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Epitaxy of mixed III–V compounds
Journal of Luminescence 7 (1973) 176—191. North-Holland Publishing Company
EPITAXY OF MIXED Ill-V COMPOUNDS J.B. MULLIN and D.T.J. HURLE Royal Radar Establishment, St. Andrews Road, Malvern, Worcs., England
A general technique (D.T.J. Hurle and J.B. Mullin, J. Phys. Chem. Solids (Supplement Proceedings ICCG, Boston 1966) (1967) 241) fnr predicting the conditions of thermodynamic equihbrium in a solid/gaseous system has been applied to the systems In—As—-P—-Cl—Fl, Ga—As—-P—Cl—Fl, Ga—In—As—Cl—H and Ga—In—P-Cl—H. The solidus curves for the mixed ternaries InAsu x)Px and GaXInu_X)As are computed as functions of the respective vapour parameters P/(As + P) and Ga/(Ga + In) where the chemical symbols represent the total molecular concentrations of the respective group V or group III bearing species in the vapour. The calculated relationships have been compared with equivalent experimentally-measured relationships and very good agreement has been obtained using a self-consistent set of thermodynamic data. Some significant changes in the thermochemical data are discussed. The theory takes account of the mixed dimers and tetramers of arsenic and phosphorus. The agreement between theory and experiment is also discussed in relationship to the relevance of equilibrium theory since growth of practical interest often occurs under conditions of kinetic control.
1. Introduction In an earlier paper [11 a general technique was published for predicting the conditions of thermodynamic equilibrium in a solid-gaseous system. The technique was applied specifically to the case of the Ga : As : Cl: H system where the solid was assumed to be stoichiometric and have a constant unit activity. The possibility of the nucleation or coexistence of an additional Ga-rich phase was ignored. The application of the technique to predict liquid formation in the above system or in the mixed ternaries is possible in principle. But, the main limitation of such an analysis would lie in our inadequate knowledge of the atomic interaction constants in the liquid. Experimentally, the major interest in vapour deposition concerns only the single solid phase region. In the present work the general technique which was used for the Ga : As : Cl : H system is extended to allow predictions of the equilibrium solidus and vapour compositions for mixed Ill-V systems. The greatest source of uncertainty in predicting the solidus composition is the accuracy of the thermochemical data used. Ideally one needs to know the enthalpies and entropies to better than -~ k cal per mole, i.e. a higher accuracy than has been attained in many cases. Accurate values for the principal species such as the Ill-V compounds and ternaries (see section 2.3) are of course particularly important. However, it has been possible to select values of the thermochemical constants which form a self-consistent set of values. Thus the 176
J.B. Mullin, D.T.J. Hurle, Epit~xyof mixed 111-V compounds
177
fact that the same constants can be used to closely predict the experimentallydetermined solidus for all the systems InAs(l_X)Px, GaAs(l_x)Px, Gaxln(l_x)As and Gaxln(l_x)P provides an internal check on the reliability of the selected data.
2. Properties of the system 2.1. Chemical species A knowledge of the presence and properties of all major molecular species is an essential requirement in any thermodynamic analysis. In the case of the mixed Ill-V compounds there is general accord on the species present in chloride or halide systems as a result of numerous epitaxial studies and mass spectrometric investigations [2, 3]. In one of the most recent investigations Ban [3] has shown that in mixed arseno-phosphide systems all the combinations of arsenic and phosphorus occur as dimers and tetramers. Thus he identified and measured the relative proportions of As2, P2, As4, P4, AsP3, As2P2, As3P in a simulated GaAs(l_x)Px transport system. Also undecomposed AsH3 and PH3 were found in the products of the mixed hydride system. Under certain conditions it was as much as 10% in the case of the more stable 4. PH3, it should noted that the flow rate had the In but the same studybethe presence of GaC1 high value of 1.2 L. min 3 was specifically sought but not found. Theoretically one would not expect it to be a major component in systems using hydrogen as a carrier gas when the temperature is around l000°Kor above. Under similar conditions the role of GaCl2 [4] would be insignificant. 2.2. Thermochemical data The thermodynamic data used in this analysis is listed in table 1. A detailed discussion of this will be given elsewhere [5], but it is pertinent to note here the significant changes to the values used in the earlier paper [1]. The most important change is the value for the enthalpy for the reaction As4(V) 2As2(V). The quoted literature value for the enthalpy is subject to considerable fluctuations often by as much as 10 kcal per mole. A basic source of error in the mass spectrometric determinations of the As2lAs4 equilibrium has recently been reported by Arthur [6]. He found that As2 molecules could recombine on metal surfaces in the filament chamber giving rise to spurious measurements of the As2/As4 ratio. Using a suitably cooled chamber which prevented molecules desorbing from the walls he obtained a value of 62.5 kcal for the above reaction. As a result of this work it has been possible to recalculate the values of z~H~98 for InAs and GaAs. Since the authors’ earlier publication the value of ~H~98 for AsH3 has been revised very markedly from 41.0 kcal mole~to 15.88 kcal mole~ [7]. This change
