Precipitation in AlxGa1-xNyAs1-y Alloys - Crystal Growth & Design

CRYSTAL GROWTH & DESIGN

Precipitation in AlxGa1-xNyAs1-y Alloys Vyatcheslav A. Elyukhin* and Lyudmila P. Sorokina Departamento de Ingenierı´a Ele´ ctrica-SEES, CINVESTAV-IPN, Me´ xico D. F., Me´ xico

Sergey A. Nikishin

2004 VOL. 4, NO. 2 337-341

Department of Electrical & Computer Engineering, Texas Tech University, Lubbock, Texas 79409, USA Received July 25, 2003;

Revised Manuscript Received September 17, 2003

ABSTRACT: We predict the decomposition peculiarities of the heavy isoelectronic impurities doped AlxGa1-xNyAs1-y alloys. The AlN and GaAs precipitates in the high GaAs and AlN content AlxGa1-xNyAs1-y epitaxial layers, respectively, should be formed. The free energy of the alloys is expressed as a sum of the free energies of the constituent compounds, strain and elastic energies, and configurational entropy term. The regular solution model is used for describing the free energies of the compounds and strain energy. The interaction parameters between the compounds are estimated by the valence force field model. The stiffness coefficients of the wurtzite AlAs and GaAs as well as the interaction parameter between AlN and AlAs are calculated. Introduction The nitrogen doped III-V semiconductors are widely studied due to their unique properties and device applications. Their physical properties are strongly dependent on nitrogen concentration.1 As it was established experimentally, heavy nitrogen doping (g 1 × 1019 cm-3) reduces dramatically the fundamental band gap of GaAs and InxGa1-xAs.2-5 Of particular interest is nitrogen doping of the InxGa1-xAs alloys since it leads to strong spatial correlation effects between the atoms.6 The origin of these effects is transformation of the bonds after redistribution of the atoms on their lattice sites. The InxGa1-xNyAs1-y alloys are the quaternary alloys of four binary compounds with four types of the bonds. Bond concentrations and atomic composition are described by three equations:

xIn∼N + xIn∼As ) x xIn∼N + xGa∼N ) y xIn∼N + xIn∼As + xGa∼N + xGa∼As ) 1 Thus, one atomic composition of the alloy, x and y, corresponds to a vast number of bond concentrations depending on the arrangement of the atoms.7,8 Redistribution of the atoms on their lattice sites transforms In∼N and Ga∼As bonds into In∼As and Ga∼N bonds or vice versa. The internal energy of the InxGa1-xNyAs1-y alloys can be separated out into the “mechanical” and “chemical” parts. The origin of the “mechanical” part is different sizes of the atoms providing the existence of the strain energy of the alloy. Better lattice-matched In∼N and Ga∼As bonds are more preferable from the “mechanical” standpoint than In∼As and Ga∼N ones. The “chemical” part is determined by bond concentrations. The sum of the cohesive energies of InN and GaAs is smaller than * To whom correspondence should be addressed. Tel.: +5257473778. Fax: +52-57477114. E-mail: [email protected].

