This document summarizes research on the electronic structure of aluminum nitride (AlN) through theoretical calculations and vacuum ultraviolet spectroscopy experiments. Key findings include:
1) The experimental results show features at 8.7 eV and 14 eV associated with two-dimensional critical points related to electronic transitions.
2) Theoretical calculations using density functional theory predict a direct bandgap at the gamma point of 4.5 eV, lower than the experimental value of 6.3 eV, as is common for DFT.
3) Both experiment and theory were modeled using sets of critical points, with good agreement between predicted and observed energies for transitions between nitrogen 2p and aluminum 3s states, and some discrepancy for higher-
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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This paper presents an intelligent control method for the maximum power point tracking (MPPT) of a
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optimization algorithm is a new optimization method that relies on the Big Bang and Big Crunch theory, one of the
theories of the evolution of the universe. In this paper, a Big Bang–Big Crunch algorithm is presented to meet the
maximum power operating point whatever the climatic conditions are from simulation results, it has been found that
BB–BC method is highly competitive for its better convergence performance.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Structural, Electronic and Gamma Shielding Properties of BxAl1-xAsIJMERJOURNAL
ABSTRACT: The structural and electronic properties of BxAl1-xAs ternary alloys in the zincblende structure were systematically investigated by using the first principles calculations. The local density approximation was used for exchanged and correlation interaction. The calculated band gap bowing parameter was discovered to be mightily composition dependent of the Boron concentration. Additionally, we have calculated some gamma shielding parameters of BxAl1-xAs ternary alloys. Primarily, the values of mass attenuation coefficients (μρ) were calculated using WinXCom computer program and then these parameters were utilized to calculate the values of electron density (Nel) and effective atomic number (Zeff) in the wide energy range (1 keV - 100 GeV).
Big Bang–Big Crunch Optimization Algorithm for the Maximum Power Point Track...IJMER
This paper presents an intelligent control method for the maximum power point tracking (MPPT) of a
photovoltaic system under variable temperature and irradiance conditions. The Big Bang–Big Crunch (BB–BC)
optimization algorithm is a new optimization method that relies on the Big Bang and Big Crunch theory, one of the
theories of the evolution of the universe. In this paper, a Big Bang–Big Crunch algorithm is presented to meet the
maximum power operating point whatever the climatic conditions are from simulation results, it has been found that
BB–BC method is highly competitive for its better convergence performance.
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spectroscopical method used on optical light sources where it is possible to organize atomic and ionic data.
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it seems to be possible to organize the luminosity of stars from different spectral classes. From that organization
it is possible to determine the temperature , density and mass of stars by using the new intensity formula. These
temperature, density and mass values agree well with literature values. It is also possible to determine the mean
electron temperature of the optical layers (photospheres) of the stars as it is for atoms in the for laboratory
plasmas. The mean value of the ionization energies of the different elements of the stars has shown to be very
significant for each star. This paper also shows that the hydrogen Balmer absorption lines in the stars follow
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transfer equation respectively. Temperature dependent material properties are used for this analysis. This
analysis includes coil voltage distribution, crucible electromagnetic power, and coil equivalent impedance
at different frequency. Induction coil geometry effect on supply voltage is also analyzed. This analysis is
useful for designing of induction coil for melting of nonferrous metal such as gold, silver, uranium etc.
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properties electric of InN/Si and AlGaN/Si photodectors with 0.2 μm of AlGaN and InN layers.
Modeling and simulation were performed by using ATLAS-TCAD simulator. Energy band
diagram, doping profile, conduction current density,I-V caracteristic , internal potential and
electric field were performed.
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molecular beam epitaxy are reported. Growth details are described,the comparison enters the
properties electric of InN/Si and AlGaN/Si photodectors with 0.2 µm of AlGaN and InN layers.
Modeling and simulation were performed by using ATLAS-TCAD simulator. Energy band
diagram, doping profile, conduction current density,I-V caracteristic , internal potential and
electric field were performed
Simulation Of Algan/Si And Inn/Si Electric - Devicesijrap
In this work, efficient solar-blind metal-semiconductor photodetectors grown on Si (111) by
molecular beam epitaxy are reported. Growth details are described,the comparison enters the
properties electric of InN/Si and AlGaN/Si photodectors with 0.2 µm of AlGaN and InN layers.