_~
caldeg mole~
kcal mole
Molecule
~
78.17
61.80
3
AsCl
60.3
16.7
mCI
~-----
15.34
20.7
GaAs
57.2
--48.45
2
As
83.8
89.4
mCI3
57.4
19.1
GaC]
~-
AsP
52.108
—34.5
P2
75
—34.4
As4
(73.0)
(—29.3)
As3P
(70.9)
(--24.2)
As2P2
79.7
107
GaCI3
31.208
0
H2
53.288
0
Cl2
39.457
—29.082
Cl
(68.9)
(—19.2)
AsP3
__________________
44.646
22.062
HO
---------------------_____________________________
(54.6)
(—41.5)
__________________
11.96
27.4
GaP
—_________________
74.49
68.6
Pd3
14.3
21.2
15.8
18.1
lnP
InAs
_____________
9~eg~ mole~ c1
kcal mole
Molecule
Table 1 Thermodynamic data used in computational analysis AsIl3
PH3
66.89
50.22
__________
53.22
—14.08 --15.88 ---1.3
P4
~
J.B. Mullin, D.T.J. Hurle, Epitaxy of mixed 111-V compounds
179
is not important in calculations where complete equilibrium is involved; AsH3 is generally present in relatively insignificant concentrations. However, in certain special cases where there are rate controlling factors in the decomposition of AsH3 commensurate with the deposition period, the thermochemical properties of the AsH3 become important and must be taken into account to explain the vapour— solidus relationship. An additional problem in the mixed Ill-V compounds, which is absent in the pure binaries, is the presence of the mixed arseno-phosphides mentioned earlier. They have been a subject of mass spectrographic investigations both by Gutbier [21and by Ban [3] in connection with dissociation and pseudo-deposition studies on GaAs(l_x)Px and InAs056P044 respectively. In these studies dimer recombination in the source of the mass spectrometer as reported by Arthur [6] and noted earlier could have effected the measured relative abundances of the species. No attempt has been made therefore to interpret thermodynamic properties from their data. Instead, the thermochemical properties of the mixed compounds have been assessed by taking a linear interpolation of the known equivalent properties of the related monocomponent tetramers As4, P4 and dimers As2, P2. This assessment is consistent with Gutbier’s results. Thus he calculated the dissociation energies of the mixed dimers and tetramers using a linear interpolation of the mono-component species and found good agreement with the experimentally-determined dissociation energies. One further piece of basic data is required in order to predict the solidus composition of the vapour grown layers. This data is the heat of mixing of the ternary compounds. Fortunately, the liquidus-solidus equilibria along the pseudo-binary section of the ternary phase diagrams has been experimentally determined and this enables an estimate to be made of the heats of mixing. We have assumed that the liquid and solid phases form regular solutions and that the standard heat of mixing /~Hmin phase i can be written as: L~JI~ =~21X1(1—Xi),
(1)
where X, is the atom fraction of one of the variable component elements and (1 X1) is the atom fraction of the other; ~ are the atomic interaction parameters. 2~were used as selection parameters to obtain the best fit The values for ~L and & solidus and liquidus curves of the pseudo-binary phase of the theoretically-derived diagram to the experimental curves. The procedure used to derive the theoretical curves involves equating the chemical potentials p5~)of each pseudo-component (InAs and GaAs) in the two phases, where: ,IL_/JOL+RT1nYLXL (2)
(pf
/1~’=~oS
+RTlnySXS.
(3)
1 80
.J.B. Mullin, D.T.J. Hurle, Epitaxy of mixed 111-V compounds
Using regular solutions theory for y RTln~s=&~is(l ~X~)2.
(4)
The quality of the theoretical fit obtainable can be judged from fig. 1, which is the pseudo-binary section of the GaAs-InAs diagram [8}.The scatter in the experimental solidus data provides the biggest uncertainty, but it is estimated that the values of the interaction parameter obtained are probably accurate to within ±0 2 kcal/mole. 2.3. Accuracy of data
In assessing thermodynamic data it is necessary to know, if only approximately, the effect of the accuracy of the data on the predictions. In the reactions involving many species, such as the mixed ternaries, considerable calculation is required to assess the effect of even just one variation in say the enthalpy of a species. However, an approximate estimate of the accuracy required of thermochemical data can be ascertained by analysing a relatively simple system such as the Ga : As : Cl : H in terms of a single reaction (eq. (5)) 2GaCl+~As4+H2 s~2GaAs+2HCl.