this sum of InAs and GaN. Therefore, In∼As and Ga∼N bonds are “chemically” preferable. The equilibrium bond concentrations should correspond to the minimum of the free energy of the alloy. Thus, there are two origins determining the bond concentrations in the InxGa1-xNyAs1-y alloys, and these origins act in opposite directions. As it was estimated, the larger “mechanical” part provides the preference of In∼N and Ga∼As bonds in the InxGa1-xNyAs1-y alloys.6 The similar band gap reduction was also experimentally established for the AlxGa1-xAs alloys that were implanted by nitrogen and rapidly high-temperature annealed.9 The calculated band gap reductions for the nitrogen implanted Al0.27Ga0.73As alloys were larger than the measured values. The authors9 supposed that incorporation of nitrogen in the Al0.27Ga0.73As alloy is smaller than in GaAs. However, the smaller band gap reductions can have the other nature. Preferential formation of Al∼N bonds was observed in the low N-content AlxGa1-xNyAs1-y alloys grown by the molecular beam epitaxy.10 The Raman spectroscopy studies of the AlxGa1-xNyAs1-y alloys (x e 0.05, y e 0.04) have shown that the concentrations of Al∼N bonds are substantially higher than those at the random distribution of the cations and anions in their sublattices.10 The nitrogen band gap reduction in the AlxGa1-xAs alloys should be smaller than in GaAs if a part of nitrogen atoms forms the AlN-rich domains. In such a case, the concentration of nitrogen atoms decreasing the band gap will be smaller. Preference of Al∼N bonds in the AlxGa1-xNyAs1-y alloys seems very probable. The AlxGa1-xNyAs1-y and InxGa1-xNyAs1-y alloys belong to the same type of quaternary alloys. Accordingly, redistribution of atoms can transform Al∼N and Ga∼As bonds into Al∼As and Ga∼N ones or vice versa. The enthalpy of formation of AlN is significantly larger than for the other constituent binary compounds of the AlxGa1-xNyAs1-y alloys.11 As a result, Al∼N and Ga∼As bonds are thermodynamically profitable in comparison with Al∼As and Ga∼N bonds. Moreover, the lattice

10.1021/cg034143j CCC: $27.50 © 2004 American Chemical Society Published on Web 10/24/2003

338 Crystal Growth & Design, Vol. 4, No. 2, 2004

parameters as well as the elastic constants of both nitrides and both arsenides are close to each other.11 Therefore, the change of the strain energy after transformation of Al∼N and Ga∼As bonds into Al∼As and Ga∼N bonds should be insignificant. The bond concentrations in the “conventional” AxB1-xCyD1-y alloys were estimated by the quasichemical approximation (QCA) of the regular solution model.8,12 In such alloys, the difference in the free energies of the III-V compounds cannot provide a significant deviation from the random distribution of the cations and anions in their sublattices. However, for the AlxGa1-xNyAs1-y alloys the situation seems clearly distinguishable. The difference between the sums of the free energies of the AlN, GaAs and AlAs, GaN is very large and exceeds substantially the corresponding value for the InxGa1-xNyAs1-y alloys. Therefore, the preferential formation of Al∼N and Ga∼As bonds in the alloys has to be significant. Transformation of Ga∼N and Al∼As bonds into Al∼N and Ga∼As ones can lead to the phase separation in the AlxGa1-xNyAs1-y alloys. Decomposition of the AlxGa1-xNyAs1-y alloy should result in formation of the AlN- and GaAs-enriched phases. The phase separation of the multicomponent solids may be realized as spinodal decomposition or precipitation.13,14 Spinodal decomposition begins from the compositional changes that are small in degree but large in extent. Spinodal decomposition in the crystal alloys should appear in the planes ensuring the minimum of the coherency strain energy.15 The self-diffusion transfers of the atoms at the initial stage of spinodal decomposition are of the order of a lattice parameter. Therefore, the initial stage of spinodal decomposition is realized as an appearance of a set of very thin two-phase layers. As decomposition is developed, the atom transfers and thickness of the layers become larger as well as composition of the layers varies with a distance. This is the conventional type of the phase separation in the III-V alloys.13 The initial stage changes at another type of the phase separation are small in extent but large in degree.16 Precipitation in semiconductors is normally aggregation of implanted dopant atoms.14 The aggregation is a result of exceeding solubility of implanted atoms. In such a case, precipitates consist mainly of implanted dopant atoms. However, up to now, the one-compound precipitation is unknown in the III-V alloys. The GaAs- and AlN-rich alloys are of interest from the domain formation standpoint. The AlN and GaAs domains can be formed in the GaAs- and AlN-rich alloys, respectively. Precipitation in GaN- and AlAs-rich AlxGa1-xNyAs1-y alloys is hardly probable since thermodynamically preferable Al∼N and Ga∼As bonds dominate for the isoelectronic dopants. The QCA description of the AlxGa1-xNyAs1-y alloys that was executed by the authors led to the problem related to the configurational entropy. The QCA entropy of the alloy is a sum of two terms. One of the terms is a normalization factor that has a negative value and depends on the element composition only.17 This factor provides the accurate value of the configurational entropy at the random distribution of the atoms in their lattice sites. At any nonrandom distribution of the atoms, the normalization factor ensures the value of the configurational entropy that is smaller than the accurate one.17 As a result, the QCA entropy of the alloys

