Electronic properties of CdSe nanocrystals in the absence and presence of a dielectric medium

We present a detailed study of the electronic properties of CdSe nanocrystals in the absence and presence of a dielectric medium. The electronic structure of the nanocrystal is modeled within the framework of the empirical pseudopotential method. We use a real-space grid representation of the wave function, and obtain the eigenvalues and eigenstates of the one-electron Hamiltonian using a slightly modified version of the filter-diagonalization method. The band gap, density of states, charge density, multipole moments, and electronic polarizabilities are studied in detail for an isolated nanocrystal. We discuss the implications of the results for the long range electrostatic and dispersion interactions between two CdSe nanocrystals. To study the effects of the surroundings we develop a self-consistent reaction field method consistent with the empirical pseudopotential method. We use the eigenstates of the isolated nanocrystal and iterate the self-consistent equations until converged results are obtained. The results show that the electronic properties of polar CdSe nanocrystals are quite sensitive to the environment. © 1999 American Institute of Physics. @S0021-9606~99!70910-4#

[1]  A. Mizel,et al.  Electronic transitions in InAs nanocrystals using Wannier function method , 1997 .

[2]  M. Nogami,et al.  Sol-gel processing of small-sized CdSe crystal-doped silica glasses , 1991 .

[3]  Jasprit Singh,et al.  Strain distribution and electronic spectra of InAs/GaAs self-assembled dots: An eight-band study , 1997 .

[4]  Marvin L. Cohen,et al.  Band Structures and Pseudopotential Form Factors for Fourteen Semiconductors of the Diamond and Zinc-blende Structures , 1966 .

[5]  Daniel Neuhauser,et al.  Circumventing the Heisenberg principle: A rigorous demonstration of filter‐diagonalization on a LiCN model , 1994 .

[6]  B. Honig,et al.  Accurate First Principles Calculation of Molecular Charge Distributions and Solvation Energies from Ab Initio Quantum Mechanics and Continuum Dielectric Theory , 1994 .

[7]  Jacopo Tomasi,et al.  Molecular Interactions in Solution: An Overview of Methods Based on Continuous Distributions of the Solvent , 1994 .

[8]  J. Kirkwood,et al.  Theory of Solutions of Molecules Containing Widely Separated Charges with Special Application to Zwitterions , 1934 .

[9]  W. Kohn,et al.  Motion of Electrons and Holes in Perturbed Periodic Fields , 1955 .

[10]  Serdar Ogut,et al.  Ab initio Calculations for the Polarizabilities of Small Semiconductor Clusters , 1997 .

[11]  Kusunoki Volume-expansion-induced lattice instability and solid-state amorphization. , 1996, Physical review. B, Condensed matter.

[12]  Alex Zunger,et al.  DIRECT PSEUDOPOTENTIAL CALCULATION OF EXCITON COULOMB AND EXCHANGE ENERGIES IN SEMICONDUCTOR QUANTUM DOTS , 1997 .

[13]  Brus Model for carrier dynamics and photoluminescence quenching in wet and dry porous silicon thin films. , 1996, Physical review. B, Condensed matter.

[14]  L. Kronik,et al.  Surface States and Photovoltaic Effects in CdSe Quantum Dot Films , 1998 .

[15]  Louis E. Brus,et al.  Semiconductor crystallites: a class of large molecules , 1990 .

[16]  Heath,et al.  Crystallization of opals from polydisperse nanoparticles. , 1995, Physical review letters.

[17]  Louis E. Brus,et al.  Semiconductor colloids: individual nanocrystals, opals and porous silicon , 1996 .

[18]  A. Alivisatos,et al.  CdSe nanocrystals with a dipole moment in the first excited state , 1992 .

[19]  P. Guyot-Sionnest,et al.  Dielectric Dispersion Measurements of CdSe Nanocrystal Colloids: Observation of a Permanent Dipole Moment , 1997 .