(5)
The main sources of uncertainty derive in this and equivalent Ill-V epitaxial processes principally from inadequate data on the standard enthalpy of formation of the main species present in equilibrium. This would include the binary and ternary Ill-V compounds, the monochlorides and the dimers and tetramers of arsenic and or phosphorus. The effect of errors in the enthalpies in these compounds specifically in connection with eq. (5) may be seen readily in the equilibrium constant K~(eqs. (6) and (7)) K~e~RT
(6)
K’
(7)
~
where L~~G is the standard free energy change for eq. (5) and &AH is the error in the enthalpy of reaction. At l000°Ka 1 kcal mo1e~error (5~H)can lead to a 40% error in K,,. A more useful presentation of the effect of ~ can be seen in fig. 2, where the relationship between Ga/Cl ratio is plotted against temperature for two separate values of ~~1~0298for GaAs differing by 3 kcal. Curves as in fig. 2. can be used for predicting the optimum conditions for epitaxial growth or vapour transport. The 3 kcal difference can cause a maximum error in the deposition curve of’-’lOO°Ca very significant effect. It is evident therefore that one needs to know values to better than 1 kcal rnole~and preferably to better than ~ kcal mole l~
J.B. Mullin, D.T.J. Hurle, Epitdxy of mixed 111-V compounds 1300
I
181
I
T 1°C) ns 200
= ~L~°2
1 2~5K CAL MOLE K CAL MOLE1
-
0
1100
-
£
S
000
-
A A 0 90C
0 InAs
I
0.25
I
05
0.75
1-0 GaAs
Fig. 1. lnAs-GaAs pseudo-binary phase diagram. Thick lines show the theoretical fit to the experimentalliquidus (thin line) and solidus (points). Experimental data taken from [81. 1-0 09
C’S 07 0-6
~o-5
A
B
0-4 03 02 0-I
C700
BOO
I
900 000 TEMPERATURE (°Kl —
1100
1200
Fig. 2. Theoretical variation of the (Ga/Cl) ratio with temperature in the Ga—As—Cl—H system using values of AH° 298for GaAs of A) — 17.7 and B) — 20.7 kcal per mole.
182
J.B. Mullin, D.T.J. Hurle, Epitaxy of mixed III- V compounds
3. Calculation of the equilibrium surfaces 3.]. Variables
The phase rule can be readily applied to the case of a closed system in equilibrium e.g. a solid in contact with a gaseous environment. However, if we wish to apply such a model to an open flow epitaxial system, its relevance must be carefully considered since it is known that under certain conditions the growth rate of the compound can be kinetically-controlled. In an open flow system one may conveniently consider three regions; the input region I, the deposition region D and the post-deposition region PD. Normally a non-equilibrium gaseous mixture is admitted into I and this converts towards equilibrium in the region D, so that a near equilibrium mixture flows out through PD. Provided the gas in D rapidly converts to equilibrium the effect of deposition will only change the relative amounts of solid phase in D and one can treat the region D as a pseudo-equilibrium region. However, in considering the variance of the system it is to be noted that the concentrations of the components of the compound do not remain constant. Thus, in the case of InAsO_x)Px, which we will now treat as an example of a ternary system, the partial pressure of As4 in D will vary as a result of transferring lnAs(1X)PX from the solid to the vapour phase; ~As4 cannot be treated therefore as an independent variable. Nevertheless the relative amounts of the solid and gaseous phases must be independent of the equilibrium situation so that the deposition of IOAS(lx)Px involves a conserved parameter. In the equivalent case of GaAs this was identified as (Ga—As)/H a short hand syinbol for a non-dimensional variable (‘~Ga ~As)/~H, where the n’s refer to the concentrations or number densities of the components. In the case of InAs()_x)Px, (ln—As-—P)/H is used as the conserved parameter. (ln—As-—P)/H is a linear combination of the prime independent variables [(l—x) In—As] /H and [x In—P] /H and is a more convenient choice since it is independent of x and permits the latter variable to be treated as an independent parameter. Apart from pressure, P and temperature, Ta further independent variable will be Cl/H, since the amount of Cl and H remains constant in the gas phase if the relative amounts of the solid and gas phase are changed. The dependent variables are selected in order to characterise the deposition process. Thus both As/H and P/H are necessary in order to determine the. gaseous parameter P/(P + As). 3.2. Variance
The system (In—As—P—Cl—-H) has five components, a gaseous phase and a single solid phase of variable composition which is characterised by the parameter x, the mole fraction of InP in the compound InAs(l x)Px. In order to determine the dependence of the equilibrium one can relate the dependent variables As/H and P/H
J.B. Mullin, D.T.J. Hurle, Epitdxy of mixed 1II-Vcompounds
183
in terms of the five independent variables, P, T, Cl/H, (In—As—P)/H, and x. In doing so one considers the deposition of the InAs and InP as separate species which combine to form a solid solution in which the activities of these species in the InAs(lx)Px are less than unity. We can consider their activity coefficients to be respectively 7i and ~ 3.3. Procedure
The equilibrium conditions may therefore be represented by the equations In—As—P fl(P,T,x,~H
Cl As ,-~,-~-)=0
and In—As—P ~Cl P
~
The variables of interest in the system are the partial pressures of the eighteen vapour species. Following the general procedure [1], the independent variables P,T,x,
In—As—P CI H ‘H
and the dependent variables As/H, P/H can be formulated in terms of the partial pressures of the chemical species. Thus: ‘~InCl+ ~InCl
=
1~HCl+ ~Cl 3 +
+PPC13
+P
As4
2 + ~H2 + ~A~l
+PP4 +PAs2 +PP2 +PCl +PPH3 +PAsH3 +PAsP +PAs2P2
+PAP+PAsP
(8)
~InCl+
~ ~h~Cl3 + 2 ~Cl2+ ~ ~AsCl3 + ~Cl 2P+ ~HCI 3Ppfl+3PAH PHC1+ 11+
Cl]
—[lifT-
[In—As—P][~~InCl+ ~InCl H +
—
—
—
~AsCl3
—
2 4P~4 P HC1 +2P H2 +3PP1-I3 +3P AsH3 4— ~AsCl3
—
3AsH 2~AsP— 4’~As 41~As 3PPH 2p2 3PAsH ‘ PHCI+2PH 3 — — 3p 2 + 3 + 3
4PA [As] [H]
2~As
4~As 3
+
+2PA
—
—
—
~PCI3
—
2P~1
4~ASP 1 3
(10)
+PA~ +PASP+2PAP +3PAS 3P+PAsP (11) 2PH+3PpH+3PAH P~l+
184
.J.B. Mu/un, D.T.J. Hurle, Epitaxy ofmixed 111-V compounds
[P]
T1’lT
~PCl
3
+4PP4 +2Pp+Ppfl+PAsP+2PAP+PAP+3P 3
3
3~ASH
~PH
~HCi~~I-I2~
=
AsP
3
3 +
(12)
—.
