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Full-Text Articles in Physics

Polariton And Free-Exciton-Like Photoluminescence In Zno, D. C. Reynolds, David C. Look, B. Jogai, T. C. Collins Dec 2001

Polariton And Free-Exciton-Like Photoluminescence In Zno, D. C. Reynolds, David C. Look, B. Jogai, T. C. Collins

Physics Faculty Publications

An unusual photoluminescence line X has been observed in ZnO at an energy between that of the common donor-bound excitons (DBEs) and the free excitons (FEs). In the presence of a high carrier concentration, induced by a second below-band gap laser, the DBEs decrease in intensity, due to screening, and both the FEs and X increase. Thus, X has free-exciton, rather than bound-exciton, character. However, its electric-field vector lies in the plane perpendicular to the c axis, as is also found for the DBEs. The appearance of X is discussed in terms of the polariton picture.


Semiclassical Scattering Of An Electric Dipole Source Inside A Spherical Particle, James A. Lock Dec 2001

Semiclassical Scattering Of An Electric Dipole Source Inside A Spherical Particle, James A. Lock

Physics Faculty Publications

Semiclassical scattering phenomena appearing in the far-zone scattered intensity of a point source of electromagnetic radiation inside a spherical particle are examined in the context of both ray theory and wave theory, and the evolution of the phenomena is studied as a function of source position. A number of semiclassical effects that do not occur for plane-wave scattering by the sphere appear prominently for scattering by an interior source. These include a series of scattering resonances and a new family of rainbows in regions of otherwise total internal reflection. Diffractive effects accompanying the semiclassical phenomena are also examined. (C) 2001 …


Terahertz Gain In A Sige/Si Quantum Staircase Utilizing The Heavy-Hole Inverted Effective Mass, Richard A. Soref, Greg Sun Nov 2001

Terahertz Gain In A Sige/Si Quantum Staircase Utilizing The Heavy-Hole Inverted Effective Mass, Richard A. Soref, Greg Sun

Physics Faculty Publications

Modeling and design studies show that a strain-balanced Si1−xGex/Si superlattice onSi1−yGey-buffered Si can be engineered to give an inverted effective mass HH2 subband adjacent to HH1, thereby enabling a 77 K edge-emitting electrically pumped pipquantum staircase laser for THz emission at energies below the 37 meV Ge–Ge optical phonon energy. Analysis of hole-phonon scattering, lifetimes, matrix elements, and hole populations indicates that a gain of 450 cm−1 will be feasible at f = 7.3 THz during 1.7 kA/cm2 current injection.


Thermal Stability Of Isolated And Complexed Ga Vacancies In Gan Bulk Crystals, K. Saarinen, T. Suski, I. Grzegory, David C. Look Nov 2001

Thermal Stability Of Isolated And Complexed Ga Vacancies In Gan Bulk Crystals, K. Saarinen, T. Suski, I. Grzegory, David C. Look

Physics Faculty Publications

We have applied positron annihilation spectroscopy to show that 2-MeV electron irradiation at 300 K creates primary Ga vacancies in GaN with an introduction rate of 1 cm-1. The Ga vacancies recover in long-range migration processes at 500–600 K with an estimated migration energy of 1.5 (2) eV. Since the native Ga vacancies in as-grown GaN survive up to much higher temperatures (1300–1500 K), we conclude that they are stabilized by forming complexes with oxygen impurities. The estimated binding energy of 2.2 (4) eV of such complexes is in good agreement with the results of theoretical calculations.


Electrical Characterization Of 1.8 Mev Proton-Bombarded Zno, F. D. Auret, S. A. Goodman, M. Hayes, M. J. Legodi, H. A. Van Laarhoven, David C. Look Nov 2001

Electrical Characterization Of 1.8 Mev Proton-Bombarded Zno, F. D. Auret, S. A. Goodman, M. Hayes, M. J. Legodi, H. A. Van Laarhoven, David C. Look

Physics Faculty Publications

We report on the electrical characterization of single-crystal ZnO and Au Schottky contacts formed thereon before and after bombarding them with 1.8 MeV protons. From capacitance–voltage measurements, we found that ZnO is remarkably resistant to high-energy proton bombardment and that each incident proton removes about two orders of magnitude less carriers than in GaN. Deep level transient spectroscopy indicates a similar effect: the two electron traps detected are introduced in extremely low rates. One possible interpretation of these results is that the primary radiation-induced defects in ZnO may be unstable at room temperature and anneal out without leaving harmful defects …