[20]  Wang,et al.  Dielectric constants of silicon quantum dots. , 1994, Physical review letters.

[21]  Lin-wang Wang,et al.  Applicability of the k ⋅ p method to the electronic structure of quantum dots , 1998 .

[22]  A. Alivisatos Perspectives on the Physical Chemistry of Semiconductor Nanocrystals , 1996 .

[23]  Wang,et al.  Pseudopotential calculations of nanoscale CdSe quantum dots. , 1996, Physical review. B, Condensed matter.

[24]  Daniel Neuhauser,et al.  Time‐dependent reactive scattering in the presence of narrow resonances: Avoiding long propagation times , 1991 .

[25]  William L. Wilson,et al.  Luminescence properties of CdSe quantum crystallites: Resonance between interior and surface localized states , 1992 .

[26]  R. Friesner,et al.  Quantum Confinement Effects in CdSe Quantum Dots , 1995 .

[27]  S. Tolbert,et al.  High-pressure structural transformations in semiconductor nanocrystals. , 1995, Annual review of physical chemistry.

[28]  Walter A. Harrison,et al.  Electronic structure and the properties of solids , 1980 .

[29]  M. Ratner,et al.  Molecular electronics : a 'chemistry for the 21st century' monograph , 1997 .

[30]  Alex Zunger,et al.  Local-density-derived semiempirical nonlocal pseudopotentials for InP with applications to large quantum dots , 1997 .

[31]  D. Neuhauser,et al.  Avoiding long propagation times in wave packet calculations on scattering with resonances: A new algorithm involving filter diagonalization , 1997 .

[32]  M. Jaroš,et al.  ABSORPTION SPECTRA AND OPTICAL TRANSITIONS IN INAS/GAAS SELF-ASSEMBLED QUANTUM DOTS , 1997 .

[33]  Friesner,et al.  Exciton spectra of semiconductor clusters. , 1991, Physical review letters.

[34]  A. Zunger,et al.  Prediction of a strain-induced conduction-band minimum in embedded quantum dots , 1998, cond-mat/9801191.

[35]  H. C. Hamaker The London—van der Waals attraction between spherical particles , 1937 .

[36]  Nair,et al.  Optical absorption in semiconductor quantum dots: A tight-binding approach. , 1993, Physical review. B, Condensed matter.

[37]  Marvin L. Cohen,et al.  GREEN'S-FUNCTION APPROACH TO QUANTUM CONFINEMENT , 1998 .

[38]  M. Bawendi,et al.  Magnetic circular dichroism study of CdSe quantum dots , 1998 .

[39]  Ronnie Kosloff,et al.  Low-order polynomial approximation of propagators for the time-dependent Schro¨dinger equation , 1992 .

[40]  Bryant Excitons in quantum boxes: Correlation effects and quantum confinement. , 1988, Physical review. B, Condensed matter.

[41]  Louis E. Brus,et al.  Electron-electron and electron-hole interactions in small semiconductor crystallites : The size dependence of the lowest excited electronic state , 1984 .

[42]  Hodes,et al.  Room-temperature conductance spectroscopy of CdSe quantum dots using a modified scanning force microscope. , 1995, Physical review. B, Condensed matter.

[43]  A. Mizel,et al.  Electronic energy levels in semiconductor nanocrystals: A Wannier function approach , 1997 .

[44]  Hu,et al.  Surface-polarization instabilities of electron-hole pairs in semiconductor quantum dots. , 1992, Physical review. B, Condensed matter.

[45]  Louis E. Brus,et al.  Electronic wave functions in semiconductor clusters: experiment and theory , 1986 .

[46]  R. Friesner,et al.  Quantum confinement effects in semiconductor clusters , 1991 .

[47]  A. Henglein,et al.  Small-particle research: physicochemical properties of extremely small colloidal metal and semiconductor particles , 1989 .

[48]  Philippe Guyot-Sionnest,et al.  Polar CdSe nanocrystals: Implications for electronic structure , 1997 .

