Materials Sciences and Applicatio n, 2011, 2, 729738 doi:10.4236/msa.2011.27101 Published Online July 2011 (http://www.SciRP.org/journal/msa) Copyright © 2011 SciRes. MSA 729 Structural and Electronic Properties Calculations of AlxIn1–xP Alloy Mohammed Ameri1*, Ali Bentouaf1, Mohammed DouiAici2, Rabah Khenata3,4, Fatima Boufadi1, Amina Touia1 1Département de Physique, Faculté des Sciences, Université Djillali Liabès, SidiBelAbbés, Algérie; 2Laboratory Applied Materials (AML), Research Center (Ex: CFTE), Route de Mascara, University of SidiBelAbbes, Algeria ; 3Laboratoire Quantum Physics and Mathematical Modeling of Matter (M LPQ3), University de Mascara, Mascara, Algeria; 4Department of Physics and Astronomy, Faculty of Science, King Saud University, Riyadh, Saudi Arabia. Email: lttnsameri@yahoo.fr Received December 23rd, 2010; revised March 21st, 2011; accepted May 3rd, 2011. ABSTRACT The equilibrium structure and the electronic properties of IIIV zincblende AlP, InP semiconductors and their alloy have been studied in detail from firstp rinciples calculations. A fullpotential linea r muffintinorbita l (FPLMTO) me thod has been used in conjunction with both the localdensity approximation (LDA) and the generalizedgradient ap proximation (GGA) to investigate the effect of increasing the concentration of aluminum on the structural properties such as the lattice constants and the bulk moduli. Besides, we report the concentration dependence of the electronic band structure, the directindirect band gap crosso vers and bowing. Using the approach of Zunger and coworkers the microscopic origins of the gap bowing were also explained. A reasonable agreement is found in comparing our results with other theoretica l calculations. Keywords: AlP, InP, Semiconductors, FPLMTO, Bowing, Alloys 1. Introduction Understanding the electronic properties of semiconductor alloys plays a vital role in developing new technologies. The advantage of alloying is that the alloy properties, such as band gap, can be tuned by varying the alloy composition to meet the specific requirements of modern device applications [13]. With the advent of small structure systems, such as quantum wells and superlat tices, the effects of alloy compositions, size, device ge ometry, doping and controlled lattice strain can be com bined to achieve maximum tenability [4]. AlxIn1xP alloy provides wide bandgap energy in the nonnitride IIIV semiconductors and has been wide ap plied in electronic and photonic devices. The parent (bi nary) compounds such as aluminum phosphide (AlP) and indium phosphide InP, are noncentrosymmetric cubic semiconductors with zincblende structures based on the space group F43m [5,6]. Recently, these compounds have attracted a great deal of attention, [541] expecting fabrication of important electronic devices. Indeed, InP is a very promising material for solar cells and highper formance computing and communications [79]. Simi larly, AlP, with the largest direct gap of the IIIV com pound semiconductors, is undoubtedly the most “exotic”. Usually, this material is alloyed with other binary mate rials for applications in electronic devices such as light emitting diodes (e.g. aluminium gallium indium phosphi de) [10]. Motivated by the technological importance of these materials, IIIphosphides have been the subject of vari ous theoretical investigations, from empirical [42] to first principles based on the density functional theory (DFT) [43,44]. Most of these studies have been undertaken us ing the pseudopotential [45] or the fullpotential lin earizedaugmented plane wave (FPLAPW) method which considered to be one of the most accurate methods for calculating the structural and the electronic properties of solids, within the local density approximation (LDA) [46] or the generalized gradient approximation (GGA) [47]. Nevertheless, to the best of our knowledge, the (FP LMTO) method has not yet been used to study the struc tural and the electronic properties of AlxIn1–xP alloy. Below, we report the results obtained in the study of the variation of different structural and electronic pa rameters such as lattice constant, bulk modulus, band gap and effective masses with the alloy fraction using the
