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Growth limitations by the miscibility gap in liquid phase epitaxy of Ga1−xInxAsySb1−y on GaSb
Materials Science and Engineering, B9 ( 1991 ) 125-128
125
Growth limitations by the miscibility gap in liquid phase epitaxy of Gal_ xlnxAsySbl _y o n GaSb J.-L. Lazzari, E. Tourni~, F. Pitard and A. Joulli~ Equipe de Microopto~lectronique de Montpellier, Unit6 de Recherche associJe au CNRS 392, Universit6 de Montpellier II, Sciences et Techniques du Languedoc, 34095 Montpellier CJdex 5 (France)
B. Lambert Centre National d'Etudes des TJlJcommunications, Lannion B, OCM, B.P. 40, F2230l Lannion CJdex (France)
Abstract The boundary line (binodal curve) of the solid phase miscibility gap of the Ga~ _xlnxAsySb I _y quaternary alloy has been calculated from the regular solution model, taking into account the latticemismatched strain energy induced by a GaSb substrate. A calculation suggests that the miscibility gap is reduced and epitaxial layers might be deposited over the entire range of lattice-matched compositions at 615 °C. Ga~ _xlnxAsySb~ _y epitaxial layers have been grown by liquid phase epitaxy on (100)- and (111)Boriented GaSb substrates. The lattice-matched epitaxial layers which were richest in indium (x = 0.23) for the (100) orientation and x = 0.26 for the (111)B orientation have compositions located in the vicinity of the boundary of the miscibility gap calculated ignoring the strain energy, showing that stabilization by the substrate is far less effective than predicted.
1. Introduction
Long-haul, high bit rate optical communications using fluoride glass fibres [1] are predicted in the wavelength range 2.5-2.7 /~m. Liquid phase epitaxy (LPE) has been used successfully to produce low threshold laser diodes [2, 3] and high speed detectors [4] in the Ga 1_ xlnxAsySb1_ y/GaSb system operating at wavelengths near 2/~m. The existence of a large solid phase miscibility gap [5, 6, 7] has so far made it impossible to extend the wavelength range to 2.7 /~m. The question is whether stabilization by the substrate, which has been demonstrated [8] with the Gal_xlnxAsy Pl_y/InP system, should extend the range of Gal_xlnxAsySbl_y alloys that can be grown on GaSb substrates. It has been argued [9, 10] that growth inside an unstable region can still occur because the substrate tends to stabilize epitaxial layers which are nearly lattice matched. In this paper, we first study theoretically the 0921-5107/91/$3.50
contribution of the lattice-mismatch strain energy induced by the GaSb substrate to the miscibility gap, which was defined as being bounded by the binodal curve, and show that solid phase stabilization should occur. Also, we have achieved a number of LPE experiments, using (100)- and (111)B-oriented GaSb substrates, in order to grow epitaxial Ga~_xlnxAsySbl_y layers inside the calculated miscibility gap. 2. Miscibility gap of the Gal_xlnxAsySbl _y quaternary alloy
The miscibility gap was defined at a given temperature as the unstable solid phase composition domain bounded by the binodal curve. This curve gives the composition (x~,y~) of the two G a 1_xlnxAsySbl _y alloys which are in equilibrium with the same liquid solution when the peritectic solid phase decomposition occurs. The binodal curve was calculated from knowledge of the total free energy of the system G(x,y) using © Elsevier Sequoia/Printed in The Netherlands
126 GaAs
the following equations [11]: 0G
OG I=~-X
(1)
0G I 0G Oy = O y
(2)
i~X
OG 1
OG 1
G(x"yl)- Oxx x , - ~y
InAs
,'
t
"o."