The relationships between the partial pressures are given by: —l
lnCl3
InCl
H2+C12
Cl-,
+
s~2HCl
k6
=
k
2-P
3 Cl2 +-~As4
k8
2PC13
3 Cl2
k
+~ P4
=
2 As2
k 10
=
Cl
pCl23
-
pAs 2 pA~il3 —2
(15)
p
.
p
(16)
~
As4
1-P
P 1-ICI
2AsC13
~
3 Cl2
~.
As22
--2 PCI3
P As4 ~
-
2P2
2p ~ k 11 =PP2 P4
Cl2
~2Cl
k
=P
p
~.
P4
P4
12
(13) (14)
~InC1 ~C12 ~InCl,
(17) (18) (19)
2-P1~Cm —~ ~Cl 2 2
‘3C1
~ 2
-2
As
(20)
2lnCl+~As4s~2InAs+Cl2
k13
2InCl+~P4 s~2lnP+Cl2
k14y~(x)
3 H2
+
P2
2 PH3
k 15
=
pPH32 p P3—1 ~~2 —3
(22)
3 H2
+
As2
2 AsH3
k 16
=
pAsH32
(23)
2AsP
k 17
=
pAsP 2
2 AsP
As2 P2
k18
=
‘~As2P
AsP + As2
As3P
=
~As,P P
As2
+
P2
AsP+P2
AsP3
y~(l—x)
4 mCI
2PCl .p-~ P p
2 .
-2
.
-
.
2
-
‘
—~ -
As2
(21)
InCl
P H2
—~
P As2 ~ P P2 1
(24)
pAsP —2
(25)
-
—1. P —I As AsP
k2oPAsP~P
AsP
1
-P
—1 P2
(26) (27)
where the ks’s are given by the formulae k~=_~i/~~T
(28)
J.B. Mu/un, D.T.J. Hurle, Epitaxy of mixed 111-V compounds
185
The ~Gt’sare given by temperature dependent functions of the enthalpy entropy and specific heat changes for the i reactions: T
~G~=L~H98+f
T~C
~c~dT_Tzxs;98_Tf
dT.
—~
298
(29)
298
The procedure used for solving these equations involves setting values for the independent parameters and then with the aid of approximate values for the partial pressures of the vapour species, using an iterative computer technique to obtain the accurate partial pressures. Thus for a fixed P, T, Cl/H and (In—As—P)/H one can obtain a plot of x against P/(P + As).
4. Comparison of results The theoretical plots of the vapour parameters P/(P + As) and Ga/(Ga + In) against x for the respective ternaries InAs(l x)Px and Gaxln(l_x)As are shown in figs. 3 and 4. The full lines have been calculated using the procedure outlined in section 3. The points are experimentally-determined values. In the case of IC
I
I
I
.
In As11_51P5 0-75
(J.J.TIETJEN et ol I
—
-
S
x0•5-
.
-
S
025
-
-
. S
0
0.25
0-5
0-75
0
MOLE RATIO PH3/(PH3+AsH3)
Fig. 3. Comparison of the theoretical dependence — full line — of the mole fraction of InP in 3, IflAs(l_x)Pxas a function of the vapour parameter P/(P + As) with the equivalent experimental data points taken (ln—As—P)/H = —1.0 fromX [91. 10~. Theoretical parametersPl atm, T~1000°K, C1/H2.0 X i0
186
J.B. Mu//in, D.T.J. Hur/e, Epitaxy of mixed 111-V compounds c I
I
As I R.W CONRAD et oil 0-75
.