Modeling and simulation were performed by using ATLAS-TCAD simulator. Energy band
diagram, doping profile, conduction current density,I-V caracteristic , internal potential and
electric field were performed.
Stellar Measurements with the New Intensity FormulaIOSR Journals
In this paper a linear relationship in stellar optical spectra has been found by using a
spectroscopical method used on optical light sources where it is possible to organize atomic and ionic data.
This method is based on a new intensity formula in optical emission spectroscopy (OES). Like the HR-diagram ,
it seems to be possible to organize the luminosity of stars from different spectral classes. From that organization
it is possible to determine the temperature , density and mass of stars by using the new intensity formula. These
temperature, density and mass values agree well with literature values. It is also possible to determine the mean
electron temperature of the optical layers (photospheres) of the stars as it is for atoms in the for laboratory
plasmas. The mean value of the ionization energies of the different elements of the stars has shown to be very
significant for each star. This paper also shows that the hydrogen Balmer absorption lines in the stars follow
the new intensity formula.
Transient Numerical Analysis of Induction Heating of Graphite Cruciable at Di...ijeljournal
Mathematical modeling of Induction heating process is done by using 2D axisymmetric geometry.
Induction heating is coupled field problem that includes electromagnetism and heat transfer. Mathematical
modeling of electromagnetism and heat transfer is done by using maxwell equations and classical heat
transfer equation respectively. Temperature dependent material properties are used for this analysis. This
analysis includes coil voltage distribution, crucible electromagnetic power, and coil equivalent impedance
at different frequency. Induction coil geometry effect on supply voltage is also analyzed. This analysis is
useful for designing of induction coil for melting of nonferrous metal such as gold, silver, uranium etc.
Simulation of AlGaN/Si and InN/Si ELECTRIC –DEVICESijrap
In this work, efficient solar-blind metal-semiconductor photodetectors grown on Si (111) by
molecular beam epitaxy are reported. Growth details are described,the comparison enters the
properties electric of InN/Si and AlGaN/Si photodectors with 0.2 μm of AlGaN and InN layers.
Modeling and simulation were performed by using ATLAS-TCAD simulator. Energy band
diagram, doping profile, conduction current density,I-V caracteristic , internal potential and
electric field were performed.
Simulation of AlGaN/Si and InN/Si ELECTRIC –DEVICESijrap
In this work, efficient solar-blind metal-semiconductor photodetectors grown on Si (111) by
molecular beam epitaxy are reported. Growth details are described,the comparison enters the
properties electric of InN/Si and AlGaN/Si photodectors with 0.2 µm of AlGaN and InN layers.
Modeling and simulation were performed by using ATLAS-TCAD simulator. Energy band
diagram, doping profile, conduction current density,I-V caracteristic , internal potential and
electric field were performed
Simulation Of Algan/Si And Inn/Si Electric - Devicesijrap
In this work, efficient solar-blind metal-semiconductor photodetectors grown on Si (111) by
molecular beam epitaxy are reported. Growth details are described,the comparison enters the
properties electric of InN/Si and AlGaN/Si photodectors with 0.2 µm of AlGaN and InN layers.
Modeling and simulation were performed by using ATLAS-TCAD simulator. Energy band
diagram, doping profile, conduction current density,I-V caracteristic , internal potential and
electric field were performed.
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Analytical, Numerical and Experimental Validation of Coil Voltage in Inductio...ijeljournal
This paper presents, mathematical model of induction heating process by using analytical and numerical methods. In analytical method, series equivalent circuit (SEC) is used to represent induction coil and work piece. Induction coil and workpiece parameters (resistance and reactance) are calculated by standard formulas along with Nagaoka correction factors and Bessel functions. In Numerical method, magnetic vector potential formulation is done and finite element method (FEM) is used to solve the field equations. Analytically and numerically computed parameters such as equivalent coil resistance, reactance, coil voltage, work piece power are compared and found that they are in good agreement. Analytically and numerically obtained coil voltages at different frequencies are validated by experimental results. This mathematical model is useful for coil design and optimization of induction heating process.
ANALYTICAL, NUMERICAL AND EXPERIMENTAL VALIDATION OF COIL VOLTAGE IN INDUCTIO...ijeljournal
This paper presents, mathematical model of induction heating process by using analytical and numerical
methods. In analytical method, series equivalent circuit (SEC) is used to represent induction coil and work
piece. Induction coil and workpiece parameters (resistance and reactance) are calculated by standard
formulas along with Nagaoka correction factors and Bessel functions. In Numerical method, magnetic
vector potential formulation is done and finite element method (FEM) is used to solve the field equations.
