Tight-binding parameters for wurtzite and wurtzite-zincblende crystal phase heterostructures

Models in physics are simplified descriptions of real world systems that are used to explain observed properties as well as predict novel behavior. An illustrative and commonly taught example is the Bohr model of the hydrogen atom. In this model, the electron and nucleus are often likened to the orbital motions of planets around the sun. While an approximation, the Bohr atomic model allowed scientists to explain the discrete hydrogen spectrum (only certain frequencies of light are seen). Whereas the hydrogen atom has 2 particles (one electron and one proton), typical solids have on the order of Avogadro’s (≈ 10²⁶) number of particles.

While a description of each electron and proton in something like your smartwatch is inconceivable, even in the largest supercomputer, we can still describe many of the important properties by using models that target the relevant physics at different length scales. The model that is of central focus in this work is the tight-binding model, which aims to describe the electronic properties (i.e., the ways something interacts with light, current and electric fields) of a substance, such as a molecule or a crystal, by thinking of electrons as typically staying very close to an atomic nucleus (i.e., ‘Tightly Bound’) but allowed to move to nearby atoms as if by ‘hopping’. The electronic parameters used in calculations for this model are determined for a particular material by finding values that are in close agreement with experimental observations. If the parameters used in the model can still describe that material when it is deformed slightly or butted up against another material to create an interface, we say that it is ‘transferable’. If the values that describe the same atom in two different materials, say the gallium in gallium-arsenide vs in gallium-antimonide, are a little different, we say the values are ‘semi-transferable’.

I am interested in finding a new set of these model values for a group of materials that has received a great deal of attention lately, namely what are called the wurtzite III-V’s. Wurtzite is a type of crystal that has hexagonal geometry and III-V refers to their being two types of atoms in the crystal: one from column III (Al, Ga, In) in the periodic table and one from column V (P, As, Sb). These materials typically exist in a different crystal phase known as zincblende which has a cubic geometry. However, recent advances in fabrication techniques over the last decade have enabled the ability to grow small pillars, called nanowires, of layered wurtzite or zincblende. While experimental data is becoming available for these structures, theoretical models are lacking. In this work, I present my results for a new bulk wurtzite group III-V (non-nitride) and group IV tight-binding model, as well as calculations for some types of layered structures observed during nanowire growth.