Elyukhin et al.

with substantially nonrandom distribution of the atoms should be at least significantly smaller than the correct value. Our QCA estimations of the bond concentrations showed that Al∼As bonds are almost absent in the high GaAs content AlxGa1-xNyAs1-y alloys with x ) y. The absence of these bonds should mean an existence of the AlN-rich domains. However, the calculated configurational entropy of this alloy is negative. Thus, we may conclude that QCA cannot be used for calculations of the configurational entropy of the AlxGa1-xNyAs1-y alloys. The strain energies of the AxB1-xCyD1-y alloys described in refs 18 and 19 by the valence force field model are very close to those obtained by the regular solution model. The interaction parameters were calculated using the strain energy of the ternary alloys estimated by the valence force field model. Therefore, the description of the strain energy of the AlxGa1-xNyAs1-y alloys in the regular solution model seems to be reasonable. The AlxGa1-xNyAs1-y alloys are grown as epitaxial layers. Substrates lattice-matched to these alloys are absent. This means that the epitaxial layers are strained. The alloy elastic energy may also influence bond concentrations. The elastic energies of alloys with the zinc blende and wurtzite structures can be expressed as it was done in refs 20 and 21. The aim of our paper is the description of the bond concentrations in the AlxGa1-xNyAs1-y alloys considering the free energies of the compounds, the strain and elastic energies. Theoretical Section The GaAs-rich AlxGa1-xNyAs1-y alloys grown on the GaAs (001) substrate will be considered first. To estimate the bond concentrations, two limit values of the free energy of the alloy with the given values of x and y are described and calculated. In the first limit case, the alloy with the AlN domains is considered. It is assumed that the number of surface atoms is significantly smaller than the total number of atoms in the domains. In such a case, the Al∼N bond concentration is close to the lesser of x and y. Accordingly, the domains have to contain more than 103 atoms. Formation of the domains should lead to the inhomogeneous distribution of the strains in the alloy. This nonhomogeneity has to be accompanied by plastic deformation of the epitaxial layer due to the significant difference in the lattice parameters of nitrides and arsenides. The plastic deformation diminishes the strain energy of the alloy. The plastic deformation of the alloy depends on the size of the domains. Coherently formed domains should have a small size. However, the part of the surface atoms of the AlN domain increases with decreasing its size, and, accordingly, the Al∼N bond concentration decreases. The decrease of Al∼N bonds is accompanied by the same decrease of Ga∼As bonds. Therefore, the decrease of the domain sizes leads to transformation of Al∼N and Ga∼As bonds into Al∼As and Ga∼N ones. As a result, formation of the domains in which numbers of surface and internal atoms are close is hardly probable. The contribution of the AlN domains in the configurational entropy of the alloy tends to zero. Therefore, it can be supposed that the configurational entropies of the quaternary alloy with the AlN domains and of the part of this alloy without these domains are close to each other. The free energy of the alloy can be written as

f(1) ) fC(1) + uS(1) + uE(1) - Ts(1)

(1)

where fC, uS, uE, and s are the free energy of the compounds, the strain and elastic energies, and configurational entropy, respectively. The free energy of the compounds in the alloy is

Precipitation in AlxGa1-xNyAs1-y Alloys

Crystal Growth & Design, Vol. 4, No. 2, 2004 339

given as

fC(1) ) µAlNxAl-N + µAlAs(x - xAl-N) + µGaN(y - xAl-N) + µGaAs(1 - x - y + xAl-N) (2) where µAlN is the chemical potential of AlN that is given as 0 0 µAlN ) hAlN - TsAlN +