Analytically and numerically computed parameters such as equivalent coil resistance, reactance, coil
voltage, work piece power are compared and found that they are in good agreement. Analytically and
numerically obtained coil voltages at different frequencies are validated by experimental results. This
mathematical model is useful for coil design and optimization of induction heating process.
ANALYTICAL, NUMERICAL AND EXPERIMENTAL VALIDATION OF COIL VOLTAGE IN INDUCTIO...ijeljournal
This paper presents, mathematical model of induction heating process by using analytical and numerical
methods. In analytical method, series equivalent circuit (SEC) is used to represent induction coil and work
piece. Induction coil and workpiece parameters (resistance and reactance) are calculated by standard
formulas along with Nagaoka correction factors and Bessel functions. In Numerical method, magnetic
vector potential formulation is done and finite element method (FEM) is used to solve the field equations.
Analytically and numerically computed parameters such as equivalent coil resistance, reactance, coil
voltage, work piece power are compared and found that they are in good agreement. Analytically and
numerically obtained coil voltages at different frequencies are validated by experimental results. This
mathematical model is useful for coil design and optimization of induction heating process.
Simulation and Analysis of III V Characteristic and Bandgap Design for Hetero...ijtsrd
This research is the analysis of computer based simulation design for the semiconductor laser diode. The paper is emphasized by analyzing the band structure and voltage current characteristics of AlGaAs GaAs for the laser diode. In this paper, bandgap variation temperature dependence, voltage current V I , band diagram of the p n junction for laser diode are discussed briefly. On the other hand, this paper is emphasized band structure design and voltage current calculation using the mathematical model. The AlGaAs GaAs device technology is used for high speed optical communication. Thu Rein Ye Yint Win | Tin Tin Hla "Simulation and Analysis of III-V Characteristic and Bandgap Design for Heterojunction Laser Diode" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26542.pdfPaper URL: https://www.ijtsrd.com/engineering/electronics-and-communication-engineering/26542/simulation-and-analysis-of-iii-v-characteristic-and-bandgap-design-for-heterojunction-laser-diode/thu-rein-ye-yint-win
Analytical, Numerical and Experimental Validation of Coil Voltage in Inductio...ijeljournal
This paper presents, mathematical model of induction heating process by using analytical and numerical
methods. In analytical method, series equivalent circuit (SEC) is used to represent induction coil and work
piece. Induction coil and workpiece parameters (resistance and reactance) are calculated by standard
formulas along with Nagaoka correction factors and Bessel functions. In Numerical method, magnetic
vector potential formulation is done and finite element method (FEM) is used to solve the field equations.
Analytically and numerically computed parameters such as equivalent coil resistance, reactance, coil
voltage, work piece power are compared and found that they are in good agreement. Analytically and
numerically obtained coil voltages at different frequencies are validated by experimental results. This
mathematical model is useful for coil design and optimization of induction heating process.
Analytical, Numerical and Experimental Validation of Coil Voltage in Inductio...ijujournal
This paper presents, mathematical model of induction heating process by using analytical and numerical methods. In analytical method, series equivalent circuit (SEC) is used to represent induction coil and work piece. Induction coil and workpiece parameters (resistance and reactance) are calculated by standard formulas along with Nagaoka correction factors and Bessel functions. In Numerical method, magnetic
vector potential formulation is done and finite element method (FEM) is used to solve the field equations. Analytically and numerically computed parameters such as equivalent coil resistance, reactance, coil voltage, work piece power are compared and found that they are in good agreement. Analytically and
numerically obtained coil voltages at different frequencies are validated by experimental results. This mathematical model is useful for coil design and optimization of induction heating process.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Relationship between Refractive Index, Electronic Polarizavility, Optical Ene...ijceronline
Refractive index(n), Electronic Polarizability (αp), Optical Energy Gap(Eg) and optical electronegativity(Δχ* ), of I-III-VI2 and II-IV-V2 groups of ternary semiconductors have been calculated using Plasmon energy data on the basis best fit data, new relations have been proposed for the calculation of refractive index , electronic polarizability, optical energy gap and optical electronegativity. The calculated values of n, αp, Eg and (Δχ* ) from the new relations have been compared with the values reported by different researcher. An excellent agreement with calculated values and experimental values has been obtained.
