30-band k⋅p method for quantum semiconductor heterostructures

Boyer‐Richard, Soline; Raouafi, F.; Bondi, Alexandre; Pédesseau, Laurent; Katan, Claudine; Jancu, Jean–Marc; Even, Jacky

doi:10.1063/1.3600643

Cited by 18 publications

(12 citation statements)

References 28 publications

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“…We stress, however, that there are systems (for instance, GaAs/AlAs heterostructure) for which the effective mass approximation performs reasonably well. 68 Page 21 of 35 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 A c c e p t e d m a n u s c r i p t…”

Section: Validity Of the Effective Mass Approximationmentioning

confidence: 99%

Composite Nature of Layered Hybrid Perovskites: Assessment on Quantum and Dielectric Confinements and Band Alignment

et al. 2018

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Layered hybrid organic-inorganic perovskites (HOPs) have re-emerged as potential technological solutions for next-generation photovoltaic and optoelectronic applications. Their two-dimensional (2D) nature confers them a significant flexibility and results in the appearance of quantum and dielectric confinements. Such confinements are at the origin of their fascinating properties, and understanding them from a fundamental level is of paramount importance for optimization. Here, we provide an in-depth investigation of band alignments of 2D HOP allowing access to carriers' confinement potentials. 2D HOPs are conceptualized as composite materials in which pseudoinorganic and -organic components are defined. In this way, computational modeling of band alignments becomes affordable using first-principles methods. First, we show that the composite approach is suitable to study the position-dependent dielectric profiles and enables clear differentiation of the respective contributions of inorganic and organic components. Then we apply the composite approach to a variety of 2D HOPs, assessing the impact on the confinement potentials of well and barrier thickness, of the nature of the inorganic well, and of structural transitions. Using the deduced potentials, we further discuss the limitations of the effective mass approximation, scrutinizing the electronic properties of this family of composite materials. Our simulations demonstrate type-I dominant band alignment in 2D HOPs. Finally, we outline design principles on band alignment toward achieving specific optoelectronic properties. Thus, we present alternative theoretical methods to inspect the properties of 2D hybrid perovskites and expect that the composite approach will be applicable to other classes of layered materials.

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Section: Validity Of the Effective Mass Approximationmentioning

confidence: 99%

Composite Nature of Layered Hybrid Perovskites: Assessment on Quantum and Dielectric Confinements and Band Alignment

et al. 2018

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“…This may happen when a local symmetry breaking occurs at the interface or an interface-related mixing between bulk eigenstates located at different points of the Brillouin zone, drives the heterostructure electronic states. [35,[46][47][48] Thus, it is necessary to explicitly take into account the periodic part of the bulk Bloch functions. The heterostructure periodic functions !…”

Section: Effective Mass Modeling Of Quantum Confinementmentioning

confidence: 99%

“…effective mass changes with QW thickness as has been implemented for NP. [57,58] Alternatively, one could also increase the size of the Bloch function basis set, [46] use an empirical atomistic TB approach for heterostructures, [46,58] or consider the 2D hybrid crystal as a single composite material. [12,17,18] However, one may seek to keep the description as close as possible to the one that is widespread for conventional semiconductors and this will be addressed in the next section.…”

Section: Non-parabolicity Of the Electronic Dispersions In Ultrathin mentioning

confidence: 99%

Understanding Quantum Confinement of Charge Carriers in Layered 2D Hybrid Perovskites

2014

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Keywords: 2D materials, density functional calculations, hybrid perovskites, quantum confinement, semiempirical calculations Layered Hybrid Organic Perovskites (HOP) structures are a class of low-cost twodimensional (2D) materials that exhibit outstanding optical properties, related to dielectric and quantum confinement effects. While modeling and understanding of quantum confinement are well developed for conventional semiconductors, such knowledge has still to be gained for 2D HOP. In this work, concepts of effective mass and quantum well are carefully investigated and their applicability to 2D HOP is discussed. For ultrathin layers, the effective mass model fails. Absence of superlattice coupling and importance of non-parabolicity effects prevents the use of simple empirical models based on effective masses and envelope function approximations. We suggest an alternative approach where 2D HOP are treated as composite materials and introduce a first principles approach to band offsets calculations. These findings may also be relevant for other classes of layered 2D functional materials.

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“…which use the material dependent bulk Hamiltonian matrix elements H λ nm as in Eq. (12). Because the envelope functions do not have to be restricted to the first Brillouin zone, the expansion of the wavefunctions as specified in Eq.…”

Section: Envelope Function Equationmentioning

confidence: 99%

An envelope function formalism for lattice-matched heterostructures

Put

Vandenberghe

Magnus

et al. 2015

Physica B: Condensed Matter

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The envelope function method traditionally employs a single basis set which, in practice, relates to a single material because the k · p matrix elements are generally only known in a particular basis. In this work, we defined a basis function transformation to alleviate this restriction. The transformation is completely described by the known inter-band momentum matrix elements. The resulting envelope function equation can solve the electronic structure in lattice matched heterostructures without resorting to boundary conditions at the interface between materials, while all unit-cell averaged observables can be calculated as with the standard envelope function formalism. In the case of two coupled bands, this heterostructure formalism is equivalent to the standard formalism while taking position dependent matrix elements.

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30-band k⋅p method for quantum semiconductor heterostructures

Cited by 18 publications

References 28 publications

Composite Nature of Layered Hybrid Perovskites: Assessment on Quantum and Dielectric Confinements and Band Alignment

Composite Nature of Layered Hybrid Perovskites: Assessment on Quantum and Dielectric Confinements and Band Alignment

Understanding Quantum Confinement of Charge Carriers in Layered 2D Hybrid Perovskites

An envelope function formalism for lattice-matched heterostructures

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