Showing papers by "Alex Zunger published in 2011"

Doping Rules and Doping Prototypes in A2BO4 Spinel Oxides

Abstract: A2BO4 spinels constitute one of the largest groups of oxides, with potential applications in many areas of technology, including (transparent) conducting layers in solar cells. However, the electrical properties of most spinel oxides remain unknown and poorly controlled. Indeed, a significant bottleneck hindering widespread use of spinels as advanced electronic materials is the lack of understanding of the key defects rendering them as p-type or n-type conductors. By applying first-principles defect calculations to a large number of spinel oxides the major trends controlling their dopability are uncovered. Anti-site defects are the main source of electrical conductivity in these compounds. The trends in anti-sites transition levels are systemized, revealing fundamental “doping rules”, so as to guide practical doping of these oxides. Four distinct doping types (DTs) emerge from a high-throughput screening of a large number of spinel oxides: i) donor above acceptor, both are in the gap, i.e., both are electrically active and compensated (DT-1), ii) acceptor above donor, and only acceptor is in the gap, i.e., only acceptor is electrically active (DT-2), iii) acceptor above donor, and only donor is in the gap, i.e., only donor is electrically active (DT3), and iv) acceptor above donor in the gap, i.e., both donor and acceptor are electrically active, but not compensated (DT-4). Donors and acceptors in DT-1 materials compensate each other to a varying degree, and external doping is limited due to Fermi level pinning. Acceptors in DT-2 and donors in DT-3 are uncompensated and may ionize and create holes or electrons, and external doping can further enhance their concentration. Donor and acceptor in DT-4 materials do not compensate each other, and when the net concentration of carriers is small due to deep levels, it can be enhanced by external doping.

Iron Chalcogenide Photovoltaic Absorbers

Abstract: An integrated computational and experimental study of FeS₂ pyrite reveals that phase coexistence is an important factor limiting performance as a thin-film solar absorber. This phase coexistence is suppressed with the ternary materials Fe₂SiS₄ and Fe₂GeS₄, which also exhibit higher band gaps than FeS₂. Thus, the ternaries provide a new entry point for development of thin-film absorbers and high-efficiency photovoltaics.

False-positive and false-negative assignments of topological insulators in density functional theory and hybrids

Abstract: Density-functional theory (DFT) approaches have been used recently to judge the topological order of various materials despite DFT’s well-known band-gap underestimation. Use of the more accurate quasi-particle GW approach reveals few cases where DFT identifications are false positive, which can possibly misguide experimental searches for materials that are topological insulators (TIs) in DFT but not expected to be TIs in reality. We also present the case of false positives due to the incorrect choice of crystal structures and address the relevance of choice of crystal structure with respect to the ground-state one and thermodynamical instability with respect to binary competing phases. We conclude that it is necessary to consider both the correct ground-state crystal structure and the correct Hamiltonian in order to predict new TIs.

Inverse design approach to hole doping in ternary oxides: Enhancing p-type conductivity in cobalt oxide spinels

Abstract: Holes can be readily doped into small-gap semiconductors such as Si or GaAs, but corresponding $p$-type doping in wide-gap insulators, while maintaining transparency, has proven difficult. Here, by utilizing design principles distilled from theory with systematic measurements in the prototype ${A}_{2}B$O${}_{4}$ spinel Co${}_{2}$ZnO${}_{4}$, we formulate and test practical design rules for effective hole doping. Using these, we demonstrate a 20-fold increase in the hole density in Co${}_{2}$ZnO${}_{4}$ due to extrinsic (Mg) doping and, ultimately, a factor of 10${}^{4}$ increase for the inverse spinel Co${}_{2}$NiO${}_{4}$, the $x$ $=$ 1 end point of Ni-doped Co${}_{2}$Zn${}_{1\ensuremath{-}x}$Ni${}_{x}$O${}_{4}$.