;
OG 2 x2- ~OG = G(x.,y2)- ~xx y 2 Y2
f
/.' if /
/
-/j//
Yl
,
,
i1~
/
;/.° (3)
/
j"
/ 4~
i
W 0.0
The total free energy G(x,y) consists of the mixing free energy GM(x,y) and the strain energy G~t(x, y):
G(x,y) = GM(x,y) + G~t(x,y)
(4)
The mixing term G M was given by the regular solution model [11] using the thermodynamical parameters obtained by Dolginov et al. [12]. The strain energy G st for epitaxial layers which are not relaxed can be expressed as [13]
G~t(x,y)=o(x,y)
I [
1"
a(x'y)-a"ao l
Cll
O,,, = 2 C 4 4
3(C, + 2C12) C~1 + 2C12 +
Vm
0.0
1.0
X --~
In Sb
Fig. l. Composition evolution of (100)- and ( I l l ) B oriented alloys possessing a constant elastic parameter o (isoO curves).
InAs
GaAs i
1.0
i
i
i
i
i
i
i
i
(5)
where a 0 and a(x,y) are the lattice constants of the substrate ~..id the strain-free epitaxial layer respectively; a(x,y) was calculated using Vegard's law. The elastic parameter a(x,y) depends on the substrate orientation. For the (100) and (111) orientations, ato o and all I are given by [14] 0.101)= ( C I I _ Ci2) Cll J-2C,2 Vm
GaSb
(6)
(7)
C44
Vm is the molar volume of the epitaxial layer: V m = Na3(x,y)/4 where N is the Avogadro number. The Cu are the elastic constants which were calculated from the elastic constants of the binary compounds [15] using Vegard's law. The variations in the elastic parameters Ol00 and Ojl I across the composition plane of the Ga~_xlnxAsySbl y system are shown in Fig. 1. Calculations for 615 °C were performed by solving eqns. (1)-(7). This temperature was chosen because it furnishes theoretically the indiumrichest--and consequently arsenic-richest--
./
/
....
. . . .
/ " 615°C
/ 0.0
GaSb 0.0
.
.
.
.
.
.
.
X~
,
,
1.0 InSb
Fig. 2. Miscibility gap of the Gain .~InxAs,.Sb ~_, system at 615°C: . . . . , binodal curve without strain effect; - binodal curve with Ga~ xln,As,.Sb~ ,./GaSb strain effect; • typical compositions of LPE (100) epitaxial layers; ,t, typical compositions of LPE ( 111 )B epitaxial layers.
Gal_xlnxAssSbl_y alloy which can be grown lattice matched to the GaSb substrate, ignoring the subs•rate-induced stabilization effect [16]. It must be remembered that calculations were made with the assumption that the epitaxial layer is sufficiently thin to be completely in the elastic state. Figure 2 shows the binodal curves calculated with the hypothesis of stress-free solid phases (broken curves) and the binodal curves (full curves) calculated taking into account the substrate-induced strain energy G st for one solid phase composition (xl ,Yl ), the other (x2,yz) being completely relaxed. One can see a reduction in
127
the total size of the miscibility gap of the system, which is clearly visible in Fig. 2, and the existence of an extra miscible region for epitaxial layers with little or no mismatch. In that case, there is a solid phase stabilization by the substrate, and growth of Ga= _~InxAsySbl -y alloy lattice matched with GaSb is allowed in the whole domain of indium concentration 0 < x < 1. Another typical result of the calculations is that miscibility gaps are almost the same for strained (100) and strained (111) epitaxial layers. The width of the stable domain which appears along the GaSb lattice-matching line corresponds to a lattice mismatch Aa/a from about - 1 × 1 0 - 3 to + 1 × 1 0 -3 for (111) substrates and from about - 1.7x 10 -3 to + 1 x 10 -3 for (100) substrates. In fact, these results are not surprising as the parameters o ~ and 0~00 are quite comparable ((7111 ~-" 1.3Oloo). 3. L i q u i d p h a s e epitaxy o f the Gal - x l n x A s y S b l - y / G a S b s y s t e m
