198

Universitas Scientiarum, Vol. 13 N° 2, 198-207

ELECTRONIC BAND STRUCTURE OF THE ORDERED Zn0.5Cd0.5Se ALLOY CALCULATED BY THE SEMI-EMPIRICAL TIGHT-BINDING

METHOD CONSIDERING SECOND-NEAREST NEIGHBOR

ESTRUCTURA ELECTRÓNICA DE BANDAS DE LA ALEACIÓNORDENADA DE Zn0.5Cd0.5Se CALCULADA POR EL MÉTODO

SEMI-EMPÍRICO DE ENLACE FUERTE TENIENDO EN CUENTAINTERACCIÓN A SEGUNDOS VECINOS

Juan Carlos Salcedo-Reyes

Thin Films Group, Department of Physics, Faculty of SciencesPontificia Universidad Javeriana, Cra. 7 No. 40-62, Bogotá, Colombia

jsalcedo@fisica.ugto.mx; salcedo.juan@javeriana.edu.co

Abstract

Usually, semiconductor ternary alloys are studied via a pseudo-binary approach in which the semiconductoris described like a crystalline array were the cation/anion sub-lattice consist of a random distribution of thecationic/anionic atoms. However, in the case of reported III-V and II-VI artificial structures, in which anordering of either the cations or the anions of the respective fcc sub-lattice is involved, a pseudo-binaryapproach can no longer be employed, an atomistic point of view, which takes into account the localstructure, must be used to study the electronic and optical properties of these artificial semiconductoralloys. In particular, the ordered Zn

0.5Cd

0.5Se alloy has to be described as a crystal with the simple-tetragonal

Bravais lattice with a composition equal to the zincblende random ternary alloy. The change of symmetryproperties of the tetragonal alloy, in relation to the cubic alloy, results mainly in two effects: i) reduction ofthe banned gap, and ii) crystal field cleavage of the valence band maximum. In this work, the electronicband structure of the ordered Zn

0.5Cd

0.5Se alloy is calculated using a second nearest neighbor semi-empirical

tight binding method. Also, it is compared with the electronic band structure obtained by FP-LAPW (full-potential linearized augmented-plane wave) method.

Key words: band gap narrowing; electronic band structure; ordered alloys; Semi-empirical thigh bindingmethod; ZnCdSe alloy.

Resumen

Aunque la descripción de las aleaciones ternarias semiconductoras se hace tradicionalmente asumiendo laaproximación de compuesto pseudo-binario. Para el caso de aleaciones artificiales de compuestos II-VI yIII-V, en las cuales se ha reportado un ordenamiento inducido por el crecimiento, una aproximación de estetipo no es aplicable, de modo que, con el fin de hacer una descripción adecuada de las propiedades ópticasy electrónicas de dichas aleaciones artificiales, se debe asumir una descripción atomística que tenga encuenta la estructura local. En particular, para la aleación ordenada de Zn

0.5Cd

0.5Se, el cambio de simetría

implica que se debe usar una estructura tetragonal simple, dando lugar, principalmente, a dos efectos: i)disminución de la brecha prohibida del material y ii) un desdoblamiento en el máximo de la banda devalencia. En este trabajo se calcula la estructura de bandas de la aleación ordenada de Zn

0.5Cd

0.5Se usando

la aproximación semi-empírica de enlace fuerte teniendo en cuenta interacción a segundos vecinos y secompara con la estructura de bandas obtenida por el método FP-LAPW (full-potential linearized augmented-plane wave). Se obtiene una buena concordancia de las principales características entre las estructuras debandas calculadas por el método semi-empírico y el método ab initio.

Palabras clave: aleaciones ordenadas; aleaciones de ZnCdSe; Disminución de la brecha de energía; Es-tructura electrónica de bandas; Modelo de enlace fuerte.

