Quasicubic model for metal halide perovskite nanocrystals

Abstract

We present an analysis of quantum confinement of carriers and excitons, and exciton fine structure, in metal halide perovskite (MHP) nanocrystals (NCs). Starting with coupled-band k · P theory, we derive a nonparabolic effective mass model for the exciton energies in MHP NCs valid for the full size range from the strong to the weak confinement limits. We illustrate the application of the model to CsPbBr3 NCs and compare the theory against published absorption data, finding excellent agreement. We then apply the theory of electron-hole exchange, including both short- and long-range exchange interactions, to develop a model for the exciton fine structure. We develop an analytical quasicubic model for the effect of tetragonal and orthorhombic lattice distortions on the exchange-related exciton fine structure in CsPbBr3, as well as some hybrid organic MHPs of recent interest, including formamidinium lead bromide (FAPbBr3) and methylammonium lead iodide (MAPbI3). Testing the predictions of the quasicubic model using hybrid density functional theory (DFT) calculations, we find qualitative agreement in tetragonal MHPs but significant disagreement in the orthorhombic modifications. Moreover, the quasicubic model fails to correctly describe the exciton oscillator strength and with it the long-range exchange corrections in these systems. Introducing the effect of NC shape anisotropy and possible Rashba terms into the model, we illustrate the calculation of the exciton fine structure in CsPbBr3 NCs based on the results of the DFT calculations and examine the effect of Rashba terms and shape anisotropy on the calculated fine structure.

Size-Dependent Lattice Structure and Confinement Properties in CsPbI3 Perovskite Nanocrystals: Negative Surface Energy for Stabilization

“…31,33 This model, which accounts for the s-to p-coupling between conduction and valence band quantum size levels, was implemented by using energy dependent effective masses according to Eq. 6 of the main text, derived in the report by Sercel et al, 33 32 The calculated lines were drawn in two ways: CsPbBr3 NC absorption peak energy versus NC size L (solid lines in a) and the absorption peak energy plotted versus the inverse square of NC size 1/L 2 (dashed lines in b) to better illustrate the departure from linearity of energy plotted versus 1/L 2 expected in the parabolic approximation. The model parameters are derived from 2K magneto-transmission measurements on bulk CsPbBr3, 28 with the exception of the bandgap which is adjusted to achieve the best fit to the measured data.…”

Circular dichroism in non-chiral metal halide perovskites

“…To study the exciton polarization properties it is most convenient to transform into a basis of exciton states whose dipoles are oriented along the x, y, z directions. 45 This O basis is described by the |X , |Y , and |Z wave functions of the three exciton states X , Y , and Z whose dipoles are oriented along the x , y , and z directions, and the |D wave function of the dark D exciton state, which is dipole inactive. 45 The unitary transformation to this basis, developed in the Supporting Information section, results in the following matrix representation,…”

“…These are degenerate in the case of cubic symmetry but split in general in crystals with orthorhombic crystal structure. 42,45 In our calculations, for simplicity, we will start by neglecting the crystal field splitting between the X , Y and Z exciton states, setting E x = E y = E z = E t , the bright triplet energy. Although the off-diagonal terms in Hamiltonian described by Eq.…”

Optical studies of semiconductor perovskite nanocrystals for classical optoelectronic applications and quantum information technologies: a review

“…It is obvious that there are still ongoing debates as to the real origin of exciton fine structures in single perovskite NCs, which might be further influenced by the crystal phases and the shape anisotropy. 128,135,147 However, the stable existence of exciton fine structures has rendered unprecedented research opportunities in coherently manipulating the exciton wave functions for novel atomic and quantum physics, as well as for practical quantum-information-processing applications.…”

“…The chemical routes need to be continuously polished for the synthesis of more robust perovskite NCs along with judicious controls over their sizes, which are now falling largely within the weak to intermediate regimes of quantum confinement. 128,132,135,136,146,147 The chemical stability is not an obvious issue for single perovskite NCs studied at cryogenic temperatures. However, their PL linewidth is almost one order of magnitude broader than that routinely measured for single epitaxial QDs.…”