Design And Construction Of A Space-Borne Optical Tweezer Apparatus, Andrew Resnick Nov 2001

Design And Construction Of A Space-Borne Optical Tweezer Apparatus, Andrew Resnick

Physics Faculty Publications

A compact optical tweezer package has been developed for use on a microscope to be flown on the International Space Station as part of a series of experiments in colloid crystallization. A brief introduction to the principles of single-beam optical tweezer operation will be presented, after which a detailed system layout will be shown. Special design requirements due to the spaceflight nature of the hardware will also be discussed. The tweezer apparatus is capable of trapping many particles through use of a two-axis acousto-optical deflector. The trap strength is sufficient to perform the required science (50 pN at Δn=0.2). The …


Solar Activity Variations Of The Venus Thermosphere/Ionosphere, Jane L. Fox, K. Y. Sung Oct 2001

Solar Activity Variations Of The Venus Thermosphere/Ionosphere, Jane L. Fox, K. Y. Sung

Physics Faculty Publications

We present models of the low and high solar activity thermospheres and ionospheres of Venus for a background atmosphere based largely on the VTS3 model of Hedin et al. [1983]. Our background model consists of 12 neutral species, and we compute the density profiles of 13 ions and 7 minor neutrals. We find that the peak production rates of some ions, such as CO2+ and N2+, vary approximately as the solar flux and that some, whose parent neutrals are photochemically produced, such as O+, N+, and C+, show variations …


Hot Carbon Densities In The Exosphere Of Mars, Andrew F. Nagy, Michael W. Liemohn, Jane L. Fox, Jhoon Kim Oct 2001

Hot Carbon Densities In The Exosphere Of Mars, Andrew F. Nagy, Michael W. Liemohn, Jane L. Fox, Jhoon Kim

Physics Faculty Publications

Theoretical results of hot carbon densities in the exosphere of Mars are presented. The calculation is a two-step process: First a two-stream transport code is used to solve for the distribution function at the exobase, and then these results are used in a Liouville equation solution above the exobase. It is found that photodissociation of carbon monoxide is the largest source of hot carbon atoms in the upper atmosphere of Mars, larger than dissociative recombination of CO+ and much larger than the creation of hot carbon through collisions with hot oxygen atoms. It is also found that the high …


Photochemical Escape Of Atomic Carbon From Mars, Jane L. Fox, F. M. Bakalian Oct 2001

Photochemical Escape Of Atomic Carbon From Mars, Jane L. Fox, F. M. Bakalian

Physics Faculty Publications

We have modeled the escape fluxes of atomic carbon from the Martian atmosphere for low and high solar activities due to various photochemical escape mechanisms, including photodissociation of CO, dissociative recombination of CO+, electron impact dissociation and dissociative ionization of CO, photodissociative ionization of CO, and dissociative charge transfer of O++ to CO. Only photodissociation of CO and dissociative recombination of CO+ are found to be important, and the time-averaged escape flux is predicted to be controlled by the high solar activity values. The computed global average escape fluxes of C due to photodissociation of CO …


Quantal Density Functional Theory Of Excited States, Viraht Sahni, Lou Massa, Ranbir Singh, Marlina Slamet Sep 2001

Quantal Density Functional Theory Of Excited States, Viraht Sahni, Lou Massa, Ranbir Singh, Marlina Slamet

Physics Faculty Publications

We explain by quantal density functional theory the physics of mapping from any bound nondegenerate excited state of Schrödinger theory to an S system of noninteracting fermions with equivalent density and energy. The S system may be in a ground or excited state. In either case, the highest occupied eigenvalue is the negative of the ionization potential. We demonstrate this physics with examples. The theory further provides a new framework for calculations of atomic excited states including multiplet structure.