-
-
$
x 05-
•
-
. 0-25
-4•1
-
S
0-25
0-5
Go FLOW I
0.175
0
Ga FLOW + In FLOW I
Fig. 4. Comparison of the theoretical dependence -- full line — with the mole fraction of GaAs in GaxIn 0 _x)’~~ as a function of the vapour parameter Ga/(Ga + In) with the equivalent experimental data2,(In — points 1111. Theoretical parameters, P = 1 atns, T = 1023°K, + Ga——taken As)/Hfrom = 5 X i0’. Cl/H 1.0 X 10
lflA5U_x)Px these points were taken from the paper of Tietjen, Maruska and Clough [9]. They deposited epitaxial layers of the ternary compound on InAs in the temperature range 675 725°C.The agreement between theory and experiment is well within the limits of experimental error. The shape of the theoretical curve shows a slight inflexion; it differs in this respect to the relationship drawn through the points by Tietjen et al. The inflexion is probably caused by the role of dimers and tetramers in the deposition reaction. Allen and Mehl [10] have carried out a similar experimental study to that of Tietjen et al. They also reacted AsH 3 and PH3 gaseous mixtures with InCI depositing the InAsU_X)PX in the temperature range 630 750°C.However the deposition was carried out on GaAs substrates. Their results closely parallel those of Tietjen et al., the experimental curve being very slightly to the right of the currently-calculated theoretical curve. The variables temperature and chlorine to hydrogen ratio will of course both effect the shape of the curve, and the fact that the former was not held constant throughout the range of investigation from x 0 to x 1 could well account for the slight divergence of the curves. However, from the theoretical prediction viewpoint the agreement between theory and experiment is remarkably good. —
—
—
=
=
—
J.B. Mu//in, D. T.J. Hurle, Epitaxy of mixed 111-V compounds
187
The result for GaxIn(l_x)As a mixed group III ternary is shown in fig. 4. Again, the full line is theoretical. It represents the variation of the mole fraction of GaAs in the solid as a function of the Ga mole fraction of the group III bearing species in the vapour. The experimental points are replotted from Conrad et al. [11]. They transported HCI over separate sources of Ga and In and reacted the chlorides of these elements with arsenic vapour, the Gaxln(l_x)As being deposited at 745 750°Con GaAs substrates. The agreement between theory and experiment is good. The preferential deposition of GaAs is particularly marked. In an earlier study by Minden [121the same compound was deposited from the gaseous mixture resulting from flowing H2 and HC1 firstly over a boat of solid arsenic and sub—
sequently over a boat of liquid Ga/In. His results are not strictly comparable with the present theory since he plots the mole percentage of GaAs in the deposit as a function of mole percentage Ga in the source. If the source was converted to a solid of average composition equivalent to that of the liquid then the pick up of Ga and In would be in proportion to the initial Ga/In ratio in the liquid. In fact one could infer reasonable agreement with Minden’s curve. But, since both the liquid and segregated solid in the source region must play a part in the process one is uncertain as to the applicability of the present theory. Enstrom et al. [13] have also investigated the deposition of Gaxln(lx)As using arsine and separate Ga and In sources. Their results have been checked by plotting a curve similar to fig. 4. The points fit well and show good agreement with theory the maximum deviation being of the order + 0.1 in x in the region of 0.2—0.3 for the vapour parameter Ga/(Ga + In). The results are again not strictly comparable to the theoretical prediction since their Cl/H values varied from a factor of 6 less up to the currently-used value of 1.0 X 10—2. Nagai et a). [14] have recently made a theoretical and experimental study of the Ga—In—As—Cl—H system. They have not however explicitly deduced the relationship between the vapour parameter Ga/(Ga + In) and the mole fraction of GaAs in the solid compound Gaxln(l_x)As. Their results are calculated for a value of Cl/H of 2.05 X 10—2. This is twice the value which is relevant to Conrad et al.’s study and the present authors’ computation. One can deduce a composition relationship from their results similar to those investigated here but it does not give good agreement with Conrad et al.’s experimental results. The comparison between their theory and Conrad et al.’s results however may not be strictly valid since the equilibria could be quite sensitive to the value of the parameter Cl/H.
