Browsing by Author "Vukmirović, Nenad"

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    Ab Initio Construction of Symmetry-adapted k·p Hamiltonians for the Electronic Structure of Semiconductors
    Jocić, Milan; Vukmirović, Nenad
    While k·p Hamiltonians are frequently used for the description of electronic states in quantum nanostructures, a method is lacking to obtain them in their symmetrized form directly from ab initio band structure calculations of bulk material. We developed a method for obtaining the parameters and the symmetry-adapted form of the k·p Hamiltonian from the output of an ab initio band structure calculation. The method consists of (i) evaluation of momentum matrix elements between the wave functions obtained from band structure calculation; (ii) identification of the unitary transformation that transforms these wave functions to the symmetry-adapted basis; (iii) transformation of the k·p Hamiltonian to the symmetry-adapted basis. We illustrate the methodology by obtaining k·p Hamiltonians that describe the band structure of zinc-blende CdSe and then we use the Hamiltonians obtained to calculate the electronic states in CdSe quantum wells. Excellent agreement between density functional theory and k·p is obtained for the electronic structure, even for quite thin wells.
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    Ab-initio calculations of temperature dependent electronic structures of inorganic halide perovskite materials
    Jocić, Milan; Vukmirović, Nenad
    Despite wide interest in halide perovskite materials, it is still challenging to accurately calculate their electronic structure and its temperature dependence. In this work, we present ab-initio calculations of the temperature dependence of the electronic structure of CsPbX3 materials (X = Cl, Br or I) in the cubic form and of the zero temperature electronic structure of the orthorhombic phase of these materials. Phonon-induced temperature dependent band energy renormalization was calculated within the framework of Allen-Heine-Cardona theory, where we exploited the self-consistent procedure to determine both the energy level shifts and their broadenings. The phonon spectrum of the materials was obtained using the self-consistent phonon method since standard density functional perturbation theory calculations in harmonic approximation yield phonon modes with imaginary frequencies due to the fact that the cubic structure is not stable at zero temperature. Our results suggest that low energy phonon modes mostly contribute to phonon-induced band energy renormalization. The calculated values of the band gaps at lowest temperature where the material exhibits a cubic structure are in good agreement with experimental results from the literature. The same is the case for the slope of the temperature dependence of the band gap for the CsPbI3 material where reliable experimental data are available in the literature. We also found that phonon-induced temperature dependence of the band gap is most pronounced for the conduction band minimum and valence band maximum, while other bands exhibit a weaker dependence.
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    Aerosol Synthesis and Gas-Phase Photoelectron Spectroscopy of Ag-Bi-I Nanosystems
    Danilović, Danijela; Božanić, Dušan; Dojčilović, Radovan; Vukmirović, Nenad; Sapkota, Pitambar; Vukašinović, Ivana; Đoković, Vladimir; Bozek, John; Nicolas, Christophe; Ptasinska, Sylwia; Milosavljević, Aleksandar
    We report on the aerosol generation of ligand-free silver iodobismuthate (Ag-Bi-I) nanoparticles (NPs) and on in situ investigation of their electronic structure using synchrotron radiation soft X-ray aerosol photoelectron spectroscopy (XAPS). The structural and morphological characterizations revealed the aerosol to be composed of spherical rudorffite Ag3BiI6 particles, approximately 100 nm in size. The XAPS showed well-resolved signals from all expected elements (Ag, Bi, and I) and allowed estimation of the NP work function to be about 4.5 eV. The ionization energy of Ag3BiI6 NPs was determined to be 6.1 eV that is in good agreement with our calculations based on a hybrid functional approach. The presented method of production of Ag3BiI6 aerosol can prove beneficial for the future development of Ag-Bi-I-based photovoltaic materials, since it allows the deposition of Ag-Bi-I particles on large surface areas of arbitrary shape and roughness.
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    Calculations of electron mobility in II-VI semiconductors
    Vukmirović, Nenad
    Electron mobility in the conduction band of II-VI semiconductors ZnSe, CdTe, ZnTe, and CdSe was studied. Temperature dependence of mobility was calculated using the methodology based on density functional theory calculations of the electronic states, phonon modes, and electron-phonon coupling constants, along with Fourier-Wannier procedure for interpolation to a dense grid in momentum space. The mobilities obtained from calculations within generalized gradient approximation of density functional theory overestimate the experimental mobility several times. The calculation that used improved electronic band structure and high-frequency dielectric constants obtained using a hybrid functional lead to a very good agreement with experimental mobilities for most of the materials studied. It was also found that the Frohlich model provides a reasonably good estimate of mobilities around room temperature where longitudinal optical phonons provide the dominant scattering mechanism, as expected for these direct gap materials where all relevant electronic states are in the vicinity of the Gamma point. The results indicate as well that the long-ranged part of electron-phonon interaction fully determines the electron mobility in the materials studied. For this reason, the approach where only this part of electron-phonon interaction is calculated using the relevant analytical formulas allows for accurate calculation of mobility without the use of the interpolation procedure for electron-phonon coupling constants.