Electric Field Autocorrelation Functions For Beginning Multiple Rayleigh Scattering, James A. Lock Aug 2001

Electric Field Autocorrelation Functions For Beginning Multiple Rayleigh Scattering, James A. Lock

Physics Faculty Publications

The polarization-resolved electric field autocorrelation function for p-order scattering was derived from the order-of-scattering solution of the exact equations for electromagnetic multiple Rayleigh scattering and was calculated for 2 less than or equal to p less than or equal to 6 for particles undergoing diffusive motion in an idealized sample cell. It was found that the polarization-channel and the scattering-angle dependence of the p-order autocorrelation function approximately decoupled from the delay-time dependence for p greater than or similar to 3. The polarization-channel and the scattering-angle dependence were analytically calculated, and the delay-time dependence was analytically approximated. The resulting analytical model …


Predicted Maximum Mobility In Bulk Gan, David C. Look, J. R. Sizelove Aug 2001

Predicted Maximum Mobility In Bulk Gan, David C. Look, J. R. Sizelove

Physics Faculty Publications

A 300 K bulk (three-dimensional) mobility of 1245 cm2/V s has been measured in free-standing GaN. Temperature-dependent Hall-effect data on this particular sample are fitted to obtain unknown lattice-scattering parameters, as well as shallow donor (ND) and acceptor (NA) concentrations, which are ND = 6.7×1015 and NA = 1.7×1015 cm−3. Realistic values of the maximum mobility attainable in bulk GaN are then obtained by assuming two-orders-of-magnitude lower values of ND and NA, leading to a maximum 300 K mobility of 1350 cm2 …


X-Ray Photoelectron Spectroscopy (Xps) And Magnetization Studies Of Iron–Vanadium Phosphate Glasses, M. A. Salim, G. D. Khattak, Petru S. Fodor, Lowell E. Wenger Aug 2001

X-Ray Photoelectron Spectroscopy (Xps) And Magnetization Studies Of Iron–Vanadium Phosphate Glasses, M. A. Salim, G. D. Khattak, Petru S. Fodor, Lowell E. Wenger

Physics Faculty Publications

Vanadium phosphate glasses containing Fe2O3 with the chemical composition [(Fe2O3)x(V2O5)0.6−x(P2O5)0.4], where x=0.00, 0.10, 0.20, 0.25 and 0.30, have been prepared and investigated by X-ray photoelectron spectroscopy (XPS) and magnetic susceptibility measurements. The core level binding energies of V 2p, Fe 2p, P 2p and P 2s in the Fe2O3–vanadium phosphate glasses have been measured and shifts from the corresponding binding energies measured for V2O5, Fe2O3 and P2O5 powders are accounted for by changes in the next-nearest neighbor environment of these atoms in the P4O10 local structure. The O 1s spectra for the glasses are single, symmetric peaks arising from nearly …


Characterization Of Near-Surface Traps In Semiconductors: Gan, David C. Look, Z-Q. Fang Jul 2001

Characterization Of Near-Surface Traps In Semiconductors: Gan, David C. Look, Z-Q. Fang

Physics Faculty Publications

We present a simple a criterion, based on deep-level transient spectroscopy peak heights S(Vr) at two or more values of reverse bias Vr, to unequivocally determine whether or not a particular semiconductor trap is of bulk or near-surface nature. Moreover, we present an expression for S(Vr) with fitting parameters ϕB, the Schottky barrier height; δ, the trap penetration depth; and NT, the trap density. Application of the method to a thick, high-quality, epitaxial GaN layer, reveals two common traps which penetrate only 2700±300 Å into the …


Evidence For Shallow Acceptors In Gan, D. C. Reynolds, David C. Look, B. Jogai, Richard J. Molnar Jun 2001

Evidence For Shallow Acceptors In Gan, D. C. Reynolds, David C. Look, B. Jogai, Richard J. Molnar

Physics Faculty Publications

Two low-temperature photoluminescence lines in GaN, in the region of energies commonly interpreted as longitudinal optical-phonon replicas of free excitons, donor-bound excitons, or acceptor-bound excitons, are reinterpreted as acceptor-bound excitons (A0X’s) collapsing to n=2 and n=3 excited states, respectively, of the acceptors involved. Application of this model to two sets of A0X-related lines in hydride-vapor-phase-grown GaN gives acceptor energies of 85±1, and 115±1 meV, respectively. The existence of such shallow acceptor states, if confirmed, is of great technological importance.