5. Discussion In addition to the currently-discussed systems the P/(P + As) versus x relationship for GaAs(l_x)Px and the Ga/(Ga + In) versusx relationship for Gaxln(l_x)P have also been completed. Very good agreement has been obtained between the theoretical predictions and published experimental work. In achieving this agreement
188
.J.B. Mu//in, D.T.J. Hur/e, Epitaxy ofrnixedlll-Vcompounds
a preferential selection was made for certain values of ~H~98 notably for GaP and InP. The justification for this was that the same set of values successfully predicted the vapour solidus curves for all four systems InAs(l x)Px, GaAs(l_X)PX, In(l_x)GaxAs and In(l_x)GaxP. The derivation and existence of a self-consistent set of values provides in itself additional evidence on the reliability of the data. The justification for the use of equilibrium theory is that it can predict experimental results as in the present paper. However, one can criticise the use of equilibrium theory in that it does not predict or explain, for example, the experimentally-determined temperature-dependence in growth rate found in GaAs [15, 16] and GaAs(lx)Px [17]. Equilibrium theory would normally predict a con~ tinuously increasing growth rate with decreasing temperature using constant input conditions. In the case of GaAs, Shaw [15, 16] has found that growth rates increase with decreasing temperature to a maximum at ~780°— ~720°C depending on the exact As4 or GaC1 concentration in the system and then subsequently fall with further decrease in temperature. A similar behaviour has been found in GaAs(l_x)Px by Ban et a). [17]. Shaw explained the reduction in growth rate at temperatures below those giving a peak growth rate as the consequence of a heterogeneous kinetically-controlled surface reaction which had an activation energy of 49 kcal per mole. It is evident then that in GaAs, GaAs(l_x)Px and probably other 1lI-V’s, the optimum conditions for compound deposition which are currently used occur in a kinetically-controlled growth regime. In effect equilibrium theory is predicting the consequences of non-equilibrium growth. Qualitatively one may appreciate that this is a consequence of growth behaviour involving atom incorporation which is dominated by bulk equilibrium energy considerations but that the velocity is dominated by surface phenomena involving a rate transfer mechanism. Equally in the case of melt and solution growth of mixed Ill-V’s there is evidence that the solidus composition is representative of equilibrium thus enabling one, as has been done here, to construct pseudo-binary phase diagrams. Further evidence that the incorporation of the mixed group III’s or group V’s in the ternaries is controlled by bulk properties can be inferred from the experimental observations of Nagai et al. [14]. They found that the composition of Gaxln(lx)As was independent of the chemical nature of the substrate surface e.g. quartz, GaAs, InAs etc. Of course once nucleation occurs growth continues on GaxIn(l_x)As of some composition. However, differently orientated substrates also produced Gaxln(l_x)As deposits of the same composition. In conclusion it is clear that equilibrium theory can predict important experimental information and that it should help in elucidating further the mechanism of epitaxial growth. Additionally it should give greater impetus to establishing more accurate thermochemical data. Acknowledgements The authors gratefully acknowledge useful discussions with their colleagues in
J.B. Mu//in, D. T.J. Hur/e, Epitaxy of mixed III- V compounds
189
particular with the late Dr. B.D. Joyce. They also appreciate the skilful help of Mr. S. Benn for computing the results shown in fig. 2. Contributed by permission of the Director RRE. Copyright controlled HBMSO.
References [1] D.T.J. Hurle and J.B. Mullin, I. Phys. Chem. Solids — Supplement, International Conference on Crystal Growth, Boston 1966 (1967) 241. [21 H. Gutbier, Z. Naturforsch. 16a, no. 11(1961)268. [31 V.S. Ban, I. Electrochem. Soc. 118 (1971) 1473. [41 A.W. Laubengayer and F.B. Schirmer, I. Am. Chem. Soc. 62 (1940) 1578. [5] D.T.J. Hurle and J.B. Mullin, to be published. [6] J.R. Arthur, I. Phys. Chem. Solids 28 (1967) 2257. [7] D.D. Wagman, W.H. Evans, V.B. Parker, I. Halow, S.M. Bailey and R.H. Schumm, National Bureau of Standards (USA) Technical Note 270-3 (1968). [81 J. Steininger, J. Appl. Phys., 41, (1970) 2713. [9] 1.1. Tietjen, H.P. Maruska and R.B. Clough, I. Electrochem. Soc. 116 (1969) 492. [10] H.A. Allen and E.W. Mehal, I. Electrochem. Soc. 117 (1970) 1081. [111 R.W. Conrad, P.L. Hoyt and D.D. Martin, I. Electrochem. Soc. 114 (1967) 164. [121 H.T. Minden, I. Electrochem. Soc. 112 (1965) 300. [131 RE. Enstrom, D. Richman, M.S. Abrahams, J.R. Appert, D.G. Fisher, A.H. Sommer and B.F. Williams, in: Proceedings Internationa/ Symposium on Ga//ium Arsenide and re/ated compounds, Aachen (]970)(lnstitute of Physics and the Physical Society, London) 30. [14]H. Nagai, T. Shibata and H. Okamoto, lap. J. Appl. Phys. 10 (1971) 1337. [151 D.W. Shaw, I. Electrochem. Soc. 115 (1968) 405. [16] D.W. Shaw, I. Electrochem. Soc. 117 (1970) 683. [171 VS. Ban, HF. Gossenberger and J.J. Tietjen, I. Appl. Phys. 43 (1972) 2471.
Discussion F. Williams: You have shown important relations between the vapor and the average composition at the growing surface, using equilibrium thermodynamics. My question concerns subsequent processes which may occur in the solid leading to inhomogeneities, graded and without phase boundaries. This is relevant to a remark you made during the panel discussion on small gap semiconductor devices. Specifically, I am interested in whether these systems are expected to exhibit spinoidal separation and whether there is experimental evidence for its occurrence in these ternary systems. If the Gibbs free energy versus composition has a spinoid (convex maximum) at the temperature of preparation, then the system will be stable in favor of graded inhomogeneities and the kinetics then may lead to globular graded inhomogeneities on a scale of the order of a few hundred ângstroms (see works of J. Cahn). We have considered the effects on electronic and optical properties for such graded inhomogeneities, relevant to amorphous semiconductors (see Inglis and Williams, Phys. Rev. Letters (1970), 1. Non-Cryst. Sol. (1971); Martens and Williams, Warsaw Semiconductor Conf. (1971)). Do you have experimental evidence for or against spinoidal separation in the ternaries investigated? The evidence could be : (1) an Urbach tail in optical absorption due to the effective microfields of the inhomogeneities, (2) a temperature-dependent mobility arising from interglobule electronic transport, (3) annealing effects, (4) dependence of the electronic properties on the substrate temperature, and (5) actual phase separation during the final stages of spinoidal decomposition.