∫

T

298.15

cAlNdT - T

∫

cAl-N dT T

T

295.15

0 0 where hAlN , sAlN , and cAlN are the enthalpy and the entropy of STP, and the specific heat capacity at constant pressure of AlN, respectively. The strain energy of the alloy expressed by the interaction parameters between the compounds is written as

xAl-N(x - xAl-N) uS(1) ) RAlN-AlAs + x xAl-N(y - xAl-N) + RAlN-GaN y (x - xAl-N)(1 - x - y + xAl-N) RAlAs-GaAs + 1-y (y - xAl-N)(1 - x - y + xAl-N) (3) RGaN-GaAs 1-x where RAlN-AlAs is the interaction parameter between AlN and AlAs in the alloy. The contribution of the free energies of the compounds and strain energy in the free energy of the alloy is represented by the regular solution model.8 The elastic energy of the lattice mismatched alloy with the zinc blende structure grown on the substrate with orientation (001) is expressed as20

uE(1) ) v

(

)

(C11 - C12)(C11 + 2C12) a - aS C11 aS

2

(4)

where v and Cij are the molar volume and stiffness coefficients of the alloy, respectively, a and aS are the lattice parameters of the alloy and substrate, respectively. The molar volume, stiffness coefficients, and lattice parameters of the alloy are expressed as weighted means of the bond concentrations. The configurational entropy of the alloy with domains is written as

[1ζ -- ξξln(1ζ -- ξξ) + (1 - 1ζ -- ξξ)ln(1 - 1ζ -- ξξ)] (5)

s(1) ) -(1 - ξ)R

where ξ and ζ are the lesser and largest of x and y, respectively. The bond concentration, xAl∼N, in the first limit case is supposed to be equal to the lesser of x and y. The lesser of x and y is the maximally possible value of the Al∼N bond concentration. Thus, we suppose the maximal Al∼N bond concentration that is a given value. The absence of a contribution of the domains in the configurational entropy is presented in (5) by the first factor. The considered alloy consists of the AlN domains being into the ternary alloy. It was established experimentally that atoms in the mixed sublattice of the III-V ternary alloys are distributed randomly.22,23 The random distribution of the atoms in the mixed sublattice is taken into account in the last factor of (5). In the second limit case, the configurational entropy was estimated from the supposition on the random arrangement of the cations and anions in their sublattices. Thus, the configurational entropy was given as

s(2) ) -R[x ln x + (1 - x)ln(1 - x) + y ln y + (1 - y)ln(1 - y)] For other parts fC(2), uS(2) and uE(2) of the alloy free energy, the expressions are equivalent to (2-4). The bond concentration, xAl∼N, in the second case, is assumed to be in the interval

Figure 1. The free energies of the GaAs-Rich AlxGa1-xNyAs1-y alloys with the overestimated (asterisk) and underestimated (line) configurational entropies. Table 1. Stiffness Coefficients of the Wurtzite AlAs and GaAs AlAs GaAs

