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Showing papers by "Alex Zunger published in 1998"


Journal ArticleDOI
TL;DR: In this article, the authors studied the defect physics in a chalcopyrite semiconductor and showed that it takes much less energy to form a Cu vacancy in the semiconductor than to form cation vacancies in II-VI compounds and that defect formation energies vary considerably both with the Fermi energy and with the chemical potential of the atomic species.
Abstract: We studied the defect physics in ${\mathrm{CuInSe}}_{2},$ a prototype chalcopyrite semiconductor. We showed that (i) it takes much less energy to form a Cu vacancy in ${\mathrm{CuInSe}}_{2}$ than to form cation vacancies in II-VI compounds (ii) defect formation energies vary considerably both with the Fermi energy and with the chemical potential of the atomic species, and (iii) the defect pairs such as $({2\mathrm{V}}_{\mathrm{Cu}}^{\mathrm{\ensuremath{-}}}{+\mathrm{I}\mathrm{n}}_{\mathrm{Cu}}^{2+})$ and $({2\mathrm{C}\mathrm{u}}_{\mathrm{In}}^{2\mathrm{\ensuremath{-}}}{+\mathrm{I}\mathrm{n}}_{\mathrm{Cu}}^{2+})$ have particularly low formation energies (under certain conditions, even exothermic). Using (i)--(iii), we (a) explain the existence of unusual ordered compounds ${\mathrm{CuIn}}_{5}{\mathrm{Se}}_{8},$ ${\mathrm{CuIn}}_{3}{\mathrm{Se}}_{5},$ ${\mathrm{Cu}}_{2}{\mathrm{In}}_{4}{\mathrm{Se}}_{7},$ and ${\mathrm{Cu}}_{3}{\mathrm{In}}_{5}{\mathrm{Se}}_{9}$ as a repeat of a single unit of $({2\mathrm{V}}_{\mathrm{Cu}}^{\mathrm{\ensuremath{-}}}{+\mathrm{I}\mathrm{n}}_{\mathrm{Cu}}^{2+})$ pairs for each $n=4,$ 5, 7, and 9 units, respectively, of ${\mathrm{CuInSe}}_{2};$ (b) attribute the very efficient $p$-type self-doping ability of ${\mathrm{CuInSe}}_{2}$ to the exceptionally low formation energy of the shallow defect Cu vacancies; (c) explained in terms of an electronic passivation of the ${\mathrm{In}}_{\mathrm{Cu}}^{2+}$ by ${2\mathrm{V}}_{\mathrm{Cu}}^{\mathrm{\ensuremath{-}}}$ the electrically benign character of the large defect population in ${\mathrm{CuInSe}}_{2}.$ Our calculation leads to a set of new assignment of the observed defect transition energy levels in the band gap. The calculated level positions agree rather well with available experimental data.

1,138 citations


Journal ArticleDOI
TL;DR: Using first-principles all-electron band structure method, the authors systematically calculated the natural band offsets ΔEv between all II-VI and separately between III-V semiconductor compounds and found that coupling between anion p and cation d states plays a decisive role in determining the absolute position of the valence band maximum.
Abstract: Using first-principles all-electron band structure method, we have systematically calculated the natural band offsets ΔEv between all II–VI and separately between III–V semiconductor compounds Fundamental regularities are uncovered: for common-cation systems ΔEv decreases when the cation atomic number increases, while for common-anion systems ΔEv decreases when the anion atomic number increases We find that coupling between anion p and cation d states plays a decisive role in determining the absolute position of the valence band maximum and thus the observed chemical trends

686 citations


Journal ArticleDOI
TL;DR: In this article, the effects of Ga additions on the electronic and structural properties of CuInSe2 were theoretically studied using a first-principles band structure method, and it was shown that with increasing xGa, the valence band maximum of CIGS decreases slightly, while the conduction band minimum increases significantly.
Abstract: Using a first-principles band structure method we have theoretically studied the effects of Ga additions on the electronic and structural properties of CuInSe2. We find that (i) with increasing xGa, the valence band maximum of CuIn1−xGaxSe2 (CIGS) decreases slightly, while the conduction band minimum (and the band gap) of CIGS increases significantly, (ii) the acceptor formation energies are similar in both CuInSe2 (CIS) and CuGaSe2 (CGS), but the donor formation energy is larger in CGS than in CIS, (iii) the acceptor transition levels are shallower in CGS than in CIS, but the GaCu donor level in CGS is much deeper than the InCu donor level in CIS, and (iv) the stability domain of the chalcopyrite phase increases with respect to ordered defect compounds. Our results are compared with available experimental observations.

494 citations


Journal ArticleDOI
TL;DR: In this paper, it is explained phenomenologically in terms of the "doping pinning rule" that semiconductors differ widely in their ability to be doped as their band gap increases and it is usually possible to dope them either n or p type, but not both.
Abstract: Semiconductors differ widely in their ability to be doped As their band gap increases, it is usually possible to dope them either n or p type, but not both This asymmetry is documented here, and explained phenomenologically in terms of the “doping pinning rule”

424 citations


Journal ArticleDOI
TL;DR: In this paper, the authors compare two approaches for calculating inhomogeneous strain between lattice-mismatched III-V semiconductors, and compare the strain profile obtained by both approaches, including the approximation of the correct C2 symmetry by the C4 symmetry in the CE method.
Abstract: The electronic structure of interfaces between lattice-mismatched semiconductors is sensitive to the strain. We compare two approaches for calculating such inhomogeneous strain—continuum elasticity [(CE), treated as a finite difference problem] and atomistic elasticity. While for small strain the two methods must agree, for the large strains that exist between lattice-mismatched III-V semiconductors (e.g., 7% for InAs/GaAs outside the linearity regime of CE) there are discrepancies. We compare the strain profile obtained by both approaches (including the approximation of the correct C2 symmetry by the C4 symmetry in the CE method) when applied to C2-symmetric InAs pyramidal dots capped by GaAs.