190
J.B. Mullin, D. T.J. Hone, Epitaxy of mixed 111-V compounds
Reply:I have no evidence for spinoidal separation in the ternary systems discussed. This was the reason I asked a similar question of CALAWA. One could, however, expect that spinoidal separation would be thermodynamically feasible in the case of solid solutions where the pseudobinary interaction constant was large, for example in the Ga/In compounds. The condition for spinoidal separation would not necessarily occur at the growth temperature but at some temperature below this. Clearly one could take a crystal rapidly through the critical temperature T~for spinoidal separation into a region of metastability. However, subsequent fabrication techniques in the region below T~,but where diffusion is significant, could bring about separation of new sohd phase. A.T. Vink: (1) The composition curve for Inq x)GaxP deviates rather drastically from the others shown. This clearly tends to make the material technologically a difficult one. Can this behaviour of the curve be simply explained? (2) Can these calculations be easily extended to quaternaries like the Ga 0 _x)lnxAsyPo —y) system mentioned here by Onton? (3) Can the theory be applied to doping of the Ill-V compounds, e.g. the isoelectronic centre N or donors like S, Sc, Te in GaP? For these donors it is known that the incorporation is not an equilibrium process and that an “orientation effect” is present for incorporation: when growing on (111)-Ga or (111)-P faces different doping levels are found under the same conditions. Are such effects within the scope of such a theory?
Reply: (1) The “difficulty” in incorporating Ga into In0 _x)GaxP is a fundamental one associated with the chemistry of Ga in lnP. One can identify the difficulty in the pseudo-binary solid/ hquid phase diagram where the interaction constants between the InP and GaP in the liquid and solid are large. The interaction constants are small in the arsenide-phosphide systems and it is “equally” easy to incorporate phosporus or arsenic into the In or Ga ternary. (2) In principle it would be possible to apply the analysis to the quaternaries but it would be necessary to know the thermochemical properties of the quaternary compound. (3) Again, in connection with your third question it should be possible to apply the analysis to the incorporation of impurities in these compounds. However, in those specific cases where one has a significant orientation effect such as the facet effect (B.D. Joyce and J.B. Mullin, Solid State Commun. (1969)) the theory would not predict quantitatively the impurity incorporation on or close to the low index planes. Away from the low index planes there is a greater probabihty of equilibrium incorporation. H. Signiund: You are dealing with an open flow system; this means that the pressure is constant, but also that some changes in the volume of the reaction gases may occur. Could you comment about this point especially for what concerns computing growth rates? Reply: The theory which has been developed applies specifically to the equilibrium between a ternary and a gas phase immediately adjacent to the surface of the ternary. Transport effects in the vapour have not been considered. The analysis has not been carried out at constant volume but at constant pressure. In so far as the experimental conditions conform to constant pressure then the analysis will apply. In any case the potential error of considering the analysis at constant pressure when the experimental conditions may be tending to constant volume is very small, possibly a few percent. M. Bleicher: (1) Could you observe a remarkable change of the results by omitting species which occur only in minor concentrations ~ i0~ atm) such as AsH3, Cl2, Cl, PC13 or AsCl3? (2) Did the polycrystalline material deposited on the holder differ in its composition x from the monocrystalline layer? (3) In what direction does a temperature variation of the substrate shift the composition x and how strong is the influence of this temperature variation?
J.B. Mullin, D. Ti. Hunle, Epitaxy of mixed III- V compounds
191
Reply:
(1) These species will not have a significant effect on the equilibrium situation since they are present in very low concentrations (at equilibrium). (2) We have not studied the experimental composition of the deposits. Nagai et al. (Jap. J. AppI. Phys. 10 (1971)1331) as noted in the paper found the same composition of In( 1 _x)GaxAs in deposits formed on differently orientated substrates and various surfaces in the same growth run. (3) The temperature-dependence of x has not been examined. One would probably expect x to increase with temperature with all other conditions kept constant.(assuming x refers to the mole fraction of the pseudo component having the smaller absolute value of ~~H°295). We have no quantitative results for x versus Tat the moment.
EPITAXY OF MIXED Ill-V COMPOUNDS J.B. MULLIN and D.T.J. HURLE Royal Radar Establishment, St. Andrews Road, Malvern, Worcs., England
A general technique (D.T.J. Hurle and J.B. Mullin, J. Phys. Chem. Solids (Supplement Proceedings ICCG, Boston 1966) (1967) 241) fnr predicting the conditions of thermodynamic equihbrium in a solid/gaseous system has been applied to the systems In—As—-P—-Cl—Fl, Ga—As—-P—Cl—Fl, Ga—In—As—Cl—H and Ga—In—P-Cl—H. The solidus curves for the mixed ternaries InAsu x)Px and GaXInu_X)As are computed as functions of the respective vapour parameters P/(As + P) and Ga/(Ga + In) where the chemical symbols represent the total molecular concentrations of the respective group V or group III bearing species in the vapour. The calculated relationships have been compared with equivalent experimentally-measured relationships and very good agreement has been obtained using a self-consistent set of thermodynamic data. Some significant changes in the thermochemical data are discussed. The theory takes account of the mixed dimers and tetramers of arsenic and phosphorus. The agreement between theory and experiment is also discussed in relationship to the relevance of equilibrium theory since growth of practical interest often occurs under conditions of kinetic control.