UNIVERSITAS SCIENTIARUMDisponible en línea en:

www.javeriana.edu.co/universitas_scientiarumVol. 13 N° 2, 198-207

Artículo original

Facultad de Ciencias

Recibido: 23-07-2007: Aceptado: 14-10-2008:

199

Salcedo-Reyes

INTRODUCTION

From the traditional point of view, when two zincblendebinary compounds AC and BC are mixed homogeneouslyobtaining a random ternary alloy A

1-xB

xC, the ternary II-VI

and III-V semiconductors alloys are treated as pseudo-binary compounds (Bernard and Zunger, 1987), in which,traveling along the [001] direction, a sequence of cation-anion planes can be found. The A and B cations, in a pseudo-binary alloy, are randomly distributed in each cation plane.In particular, for the II-VI pseudo-binary zincblendeZn

0.5Cd

0.5Se alloy, the Se layers are alternating with

Zn0.5

Cd0.5

layers with a random distribution in average ofthe same amount of Cd and Zn atoms. However, orderingof isovalent A

0.5B

0.5C semiconductors alloys has been

widely observed and studied (Kuan et al., 1985; Su et al.,1994; Lu et al., 1987; Wei and Zunger, 1991). That is how,at least four ordered structures related to the zincblendestructure have been found to date (see Table 1): CuPt(Gomyo et al., 1987), CuAu (Mowgray et al., 1992),femetinite (Wang, 1989), and chalcopyrite (Jen et al., 1986).

In particular, in the CuAu ordered structure, a sequence ofA-C-B-C-A-C-… planes along the [001] azimuth is found.Sometimes, this structure is described as an (AC)

1(BC)

1

superlattice. However, it is not a true superlattice. It is acrystal with the simple tetragonal Bravais lattice and thesame A

0.5B

0.5C composition of a zincblende random ternary

alloy. Due to changes in symmetry, local ordering, and, inparticular, to the change from zincblende unit cell -withspace group T2

d - to simple tetragonal primitive cell -with

space group D52d

- predicted and observed changes in ma-terial properties such as band gap reduction, valence bandsplitting, polarization dependence of optical transitions,vibrational spectrum, and others may be expected (Salcedo-Reyes and Hernández-Calderón, 2005). In the case of apseudo-binary alloy most of the optical, structural andelectronic properties are correctly described by the virtualcrystal approximation (VCA). However, it is evident thatin the case of an ordered alloy, with x=0.5, the VCA approachcan no longer be employed to explain the physicalproperties and a more suitable crystalline structure mustbe considered.

TABLE 1. Different ordered structures related to the zincblende structure, that have been found to date. The relatedcompounds, the growth method (MOCVD, Metal-Organic Chemical Vapor Deposition, MBE, Molecular Beam

Epitaxy, and/or LPE, Liquid Phase Epitaxy), and a example of the semiconductor allow obtained as shown.

200

Universitas Scientiarum, Vol. 13 N° 2, 198-207

On the other hand, the Semiempirical Tight-Binding (STB)is one example of the so- called simplified quantummechanical methods, in which a compromise between thecomputational efficiency and the physical correctness ofthe approximation is used. The usefulness of theseapproximated methods comes from the balance betweentheoretical rigor and pragmatism, speed, and accuracy. Thatis, despite the generality and transferability of the methodis limited, the heavy computational effort of first-principlescalculations is avoided by replacing difficult integrals, i.e.the so called two centers (Coulombic) integrals, byempirical parameters to fit experimental results. In generalterms, in the STB method the solution to the time-independent single electron Schrödinger equation isassumed as a linear combination of atomic orbitals centeredat each lattice point. The atomic orbitals are assumed to bevery small at distances exceeding the lattice constant (thisis what is meant by tight-binding), and, therefore,practically all matrix elements are approached by analyticalfunctions of the inter-atomic separation and of the atomicenvironment. In section 2, the STB method, taking intoaccount all first and second nearest-neighbor interaction,is applied in order to obtain the tight binding parameters(TBP) of the binary compounds ZnSe and CdSe. In section3, the tetragonal STB Hamiltonian is deduced and, inaddition to those second nearest neighbor TBP, theelectronic band structure of the ordered ZnCdSe alloy isobtained, and then, in section 4 it is compared with theband structure obtained by FP-LAPW.

