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Band Anti-crossing Model

Alloying presents the opportunity to tune the optical and electronic properties of a semiconductor simply by altering its composition, and with advancements in thin film growth techniques, it is now possible to fabricate single-phase materials composed of highly immiscible compounds.? Among these new alloys, semiconductors known as highly mismatched alloys (HMA) undergo a dramatic change in their optical and electrical properties upon the addition of only a few percent of the alloying species, which is highly desirable for bandgap engineering applications.? Our group conducts theoretical and experimental research into the fundamental physical origins of this behavior in order to understand how these materials may be applied to various applications.

Highly mismatched alloys include those compound semiconductors wherein the anion species has been partially replaced by an isovalent impurity of much different electronegativity or size.? Examples include GaNxAs1-x, GaNxP1-x, ZnOxTe1-x, GaSbxAs1-x, GaBixAs1-x, and ZnTexS1-x.? The bandgaps of these alloys have an unusually strong dependence on the composition as well as pressure and in some instances possess an extra impurity-derived band (ZnOxTe1-x).? In order to explain these unusual properties, we have developed a band anticrossing (BAC) model, which takes into account the interaction of the impurity species with the host crystal.? Although electrically neutral, these impurities introduce localized states that undergo an anticrossing interaction with the delocalized states of the host crystal.? When the impurity species has a much greater electronegativity than that of the host anion, the defect states of the impurity atoms are often located near the conduction band edge of the host.? Electrons are localized near the impurity sites, and it is thes-like states that interact.? As a result, the conduction band is split into E+ and E- sub-bands according to the equation:


where Ed is the energy level of the defect state and EM(k) is the dispersion relation of the host semiconductor.? The matrix element Vdescribes the coupling between the localized and delocalized states and is dependent on the difference in the electronegativities between the two anion elements.

Link to more detailed description of nitrides and oxides

Conversely, when the impurity species has a much smaller first ionization energy than the host anion, the defect states of these metallic atoms often lie near the valence band edge of the host.? Holes are localized at the impurities sites, and the p-like states interact.? The restructuring of the valence band may be calculated with a 12 x 12 Hamiltonian matrix, which consists of the conventional 6 x 6 k�Epmatrix describing the delocalized states of the host semiconductor augmented with the six localized states of the impurity atoms.? Like the anticrossing interactions in the conduction band, the hybridization the host and impurity states can be written in terms of a coupling parameter, CNM, and is also dependent on the difference in ionization energy between the two anion elements.? Accordingly, the anticrossing interaction splits the valence band into heavy hole, light hole and spin-orbit split-off -derived E+ and E- bands.

The valence band anticrossing (VBAC) model has been used to describe the unusual properties of a variety of III-V and II-VI alloys, including GaSbxAs1-x, GaBixAs1-x, GaAsxN1-x, ZnTexS1-x and ZnTexSe1-x.? The defect states of Sb and Bi are both resonant with the valence band of GaAs.? Consequently, the bandgap bowing exhibited by both GaSbxAs1-x and GaBixAs1-x in the dilute range (x < 0.15) has been attributed to the upward movement of the heavy hole E+ band induced by the anticrossing interaction with the related E- band below.? The bandgap bowing in ZnTexS1-x and ZnTexSe1-x occurs by a similar mechanism.? In some cases, the localized state may lie above the valence band maximum of the host semiconductor.? For instance, the incorporation of As into GaN produces a narrow As-derived band within the gap, leading to a discontinuous reduction in the band gap of the alloy.