Fine Structure On The Green Band In Zno, D. C. Reynolds, David C. Look, B. Jogai Jun 2001

Fine Structure On The Green Band In Zno, D. C. Reynolds, David C. Look, B. Jogai

Physics Faculty Publications

An emission band at 2.4 eV, called the green band, is observed in most ZnO samples, no matter what growth technique is used. Sometimes this band includes fine structure, which consists mainly of doublets, repeated with a longitudinal-optical-phonon-energy spacing (72 meV). We have developed a vibronic model for the green band, based on transitions from two separate shallow donors to a deep acceptor. The donors, at energies 30 and 60 meV from the conduction-band edge, respectively, are also found from Hall-effect measurements.


Microcathodoluminescence Of Impurity Doping At Gallium Nitride/Sapphire Interfaces, S. H. Goss, X. L. Sun, A. P. Young, L. J. Brillson, David C. Look, Richard J. Molnar Jun 2001

Microcathodoluminescence Of Impurity Doping At Gallium Nitride/Sapphire Interfaces, S. H. Goss, X. L. Sun, A. P. Young, L. J. Brillson, David C. Look, Richard J. Molnar

Physics Faculty Publications

We have used low-temperature cathodoluminescence spectroscopy (CLS) to probe the spatial distribution and energies of electronic defects near GaN/Al2O3 interfaces grown by hydride vapor phase epitaxy (HVPE). Cross sectional secondary electron microscopy CLS shows systematic variations in impurity/defect emissions over a wide range of HVPE GaN/Sapphire electronic properties. These data, along with electrochemical capacitance–voltage profiling and secondary ion mass spectrometry, provide a consistent picture of near-interface doping by O diffusion from Al2O3 into GaN, over a range 100–1000 nm.


Phonon-Pumped Terahertz Gain In N-Type Gaas/Algaas Superlattices, Greg Sun, Richard A. Soref May 2001

Phonon-Pumped Terahertz Gain In N-Type Gaas/Algaas Superlattices, Greg Sun, Richard A. Soref

Physics Faculty Publications

Local population inversion and far-IR gain are proposed and theoretically analyzed for an unbiased n-doped GaAs/Al0.15Ga0.85As superlattice pumped solely by phonons. The lasing transition occurs at the Brillouin zone boundary of the superlattice wave vector kzbetween the two conduction minibands CB1 and CB2 of the opposite curvature in kzspace. The proposed waveguided structure is contacted above and below by heat sinks at 300 K and 77 K, respectively. Atop the superlattice, a heat buffer layer confines longitudinal optical phonons for enhanced optical-phonon pumping of CB1 electrons. A gain of 345 cm …


Supernumerary Spacing Of Rainbows Produced By An Elliptical-Cross-Section Cylinder. Ii. Experiment, Charles L. Adler, David Phipps, Kirk W. Saunders, Justin K. Nash, James A. Lock May 2001

Supernumerary Spacing Of Rainbows Produced By An Elliptical-Cross-Section Cylinder. Ii. Experiment, Charles L. Adler, David Phipps, Kirk W. Saunders, Justin K. Nash, James A. Lock

Physics Faculty Publications

We measured the supernumerary spacing parameter of the first- and second-order rainbows of two glass rods, each having an approximately elliptical cross section, as a function of the rod's rotation angle. We attribute large fluctuations in the supernumerary spacing parameter to small local inhomogeneities in the rod's refractive index. The low-pass filtered first-order rainbow experimental data agree with the prediction of ray-tracing-wave-front modeling to within a few percent, and the second-order rainbow data exhibit additional effects that are due to rod nonellipticity. (C) 2001 Optical Society of America.


Deep Centers In A Free-Standing Gan Layer, Z-Q. Fang, David C. Look, P. Visconti, D. F. Wang, C. Z. Lu, F. Yun, H. Morkoç, Seong-Ju S. Park, K. Y. Lee Apr 2001

Deep Centers In A Free-Standing Gan Layer, Z-Q. Fang, David C. Look, P. Visconti, D. F. Wang, C. Z. Lu, F. Yun, H. Morkoç, Seong-Ju S. Park, K. Y. Lee

Physics Faculty Publications

Schottky barrier diodes, on both Ga and N faces of a ∼300-μm-thick free-standing GaN layer, grown by hydride vapor phase epitaxy (HVPE) on Al2O3 followed by laser separation, were studied by capacitance–voltage and deep level transient spectroscopy (DLTS) measurements. From a 1/C2 vs V analysis, the barrier heights of Ni/Au Schottky contacts were determined to be different for the two polar faces: 1.27 eV for the Ga face, and 0.75 eV for the N face. In addition to the four common DLTS traps observed previously in other epitaxial GaN including HVPE-grown GaN a new trap …


