Waves and particles in the crystal

This chapter provides the groundwork necessary to mathematically describe the crystalline solid that is to be the semiconductor used to explore the variety of interactions and cause and chance behaviors that physics builds insights into. The crystalline environment can be portrayed as a space-filling periodic arrangement consisting of a lattice with an atomic basis. The periodic arrangement leads to real space and reciprocal space descriptions with unit cells—the Wigner-Seitz cell and the Brillouin and Jones zones—where a variety of characteristics can be represented. Bloch’s theorem with its modulation function of the plane wave of a quantized wavevector, momentum versus crystal momentum, together with the consequences of symmetries and periodic perturbation in the appearance of bandgaps, is discussed for electron states. Phonons as particles for periodic oscillations of atoms, their modes and various branches, and consequences of ionicity leading to frequency-dependent permittivity are discussed.

A structure-property study toward π-extended phosphole chromophores with ambipolar redox properties

We report the synthesis of a series of π-extended dithienophospholes with phenyl or biphenyl terminal groups via Suzuki Miyaura cross-coupling procedures. The incorporation of the dithienophosphole core into the scaffold on oligophenylenes was found to lead to pronounced luminescence properties in solution and the solid state, the latter of which also responded to different solid-state morphologies, i.e., powder versus crystal. More importantly, the investigated molecular architectures also allowed — for the first time — the observation of ambipolar redox behavior of such species, with the biphenyl-extended species in particular showing quasi-reversible reduction and oxidation processes; the observed experimental features were correlated with computational density functional theory studies.