
Atom/Electron Papers and Abstracts
See also our main Papers and Publications page, as well as the publications pages of the Fink, Johnson, and Soljacic groups.

[198]

K. C. Huang, T. Wang, and J. D. Joannopoulos, “Nanoscale properties of melting
at the surface of semiconductors,” Physical Review B, vol. 72,
p. 195314, November 2005.
[ bib 
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In this study, we use densityfunctional simulations to investigate how nanoscale surface coatings can alter the melting dynamics of semiconductor surfaces. We demonstrate that a singlemonolayer coating of GaAs can dramatically reduce the diffusive motion of the surface atoms of a Ge(110) crystal and cause superheating of the bulk at temperatures well above the Ge melting point on the 10 ps time scale. In direct contrast, a singlemonolayer coating of Ge will induce surface melting of a GaAs(110) structure 300 K below the GaAs melting point. We also identify a metallization of the band structure and bond alterations in the charge density near the melting transition. In addition, we suggest that the Ge monolayer causes the GaAs(110) surface to melt through transient penetration of the Ge atoms into the bulk, which locally initiates the collective diffusive motion of large groups of Ga and As atoms. These studies on the effect of coatings in semiconductors clearly point to the surface material as the dominant determinant of the melting characteristics of a hybrid structure. These simulations have important implications for hightemperature materials design while simultaneously probing the fundamental features of the melting transition.

[197]

M. H. Evans, X.G. Zhang, J. D. Joannopoulos, and S. T. Pantelides,
“Firstprinciples mobility calculations and atomicscale interface roughness
in nanoscale structures,” Physical Review Letters, vol. 95, p. 106802,
September 2005.
[ bib 
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Calculations of mobilities have so far been carried out using approximate methods that suppress atomicscale detail. Such approaches break down in nanoscale structures. Here we report the development of a method to calculate mobilities using atomicscale models of the structures and density functional theory at various levels of sophistication and accuracy. The method is used to calculate the effect of atomicscale roughness on electron mobilities in ultrathin doublegate silicononinsulator structures. The results elucidate the origin of the significant reduction in mobility observed in ultrathin structures at low electron densities.

[196]

M. H. Evans, J. D. Joannopoulos, and S. T. Pantelides, “Electronic and
mechanical properties of planar and tubular boron structures,” Physical
Review B, vol. 72, p. 045434, July 2005.
[ bib 
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We report the results of firstprinciples calculations showing that boron can form a wide variety of metastable planar and tubular forms with unusual electronic and mechanical properties. The preferred planar structure is a buckled triangular lattice that breaks the threefold ground state degeneracy of the flat triangular plane. When the plane is rolled into a tube, the ground state degeneracy leads to a strong chirality dependence of the binding energy and elastic response, an unusual property that is not found in carbon nanotubes. The achiral (n,0) tubes derive their structure from the flat triangular plane. The achiral (n,n) boron nanotubes arise from the buckled plane, and have large cohesive energies and different structures as a result. (n,n) boron nanotubes have an internal relaxation mechanism that results in a very low Poisson ratio. The strong variation in elastic properties of boron nanotubes makes them the mechanical analogue of carbon nanotubes, and may make them ideal candidates for applications in composite materials and nanoelectromechanical systems.

[195]

K. C. Huang, T. Wang, and J. D. Joannopoulos, “Superheating and induced
melting at semiconductor interfaces,” Physical Review Letters,
vol. 94, p. 175702, May 2005.
[ bib 
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We present ab initio densityfunctional simulations of the state of several semiconductor surfaces at temperatures near the bulk melting temperatures. We find that the solidliquid phasetransition temperature at the surface can be altered via a microscopic (singlemonolayer) coating with a different latticematched semiconducting material. Our results show that a singlemonolayer GaAs coating on a Ge(110) surface above the Ge melting temperature can dramatically reduce the diffusion coefficient of the germanium atoms, going so far as to prevent melting of the bulk layers on the 10 ps time scale. In contrast, a singlemonolayer coating of Ge on a GaAs(110) surface introduces defects into the bulk and induces melting of the top layer of GaAs atoms 300 K below the GaAs melting point. To our knowledge, these calculations represent the first ab initio investigation of the superheating and induced melting phenomena.

[194]

M. Skorobogatiy, I. J. Park, and J. D. Joannopoulos, “The nature of a floating
electron,” Computational Materials Science, vol. 32, pp. 96–106,
January 2005.
[ bib 
DOI ]
Dynamics of electron solvation at the water surface is studied using extensive ab initio simulations. Calculations have been performed on semiclassical water at 300 K temperature with an excess quantum electron on its surface. It is found that after a very fast 30–50 fs initial localization, there follow fast 50–70 fs rotationally mediated transitions of the excess electron between surface trap states with a lifetime of 150–400 fs. In less then 2 ps the excess electron gets trapped in an ordered “floating” electron state on the surface of water with a lifetime of more than 7 ps. The excess electron diffusion coefficient and spectrum of its velocity autocorrelation function change over time to reflect a transition from a very mobile phase (first 2 ps) to a trapped “floating” electron phase (2–7 ps).

[193]

I. Appelbaum, T. Wang, J. D. Joannopoulos, and V. Narayanamurti, “Ballistic
hotelectron transport in nanoscale semiconductor heterostructures: Exact
selfenergy of a threedimensional periodic tightbinding Hamiltonian,”
Physical Review B, vol. 69, p. 165301, April 2004.
[ bib 
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As the length scale for semiconductor heterostructures approaches the regime of the lattice constant, our current theory for calculating ballistic hotelectron transport becomes inapplicable. In this case, a method such as the Green's function formalism should be used to calculate ballistic electron transmission functions from the exact, periodic lattice potential. We present a method for directly calculating the exact surface Green's function for threedimensional periodic leads which is necessary for such a scheme. Except in cases of high crystal symmetry, the method is limited by the difficulty to solve a nonsymmetric matrix Riccati equation.

[192]

E. J. Reed, L. E. Fried, and J. D. Joannopoulos, “A method for tractable
dynamical studies of single and double shock compression,” Physical
Review Letters, vol. 90, p. 235503, June 2003.
[ bib 
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A new multiscale simulation method is formulated for the study of shocked materials. The method combines molecular dynamics and the Euler equations for compressible flow. Treatment of the difficult problem of the spontaneous formation of multiple shock waves due to material instabilities is enabled with this approach. The method allows the molecular dynamics simulation of the system under dynamical shock conditions for orders of magnitude longer time periods than is possible using the popular nonequilibrium molecular dynamics approach. An example calculation is given for a model potential for silicon in which a computational speedup of 10^{5} is demonstrated. Results of these simulations are consistent with the recent experimental observation of an anomalously large elastic precursor on the nanosecond time scale.

[191]

I. Appelbaum, J. D. Joannopoulos, and V. Narayanamurti, “Alternative paradigm
for physical computing,” Physical Review E, vol. 66, p. 066612,
December 2002.
[ bib 
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We identify a different class of physical systems that are able to form universal logic gates. By analogy with Si(100) surface dimers, we present a model to analyze the trajectories of the fixed points (interpreted as logic states) under variation of the basic parameters. Using the perspective of catastrophe theory, we show that information processing is the result of cycling the parameters of such systems through a path containing a cusptype catastrophe. We apply this analysis to the construction of an example based on magnetic memory.

[190]

I. Park, K. Cho, S. Lee, K. S. Kim, and J. D. Joannopoulos, “Ab initio
atomistic dynamical study of an excess electron in water,”
Computational Materials Science, vol. 21, pp. 291–300, July 2001.
[ bib 
DOI ]
The microscopic transport processes of an excess electron in bulk water are studied using hybrid ab initio molecular dynamics calculations. In contrast to the typical cavity obtained with solvated anions, the electron cavity structure is found to be much more variable, with water molecules easily exchanging at the surface of the cavity. The microscopic mechanism of electron transport involves a novel sequence of opportunistic electron redistributions driven by a positive feedback between thermal fluctuations and the attraction of the electron to hydrogen atoms that are not saturated in hydrogen bonding.

[189]

J. M. Soler, I. L. Garzón, and J. D. Joannopoulos, “Structural patterns
of unsupported gold clusters,” Solid State Communications, vol. 117,
pp. 621–625, February 2001.
[ bib 
DOI ]
The structure of metal clusters is essential to predict many of their physical and chemical properties. Using first principles density functional calculations it was recently found that even “magic” cluster sizes, for which very compact and symmetric structures exist, have lowerenergy structures. The origin of these structures was shown to lie in the nonpairwise metallic interactions; while the compact ordered geometries are very stable for pair potentials, they are destabilized by the tendency of metallic bonds to contract at the surface. Here we identify important patterns of the resulting “amorphous” structures, showing why they are optimal for the metallic potential, and how they can be used to predict structures for other cluster sizes.

[188]

E. J. Reed, J. D. Joannopoulos, and L. E. Fried, “Electronic excitations in
shocked nitromethane,” Physical Review B, vol. 62, pp. 16500–16509,
December 2000.
[ bib 
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The nature of electronic excitations in crystalline solid nitromethane under conditions of shock loading and static compression are examined. Densityfunctional theory calculations are used to determine the crystal bandgap under hydrostatic stress, uniaxial strain, and shear strain. Bandgap lowering under uniaxial strain due to molecular defects and vacancies is considered. Ab initio moleculardynamics simulations are done of all possible nearestneighbor collisions at a shock front, and of crystal shearing along a sterically hindered slip plane. In all cases, the bandgap is not lowered enough to produce a significant population of excited states in the crystal. The nearly free rotation of the nitromethane methyl group and localized nature of the highest occupied molecular orbital and lowest unoccupied molecular orbital states play a role in this result. Dynamical effects have a more significant effect on the bandgap than static effects, but relative molecule velocities in excess of 6 km/s are required to produce a significant thermal population of excited states.

[187]

T. Wang, N. Moll, K. Cho, and J. D. Joannopoulos, “Computational design of
compounds for monolithic integration in optoelectronics,” Physical
Review B, vol. 63, p. 035306, January 2000.
[ bib 
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A class of semiconductors is introduced and their physical properties are examined using both ab initio totalenergy calculations and quasiparticle GW calculations. These compounds are designed to address problems of latticeconstant mismatch and polarity mismatch that are common issues in heteroepitaxial growth of IIIV alloys on silicon substrates. A variety of configurations of these materials is explored. It is found that their lattice constants and band gaps fall into a region of phase space different from that of conventional semiconductors, making them potential candidates for the basis of optical devices—infrared emitters and detectors. A particular suitable configuration is identified that is latticeconstant matched to Si and has a direct band gap of 0.8 eV. This gap corresponds to the canonical wavelength of 1.5 μm in optoelectronics. Thus this material could ultimately enable tractable monolithic integration of optics with electronics. The characteristics of this particular configuration are examined in depth, including its temperature dependence, its bulk energetics, and its growth energetics. The results of these analyses indicate that fabrication of these compounds using heteroepitaxial growth techniques should be feasible.

[186]

N. Moll, T. Wang, K. Cho, and J. D. Joannopoulos, “Semiconductor alloys for
monolithic integration with Si microelectronics,” Materials Science &
Engineering B, vol. 67, pp. 17–22, December 1999.
[ bib 
DOI ]
We introduce a novel class of semiconductors which is optically active and solves the problems with latticeconstant mismatches and polarity mismatches that are normally an issue in heteroepitaxial growth of III–V alloys on silicon substrates. Using ab initio total energy calculations and quasiparticle GW calculations we examine physical properties of various configurations of these novel materials and identify a particular suitable configuration. This configuration is latticeconstant matched to Si and has a direct band gap very close to the operating wavelength of optical fibers. Therefore, this novel class could lead to monolithic integration of optical materials and Si circuits.

[185]

S. Mirbt and N. Moll, “Cationrich (100) surface reconstructions of inp and
gap,” Physical Review B, vol. 60, pp. 13283–13286, November 1999.
[ bib 
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The trimer reconstruction of the (100) InP surface which has been discovered experimentally is confirmed by firstprinciple calculations. The charge density of atomic configuration, which has the lowest surface energy is in perfect agreement with experimental scanning tunneling microscopy images. We predict the same trimer reconstruction also to be observable on GaP (100) surfaces and discuss how local stress makes this reconstruction energetically unfavorable for GaAs.

[184]

M. Skorobogatiy and J. D. Joannopoulos, “Nonzerotemperature pathintegral
method for fermions and bosons: A grand canonical approach,” Physical
Review B, vol. 60, pp. 1433–1436, July 1999.
[ bib 
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The calculation of the density matrix for fermions and bosons in the grand canonical ensemble allows an efficient way for the inclusion of fermionic and bosonic statistics at all temperatures. It is shown that in a path integral formulation the oneparticle density matrix can be expressed via an integration over a novel representation of the universal temperaturedependent functional. In this paper we discuss a representation for the universal functional in terms of Hankel functions which is convenient for computational applications. Temperature scaling for the universal functional and its derivatives is also introduced thus allowing an efficient rescaling rather then recalculation of the functional at different temperatures. We expect that our method will give rise to a numerically efficient pathintegral approach for calculation of a density matrix in the grand canonical ensemble.

[183]

T. Wang, N. Moll, K. Cho, and J. D. Joannopoulos, “Deliberately designed
materials for optoelectronics applications,” Physical Review Letters,
vol. 82, pp. 3304–3307, April 1999.
[ bib 
http ]
A novel class of semiconductors is introduced, based on computational design, to solve the longstanding problem of lattice and polarity mismatch in heteroepitaxial growth of III–V alloys on silicon substrates. Ab initio totalenergy calculations and quasiparticle GW calculations are used to investigate the physical properties of these new semiconductors. One particular configuration is designed to match lattice constant and polarity with the Si(100) surface and to possess a direct band gap of 1.59 μm, which is close to the canonical frequency used by the optoelectronics industry. These results could pave the way for eventual monolithic integration of optical materials on silicon.

[182]

T. Wang, N. Moll, K. Cho, and J. D. Joannopoulos, “Deliberately designed
interfaces for monolithic integration in optoelectronics,” Journal of
Vacuum Science and Technology B, vol. 17, pp. 1612–1616, March 1999.
[ bib 
DOI ]
A novel class of semiconductors is introduced, based on computational design, to solve the longstanding problem of lattice and polarity mismatch in heteroepitaxial growth of III–V alloys on silicon substrates. Ab initio totalenergy calculations and quasiparticle GW calculations are used to investigate the physical properties of these new semiconductors. One particular configuration is designed to match lattice constant and polarity with the Si(100) surface and to possess a direct band gap of 1.59 μm, which is close to the canonical frequency used by the optoelectronics industry. These results could pave the way for eventual monolithic integration of optical materials on silicon.

[181]

S. Mirbt, N. Moll, A. Kley, and J. D. Joannopoulos, “A general rule for
surface reconstructions of III–V semiconductors,” Surface
Science, vol. 422, pp. L177–L182, February 1999.
[ bib 
DOI ]
First principles total energy calculations are performed for a large number (70) of III–V semiconductor surfaces in order to establish a database from which a general rule is extracted to help isolate and predict the lowest energy atomic surface geometries for these complex systems. The general rule involves minimizing a single, material and geometryindependent, parameter, whose value depends only on a weighted sum of specific surface atom and bond structural units.

[180]

R. B. Capaz, L. V. C. Assali, L. C. Kimerling, K. Cho, and J. D. Joannopoulos,
“Mechanism for hydrogenenhanced oxygen diffusion in silicon,”
Physical Review B, vol. 59, pp. 4898–4900, February 1999.
[ bib 
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Oxygen diffuses in silicon with an activation energy of 2.53–2.56 eV. In hydrogenated samples, this activation energy is found to decrease to 1.6–2.0 eV. In this paper, a microscopic mechanism for hydrogenenhanced oxygen diffusion in pdoped silicon is proposed. A path for joint diffusion of O and H is obtained from an ab initio moleculardynamics simulation in which the O atom is “kicked” away from its equilibrium position with a given initial kinetic energy. After reaching a maximum potential energy of 1.46 eV above the ground state, the system relaxes to a metastable state on which a SiSi bond is broken and the H atom saturates one of the dangling bonds. With an extra 0.16 eV, the SiH bond is broken and the system relaxes to an equivalent groundstate configuration. Therefore, the migration pathway is an intriguing twostep mechanism. This path represents a 0.54eV reduction in the static barrier when compared with the diffusion of isolated O in Si, in excellent agreement with experiments. This mechanism elucidates the role played by the H atom in the process: it not only serves to “open up” a SiSi bond to be attacked by the oxygen, but it also helps in reducing the energy of an important intermediate state in the diffusion pathway.

[179]

R. B. Capaz, A. Dal Pino, Jr., and J. D. Joannopoulos, “Theory of
carboncarbon pairs in silicon,” Physical Review B, vol. 58,
pp. 9845–9850, October 1998.
[ bib 
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Interstitialsubstitutional carbon pairs (C_{i}C_{s}) in silicon display interesting metastable behavior associated with two different structural configurations. In this work, we perform extensive ab initio calculations on this system. Our results show the following. (i) The metastable configuration for the neutral charge state displays C_{1h} symmetry and it is reminiscent of the isolated interstitial carbon configuration, i.e., a split interstitial CSi pair with the substitutional carbon bonded to the silicon interstitial. (ii) The groundstate configuration also has C_{1h} symmetry, but it consists of a single silicon interstitial twofold coordinated in an unusual bridge configuration between two substitutional carbon atoms. With an activation energy of 0.07 eV, this configuration becomes a motionalaveraged state with C_{3v} symmetry. (iii) The ground state is lower in energy by 0.11 eV with respect to the metastable state. The jump from one configuration to the other corresponds to bondswitching mechanism with a calculated energy barrier of 0.13 eV. (iv) Both configurations have two electronic states in the gap, with gapstate wave functions consistent with the local bonding of the defect complex in each case. (v) Analysis of localmode vibrations on the groundstate configuration indicates a stronger component in one of the carbon atoms, which explains the experimentally observed isotope splittings. Vibrational frequencies for the metastable configuration are also predicted. All of these results are in satisfactory agreement with experiments.