Structural and Electronic Properties Calculations of Al In P Alloy 730 x1–x (FPLMTO) method. In our calculations, we have adopted the “special quasirandom structures” (SQS) ap proach [48,49] which is based on the observation that (for any given composition) atomic disorder mainly af fects the electronic properties of an alloy through the shortrange atomic structure. In fact, Zunger and co workers have introduced “SQS” approach by the princi ple of close reproduction of the perfectly random net work for the first few shells around a given site. The paper is divided in three parts. In Section 2, we briefly describe the computational techniques used in this study. The most relevant results obtained for the ground state properties as well as the bandgap, optical bowing and effective masse are presented and discussed in Sec tion 3. Finally, in Section 4 we summarize the main con clusions of our work. 2. Computational Details The calculations reported here were carried out using the abinitio fullpotential linear muffintin orbital (FP LMTO) method [50,51] as implemented in the Lmtart code [52]. The exchange and correlation potential was calculated using the local density approximation (LDA) [46] and the generalized approximation (GGA) [47]. This is an improved method compared to previous (LMTO) methods. The FPLMTO method treats muffintin spheres and interstitial regions on the same footing, leading to improvements in the precision of the eingen values. At the same time, the FPLMTO method, in which the space is divided into an interstitial regions (IR) and non overlapping muffintin spheres (MTS) sur rounding the atomic sites, uses a more complete basis than its predecessors. In the IR regions, the basis func tions are represented by Fourier series. Inside the MTS spheres, the basis functions are represented in terms of numerical solutions of the radial Schrödinger equation for the spherical part of the potential multiplied by spherical harmonics. The charge density and the potential are represented inside the MTS by spherical harmonics up to lmax = 6. The integrals over the Brillouin zone are performed up to 35 special kpoints for binary com pounds and 27 special kpoints for the alloys in the irre ducible Brillouin zone (IBZ), using the Blöchl’s modi fied tetrahedron method [53]. The selfconsistent calcu lations are considered to be converged when the total energy of the system is stable within 10–5 Ry. In order to avoid the overlap of atomic spheres the MTS radius for each atomic position is taken to be different for each case. Both the plane waves cutoff are varied to ensure the total energy convergence. The values of the sphere radii (MTS), number of plane waves (NPLW), used in our calculation are summarized in Table 1. 3. Results and Discussions 3.1. Structural Parameters To investigate the structural properties of AlP and InP compounds and their alloys in the cubic structure, we have started our FPLMTO calculation with the zincblende structure and let the calculation forces to move the atoms to their equilibrium positions. We have chosen the basic cubic cell as the unit cell. In the unit cell there are four C anions , three A and one B, two A and two B, and one A and three B cations, respectively, for x = 0.25, 0.50 and 0.75. For the considered structures, we perform the structural optimization by calculating the total energies for different volumes around the equilibrium cell volume V0 of the binary AlP, InP compound and their alloy. The Table 1. The plane wave number PW, energy cutoff (in Ry) and the muffintin radius (MTS) (in a.u.) used in calculation for binary AlP and InP and their alloy in zinc ble nde (ZB) str uc ture. PW Ecut total (Ry) MTS (a.u) x LDA GGA LDA GGA LDA GGA 0 5064 12050 92.120 156.381 In 2.453 2.510 P 2.357 2.412 0.25 33400 65266 131.543 197.867 Al 2.395 2.411 In 2.395 2.411 P 2.348 2.939 0.50 33400 65266 136.726 205.941 Al 2.349 2.393 In 2.349 2.393 P 2.303 2.346 0.75 33400 65266 142.279 215.299 Al 2.280 2.340 In 2.280 2.340 P 2.280 2.294 1 5064 12050 105.387 184.707 Al 2.248 2.264 P 2.248 2.264 Copyright © 2011 SciRes. MSA
Structural and Electronic Properties Calculations of Al In P Alloy 731 x1–x calculated total energies are fitted to the Murnaghan’s equation of state [54] to determine the ground state prop erties such as the equilibrium lattice constant a, and the bulk modulus B. The calculated equilibrium parameters (a and B) are given in Table 2 which also contains results of previous calculations as well as the experimental data. The lattice constants obtained within the LDA for the parent binary system InP and AlP are respectively 0.17 % and 0.03 % lower than the experimental value, while the corresponding bulk modulus are 0.7% and 1.2% larger than the experimental value, which is the usual level of accuracy of the LDA. When comparing the results ob tained within GGA, the lattice constant are 2.6 % for InP and 1.6 % for AlP larger than the experimental values and the corresponding bulk modulus are 15.14% and 4.7% smaller than the corresponding experimental values. Hence it is safe to conclude that the LDA bulk modulus and lattice constants is in fact in better agreement with the experimental data than the GGA values. The calculated bulks modulus using both approximation LDA and GGA decreases in going from AlP to InP, suggesting the more compressibility for InP compared to that for AlP. Usually, in the treatment of alloys when the experi mental data are scare, it is assumed that the atoms are located at the ideal lattice sites and the lattice constants varies linearly with concentration x according to the socalled Vegard’s law [55]. 