394 citations


Journal ArticleDOI
TL;DR: In this article, the phase stability, thermodynamic properties, and bond lengths of noble-metal alloys were investigated using the fully relaxed general-potential linearized augmented plane-wave (LAPW) total energies of a few ordered structures.
Abstract: The classic metallurgical systems---noble-metal alloys---that have formed the benchmark for various alloy theories are revisited. First-principles fully relaxed general-potential linearized augmented plane-wave (LAPW) total energies of a few ordered structures are used as input to a mixed-space cluster expansion calculation to study the phase stability, thermodynamic properties, and bond lengths in Cu-Au, Ag-Au, Cu-Ag, and Ni-Au alloys. (i) Our theoretical calculations correctly reproduce the tendencies of Ag-Au and Cu-Au to form compounds and Ni-Au and Cu-Ag to phase separate at $T=0$ K. (ii) Of all possible structures, ${\mathrm{Cu}}_{3}\mathrm{Au}$ ${(L1}_{2})$ and CuAu ${(L1}_{0})$ are found to be the most stable low-temperature phases of ${\mathrm{Cu}}_{1\ensuremath{-}x}{\mathrm{Au}}_{x}$ with transition temperatures of 530 K and 660 K, respectively, compared to the experimental values 663 K and \ensuremath{\approx}670 K. The significant improvement over previous first-principles studies is attributed to the more accurate treatment of atomic relaxations in the present work. (iii) LAPW formation enthalpies demonstrate that ${L1}_{2}$, the commonly assumed stable phase of ${\mathrm{CuAu}}_{3}$, is not the ground state for Au-rich alloys, but rather that ordered (100) superlattices are stabilized. (iv) We extract the nonconfigurational (e.g., vibrational) entropies of formation and obtain large values for the size-mismatched systems: 0.48 ${k}_{B}$/atom in ${\mathrm{Ni}}_{0.5}{\mathrm{Au}}_{0.5}$ $(T=1100$ K), 0.37 ${k}_{B}$/atom in ${\mathrm{Cu}}_{0.141}{\mathrm{Ag}}_{0.859}$ $(T=1052$ K), and 0.16 ${k}_{B}$/atom in ${\mathrm{Cu}}_{0.5}{\mathrm{Au}}_{0.5}$ $(T=800$ K). (v) Using 8 atom/cell special quasirandom structures we study the bond lengths in disordered Cu-Au and Ni-Au alloys and obtain good qualitative agreement with recent extended x-ray-absorption fine-structure measurements.

239 citations


Journal ArticleDOI
TL;DR: In this paper, the authors present a first-principles technique for predicting the ordered vacancy ground states, intercalation voltage profiles, and voltage-temperature phase diagrams of Li battery electrodes.
Abstract: We present a first-principles technique for predicting the ordered vacancy ground states, intercalation voltage profiles, and voltage-temperature phase diagrams of Li intercalation battery electrodes. Application to the Li{sub x}CoO {sub 2} system yields correctly the observed ordered vacancy phases. We further predict the existence of additional ordered phases, their thermodynamic stability ranges, and their intercalation voltages in Li{sub x}CoO {sub 2}/Li battery cells. Our calculations provide insight into the remarkable electronic stability of this system with respect to Li removal: A rehybridization of the Co-O orbitals acts to restore charge to the Co site ({open_quotes}self-regulating response{close_quotes}), thereby minimizing the effect of the perturbation. {copyright} {ital 1998} {ital The American Physical Society}

232 citations


Journal ArticleDOI
TL;DR: In this article, the electronic and atomic structure of isovalent substitutional P and As impurities in GaN was studied theoretically using a self-consistent plane-wave pseudopotential method.
Abstract: The electronic and atomic structure of isovalent substitutional P and As impurities in GaN is studied theoretically using a self-consistent plane-wave pseudopotential method. In contrast with the conventional isovalent III-V systems, $\mathrm{GaN}\mathrm{}:\mathrm{P}$ and $\mathrm{GaN}\mathrm{}:\mathrm{A}\mathrm{s}$ are shown to exhibit deep gap levels. The calculated donor energies are $\ensuremath{\epsilon}(+/0)={\ensuremath{\epsilon}}_{v}+0.22$ and ${\ensuremath{\epsilon}}_{v}+0.41$ eV, respectively, and the double donor energies are $\ensuremath{\epsilon}(++/+)={\ensuremath{\epsilon}}_{v}+0.09$ and ${\ensuremath{\epsilon}}_{v}+0.24$ eV, respectively. The $p$-like gap wave function is found to be strongly localized on the impurity site. Outward atomic relaxations of $\ensuremath{\sim}13%$ and $\ensuremath{\sim}15%$ are calculated for the nearest-neighbor Ga atoms surrounding neutral ${\mathrm{GaN}\mathrm{}:\mathrm{P}}^{0}$ and ${\mathrm{GaN}\mathrm{}:\mathrm{A}\mathrm{s}}^{0},$ respectively. The relaxation increases by $\ensuremath{\sim}1%$ for the positively charged impurities. The impurity-bound exciton binding energy is calculated at ${E}_{b}=0.22$ and ${E}_{b}=0.41$ eV for $\mathrm{GaN}:P$ and $\mathrm{GaN}:As.$ The former is in good agreement with the experimental data ${(E}_{b}=0.232$ eV) whereas the latter is offered as a prediction. No clear Jahn-Teller symmetry lowering ${(T}_{d}\ensuremath{\rightarrow}{C}_{3v})$ distortion, suggested by the one-electron configuration, is found for $\mathrm{GaN}:{\mathrm{P}}^{+}$ and $\mathrm{GaN}:{\mathrm{As}}^{+}.$