[178]

J. Ireta, M. Galván, K. Cho, and J. D. Joannopoulos, “Local reactivity
of charybdotoxin, a k^{+} channel blocker,” Journal of the American
Chemical Society, vol. 120, pp. 9771–9778, September 1998.
[ bib ]
Charybdotoxin (ChTX) is a 37residue polypeptide that has been extensively used in sitedirected mutagenesis experiments as a template to deduce models for the external pore appearance of K^{+} channels. The microscopic details of the ChTXchannel interaction, however, remain as a challenge for experimental and theoretical approaches. In this work, regional chargetransfer abilities, measured by chemical softness, s(r), are used as companion properties of the electrostatic potential, V(r), in the search for a qualitative structurefunction relationship in the ChTXK^{+} channel interaction. Both quantities were obtained with an ab initio methodology in massively parallel computers. In the analysis of s(r) and V(r), regions of the size of amino acids were considered because this is the appropriate scale to correlate with sitedirected mutagenesis experiments. The correspondence between experimentally identified crucial amino acids sites and regional softnesses indicates that charge transfer to ChTX could be one of the main stabilization effects in the ChTXchannel complex. Also, it provides an explanation for the strong dependence of the dissociation constant of the complex on mutations of crucial amino acids. In addition, it is shown to be feasible to find structurefunction relationships by combining local reactivity parameters and experimental data involving site directed mutagenesis.

[177]

K. Cho, E. Kaxiras, and J. D. Joannopoulos, “Theory of adsorption and
desorption of h_{2} molecules on the Si(111)(7×7) surface,”
Physical Review Letters, vol. 79, pp. 5078–5081, December 1997.
[ bib 
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The physics of adsorption and desorption of H_{2} molecules on the Si(111)(7×7) surface is investigated through firstprinciples density functional theory calculations. The calculated adsorption and desorption energy barriers are 0.8 and 2.4 eV, respectively. The process of adatom backbond breaking is identified as the fundamental microscopic mechanism determining the adsorption energy barrier and the kinetic energy of the desorbed H_{2} molecule. These results shed light on controversial experimental findings for this classic surface–molecule system.

[176]

M. K. Aydinol, A. F. Kohan, G. Ceder, K. Cho, and J. Joannopoulos, “Ab initio
study of lithium intercalation in metal oxides and metal dichalcogenides,”
Physical Review B, vol. 56, pp. 1354–1365, July 1997.
[ bib 
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A study of the average voltage to intercalate lithium in various metal oxides is presented. By combining the ab initio pseudopotential method with basic thermodynamics the average intercalation voltage can be predicted without the need for experimental data. This procedure is used to systematically study the effect of metal chemistry, anion chemistry, and structure. It is found that Li is fully ionized in the intercalated compounds with its charge transferred to the anion and to the metal. The substantial charge transfer to the anion is responsible for the large voltage difference between oxides, sulfides, and selenides. Ionic relaxation, as a result of Li intercalation, causes nonrigidband effects in the density of states of these materials. Suggestions for compounds that may have a substantially larger voltage than currently used materials are also presented.

[175]

R. B. Capaz and J. D. Joannopoulos, “Unified approach for the calculation of
force constants and accelerated convergence of atomic coordinates,”
Physical Review B, vol. 54, pp. 13402–13405, November 1996.
[ bib 
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A method which simultaneously computes the forceconstant matrix (FCM) and relaxes the atomic coordinates to the ground state of a generic system is introduced. The method is based on the optimization of the FCM as the atomic coordinates evolve to their groundstate configuration, using the variations in atomic positions and forces from previous iterations as inputs. Striking accelerated convergence as compared to traditional methods is obtained, as well as accurate vibrational frequencies with no additional cost.

[174]

K. Cho and J. D. Joannopoulos, “Intrinsic surface atom manipulations in STM
and AFM,” Applied Surface Science, vol. 104–105, pp. 286–290,
September 1996.
[ bib 
DOI ]
Stateoftheart firstprinciples simulations are performed to investigate the possibility of using a tungsten tip in atomic force microscopy (AFM) as a mechanical tool to manipulate the surface atoms of Si(100). Calculations of total energy and electronic structure are used to study the energetics and bonding properties associated with the tip and surface for a variety of atomic configurations. The results predict that under certain protocols the tip can be used effectively to flip dimers on the surface, from one buckled configuration to another, reversibly, and without inducing damage to either the intrinsic surface or the tip. This leads directly to the exciting possibility of using the intrinsic (100) surface of silicon as an ultrahigh memory storage device approaching the ultimate limit of one bit of data per atom.

[173]

P. D. Tepesch, A. F. Kohan, G. D. Garbulsky, G. Ceder, C. Coley, H. T. Stokes,
L. L. Boyer, M. J. Mehl, B. P. Burton, K. Cho, and J. Joannopoulos, “A model
to compute phase diagrams in oxides with empirical or firstprinciples energy
methods and application to the solubility limits in the CaO–MgO
system,” Journal of the American Ceramic Society, vol. 79,
pp. 2033–2040, August 1996.
[ bib 
DOI ]
The CaO–MgO system is used as a prototype system to evaluate the accuracy of several energy and entropy approximations for predicting solidstate phase diagrams in ionic materials. Configurational disorder between the cations is parameterized with the cluster expansion technique. The vibrational contribution to the free energy is incorporated with a harmonic model that accounts for the dependence of the vibrational density of states on the cation configuration. The CaO–MgO hase diagram can be predicted very accurately with quantum mechanical energy methods, without the use of any adjustable parameters. Published empirical potential parameters for the CaO–MgO system reproduce the qualitative features of the phase diagram but significantly underestimate the solubility limits. Parameters that reasonably reproduce the quantum mechanical results are presented.

[172]

H. Lim, K. Cho, R. B. Capaz, J. D. Joannopoulos, K. D. Brommer, and B. E.
Larson, “Ab initio studies of adatom vacancies on the Si(111)(7×7)
surface,” Physical Review B, vol. 53, pp. 15421–15424, June 1996.
[ bib 
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Ab initio totalenergy calculations are used to investigate adatom vacancies on the Si(111)(7×7) surface. In striking contrast to recent experimental estimates, vacancy formation energies are calculated to be 0.9 eV on average, with ∼0.1eV variations depending on the type of adatom. We find that faulted or corner adatoms can be removed more easily than unfaulted or edge adatoms, respectively. Structural relaxations induce large changes in the electronic structure of the surface states. Calculation of scanning tunneling microscopy (STM) images show that the predicted variations should be readily observed in differential STM measurements.

[171]

S. Lee, S. J. Lee, J. Y. Lee, J. Kim, K. S. Kim, I. Park, K. Cho, and J. D.
Joannopoulos, “Ab initio study of water hexamer anions,” Chemical
Physics Letters, vol. 254, pp. 128–134, May 1996.
[ bib 
DOI ]
The wet electron—an electron interacting with a small cluster of water molecules—is a simple yet fundamental system for understanding the behavior of electrons in complex molecular systems. A comprehensive post HartreeFock ab initio study is performed on the wet electron in various water hexamer clusters including the lowlying energy conformers of the neutral species. The predicted geometries, total energies, photoemission ionization energies, electronic structure and orbital character of the excess electron in ground and excited states are discussed. To understand the behavior of the excess electron in the clusters, the sorbitallike character of the HOMOs and the porbitallike character of the LUMOs are investigated.

[170]

K. S. Kim, I. Park, S. Lee, K. Cho, J. Y. Lee, J. Kim, and J. D. Joannopoulos,
“The nature of a wet electron,” Physical Review Letters, vol. 76,
pp. 956–959, February 1996.
[ bib 
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A comprehensive stateoftheart ab initio study is performed on the wet electron—n electron interacting with a small cluster of molecules waterin the water hexamer system. Predictions include two previously unknown distinctive geometries which bind the excess electron as internal and external states, photoemission ionization energies in agreement with experiment, identification of generic electrophilic sites involving dangling hydrogen atoms, and the tendency of all hydrogen atoms to be saturated in hydrogen bonding or in interaction with the excess electron. An emerging insight is the capability of electrophilic sites to be actuators of electron transport pathways in biomolecular systems.

[169]

K. Cho and J. D. Joannopoulos, “Flipping silicon dimers on Si(100) using
scanning tip microscopy: A theoretical investigation,” Physical
Review B, vol. 53, pp. 4553–4556, February 1996.
[ bib 
http ]
Stateoftheart firstprinciples calculations are performed to investigate the possibility of using a tungsten tip in scanning tunneling microscopy or atomic force microscopy as a tool to manipulate the surface atoms of Si(100). Calculations of total energy and electronic structure are used to study the energetics and bonding properties associated with the tip and surface for a variety of atomic configurations. The results predict that under certain protocols the tip can be used to flip dimers on the surface, from one buckled configuration to another, reversibly, and without inducing damage to either the intrinsic surface or the tip. The implications of these results for using the intrinsic (100) surface of silicon as an ultrahigh density memory storage medium approaching one bit of data per dimer are discussed.

[168]

K. Cho, J. D. Joannopoulos, and A. N. Berker, “Vicinal Si(100) surfaces
under external strain,” Physical Review B, vol. 53, pp. 1002–1005,
January 1996.
[ bib 
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The phase diagram of vicinal Si(100) surfaces is calculated as a function of misorientation angle, temperature, and applied external strain. It is shown that a change of the applied external strain can lead to a phase transition between the singlelayer step surface phase and the doublelayer step surface phase. The effect of temperature is shown to be negligible up to 300 K. The order parameter of the surface phase transition is also calculated to make contact with experimental measurements.

[167]

K. Cho and J. D. Joannopoulos, “Reversible tipinduced structural
modifications in scanning tip microscopy,” Japanese Journal of Applied
Physics, vol. 35, pp. 3714–3718, 1996.
[ bib ]

[166]

H. Lim, K. Cho, I. Park, J. D. Joannopoulos, and E. Kaxiras, “Ab initio study
of hydrogen adsorption on the Si(111)(7×7) surface,”
Physical Review B, vol. 52, pp. 17231–17237, December 1995.
Erratum: ibid., vol. 54, p. 5179 (1996).
[ bib 
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Firstprinciples totalenergy pseudopotential calculations are performed to investigate the adsorption interaction of a H atom with dangling bonds on the Si(111)(7×7) surface. he binding energies for adsorption of H at the adatom, rest atom, and corner hole sites are calculated to be 2.9, 3.2, and 3.5 eV, respectively. Spectral analysis of the electronic states shows that nonlocal changes of chemical reactivity are induced by charge transfer upon H adsorption. It is found that H adsorption on the adatoms or rest atoms induces a charge transfer onto the SiH bond and a shift in energy of the remaining danglingbond states. Adsorption on the corner hole, however, does not involve any charge transfer. The relationship between charge transfer and binding energies is discussed.

[165]

R. B. Capaz, K. Cho, and J. D. Joannopoulos, “Signatures of bulk and surface
arsenic antisite defects in GaAs(110),” Physical Review Letters,
vol. 75, pp. 1811–1814, August 1995.
[ bib 
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Scanning tunneling microscopy (STM) has recently been used in the study of bulk arsenic antisite defects in GaAs. In this work, we report extensive theoretical calculations of such defects in the vicinity of a GaAs(110) surface, which provide essential information for the interpretation of experiments. Defects display remarkably distinct properties depending on whether they are fourfold or threefold coordinated. The nature of “satellite peaks” observed in experiment is elucidated. We predict the conditions under which STMmeasured properties will be faithful to the properties of the bulk defect.

[164]

R. B. Capaz, H. Lim, and J. D. Joannopoulos, “Ab initio studies of GaN
epitaxial growth on SiC,” Physical Review B, vol. 51,
pp. 17755–17757, June 1995.
[ bib 
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Ab initio methods were used to investigate the initial stages of GaN epitaxial growth on (0001) 6HSiC. Total energies of four types of interfaces were calculated. Polarity matching at the interface plays a fundamental role in determining the lowerenergy structures, yielding strong binding for SiN and CGa interfaces and very weak binding for SiGa and CN. We therefore predict that Siterminated substrates will produce ideally Gaterminated films, whereas Cterminated substrates will produce ideally Nterminated films. This prediction suggests reinterpretation of recent experiments.

[163]

K. Cho and J. D. Joannopoulos, “Mechanical hysteresis on an atomic scale,”
Surface Science, vol. 328, pp. 320–324, May 1995.
[ bib 
DOI ]
A micromechanical hysteresis associated with intimate atomic force microscopy (AFM) on the Si(100) surface is discovered using ab initio total energy pseudopotential density functional calculations. It is predicted that it is possible to cycle repeatedly between two buckled configurations of a surface dimer along two different paths, one of which involves a discontinuous change of the equilibrium dimerangle, by varying appropriately the vertical movement of the AFM tip. This microscopic mechanical hysteresis effect should be detectable experimentally in low temperature AFM measurements.

[162]

K. Cho and J. D. Joannopoulos, “Tipinduced modifications in STM and
AFM,” Scanning Microscopy, vol. 9, p. 381, 1995.
[ bib ]

[161]

R. B. Capaz, A. Dal Pino, Jr., and J. D. Joannopoulos, “Identification of the
migration path of interstitial carbon in silicon,” Physical Review B,
vol. 50, pp. 7439–7442, September 1994.
[ bib 
http ]
We have performed ab initio totalenergy calculations of groundstate properties and migration paths of interstitial carbon in silicon. The ground state involves threefoldcoordinated carbon and silicon atoms and its geometry suggests primarily p and sp bonding for carbon, rather than sp^{2} one would naively expect. Examination of possible migration paths reveals that only three correspond to small “jumps” involving a single “bond breaking.” Of these, we predict that only one has a barrier of considerably lower energy (∼0.5 eV) and involves an intermediate “saddlepoint” configuration of C_{2} symmetry

[160]

T. A. Arias and J. D. Joannopoulos, “Ab initio theory of dislocation
interactions: from closerange spontaneous annihilation to the longrange
continuum limit,” Physical Review Letters, vol. 73, pp. 680–683,
August 1994.
[ bib 
http ]
Parallel supercomputer technology now permits ab initio studies of systems of sufficient size to explore the interactions among dislocations in a solid. This study shows that the silicon shuffleset (110) screw dislocation is stable against spontaneous dissociation, provides an ab initio value for the dislocation core energy, demonstrates a dislocationantidislocation interaction approaching the classical limit within a few tens of angstroms, and reveals a pathway for the spontaneous mutual annihilation of a dislocation dipole of the type that occurs when a FrankRead source emits a dislocation loop.

[159]

K. D. Brommer, M. Galván, A. Dal Pino, Jr., and J. D. Joannopoulos,
“Theory of adsorption of atoms and molecules on Si(111)(7×7),”
Surface Science, vol. 314, pp. 57–70, July 1994.
[ bib 
DOI ]
Ab initio density functional theory calculations are performed to analyze a regional reactivity index based on chemical concepts of local softness and electronegativity. This leads to the prediction of a general qualitative pattern for the interaction of the Si(111)(7×7) surface with atoms and molecules that preserve the reconstruction. We successfully compare this general pattern with experimental information available. Based on this approach, we predict the reactivity behavior of the reconstruction with a wide range of chemical reactants.

[158]

A. Devenyi, K. Cho, T. A. Arias, and J. D. Joannopoulos, “Adaptive
Riemannian metric for allelectron calculations,” Physical Review B,
vol. 49, pp. 13373–13376, May 1994.
[ bib 
http ]
We present two techniques that make feasible the application of the adaptive Riemannian metric technique to allelectron localdensityfunctional calculations. The first overcomes both the real (r=0) and Fourier (G=0) space divergences of the nuclear Coulomb potential by computing the electronion energy as the smooth periodic electrostatic potential due to the electrons measured at the positions of the ions. The second overcomes the problem of slow convergence of the extreme metrics which the r=0 Coulomb divergence necessitates by giving an explicit prescription for a suitable metric for arbitrary ionic configurations. Allelectrondiamond calculations then serve as a proving ground for these ideas and demonstrate the viability of adaptive Riemannian methods for bypassing the pseudopotential approximation in solidstate calculations.

[157]

T. A. Arias and J. D. Joannopoulos, “Electron trapping and impurity
segregation without defects: Ab initio study of perfectly rebonded grain
boundaries,” Physical Review B, vol. 49, pp. 4525–4531, February
1994.
[ bib 
http ]
We present the results of an extensive ab initio study of the Σ=5 [310] grain boundary in germanium. We find that the boundary reliably reconstructs to the tetrahedrally bonded network observed in highresolution electron microscopy experiments without the proliferation of false local minima observed in similar twist boundaries. The reduced density of bonds crossing the grainboundary plane leads us to conjecture that the boundary may be a preferred fracture interface. Though there are no dangling bonds or miscoordinated sites in the reconstruction, the boundary presents electrontrap states just below the conduction band. Further, we show that lattice relaxation effects are irrelevant to the segregation of impurities to tetrahedrally reconstructed defects and that the interfacial electrontrap states give rise to an electronic frustration mechanism that selectively drives the segregation of only ntype dopants to the boundary.

[156]

K. Cho, T. A. Arias, J. D. Joannopoulos, and P. K. Lam, “Wavelets in
electronic structure calculations,” Physical Review Letters, vol. 71,
pp. 1808–1811, September 1993.
[ bib 
http ]
A threedimensional wavelet analysis is employed to develop a new formalism for electronic structure calculations. The wavelet formalism provides a systematically improvable and tractable description of electronic wave functions and overcomes limitations of conventional basis expansions. The potential power of the wavelet formalism for ab initio electronic structure calculations is demonstrated by a calculation of 1s states for all the naturally occurring nuclei on the periodic table and the interaction energies of the hydrogen molecule ion.

[155]

K. Cho and J. D. Joannopoulos, “Tipsurface interactions in scanning tunneling
microscopy,” Physical Review Letters, vol. 71, pp. 1387–1390, August
1993.
[ bib 
http ]
The tipsurface interactions in scanning tunneling microscopy (STM) of the Si(100) surface are investigated with ab initio total energy pseudopotential calculations. The results of the calculations lead to a new understanding of the microscopic STM measurement process. It is found that under typical conditions the influence of the tip is large enough to effectively flip a dimer on this surface. This leads to a reinterpretation of the “symmetric” dimer STM image as an asymmetric dimer configuration that flips as it follows the motion of the scanning tip.

[154]

K. Cho, J. D. Joannopoulos, and L. Kleinman, “Constanttemperature molecular
dynamics with momentum conservation,” Physical Review E, vol. 47,
pp. 3145–3151, May 1993.
[ bib 
http ]
The Nosé theorem of the extendedsystem method of the constanttemperature molecular dynamics is generalized by including the conservation of the total virtual momentum. It is proved that a canonical ensemble of an (N1)particle system is generated from an extended system of an Nparticle system only if the total virtual momentum is zero. It is also shown that the resulting (N1)particle system has a slightly different mass spectrum than that of the original Nparticle system. The consequences of this new mass spectrum are relevant in the calculation of dynamical properties and the relaxation times of the system, but irrelevant to thermodynamic averages. For practical considerations, numerical simulations are performed and tested against this theorem. The differences in application of the Nosé theorem and the generalized Noé theorem are discussed.