1 1 xAC aABC xaxa where AC and BC are the equilibrium lattice con stants of the binary compounds AC and BC respectively, (AxB1–xC) is the alloy lattice constant. However, the law was postulated on empirical evidence, several cases of both positive and negative deviations from this law have been documented [56,57]. Hence, it has been sug gested in the literature that the deviation from Vegard’s law can be represented by a quadratic expression: a a a 1 1 1 x xACBC aABC xaxaxxb (2) where b, is the bowing parameter accounting for the de viation from linearity. Figures 1 and 2, show the variation of the calculated equilibrium lattice constants and the bulk modulus versus concentration x for AlxIn1–xP alloy. Our calculated lattice constants were found to vary almost linearly following the Vegard’s law [55] with a marginal upward bowing parameters equal to –0.07143 Å. In going from InP to AlP, when the Alcontent increases, the values of the lattice parameters of AlxIn1–xP alloy decrease. This is due to the fact that the size of the Al atom is smaller than that of the In atom. Oppositely, one can see from Figure 2 that the value of the bulk modulus increases with the increase of Al concentration. The deviation of the GGA bulk modulus from the linear concentration dependence with a downward bowing equal to +21.9259 GPa. The bowing lattice parameters and the bulk modulus are found to be equal to –0.168 Å and +13.9569 GPa by us ing LDA approximation. In view on Table 2, it is clear BC (1) Table 2. Computed lattice parameter a and bulk modulus B compared to experimental and other theoretical values of AlP and InP and their alloy. Lattice constant a(Ǻ) Bulk modulus B(GPa) this work. exp. other calc. this work. exp. other calc. LDA GGA LDA GGA x 0 5.8509 6.014 5.861b 5.942a,5.688c,5.869d71.5399 60.25 71b 68 a,70c,73.26g ,5.8686e ,5.8783g,5.729h,5.838l,73.60h ,71l ,62l ,5.968l ,5.729m,5.930n,74m ,76n ,76s ,5.6591o ,5.93s 0.25 5.7979 5.9092 73.2808 61.4585 0.5 5.687 5.7922 75.7209 65.5753 0.75 5.5749 5.6649 80.2789 72.4857 1 5.449 5.534 5.451e 5.471c ,5.462d ,5.44285g 87.067 81.89 86f 84.5 c,95.46g,88.60h ,5.467i ,5.41700h,5.508j,5.42k,81.52j ,86.5k ,89l ,5.520n ,5.4131o ,5.43p 90,46p ,90q ,88r ,5.40q ,5.48r aRef. [11]; bRef. [12]; cRef. [13]; dRef. [14]; eRef. [17]; fRef. [18]; gRef. [19]; hRef. [20]; iRef. [23]; jRef. [24]; kRef. [25]; lRef. [26]; mRef. [27]; nRef. [29]; oRef. [31]; pRef. [32]; qRef. [33]; rRef. [34]; sRef. [39]. Copyright © 2011 SciRes. MSA
Structural and Electronic Properties Calculations of Al In P Alloy 732 x1–x Figure 1. Composition dependence of the calculated lattice constants within GGA (solid circ le) and LDA (solid squares) of AlxIn1–xP alloy compared with Vegard’s prediction (dot line). Figure 2. Composition dependence of the calculated bulk modulus within GGA (solid circle) and LDA (solid squares) AlxIn1–xP alloy. that the LDA yields higher values than the experiment while GGA provides a good agreement. 3.2. Electronic Properties The important features of the band structure (direct ΓΓ and indirect ΓX band gaps) are given in Table 3. It is clearly seen that the band gaps are on the whole underes timated in comparison with experiments results. This underestimation of the band gaps is mainly due to the fact that both the simple form of LDA or GGA do note take into account the quasiparticle self energy correctly [58] which make them not sufficiently flexible to accu rately reproduce both exchange and correlation energy and its charge derivative. We worth also mention that in general, it is far to say that the experimental data are well reproduced by the calculation. On raison for this differ ence is that in our calculations we have assumed the crystal to be at T = 0 K and thus do not include contribu tions from lattice vibrations that are present at room temperature measurements. The calculated band gaps for AlP compound and in good agreement with the available theoretical results. This agreement disappears for the case of InP compound. Figure 3 shows the plots of the concentration variation of the direct gap ( and indirect gap (ΓX) the studied alloys within