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    Charge Carrier Mobility in Systems with Local Electron-phonon Interaction
    Prodanović, Nikola; Vukmirović, Nenad
    We present a method for calculation of charge carrier mobility in systems with local electron-phonon interaction. The method is based on unitary transformation of the Hamiltonian to the form where the nondiagonal part can be treated perturbatively. The Green's functions of the transformed Hamiltonian were then evaluated using the Matsubara Green's functions technique. The mobility at low carrier concentration was subsequently evaluated from Kubo's linear response formula. The methodology was applied to investigate the carrier mobility within the one-dimensional Holstein model for a wide range of electron-phonon coupling strengths and temperatures. The results indicated that for low electron-phonon coupling strengths the mobility decreases with increasing temperature, while for large electron-phonon coupling the temperature dependence can exhibit one or two extremal points, depending on the phonon energy. Analytical formulas that describe such behavior were derived. Within a single framework, our approach correctly reproduces the results for mobility in known limiting cases, such as band transport at low temperatures and weak electron-phonon coupling and hopping at high temperatures and strong electron-phonon coupling.
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    Combination of Charge Delocalization and Disorder Enables Efficient Charge Separation at Photoexcited Organic Bilayers
    Janković, Veljko; Vukmirović, Nenad
    We study incoherent charge separation in a lattice model of an all-organic bilayer. Charge delocalization is taken into account by working in the basis of electron-hole pair eigenstates, and the separation is described as a series of incoherent hops between these states. We find that relatively weak energetic disorder, in combination with good charge delocalization, can account for efficient and weakly field- and temperature-dependent separation of the strongly bound charge transfer (CT) state. The separation efficiency is determined by the competition between the recombination from the initial CT state and the escape toward intermediate CT states, from which free-charge states can be reached with certainty. The separation of donor excitons also exhibits quite high yields, less bound excitons separating more efficiently. Overall, our results support the notion that efficient charge separation can be achieved even out of strongly bound pair states without invoking coherent effects.
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    Cumulant expansion in the Holstein model: Spectral functions and mobility
    Mitrić, Petar; Janković, Veljko; Vukmirović, Nenad; Tanasković, Darko
    We examine the range of validity of the second-order cumulant expansion (CE) for the calculation of spectral functions, quasiparticle properties, and mobility of the Holstein polaron. We devise an efficient numerical implementation that allows us to make comparisons in a broad interval of temperature, electron-phonon coupling, and phonon frequency. For a benchmark, we use the dynamical mean-field theory which gives, as we have recently shown, rather accurate spectral functions in the whole parameter space, even in low dimensions. We find that in one dimension, the CE resolves well both the quasiparticle and the first satellite peak in a regime of intermediate coupling. At high temperatures, the charge mobility assumes a power law μ∝T−2 in the limit of weak coupling and μ∝T−3/2 for stronger coupling. We find that, for stronger coupling, the CE gives slightly better results than the self-consistent Migdal approximation (SCMA), while the one-shot Migdal approximation is appropriate only for a very weak electron-phonon interaction. We also analyze the atomic limit and the spectral sum rules. We derive an analytical expression for the moments in CE and find that they are exact up to the fourth order, as opposed to the SCMA where they are exact to the third order. Finally, we analyze the results in higher dimensions.
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    Cumulant expansion in the Holstein model: Spectral functions and mobility
    Mitrić, Petar; Janković, Veljko; Vukmirović, Nenad; Tanasković, Darko
    We examine the range of validity of the second-order cumulant expansion (CE) for the calculation of spectral functions, quasiparticle properties, and mobility of the Holstein polaron. We devise an efficient numerical implementation that allows us to make comparisons in a broad interval of temperature, electron-phonon coupling, and phonon frequency. For a benchmark, we use the dynamical mean-field theory which gives, as we have recently shown, rather accurate spectral functions in the whole parameter space, even in low dimensions. We find that in one dimension, the CE resolves well both the quasiparticle and the first satellite peak in a regime of intermediate coupling. At high temperatures, the charge mobility assumes a power law μ∞T-2 in the limit of weak coupling and μ∞T-3/2 for stronger coupling. We find that, for stronger coupling, the CE gives slightly better results than the self-consistent Migdal approximation (SCMA), while the one-shot Migdal approximation is appropriate only for a very weak electron-phonon interaction. We also analyze the atomic limit and the spectral sum rules. We derive an analytical expression for the moments in CE and find that they are exact up to the fourth order, as opposed to the SCMA where they are exact to the third order. Finally, we analyze the results in higher dimensions.