C11, GPa

C12, GPa

C13, GPa

C33, GPa

128.9 129.3

65.46 58.88

40.57 34.4

153.8 153.8

from zero to the lesser of x and y. Figure 1 shows the estimation procedure of the Al∼N bond concentration in the alloy with given x and y. The free energies of the first f(1) and the second f(2) limit cases are shown by the asterisk and line, respectively. The free energy f(2) decreases with increasing Al∼N bond concentration. The first limit case leads to an underestimation of the configurational entropy and the second variant provides an overestimation. Therefore, the Al∼N bond concentrations in the first and second cases corresponding to the same value of the free energy are larger and smaller that the accurate value, respectively. Accordingly, the accurate value of the Al∼N bond concentration should be inside the interval from xAl∼N(2) to xAl∼N(1) in Figure 1. The proposed approach can describe the formation of the AlN domains if the estimated values of xAl∼N(2) and xAl∼N(1) are very neighbors. However, the substantial difference between xAl∼N(2) and xAl∼N(1) does not mean the absence of the domains, but it means that this approach cannot predict them. It is the authors’ opinion, the bond concentrations in the AlN-rich AlxGa1-xNyAs1-y alloys are of chief interest. Preference of Al∼N and Ga∼As bonds can lead to formation of the GaAs-rich domains in these alloys. The high AlN content alloys should have the wurtzite structure in the thermodynamically stable state. Therefore, apparently, the GaAs-rich domains also have to have the wurtzite structure. The bond-stretching and bond-bending elastic constants of the same binary compounds with the zinc blende and wurtzite structures should be very neighbors.24 Respectively, the strain energies of the same III-V ternary alloys with the zinc blende and wurtzite structures have to be also very similar.24 Thus, the interaction parameters between the compounds obtained for the zinc blende alloys can be used for the same wurtzite alloys. The AlN-rich alloys are commonly grown on the substrates with orientation (0001). The elastic energy of the lattice mismatched epitaxial layers grown on the (0001) substrates is written as21

(

)( )

C132 a - aS uE ) v C11 + C12 - 2 C33 aS

2

where Cij are the stiffness coefficients of the wurtzite alloy, a and aS are the lattice parameters of the alloy and substrate in the (0001) plane, respectively. The stiffness coefficients of the alloys with the wurtzite and zinc blende structures were calculated. The stiffness coefficients of AlN and GaN were taken from ref 25. The stiffness coefficients of the metastable wurtzite AlAs and GaAs shown in Table 1 were estimated from those of the same compounds with the zinc blende structure by the approach developed in ref 24.

340

Crystal Growth & Design, Vol. 4, No. 2, 2004

Table 2. Al∼N Bond Concentrations in the GaAs-Rich AlxGa1-xNyAs1-y Alloys for Temperature of 600 °C at the First (1) and Second (2) Limit Cases and the Random Arrangement of the Cations and Anions (R) x ) 0.01, y ) 0.01 x ) 0.02, y ) 0.01 x ) 0.01, y ) 0.02 x ) 0.03, y ) 0.01 x ) 0.01, y ) 0.03

xAl∼N(1)

xAl∼N(2)

xAl∼N(R)

1 × 10-2 1 × 10-2 1 × 10-2 1 × 10-2 1 × 10-2

8.8 × 10-3 7.9 × 10-3 8.9 × 10-3 7.1 × 10-3 9.0 × 10-3

1 × 10-4 2 × 10-4 2 × 10-4 3 × 10-4 3 × 10-4

The lattice parameters of the wurtzite AlAs and GaAs were estimated from those with the zinc blende structure always supposing the absence of the distortions in the wurtzite structure.

Results and Discussion The calculated concentrations of Al∼N bonds in the GaAs-rich AlxGa1-xNyAs1-y alloys grown at temperature of 600 °C on the GaAs (001) substrate are shown in Table 2. The chosen temperature is conventional for the molecular beam epitaxy of GaAs-rich alloys. The Al∼N bond concentrations, xAl∼N(1) and xAl∼N(2), correspond to the first f(1) and second f(2) limit cases of the free energy, respectively. All described alloys are outside the spinodal decomposition range but inside the miscibility gap at 600 °C. The estimations of the spinodal decomposition range and miscibility gap were accomplished by the approaches developed in refs 26 and 27, respectively. Also Table 2 contains the Al∼N bond concentrations, xAl∼N(R), estimated for the random arrangement of the cations and anions in their sublattices. These values are dramatically smaller than the ones for the first or second cases. In fact, the one-compound (AlN or GaAs) domain formation in an alloy can be classified as a precipitation.14,28 Up to now, precipitation of a compound in the alloys of the compounds has not been considered yet. Therefore, the developed approach describes a new type of decomposition of the semiconductor alloys. The data used for the calculations were taken from refs 11 and 25. The thermodynamic characteristics of the metastable cubic GaN and AlN are supposed to be equal to those of their stable hexagonal modifications. The interaction parameters between the compounds RAlAs-GaAs ) 0, RAlN-GaN ) 6.11 × 103 J/mol, and RGaAs-GaN )2.16 × 105 J/mol were taken from refs 2931. The interaction parameter RAlAs-AlN ) 3.35 × 105 J/mol was calculated from the strain energy of the AlNxAs1-x ternary alloys estimated by the valence force field model.32 As usual, the mixed sublattice of the AlNxAs1-x alloys was supposed to be undistorted. The microscopic elastic constants of GaN, GaAs, and AlAs were taken from refs 30, 33, and 34. The AlN domain formation is clear from the regular solution standpoint. The formation of AlN domains drastically decreases the quantity of As∼Al∼N triads having the largest strain energy. The energy of atomic triads in the regular solution is expressed by the interaction parameters between the compounds in an alloy. The interaction parameters are normally calculated as matching parameters at the III-V ternary phase diagrams description.29 The values of the interaction parameters RAlAs-GaAs and RInAs-GaAs obtained as matching parameters and calculated by the valence force field model are very