[49]  L. Onsager Electric Moments of Molecules in Liquids , 1936 .

[50]  Lin-wang Wang,et al.  Comparison of the k⋅p and the direct diagonalization approaches for describing the electronic structure of quantum dots , 1997 .

[51]  Alex Zunger,et al.  InP quantum dots: Electronic structure, surface effects, and the redshifted emission , 1997 .

[52]  K. B. Whaley,et al.  A theoretical study of the influence of the surface on the electronic structure of CdSe nanoclusters , 1994 .

[53]  R. Friesner,et al.  Prediction of anomalous redshift in semiconductor clusters , 1992 .

[54]  S. Louie,et al.  Self-consistent pseudopotential calculations for Si (111) surfaces: Unreconstructed (1×1) and reconstructed (2×1) model structures , 1975 .

[55]  D. Neuhauser Bound state eigenfunctions from wave packets: Time→energy resolution , 1990 .

[56]  Simone Pokrant,et al.  Exciton fine structure in CdSe nanoclusters , 1998 .

[57]  Peng,et al.  Charge separation and transport in conjugated-polymer/semiconductor-nanocrystal composites studied by photoluminescence quenching and photoconductivity. , 1996, Physical review. B, Condensed matter.

[58]  Wilson,et al.  Electronic structure and photoexcited-carrier dynamics in nanometer-size CdSe clusters. , 1990, Physical review letters.

[59]  R. Kosloff Time-dependent quantum-mechanical methods for molecular dynamics , 1988 .

[60]  Krüger,et al.  Ab initio calculations of the electronic structure of the wurtzite compounds CdS and CdSe. , 1993, Physical review. B, Condensed matter.

[61]  W. Miller,et al.  Efficient polynomial expansion of the scattering Green’s function: Application to the D+H2(v=1) rate constant , 1994 .

[62]  M. Bawendi,et al.  Synthesis and characterization of nearly monodisperse CdE (E = sulfur, selenium, tellurium) semiconductor nanocrystallites , 1993 .

[63]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[64]  Colombo,et al.  Efficient linear scaling algorithm for tight-binding molecular dynamics. , 1994, Physical review letters.

[65]  A. Alivisatos,et al.  Symmetry of Annealed Wurtzite CdSe Nanocrystals: Assignment to the C3v Point Group , 1995 .

[66]  Vicki L. Colvin,et al.  Threshold for quasicontinuum absorption and reduced luminescence efficiency in CdSe nanocrystals , 1994 .

[67]  Louis E. Brus,et al.  The Quantum Mechanics of Larger Semiconductor Clusters ("Quantum Dots") , 1990 .

[68]  H. Tal-Ezer,et al.  An accurate and efficient scheme for propagating the time dependent Schrödinger equation , 1984 .

[69]  U. Banin,et al.  Size-dependent electronic level structure of InAs nanocrystal quantum dots: Test of multiband effective mass theory , 1998 .

[70]  Y. Kayanuma,et al.  Quantum-size effects of interacting electrons and holes in semiconductor microcrystals with spherical shape. , 1988, Physical review. B, Condensed matter.

[71]  Orlando Tapia,et al.  Self-consistent reaction field theory of solvent effects , 1975 .

[72]  Quantum confinement effects in semiconductor clusters. II , 1995, chem-ph/9506001.

[73]  J. Gonzalo Muga,et al.  Time-Dependent Quantum-Mechanical Approaches to the Continuous Spectrum: Scattering Resonances in a Finite Box , 1989 .

[74]  D. Grier,et al.  Interactions and Dynamics in Charge-Stabilized Colloids , 1998 .

[75]  R. Kosloff,et al.  A fourier method solution for the time dependent Schrödinger equation as a tool in molecular dynamics , 1983 .

[76]  E. Keinan,et al.  Chemistry for the 21st Century , 2000 .