Experimental Observation Of Rainbow Scattering By A Coated Cylinder: Twin Primary Rainbows And Thin-Film Interference, Charles L. Adler, James A. Lock, Justin K. Nash, Kirk W. Saunders Mar 2001

Experimental Observation Of Rainbow Scattering By A Coated Cylinder: Twin Primary Rainbows And Thin-Film Interference, Charles L. Adler, James A. Lock, Justin K. Nash, Kirk W. Saunders

Physics Faculty Publications

We experimentally examine the primary rainbow created by the illumination of a coated cylinder. We present a simple technique for varying the coating thickness over a wide range of values, and we see evidence for two different scattering regimes. In one, where the coating thickness is large, twin rainbows are produced. In the second, where the coating is thin enough to act as a thin film, a single rainbow is produced whose intensity varies periodically as the coating thickness varies. We find good agreement with previous theoretical predictions. (C) 2001 Optical Society of America.


High Mobility In N-Type Gan Substrates, A. Saxler, David C. Look, S. Elhamri, J. R. Sizelove, William C. Mitchel, C. M. Sung, S. S. Park, K. Y. Lee Mar 2001

High Mobility In N-Type Gan Substrates, A. Saxler, David C. Look, S. Elhamri, J. R. Sizelove, William C. Mitchel, C. M. Sung, S. S. Park, K. Y. Lee

Physics Faculty Publications

No abstract provided.


Nonvolatile Grating In An Azobenzene Polymer With Optimized Molecular Reorientation, Pengfei Wu, D.V.G.L.N. Rao, B. R. Kimball, M. Nakashima, B. S. Decristofano Feb 2001

Nonvolatile Grating In An Azobenzene Polymer With Optimized Molecular Reorientation, Pengfei Wu, D.V.G.L.N. Rao, B. R. Kimball, M. Nakashima, B. S. Decristofano

Physics Faculty Publications

We demonstrated a nonvolatile grating using an azobenzene polymer film with polarized two color beams. The reorientation of azobenzene molecules can be optimized when the two color light beams are polarized perpendicularly. The stored information can be read repeatedly without volatility with the same wavelength as the writing beam.


Sige/Si Thz Laser Based On Transitions Between Inverted Mass Light-Hole And Heavy-Hole Subbands, L. Friedman, Greg Sun, Richard A. Soref Jan 2001

Sige/Si Thz Laser Based On Transitions Between Inverted Mass Light-Hole And Heavy-Hole Subbands, L. Friedman, Greg Sun, Richard A. Soref

Physics Faculty Publications

We have investigated a SiGe/Si quantum-well laser based on transitions between the light-hole and heavy-hole subbands. The lasing occurs in the region of k space where the dispersion of ground-state light-hole subband is so nonparabolic that its effective mass is inverted. This kind of lasing mechanism makes total population inversion between the two subbands unnecessary. The laser structure can be electrically pumped through tunneling in a quantum cascade scheme. Optical gain as high as 172/cm at the wavelength of 50 μm can be achieved at the temperature of liquid nitrogen, even when the population of the upper laser subband is …


Multilayer Mim Inversion Of Aem Data: Theory And Field Example, Clyde J. Bergeron Jr, Juliette W. Ioup, Yan Wu, George E. Ioup, Kenneth W. Holladay Jan 2001

Multilayer Mim Inversion Of Aem Data: Theory And Field Example, Clyde J. Bergeron Jr, Juliette W. Ioup, Yan Wu, George E. Ioup, Kenneth W. Holladay

Physics Faculty Publications

This paper presents a multilayer generalization of an algebraic method of inverting frequency-doma in airborne active electromagnetic (AEM) data in terms of 1-D layered earth models. The processing of the AEM data, which includes a recalibration procedure, is also outlined. The inversion is applied to synthetic fields generated from a multilayer model which is intended to approximate a measured conductivity profile of the water column in the Gulf of Mexico and to measured AEM data from a survey of the Barataria Bay estuary region of the Louisiana Gulf of Mexico coast. The inversion results from the synthetic data are in …