[153]

A. Dal Pino, Jr., A. M. Rappe, and J. D. Joannopoulos, “Ab initio
investigation of carbonrelated defects in silicon,” Physical
Review B, vol. 47, pp. 12554–12557, May 1993.
[ bib 
http ]
Ab initio totalenergy calculations based on the localdensityfunctional, pseudopotential, and supercell approximations are performed to investigate carbon defects in silicon. The geometry and the formation energy of substitutional and impurityvacancy defects are studied including the relaxation of nearest and nextnearest neighbors. Results for substitutional carbon appear to be consistent with a recently suggested reinterpretation of the available experimental formation energy data. Results for the interaction energy between a carbon atom and a silicon vacancy predict a small binding energy of 0.19 eV.

[152]

J. Wang, T. A. Arias, J. D. Joannopoulos, G. W. Turner, and O. L. Alerhand,
“Scanningtunnelingmicroscopy signatures and chemical identifications of
the (110) surface of sidoped gaas,” Physical Review B, vol. 47,
pp. 10326–10334, April 1993.
[ bib 
http ]
The electronic properties of the (110) surface of both pure and Sidoped bulk GaAs are studied using firstprinciples totalenergy calculations within the localdensity functional and pseudopotential approximations. The wave functions of the relaxed configurations are used to generate theoretical scanningtunnelingmicroscopy (STM) images. For the clean surface, the buckling angle of the surface GaAs bond is found to be 26^{o} and the theoretically generated STM images are in good agreement with those obtained from experiment. For the Sidoped GaAs(110) surface, the extra electron of the Si substitutional at a Ga site on the surface is found to be welllocalized around the Si atom. In addition, danglingbond states of surface As atoms bordering the Si substitutional are found to be altered due to the distinctively different chemical property of the Si substitutionals. These features should act as a signature for the location of the substitutional surface Si atoms via either voltagedependent STM imaging or currentvoltage (I–V) measurements of various positions on the surface.

[151]

J. Wang, T. A. Arias, and J. D. Joannopoulos, “Dimer vacancies and
dimervacancy complexes on the si(100) surface,” Physical Review B,
vol. 47, pp. 10497–10508, April 1993.
[ bib 
http ]
Ab initio totalenergy calculations are performed using a conjugategradients minimization technique to calculate the properties of various dimer vacancies and dimervacancy complexes on the Si(100) surface. A dimer vacancy is found to be a much more probable intrinsic defect for this surface than the recently proposed dimer interstitial. Two mechanisms are identified that contribute to the low formation energy and stability of dimer vacancies on the surface: (i) the need to eliminate dangling bonds in the second layer and (ii) the need for atoms to readjust in order to relax the strain. The results of the calculations provide a good quantitative explanation of the major features of scanningtunnelmicroscopy images obtained from the Si(100) surface. These include the abundance of dimer vacancies, the tendency of dimer vacancies to cluster, and the details of the nonthermal population distribution of distinctive vacancy complexes.

[150]

K. D. Brommer, B. E. Larson, M. Needels, and J. D. Joannopoulos, “Modeling
large surface reconstructions on the Connection Machine,” Japanese
Journal of Applied Physics, Part 1, vol. 32, pp. 1360–1367, March 1993.
[ bib 
http ]
Using a massively parallel computer, we undertake an ab initio investigation of the Si(111)(7 ×7) surface reconstruction. Calculation of the total energy of an ∼700 effective atom supercell at an 8 Ry plane wave cutoff allows us to determine (1) the energy difference between the (7 ×7) and (2 ×1) reconstructions, (2) the relaxed atomic geometry, (3) the scanning tunneling microscope topographs as a function of bias voltage and (4) the occupied and unoccupied electronic states.

[149]

M. Galvan, A. Dal Pino, Jr., J. Wang, and J. D. Joannopoulos, “Local softness,
scanning tunneling microscopy, and surface reactivity,” Journal of
Physical Chemistry, vol. 97, pp. 783–785, January 1993.
[ bib ]
Within the finite temperature extension of density functional theory, it is shown that local softness measures the ability of a chemical system to gain or donate charge as the external potential changes. This feature allows us to establish a formal connection between local softness and scanning tunneling microscopy (STM) images. We show that, under appropriate conditions, STM images can be used to measure local softness for surfaces. Finally, a potential application of those images as reactivity criteria within the context of the hard and soft acids and bases (HSAB) principle is discussed.

[148]

M. Galván, A. Dal Pino, Jr., and J. D. Joannopoulos, “Hardness and
softness in the ab initio study of polyatomic systems,” Physical Review
Letters, vol. 70, pp. 21–24, January 1993.
[ bib 
http ]
A combination of the maximum hardness (MH) principle, and the local version of the hard and soft acids and bases (HSAB) principle is tested as a tool to describe the stability and reactivity of polyatomic systems. The local HSAB principle describes regional differences in reactivity whereas the MH principle selects the most stable configuration. This approach is tested using ab initio density functional theory techniques. Totalenergy calculations fully confirm the validity of both principles.

[147]

A. Dal Pino, Jr., M. Galv'an, T. A. Arias, and J. D. Joannopoulos,
“Chemical softness and impurity segregation at grain boundaries,”
Journal of Chemical Physics, vol. 98, pp. 1606–1610, January 1993.
See erratum: ibid, vol. 98, p. 10106.
[ bib 
http ]
We analyze the process of impurity segregation at grain boundaries as a chemical reaction between the impurity and the interface. From this point of view, we test the ability of the concepts of local softness and hardness to predict the most probable sites for impurity accumulation. As a test, an ab initio investigation of the Σ=5 tilt [310] grain boundary in germanium is presented and the energetics of the accumulation of dopant atoms in this interface are studied. Our results support the utility of an analysis in terms of softness for impurity segregation problems.

[146]

M. Galván, A. Dal Pino, Jr., and J. D. Joannopoulos, “Hardness and
softness in the ab initio study of polyatomic systems,” Physical Review
Letters, vol. 70, pp. 21–24, January 1993.
[ bib 
http ]
A combination of the maximum hardness (MH) principle, and the local version of the hard and soft acids and bases (HSAB) principle is tested as a tool to describe the stability and reactivity of polyatomic systems. The local HSAB principle describes regional differences in reactivity whereas the MH principle selects the most stable configuration. This approach is tested using ab initio density functional theory techniques. Totalenergy calculations fully confirm the validity of both principles.

[145]

T. A. Arias and J. D. Joannopoulos, “Ab initio prediction of dopant
segregation at elemental semiconductor grain boundaries without coordination
defects,” Physical Review Letters, vol. 69, pp. 3330–3333, December
1992.
[ bib 
http ]
We present results of an extensive stateoftheart ab initio study of the segregation of dopants to the Σ=5 tilt (310) grain boundary in germanium. Despite the lack of reactive bond coordination defects in this boundary, we predict a significant tendency for ntype dopants to segregate to the boundary. Our results lead to a general theory of dopant segregation at tetrahedrally bonded semiconductor defects, where lattice relaxation effects are irrelevant and segregation is driven by the mixing of localized carrier states of the defect with the hydrogenic states of the dopant.

[144]

E. Kaxiras, O. L. Alerhand, J. Wang, and J. D. Joannopoulos, “Theoretical
modeling of heteroepitaxial growth initiation,” Materials Science &
Engineering B, vol. 14, pp. 245–253, November 1992.
[ bib 
DOI ]
We review recent theoretical investigations on the initiation of heteroepitaxial growth. The thermodynamic premises on which the various growth models are based are considered. A qualitatively new model which applies to polaronnonpolar heteroepitaxial growth is discussed. Specific consequences of the new growth model are explored and shown to be consistent with experimental observations of GaAs growth on Si(100) vicinal surfaces. Firstprinciples calculations of the total energy of competing structures provide support for the proposed model. The totalenergy comparisons afford a resolution to a longstanding puzzle concerning the effect of temperature on the orientation of GaAs overlayers on vicinal silicon substrates.

[143]

M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos,
“Iterative minimization techniques for ab initio totalenergy calculations:
molecular dynamics and conjugate gradients,” Reviews of Modern
Physics, vol. 64, pp. 1045–1097, October 1992.
[ bib 
http ]
This article describes recent technical developments that have made the totalenergy pseudopotential the most powerful ab initio quantummechanical modeling method presently available. In addition to presenting technical details of the pseudopotential method, the article aims to heighten awareness of the capabilities of the method in order to stimulate its application to as wide a range of problems in as many scientific disciplines as possible.

[142]

M. Needels, A. M. Rappe, P. D. Bristowe, and J. D. Joannopoulos, “Ab initio
study of a grain boundary in gold,” Physical Review B, vol. 46,
pp. 9768–9771, October 1992.
[ bib 
http ]
The total energy of a grain boundary in a transition metal is calculated in an ab initio manner. Such calculations are now feasible using a planewave basis set provided that an optimally convergent pseudopotential is used. The investigation focuses on resolving two competing atomic models for the Σ=5 [001] twist boundary in gold. It is found that the model of lower energy, which involves small atomic displacements, corresponds to a structure determined both experimentally, using quantitative xraydiffraction techniques, and theoretically, using the embeddedatom method.

[141]

A. M. Rappe, A. al Pino, Jr., M. Needels, and J. D. Joannopoulos, “Mixedbasis
pseudopotential method applied to iterative diagonalization techniques,”
Physical Review B, vol. 46, pp. 7353–7357, September 1992.
[ bib 
http ]
We apply a mixedbasis formulation of pseudopotential totalenergy electronic structure calculations in the context of iterative diagonalization techniques. The formulation combines a small set of auxiliary functions to describe the localized part of the wave function with a planewave basis set. The method is tested on lowsymmetry configurations of interstitial oxygen in silicon. This method provides accuracy comparable to planewave basisset calculations and requires less computational effort. Therefore, it appears to be a promising tool for the description of the electronic structure of systems with localized valence electrons.

[140]

J. D. Joannopoulos and M. L. Cohen, “Electronic structure of crystalline
polytypes and amorphous Si,” Physics Letters A, vol. 41, pp. 71–72,
August 1992.
[ bib 
DOI ]
We have calculated the density of states and the imaginary part of the energy dependent dielectric constant for four polytypes of Si using pseudopotential and tight binding models. Comparisons are made with the experimental results for amorphous Si.

[139]

T. A. Arias, M. C. Payne, and J. D. Joannopoulos, “Ab initio molecular
dynamics: Analytically continued energy functionals and insights into
iterative solutions,” Physical Review Letters, vol. 69,
pp. 1077–1080, August 1992.
[ bib 
http ]
We present a new method for performing finitetemperature ab initio totalenergy calculations at long length scales, which we demonstrate with a dynamics calculation of 50 Ålong phonon modes in silicon. The method involves both a prescription for the analytic continuation of tradional fermionic energy functionals into the space of nonorthonormal singleparticle orbitals (speeding convergence to the minimum) and insights into the common computational physics problem of solving by iterative refinement for the state of a complex system as a function of a continuous external parameter.

[138]

A. M. Rappe, J. D. Joannopoulos, and P. A. Bash, “Test of utility of plane
waves for the study of molecules from first principles,” Journal of the
American Chemical Society, vol. 114, p. 6466, July 1992.
[ bib ]
This paper studies the applicability of a planewave basis set for density functinal calculations of the properties of molecules from first principles. The main features of the planewave method are described, including pseudopotentials and supercells. The results for a number of small molecules are reported. The close agreement with experiment and with a standard method of quantum chemistry calculation indicates the promise which this method holds for chemical and biochemical firstprinciples computations.

[137]

R. H. Wolfe, M. Needels, T. Arias, and J. D. Joannopoulos, “Visual revelations
from silicon ab initio calculations,” IEEE Computer Graphics and
Applications, vol. 12, pp. 45–53, July 1992.
[ bib 
DOI ]
The use of volumetric rendering for interpreting the computed electronic structure of solids is discussed. The structure, manifested as an atomicscale 3D electronic charge density, is computed from a pure mathematical model. The mathematical technique represents a class of ab initio computations that predict the atomic structure by solving the equations of quantum mechanics, wherein all configuration parameters except the atomic number are under the analyst's control. Some physics aspects of electronic structure of solids are reviewed. The use of this visualization technique to interpret the computations for silicon with an oxygen impurity and for roomtemperature silicon is described.

[136]

K. Cho and J. D. Joannopoulos, “Ergodicity and dynamical properties of
constanttemperature molecular dynamics,” Physical Review A, vol. 45,
pp. 7089–7097, May 1992.
[ bib 
http ]
The assumption of ergodicity in Nosé's original formulation of the constanttemperature molecular dynamics is tested for a LennardJonespotential system. With the performance of very long simulations, it is shown that the extended system of a LennardJonespotential system is ergodic for all values of thermostat parameters tested. It is also shown, however, that the rate of convergence to the canonical ensemble strongly depends on the value of thermostat effective mass Q. The dynamical properties of the extended system are also studied using the velocity autocorrelation function and the power spectral density. From the analysis of the simulations, it is found that the dynamical properties are not correctly represented for arbitrary values of thermostat parameters. A prescription and a set of quantitative criteria are introduced to generate physically meaningful dynamics. Thus the results of this work show that with a special choice of thermostat parameters it is possible to obtain both the correct canonical ensemble and physically meaningful dynamical behavior of the physical system.

[135]

K. D. Brommer, M. Needels, B. E. Larson, and J. D. Joannopoulos, “Ab initio
theory of the Si(111)(7×7) surface reconstruction: A challenge for
massively parallel computation,” Physical Review Letters, vol. 68,
pp. 1355–1358, March 1992.
[ bib 
http ]
An ab initio investigation of the Si(111)(7×7) surface reconstruction is undertaken using the state of the art in massively parallel computation. Calculations of the total energy of an ∼700 effectiveatom supercell are performed to determine (1) the fully relaxed atomic geometry, (2) the scanningtunnelingmicroscope images as a function of bias voltage, and (3) the energy difference between the (7 ×7) and the (2 ×1) reconstructions. The (7 ×7) reconstruction is found to be energetically favorable to the (2 ×1) surface by 60 meV per (1 ×1) unit cell.

[134]

A. Dal Pino, Jr., M. Needels, and J. D. Joannopoulos, “Oxygeninduced
brokenbond defect in silicon,” Physical Review B, vol. 45,
pp. 3304–3308, February 1992.
[ bib 
http ]
The electronic and geometric structure of a recently proposed oxygenrelated defect in silicon is studied using a precise Iab initioP quantummoleculardynamics method based on localdensityfunctional theory, nonlocal pseudopotentials, and the supercell approximation. This defect is a metastable configuration of interstitial oxygen in Si (Si:O_{i}), and it is closely related to a vacancyinterstitial pair. This defect has a relatively low formation energy despite the presence of a silicon broken bond. A simple and straightforward procedure is used to identify the static barrier for the formation of an intimate vacancyinterstitial pair in silicon and the static barrier for the recombination of the broken bond in metastable Si:O_{i}. The similarities in geometric configurations for both cases are explored to introduce a mechanism for the creation of intimate vacancyinterstitiallike defects in silicon.

[133]

T. A. Arias, M. C. Payne, and J. D. Joannopoulos, “Ab initio
moleculardynamics techniques extended to largelengthscale systems,”
Physical Review B, vol. 45, pp. 1538–1549, January 1992.
[ bib 
http ]
The BornOppenheimer approximation divides the problem of quantum molecular dynamics into two familiar problems: (1) solution for the electronic wave functions for a given instantaneous arrangement of ions and (2) the motion of the atomic cores under the influence of those wave functions. A combination of conjugategradient methods to solve (1) with standard molecular dynamics to solve (2) results in a scheme that is at least two orders of magnitude more accurate than previously possible, thus allowing accurate calculation of dynamic correlation functions while maintaining tolerable energy conservation for microcanonical averages of those correlation functions over picosecond time scales. By employing conjugategradient techniques, this method is used to extend the applicability of finitetemperature ab initio techniques to systems with large length scales.

[132]

O. L. Alerhand, J. Wang, J. D. Joannopoulos, E. Kaxiras, and R. S. Becker,
“Adsorption of As on stepped Si(100): Resolution of the
sublatticeorientation dilemma,” Physical Review B, vol. 44,
pp. 6534–6537, September 1991.
[ bib 
http ]
Firstprinciples calculations are used to investigate the energetics of an As overlayer adsorbed on a stepped Si(110) surface. We show that the growth of As directly on top of the Si surface produces a metastable structure, while the replacement of the original top Si layer by As leads to a lowerenergy configuration. In the latter case, the rearrangement of the surface is driven by the relaxation of stress by surface steps. This result explains the sublatticeorientation dilemma in GaAsonSi heteroepitaxy.

[131]

O. L. Alerhand, J. Wang, and J. D. Joannopoulos, “Growth of As overlayers on
vicinal Si(100) surfaces,” Journal of Vacuum Science and
Technology B, vol. 9, pp. 2423–2426, July 1991.
[ bib 
DOI ]
Firstprinciples totalenergy calculations are used to study the structure of As overlayers deposited on a stepped Si(100) surface. It is predicted that deposition of As at low substrate temperatures allows the As to grow directly on top of the Si surface, while growth at high temperatures results in a rearrangement of the surface as if the As replaced the original top Si layer. This result explains the sublattice orientation dilemma in GaAsonSi epitaxy.

[130]

M. Needels, J. D. Joannopoulos, Y. BarYam, and S. T. Pantelides, “Oxygen
complexes in silicon,” Physical Review B, vol. 43, pp. 4208–4215,
February 1991.
[ bib 
http ]
Ab initio totalenergy calculations are performed to investigate the initial stages of oxygen aggregation in silicon. Since the volume per SiO_{2} unit in silicon dioxide is approximately twice the volume per silicon atom in crystalline silicon, it is generally believed that oxygen clustering in silicon will require the creation of selfinterstitials. In a similar vein, it is generally believed that neighboring interstitial oxygen configurations are unbound in a weakly distorted silicon lattice. In this work, several interesting phenomena that are associated with aggregation and do not require the creation of silicon selfinterstitials are predicted. These predictions are (1) oxygen atoms can cluster with large binding energies of about 1 eV; (2) this clustering can only occur for very specific geometries; and (3) the geometries are chainlike arrangements of oxygen bridging configurations. Indeed, it is the quasionedimensional nature of the proposed oxygen clusters that allows the complexes to form without the accompanying large lattice stress that can lead to the ejection of silicon interstitials. The thermal treatment necessary for aggregation is identified, and predictions of the observable effects are made.

