Transition from parabolic to ring-shaped valence band maximum in few-layer GaS, GaSe, and InSe

Abstract

By performing first-principles electronic structure calculations in frames of density functional theory we study the dependence of the valence band shape on the thickness of few-layer III-VI crystals (GaS, GaSe, and InSe). We estimate the critical thickness of transition from the bulklike parabolic to the ring-shaped valence band. Direct supercell calculations show that the ring-shaped extremum of the valence band appears in β-GaS and β-GaSe at a thickness below 6 tetralayers (∼4.6 nm) and 8 tetralayers (∼6.4 nm), respectively. Zone-folding calculations estimate the β-InSe critical thickness to be equal to 28 tetralayers (∼24.0 nm). The origin of the ring-shaped valence band maximum can be understood in terms of k·p theory, which provides a link between the curvature of the energy bands and the distance between them. We explain the dependence of the band shape on the thickness, as well as the transition between two types of extremes, by the k-dependent orbital composition of the topmost valence band. We show that in the vicinity of critical thickness the effective mass of holes in III-VI compounds depends strongly on the number of tetralayers.

Electronic and optical properties of two-dimensional InSe from a DFT-parametrized tight-binding model

“…While in its bulk form InSe [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] is a direct gap semiconductor 37 , its electronic structure undergoes significant changes upon exfoliation to few-layer or monolayer thickness, with particularly interesting optical properties observed in recent experiments 1,38 . Density functional theory (DFT) calculations for single layer crystals of InSe 39,40 predict a large increase in the band gap as compared to bulk crystals, with the valence band maximum slightly shifted from the Γ point. Despite being a van der Waals layered material, bulk InSe has a light effective mass for electrons in the conduction and valence band across the layers.…”

Linear and NLO spectroscopy of GaSe and InSe nanoparticles formed via laser ablation

“…Nanotubes of GaSe with an inner diameter of 5 nm and an outer diameter of 20 nm were formed and characterized and it was shown that thermal exfoliation of GaSe yelds scrolls, nanotubes, and nanoflowers 18 . Transitions from parabolic to ring-shaped valence band maximum in few-layer GaS, GaSe, and InSe was reported 19 . More results concerning the properties of GaSe nanoaggregates may be found [20][21][22][23][24][25][26][27][28][29][30] .…”

“…Transitions from parabolic to ring-shaped valence band maximum in few-layer GaS, GaSe, and InSe was reported 19 . More results concerning the properties of GaSe nanoaggregates may be found [20][21][22][23][24][25][26][27][28][29][30] . 4 for GaSe) and possible controlling mechanism were discussed by the authors 31 .…”

Влияние Размерных Эффектов На Электронную Структуру Гексагонального Теллурида Галлия

“…Зонная структура монослойного GaTe имеет типич-ную форму для соединений A III B VI [13,18]. Вершина валентной зоны находится на линии Ŵ−K двумерной зоны Бриллюэна, при этом на линии Ŵ−M присутствует близкий по энергии локальный максимум, обеспечива-ющий дисперсионной зависимости в окрестности т. Ŵ симметричный вид (рис.…”

“…2, a). В отличие от GaS и GaSe [18], в монослое GaTe локальный минимум верхней валентной зоны в т. Ŵ лежит очень близко к более глубоким уровням, обусловленным p x -и p y -орбиталями аниона. Переход от монослоя к структурам с большим количеством слоев сопровождается расщеплением энер-гетических зон, постепенным приближением максимума валентной зоны к т. Ŵ и сдвигом вниз находящегося в т. M дна зоны проводимости (рис.…”