TIGHT BINDING METHOD FOR ZINCBLENDE ZnSeAND CdSe BINARY COMPOUNDS

In the STB method the basis of the system is assumed as alineal combination of quasi-atomic functions centered ineach lattice point. That is, the tight binding basis is writ-ten as

∑ ⋅= −

E�L

LL��� QE�LH[S�1QE 55NN , (1)

where the numbers n runs over the atomic orbitals, the Nwavevectors k lie in the first Brillouin zone (FBZ), the siteindex, b, is either a for anions or c for cations, and theanion/cation positions are R

i. The Schrödinger equation

for the Bloch function λN , written in terms of the tightbinding basis, is

{ } �PE��PE+QE

E�P

EEQP =−∑ �NNNNN� λδδλε , (2)

where λ is the band index. In this work one s and three porbitals (p

x,p

y, and p

z) are used per every atom, that is a sp3

basis, and all first and second nearest neighbor interactionis taken into account. As every atom in a zincblende struc-ture is tetrahedrally coordinated, each atom (anion/cation)has four first nearest neighbor of the other specie (cation/

anion) to

4

3DG = , and twelve second neighbor of the same

specie (anion/cation) to

2

DG = , where d is the inter-atomic

distance. The resulting 8x8 tight binding Hamiltonian ma-trix is shown in appendix 1, were the site index b(b‘), iseither a for anions and c for cations, and α = akx/4, β = aky/4, γ = akz/4, α’ = akx/2, β’ = aky/2, γ’ = akz/2, being a thelattice constant. The Eb

n ’s are the on-site parameters, the

Ebb’nnn’

’s are the first-nearest-neighbor parameters, and theVbb’

nnnn’’s are the parameters that represent the second-near-

est-neighbor interaction. The nineteen tight binding pa-rameters (TBP) to be determined by fitting band structuredata have the same sense of those described by Slater-Koster (Slater and Koster, 1954).

In order to calculate the TBP, symmetry properties of thezincblende structure are used. From the irreducible repre-sentation (IR) of the wave vector group, g

0(k), at each high

symmetry point at the FBZ, dependence of the energy onthe TBP can be described by the relation

( ){ }�� ���

��

��( γβαβα +−±+= �N , (3)

where the plus sign corresponds to the energy of the con-duction band, in each k-value, and the minus sign to thevalence band. For the Γ point (k=(0,0,0) and g

0(k) = T

d) two

IR can be found: One three-fold degenerate, Γ4, in which α

= Ecp + 2Vc

x x + V’ c

x x, β = Ea

p + 2Va

x x + V’ a

x, x, and γ = Eac

,xx,

and one one-fold degenerate, Γ 1, in which α = Ec

s + 3Vc

s s,

β = E as + 3V a

s s, and γ = Eac

s s. For the X point (k=(2π/a,0,0)

and g0(k) = D

2d) three IR can be found: One two-fold de-

generate, X5, in which α = Ec

p – Vc

x x, β = Ea

p – Va

x x, and γ =

Eacx y,

one one-fold degenerate, X1, with α= Ec

s – Vc

s s, β = Eap

– 2Vax x

+ V’ ax x

, and γ = E acs p

, and one one-fold degenerate,X

3, in which α = Ea

s – Va

ss, β = Ec

p – 2Vc

x x + V’ c

x x, and γ =

Eacp s

. For the L point (k=(π/a, π/a, π/a) and g0(k) = C

2v) the

relationships α = Eap – Va

x x, β = Ec

p – Vc

x x, and γ = {Eac

x x +

Eacx y

}/2 can be found to the two-fold degenerate L3 IR.

Since in this work the spin-orbit interaction is not included,the single group notation of the IR’s of Parmenter (1955) isused to label the energy bands at the points and axes ofsymmetry.