both LDA and GGA. Increasing Al content leads to a shift of the conduction band (CB) upwards the Fermi energy (EF) resulting an increase of the direct energy band gap (. The calculated direct band gap values are 0.56 (0.26), 1.0 (0.83), 1.58 (1.45), 1.75 (1.74) and 3.36 (3.08) eV within of LDA (GGA) approach for x = 0.0, 0.25, 0.5, 0.75 and 1.0, respectively. The band structure calculations in the present work yield a direct gap (Γ–Γ) for InP, while for AlP compound an indirect gap (Γ–X) has been determined. Hence, one can expect that the band gap of AlxIn1–xP alloys should undergo a crossover between the direct and the indirect band in going from x = 0 to x = 1. As shown in Figure 3, this crossover oc curs at x = 0.79 for LDA and at 0.82 for GGA. For both approximation the predicted crossover value is twice larger that those determined by Onton and coauthors [59]. 6.1 6.0 5.9 5.8 5.7 5.6 5.5 5.4 0.0 0.2 0.4 0.6 0.8 1.0 The calculated band gap versus concentrations was fitted by a polynomial equation. 1 gAC BC Ex xExEbxx 1 (3) where EAC and EBC corresponds to the of the AlP and InP gaps for the AlxIn1–xP alloy. The results are shown in Figure 3 and are summarized as follows: 0.0 0.2 0.4 0.6 0.8 1.0 2 2 X1 E0.680.0562.41 (LDA) E=1.56+4.124.05Al InP x xx xx (4) 2 2 X E12.96 4.011.39(GGA) E1.73 3.813.69 xx xx It is clear from the above equations that the direct (Γ → Γ) and indirect (Γ → X) band gaps versus concentra tion have a nonlinear behavior. The direct gap (Γ → Γ) has a downward bowing with a value of 1.396, while the indirect gap (Γ → X) has an upward bowing of –3.907. These parameters are lower than those obtained using the LDA (2.38 and –4.059). The physical origins of gap bowing were investigated following the approach of Zunger and coworkers [60], which decompose it into three contributions. The overall bowing coefficient at a given average composition x measures the change in the band gap according to the formal reaction 1 AC1 BC ACBCx xeq axaABC a (5) where and AC a C a are the equilibrium lattice constant Copyright © 2011 SciRes. MSA
Structural and Electronic Properties Calculations of Al In P Alloy 733 x1–x Table 3. Direct band gap energy of AlxIn1xP alloys at different Al concentrations (all values are in eV). Energy gap (eV) (ГГ) Energy gap (eV) (ГX) this work. exp. other calc. this work. exp. other calc. LDA GGA LDA GGA x 0 0.5647 0.2674 1.39 c, 1.39 a,1.98e,1.23f, 1.6479 1.8804 0.43g ,1.5522n, 2.19r 1.35d, 1.54g,1.67h ,0.62j 1.424l, ,0.85j,1.50j,1.232k, 1.350m 1.3831n,1.34r 0.25 1.0099 0.8315 2.3836 2.7014 0.5 1.5819 1.4578 2.3997 2.5271 0.75 1.578 1.742 2.5961 2.7014 1 3.3666 3.0881 3.63b , 3.44a,2.54e ,3.26f , 1.4658 1.6386 2.50b, 2.17 a,1.44g,1.635i, 2.45d 2.55g ,3.073i, 3.3457n, ,2.52s ,1.44 j,1.57j,2.50j 3.11o ,3.62p ,3.073q ,2.500l ,1.4194n,1.41o,1.49t ,2.50p,1.635q aRef. [14]; bRef. [15]; cRef. [16]; dRef. [17]; eRef. [19]; fRef. [20]; gRef. [21]; hRef. [22]; iRef. [24]; jRef. [26]; kRef. [27]; lRef. [28]; mRef. [30]; nRef. [31]; oRef. [32]; pRef. [36]; qRef. [37]; rRef. [38]; sRef. [23]; tRef. [35] lattice constant of the alloy with the average composition x. Figure 3. Energy band gap of AlxIn1–xP alloy as a function of Al composition using LDA and GGA approximations. 3.0 2.5 2.0 1.5 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1.0 Figure 4. Calculated optical bowing parameter as a function of composition vx within LDA (xCenter Square) and GGA (Center circle). 0.5 0.0 0.2 0.4 0.6 0.8 1.0 The Equation (5) is decomposed into three steps: 3.0 AC BC AC BC aaACaBCa (6) 2.5 1 AC1 BC xx axaABC a (7) 2.0 11 xxxeq BCa ABCa (8) 1.5 1.0 The first step measures the volume deformation (VD) effect on the bowing. The corresponding contributions bVD to the bowing parameter represents the relative re sponse of the band structure of the binary compounds AC and BC to hydrostatic pressure, which here arises from the change of their individual equilibrium lattice con stants to the alloy value a = a(x). The second contribution, 0.5 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Copyright © 2011 SciRes. MSA