Matrix-embedded silicon quantum dots for photovoltaic applications: a theoretical study of critical factors

Abstract: Si Quantum dots (QD's) are offering the possibilities for improving the efficiency and lowering the cost of solar cells. In this paper we study the PV-related critical factors that may affect design of Si QDs solar cell by performing atomistic calculation including many-body interaction. First, we find that the weak absorption in bulk Si is significantly enhanced in Si QDs, specially in small dot size, due to quantum-confinement induced mixing of Γ-character into the X-like conduction band states. We demonstrate that the atomic symmetry of Si QD also plays an important role on its bandgap and absorption spectrum. Second, quantum confinement has a detrimental effect on another PV property – it significantly enhances the exciton binding energy in Si QDs, leading to difficulty in charge separation. We observe universal linear dependence of exciton binding energy versus excitonic gap for all Si QDs. Knowledge of this universal linear function will be helpful to obtain experimentally the exciton binding energy by just measuring the optical gap without requiring knowledge on dot shape, size, and surface treatment. Third, we evaluate the possibility of resonant charge transport in an array of Si QDs via miniband channels created by dot-dot coupling. We show that for such charge transport the Si QDs embedded into a matrix should have tight size tolerances and be very closely spaced. Fourth, we find that the loss of quantum confinement effect induced by dot-dot coupling is negligible – smaller than 70 meV even for two dots at intimate contact.

Universal electrostatic origin of cation ordering in A2BO4 spinel oxides.

Abstract: The crystal structures of A(2)BO(4) spinel oxides are classified as either normal or inverse, representing different distributions of the A and B cations over the tetrahedrally and octahedrally coordinated cation sites. These structures undergo characteristic structural changes as a function of temperature: (i) the nominally disordered inverse structure orders crystallographically at low T, and (ii) at finite temperatures, both inverse and normal develop characteristic distributions of cations associated with order-disorder structural changes. We show here that all of these universal features emerge naturally from a simple point-ion electrostatic (PIE) model with a single adjustable parameter. Monte Carlo simulations of the PIE Hamiltonian provide quantitative order-disorder characteristic temperatures. We show that, with the help of the PIE model, the magnitude of the temperatures can be inferred from the nominal charges of the atomic species in the spinel. Indeed, we show that characteristic order-disorder temperatures in 3-2 spinels (nominal charges Z(A) = 3 and Z(B) = 2) are approximately an order of magnitude lower than in 2-4 spinels, thus explaining why typical 3-2 samples exhibit much larger degrees of disorder than those belonging to the 2-4 class.

Using design principles to systematically plan the synthesis of hole-conducting transparent oxides: Cu 3 VO 4 and Ag 3 VO 4 as a case study

Abstract: In order to address the growing need for $p$-type transparent conducting oxides (TCOs), we present a materials design approach that allows to search for materials with desired properties. We put forward a set of design principles (DPs) that a material must meet in order to qualify as a $p$-type TCO. We then start from two prototype $p$-type binary oxides, i.e., Cu${}_{2}$O and Ag${}_{2}$O, and define a large group of compounds in which to search for unique candidate materials. From this set of compounds, we extracted two oxovanadates, Cu${}_{3}$VO${}_{4}$ and Ag${}_{3}$VO${}_{4}$, which serve as a case study to show the application of the proposed materials selection procedure driven by the DPs. Polycrystalline Ag${}_{3}$VO${}_{4}$ was synthesized by a water-based hydrothermal technique, whereas Cu${}_{3}$VO${}_{4}$ was prepared by a solid-state reaction. The theoretical study of the thermochemistry, based on first-principles electronic structure methods, demonstrates that Cu${}_{3}$VO${}_{4}$ and $\ensuremath{\alpha}$-Ag${}_{3}$VO${}_{4}$ are $p$-type materials that show intrinsic hole-producing defects along with a low concentration of ``hole-killing'' defects. Owing to its near-perfect stoichiometry, Ag${}_{3}$VO${}_{4}$ has a rather low hole concentration, which coincides with the experimentally determined conductivity limit of 0.002 S/cm. In contrast, Cu${}_{3}$VO${}_{4}$ is highly off stoichiometric, Cu${}_{3\ensuremath{-}x}$VO${}_{4}$ ($x=0.15$), which raises the amount of holes, but due to its black color, it does not fulfill the requirements for a $p$-type TCO. The onset of optical absorption in $\ensuremath{\alpha}$-Ag${}_{3}$VO${}_{4}$ is calculated to be 2.6 eV, compared to the experimentally determined value of 2.1 eV, which brings it to the verge of transparency.