MAR_Comprehensive exam on density functional theorypptx
electronic-structure_of_aluminum_nitride_-_theory
1. Electronic structure of aluminum nitride: Theory and experiment
S. Loughin and R. H. French
DuPont Co. Central Research, P.O. Box 80356, Filmington, Delaware 19880
W. Y. Ching and Y. N. Xu
C’niversity of Missouri at Kunsas City. Department of Physics, Ill0 East 48th Street, Kansas City,
Misouri 64110
G. A. Slack
General Electric Corporate Research & Development Center, I River Road, Schenectudy,
New York 12301
(Received 14 December 1992; accepted for publication 8 June 1993)
We report the results of a vacuum ultraviolet (VIJV) study of single crystal and polycrystalline
AlN over the range 4-40 eV and compare these with theoretical optical properties calculated
from first principles using an orthogonalized linear combination of atomic orbit& in the local
density approximation. The electronic structure of AIN has a two-dimensional (2D) character
indicated by logarithmic divergences at 8.7 and 14 eV. These mark t.he centers of two sets of 2.D
critical points which are associated wit-h N 2p 3 Al 3s transitions and Al = N -+Al 3p transitions,
respectively. A third feature is centered at 33 eV and associated with N &+A1 3d transitions.
Recent efforts to develop electronic.,’ optical, and
electro-optical’-” components and applications based on
wide band-gap III-V materials have generated considerable
practical interest in the electronic structure of AlN. While
a number of theoretical calculations5m10of the band struc-
ture exist, the experimental work”-‘” available for compar-
ison has been limited in either energy range or energy res-
olution. Extant experimental studies are mostly on thin
films due to the difficulty of growing high-purity bulk crys-
tals of 41N.
Aside from techuological applications, the electronic
structure of AlN is also of fundamental interest. Calcula-
tion of the electronic structure of ceramics is a developing
area of theoretical physics and the nitrides are of particular
importance because the bonding is more covalent than in
the oxides. Experimental information about the electronic
structure of AlN provides insight as to how theoretical
models based on oxides should be adapted to covalent ce-
ramics. Quantitative comparison of theory and experiment
affords the best tool for gaining this insight. To this end, we
present our results in terms of analytical critical point
models of the interband transition strength, J,, , for both a
first principles calculation and a vacuum ultraviolet
(VW) optical measurement. Our method emphasizes the
relationship among critical points grouping them into sets
representative of transitions between pairs of bands, while
other recent work” emphasizes individual critical points.
A single crystal (W201), with a thermal conductivity
of 275 W m -’ K-r grown by a modified Bridgman tech-
nique,r6 was studied. The oxygen content of the single crys-
tal was 3GOppm, as previously reported.‘” Polishing with
diamond powders suspended in high-purity dry kerosene
yields an oxide-free surface for reRectance measurements.
Oxidized surfaces give spurious results and were avoided
by nonaqueous polishing. The polished face of the single
crystal was near normal to the c axis.
The VIJV reflectance spectra were obtained with a la-
ser plasma sourced VUV spectrophotometer, described
elsewhere.9 Above the band gap at 6.2 eV, t.he spectra show
two main features. A sharp peak appears at about 9 eV and
a smaller, somewhat brozder peak appears at about l&15
eV. A small feature also appears at about 35 eV. Small
features below the band gap are due to vacancies. The
single crystal response was found to be representative of
commercial polycrystalline substrates also studied.”
The spectrum was adjustedd,consistent with an index of
jz[1.25 eV] = 2.1 A Kramers-Kriinig (KK) analysi?” re-
covered the phase information, S[h,r], and permitted cal-
culation of other optical properties,” including the com-
plex dielectric function shown in Fig. 1.
The energy band structure of AlN was calculated from
first principles, using the orthogonalized linear combina-
tion of atomic orbitals (OL.CAOj method with the local
density approximation (LDA j .” The resulting band dia-
I;;1 1)
w “
IV
h- ..:‘.;,._A-
w 2
-1 L
/.,/”‘.;.Y-;. d-j- ---i’rx,m-----lrr..,?=-_
-2 .~------
-6ii~~j,+r7.-ri -I /-.‘~I”-.~...~Tail4 8 t+1 16 aI 24 2s 32 36
EnergyI#)
FIG. 1. The imaginary (a) and real (bj parts of the dielectric function
for single crystal AlN with Elc (solid) are compared with those calcu-
lated from first principles for Elc (dashtui).