201

Salcedo-Reyes

A group of twelve equations and seventeen unknown quan-tities, then, have to be solved. The parameters E

cs p and E

as

p are used to fit the light hole (lh) and heavy hole (hh) mass

effective of each compound. The energy eigenvalues, ob-

tained from the calculated TBP shown in Table 2, are com-pared with other –experimental and theoretical– values inTable 3 and the resulting band structures for ZnSe andCdSe are shown in Figure 1.

TABLE 2. TBP (in eV) for ZnSe and CdSe. The Es represent the on-site parameters, the Enn’ parameters represent the

first-nearest-neighbor interaction, and the Vnn’ the second-nearest-neighbor interaction

ZnSe CdSe

Esc 2.498 E

sc 3.317

Esa -10.55 E

sa -10.40

Epc 7.110 E

pc 7.270

Epa -0.681 E

pa -1.016

Eacs s

-6.040 Eacs s

-0.238Eac

sx x2.427 Eac

sx x0.029

Eacsx y

5.465 Eacsx y

4.659Eac

s p2.767 Eac

s p0.213

Eacsp s

6.637 Eacsp s

3.812Vc

s s-0.668 Vc

s s-0.517

Vas s

-0.773 Vas s

-0.366Vc

sx x1.171 Vc

sx x0.892

V’ cx x

-1.054 V’ cx x

-1.453Va

x x1.277 Va

x x0.999

V’ asx x

-1.171 V’ asx x

-0.981Vc

sx y-1.221 Vc

sx y-3.249

Vasx y

-1.349 Vasx y

-0.597

TABLE 3. Comparison of the energy eigenvalues (in eV) of ZnSe at some symmetry points in the FBZ. The refer-ences are: GW (PP-LDA) in Zakharov et al. (1994), FLAPW (all-electron full-potential linear-augmented-plane-

wave) in Contineza et al. (1994), PVMB (all-electron mixed-basis approach to the density-functional formalism) inBernard and Zunger (1987), PP-LDA (ab initio pseudopotential total-energy calculations) in Lee et al. (1995), XPS(x-ray photoemission spectroscopy) in Ley et al. (1974), and (AR)-PE (Angle-resolved photoemission) in Fleszar et

al. (2004). X6, X7, and L6 correspond to double group notation.

Therein GW FLAPW PVMB PP-LDA XPS (AR)-PE

G1v -15.2 -13.49 -13.43 -12.86 -12.06 -15.2(6) -

G4v 0.0 0.0 0.0 0.0 0.0 - -

G1c 2.82 2.84 1.10 1.45 2.29 - -

G4c 9.1 7.67 5.69 5.77 6.23 - -

X1v -12.5 -12.07 -12.33 -11.79 -10.76 -12.5(4) -

X3v -5.31 -5.03 -4.92 -4.82 -4.28 -5.6(3) X

6v = -5.10

X5v -2.35 -2.08 -2.27 -2.20 -1.57 -2.1(3) X

6v = -2.36, X

7v = -2.54

X1c 4.07 4.41 2.79 2.88 3.07 - -

X3c 6.43 5.01 3.33 3.47 3.62 - -

X5c 11.0 - - - - -

L1v -13.09 -12.44 -12.61 -12.06 -11.10 -13.1(3) -

L2v -5.61 -5.23 -5.41 -5.21 -4.44 -5.6(3) L

6v = -5.55

L3v -1.0 -0.81 -0.31 -0.87 -0.56 -1.3(3) -

L1c 3.91 4.14 2.38 2.63 3.20 - -

L2c 8.02 - 6.32 - - - -

L3c 10.0 8.18 8.43 6.36 - - -

202

Universitas Scientiarum, Vol. 13 N° 2, 198-207

FIGURE 1. Second-nearest neighbor Tight Binding band structure for ZnSe (a) and CdSe (b).The simple group notation of Parmenter (1955) is used.

TABLE 4. Comparison of the energy eigenvalues (in eV) of b-CdSe at some symmetry points in the FBZ. Thereferences are: GW (PP-LDA) in Zakharov et al. (1994), TB in Pantelides and Harrison (1975), OPW (modified orthogonalized plane wave method) in Kurganski et al. (1980), AR-PE (Angle-resolved photoelectron spectroscopy)

in Magnusson et al. (1998), and Extrap. (sp3 tight-binding model) in Wang and Duke (1988). X6, X

7, and L

6

correspond to double group notation.