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    Effective Refractive-Index Approximation: A Link between Structural and Optical Disorder of Planar Resonant Optical Structures
    Gačević, Žarko; Vukmirović, Nenad
    We provide detailed insights into a link between structural and optical disorder of resonant optical structures, in particular, distributed Bragg reflectors (DBRs) and resonant microcavities (μCs). The standard (targeted) DBR structures have periodic square-wave-like refractive-index profiles, and their optical performance is determined by the refractive-index ratio of the two applied materials (n12=n1/n2, n1>n2) and the number of DBR periods (N). It is well known that its structural disorder strongly affects its optical properties, but, despite that, this influence has not been quantitatively addressed in the literature. We propose a precise quantitative definition for a structural disorder of a single DBR unit cell (disorder factor DF), completing the set of DBR fundamental parameters (n12, N, DF). Then we expose the basis for the effective refractive-index approximation (ERIA), showing that, as long as DBR optical properties are concerned, the influence of increasing structural disorder (DF↑) is virtually identical to the influence of decreasing refractive-index ratio (n12↓), with the latter influence being easily quantified. Making use of the ERIA method, simple analytical formulas, which enable rapid insights into the reflectivity and stop-band width of DBRs with different types of transient layers at the heterointerfaces, are derived and the results validated, via both transfer-matrix simulations and direct experimental measurements of imperfect DBRs. The insights of the ERIA method are then further applied on resonant μCs, providing a comprehensive link between their structural disorder and subsequent deterioration of their quality (Q) factor.
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    Effects of thermal disorder on the electronic structure of halide perovskites: Insights from MD simulations
    Mladenović, Marko; Vukmirović, Nenad
    The effects of thermal disorder on the electronic properties of organic/inorganic halide perovskites were investigated using ab initio molecular dynamics simulations. It was generally found that band gap variations due to effects of thermal disorder are the largest in materials with the smallest lattice constant. The factors that may lead to departure from this trend include the degree of rotational and translational motion of the organic cation and the strength of its dipole. It was found that the contribution of the flexible organic part to the band gap variations is considerably smaller than the contribution of the inorganic part of the material. The results of our simulations indicate that band gap variations in halide perovskites fall within the range exhibited in inorganic semiconductors.
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    Electronic Properties of Free-Standing Surfactant-Capped Lead Halide Perovskite Nanocrystals Isolated in Vacuo
    Milosavljević, Aleksandar R.; Božanić, Dušan K.; Sadhu, Subha; Vukmirović, Nenad; Dojčilović, Radovan; Sapkota, Pitambar; Huang, Weixin; Bozek, John; Nicolas, Christophe; Nahon, Laurent; Ptasinska, Sylwia
    We report an investigation of lead halide perovskite CH3NH3PbBr3 nanocrystals and associated ligand molecules by combining several different state-of-the-art experimental techniques, including synchrotron radiation-based XPS and VUV PES of free-standing nanocrystals isolated in vacuum. By using this novel approach for perovskite materials, we could directly obtain complete band alignment to vacuum of both CH3NH3PbBr3 nanocrystals and the ligands widely used in their preparation. We discuss the possible influence of the ligand molecules to apparent perovskite properties, and we compare the electronic properties of nanocrystals to those of bulk material. The experimental results were supported by DFT calculations.
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    Electronic Properties of Silver–Bismuth Iodide Rudorffite Nanoplatelets
    Danilović, Danijela; Milosavljević, Aleksandar R.; Sapkota, Pitambar; Dojčilović, Radovan; Tošić, Dragana; Vukmirović, Nenad; Jocić, Milan; Djoković, Vladimir; Ptasinska, Sylwia; Božanić, Dušan K.