Comment on “Intrinsic n -type Behavior in Transparent Conducting Oxides: A Comparative Hybrid-Functional Study of In 2 O 3 , SnO 2 , and ZnO”

Abstract: A Comment on the Letter by P\'eter \'Agoston et al. [Phys. Rev. Lett. 103, 245501 (2009)]. The authors of the Letter offer a Reply.

Asymmetric cation nonstoichiometry in spinels: Site occupancy in Co 2 ZnO 4 and Rh 2 ZnO 4

Abstract: Two cations $A$ and $B$ in ${A}_{2}B{\text{O}}_{4}$ spinels appear in precise 2:1 Daltonian ratio (``line compounds'') only at very low temperature. More typically, at finite temperature, they tend to become either $A$ rich or $B$ rich. Here we survey the experimentally observed stoichiometry asymmetries and describe the first-principles framework for calculating these. Defect calculations based on first principles are used to calculate the enthalpies of substitution of $A$ atom $\ensuremath{\Delta}H({A}_{{\mathrm{T}}_{\mathrm{d}}}$) and $B$ atom $\ensuremath{\Delta}H({B}_{{\mathrm{O}}_{\mathrm{h}}}$) and determine their site occupancies leading to (non)-stoichiometry. In Co${}_{2}$ZnO${}_{4}$, the result of the calculation for site occupancy compares well with that measured via anomalous x-ray diffraction. Further, the calculated phase boundary also compares well with that measured via Rietveld refinement of x-ray diffraction data on bulk ceramic sintered samples of Co${}_{2}$ZnO${}_{4}$ and Rh${}_{2}$ZnO${}_{4}$. These results show that Co${}_{2}$ZnO${}_{4}$ is heavily Co nonstoichiometric above 500 ${}^{\ensuremath{\circ}}$C, whereas Rh${}_{2}$ZnO${}_{4}$ is slightly Zn nonstoichiometric. We found that, in general, the calculated $\ensuremath{\Delta}H({A}_{{\mathrm{T}}_{\mathrm{d}}}$) is smaller than $\ensuremath{\Delta}H({B}_{{\mathrm{O}}_{\mathrm{h}}}$), if the $A$-rich competing phase is isostructural with the ${A}_{2}B$O${}_{4}$ host, for example, ${A}_{2}A{\text{O}}_{4}$, whereas $B$-rich competing phase is not, for example, $B$O. This observation is used to qualitatively explain nonstoichiometry and solid solutions observed in other spinels.

Absence of Intrinsic Spin Splitting in One-Dimensional Quantum Wires of Tetrahedral Semiconductors

Abstract: The energy bands of three-, two-, and one-dimensional (1D) structures are generally split at certain wave-vector values into spin components, a spin splitting (SS) that occurs even without an external magnetic field and reflects the effect of spin-orbit interaction on certain symmetries. We show via atomistic theory that 1D quantum wires made of conventional zinc-blende semiconductors have unexpected zero SS for all electron and hole bands if the wire is oriented along (001) (belonging to ${D}_{2d}$ symmetry), and for some of bands if the wire is oriented along (111) (belonging to ${C}_{3v}$ symmetry). We find that the predicted absence of a Dresselhaus SS in both (001)-oriented and (111)-oriented 1D wires is immune to perturbations lowering their original ${D}_{2d}$ and ${C}_{3v}$ structural symmetries, such as alloying of the matrix around the wire or application of an external electric field. Indeed, such perturbations induce only a Rashba SS. We find that the scaling of the SS with the wave vector is dominated by a linear term plus a minor cubic term.

Excitons and excitonic fine structures in Si nanowires: Prediction of an electronic state crossover with diameter changes