[129]

E. Tarnow, P. Dallot, P. D. Bristowe, J. D. Joannopoulos, G. P. Francis, and
M. C. Payne, “Structural complexity in grain boundaries with covalent
bonding,” Physical Review B, vol. 42, pp. 3644–3657, August 1990.
[ bib 
http ]
The structural properties of two shortperiod twist boundaries in germanium are explored using a stateoftheart totalenergy calculation. The structures of these boundaries are found to be very complex, with boundary bonds that are distorted and weak. These systems are found to exhibit a large degeneracy in the number of local energy minima. Thus the boundaries have difficulty in arriving at a locally ordered state. The situation may be unique to the semiconducting twist grain boundaries due to the inherent frustration present between the tendency to form directional bonds and the imposed twist geometry which makes the bond formation improbable. This study focuses on the energy, coordination, volume change, and electronic states characteristic of the local minima. A trend towards dimerization is found especially in the highestangle twist boundary.

[128]

O. L. Alerhand, A. N. Berker, J. D. Joannopoulos, D. Vanderbilt, R. J. Hamers,
and J. E. Demuth, “Finitetemperature phase diagram of vicinal Si(100)
surfaces,” Physical Review Letters, vol. 64, pp. 2406–2409, May 1990.
[ bib 
http ]
The phase diagram of vicinal Si(100) as a function of misorientation angle and temperature is calculated. Contrary to previous suggestions that only doublelayer steps should appear on the equilibrium surface, it is predicted that the singlelayer stepped surface is at equilibrium for small misorientation angles. This structure is stabilized by strain relaxation and by the thermal roughening of the steps. For annealed surfaces the critical angle at which the transition between the single and doublelayer stepped surface occurs is calculated to be θ_{c} ≈2^{o}.

[127]

E. Kaxiras, O. L. Alerhand, J. D. Joannopoulos, and G. W. Turner,
“Thermodynamic and kinetic aspects of GaAs growth on Si(100),”
Superlattices and Microstructures, vol. 8, no. 2, pp. 229–232, 1990.
[ bib 
DOI ]
A microscopic model of GaAs growth on Si(100) is discussed, which takes into account the role of kinetics and the morphology of the substrate. The model predicts that growth at the initial stages is dominated by GaAs islands nucleated at steps of the substrate, which begin forming upon deposition concurrently with layered growth on the terraces. This mode of growth does not fall within any of the traditional thermodynamic models of heteroepitaxial growth, and allows for different growth channels depending on deposition conditions. The predicted shape and structure of the GaAs seeds nucleated at Si steps are in agreement with recent experimental observations.

[126]

A. M. Rappe, K. M. Rabe, E. Kaxiras, and J. D. Joannopoulos, “Optimized
pseudopotentials,” Physical Review B, vol. 41, pp. 1227–1230, January
1990.
[ bib 
http ]
A planewave basis has great advantages for many calculations in the physics solids. To apply this basis to a wider class of materials, the atomic characteristic of a pseudopotential is identified which leads to rapid convergence in the solid, and a new method for generating pseudopotentials optimized according to this criterion is shown. As a test case, an ab initio planewave basis determination of the structural properties of fcc copper is performed. The results indicate that these optimized pseudopotentials will facilitate study of transition metals and firstrow nonmetals.

[125]

E. Kaxiras and J. D. Joannopoulos, “On the possibility of twodimensional
growth of GaAs on atomically flat Si(100) surfaces,” Surface
Science, vol. 224, pp. 515–524, December 1989.
[ bib 
DOI ]
The possibility of growing GaAs on atomically flat Si(100) surfaces is investigated at monolayer and bilayer coverages. Based on abinitio totalenergy calculations at zerotemperature we compare the stability of separate domains of Ga or As versus mixed monolayers, the stability of pure GaAs bilayers versus mixed bilayers and the formation of GaAs bilayer islands versus wetting of the surface. The results predict that twodimensional growth of bulk GaAs on atomically flat regions (terraces) of Si(100) is severely inhibited at the initial stages, due to chemical and rehybridization reactions of the Ga and As atoms on the Si surface.

[124]

E. L. Shirley, D. C. Allan, R. M. Martin, and J. D. Joannopoulos, “Extended
normconserving pseudopotentials,” Physical Review B, vol. 40,
pp. 3652–3660, August 1989.
[ bib 
http ]
Atomic pseudopotentials simplify electronic calculations by eliminating atomic core levels and the potentials that bind them. Outside some core radius, normconserving pseudopotentials produce the same scattering properties (radial logarithmic derivatives of wave functions for angular momenta of interest) as fullatomic potentials to zeroth and first order in energy about valencelevel eigenvalues. We extend the correctness of the radial logarithmic derivative one order further in energy and present analytic and numerical results showing that this extension improves higherorder energy derivatives as well. We also show how our change improves predictions of excited singleparticle eigenvalues in a wide variety of atoms, as well as highenergy scattering properties, with effects visible in a bandstructure calculation. Our potentials converge nearly as quickly in reciprocal space as the Vanderbilt (modified HamannSchlüterChiang) potentials from which they are derived, and are easily generated.

[123]

O. L. Alerhand, E. Kaxiras, J. D. Joannopoulos, and G. W. Turner, “Model of
epitaxial growth of GaAs on Si(100): Nucleation at surface steps,”
Journal of Vacuum Science and Technology B, vol. 7, pp. 695–699, July 1989.
[ bib 
DOI ]
A microscopic model of epitaxial growth of GaAs on Si(100) is proposed, which explains how doublelayer steps on the Si(100) surface act as nucleation sites in the initial stages of growth. On the flat terraces of Si(100), there is a strong tendency towards the formation of mixed layers of Ga and As, which inhibit growth of zincblende GaAs. The bonding topology of the surface steps supresses this mixing, and drives the growth of ideally bonded GaAs in a threedimensional mode with islands forming along the steps edges. Totalenergy calculations indicate that the proposed model for nucleation of GaAs at doublelayer steps on the surface is energetically stable.

[122]

D. Vanderbilt, O. L. Alerhand, R. D. Meade, and J. D. Joannopoulos, “Elastic
stress domains of the Si(100) surface,” Journal of Vacuum Science and
Technology B, vol. 7, pp. 1013–1016, July 1989.
[ bib 
DOI ]
It is proposed that surfaces of crystals that reconstruct with broken orientational symmetry and exhibit an anisotropic stress tensor are unstable to the formation of elastic stress domains. The ground state of such a surface is not uniform, but corresponds to a mosaic pattern of the different domains. This result is applied together with microscopic calculations of surface stress to study the Si(100) surface. A structural transition from singlelayer to doublelayer steps for vicinal Si(100) surfaces is also studied.

[121]

O. L. Alerhand, J. D. Joannopoulos, and E. J. Mele, “Thermal amplitudes of
surface atoms on Si(111) 2×1 and Si(001) 2×1,”
Physical Review B, vol. 39, pp. 12622–12629, June 1989.
[ bib 
http ]
Atomic displacementdisplacement correlation functions for the surface atoms of the Si(111) 2×1 and Si(001) 2×1 surfaces are calculated using phonon energies and eigenvectors obtained from a tightbinding theory of the lattice dynamics of Si. The temperature dependence and the possible anisotropies of the amplitudes of vibration of the surface atoms are investigated. For the πbonded chain model of Si(111) 2×1 it is found that the surface atoms have larger vibrational amplitudes perpendicular to the surface than parallel to it, and this anisotropy (1.8 in the meansquared amplitudes at 270 K) increases rapidly with increasing temperature. This is attributed to the existence of a smallwavelength acoustic phonon with an unusually low energy. For the surface atoms on Si(001) 2×1 the anisotropy between perpendicular and parallel vibrations is not as marked. The interatomic vibrational correlations between surface atoms reveal the strength of the new bonds that are formed in the reconstruction of these surfaces.

[120]

E. Kaxiras, O. L. Alerhand, J. D. Joannopoulos, and G. W. Turner, “Microscopic
model of heteroepitaxy of GaAs on Si(100),” Physical Review
Letters, vol. 62, pp. 2484–2486, May 1989.
[ bib 
http ]
A new microscopic model of heteroepitaxial growth is introduced using GaAs on Si(100) as a prototype. This model takes into account specific features of surface topology, predicts that in the prototype system conventional twodimensional epitaxy should be inhibited, and provides a fundamental explanation for threedimensional nature of the initial stages of growth. The ingredients of the model, which are supported by totalenergy calculations, include new structural geometries for each state of growth and the chemical and rehybridization reactions linking these stages.

[119]

M. C. Payne, N. Roberts, R. J. Needs, M. Needels, and J. D. Joannopoulos,
“Total energy and stress of metal and semiconductor surfaces,” Surface
Science, vol. 211–212, pp. 1–20, April 1989.
[ bib 
DOI ]
Energies and stresses of reconstructed surfaces of metals and semiconductors are calculated using pseudopotential methods. Surface stresses of aluminium, iridium, platinum, gold and silicon surfaces are calculated and the implications for reconstruction in these systems are discussed. The energies of dimer reconstructions on the (001) surfaces of silicon and germanium have been calculated and the stability of buckled dimers is investigated. The mechanism responsible for stabilising the Takayanagi reconstruction on the (111) surfaces of silicon and strained germanium is deduced from total energy calculations for substructures of the reconstructed surface.

[118]

T. A. Arias and J. D. Joannopoulos, “Reexamination of magnetic effects in the
Bose gas,” Physical Review B, vol. 39, pp. 4071–4078, March 1989.
[ bib 
http ]
The breakdown of the MeissnerOchsenfeld effect in the threedimensional Bose gas as the applied field passes through its critical value is an entropydriven weakly firstorder transition, rather than the secondorder transition usually ascribed to the system. The transition is second order at the usual Bose condensation temperature T_{c} as well as at T=0, with a line of firstorder transitions connecting these critical points. The firstorder transitions make the Bose gas resemble familiar superconductors, and a LandauGinzburg analysis indicates that the Bose gas is always a typeI superconductor.

[117]

G. GomezSantos, J. D. Joannopoulos, and J. W. Negele, “Monte Carlo study
of the quantum spin1/2 Heisenberg antiferromagnet on the square lattice,”
Physical Review B, vol. 39, pp. 4435–4443, March 1989.
[ bib 
http ]
A new Monte Carlo sampling technique is used to study the spin1/2 Heisenberg antiferromagnet on square lattices of up to 256 spins. The energy, specific heat, uniform and staggered susceptibilities, and correlation function are calculated. The correlation length as a function of temperature is deduced from correlation functions and is shown to be consistent with a quantumrenormalized classical approximation. Using the coupling constant provided by Raman scattering experiments, good agreement is found between the calculated and experimental correlation lengths in La_{2}CuO_{4}.

[116]

E. Tarnow, J. D. Joannopoulos, and M. C. Payne, “Antisites, antistructures,
and bondswitching reactions in layered chalcogenides,” Physical
Review B, vol. 39, pp. 6017–6024, March 1989.
[ bib 
http ]
State of the art ab initio totalenergy calculations are used to investigate the properties of a large number of antisite and antistructure defects in cAs_{2}Se_{3}. Calculations of their formation energies are made, and an examination of their electronic states and relaxed geometries is performed. Surprisingly it is found that a select set of the antistructures undergoes bondswitching reactions that give rise to a new peculiar class of defects. These bondswitched antistructure defects are found to have lower formation energies than any of the antistructures. One of these is of particular interest as it forms a bridging bond between the layers of cAs_{2}Se_{3}. This crosslinking defect (CLD) is examined in more detail. It is found that the associated bondswitching reaction proceeds with small or no barrier for most charge states. This is surprising as the atomic movements associated with the formation of the CLD are quite large.

[115]

Y. BarYam, S. T. Pantelides, and J. D. Joannopoulos, “Ab initio
pseudopotential solidstate calculations of highly electronegative firstrow
elements,” Physical Review B, vol. 39, pp. 3396–3399, February 1989.
[ bib 
http ]
Densityfunctional pseudopotential totalenergy calculations have been a powerful tool in studies of the electronic and structural properties of semiconductors and simple metals. The inclusion of highly electronegative firstrow elements such as oxygen and fluorine has not, in general, been tractable. In this paper we address the inherent difficulties and demonstrate that they can be overcome. Focusing on oxygensilicon systems the precision of our method is demonstrated particularly through the study of angular stability of SiOSi bridge bonds in silica. The results predict bending to an equilibrium angle of 140^{o} ±5^{o}, as observed, with an energy gain of only ∼0.15 eV.

[114]

E. Tarnow, M. C. Payne, and J. D. Joannopoulos, “Pairing of electrons by a
point defect in cAs_{2}Se_{3},” Physical Review Letters,
vol. 61, pp. 1772–1775, October 1988.
[ bib 
http ]
By use of ab initio densityfunctional totalenergy calculations a point defect with a negative Hubbard U is identified, for the first time, in a chalcogenide system. It is found that in cAs_{2}Se_{3} two noninteracting neutral Se antisite defects are unstable toward the formation of a pair of noninteracting oppositely charged Se antisites. The correlation energy gained is 0.3 eV per electron pair.

[113]

O. L. Alerhand, D. Vanderbilt, R. D. Meade, and J. D. Joannopoulos,
“Spontaneous formation of stress domains on crystal surfaces,”
Physical Review Letters, vol. 61, pp. 1973–1976, October 1988.
[ bib 
http ]
It is proposed that surfaces of crystals which reconstruct with broken orientational symmetry and exhibit an anisotropic intrinsic stress tensor are unstable to the formation of elasticstress domains. Thus the ground state of such a surface is not uniform, contrary to previous expectations. Evidence of this for the Si(001) surface is discussed.

[112]

M. Needels, M. C. Payne, and J. D. Joannopoulos, “Highorder reconstructions
of the Ge(100) surface,” Physical Review B, vol. 38, pp. 5543–5546,
September 1988.
[ bib 
http ]
We have performed ab initio densityfunctional calculations of total energies of the Ge(100) surface to compare the ground states of (2×1), c(4×2), p(2×2), and p(4×1) symmetry dimer reconstructions. We find that p(2×2) and c(4×2) are the lowestenergy reconstructions and are nearly degenerate in energy. From these ab initio total energies, we compute the coupling constants for a model Hamiltonian for the surface and predict the phasetransition temperature from either an ordered c(4×2) or p(2×2) state to a disordered buckled b(2×1) state.

[111]

X. Wang, Y. BarYam, D. Adler, and J. D. Joannopoulos, “dc conductivity and
the MeyerNeldel rule in aSi:H,” Physical Review B,
vol. 38, pp. 1601–1604, July 1988.
[ bib 
http ]
Disorder in amorphous semiconductors results in unusual properties of dc conductivity. We demonstrate a quantitative description of the temperature dependence of conductivity in aSi:H. The universal activation energy dependence of the conductivity prefactor (the MeyerNeldel rule) is reproduced. Excellent agreement with experimental results is obtained by describing disorder and defects using the general thermodynamic ensemble theory for the structure of disordered systems.

[110]

M. C. Payne, M. Needels, and J. D. Joannopoulos, “Symmetry breaking in the
moleculardynamics method for ab initio totalenergy calculations,”
Physical Review B, vol. 37, pp. 8138–8144, May 1988.
[ bib 
http ]
An analysis of the symmetry of the electron wave functions as they evolve under the moleculardynamics equation of motion is presented. It is found that symmetry in the initial conditions, corresponding to wave functions of two or more bands being partner functions, can prevent wave functions from converging to eigenfunctions of the Hamiltonian. This artificial symmetry is broken by the GramSchmidt orthogonalization procedure so any convenient initial conditions will lead to convergence to eigenstates of the Hamiltonian.

[109]

E. Kaxiras and J. D. Joannopoulos, “Hydrogenation of semiconductor surfaces:
Si and ge (111),” Physical Review B, vol. 37, pp. 8842–8848, May
1988.
[ bib 
http ]
The relaxations of hydrogenated Si and Ge (111) surfaces are determined using ab initio selfconsistent calculations in a slab configuration. The SiH and GeH bonds are found to be considerably larger than the sum of covalent radii. The substrate relaxations are small and their physical origin can be explained in terms of electronic charge transfer which eliminates the surface dipole moment. The calculated frequencies of the hydrogen vibrational modes are in excellent agreement with experiment. A surfaceatom vibrational mode is compared to similar modes in the amorphous hydrogenated materials. The comparison predicts that internal surfaces (microvoids) in the amorphous network are locally much softer than the corresponding crystalline surface configuration.

[108]

Y. BarYam and J. D. Joannopoulos, “Theories of defects in amorphous
semiconductors,” Journal of NonCrystalline Solids, vol. 97–98,
pp. 467–474, December 1987.
[ bib 
DOI ]
The existence of defects in amorphous semiconductors is itself an problem of fundamental interest. Conventional approaches accept their existence only phenomenologically. We described a new approach to defining and understanding defects. The existence of defects is a natural outgrowth of our thermodynamical ensemble theory of electronic states in disordered systems. Specific properties are also predicted through properties of thermodynamic ensembles and the relationship between defect electronic properties and structural energies. Thus we obtain directly electronic properties without a need for detailed microscopic information.

[107]

G. GomezSantos and J. D. Joannopoulos, “Application of spinwave theory to
the ground state of XY quantum hamiltonians,” Physical Review B,
vol. 36, pp. 8707–8711, December 1987.
[ bib 
http ]
Spinwave theory is successfully applied to study the ground state of the quantum XY Hamiltonian. It is found that a judicious choice of the quantized spin axis removes difficulties of previous applications. Results for the simplest one, two, and threedimensional lattices are shown to compare favorably with either exact or other approximate calculations.

[106]

K. M. Rabe and J. D. Joannopoulos, “Theory of the structural phase transition
of GeTe,” Physical Review B, vol. 36, pp. 6631–6639, October 1987.
[ bib 
http ]
A completely ab initio theoretical investigation of the rocksaltrhombohedral structural phase transition of GeTe is described. Starting from an anharmonic lattice Hamiltonian, a model Hamiltonian that includes coupling of the order parameter to longwavelength strain is constructed. The parameters appearing in the model are calculated using the selfconsistent ab initio pseudopotential totalenergy method. The phase transition in the model system is studied through a momentumspace renormalizationgrouptheory approach, leading to the prediction of a fluctuation driven firstorder transition at 657 ±100 K. The strain coupling is found to be crucial in determining the firstorder character of the transition. A discussion of approximations made in this approach and considerations relevant to its application to structural transitions in other systems is included.

[105]

K. M. Rabe and J. D. Joannopoulos, “Ab initio determination of a structural
phase transition temperature,” Physical Review Letters, vol. 59,
pp. 570–573, August 1987.
[ bib 
http ]
The temperature of the structural phase transition in GeTe is calculated complete ab initio from a model latticedynamical Hamiltonian that is constructed from microscopic quantummechanical totalenergy calculations. The phase transition in the model system is studied through a renormalizationgrouptheory approach, leading to the prediction of a fluctuationdriven firstorder transition at 657 ±100 K.

