Monte Carlo simulations applied to AlxGayIn1xyX quaternary alloys X=As,P,N:A comparative study
M. Marques,1 L. G. Ferreira,2 L. K. Teles,1 and L. M. R. Scolfaro1,*1Instituto de Fsica, Universidade de So Paulo, Caixa Postal 66318, 05315-970 So Paulo, So Paulo, Brazil
2Instituto de Fsica Gleb Wataghin, Universidade Estadual de Campinas, Caixa Postal 6165, 13083-970 Campinas, So Paulo, BrazilsReceived 18 October 2004; published 13 May 2005d
We develop a different Monte Carlo approach applied to the AxByC1xyD quaternary alloys. Combined withfirst-principles total-energy calculations, the thermodynamic properties of the sAl,Ga, IndX sX=As, P, or Ndsystems are obtained and a comparative study is developed in order to understand the roles of As, P, and Natoms as the anion X in the system AlxGayIn1xyX. Also, we study the thermodynamics of specific composi-tions in which AlGaInN, AlGaInP, and AlGaInAs are lattice matched, respectively, to the GaN, GaAs, and InPsubstrates. We verify that the tendency for phase separation is always towards the formation of an In-richphase. For arsenides and phosphides this occurs in general for lower temperatures than for their usual growthtemperatures. This makes these alloys very stable against phase separation. However, for nitrides the In and/orAl concentrations have to be limited in order to avoid the formation of In-rich clusters and, even for lowconcentrations of In and/or Al, we observe a tendency of composition fluctuations towards the clustering of theternary GaInN. We suggest that this latter behavior can explain the formation of the InGaN-like nanoclustersrecently observed in the AlGaInN quaternary alloys.
DOI: 10.1103/PhysRevB.71.205204 PACS numberssd: 61.66.Dk, 64.75.1g, 71.20.Nr, 71.22.1i
In the development of heterostructure-based devices, thedouble requirement of high-quality crystalline layers epitaxi-ally grown on a given substrate with low-misfit-dislocationdensity and an optimized electronic structure are generallyvery difficult to achieve using the common binary and ter-nary compounds. Quaternary semiconducting alloys of theAxByC1xyD kind are very interesting materials, becausetheir use can be considered as an effective approach to re-duce defect density in the heterostructures. Such systems al-low the independent control of both lattice parameter andband-gap energy sthrough x and yd, avoiding the lattice mis-matching and, at the same time, providing an adjustable en-ergy gap for barriers and active layers. In this sense, thelattice-matched systems such as, e.g., AlGaInAs/ InP andAlGaInP/GaAs, have been extensively studied from the ex-perimental point of view. More recently, the AlGaInN/GaNsystem has been studied, showing aspects not observed be-fore. In spite of the great number of experimental works onthe quaternary semiconductor alloys, there are only a fewtheoretical studies,1 mainly due to the complex treatment ofthese systems in a more rigorous way. Particularly, the theo-retical works that involve quaternary alloys make use of verysimplified models, because the more rigorous treatments,such as first principles and Monte Carlo thermodynamics, arevery difficult to apply. Therefore, it is highly desirable tohave a method which gives very rigorous results togetherwith a reasonable computational effort. In the present work,we develop a different Monte Carlo approach, to be usedtogether with first-principles, self-consistent, total-energycalculations for the study of quaternary alloys. We apply thisapproach to study the phase-separation process of the seriesof III-V face-centered-cubic sfccd pseudoternary semicon-ductor alloys AlxGayIn1xyAs, AlxGayIn1xyP, and
AlxGayIn1xyN, in which a microscopic description of thephase separation is performed. We make a comparative studyand an individual study of each alloy for the lattice-matchedsystems of experimental importance.
The motivation for the study of the AlxGayIn1xyAs/InPlattice-matched system arises from its importance for deviceapplications relevant to optical communications such asemitters, waveguides, lasers, and infrared detectors.2,3 This ismainly because the band-gap energy range covered bylattice-matched quaternary alloys overlaps the region ofminimum loss and dispersion current s0.81.2 eVd for opti-cal fibers. The lattice-matched condition with an InP sub-strate is sGa0.47In0.53AsdzsAl0.48In0.52Asd1z, with z from 0 to1, providing a direct energy-gap variation from0.74 to 1.45 eV. However, a shorter lasing wavelength is re-quired for high-density optical information processing sys-tems. Despite the fact that AlP and GaP binary compoundspresent an indirect energy gaps, the phosphide ternaries andquaternaries may have higher direct energy gaps than thearsenides. Particularly, the sAlxGa1xd0.5In0.5P quaternary al-loy is lattice matched to GaAs and, except for the nitrides, ithas the largest direct energy gap among the III-V semicon-ductors, with the emission wavelength being tunable fromred to green by changing the amount of Al. For laser diodes,the AlGaInP forms the barrier with the active layer being theGaInP ternary compound or even the quaternary compoundwith a lower Al concentration. The main commercial interestin devices based on these systems is in the continuing evo-lution of compact-disk technology snow based on theAlGaAs/GaAs system, providing a 780-nm emissiond to-wards the digital-video-disk sDVDd technology. The currentgeneration of DVDs uses an AlGaInP red laser with anemission wavelength of 650 nm. Shorter wavelengthsshigher band gapsd, though desirable, lead to poor AlGaInP-sample quality and an indirect band gap. These two factorsimply a very-low-emission efficiency.