138 citations


Journal ArticleDOI
TL;DR: In this paper, the electronic structure of strained InAs pyramidal quantum dots embedded in a GaAs matrix, for a few height $(h)$-to-base$(b)$ ratios, corresponding to different facet orientations, was calculated.
Abstract: Using a pseudopotential plane-wave approach, we have calculated the electronic structure of strained InAs pyramidal quantum dots embedded in a GaAs matrix, for a few height $(h)$-to-base$(b)$ ratios, corresponding to different facet orientations ${101}$, ${113},$ and ${105}$. We find that the dot shape (not just size) has a significant effect on its electronic structure. In particular, while the binding energies of the ground electron and hole states increase with the pyramid volumes ${(b}^{2}h)$, the splitting of the $p\ensuremath{-}$like conduction states increases with facet orientation $(h/b),$ and the $p\ensuremath{-}$to-$s$ splitting of the conduction states decreases as the base size $(b)$ increases. We also find that there are up to six bound electron states (12 counting the spin), and that all degeneracies other than spin, are removed. This is in accord with the conclusion of electron-addition capacitance data, but in contrast with simple k\ensuremath{\cdot}p calculations, which predict only a single electron level.

121 citations


Journal ArticleDOI
TL;DR: Using a combination of first-principles total energies, a cluster expansion technique, and Monte Carlo simulations, the authors studied the Li/Co ordering in the octahedral system.
Abstract: Using a combination of first-principles total energies, a cluster expansion technique, and Monte Carlo simulations, we have studied the Li/Co ordering in ${\mathrm{LiCoO}}_{2}$ and Li-vacancy/Co ordering in the $\ensuremath{\square}{\mathrm{CoO}}_{2}$. We find: (i) A ground-state search of the space of substitutional cation configurations yields the CuPt structure as the lowest-energy state in the octahedral system ${\mathrm{LiCoO}}_{2}$ (and $\ensuremath{\square}{\mathrm{CoO}}_{2})$, in agreement with the experimentally observed phase. (ii) Finite-temperature calculations predict that the solid-state order-disorder transitions for ${\mathrm{LiCoO}}_{2}$ and $\ensuremath{\square}{\mathrm{CoO}}_{2}$ occur at temperatures $(\ensuremath{\sim}5100 \mathrm{K}$ and $\ensuremath{\sim}4400 \mathrm{K}$, respectively) much higher than melting, thus making these transitions experimentally inaccessible. (iii) The energy of the reaction ${E}_{\mathrm{tot}}(\ensuremath{\sigma},\mathrm{Li}\mathrm{Co}{\mathrm{O}}_{2})\ensuremath{-}{E}_{\mathrm{tot}}(\ensuremath{\sigma},\ensuremath{\square}\mathrm{Co}{\mathrm{O}}_{2})\ensuremath{-}{E}_{\mathrm{tot}}(\mathrm{L}\mathrm{i},\mathrm{}\mathrm{bcc})$ gives the average battery voltage $\overline{V}$ of a ${\mathrm{Li}}_{x}{\mathrm{CoO}}_{2}/\mathrm{Li}$ cell for the cathode in the structure $\ensuremath{\sigma}$. Searching the space of configurations $\ensuremath{\sigma}$ for large average voltages, we find that $\ensuremath{\sigma}=\mathrm{CuPt}$ [a monolayer $〈111〉$ superlattice] has a high voltage $(\overline{V}=3.78 \mathrm{V})$, but that this could be increased by cation randomization $(\overline{V}=3.99 \mathrm{V})$, by partial disordering $(\overline{V}=3.86 \mathrm{V})$, or by forming a two-layer ${\mathrm{Li}}_{2}{\mathrm{Co}}_{2}{\mathrm{O}}_{4}$ superlattice along $〈111〉$ $(\overline{V}=4.90 \mathrm{V})$.