The epitaxial layers of thickness 0.4-2 /~m were grown by the step-cooling method on GaSb substrates, either (100) or ( l l l ) B oriented, at temperatures near 600 °C, from liquid solutions of constant antimony concentration (XsbL= 0.50) [16, 17]. The solid phase composition was determined using electron microprobe analysis on thick samples. The conditions of lattice matching are given in Fig. 3, which indicates the measured lattice mismatch Aa/a = (alayer-- asubstrat e)/asubstrat e as a function of XA~L, for various initial supercoolings A T = Tequilibriu m - - Zgrowt h . This study allowed us to grow in a reproducible manner lattice-matched layers (Aa/a = 0) or slightly mismatched layers (Aa/a=lO -3) with quite a good surface morphology. No crosshatched pattern could be detected even for thick layers (about 2 ¢tm), suggesting that the layers are in the elastic state. For near-equilibrium growth (AT=10°C), lattice-matched ( 111 )B and (100) epitaxial layers have the same composition when grown from melts having the same indium and antimony contents. The most indium-rich lattice-matched layer which could be deposited is G a 0 . 7 7 I n 0 . 2 3 A s 0 . 2 0 Sb0.80 [16, 17]. When the initial supersaturation of the melt is increased (A T> 10 °C), the composition of ( 100)oriented lattice-matched layers remains the same (x = 0.23; y = 0.20). Conversely, ( 111 )B-oriented
I: 12 1p AT(*C) 10 , 215 IL~
I
I
2t~~ I T ~ ~ I, ~ , lt ' ',~'1
/
;,\,
~I / t
30
t
-1
~t
',
~
"
2.5
~" /XL(In):'4
/XL(Sb)=.5
115 I ",
I
(100) (111)B
30
I , '
=o
..... ,--
='~',
21~,
I
~,
3.0
3.5
XL(As) xlO 3 ~
Fig. 3. Variation in the perpendicular lattice mismatch vs. liquid atomic fraction of arsenic, for various initial supersaturations AT, in the case of (100)- and (111)B-oriented epitaxial layers.
H
(100)_~
AT~
t
lOt:
•~
2o*c
(11~~.2 K
,-I
n.
,
,
2.2
2.0 ~Mprn)
#
,
..
2.2 20 ~.,l,(prn )
Fig. 4. PL emission intensity (in arbitrary units (a.u.)) at 2 K of (100) and ( I I 1 ) B lattice-matched LPE layers grown under different initial supercoolings A T.
lattice-matched layers show an increase in their indium and arsenic contents up to x = 0 . 2 6 , y = 0.23, for A T = 25 °C. For higher supercoolings (AT> 25 °C), homogeneous nucleation appears within the liquid, and satisfactory LPE growth could not be achieved [17]. Photoluminescence (PL) experiments performed at 2 K confirm these results (Fig. 4).
128 W h e n A T is increased, there is no change in the peak position of the PL emission of (100)oriented samples whereas a shift towards the longer wavelengths is clearly noticeable with ( i l l ) B - o r i e n t e d samples: 2 c = 2 . 1 8 /~m for A T = 2 0 ° C and 2 ~ = 2 . 2 0 /zm for A T = 2 5 ° C . Figure 2 shows that this composition, which is the most indium rich that we could obtain, is situated slightly inside the miscibility gap of strain-free solid phase, and plainly outside the miscibility gap relating to a strained layer.
4. Discussion Taking account of the strain energy induced by the substrate, a theoretical evaluation of the miscibility gap of the G a l _ x l n x A s y S b l _ y / G a S b system predicts a reduction in the instability domain b o u n d e d by the binodal curve and the possibility of depositing elastic layers with little or no mismatch ( A a / a < 10 -3) over the entire range of compositions. O u r attempts to grow this kind of layer by L P E were unsuccessful; lattice-matched G a l _ xlnxAsySb~ _y layers grown under near-equilibrium conditions have the highest indium content (x = 0.23) at the boundary of the miscibility gap calculated ignoring the strain effect. It was only possible to increase a little the indium concentration of the solid phase (up to x = 0.26) by using high initial supercooling and ( 111 )B orientation. As suggested by some workers [18, 19], this result can be explained by the difference between the growth kinetics of ( 111 )B- and ( 100)-oriented samples. Effectively, the d e p e n d e n c e of the layer thickness vs. the growth time e(t) was found to be el00(t) = K l o o A T t 1/2 with K=0.035btmoC
1 s 1/2
(8)
and ell~(t)=Kij~ATt
with K = 30 A ° C
is
~ (9)
Equation (8) is typical of a growth rate controlled by the solute diffusion in the liquid solution [20] as eqn. (9) can be interpreted by a growth controlled by surface attachment kinetics of the first order (which c o r r e s p o n d to diffuse growth [21]). In conclusion, the stabilization effect by the substrate-induced strain energy seems to be far
less effective than theoretically predicted. It seems necessary to include orientation dependence of growth kinetics to explain our experimental results.
Acknowledgments T h e authors wish to thank D. Barbusse and R. Fourcade of the Laboratoire des Agr6gats Mol6culaires et des Mat6riaux Inorganiques, Montpellier University, for their X-ray doublediffraction measurements. This work has been partially supported by France T616com (Convention D A I I 89 35 109) and by C G E - L a b o r a t o i r e s de Marcoussis (Convention 306/C/89).
References I S.D. Walker and R. A. Garnham, Br. Telecommun. Tech. J., 5 (1987) 5. 2 C. Caneau, J. L. Zyskind, J. W. Sulhoff, T. E. Glover, J. Centanni, C. A. Burrus, A. G. Dental and M. A. Pollack, Appl. Phys. Lett., 51 (1987) 764. 3 A. E. Drakin, R G. Eliseev, B. N. Sverdlov, A. E. Bochkarev, L. M. Dolginov and L. V. Druzhinina, lEEE J. Quantum Electron., 23 (1987) 1089. 4 I.A. Andreev, M. A. Afrailov, A. N. Baranov, S. G. Konnikov, M. A. Mirsagatov, M. E Mikhailova, O. V. Salata, U. B. Umanskii, G. M. Filaretova and Yu. R Yakovlev, Sov. Phys.-- Tech. Phys. Lett., 15(1989) 15. 5 G.B. Stringfellow,J. Cryst. Growth, 58 (1982) 194. 6 K. Onabe, Jpn. J. Appl. Phys., 21 (1982) 964. 7 E Karouta, A. Marbeuf, A. Joulli6 and J. H. Fan, J. Cryst. Growth, 79(1986) 445. 8 M. Quillec, C. Daguet, J. L. Benchimol and H. Launois, Appl. Phys. Lett., 40(1982) 325. 9 M. Ishikawa and R. Ito, Jpn. J. Appl. Phys., 23 (1984) L21. 10 B. de Cremoux, J. Phys., Paris, Colloq. ('5, 43(1982) 5. 11 K. Onabe, NEC Res. Dev., 72 (1984) 1. 12 L. M. Dolginov, E G. Eliseev, A. N. Lapshin and M. G. Mildviskii, Krist. Tech., 13 (1978) 631. 13 W. A. Jesser and D. Kuhlmann-Wilsdoff, Phys. Status Solidi, 19 (1967) 95. 14 W.A. Brantley, J. Appl. Phys., 44(1973) 534. 15 J. Hornstra and W. J. Bartels, J. Cryst. Growth, 44 (1978) 513. 16 E. Tournie, E Pitard, A. Joulli6 and R. Fourcade, J. Cryst. Growth, 104 (1990) 683. 17 E. Tourni6, J.-L. Lazzari, E Pitard, C. Alibert, A. Joulli6 and B. Lambert, J. Appl. Phys., to be published. 18 M. C. Joncour, J. L. Benchimol, J. Burgeat and M. Quid lec, J. Phys., Paris, Colloq. C5, 49(1982) 3. 19 J. Ohta, M. Ishikawa, R. lto and N. Ogasawara, Jpn. J. Appl. Phys., 22 (1983) L 136. 20 J.J. Hsieh, J. Cryst. Growth, 27(1974) 49. 21 J.C. Brice, J. Cryst. Growth, l (1967) 218.
125
Growth limitations by the miscibility gap in liquid phase epitaxy of Gal_ xlnxAsySbl _y o n GaSb J.-L. Lazzari, E. Tourni~, F. Pitard and A. Joulli~ Equipe de Microopto~lectronique de Montpellier, Unit6 de Recherche associJe au CNRS 392, Universit6 de Montpellier II, Sciences et Techniques du Languedoc, 34095 Montpellier CJdex 5 (France)
B. Lambert Centre National d'Etudes des TJlJcommunications, Lannion B, OCM, B.P. 40, F2230l Lannion CJdex (France)
Abstract The boundary line (binodal curve) of the solid phase miscibility gap of the Ga~ _xlnxAsySb I _y quaternary alloy has been calculated from the regular solution model, taking into account the latticemismatched strain energy induced by a GaSb substrate. A calculation suggests that the miscibility gap is reduced and epitaxial layers might be deposited over the entire range of lattice-matched compositions at 615 °C. Ga~ _xlnxAsySb~ _y epitaxial layers have been grown by liquid phase epitaxy on (100)- and (111)Boriented GaSb substrates. The lattice-matched epitaxial layers which were richest in indium (x = 0.23) for the (100) orientation and x = 0.26 for the (111)B orientation have compositions located in the vicinity of the boundary of the miscibility gap calculated ignoring the strain energy, showing that stabilization by the substrate is far less effective than predicted.
1. Introduction
Long-haul, high bit rate optical communications using fluoride glass fibres [1] are predicted in the wavelength range 2.5-2.7 /~m. Liquid phase epitaxy (LPE) has been used successfully to produce low threshold laser diodes [2, 3] and high speed detectors [4] in the Ga 1_ xlnxAsySb1_ y/GaSb system operating at wavelengths near 2/~m. The existence of a large solid phase miscibility gap [5, 6, 7] has so far made it impossible to extend the wavelength range to 2.7 /~m. The question is whether stabilization by the substrate, which has been demonstrated [8] with the Gal_xlnxAsy Pl_y/InP system, should extend the range of Gal_xlnxAsySbl_y alloys that can be grown on GaSb substrates. It has been argued [9, 10] that growth inside an unstable region can still occur because the substrate tends to stabilize epitaxial layers which are nearly lattice matched. In this paper, we first study theoretically the 0921-5107/91/$3.50
contribution of the lattice-mismatch strain energy induced by the GaSb substrate to the miscibility gap, which was defined as being bounded by the binodal curve, and show that solid phase stabilization should occur. Also, we have achieved a number of LPE experiments, using (100)- and (111)B-oriented GaSb substrates, in order to grow epitaxial Ga~_xlnxAsySbl_y layers inside the calculated miscibility gap. 2. Miscibility gap of the Gal_xlnxAsySbl _y quaternary alloy
The miscibility gap was defined at a given temperature as the unstable solid phase composition domain bounded by the binodal curve. This curve gives the composition (x~,y~) of the two G a 1_xlnxAsySbl _y alloys which are in equilibrium with the same liquid solution when the peritectic solid phase decomposition occurs. The binodal curve was calculated from knowledge of the total free energy of the system G(x,y) using © Elsevier Sequoia/Printed in The Netherlands
126 GaAs
the following equations [11]: 0G
OG I=~-X
(1)
0G I 0G Oy = O y
(2)
i~X
OG 1
OG 1
G(x"yl)- Oxx x , - ~y
InAs
,'
t
"o."
;
OG 2 x2- ~OG = G(x.,y2)- ~xx y 2 Y2
f
/.' if /
/
-/j//
Yl
,
,
i1~
/
;/.° (3)
/
j"
/ 4~
i
W 0.0
The total free energy G(x,y) consists of the mixing free energy GM(x,y) and the strain energy G~t(x, y):
G(x,y) = GM(x,y) + G~t(x,y)
(4)
The mixing term G M was given by the regular solution model [11] using the thermodynamical parameters obtained by Dolginov et al. [12]. The strain energy G st for epitaxial layers which are not relaxed can be expressed as [13]
G~t(x,y)=o(x,y)
I [
1"
a(x'y)-a"ao l
Cll
O,,, = 2 C 4 4
3(C, + 2C12) C~1 + 2C12 +
Vm
0.0
1.0
X --~
In Sb
Fig. l. Composition evolution of (100)- and ( I l l ) B oriented alloys possessing a constant elastic parameter o (isoO curves).
InAs
GaAs i
1.0
i
i
i
i
i
i
i
i
(5)
where a 0 and a(x,y) are the lattice constants of the substrate ~..id the strain-free epitaxial layer respectively; a(x,y) was calculated using Vegard's law. The elastic parameter a(x,y) depends on the substrate orientation. For the (100) and (111) orientations, ato o and all I are given by [14] 0.101)= ( C I I _ Ci2) Cll J-2C,2 Vm
GaSb
(6)
(7)
C44
Vm is the molar volume of the epitaxial layer: V m = Na3(x,y)/4 where N is the Avogadro number. The Cu are the elastic constants which were calculated from the elastic constants of the binary compounds [15] using Vegard's law. The variations in the elastic parameters Ol00 and Ojl I across the composition plane of the Ga~_xlnxAsySbl y system are shown in Fig. 1. Calculations for 615 °C were performed by solving eqns. (1)-(7). This temperature was chosen because it furnishes theoretically the indiumrichest--and consequently arsenic-richest--
./
/
....
. . . .
/ " 615°C
/ 0.0
GaSb 0.0
.
.
.
.
.
.
.
X~
,
,
1.0 InSb
Fig. 2. Miscibility gap of the Gain .~InxAs,.Sb ~_, system at 615°C: . . . . , binodal curve without strain effect; - binodal curve with Ga~ xln,As,.Sb~ ,./GaSb strain effect; • typical compositions of LPE (100) epitaxial layers; ,t, typical compositions of LPE ( 111 )B epitaxial layers.
Gal_xlnxAssSbl_y alloy which can be grown lattice matched to the GaSb substrate, ignoring the subs•rate-induced stabilization effect [16]. It must be remembered that calculations were made with the assumption that the epitaxial layer is sufficiently thin to be completely in the elastic state. Figure 2 shows the binodal curves calculated with the hypothesis of stress-free solid phases (broken curves) and the binodal curves (full curves) calculated taking into account the substrate-induced strain energy G st for one solid phase composition (xl ,Yl ), the other (x2,yz) being completely relaxed. One can see a reduction in
127
the total size of the miscibility gap of the system, which is clearly visible in Fig. 2, and the existence of an extra miscible region for epitaxial layers with little or no mismatch. In that case, there is a solid phase stabilization by the substrate, and growth of Ga= _~InxAsySbl -y alloy lattice matched with GaSb is allowed in the whole domain of indium concentration 0 < x < 1. Another typical result of the calculations is that miscibility gaps are almost the same for strained (100) and strained (111) epitaxial layers. The width of the stable domain which appears along the GaSb lattice-matching line corresponds to a lattice mismatch Aa/a from about - 1 × 1 0 - 3 to + 1 × 1 0 -3 for (111) substrates and from about - 1.7x 10 -3 to + 1 x 10 -3 for (100) substrates. In fact, these results are not surprising as the parameters o ~ and 0~00 are quite comparable ((7111 ~-" 1.3Oloo). 3. L i q u i d p h a s e epitaxy o f the Gal - x l n x A s y S b l - y / G a S b s y s t e m
The epitaxial layers of thickness 0.4-2 /~m were grown by the step-cooling method on GaSb substrates, either (100) or ( l l l ) B oriented, at temperatures near 600 °C, from liquid solutions of constant antimony concentration (XsbL= 0.50) [16, 17]. The solid phase composition was determined using electron microprobe analysis on thick samples. The conditions of lattice matching are given in Fig. 3, which indicates the measured lattice mismatch Aa/a = (alayer-- asubstrat e)/asubstrat e as a function of XA~L, for various initial supercoolings A T = Tequilibriu m - - Zgrowt h . This study allowed us to grow in a reproducible manner lattice-matched layers (Aa/a = 0) or slightly mismatched layers (Aa/a=lO -3) with quite a good surface morphology. No crosshatched pattern could be detected even for thick layers (about 2 ¢tm), suggesting that the layers are in the elastic state. For near-equilibrium growth (AT=10°C), lattice-matched ( 111 )B and (100) epitaxial layers have the same composition when grown from melts having the same indium and antimony contents. The most indium-rich lattice-matched layer which could be deposited is G a 0 . 7 7 I n 0 . 2 3 A s 0 . 2 0 Sb0.80 [16, 17]. When the initial supersaturation of the melt is increased (A T> 10 °C), the composition of ( 100)oriented lattice-matched layers remains the same (x = 0.23; y = 0.20). Conversely, ( 111 )B-oriented
I: 12 1p AT(*C) 10 , 215 IL~
I
I
2t~~ I T ~ ~ I, ~ , lt ' ',~'1
/
;,\,
~I / t
30
t
-1
~t
',
~
"
2.5
~" /XL(In):'4
/XL(Sb)=.5
115 I ",
I
(100) (111)B
30
I , '
=o
..... ,--
='~',
21~,
I
~,
3.0
3.5
XL(As) xlO 3 ~
Fig. 3. Variation in the perpendicular lattice mismatch vs. liquid atomic fraction of arsenic, for various initial supersaturations AT, in the case of (100)- and (111)B-oriented epitaxial layers.
H
(100)_~
AT~
t
lOt:
•~
2o*c
(11~~.2 K
,-I
n.
,
,
2.2
2.0 ~Mprn)
#
,
..
2.2 20 ~.,l,(prn )
Fig. 4. PL emission intensity (in arbitrary units (a.u.)) at 2 K of (100) and ( I I 1 ) B lattice-matched LPE layers grown under different initial supercoolings A T.
lattice-matched layers show an increase in their indium and arsenic contents up to x = 0 . 2 6 , y = 0.23, for A T = 25 °C. For higher supercoolings (AT> 25 °C), homogeneous nucleation appears within the liquid, and satisfactory LPE growth could not be achieved [17]. Photoluminescence (PL) experiments performed at 2 K confirm these results (Fig. 4).
128 W h e n A T is increased, there is no change in the peak position of the PL emission of (100)oriented samples whereas a shift towards the longer wavelengths is clearly noticeable with ( i l l ) B - o r i e n t e d samples: 2 c = 2 . 1 8 /~m for A T = 2 0 ° C and 2 ~ = 2 . 2 0 /zm for A T = 2 5 ° C . Figure 2 shows that this composition, which is the most indium rich that we could obtain, is situated slightly inside the miscibility gap of strain-free solid phase, and plainly outside the miscibility gap relating to a strained layer.
4. Discussion Taking account of the strain energy induced by the substrate, a theoretical evaluation of the miscibility gap of the G a l _ x l n x A s y S b l _ y / G a S b system predicts a reduction in the instability domain b o u n d e d by the binodal curve and the possibility of depositing elastic layers with little or no mismatch ( A a / a < 10 -3) over the entire range of compositions. O u r attempts to grow this kind of layer by L P E were unsuccessful; lattice-matched G a l _ xlnxAsySb~ _y layers grown under near-equilibrium conditions have the highest indium content (x = 0.23) at the boundary of the miscibility gap calculated ignoring the strain effect. It was only possible to increase a little the indium concentration of the solid phase (up to x = 0.26) by using high initial supercooling and ( 111 )B orientation. As suggested by some workers [18, 19], this result can be explained by the difference between the growth kinetics of ( 111 )B- and ( 100)-oriented samples. Effectively, the d e p e n d e n c e of the layer thickness vs. the growth time e(t) was found to be el00(t) = K l o o A T t 1/2 with K=0.035btmoC
1 s 1/2
(8)
and ell~(t)=Kij~ATt
with K = 30 A ° C
is
~ (9)
Equation (8) is typical of a growth rate controlled by the solute diffusion in the liquid solution [20] as eqn. (9) can be interpreted by a growth controlled by surface attachment kinetics of the first order (which c o r r e s p o n d to diffuse growth [21]). In conclusion, the stabilization effect by the substrate-induced strain energy seems to be far
less effective than theoretically predicted. It seems necessary to include orientation dependence of growth kinetics to explain our experimental results.
Acknowledgments T h e authors wish to thank D. Barbusse and R. Fourcade of the Laboratoire des Agr6gats Mol6culaires et des Mat6riaux Inorganiques, Montpellier University, for their X-ray doublediffraction measurements. This work has been partially supported by France T616com (Convention D A I I 89 35 109) and by C G E - L a b o r a t o i r e s de Marcoussis (Convention 306/C/89).
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