PHYSICAL REVIEW B 71, 205204 s2005d
1098-0121/2005/71s20d/205204s11d/$23.00 2005 The American Physical Society205204-1
Bulk AlGaInP, like AlGaInAs, is very stable against clus-tering or phase separation. In the whole compositional rangeof the quaternary lattice matched to GaAs, a good structuralquality and high compositional uniformity is obtained.4However, there are surface effects that lead to differentphases rather than solid solution. Through the combined ef-fects of the surface thermodynamics and kinetics, the com-position modulation and the CuPt-ordered structure can existtogether in the AlGaInP matrix.5 The ordering dramaticallyaffects the electronic properties of the material, and in par-ticular reduces the direct-energy-gap. Therefore, this phase isundesirable for device applications as it leads to longerwavelength emission, and, because the ordering is not uni-form, the resulting large-crystal inhomogeneity likely leadsto inferior device performance. But the generation of orderedstructures can be suppressed by several means, such as theincrease of the growth temperature6 above 700 C, the use ofmisoriented substrates, and the use of p-type doping.7
In the last few years, great progress has been made in theresearch of GaN and related semiconductors, which presentlarger energy gaps than the phosphides and arsenides. As aresult, blue-green light-emission diodes sLEDsd as well asultraviolet sUVd laser diodes sLDsd have been commer-cialized.8 Recently, the AlGaInN quaternary alloys attractedmuch attention due to the fact that lattice-matched materialscan be obtained with a possible energy gap in the deep-UVregion. In addition, the incorporation of Indium in the AlGaNternary alloy, forming the AlGaInN quaternary alloy has nowbeen demonstrated to improve the optical quality of the alloylayer for the UV-emission alloy,9 even when the Al content isincreased. Until now it had not been possible to grow good-quality material in the whole compositional range, and themajority of the samples presents an In concentration lowerthan 4%. But, despite these problems, an increasing numberof experimental works on AlGaInN have been presented. Thesuccessful applications are the recently produced nearlylattice-matched AlGaInN/GaInN UV LDs,10 theAlGaInN/AlGaInN deep-UV LEDs, and the UV LDs.11,12These optical devices can emit a wavelength smaller than400 nm, which is a great improvement in our capacity forinformation storage. Nevertheless, questions concerning thiscomplex system remain still open. For example, the emissionmechanism involved in the UV spectra is frequently associ-ated to the existence of In-rich phases or GaInN-like clusters,and not to the band-to-band transition in the quaternary alloyitself.13,14 Moreover, some samples show a green emissionaround 2.4 eV besides the UV emission.15 These facts lead tothe possibility of a phase-separation process in this alloy.Several works show evidence of alloy inhomogeneities, withthe formation of possible clusters in the matrix of thealloy.13,14 But the questions of how the In nucleation takesplace in the bulk of the AlGaInN quaternary alloys sin whichcomponents the alloy separatesd and what the relation is be-tween the In-separated phases remain under discussion.
Therefore, we not only develop an approach for the studyof AxByC1xyD quaternary systems, but also present a rigor-ous and systematic theoretical study of the thermodynamicproperties of some important quaternary systems, from
which we can obtain new features of their phase-separationprocesses. The paper is organized as follows. In Sec. II wedescribe the details of the calculation methods. In Sec. III wediscuss alloy stabilities and analyze the experimentally rel-evant lattice-matched systems. Finally, a summary is given inSec. IV.
II. CALCULATION METHODS
In this section we describe the main ideas behind the com-putational methods used in this paper.
A. The ternary expansion and the Monte Carlo approach
In a ternary alloy AxByC1xy or pseudoternary squater-naryd alloy AxByC1xyD, the sites of a crystal lattice areoccupied by A, B, and C atoms in different configurations. Toperform Monte Carlo studies o