110 citations


Journal ArticleDOI
TL;DR: In this article, an atomistic direct diagonalization pseudopotential approach was used to analyze the optical excitation spectra of CdSe quantum dots for up to 1.5 eV about the band gap.
Abstract: An atomistic direct diagonalization pseudopotential approach has been used to analyze the optical excitation spectra of CdSe quantum dots for up to 1.5 eV about the band gap. Good agreement is obtained with experiment for all the eight excitonic transitions, without resorting to fitting to the experimental data on dots. The observed excitonic transitions are identified in terms of specific pairs of valence and conduction single-particle states. For the lowest few transitions, the assignments agree with the conventional k.p effective-mass result, but this is not the case for the higher peaks. Indeed, we find in our atomistic approach that many more valence states exist within a given energy range than in the continuum k.p approach. Furthermore, we find that the mixing of even and odd angular momentum symmetry, disallowed in the contemporary simple k.p models, is actually permitted in the more general atomistic approach.

Journal ArticleDOI
TL;DR: In this article, the voltage of a battery based on the intercalation reaction energy was derived from first-principles of the quantum-mechanical electronic structure theory of solids.
Abstract: It is now possible to use a quantum-mechanical electronic structure theory of solids and derive, completely from first-principles, the voltage of a battery based on intercalation reaction energetics. Using such techniques, the authors investigate the structural stability, intercalation energies, and battery voltages of the two observed ordered phases (layered and cubic) of LiCoO{sub 2}. They perform calculations for not only fully lithiated LiCoO{sub 2}, but also fully delithiated cubic CoO{sub 2} and partially delithiated Li{sub 0.5}CoO{sub 2}. The calculations demonstrate that removal of Li from the cubic phase results in movement of the Li atoms from their original octahedral sites to tetrahedral sites, forming a low-energy LiCo{sub 2}O{sub 4} spinel structure. The energetics of the spinel phase are shown to account for the observed marked differences in battery voltages between the cubic and layered phases of LiCoO{sub 2}. A small energy barrier exists for Li motion between octahedral and tetrahedral sites, thus indicating the metastability of the high-energy octahedral sites. Finally, the authors point out a possible pressure-induced layered to cubic transition in LiCoO{sub 2}.

Journal ArticleDOI
TL;DR: In this article, the effect of the different underlying wave-function representations used in $\mathbf{k}ensuremath{\cdot}\mathbf {p}$ and in the more exact pseudopotential direct diagonalization was investigated.
Abstract: The $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ method has become the ``standard model'' for describing the electronic structure of nanometer-size quantum dots. In this paper we perform parallel $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ $(6\ifmmode\times\else\texttimes\fi{}6$ and $8\ifmmode\times\else\texttimes\fi{}8)$ and direct-diagonalization pseudopotential studies on spherical quantum dots of an ionic material---CdSe, and a covalent material---InP. By using an equivalent input in both approaches, i.e., starting from a given atomic pseudopotential and deriving from it the Luttinger parameters in $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ calculation, we investigate the effect of the different underlying wave-function representations used in $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ and in the more exact pseudopotential direct diagonalization. We find that (i) the $6\ifmmode\times\else\texttimes\fi{}6\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ envelope function has a distinct (odd or even) parity, while atomistic wave function is parity-mixed. The $6\ifmmode\times\else\texttimes\fi{}6\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ approach produces an incorrect order of the highest valence states for both InP and CdSe dots: the $p$-like level is above the $s$-like level. (ii) It fails to reveal that the second conduction state in small InP dots is folded from the $L$ point in the Brillouin zone. Instead, all states in $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ are described as \ensuremath{\Gamma}-like. (iii) The $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ overestimates the confinement energies of both valence states and conduction states. A wave-function projection analysis shows that the principal reasons for these $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ errors in dots are (a) use of restricted basis set, and (b) incorrect bulk dispersion relation. Error (a) can be reduced only by increasing the number of basis functions. Error (b) can be reduced by altering the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ implementation so as to bend upwards the second lowest bulk band, and to couple the conduction band into the $s$-like dot valence state. Our direct diagonalization approach provides an accurate and practical replacement to the standard model in that it is rather general, and can be performed simply on a standard workstation.

Journal ArticleDOI
TL;DR: In this article, the importance of vibrational effects on the phase stability of Cu-Au alloys was investigated via a combination of first-principles linear response calculations and a statistical mechanics cluster expansion method.
Abstract: The importance of vibrational effects on the phase stability of Cu-Au alloys is investigated via a combination of first-principles linear response calculations and a statistical mechanics cluster expansion method. We find that (i) the logarithmic average of the phonon density of states in ordered compounds is lower than in the pure constituents, thus leading to positive vibrational entropies of formation and to negative free energies of formation, stabilizing the compounds and alloys with respect to the phase separated state. (ii) The vibrational free energy is lower in the configurationally random alloy than in ordered ground states, which leads to lower order-disorder transition temperatures. (iii) The random alloys have larger thermal expansion coefficients than ordered ground states, and therefore the vibrational entropy difference between the random and ordered states is a strongly increasing function of temperature. However, (iv) due to the associated increase in the static internal energy, the effect of thermal expansion on the free energy (and thus on the phase diagram) is only half that of the entropy alone.