Abstract: Si nanowires have attracted considerable attention as promising candidates for electronic, thermoelectric, photonic, and photovoltaic devices, yet there appears to be only limited understanding of the underlying electronic and excitonic structures on all pertinent energy scales. Using atomistic pseudopotential calculations of single-particle as well as many-body states, we have identified remarkable properties of Si nanowires in three energy scales: (i) In the ``high-energy'' $\ensuremath{\sim}$1-eV scale, we find an unusual electronic state crossover whereby the nature of the lowest unoccupied molecular orbital (LUMO) state changes its symmetry with wire diameters for [001]-oriented wires but not for [011]-oriented wires. This change leads to orbitally allowed transitions becoming orbitally forbidden below a certain critical diameter for [001] wires. (ii) In the ``intermediate-energy'' $\ensuremath{\sim}$10${}^{\ensuremath{-}1}$-eV scale, we describe the excitonic binding, finding that in [001] wires the diameter ($D$) dependence of excitonic gap scales as $1/{D}^{1.9}$, not as $1/{D}^{1}$ as expected. The exciton binding energy increases from 52 meV at $D=7.6$ nm to 85 meV at $D=3.3$ nm and 128 meV at $D=2.2$ nm. (iii) In the ``low-energy'' $\ensuremath{\sim}$10${}^{\ensuremath{-}3}$-eV scale, we describe dark/bright excitonic states and predict how orbitally allowed transitions [in scale (i)] become spin-forbidden due to the electron-hole exchange interaction, whereas the spin-allowed states in the orbitally forbidden diameter region remain dark. The diameter dependence of the fine-structure splitting of excitonic states scales as $1/{D}^{2.3}$ in [001] wires and as $1/{D}^{2.6}$ in [011] wires. Surface-polarization effects are found to significantly enhance electron-hole Coulomb interaction, but have a small effect on the exchange fine-structure splitting. The present work provides a road map for a variety of electronic and optical effects in Si nanowires that can guide spectroscopic studies.

Geometry of epitaxial GaAs/(Al,Ga)As quantum dots as seen by excitonic spectroscopy

Abstract: It is shown that exciton and multiexciton emission lines (``spectral barcode'') of a quantum dot conceal nontrivial structural information on the shape and size of the dot, information which can be uncovered by comparison with atomistic many-body theory. Application to the newly established strain-free GaAs quantum dots grown via ``droplet epitaxy'' onto AlGaAs matrix reveal the shape and size as ``seen'' by spectroscopy. The results show that the previously determined dot height ($\ensuremath{\sim}14$ nm) as ``seen'' by cross-sectional scanning tunneling microscopy (XSTM) could not possibly be consistent with the excitonic signature (1.7--1.9 eV), as the latter must reflect dot height of 1--4 nm. Multiexciton ``barcode'' and fine structure spitting suggest GaAs/AlGaAs dots are in Gaussian-shape in agreement with XSTM measurement. Both spectroscopy and XSTM measurements were done on GaAs dots capped by the Al${}_{0.3}$Ga${}_{0.7}$As barrier layer. The fact that XSTM sees tall dots and spectroscopy sees short dots is thus not because the dot change its height in one experiment relative to the other but because different dots must have been used. This was uncovered by theoretical simulation of the experiment showing that the two experiments could not possibly correspond to the same dot.

Localized interface states in coherent isovalent semiconductor heterojunctions

Abstract: q point of the two-dimensional Brillouin zone and (ii) are allowed by symmetry to couple at this point � q. In this case, the system manifests two potential wells of opposite attractiveness, such as a well for � states and a barrier for X states. For InP/GaP this leads to the formation of an interface-localized state already in a single heterojunction, lying energetically between theedge of InP and the X edge of GaP. When the InP/GaP quantum well is formed, this single state evolves into a pair of interface-localized states, located deep in the band gap. Because of their mixed � -X character, these interface-localized states possess a strong optical signature. This new understanding allows us to provide a different interpretation to the previously observed photoemission data for InP/GaP quantum wells and dots. We find analogous states in GaAs/AlAs and GaAs/GaP but now these levels are resonant within the continuum of states of the matrix conduction band and are therefore less pronounced.

Learning to Predict Physical Properties using Sums of Separable Functions

Abstract: We present an algorithm for learning the function that maps a material structure to its value on some property, given the value of this function on several structures. We pose this problem as one of learning (regressing) a function of many variables from scattered data. Each structure is first converted to a weighted set of points by a process that removes irrelevant translations and rotations but otherwise retains full information about the structure. Then, incorporating a weighted average for each structure, we construct the multivariate regression function as a sum of separable functions, following the paradigm of separated representations. The algorithm can treat all finite and periodic structures within a common framework, and in particular does not require all structures to lie on a common lattice. We show how the algorithm simplifies when the structures do lie on a common lattice, and we present numerical results for that case.