Therein GW TB OPW AR-PE Extrap.

Γ1v -11.5 -12.71 -11.5 -13.6 - -11.5

Γ4v 0.0 0.0 0.0 0.0 -

Γ1c 1.77 2.01 - - - 1.9

Γ4c 7.6 7.60 - - - 6.25

X1v -11.0 -11.65 -11.0 -13.4 -

X3v -4.0 -4.22 -3.9 -3.6 X

6v = -4.0 -5.1

X5v -2.05 -1.78 -1.6 -1.6 X

6v = -1.95, X

7v = -2.15 -2.45

X1c 3.84 4.37 - - - 3.81

X3c 5.0 5.20 - - -

X5c 10.73 - - - -

L1v -11.49 -11.91 -11.1 -13.5 -

L2v -4.99 -4.42 -3.7 -3.6 L

6v = -5.55

L3v -0.9 -0.71 -0.8 -0.8 - -1.20

L1c 3.31 3.87 - - - 3.36

L2c 4.64 - - - -

L3c 11.0 8.04 - - -

203

Salcedo-Reyes

The matrixes on the diagonal are

The functions g1, g

2, g

3, and g

4 are given by

g1 = cosα’cosβ’,

g2 = i sinα’cosβ’,

g3 = i cosα’sinβ’,

andg

4 = sina’sinb’.

The off-diagonal matrixes are

where

g5 = {cosαcosβcosγ - sinαsinβsinγ} + i {cosαcosβsinγ -

sinαsinβsinγ},

and

g6 = {-sinαcosβsinγ - cosαsinβcosγ} + i {cosαsinβcosγ -

sinαcosβcosγ}.

TIGHT BINDING METHOD FOR THE ORDEREDZn

0.5Cd

0.5Se

In order to calculate the electronic band structure of thetetragonal Zn

0.5Cd

0.5Se alloy, their crystal structure has to

be taken into account. In this case each cation (Cd, forexample) has four anions (Se) first-nearest neighbors, to, and eight cations of the same specie (Cd) and four cationsof the other specie (Zn) as second-nearest neighbors, to, as is shown in Figure. 2.

FIGURE 2. Crystal structure (not the unit cell) used tocalculate the electronic band structure of the

tetragonal Zn0.5

Cd0.5

Se alloy.

It is very important to note that the Hamiltonian matrix hasto be invariant under the chosen origin. That is, it has thesame form when the origin coincides with one cation orwhen it coincides with one anion.

In this work, the ZnSe and CdSe first and second nearestneighbor TBP’s are used to simulate the parameters of theordered alloy. The 16x16 ordered STB-Hamiltonian ma-trix, in the sp3 basis, is

(5)

,

204

Universitas Scientiarum, Vol. 13 N° 2, 198-207

Also

and

withg

7 = cosγ’{ cosα’ + cosβ’},

g8 = i sinα’cos γ’,

g9 = i sinβ’cos γ’,

g10

= i sin’ { cosα’+ cosb’},

g11

= cosα’cosγ’,

g12

= cosβ’cosγ’,

g13

= sinα’sinγ’,

andg

14 = sinβ’sinγ’.

In all cases, the ZnCd parameters are the average betweenthe corresponding ZnSe-CdSe parameters, α, β, γ, α’ , β’ , γ

γ’are like in the zincblende case, and a the lattice constantcalculated from the Vegard’s law.

RESULTS

Since there is no experimental information on optical tran-sitions of the ordered Zn

0.5Cd

0.5Se alloy, the band structure

obtained by STB is compared to the electronic band struc-ture obtained by the FP-LAPW method (that do not in-clude spin-orbit interaction), as it is implemented in theWien97 code (Blaha et al., 1997), in the Fig 3, along the[100] direction of the FBZ of the simple tetragonal lattice,and in the Fig. 4, along the [110] direction. It is remarkablethe good qualitative agreement between both methods.