Structural and Electronic Properties Calculations of Al In P Alloy 734 x1–x 1 the charge exchange (CE) contribution bCE, reflects the charge transfer effect which is due to the different (aver aged) bonding behavior at the lattice constant a. The fi nal step measures changes due to the structural relaxation (SR) in passing from the unrelaxed to the relaxed alloy by bSR. Consequently, the total bowing parameter is de fined as b = bVD + bCE + bSR. (9) The general representation of the compositiondepen dent band gap of the alloys in terms of binary compounds gaps of the, EAC(aAC) and EBC(aBC), and the total gap bowing parameter b is defined as: 1 gACAC BCBC Ex xEaxEabxx (10) This allows a division of the total gap bowing b into three contributions according the following expressions: 1 AC ACACBCBCBC VD EaEa EaEa bxx (11) 1 AC BC ABC CE EaEaE a b1 xx x (12) 1 ABCABC eq SR EaEa bxx (13) All terms presented in Equations (11)(13) are com puted separately via selfconsistent band structure calcu lations. The different contributions to the gap bowing were calculated using the LDA and the GGA schemes and the results are given in Table 4. The calculated band gap bowing coefficient for random AlxIn1–xP alloy ranges from 1.3614 eV (x = 0.25) to 5.8396 (x = 0.75). Our re sult for x = 0.5 is higher than the experimental one and is in excellent agreement with those obtained by Ferhat and coauthors [61] using the full potential linearized aug mented plane wave. One can note that for x = 0.25 and 0.50 the main contribution to the gap bowing is due to the volume deformation (VD) effect. The importance of bVD can be correlated with the mismatch of the lattice constants of the corresponding binary compounds. Con sequently, the main contribution to the gap bowing is raised from the volume deformation effect. In the case of x = 0.75, the contribution of the charge transfer bCE has been found greater than those of the volume deformation bVD. This contribution is due to the different electronega tivities of the In and Al or P atoms. Indeed, bCE scales with the electronegativity mismatch. The contribution of the structural relaxation is negligible and the band gap bowing is due essentially to the charge exchange effect. Finally, it is clearly seen that our LDA values for bowing parameters are larger than the corresponding values within GGA. 3.3. Calculated Effective Masses The knowledge of the electron and hole effective mass values is indispensable for the understanding of transport phenomena, exciton effects and electrohole in semicon ductors. Therefore, it would be of much interest to de termine the electron and hole effective mass values for the alloys for various Al content. We have computed the electron effective mass at the conduction band minima (CBM) and hole effecRtive mass at the valence band maxima (VBM) for the studied alloy. The electron and hole effective masses values are obtained from the cur vature of the energy band near the Γpoint at the CBM and VBM for all concentration. At the Гpoint the slike conduction band effective mass can be obtained through a simple parabolic fit using the definition of the effective mass as the second derivative of the energy band with respect to the wave vector, k, via: m* /m0 =– (ћ2/m0)·1/(d2E/d k2) (14) Table 4. Decomposition of optical bowing into volume deformation (VD), charge exchange (CE) and structural relaxation (SR) contributions (all values in eV). this work. exp other cal. LDA GGA x 0.25 bVD 0.6354 0.6873 b CE –0.0756 –0.1583 b SR 0.8016 0.2234 b 1.3614 0.7524 0.5 bVD –0.039 0.7376 0.740b b CE 0.986 –0.09087 0.265b b SR –0.1312 0.2333 –0.172b b 0.815 0.880 0.38a, 0.568a 0.834b 0.75 bVD 0.7286 0.7941 b CE 5.2214 2.6625 b SR –0.1104 –0.0399 b 5.8396 3.4167 aRef. [40]; bRef. [61] Copyright © 2011 SciRes. MSA
Structural and Electronic Properties Calculations of Al In P Alloy735 x1–x Table 5. Electron (), light hole () and heavy hole () effective mass (in units of free electron mass m0) of the ternary alloys under investigation compared with the available experimental and theoretical predictions. * e m* lh m* hh m * lh m * hh m * lh m this work. other calc. this work. other calc. this work. other calc. x LDA GGA LDA GGA LDA GGA 0 0.004 0.032 0.095a, 0.058a 0.351 0.603 0.389a, 0.477a 0.098 0.103 0.093a, 0.057a 0.570 b, 0.060b 0.430 b, 0.400b 0.097 a, 0.078a 0.079 b, 0.081b 0.47 b, 0.895a 0.104 b, 0.118b 0.520 b,0.610b 0.052 a, 0.074a 0.970 b, 0.90b 0.051 a 0.63 b, 0.950b 0.25 0.0042 0.047 0.804 0.770 0.219 0.367 0.50 0.032 0.042 4.126 0.7648 4.214 0.2602 0.75 0.0427 0.0428 0.857 0.8448 0.269 0.2870 1 0.167 0.024 0.176a, 0.170a 0.462 6.194 0.489a, 0.509a 0.159 0.182 0.187a, 0.181a aRef. [31]; bRef. [41]; cRef. [62] where m* is the conduction electron effective mass and m0 is the free electron mass. We can calculate the curva ture of the valence band maximum using the following approach: if the spinorbit interaction were neglected, the top of the valence band would have a parabolic behavior; this implies that the highest valence bands are parabolic in the vicinity of the Гpoint. In this work, all the studied systems satisfy this parabolic condition of the valence band maximum at the Гpoint. Within this approach, and by using the appropriate expression