Elyukhin et al. Table 3. Ga∼As Bond Concentrations in the AlN-Rich AlxGa1-xNyAs1-y Alloys for Temperature of 800 °C at the First (1) and Second (2) Limit Cases and the Random Arrangement of the Cations and Anions (R) x ) 0.99, y ) 0.99 x ) 0.98, y ) 0.99 x ) 0.99, y ) 0.98 x ) 0.97, y ) 0.99 x ) 0.99, y ) 0.97

xGa∼As(1)

xGa∼As(2)

xGa∼As(R)

1 × 10-2 1 × 10-2 1 × 10-2 1 × 10-2 1 × 10-2

8.5 × 10-3 8.1 × 10-3 8.7 × 10-3 7.9 × 10-3 8.7 × 10-3

1 × 10-4 2 × 10-4 2 × 10-4 3 × 10-4 3 × 10-4

neighbors. The interaction parameters between the compounds in the N-contained ternary systems cannot be estimated as liquid-solid phase diagram matching parameters since the concentration of N in the III-V ternary liquid solutions is too small. Therefore, the valence-force field model is used to estimate the interaction parameters between the compounds in the nitride alloys.30,31 The interaction parameters were obtained from the strain energies of the ternary alloys that were interpolated as uS(AxB1-xC) ) RAC-BCx(1 - x). However, the triads consisting of two types of atoms do not make a contribution in the strain energy expressed by the regular solution model. It can be explained as a partial plastic deformation of the domains. This deformation seems reasonable due to the substantial difference between the lattice parameters of the nitrides and arsenides. The heavy nitrogen doped alloys can be formed only at nonequilibrium growth conditions. Therefore, formation of the domains should depend on growth conditions as well as a post growth annealing. Diffusion processes during the growth or thermal treatment should determine the crystal structure peculiarities of the alloys. Higher growth or annealing temperatures should stimulate the formation of Al∼N and Ga∼As bonds. The similar redistribution of the N-bonding configuration within the InxGa1-xNyAs1-y alloys during annealing was established experimentally.35 The concentration of In∼N bonds in the InxGa1-xNyAs1-y alloys increased after annealing. Redistribution of the atoms on the lattice sites leads to transformation of In∼N and Ga∼As bonds into In∼As and Ga∼N bonds or vice versa. The sum of the free energies of InN and GaAs is smaller than that of InAs and GaN. Therefore, there is a thermodynamic preference for formation of In∼N and Ga∼As bonds. Moreover, from a local strain point of view, In∼N and Ga∼As bonds are more favorable than In∼As and Ga∼N bonds. Thus, there are two origins of the preferential formation of In∼N and Ga∼As bonds in the InxGa1-xNyAs1-y alloys. One of the possible growth scenarios of the AlN-rich AlxGa1-xNyAs1-y alloys on the GaN (0001) substrate is considered below. All calculations were done for two temperatures of 800 and 900 °C. The chosen temperatures are typical for the molecular beam epitaxy of AlNrich alloys.36 All described alloys are outside the spinodal decomposition range but inside the miscibility gap at the temperatures of 800-900 °C. The estimations of the spinodal decomposition range and miscibility gap were accomplished by the approaches developed in refs 26 and 27. The estimated stiffness coefficients of the GaAs and AlAs with the wurtzite structure are shown in Table 1. The calculated Ga∼As bond concentrations are shown in Tables 3 and 4 for the alloys grown at 800 and 900 °C, respectively.