SUMMARY

An improved STB calculation of the band structure of theZn

0.5Cd

0.5Se ordered alloy, employing a sp3 basis that takes

into account second nearest neighbor interaction, necessaryto describe the alloy ordering, was made. A completedescription of the electronic band structure of the tetragonalalloy employing both, the STB and FP-LAPW methods,was done obtaining numerical values for crystal field

FIGURE 3. Calculated electronic band structure of the Zn0.5

Cd0.5

Se ordered alloy along the [100] direction (Λ axis).(a) Band structure from an ETB calculation. (b) Band structure from FP-LAPW method.

205

Salcedo-Reyes

splitting of the valence band maximum and for the bandgap reduction in relation to the band gap of the disorderedalloy. A good qualitative agreement is observed betweenthe obtained STB band structure (do not include spin-orbitinteraction) and the band structure calculated by FP-LAPW.

ACKNOWLEDGEMENTS

The author gratefully acknowledges I. Hernández-Calde-rón at Centro de Investigación y de Estudios Avanzadosdel IPN, Centro de Investigación y de Estudios Avanzadosdel IPN, Cinvestav (México) and H. Méndez at PontificiaUniversidad Javeriana (Colombia) for helpful discussionsand D. Olguín at Centro de Investigación y de EstudiosAvanzados del IPN, Centro de Investigación y de EstudiosAvanzados del IPN, Cinvestav (México) for his advice inthe FP-LAPW calculations.

REFERENCES

BERNARD, J.E. and ZUNGER, A. Electronic structure of ZnS,ZnSe, ZnTe, and their pseudobinary alloys. PhysicalReview B, 1987, 36, 3199-3228.

BLAHA, P.; SCHWARTZ, K. and LUITZ, J. Wien97, Vienna Uni-versity of Technology, 1997. (Improved and updatedUnix version of the original copyrighted WIEN code,which was originally published in Blaha P., SchwarzK., Sorantin P. and Trickey S. B., Full potential, lin-earized augmented plane wave programs for crystal-line systems, Computer Physics Communications,1990, 59, 399-415.

CONTINENZA, A.; MASSIDDA, A. and FREEMAN A.J., Structuraland electronic properties of bulk ZnSe, Physical Re-view B, 1994, 38, 12996-13001.

FLESZAR, A.; HANKE, W.; WEIGAND, W.; KUMPF, C.; HESKE, C.;UMBACH, E.; SCHALLENBERG, T. and MOLENKAMP, L.W.,Valence-band electronic structure of ZnSe(001) thinfilms: Theory and experiment, Physical Review B,2004, 125308-125318.

GOMYO, A.; KOBAYASHI, K.; KAWATA, S.; HINO, I.; SUZUKI, T. andYUASA, T., Studies of Ga

xIn

1-xP layers grown by

metalorganic vapor phase epitaxy; Effects of V/III ra-tio and growth temperature, Journal of Crystal Growth,1986, 77, 367-373.

GOMYO, A.; SUZUKI, T.; KOBAYASHI, K.; KAWATA, S.; HINO, I. andYUASA, T. Evidence for the existence of an orderedstate in Ga

0.5In

0.5P grown by metalorganic vapor phase

FIGURE 4. Calculated electronic band structure of the Zn0.5

Cd0.5

Se ordered alloy along the [110] direction (Λ axis).(a) Band structure from an ETB calculation. (b) Band structure from FP-LAPW method.

206

Universitas Scientiarum, Vol. 13 N° 2, 198-207

epitaxy and its relation to band-gap energy. AppliedPhysics Letters, 1987, 50, 673-675.

JEN, H.R.; CHENG, M.J.; STRINGFELLOW, B. Ordered structuresin GaAs

0.5Sb

0.5 alloys grown by organometallic vapor

phase epitaxy. Applied Physcis Letters, 1986, 48,1603-1605.