of Equation (14) (us ing a plus sign instead of the minus sign in the prefactor), we have computed the effective masses of the heavy and light holes at the Гpoint. The calculated electron and hole effective mass values for the parent binary compounds InP and AlP and their alloy are given in Table 5. Results from earlier theoretical works are also quoted for comparison. Our results for the binary compounds are in fairly good agreement with the available theoretical data. We would like mentioning here that the divergence of some values should be expected since the computation of the effective mass is very sensitive to the form of the energy band. The highest curvature of the electronic band yields the smallest effective mass of the charge carriers and the highest conductivity. From Table 5 data, we can outline that holes are much heavier than electrons, for all con centrations in AlxIn1–xP alloy, so carrier transport in this alloy should be dominated by electrons. 4. Conclusions We have performed firstprinciples calculations using (FPLMTO) method within the LDA and GGA for the zincblende AlxIn1xP alloy (x = 0.0; 0.25; 0.50; 0.75; 1.00). We have found that lattice parameter follows Ve gard’s law, the bulk modulus varies significantly with the composition x and the electronic band structure has a nonlinear dependence on the composition. We have cha racterized the deviation from the linear behavior by cal culating the optical bowing parameter. The main contri bution to the total bowing parameter arises from struc tural (volume deformation) and chemical effects. The computed effective masses of the systems studied are found comparable to those reported in literature. Our results provide an estimate of this important compound. 5. Acknowledgements The author Rabah KHENATA extends his appreciation to the Deanship of Scientific Research at King Saud Uni versity for funding the work through the research group project No RGPVPP088. REFERENCES [1] S. Dissanayake, S. X. Huang, H. X. Jiang and J. Y. Lin, “Charge Storage and Persistent Photoconductivity in a CdS0.5Se0.5 Semiconductor Alloym,” Physical Review B, Vol. 44, No. 24, 1991, pp. 1334313348. doi:10.1103/PhysRevB.44.13343 [2] H. X. Jiang, G. Brown and J. Y. Lin, “Persistent Photo conductivity in IIVI and IIIV Semiconductor Alloys and a Novel Infrared Detector,” Journal of Applied Physics, Vol. 69, No. 9, 1991, pp. 67016704. doi:10.1063/1.348889 [3] S. Krishnamurthy, A. Sher, M. Madou and A.B. Chen, “Semiconductor Alloys for Fast Thermal Sensors,” Jour nal of Applied Physics, Vol. 64, No. 3, 1988, pp. 1530 1532. doi:10.1063/1.341828 [4] M. Othman, E. Kasap and N. Korozlu, “AbInitio Inves tigation of Electronic and Optical Properties of InAs1xPx alloys,” Journal of Alloys and Compounds, Vol. 23, No. 2, 2009, pp. 149153. Copyright © 2011 SciRes. MSA
Structural and Electronic Properties Calculations of Al In P Alloy 736 x1–x [5] R. W. G. Wyckoff, “Crystal Structures,” 2nd Edition, Vol. 1, Robert E. Kreiger Publishing Company, Malabar, 1986, p. 239. [6] O. Madelung and L. Bornstein, “Numerical Data and Functional Relationships in Science and Technology New Series,” Springer, Berlin, 1982. [7] T. J. Coutts and S. Naseem, “High Efficiency Indium Tin Oxide/Indium Phosphide Solar Cells,” Applied Physics Letters, Vol. 46, No. 2, 1985, pp. 164167. doi:10.1063/1.95723 [8] M. S. Gudiksen, L. J. Lauhon, J. Wang, D. C. Smith and C. M. Lieber, “Growth of Nanowire Superlattice Struc tures for Nanoscale Photonics and Electronics,” Nature, Vol. 415, 2002, pp. 617620. doi:10.1038/415617a [9] J. F. Wang, M. S. Gudiksen, X. F. Duan, Y. Cui and C. M. Lieber, “Highly Polarized Photoluminescence and Pho todetection from Single Indium Phosphide Nanowires,” Science, Vol. 293, 2001, pp. 14551457. doi:10.1126/science.1062340 [10] D. E. C. Corbridge, “Phosphorus: An Outline of Its Che mistry, Biochemistry, and Technology,” 5th Edition, El sevier, Amsterdam, 1995. [11] A. Mujica and R. J. Needs, “Theoretical Study of the HighPressure Phase Stability of GaP, InP, and InAs,” Physical Review B, Vol. 55, No. 15, 1997, pp. 96599670. doi:10.1103/PhysRevB.55.9659 [12] O. Madelung and L. Bornstein, “Semiconductors, Physics of Group IV Elements and IIIV Compounds,” Vol. 17, New Series, Group III, Springer Verlag, Berlin, 1982. [13] S. B. Zhang and M. L. Cohen, “HighPressure Phases of IIIV ZincBlende Semiconductors,” Physical Review B, Vol. 35, No. 14, 1987, pp. 76047610. doi:10.1103/PhysRevB.35.7604 [14] M.Z. Huang and W. Y. Ching, “Calculation of Optical Excitations in Cubic Semiconductors. I. Electronic Struc ture and Linear Response,” Physical Review B, Vol. 47, No. 15, 1993, pp. 