Journal ArticleDOI
TL;DR: In this paper, a first-principles technique for calculating the short-range order (SRO) in disordered alloys, even in the presence of large anharmonic atomic relaxations, was described.
Abstract: We describe a first-principles technique for calculating the short-range order (SRO) in disordered alloys, even in the presence of large anharmonic atomic relaxations. The technique is applied to several alloys possessing large size mismatch: Cu-Au, Cu-Ag, Ni-Au, and Cu-Pd. We find the following: (i) The calculated SRO in Cu-Au alloys peaks at (or near) the $〈100〉$ point for all compositions studied, in agreement with diffuse scattering measurements. (ii) A fourfold splitting of the $X$-point SRO exists in both ${\mathrm{Cu}}_{0.75}{\mathrm{Au}}_{0.25}$ and ${\mathrm{Cu}}_{0.70}{\mathrm{Pd}}_{0.30},$ although qualitative differences in the calculated energetics for these two alloys demonstrate that the splitting in ${\mathrm{Cu}}_{0.70}{\mathrm{Pd}}_{0.30}$ may be accounted for by $T=0$ K energetics while $T\ensuremath{ e}0$ K configurational entropy is necessary to account for the splitting in ${\mathrm{Cu}}_{0.75}{\mathrm{Au}}_{0.25}.$ ${\mathrm{Cu}}_{0.75}{\mathrm{Au}}_{0.25}$ shows a significant temperature dependence of the splitting, in agreement with recent in situ measurements, while the splitting in ${\mathrm{Cu}}_{0.70}{\mathrm{Pd}}_{0.30}$ is predicted to have a much smaller temperature dependence. (iii) Although no measurements exist, the SRO of Cu-Ag alloys is predicted to be of clustering type with peaks at the $〈000〉$ point. Streaking of the SRO peaks in the $〈100〉$ and $〈1\frac{1}{2}0〉$ directions for Ag- and Cu-rich compositions, respectively, is correlated with the elastically soft directions for these compositions. (iv) Even though Ni-Au phase separates at low temperatures, the calculated SRO pattern in ${\mathrm{Ni}}_{0.4}{\mathrm{Au}}_{0.6},$ like the measured data, shows a peak along the $〈\ensuremath{\zeta}00〉$ direction, away from the typical clustering-type $〈000〉$ point. (v) The explicit effect of atomic relaxation on SRO is investigated and it is found that atomic relaxation can produce significant qualitative changes in the SRO pattern, changing the pattern from ordering to clustering type, as in the case of Cu-Ag.

Journal ArticleDOI
TL;DR: In this paper, the local density approximation (LDA)-corrected formalism was used to calculate the band-gap reduction and spin-orbit splitting for ordered alloys, and the x-ray structure factors for these materials as a function of the degree of long range order.
Abstract: Spontaneous CuPt ordering induces a band-gap reduction $\ensuremath{\Delta}{E}_{g}$ relative to the random alloy, a crystal field splitting ${\ensuremath{\Delta}}_{\mathrm{CF}}$ at valence-band maximum, as well as an increase of spin-orbit splitting ${\ensuremath{\Delta}}_{\mathrm{SO}}$ We calculate these quantities for ${\mathrm{Al}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{P},$ ${\mathrm{Al}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{As},$ ${\mathrm{Ga}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{P},$ and ${\mathrm{Ga}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{As}$ using the local density approximation (LDA), as well as the more reliable LDA-corrected formalism We further provide these values and the valence-band splittings $\ensuremath{\Delta}{E}_{12}$ (between ${\overline{\ensuremath{\Gamma}}}_{4,5v}$ and ${\overline{\ensuremath{\Gamma}}}_{6v}^{(1)}$) and $\ensuremath{\Delta}{E}_{13}$ (between ${\overline{\ensuremath{\Gamma}}}_{4,5v}$ and ${\overline{\ensuremath{\Gamma}}}_{6v}^{(2)}$) for these materials as a function of the degree \ensuremath{\eta} of long range order In the absence of an independent measurement of \ensuremath{\eta}, experiment is currently able to deduce only the ratio $\ensuremath{\Delta}{E}_{g}/{\ensuremath{\Delta}}_{\mathrm{CF}}$ Our LDA-corrected results for this quantity compare favorably with recent experiments for ${\mathrm{Ga}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{P}$ and ${\mathrm{Ga}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{As},$ but not for ${\mathrm{Al}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{P},$ where our calculation does not support the experimental assignment The ``optical LRO parameter \ensuremath{\eta}'' can be obtained by fitting our calculated $\ensuremath{\Delta}{E}_{g}(\ensuremath{\eta})$ to the measured $\ensuremath{\Delta}{E}_{g}(\ensuremath{\eta}),$ and by expressing the measured $\ensuremath{\Delta}{E}_{12}(\ensuremath{\eta})$ and $\ensuremath{\Delta}{E}_{13}(\ensuremath{\eta})$ in terms of our calculated ${\ensuremath{\Delta}}_{\mathrm{CF}}(\ensuremath{\eta})$ and ${\ensuremath{\Delta}}_{\mathrm{SO}}(\ensuremath{\eta})$ We also provide the calculated x-ray structure factors for ordered alloys that can be used experimentally to deduce \ensuremath{\eta} independently

