbO₃ shows a preference for single in-phase rotation, i.e., a⁰a⁰c⁺ in Glazer’s notation. This is in contrast to the out-of-phase rotation, a⁰a⁰c⁻, which is common in other perovskite oxides. The inphase (out-of-phase) rotation means that each adjacent octahedra is rotated in the same (alternating) direction. Biaxial compressive strain was found to stabilize the rotations around the out-of-plane axis, while tensile strain stabilizes rotations around the in-plane axes. Due to the interest in using SrNbO₃ as a transparent electrode, I then evaluated the optical properties as a function of the likely distortions. The optical excitations are found to be shifted up to ca. 0.25 eV in the visible regime due to octahedral rotations.

By comparing unfolded DFT bands of SrNbO₃ with angle-resolved photoemission spectroscopy (ARPES) data, fingerprints of the a⁰a⁰c⁺ rotation are observed in the ARPES bands. This further indicates that a0a0c+ is a stable rotation in SrNbO₃. Motivated by this, I then studied the electronic states of the a⁰a⁰c⁺ rotated SrNbO₃ with emphasis on Berry phase-related properties. Dirac nodal lines were observed at the boundary of and within the Brillouin zone. Breaking of time-reversal symmetry, using a ferromagnetic spin ordering, leads to large Berry curvatures near the band crossings which are present due to octahedral rotations. This further indicates how octahedral distortions could be leveraged to introduce and tune fascinating physics in oxides.

While it has been understood that oxygen vacancies result in changes to the electronic transport, it is difficult to find quantitative results of how much the vacancies scatter electrons. I, therefore, calculated the reduction in electrical conductance for different oxygen vacancy configurations in SrNbO₃. This was done using non-equilibrium Green’s functions (NEGFs). As expected, a vacancy blocks the electronic transport, and scattering cross sections of ca 0.8−1.5a² were found. A value of 1a² means that one vacancy reduces the effective transport area with one unit cell area. Interestingly, enabling spin-polarization leads to spin-dependent transport, but also to stronger scattering and the effect was enhanced in ultra-thin slabs compared to bulk. This shows that it is reasonable to expect oxygen vacancies to reduce the conductance, especially in ultra-thin samples where the vacancies induce magnetic moments.

Finally, Fourier’s law of conduction was put to the test against the more general Boltzmann transport equation (BTE). This was done for the phonons in doped Si at room temperature. DFT was used to calculate the phonon dispersion and anharmonic scattering rates of undoped Si, and the effect of doping was introduced using simple scattering rate models. Comparisons were made between the temperature rise from a nanoscopic heater as predicted using Fourier’s law and BTE. At the microscale, the long mean free path phonons in Si carry a substantial part of the heat. Therefore, a length-dependent reduction in the effective thermal conductivity is observed. Doping has a surprisingly small impact on non-diffusive phonon transport. Preliminary experiments on doped Si showed similar length-dependent thermal properties. These results act as a warning against using Fourier’s law for modelling phonon transport at the microscale even for doped Si systems.