94499463. doi:10.1103/PhysRevB.47.9449 [15] W. A. Harrison, “Electronic Structure and the Properties of Solids,” Freeman, San Francisco, 1980. [16] E. Brustein, H. Brodsky and G. Lucousky, International Journal of Quantum Chemistry, Vol. 756, 1987. [17] S. M. Sze, “Physics of Semiconductor Device,” Wiley Interscience Publication, New York 1981, pp. 848849. [18] L. Bornshtein, “Numerical Data and Functional Rela tionships in Science and Technology. New Series. Grou pIII: Crystal and Solid State Physics. Semiconductors. Physics of Group IV Elements and IIIV Compounds,” Vol. 22, Springer Verlag, Berlin, 1987. [19] V. Khanin and S. E. Kul’kova,” Electronic Properties of IIIV Semiconductors,” Russian Physics Journal, Vol. 48, No. 1, 2005, pp. 6167. doi:10.1007/s1118200500861 [20] S. O. Wang and H. O. Ye, “PlaneWave Pseudopotential Study on Mechanical and Electronic Properties for IV and IIIV Crystalline Phases with ZincBlende Structure,” Physical Review B, Vol. 66, No. 23, 2002, pp. 235111 235118. doi:10.1103/PhysRevB.66.235111 [21] K. A. Johnson, “Corrections to DensityFunctional The ory Band Gaps,” Physical Review B, Vol. 58, No. 23, 1998, pp. 1554815556. doi:10.1103/PhysRevB.58.15548 [22] R. W. Jansen and O. F. Sankey, “Ab Initio Linear Com bination of PseudoAtomicOrbital Scheme for the Elec tronic Properties of Semiconductors: Results for Ten Ma terials,” Physical Review B, Vol. 36, No. 12, 1987, pp. 65206531. doi:10.1103/PhysRevB.36.6520 [23] I. Vurgaftman, J. R. Meyer and L. R. RamMohan, “Band Parameters for IIIV Compound Semiconductors and Their Alloys,” Journal of Applied Physics, Vol. 89, No. 11, 2001, pp. 58155876. doi:10.1063/1.1368156 [24] L. H. Yu, K. L. Yao and Z. L. Liu, “Electronic Band Structures of Filled Tetrahedral Semiconductor LiMgP and ZincBlende AlP,” Solid State Communications, Vol. 135, No. 12, 2005, pp. 124128. doi:10.1016/j.ssc.2005.03.041 [25] S. Froyen and M. L. Cohen, “Structural Properties of IIIV ZincBlende Semiconductors under Pressure,” Phy sical Review B, Vol. 28, No. 6, 1983, pp. 32583265. doi:10.1103/PhysRevB.28.3258 [26] R. Ahmed, FazaleAleem, S. J. Hashemifar and H. Ak barzadeh, “FirstPrinciples Study of the Structural and Electronic Properties of IIIPhosphides,” Physica B, Vol. 403, No. 1011, 2008, pp. 18761881. doi:10.1016/j.physb.2007.10.342 [27] F. E1. Haj Hassan1, H. Akbarzadeh and M. Zoaeter, “Structural Properties of Boron Compounds at High Pressure,” Journal of Physics: Condensed Matter, Vol. 16, 2004, pp. 293301. doi:10.1088/09538984/16/3/009 [28] R. W. G. Wyckoff, “Crystal Structures,” Second Edition, Krieger, Malabar, 1986. [29] O. Madelung and L. Bornstein, “Semiconductors, Physics of Group IV Elements and IIIV Compounds,” Vol. 17, New Series, Group III, Springer Verlag, Berlin, 1982. [30] S. Q. Wang and H. Q. Ye, “PlaneWave Pseudopotential Study on Mechanical and Electronic Properties for IV and IIIV Crystalline Phases with ZincBlende Structure,” Physical Review B, Vol. 66, No. 23, 2002, pp. 235111 235118. doi:10.1103/PhysRevB.66.235111 [31] S. Z. Karazhanov and L. C. Lew Yan Voon, “Ab Initio Studies of the Band Parameters of IIIV and IIVI Zinc Blende Semiconductors,” Semiconductors, Vol. 39, No. 2, 2005, pp. 161173. [32] S. Aouadi, P. RodriguezHernandez, K. Kassali and A. Muñoz, “Lattice Dynamics Properties of ZincBlende and Nickel Arsenide Phases of AlP,” Physics Letters A, Vol. 372, No. 32, 2008, pp. 53405345. doi:10.1016/j.physleta.2008.06.010 [33] P. RodriguezHernández and A. Muñoz, “Ab Initio Cal culations of Electronic Structure and Elastic Constants in AlP,” Semiconductor Science and Technology, Vol. 7, No. 12, 1992, p. 1437. doi:10.1088/02681242/7/12/002 [34] L. Börstein, “Semicondutors Physics of Group IV Ele Copyright © 2011 SciRes. MSA
Structural and Electronic Properties Calculations of Al In P Alloy737 x1–x ments and IIIV Compounds,” Vol. III/17a, Springer Verlag, Berlin, 1992. [35] A. H. Reshak and S. Auluck, “Investigation of the Elec tronic Properties, First and Second Harmonic Generation for AXIIIBXV ZincBlende Semiconductors,” Physica B, Vol. 395, No. 12, 2007, pp. 143150. doi:10.1016/j.physb.2007.03.012 [36] I. Vurgaftman, J. R. Meyer and L. R. RamMohan, “Band Parameters for IIIV Compound Semiconductors and Their alloys,” Journal of Applied Physics, Vol. 89, No. 11, 2001, pp. 58155876. doi:10.1063/1.1368156 [37] L. H. Yu, et al., “Electronic Band Structures of Filled Tetrahedral Semiconductor LiMgP and ZincBlende AlP,” Solid State Communications, Vol. 135, No. 12, 2005, pp. 124128. doi:10.1016/j.ssc.2005.03.041 [38] Bechiri, F. Benmakhlouf and N. Bouarissa, “Band Struc ture of IIIV Ternary Semiconductor Alloys beyond the VCA,” Materials