[104]

K. M. Rabe and J. D. Joannopoulos, “Structural properties of GeTe at
T=0,” Physical Review B, vol. 36, pp. 3319–3324, August 1987.
[ bib 
http ]
The equilibrium lattice parameters, bulk modulus, shear elastic constant C_{44}, and cohesive energy of GeTe are calculated with use of the ab initio scalar relativistic pseudopotential in the localdensity approximation. The convergence of the structural properties in basisset size and Brillouinzone averaging is discussed. For the rocksalt structure, valence charge densities and the band structure are presented. For the rhombohedral structure, the band structure is presented and the shear deformation potential is calculated. Good agreement of calculated quantities with available experimental results is obtained.

[103]

E. Kaxiras, Y. BarYam, J. D. Joannopoulos, and K. C. Pandey, “Ab initio
theory of polar semiconductor surfaces. i. methodology and the (2×2)
reconstructions of GaAs(111),” Physical Review B, vol. 35,
pp. 9625–9635, June 1987.
[ bib 
http ]
A methodology is developed for the theoretical study of the polar surfaces of compound semiconductors. It is based on the calculation of the total energy in the context of densityfunctional theory in the pseudopotential approximation. The method is used to investigate the (2×2) reconstructions of GaAs(111). Emphasis is given to the relative chemical potential, which plays a crucial role in determining the lowestenergy geometry for surfaces with different stoichiometries. The totalenergy versus chemicalpotential curves indicate that there are at least two stable reconstructions. We predict one to be an Astriangle geometry and the other the Ga vacancy.

[102]

E. Kaxiras, Y. BarYam, J. D. Joannopoulos, and K. C. Pandey, “Ab initio
theory of polar semiconductor surfaces. ii. (2×2) reconstructions and
related phase transitions of GaAs(111),” Physical
Review B, vol. 35, pp. 9636–9643, June 1987.
[ bib 
http ]
The (2×2) reconstructions of GaAs(111) are studied with use of a theoretical approach based on the calculation of the total energy in the context of densityfunctional theory and the pseudopotential approximation. New models are proposed for the Asrich and Garich reconstructions. The relative chemical potential plays a crucial role in determining the lowestenergy configuration. The totalenergy versus chemicalpotential curves indicate the possibility of phase transitions between different configurations. One such transition concerning the experimentally observed (sqrt19×√(19)) reconstruction can be explained as an intermediate phase between the proposed lowenergy (2×2) reconstructions.

[101]

M. Needels, M. C. Payne, and J. D. Joannopoulos, “Ab initio molecular dynamics
on the Ge(100) surface,” Physical Review Letters, vol. 58,
pp. 1765–1768, April 1987.
[ bib 
http ]
An ab initio totalenergy approach to molecular dynamics and simulated quenching is applied for the first time and used to study the structure of the Ge(100) surface. The geometry of the lowestenergy c(4×2)symmetry dimer model is predicted. A soft energy surface for displacement of dimers in the [110] direction is discovered which could lead to a new type of symmetry breaking.

[100]

M. C. Payne, P. D. Bristowe, and J. D. Joannopoulos, “Ab initio determination
of the structure of a grain boundary by simulated quenching,” Physical
Review Letters, vol. 58, pp. 1348–1351, March 1987.
[ bib 
http ]
Results of the first completely ab initio investigation of the microscopic structure of a grain boundary in a semiconductor are presented. By use of the moleculardynamics–simulated annealing method for performing totalenergy calculations within the localdensity–functional and pseudopotential approximation, the Σ=5 (001) twist boundary in germanium is studied. A number of rotationandtranslation states are investigated leading to a prediction for the structure of this geometry. Evidence for the possible presence of novel defects and glasslike tunneling mode states at grain boundaries is presented.

[99]

E. Tarnow, A. Antonelli, and J. D. Joannopoulos, “Crystalline
As_{2}Se_{3}: Optical properties,” Physical Review B, vol. 34,
pp. 8718–8727, December 1986.
[ bib 
http ]
Realistic ab initio totalenergy calculations are performed to investigate the optical properties of crystalline As_{2}Se_{3}. The complete dielectric tensor is calculated using interband transitions. This includes the offdiagonal element, which has not previously been considered in the literature. The presence of the offdiagonal element leads to optical axes which are not aligned with the crystal axes and whose directions change with frequency. Comparisons with experimental results on diagonal elements are made and a prediction of the offdiagonal reflectivity is given. The origin of the offdiagonal element is investigated, and the element is found to arise solely from interlayer interactions. Accordingly, experimental measurements of the offdiagonal element may reveal unique and interesting features of the environment in between the layers.

[98]

E. Tarnow, A. Antonelli, and J. D. Joannopoulos, “Crystalline
As_{2}Se_{3}: Electronic and geometric structure,” Physical
Review B, vol. 34, pp. 4059–4073, September 1986.
[ bib 
http ]
Realistic ab initio totalenergy calculations are performed to investigate the electronic and geometric structure of crystalline As_{2}Se_{3}. Results include the following: total energies for various distortions, the equilibrium geometric structure, intralayer and interlayer cohesive energies, charge densities, the density of states, the band structure, rigidlayer phonon frequencies, and effective masses. Specific attention is focused on studying the nature of bonding within and between layers, as well as elucidating the nature of the electron and hole wave functions in the vicinity of the fundamental gap. In particular it is found that the interactions between the layers are crucial in determining the properties of the wave functions at the band edges. Moreover, the electron and hole masses are predicted to exhibit a large and unusual anisotropy.

[97]

E. Kaxiras, Y. BarYam, J. D. Joannopoulos, and K. C. Pandey, “Variable
stoichiometry surface reconstructions: New models for
GaAs(111)(2×2) and
(√(19)×√(19)),” Physical Review Letters, vol. 57,
pp. 106–109, July 1986.
[ bib 
http ]
The (111) surface of GaAs exhibits three stable reconstructions. Two are (2×2), As stabilized and Ga stabilized respectively, and the third is (√(19)×√(19)). Transitions between these structures are obtained by variation of the experimental conditions. We propose new models for all of the above reconstructions, based on ab initio totalenergy calculations and experimental information regarding surface composition.

[96]

Y. BarYam, D. Adler, and J. D. Joannopoulos, “Structure and electronic states
in disordered systems,” Physical Review Letters, vol. 57,
pp. 467–470, July 1986.
[ bib 
http ]
We adopt the view that the structure of disordered systems is itself determined by the formation energy of structural deviations from an ideally bonded network. By developing an equilibrium statistical mechanical model for disorder we predict properties of electronic band tails, defects, defect densities of states, and impurity doping.

[95]

E. Kaxiras, K. C. Pandey, Y. BarYam, and J. D. Joannopoulos, “Role of
chemical potentials in surface reconstruction: A new model and phase
transition of GaAs(111)2 ×2,” Physical Review Letters,
vol. 56, pp. 2819–2822, June 1986.
[ bib 
http ]
The role of chemical potentials in surface reconstructions is examined and shown to be crucial for binary semiconductor srufaces such as GaAs(111)2 ×2. We predict that under Asrich conditions a new model, the As triangle, is the lowestenergy geometry, whereas the Gavacancy model is appropriate for Garich conditions. A change in the relative chemical potential of Ga and As should produce a phase transition between the two structures.

[94]

Y. BarYam and J. D. Joannopoulos, “Dangling bond in aSi:ZZH,”
Physical Review Letters, vol. 56, pp. 2203–2206, May 1986.
[ bib 
http ]
The configurationcoordinate diagram for a model danglingbond geometry is obtained by ab initio totalenergy calculations. The results yield equilibrium geometries for different charge states, thermodynamic and optical transition energies, large Stokes shifts (0.50.6 eV), and a negative effective correlation energy (0.2 ±0.2 eV). Implications of these results for the current experimental and theoretical understanding are discussed.

[93]

E. Kaxiras, Y. BarYam, J. D. Joannopoulos, and K. C. Pandev, “(2×2)
reconstructions of the {111} polar surfaces of GaAs,” Physical
Review B, vol. 33, pp. 4406–4409, March 1986.
[ bib 
http ]
Ab initio totalenergy calculations were used to examine (2 ×2) reconstruction models for the (111) and (111) surfaces of GaAs. For the (111) surface the lowestenergy Gavacancy geometry is determined; several mechanisms for Gavacancy formation are examined and other reconstructions are discussed. For the (111) surface it is shown that the Asvacancy model is unlikely and other geometries are considered.

[92]

A. Antonelli, E. Tarnow, and J. D. Joannopoulos, “New insight into the
electronic structure of a As_{2}Se_{3},” Physical Review B,
vol. 33, pp. 2968–2971, February 1986.
[ bib 
http ]
Results of a realistic ab initio investigation of the geometric structure and electronic properties of the compound chalcogenide prototype As_{2}Se_{3} are presented. Structural parameters are accurate to within a few percent of their experimental values. The nature of bonding within and between layers is revealed and the character of states near the band edges is obtained, including predictions for the electron and hole effective masses.

[91]

D. H. Lee, J. D. Joannopoulos, J. W. Negele, and D. P. Landau, “Symmetry
analysis and Monte Carlo study of a frustrated antiferromagnetic planar
(xy) model in two dimensions,” Physical Review B, vol. 33,
pp. 450–475, January 1986.
[ bib 
http ]
The antiferromagnetic planar (XY) model on a triangular lattice is investigated using grouptheoretical symmetry arguments combined with extensive Monte Carlo simulations and a detailed finitesizescaling analysis. This approach allows for a systematic exploration of all possible symmetrybreaking transitions and their associated critical behavior. The entire magneticfield–versus–temperature phase diagram is deduced. A rich class of possible new critical phenomena is obtained, including the introduction of a new multicritical point describing the confluence of the Ising and KosterlitzThouless universality classes. The existence of the critical point is associated with a domainwallinduced vortexantivortex–unbinding transition.

[90]

E. Tarnow, A. Antonelli, and J. D. Joannopoulos, “Ground state properties of
crystalline As_{2}Se_{3},” Journal of NonCrystalline Solids,
vol. 77–78, pp. 95–98, December 1985.
[ bib 
DOI ]
An abinitio pseudopotential calculation in the local density approximation is performed on crystalline As_{2}Se_{3}. Total energies, charge densities, and density of states are presented and compared with experiment.

[89]

Y. BarYam and J. D. Joannopoulos, “Correlation energy of deep level traps in
aSi:H,” Journal of NonCrystalline Solids, vol. 77–78,
pp. 99–102, December 1985.
[ bib 
DOI ]
We report the first realistic calculation of the effective electronic correlation energy of the dangling bond in amorphous hydrogenated silicon. Total energies obtained using abinitio pseudopotential density functional theory yield a full configuration coordinate diagram. When host distortions of the amorphous material are included by use of a simple model, both the effective electronic correlation energy and the position of the electronic states in the gap are affected. We obtain a distribution of effective electronic correlation energies, and a distortion of electronic transition energies in the gap.

[88]

K. M. Rabe and J. D. Joannopoulos, “Ab initio relativistic pseudopotential
study of the zerotemperature structural properties of SnTe and PbTe,”
Physical Review B, vol. 32, pp. 2302–2314, August 1985.
[ bib 
http ]
The equilibrium lattice parameters, bulk moduli, cohesive energies, k=0 TOphonon frequencies and elastic constant C_{44} of SnTe and PbTe are calculated completely from first principles with use of the localdensityfunctional pseudopotential totalenergy method including relativistic effects. Good agreement with experiment is obtained. The approximation of neglecting spinorbit coupling is found to be adequate for most purposes. Band structures and valence charge densities are presented. The latter are seen to differ significantly from previous empiricalpseudopotentialmethod calculations. The form of ω_{}TO(P) in PbTe is found to be linear for small pressures P. Some possibilities for further applications of this method to these materials are discussed.

[87]

D. H. Lee, J. D. Joannopoulos, and J. W. Negele, “Monte Carlo solution of
antiferromagnetic quantum Heisenberg spin systems,” Physical
Review B, vol. 30, pp. 1599–1602, August 1984.
[ bib 
http ]
A Monte Carlo method is introduced that overcomes the problem of alternating signs in Handscomb's method of simulating antiferromagnetic quantum Heisenberg systems. The scheme is applied to both bipartite and frustrated lattices. Results of internal energy, specific heat, and uniform and staggered susceptibilities are presented suggesting that quantum antiferromagnets may now be studied as extensively as classical spin systems using conventional Monte Carlo techniques.

[86]

Y. BarYam and J. D. Joannopoulos, “Electronic structure and totalenergy
migration barriers of silicon selfinterstitials,” Physical Review B,
vol. 30, pp. 1844–1852, August 1984.
[ bib 
http ]
Pseudopotential densityfunctional calculations have been performed on silicon selfinterstitial supercell model geometries to yield extensive information on electronic states. We present band structures, charge densities, and densities of states to identify and characterize electronic states associated with silicon selfinterstitials in the geometries studied. Total energies obtained yield migration barriers for both Si^{(0)} and Si^{(2+)} interstitials. We also present the results of preliminary totalenergy relaxation studies and show their effects on electronic states and totalenergy calculations, demonstrating the importance of relaxation in determining migration barriers. Electronassisted migration is shown to occur, thus solving the mystery of the disappearing selfinterstitial and providing an initial understanding of migration in lowtemperature irradiated silicon.

[85]

Y. BarYam and J. D. Joannopoulos, “Silicon selfinterstitial migration:
Multiple paths and charge states,” Physical Review B, vol. 30,
pp. 2216–2218, August 1984.
[ bib 
http ]
Total energy calculations performed to study the migration of silicon selfinterstitials reveal a great complexity of migration paths. Si^{(++)} and Si^{(0)} each migrate along more than one path and different paths from each other. Some paths involve interchange with bulk atoms. Electronassisted transport occurs for the Si^{(++)} stable tetrahedral site in all directions. Si^{(0)} has several almostdegenerate lowestenergy configurations. The lowest is the exchange configuration which also has the possibility of being negative (Si^{()}).

[84]

D. H. Lee, R. G. Caflisch, J. D. Joannopoulos, and F. Y. Wu,
“Antiferromagnetic classical XY model: A meanfield analysis,”
Physical Review B, vol. 29, pp. 2680–2684, March 1984.
[ bib 
http ]
The antiferromagnetic classical XY (planarrotator) model is analyzed under the meanfield approximation. Phase diagrams are obtained and found to be strongly dependent on the underlying lattice geometry. For bipartite lattices, there exists a secondorder transition across a unique phase boundary. For tripartite lattices, there exist two phase boundaries, separating an intermediate “nonhelical” phase from a lowtemperature “helical” phase and the hightemperature paramagnetic phase. The two phase boundaries merge into a single critical point at finite temperature and zero magnetic field.

[83]

Y. BarYam and J. D. Joannopoulos, “Barrier to migration of the silicon
selfinterstitial,” Physical Review Letters, vol. 52, pp. 1129–1132,
March 1984.
[ bib 
http ]
The first totalenergy calculations of barriers to interstitial migration have been used to study silicon selfinterstitial migration. Migration occurs through the lowelectrondensity path. Relaxation was found to be important in determining the barrier for both Si^{(0)} and Si^{(++)}. Electronassisted migration has been demonstrated. Si^{(++)} was found to have lower energy at the tetrahedral site while Si^{(0)} has lower energy at the hexagonal site.

[82]

D. H. Lee and J. D. Joannopoulos, “Magnetic properties of the Si(111)
unreconstructed surface,” Physical Review B, vol. 29, pp. 1472–1473,
February 1984.
[ bib 
http ]
The solution of the twodimensional Hubbard Hamiltonian for describing the magnetic properties of the Si(111) unreconstructed surface is discussed.

[81]

D. H. Lee, J. D. Joannopoulos, J. W. Negele, and D. P. Landau,
“Discretesymmetry breaking and novel critical phenomena in an
antiferromagnetic planar (XY) model in two dimensions,” Physical
Review Letters, vol. 42, pp. 433–436, February 1984.
[ bib 
http ]
LandauGinzburgWilson symmetry analyses and Monte Carlo calculations for the classical antiferromagnetic planar (XY) model on a triangular lattice reveal a wealth of interesting critical phenomena. From this simple model arise a zerofield transition to a state of longrange order, a new mechanism for spin disordering, and a critical point associated with a possible new universality class.

[80]

D. Vanderbilt and J. D. Joannopoulos, “Total energies of structural defects in
glassy Se,” Journal of NonCrystalline Solids, vol. 59–60,
pp. 937–944, December 1983.
[ bib 
DOI ]
The effective Hubbard U is calculated for the interconversion of 1fold and 3fold bonding coordination defects in glassy Se. This is accomplished by applying local density total energy calculations directly to charged defects in a superlattice configuration. It is found that the defect remains 1fold coordinated in the D^{} and D^{0} charge states, but spontaneously forms a 3fold center in the D^{+} charge state. The structural relaxation energy involved in the bond switching gives rise to a sizable negative contribution to U, but a still larger Coulomb repulsion gives rise to an overall positive U. This result is not, however, inconsistent with a negative U in the compound chalcogenide glasses.

[79]

J. Ihm, D. H. Lee, J. D. Joannopoulos, and J. J. Xiong, “Structural phase
diagrams for the surface of a solid: A totalenergy, renormalizationgroup
approach,” Physical Review Letters, vol. 51, pp. 1872–1875, November
1983.
[ bib 
http ]
Totalenergy calculations based on microscopic electronic structure are combined with positionspace renormalizationgroup calculations to predict the structural phase transitions of the Si(100) surface as a function of temperature. It is found that two distinct families of reconstructed geometries can exist on the surface, with independent phase transitions occurring within each. Two critical temperatures representing orderdisorder transitions are calculated.

[78]

J. Ihm, D. H. Lee, J. D. Joannopoulos, and A. N. Berker, “Study of high order
reconstructions of the Si(100) surface,” Journal of Vacuum Science
and Technology B, vol. 1, pp. 705–708, July 1983.
[ bib 
DOI ]
The structure of the reconstructed Si(100) surface is studied using the tightbinding energy minimization method combined with a renormalizationgroup calculation. (2×1), c(2×2), p(2×2), (4×1), c(4×2), and p(4×2) structures are studied and compared. They are classified into two groups which are separated by a large activation barrier. In one group, (2×1), p(2×2), and c(4×2) structures are almost degenerate in energy, which can result in diffuse (2×1) LEED patterns. In the other group, a secondorder phase transition can occur from the c(2×2) to the disordered structure at ∼800 K. Domains of different structures may coexist on the actual surface.

[77]

D. Vanderbilt and J. D. Joannopoulos, “Total energies in Se. I. the
trigonal crystal,” Physical Review B, vol. 27, pp. 6296–6301, May
1983.
[ bib 
http ]
The equilibrium crystal structure (lattice constants and chain radius) of trigonal selenium, a molecular crystal, are determined by minimizing the total energy, as calculated in the localdensity and frozencore approximations. The cohesive energy and Γ_{1}(A_{1}) phonon frequency are also computed. Comparison with experiment shows excellent agreement for intrachain properties, and satisfactory agreement for interchain properties. This indicates that ab initio localdensity totalenergy calculations are viable for the case of molecular crystals.

[76]

D. Vanderbilt and J. D. Joannopoulos, “Total energies in Se. II. vacancy
in the crystal,” Physical Review B, vol. 27, pp. 6302–6310, May 1983.
[ bib 
http ]
Ab initio totalenergy calculations are used to determine theoretically the structural configuration of the vacancy in trigonal Se. The method consists of calculating the forces, as well as the total energies, within the localdensity and frozencore approximations, for a superlattice structure containing a vacancy. In this way, relaxations at the vacancy can be fully taken into account, including a possible selfhealing of the vacancy. A slightly relaxed symmetric version of the ideal vacancy is the lowestenergy structure found; neither asymmetric relaxation nor valence alternation appears to occur. A simple Hubbard Hamiltonian is used to analyze the spin configuration of the lowestenergy structure.

[75]

D. Vanderbilt and J. D. Joannopoulos, “Total energies in Se. II. defects
in the glass,” Physical Review B, vol. 27, pp. 6311–6321, May 1983.
[ bib 
http ]
The effective Hubbard U for the bonding coordination defect in glassy Se is investigated. This is accomplished by applying localdensity totalenergy calculations directly to charged defects in a superlattice configuration. The existence of a large negative contribution to U, arising from interconversion between danglingbond and threefoldcoordinated structures, is confirmed. However, a still larger Coulomb repulsion gives rise to an overall positive U.

[74]

J. Ihm, D. J. Chadi, and J. D. Joannopoulos, “Study of the reconstructed
GaAs(100) surface,” Physical Review B, vol. 27, pp. 5119–5121,
April 1983.
[ bib 
http ]
The reconstruction of an Asterminated GaAs(100) surface has been studied using the selfconsistent pseudopotential method. Total energies for the (1 ×1) ideal surface and the c(2 ×2) and p(2×2) econstructed surfaces within the dimer model are compared. Unlike the Si(100) surface, at least two inequivalent dimers are required to produce the semiconducting surface and stabilize the system. Important features in the density of states and the valencecharge distribution are presented.

[73]

D. J. Chadi, J. Ihm, C. Tanner, and J. D. Joannopoulos, “Theoretical study of
the As(100) surface reconstruction of GaAs,” Physica B+C,
vol. 117–118, pp. 798–800, March 1983.
[ bib 
DOI ]
The reconstruction of the Asterminated GaAs(100) surface was examined using both the tightbinding and the selfconsistent pseudopotential methods. Dimer models with unit cells as large as the c4×4 one seen in electrondiffraction experiments were tested. Unlike the Si(100) surface, symmetric as well as asymmetric dimers are predicted to occur in equal densities at the surface.

[72]

A. D. Stone, D. C. Allan, and J. D. Joannopoulos, “Phase randomness in the
onedimensional Anderson model,” Physical Review B, vol. 27,
pp. 836–843, January 1983.
[ bib 
http ]
The probability distribution P(ν) of the phase ν which determines the scaling properties of the dimensionless resistance R/T is analyzed for the onedimensional Anderson model with diagonal disorder. For weak disorder (W/V 1) and E ≠0 we find that P(ν) is initially sharply peaked for short chains but becomes uniform over 2π as N increases. Moreover, the length at which P(ν) becomes uniform is found to be independent of W/V (as long as W/V 1); instead it appears to depend only on the distance in energy from band center, i.e., on the extent to which the electron's wavelength is incommensurate with the lattice. Thus, unlike the disordered KronigPenny model, there is a phase randomness length, shorter than the localization length but longer than the lattice spacing. P(ν) is also studied in the limit of large disorder and analytic expressions for the mean and variance of the inverse localization length are derived for weak and strong disorder. Our results suggest that uniform phase randomness is indeed a property of most disordered 10 systems in the limit of weak disorder.

[71]

J. Ihm and J. D. Joannopoulos, “Structure of the AlGaAs(110) interface
from an energyminimization approach,” Physical Review B, vol. 26,
pp. 4429–4435, October 1982.
[ bib 
http ]
The structure of the AlGaAs(110) interface at the initial stages of Al deposition has been studied. In this system, the adatomsubstrate and the adatomadatom interactions are not necessarily weak, and the interface region may be strongly perturbed. The pseudopotentialenergy minimization method is ideally suited for determining the stable structure of such systems involving significant energy change, and this method is successfully applied to the AlGaAs system in the present study. By the calculation of the chemisorption energy of the Al atom at different sites on the entire GaAs surface, an energy contour map is obtained for the first time. Favorable channels of migration of Al atoms on this map are identified, which suggests preferential surface diffusion along Ga theAs bonding chain direction. The calculated surface hopping diffusion is sufficiently high even at room temperature so that Al atoms frequently encounter and interact with other Al atoms to form Al clusters. The Al clusters are found to have lower free energy than chemisorbed Al atoms. Al atoms eventually replace substrate Ga atoms and Al formAs bonds in the interface region to minimize the energy of the system.

[70]

D. Vanderbilt and J. D. Joannopoulos, “Bonding coordination defect in
gSe: A “positiveU” system,” Physical Review Letters,
vol. 49, pp. 823–826, September 1982.
[ bib 
http ]
The effective Hubbard U for the bonding coordination defect in glassy Se is investigated. This is accomplished by applying localdensity totalenergy calculations directly to charged defects. The existence of a sizable negative contribution to U from structural relaxation is confirmed. However, a still larger Coulomb repulsion gives rise to an overall positive U. This result is not inconsistent with a negative U in the compound chalcogenide glasses.

[69]

D. Vanderbilt and J. D. Joannopoulos, “Offdiagonal occupation numbers in
localdensity theory,” Physical Review B, vol. 26, pp. 3203–3210,
September 1982.
[ bib 
http ]
We introduce a new method for specifying the occupations of states in localdensity theory by allowing “offdiagonal occupation numbers” (i.e., a generalized density matrix). We show that this technique has important applications to superlattice and slab geometries, allowing bondingtype interactions between defects, molecules, or surfaces to be effectively eliminated. Moreover, previously inaccessible charge states may now be studied. The method is shown to have the full sanction of localdensity theory.

[68]

J. Ihm and J. D. Joannopoulos, “Firstprinciples determination of the
structure of the Al/GaAs(110) surface,” Journal of Vacuum Science
and Technology, vol. 21, pp. 340–343, July 1982.
[ bib 
DOI ]
The structure of Al atoms deposited on the GaAs (110) surface has been studied using a first principles pseudopotential energy minimization calculation. The lowest energy configurations are determined by minimizing the total energy of the system with respect to its structural degrees of freedom. The most stable configuration is such that Al atoms replace the second (or deeper) layer Ga atoms. At temperatures where this reaction cannot be activated, two important processes are found to exist. In the low coverage limit, atoms favor twofold sites connecting an As atom and a Ga atom (in the next zigzag chain) on the surface, forming strong chemical bonds with the substrate. At higher coverages, on the other hand, Al atoms tend to cluster and make new bonds among themselves. The chemisorption energy map over the surface has been obtained and the possible path of the migration of Al atoms for clustering is investigated.

[67]

D. H. Lee and J. D. Joannopoulos, “Ideal and relaxed surfaces of SiC,”
Journal of Vacuum Science and Technology, vol. 21, pp. 351–357, July 1982.
[ bib 
DOI ]
During the past few years there has been considerable interest in the relaxation of GaAs(110) and Si(100)(2×1) surfaces. The surfaces of SiC, however, provide an intermediate system between these heteropolar and homopolar structures. It is interesting therefore to investigate the kinds of relaxation that might occur at the zincblende and wurtzite surfaces of SiC. We perform calculations using Chadi's energy minimization scheme, with the coefficients of linear, quadratic, and cubic energy correction terms fitted to the bulk lattice constant, bulk modulus, and thermal expansion coefficient. To check the validity of this model, we calculate six experimentally known phonon frequencies. The agreement between theory and measured values is quite good. With this model, we investigate the relaxation at the SiC(110) surface in the zincblende structure and SiC(1010) and (1120) surfaces in the wurtzite structure. The results show a combination of downward movement and buckling for all three surfaces. The reduction in total energy is about 0.21 eV/atom for the (110) surface, and 0.24 eV/atom, 0.18 eV/atom for (1010) and (1120), respectively. Further results include the determination of ideal and relaxed electronic structure and optimum relaxed geometries. Finally, a new theory which extends Chadi's scheme to do first principles phonon calculations is presented and discussed.

[66]

D. H. Lee and J. D. Joannopoulos, “Simple scheme for deriving atomic force
constants: Application to SiC,” Physical Review Letters, vol. 48,
pp. 1846–1849, June 1982.
[ bib 
http ]
A scheme is presented for deriving atomic force constants that is fairly accurate, yet simple enough to allow determination of the dynamical matrix of bulk solids, relaxed and reconstructed surfaces, defects, etc. For illustrative purposes, the method is applied to bulk SiC to predict the phonon dispersion curves throughout the entire Brillouin zone, and to a carbon vacancy in SiC to study the change of atomic force constants due to atomic relaxations.

[65]

K.M. Ho, J. Ihm, and J. D. Joannopoulos, “Dielectric matrix scheme for fast
convergence in selfconsistent electronicstructure calculations,”
Physical Review B, vol. 25, pp. 4260–4262, March 1982.
[ bib 
http ]
A scheme is devised which drastically reduces the number of iterations required to reach selfconsistency in electronicstructure calculations. This scheme is particularly helpful in calculations for systems with large unit cells.

[64]

D. H. Lee and J. D. Joannopoulos, “A new theory of electronic surface
states,” Journal of Vacuum Science and Technology, vol. 19,
pp. 355–359, September 1981.
[ bib 
DOI ]
Presently, stateoftheart theoretical studies of elementary excitations at surfaces involve large, time consuming, and often cumbersome calculations, which are not very practical for surfaces with low symmetry. A new method has just been developed that directly yields more information and is computationally faster (by an order of magnitude) than any current method available. This method will allow calculations of complicated surface systems not previously possible. The ingredients of the theory are any semiinfinite system of atomic layers, any set of basis functions spanning each layer, and one single matrix which depends only on the interaction matrix elements among the atomic layers. What is remarkable is that the eigenanalysis of this matrix gives a complete quantum mechanical description of the elementary excitations of the system. Therefore with just a diagonalization of this matrix, the knowledge of its eigenvalues and eigenvectors give directly (1) the projected bandstructure (without having to diagonalize the bulk Hamiltonian for a large number of K_{⊥}'s); (2) the bona fide surface bands with high accuracy (without the need of a bulk Green function first); (3) the surface Green function as a function of energy E+iδ, in the correct limit that δ→0! (without the need to solve slowly convergent iterative equations for complex energies); and (4) the precise decay length, orbital character, and symmetry of the wave function. The method, although versatile, is also conceptually simple. All the properties mentioned above are obtained from a simple set of rules. A tutorial discussion of the formalism will be presented along with several instructive examples illustrating its use.

[63]

E. J. Mele and J. D. Joannopoulos, “Electronic structure of the zincblende
and rocksalt phases of InSb,” Physical Review B, vol. 24,
pp. 3145–3154, September 1981.
[ bib 
http ]
The electronic structure of InSb in the common zincblendecrystal phase and in a rocksaltcrystal phase (which is metastable at standard temperature and pressure) are investigated using a selfconsistent pseudopotential formalism including relativistic effects. For the zincblende structure we find that a local sp potential for the valence electrons yields, in a selfconsistent calculation for the solid, a charge density in excellent agreement with previous calculations employing empirical nonlocal potentials. Relativistic effects are found to be very important in order to obtain a good description of the band gap and overall bandwidth. For the rocksalt phase we obtain a metallic solid, in agreement with experiment, and observe (in comparison with the zincblende results) substantial changes in the valenceband density of states. These results are in very good agreement with the experimental xrayphotoemissionspectroscopy studies of these two phases. Unlike the situation for the covalently bonded zincblende crystal, we obtain very large charge transfer from the cations to the anions (estimated to be 0.9e^{}) in the metallic rocksalt phase, which we speculate helps to stabilize the solid. Bandstructure, densitiesofstates, chargedensity, and Fermisurface results are presented.

[62]

A. D. Stone and J. D. Joannopoulos, “Probability distribution and new scaling
law for the resistance of a onedimensional Anderson model,” Physical
Review B, vol. 24, pp. 3592–3595, September 1981.
[ bib 
http ]
The exact probability distributions of the resistance ρ, the conductance, and ln(1+ρ) are calculated for the 1D Anderson model with purely offdiagonal disorder at E=0. Analysis of the distribution yields the surprising results that ρ grows exponentially with length, despite previous studies indicating that the state at E=0 is extended, and the typical resistance ρ increases as exp(L^{1/2}). The relationship between this behavior and the temperature dependence of the resistance of thin wires is discussed.

[61]

J. Ihm and J. D. Joannopoulos, “Structural energies of A1 deposited on the
GaAs(110) surface,” Physical Review Letters, vol. 47, pp. 679–682,
August 1981.
[ bib 
http ]
Major controversies over the structure of A1 atoms deposited on the GaAs(110) surface have been resolved by using a firstprinciples energyminimization method. The most stable configuration is that of A1 atoms replacing the second layer Ga atoms beneath the surface. At temperatures where this reaction cannot be activated, two important processes are found to exist. In the lowcoverage limit, A1 atoms favor twofold sites to form strong bonds with the substrate atoms. At higher coverages, A1 atoms tend to cluster and make new bonds among themselves.

[60]

D. H. Lee and J. D. Joannopoulos, “Simple scheme for surfaceband
calculations. I,” Physical Review B, vol. 23, pp. 4988–4996, May
1981.
Erratum: Phys. Rev. Lett., vol. 52, p. 1054 (1984).
[ bib 
http ]
A simple, efficient scheme for calculating the electronic structure of a surface is presented. The scheme is applicable to any general Hamiltonian that can be described within a localizedorbital basis. The method is much faster than the current techniques available. The basic concept is that of wavefunction matching through a transfer matrix. The eigensolutions of this matrix then provide all the information concerning the projected band structure, surfacestate energies, orbital character, and decay lengths. A rather detailed discussion of the formalism is presented for a general surface system. A comprehensive and illustrative example is also presented for readers who are interested in using the scheme but not in the details of the theory.

[59]

D. H. Lee and J. D. Joannopoulos, “Simple scheme for surfaceband
calculations. II. the Green's function,” Physical Review B,
vol. 23, pp. 4997–5004, May 1981.
[ bib 
http ]
We present a very simple scheme for calculating the Green's function of a semiinfinite surface system described within a localized orbital basis. By generating a series of matching conditions for the Green's function we can calculate its matrix elements much faster than any method currently available. We present the formalism for a specific class of systems and include a simple example to illustrate the use of the technique.

[58]

W. B. Pollard and J. D. Joannopoulos, “Vibrational properties of amorphous
silicon alloys,” Physical Review B, vol. 23, pp. 5263–5268, May 1981.
[ bib 
http ]
A theoretical model of the vibrational states of recently reported amorphous siliconfluorine alloys is presented. The infrared absorption, polarized Raman scattering, and phonon state density spectra are calculated for different local siliconfluorine bonding arrangements. Changes in the infrared and Raman spectra associated with the incorporation of oxygen and hydrogen in the amorphous alloy is also discussed. Our results suggest that unlike the situation in amorphous siliconhydrogen alloys, the presence of SiF bonds in the fluorinated materials significantly disturb the bulk Si vibrational bands. It is found that the signatures of isolated SiF_{2} and SiF_{3} complexes are stretching modes in the region of 800 to 1000 cm^{1} accompanied by one (SiF_{2}) or two (SiF_{3}) sharp resonances in the region of 400 to 500 cm^{1}, while the SiF unit is distinguished by a single stretching mode near 800 cm^{1}. Finally, our results also indicate that SiH bonds in close proximity with SiF bonds alter the fluorine vibrational modes. SiO bonds, on the other hand, do not affect the SiF stretching mode near 800 cm^{1}.

[57]

D. Vanderbilt and J. D. Joannopoulos, “Theory of defect states in glassy
As_{2}Se_{3},” Physical Review B, vol. 23, pp. 2596–2606, March
1981.
[ bib 
http ]
Structural defects in glassy As_{2}Se_{3} are classified and labeled according to the constituent likeatom bonds and malcoordinated atoms. A selection rule is formulated to reduce the number of allowed Fermilevel pinning reactions. An elementary Bethelattice model is introduced as a starting point for a discussion of the electronic structure of simple defects. The defect states are found to be very different from those in Se; deep gap states arise in As_{2}Se_{3} because of unique bond orbitals, whereas they occur in Se due to unique π interactions between orbitals. Malcoordinated Se atoms are expected to give rise to hydrogenic levels in As_{2}Se_{3}, in contrast to Se. Surprisingly, the undercoordinated pnictide defects are positively charged in this model. Finally, defect creation energies and densities at T_{g} are discussed.

[56]

Y. Wang and J. D. Joannopoulos, “The Ga core exciton at unrelaxed GaAs
(110),” Journal of Vacuum Science and Technology, vol. 17,
pp. 997–1000, September 1980.
[ bib 
DOI ]
ore excitonic effects at an unrelaxed GaAs (110) surface are studied using a localized orbital approach. A realistic Hamiltonian for the conduction bands is obtained with inclusion of 5s orbitals and third nearest neighbor interactions. The binding energies of core excitons both in the bulk and at the surface are calculated. The results are in good agreement with experimental measurements, with a contact potential of ∠1.0eV. In addition it is shown that the binding energy has a maximum value and the limiting case can be thought of as an ideal vacancy.

[55]

D. H. Lee and J. D. Joannopoulos, “Surface states at unrelaxed
ZnO(1010),” Journal of Vacuum Science and Technology,
vol. 17, pp. 987–988, September 1980.
[ bib 
DOI ]
The electronic structure of an ideal ZnO(1010) surface has been studied using a tightbinding approach, with the surface modeled in a semiinfinite geometry. It is found that the surface states follow the band edge very closely due to the ionic character of the surface. Moreover, the close spacing between Zn 3d and O 2p levels produces a small but not negligible amount of d character in the surface states.

[54]

D. Vanderbilt and J. D. Joannopoulos, “Theory of defect states in glassy
selenium,” Physical Review B, vol. 22, pp. 2927–2939, September 1980.
[ bib 
http ]
A realistic approach to the electronic theory of bondcoordination defects in chalcogenides, based on selfconsistent pseudopotential calculations, is used to study glassy Se. The results of the pseudopotential calculations are interpreted in terms of simpler tightbinding models. The onefold and threefold coordination defects are both found to give rise to nondegenerate, nonhydrogenic gap states, whose properties are unique to the chalcogenides in several respects. The existence of π interactions between nonbonding orbitals at defect sites is found to be crucial to an understanding of the electronic structure. These interactions are responsible for large charge transfers between atoms and consequently large energy shifts of atomic valence orbitals, which make these defects quite unlike those in other semiconductors. The origin, character, energy location, and localization of the defect states associated with bondcoordination defects, and with defect pairs and certain relaxed defects, are discussed.

[53]

D. Vanderbilt and J. D. Joannopoulos, “Structural excitation energies in
Selenium,” Solid State Communications, vol. 35, pp. 535–538, August
1980.
[ bib 
DOI ]
A realistic selfconsistent pseudopotential approach, capable of generating accurate structural ground state and excitation energies, is used to settle the controversy regarding neutral bond coordination defects in glassy Se. Many surprising results emerge. The threefold defect is not even metastable, but decays immediately into a onefold defect. The latter is the lowerst energy simple defect, with a remarkably low formation energy of reverse similar, equals ≅0.5eV. Relaxations are found to be unexpectedly small.

[52]

R. B. Laughlin, J. D. Joannopoulos, and D. J. Chadi, “Theory of the electronic
structure of the SiSiO_{2} interface,” Physical Review B,
vol. 21, pp. 5733–5744, June 1980.
[ bib 
http ]
A theory of the SiSiO_{2} interface based on recent experimental findings for silicon surfaces and their oxidation is presented. It is proposed that a simple localorbital picture can simultaneously describe silicon, its oxidation, and the SiSiO_{2} interface and that two dimensionality is not essential to physically meaningful calculations of interface local densities of states. Calculations are performed which show that interface states do not arise simply from the presence of a boundary. It is argued that band tailing at the interface, like that in amorphous silicon, is due primarily to strain rather than to charged centers, and that dangling bonds at the interface should give rise to an inhomogeneously broadened discrete level at midgap.

[51]

D. C. Allan and J. D. Joannopoulos, “Electronic structure of hydrogenated
amorphous silicon,” Physical Review Letters, vol. 44, pp. 43–47,
January 1980.
[ bib 
http ]
alculations of the electronic states and total energies of various bonding conformations in hydrogenated amorphous Si are presented. Various surprising results emerge, including identification of peaks in photoemission spectra as signatures of nearestneighbor SiH configurations, a gap increasing with increasing H content while the conduction band remains essentially unchanged, and localized states in the gap arising from various defects whose energies are in sharp contrast to recently proposed simple model estimates.

[50]

W. B. Pollard and J. D. Joannopoulos, “Vibrational excitations of defect sites
in amorphous groupV semiconductors,” Physical Review B, vol. 21,
pp. 760–766, January 1980.
[ bib 
http ]
A study of the vibrational excitations of structural defects in amorphous pnictide semiconductors is presented. Amorphous As is chosen as a prototype for this study. The local phonon densities of states, infrared absorption, and Ramanscattering spectra of twofold coordinated As atoms, fourfold coordinated As atoms, intimate valence alternation pairs, and vacancy defects are presented. The effects of relaxations, disorders, and distortions upon the vibrational states of the defects are discussed. The results suggest that only the relaxed twofold coordinated As atoms (or vacancylike defects) give rise to localized vibrational modes with optical activities consistent with sharp weak features observed in the experimental infrared and Raman spectra of bulk amorphous As. The implications of our results for amorphous P and Sb, as well as the relationships between spectroscopic measurements and other optical measurements are also discussed.

[49]

R. B. Laughlin, J. D. Joannopoulos, and D. J. Chadi, “Bulk electronic
structure of SiO_{2},” Physical Review B, vol. 20, pp. 5228–5237,
December 1979.
[ bib 
http ]
The electronic structures of crystalline and amorphous SiO_{2} are examined via the tightbinding method. A new tightbinding Hamiltonian, fit to experiment and to the pseudopotential band structure of α quartz, is used to calculate densities of states for both α quartz and an SiO_{2} Bethe lattice. These are shown to compare favorably with xray photoemission spectra of α quartz and amorphous SiO_{2}. The computational results are analyzed qualitatively using the bondorbital approach. For both crystalline and amorphous SiO_{2} it is suggested that oxygen 2s character in the lower conduction bands may be necessary to account for the large gap. Local symmetries of the lonepairlike bands of possible relevance to the optical properties are discussed.

[48]

G. Doerre and J. D. Joannopoulos, “Electronic states of Te above the
highpressure phase transition,” Physical Review Letters,
vol. 1040–1042, pp. 1040–1042, October 1979.
[ bib 
http ]
A selfconsistent pseudopotential bandstructure calculation for the recently determined highpressure (above 38 kbar) monoclinic tellurium structure is presented. The density of states and charge densities for representative regions within the unit cell are calculated. Our results show that highpressure monoclinic tellurium is metallic, and that a crystal bondlength asymmetry is caused by an electronically driven distortion. The results also predict a highly anisotropic conductivity.

[47]

R. B. Laughlin, J. D. Joannopoulos, and D. J. Chadi, “Use of the
cluster–Bethelattice method in surface studies,” Journal of Vacuum
Science and Technology, vol. 16, pp. 1327–1330, September 1979.
[ bib 
DOI ]
A general review of the cluster–Bethelattice method is presented which emphasizes its use as a tool in surface studies. The basic elements of the method are summarized, with simple models used to illustrate the most important ideas. The strengths and weaknesses of the method are contrasted, and the types of questions the method can best deal with ar identified. The method is then illustrated with an example. Recent results are presented which show that both bondangle and structural disorder can produce localized states at the Si–SiO_{2} interface which have no analog in either bulk silicon or bulk SiO_{2}. Inhomogeneities at the interface, particularly small ”peninsulas” of silicon protruding into the oxide, are found to produce strong interface resonances approximately 2 eV below the valence band maximum. Distortions of the Si–O–Si angle near the interface are found to cause tailing into the gap in the oxide near 10 eV below the silicon valence band edge. Finally, distortions of the tetrahedral angles on a silicon atom at the interface are investigated and found to have effects similar to those observed in bulk elemental silicon.

[46]

E. J. Mele and J. D. Joannopoulos, “Electronic structure of Al chemisorbed
on GaAs(110),” Journal of Vacuum Science and Technology, vol. 16,
pp. 1154–1158, September 1979.
[ bib 
DOI ]
We report results of tight binding calculation for ordered half monolayer coverages of Al on GaAs(110) in a variety of chemisorption configurations. We find that differences between the chemisorption geometries and relaxations of these configurations lead to a variety of electrical characteristics of the surfaces. The relation of this result to the barrier formed at higher coverages is discussed.

[45]

W. B. Pollard and J. D. Joannopoulos, “Electronic structure of defects in
amorphous arsenic,” Physical Review B, vol. 19, pp. 4217–4223, April
1979.
[ bib 
http ]
The clusterBethelattice method, selfconsistent pseudopotentials, and tightbinding Hamiltonians are used to study the electronic structure of various possible defects in amorphous As. The electronic densities of states of isolated twofold coordinated As atoms, fourfold coordinated As atoms, “intimate valence alternation pairs,” and vacancies are calculated. The origin, character, and localization of the resulting gap states are discussed. It is found that isolated fourfold coordinated As atoms give rise to states in the gap that are nondegenerate, fairly localized, and predominantly plike in character. Moreover, our investigation indicates that the character and localization of the gap states arising from the “valence alternation pair” are consistent with the properties of optically induced paramagnetic states observed in amorphous As, while the electronic gap states of the vacancy defect may be consistent with the recently observed thermally generated paramagnetic states in this material.

[44]

E. J. Mele and J. D. Joannopoulos, “Surfacebarrier formation for A1
chemisorbed on GaAs(110),” Physical Review Letters, vol. 42,
pp. 1094–1097, April 1979.
[ bib 
http ]
Using a localized orbital theory, we have studied the electronic and electrical properties of A1 chemisorbed on GaAs(110). We find that both the microscopic data and the macroscopic induced barrier are fully explained by the electronic structure of a new AlAsGa complex on the surface. This complex results from an exchange reaction in which Al replaces the surface Ga and an unexpected structural relaxation induced by the chemisorption of the metal.

[43]

D. Vanderbilt and J. D. Joannopoulos, “Calculation of defect states in
amorphous selenium,” Physical Review Letters, vol. 42, pp. 1012–1015,
April 1979.
[ bib 
http ]
Selfconsistent pseudopotential and tightbinding techniques are used to study glassy Se. Both onefold and threefold corrdinated defects give rise to nondegenerate, nonhydrogenic gap states. The former state arises from an interaction, unique to the chalcogenides, between a dangling bond and a neighboring lone pair. The latter state is surprisingly delocalized, involving interactions between many orbitals. It is shown that defect electronic configurations, and repulsive interatomic terms, are crucial to the calculation of total energies.

[42]

E. J. Mele and J. D. Joannopoulos, “Doubledanglingbond defects and band
bending at the GaAs (110) surface,” Physical Review B, vol. 19,
pp. 2928–2932, March 1979.
[ bib 
http ]
We note that contactpotential measurements which have shown band bending at the nonpolar GaAs surface can be interpreted with a simple model for cleavage defects at the surface. We find that defects with two dangling bonds at the surface produce both filled and empty defect states in the gap. This result then supports experimental work indicating that band bending at GaAs(110) is defect related.

[41]

J. D. Joannopoulos, “Use of Cayley trees to study excitations in disordered
solids,” Journal of NonCrystalline Solids, vol. 32, pp. 241–255,
February 1979.
[ bib 
DOI ]
It is shown how, and why, Cayley trees (Bethelattices) are useful models for studying elementary excitations in disordered solids. Special attention is focused on the effects of disorder on the electronic states of various amorphous bonded solids. Specific examples are drawn from problems involving: (1) bondangle distortions and localized states in amorphous Ge, (2) hydrogen configurations in hydrogenated amorphous Si, (3) bondingcoordination defects in amorphous As and (4) amorphous Si—SiO_{2} interfaces.

[40]

T. Starkloff and J. D. Joannopoulos, “Theory of the pressure dependence of the
electronic and optical properties of trigonal Te,” Physical
Review B, vol. 19, pp. 1077–1088, January 1979.
[ bib 
http ]
Using a selfconsistent pseudopotential formalism based on realistic pseudopotentials of the free ion and atom, the influence of hydrostatic pressure on the electronic structure and the optical spectra of trigonal Te is investigated. The pressure derivative of the fundamental gap is found to be in good agreement with experimental results. The joint density of states, ɛ_{1} and ɛ_{2}, energyloss function, reflectivity, and absorption coefficient are calculated from 0 to 13 eV. Very good agreement is obtained with experimental spectra. The very strong pressureinduced enhancement of the reflectivity can be reproduced. The anisotropy anomaly in the reflectivity at high energies is explained and traced to distinct transitions in the Brillouin zone. Predictions are made about the pressure dependence of the optical spectra above 4 eV. Finally, selfconsistent charge densities and the electronic density of states are also presented.

[39]

W. B. Pollard and J. D. Joannopoulos, “Vibrational excitations at defect sites
in amorphous tetrahedral and pnictide semiconductors,” Journal of
NonCrystalline Solids, vol. 35–36, pp. 1179–1184, January 1979.
[ bib 
DOI ]
The vibrational properties of defects in amorphous As, amorphous Si, and fluorinated amorphous Si are investigated. Infrared absorption, Raman scattering, and densities of states spectra are calculated for a variety of bonding coordination defects within the clusterBethelattice formalism. A new technique for solving arbitrary Bethe lattices is also briefly discussed.

[38]

J. D. Joannopoulos, “Theoretical calculations of defect states in amorphous
semiconductors,” Journal of NonCrystalline Solids, vol. 35–36,
pp. 781–792, January 1979.
[ bib 
DOI ]
A review of realistic theoretical calculations of the electronic structure of defects in amorphous As, amorphous Se, amorphous As_{2}Se_{3} and hydrogenated amorphous Si is presented.

[37]

E. J. Mele and J. D. Joannopoulos, “Theory of oxygen chemisorption on
GaAs(110),” Physical Review B, vol. 18, pp. 6999–7010, December
1978.
[ bib 
http ]
Using a localizedorbital representation, we have calculated the electronic structure of oxygen chemisorbed on the GaAs (110) surface in various bonding configurations. Two principal results which emerge are (i) that the effects of chemisorption on the surface species are strongly affected by allowing the surface to relax, and (ii) that molecularlike correlations persist and are important for localized nonbonding orbitals in the adsorbate. Our results provide detailed interpretations of xray photoemission spectroscopy, ultraviolet photoemission spectroscopy, and electronloss spectroscopy studies of the oxidation of GaAs(110), and a comparison with all the experimental data strongly indicates that in the initial stages of oxidation O_{2} chemisorbs principally on the surface As, with the surface maintaining its relaxed configuration.

[36]

E. J. Mele and J. D. Joannopoulos, “Intrinsic surface states and Fermilevel
pinning at metal–semiconductor interfaces,” Journal of Vacuum Science
and Technology, vol. 15, pp. 1370–1373, July 1978.
[ bib 
DOI ]
We find that the wellknown transition in the Fermilevel pinning behavior of metal–semiconductor contacts can be quantitatively characterized in a fundamental way. Our model makes use of the clean semiconductor surface state energies, predicts the onset of the covalent–ionic transition, and explains strong Fermilevel pinning at metal contacts to covalent materials with large optical gaps and low bond polarizabilities.

[35]

J. D. Joannopoulos and E. J. Mele, “Extrinsic surface states for oxygen
chemisorbed on the GaAs (110) surface,” Journal of Vacuum Science and
Technology, vol. 15, pp. 1287–1289, July 1978.
[ bib 
DOI ]
The electronic structure of various configurations of oxygen chemisorbed on GaAs (110) is studied using a localized orbital approach. Recent conflicting interpretations of experimental measurements, concerning the site of chemisorption, are resolved. It is concluded that for low averages, oxygen prefers to chemisorb to the surface arsenics and chemisorbs as an O_{2} molecule.

[34]

R. B. Laughlin and J. D. Joannopoulos, “Theory of surface phonons in amorphous
silica,” Physical Review B, vol. 17, pp. 4922–4930, June 1978.
[ bib 
http ]
A new theoretical approach to studying surface vibrations in amorphous solids is applied to silicon dioxide. The method entails modeling the surface as a Bethe lattice with a dangling bond, and treating the twodimensional nature of the surface and the surface topography as small perturbations. The theory successfully describes the nature and origin of the surface states, as well as their relative intensities as observed in recent infraredreflectivity and Ramanscattering experiments. Both intrinsic surface effects and those caused by the presence of adsorbates are discussed.

[33]

R. J. Nemanich, G. Lucovsky, W. Pollard, and J. D. Joannopoulos,
“Spectroscopic evidence for bonding coordination defects in amorphous
As,” Solid State Communications, vol. 26, pp. 137–139, April 1978.
[ bib 
DOI ]
Spectroscopic evidence for fourfold and possibly, twofold coordinated defects in amorphous As is presented. Structure in Raman scattering and infrared absorption measurements is interpreted using forceconstant models and the clusterBethelattice method. The positions and intensities of certain peaks suggest that these defects may be the analogues of valence alternation pairs in amorphous chalcogenide glasses.

[32]

R. B. Laughlin and J. D. Joannopoulos, “Effect of secondnearestneighbor
forces on the vibrations of amorphous SiO_{2},” Physical Review B,
vol. 17, pp. 2790–2792, March 1978.
[ bib 
http ]
A method is presented of solving for the vibrational Green's function of a silicondioxide Bethe lattice when it contains secondnearestneighbor interactions. The method is used to find the density of states of a Bethe lattice constructed with a Keating Hamiltonian. The primary effect of the secondnearestneighbor interactions is a softening of the rocking bands below 450 cm^{1}.

[31]

R. B. Laughlin, J. D. Joannopoulos, C. A. Murray, K. J. Hartnett, and T. J.
Greytak, “Intrinsic surface phonons in porous glass,” Physical Review
Letters, vol. 40, pp. 461–465, February 1978.
[ bib 
http ]
Raman scattering and infrared reflectivity measurements have been performed on samples of porous Vycor glass. Three features in the spectra are due to intrinsic surface phonons. This identification is supported by a simple new theory for the surface.

[30]

E. J. Mele and J. D. Joannopoulos, “Theory of metalsemiconductor
interfaces,” Physical Review B, vol. 17, pp. 1528–1539, February
1978.
[ bib 
http ]
We present a microscopic model for the formation of Schottky barriers at metalsemiconductor contacts. The theory proposes that Schottky barriers are determined by “metalinduced gap states” at the semiconductor surface, which are danglingbond derived resonances. The danglingbond character of these states implies that the energies of surface states at clean semiconductor surfaces are very important in Schottkybarrier formation. This work introduces an ionicity parameter, obtained from atomicterm values, to quantitatively characterize the wellknown transition from covalent to ionic behavior at metalsemiconductor interfaces. This model directly associates this transition with a truly fundamental change in the electronic structure of the semiconductor substrate and provides a natural interpretation of strong Fermilevel pinning at metal contacts to covalent materials with large optical gaps and low bond polarizabilities.

[29]

W. B. Pollard and J. D. Joannopoulos, “Excitations in amorphous pyramidally
bonded solids. I. electrons,” Physical Review B, vol. 17,
pp. 1770–1777, February 1978.
[ bib 
http ]
The electronic and phonon state densities of amorphous pyramidally bonded solids are calculated. These solids are shown to exhibit a unique isomorphism between the electronic and vibrational state densities. This atypical correspondence between the state densities suggests that a study of the electronic states can be used to understand the vibrational states. Arsenic, which epitomizes pyramidally bonded solids, is chosen as a prototype. Our results reproduce the trends founds in the xray photoemission data (XPS) for rhombohedral and amorphous As. The effects of bondangle variations and topological disorder upon the s and p like regions of the XPS spectra are investigated. A prescription is given by which the behavior of the plike electrons in pyramidally bonded solids can be understood in terms of the behavior of the slike electrons.