Evolution Of Deep Centers In Gan Grown By Hydride Vapor Phase Epitaxy, Z-Q. Fang, David C. Look, J. Jasinski, M. Benamara, Z. Liliental-Weber, Richard J. Molnar Jan 2001

Evolution Of Deep Centers In Gan Grown By Hydride Vapor Phase Epitaxy, Z-Q. Fang, David C. Look, J. Jasinski, M. Benamara, Z. Liliental-Weber, Richard J. Molnar

Physics Faculty Publications

Deep centers and dislocation densities in undoped n GaN, grown by hydride vapor phase epitaxy (HVPE), were characterized as a function of the layer thickness by deep level transient spectroscopy and transmission electron microscopy, respectively. As the layer thickness decreases, the variety and concentration of deep centers increase, in conjunction with the increase of dislocation density. Based on comparison with electron-irradiation induced centers, some dominant centers in HVPE GaN are identified as possible point defects.


Exclusive Electroproduction Of ᵠ Mesons At 4.2 Gev, M. Bektasoglu, L. Ciciani, G. E. Dodge, T. A. Forest, C. E. Hyde-Wright, S. E. Kuhn, L. M. Qin, F. Sabatié, L. B. Weinstein, Et Al., The Clas Collaboration Jan 2001

Exclusive Electroproduction Of ᵠ Mesons At 4.2 Gev, M. Bektasoglu, L. Ciciani, G. E. Dodge, T. A. Forest, C. E. Hyde-Wright, S. E. Kuhn, L. M. Qin, F. Sabatié, L. B. Weinstein, Et Al., The Clas Collaboration

Physics Faculty Publications

We studied the exclusive reaction ep → e' p' ᵠ using the ᵠ →K+K- decay mode. The data were collected using a 4.2 GeV incident electron beam and the CEBAF Large Acceptance Spectrometer (CLAS) at the Thomas Jefferson National Accelerator Facility. Our experiment covers the range in Q2 from 0.7 to 2.2 GeV2and W from 2.0 to 2.6 GeV. Taken together with all previous data, we find a consistent picture of ᵠ production on the proton. Our measurement shows the expected decrease of the t slope with the vector-meson formation time c Δ t …


Gamma Echo Interpreted As A Phase-Shift Induced Transparency, Gilbert R. Hoy, Jos Odeurs Jan 2001

Gamma Echo Interpreted As A Phase-Shift Induced Transparency, Gilbert R. Hoy, Jos Odeurs

Physics Faculty Publications

In the gamma-echo technique a radioactive source is moved, with respect to a nuclear-resonant absorber, during the lifetime of first-excited nuclear state. This introduces a phase shift between the source radiation and the radiation from the absorber. If the source is moved abruptly, introducing a pi phase shift, the time-dependent intensity shows a sharp increase in the intensity at that time, the "gamma echo." Using the recently developed one-dimensional quantum-mechanical model, based on the technique developed by Heitler and Harris, the gamma-echo effect is seen to be a phase-shift-induced transparency. A closed-form solution for the time-dependent transmitted intensity has been …


Effective Field Theory For The Small-X Evolution, I. Balitsky Jan 2001

Effective Field Theory For The Small-X Evolution, I. Balitsky

Physics Faculty Publications

The small-x behavior of structure functions in the saturation region is determined by the non-linear generalization of the BFKL equation. I suggest the effective field theory for the small-x evolution which solves formally this equation. The result is the 2+1 functional integral for the structure functions at small x.


Coherent-Path Model For Nuclear Resonant Scattering Of Gamma Radiation From Nuclei Excited By Synchrotron Radiation, Gilbert R. Hoy, Jos Odeurs, Romain Coussement Jan 2001

Coherent-Path Model For Nuclear Resonant Scattering Of Gamma Radiation From Nuclei Excited By Synchrotron Radiation, Gilbert R. Hoy, Jos Odeurs, Romain Coussement

Physics Faculty Publications

Previous theoretical descriptions of nuclear resonant scattering of synchrotron radiation have been based on the semiclassical optical model or on several quantum mechanical models. These models are fine but do not give a clear physical picture of all the processes. The theory presented here gives a clear physical picture of all the relevant aspects of nuclear resonant scattering. The model treats the nuclear resonant sample as a one-dimensional chain of "effective" nuclei. However, the model is deceptive. It only appears to be one dimensional. It actually treats the sample as a series of "effective" planes. The analysis uses the time-dependent …