KUAN, T.S.; KUECH, T.F.; WANG, W.I. and WILKIE L. Long-Range Order in Al

xGa

1-xAs. Physical Review Letters,

1985, 54, 201-204.

KURGANSKI, S.I.; FARBEROVICH, O.V. and DOMASHEVSKAYA, É.P.Energy band structure of II–VI compounds. I. Calcu-lation by the modified OPW method and interpreta-tion, Soviet Physics - Semiconductors, 1980, 14,775-780.

LEE, G.D.; LEE M.H. and IHM, J. Role of d electrons in thezinc-blende semiconductors ZnS, ZnSe, and ZnTe,Physical Review B, 1995, 52, 1459-1462.

LEY, L.; POLLAK, R.A.; MCFEELY, F.R.; KOWALCZYK, S.P. andSHIRLEY, D.A. Total valence-band densities of states ofIII-V and II-VI compounds from x-ray photoemissionspectroscopy, 1974, Physical Review B, 9,600-621.

LU, Q.; BUNKER, B.A.; LUO, H.; KROPF, A.J.; KEMMER, K.M. andFURDYNA, J.K. X-ray study of atomic correlations inZn

0.5Cd

0.5Se

0.5Te

0.5 epitaxial thin films. Physical Re-

view B, 1987, 55, 9910-9914.

MAGNUSSON, K.O.; NEUHOLD, G.; HORN, K. and EVANS, D.A.,Electronic band structure of cubic CdSe determinedby angle-resolved photoemission: Cd 4d and valence-level states, Physical Review B, 1998, 57, 8945-8950.

MOWGRAY, D.J.; HOGG, R.A.; SKOINICK, M.S.; DELONG, M.C.;KURTZ, J.M. and OLSON, J.M. Valence-band splitting inordered Ga

0.5In

0.5P measured by polarized photolumi-

nescence excitation spectroscopy. Physical Review B,1992, 46, 7232-7235.

PANTELIDES, S.T. and HARRISON, W.A. Structure of the valencebands of zinc-blende-type semiconductors, PhysicalReview B, 1975, 11, 3006-3021.

PARMENTER, R.H. Symmetry Properties of the Energy Bandsof the Zinc Blende Structure, Physical Review, 1955,100, 573-579.

SALCEDO-REYES, J.C. and HERNÁNDEZ-CALDERÓN, I. Symmetryproperties and electronic band structure of orderedZn0.5Cd0.5Se alloys. Microelectronics Journal, 2005,36, 342-346.

SLATER, J.C. and KOSTER, G.F. Simplified LCAO Method forthe Periodic Potential Problem, Physical Review, 1954,94, 1498-1524.

SU, L.C.; HO, L.H.; STRINGFELLOW, B. Effects of substratemisorientation and growth rate on ordering in GaInP.Journal of Applied Physics, 1994, 75, 5135-5141.

WANG, C.T. Introduction to semiconductor technology:GaAs and related compounds. 1 edition, Wiley-Interscience, New York, 1990, 624 pages.

WANG, Y.R. and DUKE, C.B. Cleavage faces of wurtzite CdSand CdSe: Surface relaxation and electronic structure,Physical Review B, 1988, 37, 6417-6424.

WEI, S. and ZUNGER, A. Disorder effects on the density ofstates of the II-VI semiconductor alloys Hg

0.5Cd

0.5Te,

Cd0.5

Zn0.5

Te, and Hg0.5

Zn0.5

Te. Physical Review B,1991, 43, 1662-1677.

ZAKHAROV, O.; RUBIO, A.; BLASÉ, X.; COHEN, M.L. and LOUIE

S.G. Quasiparticle band structures of six II-VI com-pounds: ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe, Physi-cal Review B, 1994, 50, 10780-10787.

ZAKHAROV, O.; RUBIO, A.; BLASÉ, X.; COHEN, M.L. and LOUIE,S.G. Quasiparticle band structures of six II-VI com-pounds: ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe, Physi-cal ReviewB, 1994, 50, 10780-10787.

207

Salcedo-Reyes

APPENDIX 1

where: