Composition dependence of the bond lengths in the quaternary semiconducting alloy (A1−xBxC1−yDy)

Solid State Communications, Vol. 98, No. 9, pp. 825-828, 1996 Copyright 0 1996 Else&r Science Ltd F’rinted in Great Britain. All rights reserved 0038-1098/96 $12.00 + .OO

PI1 soo38-10!28(%)ooo16-6

COMPOSITION

DEPENDENCE OF THE BOND LENGTHS IN THE QUATERNARY SEMICONDUCTING ALLOY (A,_,B,C,_,D,,) Kyurhee Shim and Jung-Wook Bae

Department

of Physics, Kyonggi University, Suwon, 440-760, Korea So-Yeon Jeong and Heh-Jeong Moh

Department

of Physics, Ewha Woman’s University, Seoul 120-750, Korea and D.N. Talwar

Department

of Physics, Indiana University of Pennsylvania, PA15705, U.S.A.

(Received 4 December 1995; accepted 26 December 1996 by C.N.R. Rao)

The composition variation of the bond lengths in the quaternary semiconducting alloy has been formulated in terms of the distorted bond length by substitutional impurity and the host bond length, in which the effect of composition disorder is involved properly. We calculated the bond lengths in In,_,Ga,Asi_,,PY alloy through whole composition range and examined the alloy disorder extent against the composition mixing ratio. Copyright 0 1996 Elsevier Science Ltd Keywords: A. semiconductors, order-disorder effects.

C. crystal structure and symmetry, D.

THE LOCAL atomic structure of III-V ternary and quarternary alloys has received much attention because of their uses as substrates and active layers of optoelectronic devices for applications. Most of the semiconducting alloys are fabricated by epitaxial techniques, where the bond-length is the important alloy characteristic for understanding the local atomic structure of alloy semiconductors. It has become essential to construct simple structural models for characterizing the local atomic arrangements of the mixed crystals and to account for their fundamental properties. Several researchers have investigated and reported the composition dependence of the bond length for III-V ternary and quaternary alloys (InGaAs, GaAsP, InGaAsP and InGaSbAs) [l-4]. The bond lengths have been experimentally determined by the extended X-ray absorption fine-structure (EXAFS) and theoretically studied on the basis of the valenceforce-field (VFF) model [5], the pseudopotential scheme [6], the coherent potential approximation (CPA) [7], and the tight binding (TB) scheme using the bond-orbital model (BOM) [8].

In this letter, we formulate the equation of the composition dependence of bond lengths in Ai_,B,Ci_,D, quaternary alloy semiconductors based on TB and BOM, in which the composition disorder effect is involved appropriately in terms of the host bond length and the distorted bond length by substitutional impurity without any other adjustable or experimental parameters. From this approach, the composition bond lengths in Ini_,Ga,Asi_yPy quaternary alloy and the growth conditions for Ini_,Ga,Asi_yPy lattice-matched to InP and GaAs are obtained and the alloy disorder extent against the composition mixing ratio is examined. As in the previous study [8], we have already developed a TB method based on BOM to investigate the bond length relaxation around isovalent impurities and its effect on the electronic and vibrational properties of semiconductors [9]. This technique provides us with simple analytical expressions for the change in impurity-host bond energy and suggests a compositionally efficient and reasonable method (with no adjustable parameters) to estimate the bond length distortions. This approach has been used in ternary 825

BOND LENGTHS

826

IN Ai_,B,C,_,D,

Vol. 98, No. 9

alloys (Ai_,B,C) where an atomic structure model Substituting equation (3) to equation (2), the average of the type A(3)B(l)C was considered in the dilute bond length in the quaternary alloys can be written as, limit [lo]. The variations of the bond lengths dAccX) + (1 - x)yd&, and dBc(X)in the A,_,B,C have been obtained by the d(x,y) = (1 -x)(1 -y)d& linear interpolation between the host bond length + x( 1 - y)dic + xyd& (doAc and don,-) and the distorted bond length by -t (1 - x)y(l -y)Ad(AC&AD) substitutional impurity in the dilute limit [d(AC : B) and d(BC : A)][1 I]; + xy( 1 - y)Ad(BC & BD) d&x)

+ (1 -y)x(l

= d;, + x[d$ - d(AC : B)],

da,-(x) = d& + (1 - x)[&

- d(BC : A)].

The average bond length can be obtained by the compositionally weighted average with the anion and cation bond length and can be written as d(x) = (1 - x)d;,

+ xdic + x(1 - x)[AdAc + Adnc],

(2) where Ad,, = di, - d(BC : A) and Aduo = d& d(AC : B) are the total difference of bond lengths for the AC and BC host atoms from those of virtual crystal approximation (VCA). It is found that the average bond length in an At_,B,C alloy does not array uniformly but relaxes more than predicted by the VCA by gaining excess energy due to the composition disorder. In quaternary alloy (At_,B,Ci_,D,), the theoretical approach is similarly used to that in ternary alloys. In A,_,B,C1_,D, alloy, the A and B atoms are considered to be randomly distributed on the cation site with (1 - x) :x probability, while the C and D atoms occupy the anion sites of a zinc-blende structure with the probability of (1 - JJ) : y. Therefore the terms d,&, Ad,,, die, and Ad,, in equation (2) are not constant but vary with the composition y in the ACt_,D, and BCi_,D, alloy. d:,

+ &c(y)

= Cl-

Writ

x {d;,

+ .d:,

- d(AC : D) + d;,

+yd&

+y(1 -v)

x {d& - d(BC : D) + d&, - d(BD : C)},

Ad,,

--$ Ad,,(y)

= (1 - y){&

+ y(d,&, Ad,,

+ Ad,,(y)

= (1 - y){&

- d(AC : B)} - d(AD

: B))

- d(BC : A)}

+ y{d,!& - d(BD : A)}.

- x)Ad(AD&BD),

(3)

(4)

where the first four terms in the right side of equation (4) represent the average bond length in the VCA limit and the remaining terms express the alloy disorder which make the average bond length bow. Ad(AC &AD) equals d& - d(AC : D) + d&, d(AD : C) which implies the total difference of anion and cation bond lengths from VCA in ACt_,D, alloy, and vice versa. The average bond length [equation (4)] can be distributed with four bond lengths (dAc, dac, &o, duo) such as d(x,Y) = (1 -x)(l

-Y)&&Y)

+ (1 - x)Y&&Y)

+X(l -Y)di.&Y) + xYdr&J’),

(5)

where dAc(x,y)

= d& + x{djc + y{d&

- d(AC : B)}

- d(AC : D)},

d,c(X,_Y) = die + (1 - x){d,&

- d(BC : A)}

+ J’{d;o - d(BC : D)}, dAD(X,J') = d:,+X{d&

+ (1 - y){d&

- d(AD:B)} - d(AD : C)},

d&X,_&')= d& + (1 -X){d&

+ (1 - y){dic

+ ~(1-14

- d(AD : C)},

d:‘, + &c(y) = (1 -y)&

+xy(l

(1)

-x)Ad(AC&BC)

- d(BD:

(6)

A)}

- d(BD : C)}.

Using the above equations and Table 1, the average bond length and four bond lengths (dIn_Asr dGa-As, din-P, dGa_P) for Int_,Ga,Asi_YPY can be calculated through whole composition range x and y. The composition variations of the bond lengths in In,_,Ga,As,_,P, are shown in Fig. 1 where composition (X,JJ) varies from (0, 0) to (1, 1). We found that: (a) the composition variation of the average bond length does not follow the VCA result but bows convexly from the VCA, and (b) the amount of chang: in each bond lengfh is that: LidIn_As F AdIn+ = 0.085 A, 0.077 A, AdGa,As = 0.105 A, Ad,,_, = 0.133 A, where the change is largest in Ga-P bond length and smallest in In-As bond length. In

BOND LENGTHS

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IN A, _,B,C, _YD,,

827

Table 1. The host and distorted bond lengths for the substitutional impurities in the constituent semiconductors for the Inl_,Ga,Ast_YPY quaternary alloy [8] Constituent semiconductors

Host bond length (A)

Distorted system and bond !ength by substitutional impurity (A)

InAs

2.623

GaAs

2.448

InP

2.541

GaP

2.358

d(InAs : Ga) : 2.053 d(InAs : P) : 2.563 d(GaAs : In) : 2.548 d(GaAs : P) : 2.388 d(InP : Ga) : 2.421 d(InP : As) : 2.601 d(GaP : In) : 2.448 d(GaP : As) : 2.408

order to compare our result with available experimental data, we calculated the In-As and Ga-As bond lengths for y = 0 in Ini_,Ga,Asi_,P, and compared those with EXAFS data [l] expressed by full circle in Fig. 2. Figure 2 shows good agreement between theory and experiment. Figure 3 represents our resulted combinations of x and y which yield a lattice matching either to InP (d,& = 2.541 A) or GaAs (d& = 2.448 A) constituent semiconductors. A definite relationship between x and y exists for lattice-matched quaternary alloy which is

(ii) 2.65~

-.__ (0.0)

(.2,.2)

1.4,.4)

(.6,.6)

(.8,.8)

(1.1)

(KY)

Fig. 1. The composition variation of the average bond length (d) and each four bond lengths [d(In-AS), d(Ga-As), d(In-P), d(Ga-P)] in an Ini_,Ga,Asl_YPy quaternary alloy vs alloy composition (x, y). The dashed line represents the average bond length in the VCA limit (dvCA).

x = 0.49(1 - y) (0 < x < 0.49) for In,_,Ga,As,_YPY lattice matched to InP and x = 1 - 0.45~ (0.55 < x < 1) for In,_,Ga,As,_,P, lattice matched to GaAs, respectively. In the coherent-potential approximation (CPA) [7], the growth conditions of Ini_,Ga,Ast_,,PY quaternary alloy were obtained as x = 0.47(1 - y) for lattice matched to InP and x = 1 - 0.52~ for lattice matched to GaAs. Comparing our resulting growth conditions with the CPA’s, there is a better agreement for Ini_,Ga,As,_YPY lattice matched to InP than that to GaAs. In Fig. 4, the average bond lengths for the various anion to cation composition mixing ratios (y/x) are plotted with solid lines as a function of alloy concentration y. The dashed lines display VCA results. The

2.44’

0

0.2

0.4

0.6

0.8

X

Fig. 2. The calculated bond lengths of d(In-As), d(Ga-As) and d vs composition x for y = 0 in In,_,Ga,Asr_,,P,, (i.e., Ini_,Ga,As ternary alloy). The experimental data (0) are obtained from the EXAFS measurements [ 11.The dashed line represents the average bond length in the VCA limit (dvCA).

BOND LENGTHS

828

Fig. 3. The reported relation between x and y alloy compositions for lattice matched Ini_,Ga,As,_yPy on InP and GaAs. The solid and dashed lines represent our and the CPA’s results [7l, respectively. calculated results bows convexly from VCA values which is considered as the alloy disorder effect. The bowing diminishes more as the limit y/x + 0 or y/x -+ co. This indicates that y -+ 0 or x -+ 0 (i.e., in the quatemary alloys A,_,B,C or ACi_,D,) Ai_,B,Ci_,D, makes the disorder effect minimize. Comparing the bowing ofy/x = 0.5 (x :y = 2 : 1) with

IN A,_,B,C,_,D~

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y/x = 2(x : y = 1: 2), the value of y/x = 2 bowed more than that of y/x = 0.5. This suggests that the mixing ratio of the anion to cation site in quaternary is responsible and influential factor for the disorder extent. In conclusion, our theoretical approach to calculate the composition dependence of bond lengths in ternary and quaternary alloys is convenient and reasonable since the effects of alloy disorder are completely governed by the differences between the distorted bond length of substitutional impurity in dilute limits and the host bond length without any other adjustable parameters. The proposed equation to examine the local atomic structure can be applied universally for the III-V semiconducting alloys and provides an accurate information for the bond lengths in the quaternary alloy which is required for the design of the devices.

Acknowledgements

- This work was supported by the Basic Science Research Institute Program, Ministry of Education under Project No. BSRI 2430,2428, and Kyonggi University. The work of DNT was supported in part by the Research Corporation, American Chemical Society (Petroleum Research Fund #PRF 30145-B3), National Science Foundation (#ECS-9521659) and by the National Research Council Associateship program.

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Fig. 4. The composition variation of the average bond length in an In,_,Ga,Asi_yPy alloy for the various alloy composition mixing ratio (y/x). The dashed lines are those in the VCA limit.

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