Journal ArticleDOI
TL;DR: In this article, the effects of atomic short-range order (SRO) on the electronic and optical properties of dilute and concentrated GaAsN, GaInN, and GaInAs alloys were investigated.
Abstract: Using large ({approx}500{endash}1000atoms) pseudopotential supercell calculations, we have investigated the effects of atomic short-range order (SRO) on the electronic and optical properties of dilute and concentrated GaAsN, GaInN, and GaInAs alloys. We find that in concentrated alloys the clustering of like atoms in the first neighbor fcc shell (e.g., N-N in GaAsN alloys) leads to a large decrease of both the band-gap and the valence-to-conduction dipole transition-matrix element in GaAsN and in GaInN. On the other hand, the optical properties of GaInAs depend only weakly on the atomic SRO. The reason that the nitride alloys are affected strongly by SRO while GaInAs is affected to a much lesser extent is that in the former case there are band-edge wave-function localizations around specific atoms in the concentrated random alloys. The property for such localization is already evident at the (dilute) isolated impurity and impurity-pair limits. {copyright} {ital 1998} {ital The American Physical Society}

Journal ArticleDOI
TL;DR: In this paper, the electron-hole exchange interaction in semiconductor quantum dots is characterized by a large, previously neglected long-range component, originating from monopolar interactions of the transition density between different unit cells.
Abstract: Using a many-body approach based on atomistic pseudopotential wave functions we show that the electron-hole exchange interaction in semiconductor quantum dots is characterized by a large, previously neglected long-range component, originating from {ital monopolar} interactions of the transition density between different unit cells. The calculated electron-hole exchange splitting of CdSe and InP nanocrystals is in good agreement with recent experimental measurements. {copyright} {ital 1998} {ital The American Physical Society}

Journal ArticleDOI
TL;DR: In this article, a new way of analyzing the alloy electronic structures based on a majority representation of the reciprocal space spectrum P(bold k) of the wave function is presented, which provides a quantitative answer to the questions: When can an alloy state be classified according to the crystal Bloch state symmetry, and under what circumstances are the conventional theoretical alloy models applicable.
Abstract: Despite the lack of translational symmetry in random substitutional alloys, their description in terms of single Bloch states has been used in most phenomenological models and spectroscopic practices. We present a new way of analyzing the alloy electronic structures based on a {open_quotes}majority representation{close_quotes} phenomenon of the reciprocal space spectrum P({bold k}) of the wave function. This analysis provides a quantitative answer to the questions: When can an alloy state be classified according to the crystal Bloch state symmetry, and under what circumstances are the conventional theoretical alloy models applicable. {copyright} {ital 1998} {ital The American Physical Society}

Journal ArticleDOI
TL;DR: In this article, the one-electron levels of the dot reflect quantum size, quantum shape, interfacial strain, and surface effects and the nature of many-particle interactions such as electron-hole exchange (underlying the red shift) and Coulomb-blockade effects.
Abstract: Progress made in the growth of “free-standing” (e.g., colloidal) quantum dots (see also articles in this issue by Nozik and Micic, and by Alivisatos) and in the growth of semiconductor-embedded (“self-assembled”) dots (see also the article by Bimberg, Grundmann, and Ledentsov in this issue) has opened the door to new and exciting spectroscopic studies of quantum structures. These have revealed rich and sometimes unexpected features such as quantum-dot shape-dependent transitions, size-dependent (red) shifts between absorption and emission, emission from high excited levels, surface-mediated transitions, exchange splitting, strain-induced splitting, and Coulomb-blockade transitions. These new observations have created the need for developing appropriate theoretical tools capable of analyzing the electronic structure of 103–106-atom objects. The main challenge is to understand (a) the way the one-electron levels of the dot reflect quantum size, quantum shape, interfacial strain, and surface effects and (b) the nature of “many-particle” interactions such as electron-hole exchange (underlying the “red shift”), electron-hole Coulomb effects (underlying excitonic transitions), and electron-electron Coulomb (underlying Coulomb-blockade effects).Interestingly, while the electronic structure theory of periodic solids has been characterized since its inception by a diversity of approaches (all-electron versus pseudopotentials; Hartree Fock versus density-functional; computational schemes creating a rich “alphabetic soup,” such as APW, LAPW, LMTO, KKR, OPW, LCAO, LCGO, plane waves, ASW, etc.), the theory of quantum nano-structures has been dominated mainly by a single approach so widely used that I refer to it as the “Standard Model”: the effective-mass approximation (EMA) and its extension to the “k · p” (where k is the wave vector and p is the momemtum). In fact, speakers at nanostructure conferences often refer to it as “theory” without having to specify what is being done. The audience knows.

Journal ArticleDOI
TL;DR: In this article, the stability of superlattices is discussed in terms of the coherency strain and interfacial energies, and it is shown that in phase separating systems such as Cu-Ag and Ni-Au, the formation energy increases with period, and the interfacial energy is negative.
Abstract: Epitaxial strain energies of epitaxial films and bulk superlattices are studied via first-principles total-energy calculations using the local-density approximation. Anharmonic effects due to large lattice mismatch, beyond the reach of the harmonic elasticity theory, are found to be very important in Cu/Au (lattice mismatch 12%), Cu/Ag (12%), and Ni/Au (15%). We find that $〈001〉$ is the elastically soft direction for biaxial expansion of Cu and Ni, but it is $〈201〉$ for large biaxial compression of Cu, Ag, and Au. The stability of superlattices is discussed in terms of the coherency strain and interfacial energies. We find that in phase separating systems such as Cu-Ag the superlattice formation energies decrease with superlattice period, and the interfacial energy is positive. Superlattices are formed easiest on (001) and hardest on (111) substrates. For ordering systems, such as Cu-Au and Ag-Au, the formation energy of superlattices increases with period, and interfacial energies are negative. These superlattices are formed easiest on (001) or (110) and hardest on (111) substrates. For Ni-Au we find a hybrid behavior: superlattices along $〈111〉$ and $〈001〉$ behave like phase separating systems, while for $〈110〉$ they behave like ordering systems. Finally, recent experimental results on epitaxial stabilization of disordered Ni-Au and Cu-Ag alloys, immiscible in the bulk form, are explained in terms of destabilization of the phase separated state due to lattice mismatch between the substrate and constituents.