Chemistry and Physics, Vol. 77, No. 2, 2002, pp. 507510. doi:10.1016/S02540584(02)001244 [39] M. Causà, R. Dovesi and C. Roetti, “Pseudopotential HartreeFock Study of Seventeen IIIV and IVIV Semi conductors,” Physical Review B, Vol. 43, No. 14, 1991, pp. 1193711943. doi:10.1103/PhysRevB.43.11937 [40] M. Moser, R. Wienterhoff, C. Geng, J. Quisser, F. Scholz and A. Dörden, “Refractive Index of (AlxGa1−x)0.5In0.5P Grown by Metalorganic Vapor Phase Epitaxy,” Applied Physics Letters, Vol. 64, No. 2, 1994, pp. 235238. doi:10.1063/1.111514 [41] H. Fu and A. Zunger, “LocalDensityDerived Semiem pirical Nonlocal Pseudopotentials for InP with Applica tions to Large Quantum Dots,” Physical Review B, Vol. 55, No. 55, 1997, pp. 16421653. doi:10.1103/PhysRevB.55.1642 [42] M. Ferhat, A. Zaoui, M. Certier and H. Aourag, “Elec tronic Structure of BN, BP and Bas,” Physica B, Vol. 252, No. 3, 1998, pp. 229236. doi:10.1016/S09214526(98)001495 [43] P. Hohenberg and W. Kohn, “Inhomogeneous Electron Gas,” Physical Review, Vol. 136, No. 3B, 1964, pp. B864B871. [44] W. Kohn and L. J. Sham, “SelfConsistent Equations Including Exchange and Correlation Effects,” Physical Review A, Vol. 140, No. 4A, 1965, pp. A1133A1138. doi:10.1103/PhysRev.140.A1133 [45] W. E. Pickett, “Pseudopotential Methods in Condensed Matter Applications,” Computer Physics Reports, Vol. 9, No. 3, 1989. pp. 115197. doi:10.1016/01677977(89)900026 [46] J.P. Perdew and Y. Wang, “Accurate and Simple Analytic Representation of the ElectronGas Correlation Energy,” Physical Review B, Vol. 45, No. 13, 1992, pp. 13244 13249. doi:10.1103/PhysRevB.45.13244 [47] J. P. Perdew, S. Burke and M. Ernzerhof, “Generalized Gradient Approximation Made Simple,” Physical Review Letters, Vol. 77, No.18, 1996, pp. 38653868. doi:10.1103/PhysRevLett.77.3865 [48] Zunger, S.H. Wei, L. G. Ferreira and J. E. Bernard, “Special Quasirandom Structures,” Physical Review Let ters, Vol. 65, No. 3, 1990, pp. 353356. doi:10.1103/PhysRevLett.65.353 [49] S.H. Wei, L. G. Ferreira, J. E. Bernard and A. Zunger, “Electronic Properties of Random Alloys: Special Qua sirandom Structures,” Physical Review B, Vol. 42, No. 15, 1990, pp. 96229649. doi:10.1103/PhysRevB.42.9622 [50] S. Savrasov and D. Savrasov, “FullPotential Linear MuffinTinOrbital Method for Calculating Total Ener gies and Forces,” Physical Review B, Vol. 46, No.19, 1992, pp. 1218112195. doi:10.1103/PhysRevB.46.12181 [51] S. Y. Savrasov, “LinearResponse Theory and Lattice Dynamics: A MuffinTinOrbital Approach,” Physical Review B, Vol. 54, No. 23, 1996, pp. 1647016486. doi:10.1103/PhysRevB.54.16470 [52] 2007. Internet Available: http://www.physics.ucdavis.edu/_savrasov/S [53] P. Blochl, O. Jepsen and O. K. Andersen, “Improved Tetrahedron Method for BrillouinZone Integrations,” Physical Review B, Vol. 49, No. 23, 1994, pp. 16223 16233. doi:10.1103/PhysRevB.49.16223 [54] F. D. Murnaghan, “The Compressibility of Media under Extreme Pressures,” Proceedings of the National Acad emy of Sciences USA, Vol. 30, 1944, pp. 244247. doi:10.1073/pnas.30.9.244 [55] L. Vegard, “Formation of Mixed Crystals by SolidPhase Contact,” Journal of Physics, Vol. 5, No. 5, 1921, pp. 393395. [56] Jobst, D. Hommel, U. Lunz, T. Gerhard and G. Landwehr, “E0 BandGap Energy and Lattice Constant of Ternary Zn1−xMgxSe as Functions of Composition,” Applied Physics Letters, Vol. 69, No. 1, 1996, pp. 97100. doi:10.1063/1.118132 [57] F. El Haj Hassan and H. Akdarzadeh, “FirstPrinciples Investigation of BNxP1–x, BNxAs1–x and BPxAs1–x Ternary Alloys,” Materials Science and Engineering, Vol. 121, 2005, pp. 171178. [58] S. N. Rashkeev and W. R. L. Lambrecht, “SecondHar monic Generation of IIIIVI2 Chalcopyrite Semiconduc tors: Effects of Chemical Substitutions,” Physical Review B, Vol. 63, No. 16, 2001, pp. 165212165224. doi:10.1103/PhysRevB.63.165212 [59] A. Onton and R. J. Chicotka, “Conduction Bands in In1−xAlxP,” Journal of Applied Physics, Vol. 41, No. 10, 1970. pp. 42054208. [60] J. E. Bernard and A. Zunger, “Optical Bowing in Zinc Chalcogenide Semiconductor Alloys,” Physical Review B, Vol. 34 , No. 8, 1986, pp. 59925995. doi:10.1103/PhysRevB.34.5992 [61] M. Ferhat, “Computational Optical Band Gap Bowing of IIIV Semiconductors Alloys,” Physica Status Solidi (B), Vol. 241, No. 10, 2004, pp. R38R41. doi:10.1002/pssb.200409048 [62] M.Z. Huang and W. Y. Ching, “A Minimal Basis Semi Ab Initio Approach to the Band Structures of Semicon Copyright © 2011 SciRes. MSA
Structural and Electronic Properties Calculations of AlxIn1–xP Alloy Copyright © 2011 SciRes. MSA 738 ductors,” Journal of Physics and Chemistry of Solids, Vol. 46, No. 8, 1985, pp. 977995. doi:10.1016/00223697(85)901015