    Silver-bismuth iodide (Ag-Bi-I) rudorffites are chemically stable and non-toxic materials that can act as a possible lead-free replacement for methylammonium lead halides in optoelectronic applications. We report on a simple route for fabricating Ag-Bi-I colloidal nanoplatelets approximately 160 nm in lateral dimensions and 1-8 nm in thickness via exfoliation of Ag-Bi-I rudorffite powders in acetonitrile. The valence band electronic structure of isolated Ag-Bi-I nanoplatelets was investigated using synchrotron radiation to perform X-ray aerosol photoelectron spectroscopy (XAPS). The ionization energy of the material was found to be 6.1 +/- 0.2 eV with respect to the vacuum level. UV-vis absorption and photoluminescence spectroscopies of the Ag-Bi-I colloids showed that the optical properties of the nanoplatelets originate from I 5p to Bi 6p and I 5p to I 5p transitions, which is further confirmed by density functional theory (DFT) calculations. Finally, calculations based on the DFT and k . p theoretical methods showed that the quantum confinement effect is very weak in the system studied.
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    Energy-Temporal Pathways of Free-Charge Formation at Organic Bilayers: Competition of Delocalization, Disorder, and Polaronic Effects
    Janković, Veljko; Vukmirović, Nenad
    We investigated the charge separation process in organic semiconductor bilayers from the moment of creation of a donor exciton to the time when all charge pairs have either recombined or reached external contacts. The system was modeled using a one-dimensional microscopic Hamiltonian that includes the effects of carrier delocalization, electron-hole interaction, static disorder, and carrier-phonon interaction. Transition rates between excitonic states were modeled using modified Redfield approach which takes into account polaronic effects by exact treatment of diagonal exciton-phonon interaction. An efficient numerical scheme was developed that enabled us to obtain the time dependence of energy-resolved populations of relevant exciton states on a time scale as long as 1 μs. Our results indicated that charge separation proceeds via the so-called cold pathway in which donor excitons convert to relaxed charge-transfer excitons which further transform to the states of separated charges. We found that for lower disorder strengths the time scale for conversion of donor excitons to charge transfer excitons is ∼(1-10) ps, while further separation to free charges takes place on the time scale reaching ∼1 ns. These time scales are extended for larger disorder strengths because diffusion of donor excitons to the interface and transport of separated charges toward external contacts are slowed down. We also found that charge separation yield has a rather weak dependence on electron-phonon interaction strength.
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    Gaussian basis implementation of the charge patching method
    Bodroški, Žarko; Vukmirović, Nenad; Škrbić, Srđan
    We present the implementation of the density functional theory based charge patching method using the basis of Gaussian functions. The method is based on the assumption that the electronic charge density of a large system is the sum of contributions of individual atoms, so called charge density motifs, that are obtained from calculations of small prototype systems. In our implementation wave functions and electronic charge density are represented using the basis of Gaussian functions, while charge density motifs are represented using a real space grid. A constrained minimization procedure is used to obtain Gaussian basis representation of charge density from real space representation of motifs. The code based on this implementation exhibits superior performance in comparison to previous implementation of the charge patching method using the basis of plane waves. It enables calculations of electronic structure of systems with around 1000 atoms on a single CPU core with computational time of just several hours.
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    Investigation of carrier confinement in direct bandgap GeSn/SiGeSn 2D and 0D heterostructures
    Rainko, Denis; Ikonic, Zoran; Vukmirović, Nenad; Stange, Daniela; von den Driesch, Nils; Grützmacher, Detlev; Buca, Dan
    Since the first demonstration of lasing in direct bandgap GeSn semiconductors, the research efforts for the realization of electrically pumped group IV lasers monolithically integrated on Si have significantly intensified. This led to epitaxial studies of GeSn/SiGeSn hetero- and nanostructures, where charge carrier confinement strongly improves the radiative emission properties. Based on recent experimental literature data, in this report we discuss the advantages of GeSn/SiGeSn multi quantum well and quantum dot structures, aiming to propose a roadmap for group IV epitaxy. Calculations based on 8-band k∙p and effective mass method have been performed to determine band discontinuities, the energy difference between Γ- and L-valley conduction band edges, and optical properties such as material gain and optical cross section. The effects of these parameters are systematically analyzed for an experimentally achievable range of Sn (10 to 20 at.%) and Si (1 to 10 at.%) contents, as well as strain values (−1 to 1%). We show that charge carriers can be efficiently confined in the active region of optical devices for experimentally acceptable Sn contents in both multi quantum well and quantum dot configurations.
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    Method for obtaining polaron mobility using real and imaginary time path-integral quantum Monte Carlo
    Miladić, Suzana; Vukmirović, Nenad
    We developed a path-integral quantum Monte Carlo-based methodology for calculation of polaron mobility in systems with electron-phonon interaction. Within the method, the current-current correlation function in both the imaginary and real time is calculated in a numerically exact way. The choice of basis for representation of the path integral enabled us to reduce the sign problem and perform real-time calculations for longer times. The DC polaron mobility was extracted by performing analytic continuation that makes use of both the real and imaginary-time data. The method was applied to the Holstein polaron model in one dimension. We obtained reliable results for the temperature dependence of the Holstein polaron mobility for interactions ranging from weak to strong and temperatures that are not too low.