Journal ArticleDOI
TL;DR: In this article, the results of a first-principles calculation of the direct band-gap pressure coefficient a{sub g} for a series of Ga and In semiconductor compounds with both the chalcopyrite and the zinc-blende structures (e.g., GaAs and InAs) were presented.
Abstract: We present the results of a first-principles calculation of the direct band-gap pressure coefficient a{sub g} for a series of Ga and In semiconductor compounds with both the chalcopyrite (e.g., CuGaSe{sub 2} and CuInSe{sub 2}) and the zinc-blende structures (e.g., GaAs and InAs). We found good agreement between the calculated and experimental pressure coefficients. We found that a{sub g} in chalcopyrites are dramatically reduced relative to zinc-blende compounds, and that the Ga{r_arrow}In substitution lowers a{sub g} in chalcopyrites more than in zinc-blende compounds. As a result, the empirical rule suggested for zinc-blende compounds, stating that for a given transition (e.g., {Gamma}{sub 15v}{r_arrow}{Gamma}{sub 1c}) a{sub g} does not depend on substitutions, has to be modified for chalcopyrites. Based on our results we question the currently accepted experimental value for CuInTe{sub 2} (2.2 meV/kbar); we calculate this value to be close to 5.9 meV/kbar. {copyright} {ital 1998} {ital The American Physical Society}

Journal ArticleDOI
TL;DR: Semiconductor quantum dots refer to nanometer-sized, giant (103-105 atoms) molecules made from ordinary inorganic semiconductor materials such as Si, InP, CdSe, etc as discussed by the authors.
Abstract: Semiconductor “quantum dots” refer to nanometer-sized, giant (103–105 atoms) molecules made from ordinary inorganic semiconductor materials such as Si, InP, CdSe, etc. They are larger than the traditional “molecular clusters” (~1 nanometer containing ≤100 atoms) common in chemistry yet smaller than the structures of the order of a micron, manufactured by current electronic-industry lithographic techniques. Quantum dots can be made by colloidal chemistry techniques (see the articles by Alivisatos and by Nozik and Micic in this issue), by controlled coarsening during epitaxial growth (see the article by Bimberg et al. in this issue), by size fluctuations in conventional quantum wells (see the article by Gammon in this issue), or via nano-fabrication (see the article by Tarucha in this issue).

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TL;DR: In this paper, the excitonic spectrum of InP quantum dots is investigated using an atomistic pseudopotential approach for the single-particle problem and a state-dependent screened Coulomb interaction for the many-body problem.
Abstract: The excitonic spectrum of InP quantum dots is investigated using an atomistic pseudopotential approach for the single-particle problem and a state-dependent screened Coulomb interaction for the many-body problem. Our calculations show a different energy distribution of single-particle states relative to the commonly used $\mathbf{k}\mathbf{\ensuremath{\cdot}}\mathbf{p}$ theory as well as significant parity mixing in the envelope functions, forbidden in $6\ifmmode\times\else\texttimes\fi{}6$ $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$. The calculated excitonic spectrum, including seven excitons, explains well the recent experimental measurements.

Journal ArticleDOI
TL;DR: In this article, the authors predict that the difference in quantum confinement energies of G-like and X-like conduction states in a covalent quantum dot will cause the direct-to-indirect transition to occur at substantially lower pressure than in the bulk material.
Abstract: We predict that the difference in quantum confinement energies of G-like and X-like conduction states in a covalent quantum dot will cause the direct-to-indirect transition to occur at substantially lower pressure than in the bulk material. Furthermore, the first-order transition in the bulk is predicted to become, for certain dot sizes, a second-order transition. Measurements of the “anticrossing gap” could thus be used to obtain unique information on the G-X-L intervalley coupling, predicted here to be surprisingly large (50 ‐ 100 meV). [S0031-9007(98)06301-7] PACS numbers: 71.24. + q, 73.20.Dx Reduced dimensions usually cause pressure-induced structural phase transitions to occur at elevated pressures relative to the bulk solid. This is the case for the AlAs layers in AlAsyGaAs superlattices [1], for the transition to b-Sn structure in Si nanocrystals [2], and for the wurzite-to-rocksalt structure in CdSe dots [3]. Here, we show that reduced dimensionality causes another type of pressure-induced transition— the electronic direct-toindirect transition—to occur at reduced pressures relative