[77]  A. Alivisatos Semiconductor Clusters, Nanocrystals, and Quantum Dots , 1996, Science.

[78]  U. Landman,et al.  Structure, dynamics, and thermodynamics of passivated gold nanocrystallites and their assemblies , 1996 .

[79]  A. Ekimov Growth and optical properties of semiconductor nanocrystals in a glass matrix , 1996 .

[80]  J. Chelikowsky,et al.  Self-consistent pseudopotential calculation for the relaxed (110) surface of GaAs , 1979 .

[81]  Lin-wang Wang,et al.  Comparison of the electronic structure of InAs/GaAs pyramidal quantum dots with different facet orientations , 1998 .

[82]  D. D. Yue,et al.  Theory of Electric Polarization , 1974 .

[83]  R. Baer,et al.  Electronic structure of large systems: Coping with small gaps using the energy renormalization group method , 1998 .

[84]  Joseph L. Birman,et al.  ORIGIN OF POLARIZATION IN POLAR NANOCRYSTALS , 1998 .

[85]  A. Zunger,et al.  QUANTUM-SIZE EFFECTS ON THE PRESSURE-INDUCED DIRECT-TO-INDIRECT BAND-GAP TRANSITION IN INP QUANTUM DOTS , 1998 .

[86]  A. Zunger,et al.  GaAs quantum structures: Comparison between direct pseudopotential and single‐band truncated‐crystal calculations , 1996 .

[87]  Norris,et al.  Band-edge exciton in quantum dots of semiconductors with a degenerate valence band: Dark and bright exciton states. , 1996, Physical review. B, Condensed matter.

[88]  Rabitz,et al.  Optimal control of optical pulse propagation in a medium of three-level systems. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[89]  D. Bertho,et al.  Confinement and shape effects on the optical spectra of small CdSe nanocrystals , 1998 .

[90]  Lin-Wang Wang,et al.  Electronic Structure Pseudopotential Calculations of Large (.apprx.1000 Atoms) Si Quantum Dots , 1994 .

[91]  B. Korgel,et al.  CONDENSATION OF ORDERED NANOCRYSTAL THIN FILMS , 1998 .

[92]  J. Chelikowsky,et al.  Electronic Structure and Optical Properties of Semiconductors , 1989 .

[93]  R. Kosloff Propagation Methods for Quantum Molecular Dynamics , 1994 .

[94]  R. Friesner,et al.  Quantum chemistry of semiconductor clusters , 1993 .

[95]  R. Wyatt,et al.  Dynamics of molecules and chemical reactions , 1996 .

[96]  T. K. Bergstresser,et al.  Electronic Structure and Optical Properties of Hexagonal CdSe, CdS, and ZnS , 1967 .

[97]  Louis E. Brus,et al.  SYNTHESIS, STABILIZATION, AND ELECTRONIC STRUCTURE OF QUANTUM SEMICONDUCTOR NANOCLUSTERS , 1989 .

[98]  R. Ahlrichs,et al.  Cadmium selenide semiconductor nanocrystals: a theoretical study , 1998 .

[99]  K. Jensen,et al.  Synthesis of Luminescent Thin-Film CdSe/ZnSe Quantum Dot Composites Using CdSe Quantum Dots Passivated with an Overlayer of ZnSe , 1996 .

[100]  Lannoo,et al.  Comparison between calculated and experimental values of the lowest excited electronic state of small CdSe crystallites. , 1990, Physical review. B, Condensed matter.

[101]  James J. P. Stewart,et al.  Calculation of the nonlinear optical properties of molecules , 1990 .

[102]  Uri Banin,et al.  Colloidal chemical synthesis and characterization of InAs nanocrystal quantum dots , 1996 .

[103]  Daniel Neuhauser,et al.  Extraction, through filter‐diagonalization, of general quantum eigenvalues or classical normal mode frequencies from a small number of residues or a short‐time segment of a signal. I. Theory and application to a quantum‐dynamics model , 1995 .