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    Naturally safe: Cellular noise for document security
    Pavlović, Danica; Rabasović, Mihailo; Krmpot, Aleksandar; Lazović, Vladimir; Čurčić, Srećko; Stojanović, Dejan; Jelenković, Branislav; Zhang, Wang; Zhang, Di; Vukmirović, Nenad; Stepanenko, Dimitrije; Kolarić, Branko; Pantelić, Dejan
    Modern document protection relies on the simultaneous combination of many optical features with micron and submicron structures, whose complexity is the main obstacle for unauthorized copying. In that sense, documents are best protected by the diffractive optical elements generated lithographically and mass‐produced by embossing. The problem is that the resulting security elements are identical, facilitating mass‐production of both original and counterfeited documents. Here, we prove that each butterfly wing‐scale is structurally and optically unique and can be used as an inimitable optical memory tag and applied for document security. Wing‐scales, exhibiting angular variability of their color, were laser‐cut and bleached to imprint cryptographic information of an authorized issuer. The resulting optical memory tag is extremely durable, as verified by several century‐old insect specimens still retaining their coloration. The described technique is simple, amenable to mass‐production, low cost and easy to integrate within the existing security infrastructure.
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    Nonequilibrium Thermodynamics of Charge Separation in Organic Solar Cells
    Kaiser, Waldemar; Janković, Veljko; Vukmirović, Nenad; Gagliardi, Alessio
    This work presents a novel theoretical description of the nonequilibrium thermodynamics of charge separation in organic solar cells (OSCs). Using stochastic thermodynamics, we take realistic state populations derived from the phonon-assisted dynamics of electron-hole pairs within photoexcited organic bilayers to connect the kinetics with the free energy profile of charge separation. Hereby, we quantify for the first time the difference between nonequilibrium and equilibrium free energy profile. We analyze the impact of energetic disorder and delocalization on free energy, average energy, and entropy. For a high disorder, the free energy profile is well-described as equilibrated. We observe significant deviations from equilibrium for delocalized electron-hole pairs at a small disorder, implying that charge separation in efficient OSCs proceeds via a cold but nonequilibrated pathway. Both a large Gibbs entropy and large initial electron-hole distance provide an efficient charge separation, while a decrease in the free energy barrier does not necessarily enhance charge separation
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    Polaron mobility obtained by a variational approach for lattice Fröhlich models
    Kornjača, Milan; Vukmirović, Nenad
    Charge carrier mobility for a class of lattice models with long-range electron–phonon interaction was investigated. The approach for mobility calculation is based on a suitably chosen unitary transformation of the model Hamiltonian which transforms it into the form where the remaining interaction part can be treated as a perturbation. Relevant spectral functions were then obtained using Matsubara Green's functions technique and charge carrier mobility was evaluated using Kubo's linear response formula. Numerical results were presented for a wide range of electron–phonon interaction strengths and temperatures in the case of one-dimensional version of the model. The results indicate that the mobility decreases with increasing temperature for all electron–phonon interaction strengths in the investigated range, while longer interaction range leads to more mobile carriers.
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    Spectral and thermodynamic properties of the Holstein polaron: Hierarchical equations  of motion approach
    Janković, Veljko; Vukmirović, Nenad
    We develop a hierarchical equations of motion (HEOM) approach to compute real-time single-particle correlation functions and thermodynamic properties of the Holstein model at finite temperature. We exploit the conservation of the total momentum of the system to formulate the momentum-space HEOM whose dynamical variables explicitly keep track of momentum exchanges between the electron and phonons. Our symmetry-adapted HEOM enable us to overcome the numerical instabilities inherent to the commonly used real-space HEOM. The HEOM method is then used to study the spectral function and thermodynamic quantities of chains containing up to ten sites. The HEOM results compare favorably to existing literature. To provide an independent assessment of the HEOM approach and to gain insight into the importance of finite-size effects, we devise a quantum Monte Carlo (QMC) procedure to evaluate finite-temperature single-particle correlation functions in imaginary time and apply it to chains containing up to twenty sites. QMC results reveal that finite-size effects are quite weak, so that the results on 5 to 10-site chains, depending on the parameter regime, are representative of larger systems. A detailed comparison between the HEOM and QMC data place our HEOM method among reliable methods to compute real-time finite-temperature correlation functions in parameter regimes ranging from low- to high-temperature, and weak- to strong-coupling regime.