Strain and Stress: Derivation, Implementation, and Application to Organic Crystals

Organic semiconductors form an active and promising field of research since they can be used to develop and construct highly efficient and flexible (opto)electronic devices with tailored structural and electronic properties, e.g., band gaps and conductivities. Typically, these properties do not only depend on the chemical composition but also on the growth conditions, e.g., on the strain or pressure applied during fabrication. However, little is yet known about these dependencies since a systematic assessment of these effects is challenging for experiment and theory alike. To shed light on these aspects, we have developed and implemented techniques to study the pressure dependence of the geometry and of the electronic structure of organic semiconductors with the help of density-functional theory. Nowadays, isolated molecules (< 100 atoms) can be described with high accuracy by quantum chemistry methods. Applying these techniques to molecular crystals, i.e., periodic lattices of such molecules, is to date computationally extremely challenging. Therefore, density-functional theory is still the workhorse electronic-structure tool to investigate these systems - in spite of its deficiencies. In this thesis, we critically discuss to which extent they can be cured by van der Waals corrections and hybrid functionals, which include a portion of Hartree-Fock exchange. To investigate the pressure dependencies, the stress tensor defined as the total energy derivative with respect to the strain tensor is required. In this thesis, the analytical strain derivatives have been derived and implemented in the electronic-structure code FHI-aims including the terms that stem from van der Waals corrections and Hartree-Fock exchange. The excellent accuracy and performance of our implementation is demonstrated by extensive benchmark calculations for a wide range of inorganic and organic crystals. In particular, we discuss the prototypical organic semiconductors anthracene and polyacetylene, which are built from molecules and polymer chains, respectively. To capture their weakly bonded nature, van der Waals corrections are required, and for polyacetylene, hybrid functionals are critical for the correct description of the equilibrium geometry. We find that the interactions between the molecules or chains of the organic crystals significantly influence the electronic band structure and lead to band splitting. Under hydrostatic pressure, both crystals are strongly compressed, which increases these interactions, thereby modifying the band structure. Eventually, the electrical band conductivity of both organic semiconductors is investigated with the Boltzmann transport equation in the constant relaxation time approximation to clarify to which extent the discussed changes in geometry and electronic structure can affect macroscopic properties. We calculate the pressure-dependent trend of the charge carrier concentration and band conductivity for intrinsic and doped systems and point out the dominant transport directions. It is discussed how the behavior of the conductivity can be attributed to the changes in the band structure. Comparison with experiments shows that our calculations yield consistent results