Journal ArticleDOI
TL;DR: In this article, the effects of quantum confinement in conjunction with coherent strain suggest there will be a critical diameter of dot, above which the dot is direct, type I, and below which it is indirect, type II.
Abstract: Free-standing InP quantum dots have previously been theoretically and experimentally shown to have a direct band gap across a large range of experimentally accessible sizes. We demonstrated that when these dots are embedded coherently within a GaP barrier material, the effects of quantum confinement in conjunction with coherent strain suggest there will be a critical diameter of dot ({approx}60 {Angstrom}), above which the dot is direct, type I, and below which it is indirect, type II. However, the strain in the system acts to produce another conduction state with an even lower energy, in which electrons are localized in small pockets at the interface between the InP dot and the GaP barrier. Since this conduction state is GaP X{sub 1c} derived and the highest occupied valence state is InP, {Gamma} derived, the fundamental transition is predicted to be indirect in both real and reciprocal space ({open_quotes}type II{close_quotes}) for all dot sizes. This effect is peculiar to the strained dot, and is absent in the freestanding dot. {copyright} {ital 1998} {ital The American Physical Society}

Journal ArticleDOI
TL;DR: In this article, it was shown that this strain can lead to localization of a GaAs-derived X{sub 1c}-type interfacial electron state, and the discrepancy between these values in the light of wave function localization and the pressure dependence of the hole binding energy was examined.
Abstract: The interface between an InAs quantum dot and its GaAs cap in {open_quotes}self-assembled{close_quotes} nanostructures is nonhomogeneously strained. We show that this strain can lead to localization of a GaAs-derived X{sub 1c}-type interfacial electron state. As hydrostatic pressure is applied, this state in the GaAs barrier turns into the conduction-band minimum of the InAs/GaAs dot system. Strain splits the degeneracy of this X{sub 1c} state and is predicted to cause electrons to localize in the GaAs barrier above the pyramidal tip. Calculation (present work) or measurement (Itskevich {ital et al.}) of the emission energy from this state to the hole state can provide the hole binding energy, {Delta}{sub dot}{sup (h)}. Combining this with the zero-pressure electron-hole recombination energy gives the electron binding energy, {Delta}{sub dot}{sup (e)}. Our calculations show {Delta}{sub dot}{sup (h)}{approximately}270thinspmeV (weakly pressure dependent) and {Delta}{sub dot}{sup (e)}{approximately}100thinspmeV at P=0. The measured values are {Delta}{sub dot}{sup (h)}{approximately}235thinspmeV (weakly pressure dependent) and {Delta}{sub dot}{sup (e)}{approximately}50thinspmeV at P=0. We examine the discrepancy between these values in the light of wave-function localization and the pressure dependence of the hole binding energy. {copyright} {ital 1998} {ital The American Physical Society}

Journal ArticleDOI
TL;DR: It is shown that the CVM produces correlation functions that are too close to zero, which leads to an overestimation of the exact energy, E, and at the same time, to an underestimation of −TS, so the free energy F=E−TS is more accurate than either of its parts.
Abstract: The success of the “cluster variation method” (CVM) in reproducing quite accurately the free energies of Monte Carlo (MC) calculations on Ising models is explained in terms of identifying a cancellation of errors: We show that the CVM produces correlation functions that are too close to zero, which leads to an overestimation of the exact energy, E, and at the same time, to an underestimation of −TS, so the free energy F=E−TS is more accurate than either of its parts. This insight explains a problem with “hybrid methods” using MC correlation functions in the CVM entropy expression: They give exact energies E and do not give significantly improved −TS relative to CVM, so they do not benefit from the above noted cancellation of errors. Additionally, hybrid methods suffer from the difficulty of adequately accounting for both ordered and disordered phases in a consistent way. A different technique, the “entropic Monte Carlo” (EMC), is shown here to provide a means for critically evaluating the CVM entropy. Ins...

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TL;DR: In this article, the basic structure of modern "first-principles theory of real materials" (including old references) is defined, and a review of recent applications to electronic materials is presented.
Abstract: In this article, I first define the basic structure of modern ‘first-principles theory of real materials' (including old references), and then I review recent applications to electronic materials. I argue that electronic structure theory of real materials has advanced to the point where bold predictions of yet unmade materials and of unsuspected physical properties are being made, fostering a new type of interaction with experimentalists. I review the basic characteristics of this new style of theory, illustrating a few recent applications, and express opinions as to future challenges.

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TL;DR: In this article, the theory of epitaxial strain energy is extended beyond the harmonic approximation to account for large film/substrate lattice mismatch, and it is shown that for fcc noble metals (i) directions 〈001〉 and ǫ-111〉 soften under tensile biaxial strain (unlike zincblende semiconductors) while (ii) à −110 à and à -201 à soften under compressive biaxonial strain.
Abstract: The theory of epitaxial strain energy is extended beyond the harmonic approximation to account for large film/substrate lattice mismatch. We find that for fcc noble metals (i) directions 〈001〉 and 〈111〉 soften under tensile biaxial strain (unlike zincblende semiconductors) while (ii) 〈110〉 and 〈201〉 soften under compressive biaxial strain. Consequently, (iii) upon sufficient compression 〈201〉 becomes the softest direction (lowest elastic energy), but (iv) 〈110〉 is the hardest direction for large tensile strain. (v) The dramatic softening of 〈001〉 in fcc noble metals upon biaxial tensile strain is caused by small fcc/bcc energy differences for these materials. These results can be used in selecting the substrate orientation for effective epitaxial growth of pure elements and ApBq superlattices, as well as to explain the shapes of coherent precipitates in phase separating alloys.