Precipitation in AlxGa1-xNyAs1-y Alloys

Crystal Growth & Design, Vol. 4, No. 2, 2004 341

Table 4. Ga∼As Bond Concentrations in the AlN-Rich AlxGa1-xNyAs1-y Alloys for Temperature of 900 °C at the First (1) and Second (2) Limit Cases and the Random Arrangement of the Cations and Anions (R) x ) 0.99, y ) 0.99 x ) 0.98, y ) 0.99 x ) 0.99, y ) 0.98 x ) 0.97, y ) 0.99 x ) 0.99, y ) 0.97

xGa∼As(1)

xGa∼As(2)

xGa∼As(R)

1 × 10-2 1 × 10-2 1 × 10-2 1 × 10-2 1 × 10-2

8.4 × 10-3 7.9 × 10-3 8.5 × 10-3 7.7 × 10-3 8.6 × 10-3

1 × 10-4 2 × 10-4 2 × 10-4 3 × 10-4 3 × 10-4

The Ga∼As bond concentrations, xGa∼As(R), estimated for the random arrangement, are also shown in Tables 3 and 4. We found the Ga∼As bond concentrations estimated for the second limit case very weakly depend on the growth temperature. It is a result of the small contribution of the entropy term in the free energy of the alloy and the insignificant variations in the free energies of the constituent compounds. Thus, the GaAs domains should appear in the AlN-rich alloys. Formation of the GaAs domains in the AlN-rich quaternary alloys may be very important for potential device applications. The GaAs domains can be an analogue of quantum dots formed in the wide band gap semiconductor material. However, physical properties of the alloy with the domains will be determined by growth and treatment conditions. Conclusions The GaAs- and AlN-rich AlxGa1-xNyAs1-y alloys grown on GaAs (001) and GaN (0001) substrates should contain the domain of AlN and GaAs, respectively. The considered alloys are outside the spinodal decomposition range. The thermodynamic preference of the AlN and GaAs formation in contrast to AlAs and GaN is the main origin of the domain formation. The interaction parameters between the compounds were estimated by the valence force field model. The stiffness coefficients of AlAs and GaAs with the wurtzite structure as well as the interaction parameter between AlN and AlAs were calculated. The proposed model is in excellent agreement with recent experimental results. References (1) Kent, P. R. C.; Zunger, A. Phys. Rev. Lett. 2001, 86, 26132616. (2) Weyes, M.; Sato, M.; Ando, H. Jpn. J. Appl. Phys., Part 2 1992, 31, L853-L855. (3) Malikova, L.; Pollack, F. H.; Bhat, R. J. Electron. Mater. 1998, 27, 484-487. (4) Gu¨ning, H.; Chen, L.; Hartmann, Th.; Klar, P. J.; Heimbrodt, W.; Ho¨hnsdorf, F.; Koch, J.; Stoltz, W. Phys. Status Solidi B 1999, 215, 39-45.