[28]

W. B. Pollard and J. D. Joannopoulos, “Excitations in amorphous pyramidally
bonded solids. II. phonons,” Physical Review B, vol. 17,
pp. 1778–1784, February 1978.
[ bib 
http ]
Phonon state densities are calculated for crystalline and amorphous As. The results indicate a strong analogy between the electronic p states and the vibrational states. This isomorphism is used to derive relationships between the electronic and phonon coupling constants. The effects of topology upon the vibrational excitations in pyramidal solids are studied. A new model for infrared absorption is presented. The resulting spectra agree well with experimental measurements. Finally, inelastic neutronstructure factors are calculated and are used to interpret recent experimental results.

[27]

E. J. Mele and J. D. Joannopoulos, “Electronic states at unrelaxed and relaxed
GaAs (110) surfaces,” Physical Review B, vol. 17, pp. 1816–1827,
February 1978.
[ bib 
http ]
We have shown that, using a general class of Hamiltonians, the transfermatrix technique may be used to obtain exact solutions for the electronic states at any crystal surface bounded by semiinfinite bulk. This result is formally generalized as a theorem and is used to study the electronic states at a clean GaAs (110) surface. The calculation employs an empirical tightbinding Hamiltonian which realistically models the GaAs surface and allows meaningful comparison with both experiments and selfconsistent pseudopotential calculations. Surface states are calculated for the clean (110) surface, and a variety of structural relaxations are studied.

[26]

E. J. Mele and J. D. Joannopoulos, “Site of oxygen chemisorption on the
GaAs(110) surface,” Physical Review Letters, vol. 40, pp. 341–344,
January 1978.
[ bib 
http ]
We reconcile energyloss spectroscopy and chemicalshift studies of the oxidation of the GaAs(110) surface, which previously have led to contradictory conclusions about the oxygen bonding site. We have calculated densities of states and 100eV ultravioletphotoelectronspectroscopy (UPS) valenceband spectra to examine the site and molecular species of the chemisorbed oxygen. We conclude that for low coverages oxygen prefers to chemisorb to the surface arsenic atoms and chemisorbs as an O_{2} molecule.

[25]

T. Starkloff and J. D. Joannopoulos, “Local pseudopotential theory for
transition metals,” Physical Review B, vol. 16, pp. 5212–5215,
December 1977.
[ bib 
http ]
A simple localpseudopotential formalism capable of describing dband metals is introduced. The theory involves a straightforward method for generating a local pseudopotential for both valence and outermostcoreshell electrons. Niobium is used as a prototype to demonstrate the applicability of this method. Excellent agreement with nonlocal selfconsistent pseudopotential and augmentedplanewave band structures is obtained using a modest number of plane waves. The electronic density of states and core 4p absorption spectra are calculated. Two regions of distinctly different electronic character in the density of states could be demonstrated.

[24]

J. D. Joannopoulos, “Theory of fluctuations and localized states in amorphous
tetrahedrally bounded solids,” Physical Review B, vol. 16,
pp. 2764–2774, September 1977.
[ bib 
http ]
We present a general solution of a Bethe lattice with arbitrary coordination for a Hamiltonian with an arbitrary number of degrees of freedom per site and an arbitrary number of interaction integrals. This solution is used in conjunction with a realistic tightbinding Hamiltonian to study the effects of rings and bondangle fluctuations on the plike region and gap region of the electronic density of states of amorphous tetrahedrally bonded solids. It is shown that even for completely connected networks with no dangling bonds, bondangle fluctuations create welldefined localized states which lie predominantly at the top of the valence band. These fluctuations also account for the steepening of the valenceband edge with disorder as observed experimentally in photoemission measurements. It is shown that rings do not play a direct role in this effect.

[23]

R. B. Laughlin and J. D. Joannopoulos, “Phonons in amorphous silica,”
Physical Review B, vol. 16, pp. 2942–2952, September 1977.
[ bib 
http ]
A new theory of lattice vibrations in amorphous silicon dioxide is presented in which the randomness of the solid is treated separately from its chemistry. The theory attributes all measurable properties of phonons in silica to the nearly crystalline nearestneighbor geometry of the lattice and to the disruptive effects of bondangle disorder. Neutron, infrared, and Raman spectra are calculated and compared with experiment. The theory is an application of the recently developed clusterBethelattice approach to studying amorphous solids.

[22]

E. J. Mele and J. D. Joannopoulos, “Electronic states near the band gap for
the GaAs(110) surface,” Surface Science, vol. 66, pp. 38–44, August
1977.
[ bib 
DOI ]
The recent theoretical controversy regarding empty surface states at the GaAs cleavage plane is examined by the exact solution of several tight binding models applied to a semiinfinite crystal. We correlate the existence of an empty surface gap state with the anion p/cation p character of this state. This work isolates the specific properties of a Hamiltonian for GaAs which yield band gap states on a relaxed surface and clarifies the essential differences among current theoretical treatments.

[21]

J. D. Joannopoulos, T. Starkloff, and M. Kastner, “Theory of pressure
dependence of the density of states and reflectivity of selenium,”
Physical Review Letters, vol. 38, pp. 660–663, March 1977.
[ bib 
http ]
The pressure dependence of the density of states and the reflectivity of trigonal Se is calculated using a new selfconsistent pseudopotential technique. The results show that pressuredependent reflectivity experiments may be interpreted without the need for microscopic fields.

[20]

E. J. Mele and J. D. Joannopoulos, “Gaussian relaxation method. I.
homopolar tetrahedral solids,” Physical Review B, vol. 15,
pp. 901–908, January 1977.
[ bib 
http ]
We present a method for extending an empirical tightbinding theory to the calculation of densities of states of very large but finite systems. We also derive a set of bondcentered analytic wave functions which can be used to obtain realistic energydependent charge densities from a tightbinding calculation. As an example, we apply the method to a model homopolar tetrahedral solid representative of Ge.

[19]

J. D. Joannopoulos and W. B. Pollard, “Electrons and phonons in amorphous
pyramidally bonded solids,” Solid State Communications, vol. 20,
pp. 947–950, December 1976.
[ bib 
DOI ]
Electronic and phonon state densities of amorphous pyramidally bonded solids are calculated with As as a prototype. Using a Bethelattice, the GreavesDavis random network model and the ClusterBethelattice method, the results show: (1) the phonon states are isomorphic to, and obtained from, the plike electron states, (2) the photoemission and infrared measurements are easily interpreted, and (3) the electronic and phonon state densities are extremely sensitive to the local topology.

[18]

F. Yndurain and J. D. Joannopoulos, “Study of the electronic local density of
states using the clusterBethelattice method: Application to amorphous
IIIV semiconductors,” Physical Review B, vol. 14, pp. 3569–3577,
October 1976.
[ bib 
http ]
The clusterBethelattice method is extended to study the WeaireThorpe sp^{3} Hamiltonian. We derive a transformation which makes it possible to calculate the local density of states of a system described with a fourorbital Hamiltonian by using the local Green's function of a oneorbital Hamiltonian. We study the effects on the density of states of the presence of likeatom bonds in amorphous IIIV semiconductors. We analyze two models: (a) likeatom bond in tetrahedral configuration, and (b) likeatom bond in triangular pyramidal configuration. Our results are in agreement with the experimental data.

[17]

J. D. Joannopoulos and M. Kastner, “Evidence for weak sp hybridization in
chalcogens,” Solid State Communications, vol. 17, pp. 221–224, July
1975.
[ bib 
DOI ]
Recent arguments supporting strong sp hybridization in crystalline S and Se based on ultraviolet photoemission spectroscopy and molecular orbital models are inconsistent with the results of Xray spectroscopy. However, all this data can be explained by weak sp hybridization and the inclusion of a small admixture of d states.

[16]

F. Yndurain and J. D. Joannopoulos, ““cluster–Bethelattice” method: The
electronic density of states of heteropoloar systems,” Physical
Review B, vol. 11, pp. 2957–2964, April 1975.
[ bib 
http ]
The “cluster–Bethelattice” method is extended to the study of heteropolar systems. The Bethe lattice is solved for binary compounds of arbitrary coordination using simple tightbinding models. In particular systems with tetrahedral coordination, such as the zincblende, BC8, and randomnetwork structures are examined in detail. The results are compared with recent experimental photoemission data on the amorphous phases of binary compounds and interpreted in terms of topology.

[15]

J. D. Joannopoulos, M. chlüter, and M. L. Cohen, “Electronic structure
of trigonal and amorphous Se and Te,” Physical Review B, vol. 11,
pp. 2186–2199, March 1975.
[ bib 
http ]
The electronic structure of trigonal and amorphous Se and Te is investigated using the empirical pseudopotential method (EPM), chargedensity calculations, and simple tightbinding models. Band structures and electronic densities of states are obtained which are in excellent agreement with recent photoemission measurements. The tightbinding models are used to obtain analytic expressions for the energy bands and to interpret the EPM band structures in terms of realspace orbitalorbital interactions. Chargedensity calculations obtained as a function of energy and evaluated within specific energy intervals are used to interpret various structure in the density of states. Specifically certain easily resolvable peaks in the experimental photoemission spectra are associated with intrachain and interchain localized states, respectively. By taking only shortwavelength components of the charge density, a bonding charge can be defined which gives an estimate of the intrachain vs interchain bonding strengths. The trigonal results along with model calculations to investigate the effects of bondangle variations on chains and the presence of eight and sixfold rings of bonds are used to interpret the changes observed in the experimental spectra of amorphous Se and Te. A new model of amorphous Se is proposed.

[14]

J. D. Joannopoulos and F. Yndurain, “Moments and averages of the electronic
density of states of amorphous and crystalline homopolar solids,”
Physics Letters A, vol. 51, pp. 79–80, February 1975.
[ bib 
DOI ]
We have calculated the first fifteen moments of the density of states of the BC8 and ST12 structures and of the Polk random network model. Using these moments we calculate exact averages of the density of states of these structures.

[13]

J. D. Joannopoulos and M. L. Cohen, “Intrinsic surface states of (110)
surfaces of group IV and IIIV semiconductors,” Physical
Review B, vol. 10, pp. 5075–5081, December 1974.
[ bib 
http ]
Electronic local and total density of states calculations have been performed using tight binding models on the (110) surface of a group IV and IIIV semiconductor. Ge and GaAs are taken as prototypes and the surface is assumed to be unrelaxed. Several new surface states are obtained near the bottom of the valence bands. The origin, localization, and character of the surface states are examined.

[12]

J. D. Joannopoulos and F. Yndurain, ““clusterBethelattice” method:
Electronic density of states of amorphous and crystalline homopolar solids,”
Physical Review B, vol. 10, pp. 5164–5174, December 1974.
[ bib 
http ]
A new method is developed to study the electronic density of states of infinite networks of atoms. The method involves treating part of the system exactly as a cluster and simulating the effects of the rest of the environment by connecting a Bethe lattice (Cayley tree) to the surface of the cluster. Calculations show that the local ringlike topologies of each atom are of primary importance in determining structure in the electronic density of states. The densities of states of the diamond, BC8, and ST12 structures are studied in detail using this method. These calculations are in excellent agreement with the exact results. Because of this, the method is used to obtain the density of states of the Polk and Connell randomnetwork models. These models give the same radial distribution functions but exhibit striking differences in their densities of states which are interpreted in terms of topology.

[11]

M. Schlüter, J. D. Joannopoulos, M. L. Cohen, L. Ley, S. P. Kowalczyk,
R. A. Pollak, and D. A. Shirley, “Structural nature of amorphous Se and
Te,” Solid State Communications, vol. 15, pp. 1007–1010, September
1974.
[ bib 
DOI ]
We present new photoemission measurements on amorphous and trigonal Te. These results and other recent photoemission experiments on amorphous and trigonal Se are interpreted using density of states and charge density calculations. These studies result in new insights into the possible structural nature of the amorphous phase.

[10]

J. D. Joannopoulos and M. L. Cohen, “Effects of disorder on the electronic
density of states of IIIV compounds,” Physical Review B, vol. 10,
pp. 1545–1559, August 1974.
[ bib 
http ]
We investigate the effects of two types of disorder on the electronic density of states of IIIV semiconductors using simple tightbinding models and the empirical pseudopotential method. For the first type of disorder we consider a stoichiometric system with fourfold coordination, all bonds satisfied, variations in the bond lengths and angles, and only unlikeatom bonds. The second type of disorder includes the properties of the first with the addition of likeatom bonds. These two types of disorder are studied explicitly by taking GaAs as a prototype and making various GaAs structures using the atomic positions of certain crystal structures with shortrange disorder. These structures are crystals; however, they have atoms in the primitive cells arranged in varying fashions. A comparison of the trends observed in the densities of states with the inclusion of different types of disorder reveals valuable information concerning the relationship of the structural nature of an amorphous system to its density of states. We present a model of the density of states of our amorphous prototype GaAs, for each type of disorder, which we believe would be consistent with some of the present experimental radialdistributionfunction data. The effects of these types of disorder are discussed in general, and hopefully they will be useful in identifying specific types of disorder in amorphous samples.

[9]

F. Yndurain, J. D. Joannopoulos, M. L. Cohen, and L. M. Falicov, “New
theoretical method to study densities of states of tetrahedrally coordinated
solids,” Solid State Communications, vol. 15, pp. 617–620, August
1974.
[ bib 
DOI ]
A new simple method is proposed to calculate local densities of states of arbitrary tetrahedrally coordinated solids. It involves the selection of a finite cluster of atoms connected to an infinite Bethe lattice of coordination four. The method is accurate, is easily handled numerically, and converges fast. Loworder approximations yield sufficient information which is susceptible to consistent physical interpretation. This has been made for the diamond, BC8 and ST12 structures in terms of the ring topology around a given atom. Comparison with exact calculations is very good and the ring interpretation is physical and conceptually appealing.

[8]

J. D. Joannopoulos and M. L. Cohen, “Electronic density of states of amorphous
III–V semiconductors,” Solid State Communications, vol. 15,
pp. 105–108, July 1974.
[ bib 
DOI ]
A shortrange disorder model is used to predict the predominant features of the density of states of amorphous III–V semiconductors. Confirmation of this model would help establish the existence of IIIIII and VV bonds in these materials.

[7]

M. Schlüter, J. D. Joannopoulos, and M. L. Cohen, “New interpretation of
the softXray absorption spectra of several alkali halides,”
Physical Review Letters, vol. 33, pp. 89–91, July 1974.
[ bib 
http ]
New pseudopotential calculations of the densities of states of trigonal Se and Te (in excellent agreement with recent photoemission measurements) are used to show that two easily resolved peaks in the photoemission data are directly related to interchain and intrachain bonding. This identification is accomplished by calculating electronic charge densities as a function of energy for different energy regions. Finally we introduce a new method for determining bonding charges by extracting shortwavelength components of the electronic charge density.

[6]

M. Schlüter, J. D. Joannopoulos, and M. L. Cohen, “New interpretation of
photoemission measurements of trigonal Se and Te,” Physical Review
Letters, vol. 33, p. 337, July 1974.
[ bib 
http ]

[5]

J. D. Joannopoulos and M. L. Cohen, “New insight into the optical properties
of amorphous Ge and Si,” Solid State Communications, vol. 13,
pp. 1115–1118, October 1973.
[ bib 
DOI ]
A short range disorder model, unlike present long range disorder theories, has been able to account well for both the density of states and the optical properties of amorphous Ge and Si. Our results indicate that the imaginary part of the dielectric function for amorphous Ge and Si has the same form as an averaged gradient matrix element as a function of energy. This conclusion should be valid for all tetrahedrally bonded amorphous solids.

[4]

J. D. Joannopoulos and M. L. Cohen, “Electronic properties of complex
crystalline and amorphous phases of Ge and Si. II. band structure and
optical properties,” Physical Review B, vol. 8, pp. 2733–2755,
September 1973.
[ bib 
http ]
We present calculations of the band structures and the imaginary part of the dielectric function ε2 as a function of energy for Ge and Si in the diamond, wurtzite, SiIII (BC8) and GeIII (ST12) structures using the empirical pseudopotential method. In particular we have obtained the symmetries of wave functions along important symmetry directions and identified the major contributions to the optical structure. A further study is made into the optical properties of amorphous Ge and Si using our shortrangedisorder model. We find that, unlike longrangedisorder models, shortrange disorder can explain both the amorphous density of states and the amorphous ɛ_{2}. In particular we find that the ɛ_{2} spectrum has the same form as an averaged matrix element as a function of frequency.

[3]

J. D. Joannopoulos and M. L. Cohen, “Electronic properties of complex
crystalline and amorphous phases of Ge and Si. I. density of states and
band structures,” Physical Review B, vol. 7, pp. 2644–2657, March
1973.
[ bib 
http ]
We present calculations of the band structures and densities of states of Ge and Si in the diamond, wurzite, SiIII (BC8), and GeIII (ST12) structures using the empiricalpseudopotential method and the tightbinding model used recently by Weaire. The increasing complexity of the crystal structures indicates that shortrange disorder is able to account well for the density of states and optical properties of amorphous Ge and Si. This calculation also provides a method for explaining various features in the amorphous density of states and shows what structural aspects of the amorphous state are responsible for these features.

[2]

R. A. Pollak, L. Ley, S. Kowalczyk, D. A. Shirley, J. D. Joannopoulos, D. J.
Chadi, and M. L. Cohen, “Xray photoemission valenceband spectra and
theoretical valenceband densities of states for Ge, GaAs, and ZnSe,”
Physical Review Letters, vol. 29, pp. 1103–1105, October 1972.
[ bib 
http ]
The first highresolution valenceband xray photoemission spectra for Ge, GaAs, and ZnSe are compared with pseudopotential densityofstates calculations. The general agreement between the experimental and theoretical results is quite good. For ZnSe the photoemission spectrum shows the Zn 3d states to be higher in energy than the lowest valenceband s state. In order to obtain this ordering of states in the theoretical calculation, a pseudopotential with an explicit energy dependence is required.

[1]

J. D. Joannopoulos and M. L. Cohen, “Comparison of the electronic structure of
amorphous and crystalline polytopes of Ge,” Solid State
Communications, vol. 11, pp. 549–553, August 1972.
[ bib 
DOI ]
We have calculated the density of states and the imaginary part of the dielectric constant as a function of energy for four polytypes of Ge using the EPM and the tight binding model developed by Weaire. The increasing complexity of the crystal structures indicates that short range disorder is able to account well for the optical properties and density of states of amorphous Ge. Furthermore, we predict the form of the optical properties and density of states for Ge III and Ge IV.
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