1182 Appl. Phys. Lett. 63 (9), 30 August 1993 0003-6951/93/63(9)/1182/3/$6.00 (3 1993 American Institute of Physics 1182
Downloaded 21 Dec 2000 to 134.105.248.68. Redistribution subject to AIP copyright, see http://ojps.aip.org/aplo/aplcpyrts.html.
2. r- I; ki ,4 I’ hl 1. A
i,~ - - 14-~
---i.”
A
/’ l;
I’l:-:~~
..:2..._lihl
i i/
FIG. 2. The energy hand structure of AIN is shown with the k-space
directions referenced to the Hrillouin zone as shown.
gram and total density of states (DOS) are shown in Fig.
2.
The calculated band gap occurs at the zone center,
&=-4.5 eV. The conduction-band minimum at r has a
simple parabolic shape in all three directions, however, the
valence-band maximum is relatively flat in the r to K and
r to M directions, but falls off sharply in the r to A di-
rection. Thus, the hole effective mass, normalized to the
rest mass of the electron, is nearly an order of magnitude
larger in the basal plane (t?z*=3.52 I---M and 3.40 r-k’)
than in the c-axis direction (irz*=O.30 T-A). As dis-
cussed by Naka# such anisotropy in the bands leads to a
reduction in the dimensionality of the optical response.
Along with similar anisotropies occurring for other band
pairings, this supports the possibility that features in the
reflectance spectra are quasi-two dimensional.
The optical conductivity and matrix elements of mo-
mentum were evaIuatcd21”J to determine the optical prop-
erties predicted by the first-principles calculation. The
imaginary part of the dielectric function, 2cr/(kv), fol-
lowed by KK analysis, yielded the complex dielectric func-
tion, ~~-tic~, for Elc, as shown in Fig. 1.
?Vith the experimental and theoretical results both in
terms of the complex dielectric function, one can qualita-
tively compare the two. However, to gain further insight
into how the differences relate to fundamental properties of
the material requires a qzmztitatizx? comparison, achieved
through the use of analyt.ical critical point models.““- 27Un-
fortunately, the established approach of fitting the second
derivative is difikult when the band structure and the ex-
perimcntal results are not well established, as is the case for
most ceramics. We thercfcare fit the spectra using an
umd@wz tided model.” The interband transition strength
J,,: is proportional to (h*l)‘tr”. As with other optical prop-
erties, we can define a complex J,, as
Each of the critical points can be referenced to the
band structure of AIN. The calculated band diagram indi-
cates that ,41N has a direct band gap occurring at the I-
point with an energy separation of 4.5 eV, which is con-
siderably lower t.han the 6.3 eV found experimentally.
However, LDA calculations generally give lower than ob-
served values for the gap.
where i- is the usual complex dielectric function and the A two-dimensional CP has been assigned to t.he band
asterisk denotes cornplea conjugation. For computational gap, suggesting that the reduced effective mass is consid-
1 (4 ~OLCAOILDA Calculation 1
“0 5 10 15 20 25 30 35 40
Energy (eV)
FIG. 3. The interband transition strength has been modeled using bal-
anced sets of analytical critical point line shapes for both experiment (a)
and theory (b).
convenience, we take the prefactor (m2fii-‘e-‘) to be
unity. The complex interband transition strength is then fit
to
( 1
*f,,,-i C-t (hv)‘- ; A~&x(hv-EkfiTIc)“k . (29
C is a comples constant, hv is photon energy, and k in-
dexes the critical points (CPs). The CP parameters are *‘lk,
Sk, Ek, rk, and rl2~,respectively identified as the ampli-
tude, phase, energy, width, and dimensional exponen?’ for
each critical point. Individual critical points are grouped
into sets corresponding to transitions between a valence-
and conduction-band pair. Transitions between a valence
and a conduction band have well defined energies for the
onset and exhaustion of transition strength. By demanding
that Re[J,J arising from each set is asymptotic to zero at
energies well outside the range of the set, we constrain the
model to physically realistic, halmced sets of CPs.