(5) Zhang, Y.; Mascarenhas, A.; Xin, H. P.; Tu, C. W. Phys. Rev. B 2001, 63, 161303. (6) Kim, K.; Zunger, A. Phys. Rev. Lett. 2001 86, 2609-2612. (7) Elyukhin, V. A.; Karpov, S. Yu.; Sorokina, L. P.; Frontz K. Sov. Phys. Crystallogr. 1982, 7, 668-670. (8) Onabe, K. J. Phys. Chem. Solids 1982, 43, 1071-1085. (9) Shan, W.; Yu, K. M.; Walukiewisz, W.; Ager, J. W.; Haller, E. E.; Ridgway, M. C. Appl. Phys. Lett. 1999, 75, 14101412. (10) Geppert, T.; Wagner, J.; Ko¨hler, K.; Ganser, P.; Maier, M. Appl. Phys. Lett. 2002, 80, 2081-2083. (11) Landolt-Bo¨ rnstein, New Series, Madelung O., Schultz M., Weiss H., Eds.; Springer: Berlin, 1984; Vol. 17d; pp 1316. (12) Elyukhin, V. A.; Karpov, S. Yu.; Sorokina, L. P. Russ. J. Phys. Chem. 1985, 59, 486-488. (13) Phillips, J. C. Bonds and Bands in Semiconductors; Academic: New York, 1973; pp 208-210. (14) Jones, K. S. In Handbook of Compound Semiconductors; Holloway, P. H., McGuire, G. E, Eds.; Noyes: Park Ridge, New Jersey, 1995; pp 316-319. (15) Cahn J. W. Acta Metall. 1962, 10, 179-183. (16) Cahn, J. W. Acta Metall. 1961, 9, 795-801. (17) Hill, T. L. Statistical Mechanics; McGraw-Hill: New York, 1956; pp 345-353. (18) Ichimura, M.; Sasaki, A. Phys. Rev. B 1987, 36, 9694-9702. (19) Ichimura, M.; Sasaki, A. Jpn. J. Appl. Phys. 1988, 27, 19101915. (20) Tsao, J. Materials Fundamentals of Molecular Beam Epitaxy; Academic: Boston, 1993; pp 107-109. (21) Bottomley, D. J.; Fons, P. Jpn. J. Appl. Phys., Part 2 1995, 34, L1616-L1619. (22) Mikkelsen, J. C., Jr. J. Electrochem. Soc. 1985, 132, 500505. (23) Miyano, K. E.; Woicik, J. C.; Robins, L. H.; Bouldin, C. E., Wickenden, D. Appl. Phys. Lett. 1997, 70, 2107-2109. (24) Martin, R. Phys. Rev. B 1972, 6, 4546-4553. (25) Kim, K.; Lambrecht, W. R. L.; Segall, B. Phys. Rev. B 1996, 53, 16310-16326. (26) Asomoza, R.; Elyukhin, V. A.; Pen˜a-Sierra, R. Appl. Phys. Lett. 2002, 81, 1785-1787. (27) Elyukhin, V. A.; Ebanoidze, M. K. Russ. J. Phys. Chem. 1987, 61, 1461-1463. (28) Guinier, A. In Solid State Physics; Seitz, F., Turnbull, D., Eds.; Academic: New York, 1959; Vol. 9, pp 293-398. (29) Panish, M. B.; Ilegems, M. In Progress in Solid State Chemistry; Reiss, H., McCaldin, J. O., Eds.; Pergamon: Oxford, 1972; Vol. 7, pp 39-83. (30) Elyukhin, V. A.; Nikishin, S. A. Semicond. Sci. Technol. 1996, 11, 917-920. (31) Qui, Y.; Nikishin, S. A.; Temkin, H.; Elyukhin, V. A.; Kudriavtsev, Yu. A. Appl. Phys. Lett. 1997, 70, 2831-2833. (32) Elyukhin, V. A.; Sorokina, L. P. Sov. Phys. Dokl. 1986, 31, 342-344. (33) Martin, R. M. Phys. Rev. B 1970, 1, 4005-4011. (34) Martins, J. L.; Zunger, A. Phys. Rev. B 1984, 30, 62176220. (35) Tournie´, E.; Pinault, M.-A.; Guzma´n, A. Appl. Phys. Lett. 1999, 86, 5584-5586. (36) King, S. W.; Carison, E. P.; Therrien, R. J.; Christman, J. A.; Nemanich, R. J.; Davis, R. F. J. Appl. Phys. 1999, 86, 5584-5593.

CG034143J