Figure 3 shows the models constructed using
Levenberg-Marquardt optimization for the Elc JCL,,both
as measured VUV and as calculated OLCAO/I,DA. The
parameiers for these models are compared in Table I. Due
to band splitting at the valence- and conduction-band
edges, a double, overlapping set was used to model the low
energy feature with a single saddle point.
1183 Appt. Phys. Mt., Vol. 63, No. 9, 30 August 1993 Loughin et a/. 1183
Downloaded 21 Dec 2000 to 134.105.248.68. Redistribution subject to AIP copyright, see http://ojps.aip.org/aplo/aplcpyrts.html.
3. TABLE I. The fit parameters for the models of experiment and theory are
compared. The models had a reduced xL of 62, with C=ZO.OS+i1.34
(experiment) 2 of 48, with C=25.93+il.87 (theory).
Critical pt.
k/type
Energy (eV ) Width (eV) Amplitude
Expt. Theory Expt. Theory Expt. Theory
l/o, 6.29 4.69 0.38 0.31 1.32 0.11
~/DO 8.02 6.86 0.38 0.31 3.17 1.21
3/01 8.6s 8.54 0.38 0.31 4.45 1.32
‘+I/4 9.16 9.10 0.38 0.31 2.32 0.29
5/D2 10.39 9.87 0.38 0.31 2,18 1.07
6iDo 10.22 9.24 0.78 0.30 1.16 1.23
710, 14.00 12.31 0.78 0.78 1.08 1.91
S/D2 25.67 16.87 1.84 1.18 0.99 1.14
9/S” 33.85 33.03 5.64 10.0 26.13 36.2
erably different in one of the three directions. From the
calculated band structure results, the reduced masses are
prd,=0.36, ,urAK=0.37, and ~r+~=0.16. So ,++a is
43% of p in the other directions. Table II presents a
scheme for assigning the critic.al point energies to specific
transitions where the majuscule labels the symmetry with
reference to Fig. 2, and the subscripts index the set mem-
bership and type of critical point. Orbital origins, based on
the partial DOS from the OLCAO/LDA calculation, aid
in identifying the nature of transition typical of each set,
although we recognize that they are not formally correct.
The optical response of single crystal AlN includes
several prominent features which were resolved into three
sets of balanced critical points. The first set ranges from the
band gap at 6.3-10.4 eV, the point at which transitions
between the upper valence band and lower conduction
band are exhausted. The conventional direct gap fit of
a”(h)‘, with the absorption coefficient, 01,calculated from
the first set, gives a gap of 6.2 eV. Based on analysis of the
orbital decomposition of the density of states, this set was
attributed to transitions between N 2p to Al 3s states.
These lower energy features have a quasi-two-dimensional
character, which is suggested by the existence of a single
sharp maximum in the optical response at 8.7 eV.
Above 10.2 eV, another set of features appears, which
is also two dimensional in character, and includes an onset
at 10.2 eV, a logarithmic divergent peak at 14.0 eV, and a
broad interband maximum centered at 25.7 eV. This set is
identified with transitions between Al=-N bonding states
and Al 3p antibonding states. A third set, at much higher
TABLE II. Assignment of features in the elexztronic structure of PLlN.
Energy Interband Predominant orbital
CeV) Type Assignment A(eV) character
6.3 43 r 0 I 4.5
8.0 Du r:,, 7.2
8.7 4 AlI 9.9 N 2p-+Al 3s
9.2 4 Hz, 1I.5
10.4 4 Hi, 12.5
10.2 4 ‘401 11.1
14.0 4 ri2 13.2 A1zxN-.Al 3p
25.7 4 Hz:, 19
33.9 & r Q? 27-37 N 2p~Al3d
energies, could not be resolved into discrete critical points
and was modeled as a broad zero-dimensional feature at
33.8 eV, probably arising from N 2s to Al 3d transitions.
The optical response calculated from the LDA band
structure was also resolved into three sets of balanced crit-
ical points. Using the same orbital character assignments,
the predicted energies for the N 2p to Al 3s set of transi-
tions agreed closely with the experiment, except at the
band gap. The energies for the Al-lN to Al 3p set of tran-
sitions were lower than experimental values by about 2 eV.
The N 2s to AI 3d transitions did not appear as a coherent
set, however, the calculated response did include transi-
tions in this energy range.
The authors are grateful for the assistance of D. J.
Jones at DuPont, D. N. Elliott at Martin Marietta, and to
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