1. Introduction In an earlier paper [11 a general technique was published for predicting the conditions of thermodynamic equilibrium in a solid-gaseous system. The technique was applied specifically to the case of the Ga : As : Cl: H system where the solid was assumed to be stoichiometric and have a constant unit activity. The possibility of the nucleation or coexistence of an additional Ga-rich phase was ignored. The application of the technique to predict liquid formation in the above system or in the mixed ternaries is possible in principle. But, the main limitation of such an analysis would lie in our inadequate knowledge of the atomic interaction constants in the liquid. Experimentally, the major interest in vapour deposition concerns only the single solid phase region. In the present work the general technique which was used for the Ga : As : Cl : H system is extended to allow predictions of the equilibrium solidus and vapour compositions for mixed Ill-V systems. The greatest source of uncertainty in predicting the solidus composition is the accuracy of the thermochemical data used. Ideally one needs to know the enthalpies and entropies to better than -~ k cal per mole, i.e. a higher accuracy than has been attained in many cases. Accurate values for the principal species such as the Ill-V compounds and ternaries (see section 2.3) are of course particularly important. However, it has been possible to select values of the thermochemical constants which form a self-consistent set of values. Thus the 176
J.B. Mullin, D.T.J. Hurle, Epit~xyof mixed 111-V compounds
177
fact that the same constants can be used to closely predict the experimentallydetermined solidus for all the systems InAs(l_X)Px, GaAs(l_x)Px, Gaxln(l_x)As and Gaxln(l_x)P provides an internal check on the reliability of the selected data.
2. Properties of the system 2.1. Chemical species A knowledge of the presence and properties of all major molecular species is an essential requirement in any thermodynamic analysis. In the case of the mixed Ill-V compounds there is general accord on the species present in chloride or halide systems as a result of numerous epitaxial studies and mass spectrometric investigations [2, 3]. In one of the most recent investigations Ban [3] has shown that in mixed arseno-phosphide systems all the combinations of arsenic and phosphorus occur as dimers and tetramers. Thus he identified and measured the relative proportions of As2, P2, As4, P4, AsP3, As2P2, As3P in a simulated GaAs(l_x)Px transport system. Also undecomposed AsH3 and PH3 were found in the products of the mixed hydride system. Under certain conditions it was as much as 10% in the case of the more stable 4. PH3, it should noted that the flow rate had the In but the same studybethe presence of GaC1 high value of 1.2 L. min 3 was specifically sought but not found. Theoretically one would not expect it to be a major component in systems using hydrogen as a carrier gas when the temperature is around l000°Kor above. Under similar conditions the role of GaCl2 [4] would be insignificant. 2.2. Thermochemical data The thermodynamic data used in this analysis is listed in table 1. A detailed discussion of this will be given elsewhere [5], but it is pertinent to note here the significant changes to the values used in the earlier paper [1]. The most important change is the value for the enthalpy for the reaction As4(V) 2As2(V). The quoted literature value for the enthalpy is subject to considerable fluctuations often by as much as 10 kcal per mole. A basic source of error in the mass spectrometric determinations of the As2lAs4 equilibrium has recently been reported by Arthur [6]. He found that As2 molecules could recombine on metal surfaces in the filament chamber giving rise to spurious measurements of the As2/As4 ratio. Using a suitably cooled chamber which prevented molecules desorbing from the walls he obtained a value of 62.5 kcal for the above reaction. As a result of this work it has been possible to recalculate the values of z~H~98 for InAs and GaAs. Since the authors’ earlier publication the value of ~H~98 for AsH3 has been revised very markedly from 41.0 kcal mole~to 15.88 kcal mole~ [7]. This change
_~
caldeg mole~
kcal mole
Molecule
~
78.17
61.80
3
AsCl
60.3
16.7
mCI
~-----
15.34
20.7
GaAs
57.2
--48.45
2
As
83.8
89.4
mCI3
57.4
19.1
GaC]
~-
AsP
52.108
—34.5
P2
75
—34.4
As4
(73.0)
(—29.3)
As3P
(70.9)
(--24.2)
As2P2
79.7
107
GaCI3
31.208
0
H2
53.288
0
Cl2
39.457
—29.082
Cl
(68.9)
(—19.2)
AsP3
__________________
44.646
22.062
HO
---------------------_____________________________
(54.6)
(—41.5)
__________________
11.96
27.4
GaP
—_________________
74.49
68.6
Pd3
14.3
21.2
15.8
18.1
lnP
InAs
_____________
9~eg~ mole~ c1
kcal mole
Molecule
Table 1 Thermodynamic data used in computational analysis AsIl3
PH3
66.89
50.22
__________
53.22
—14.08 --15.88 ---1.3
P4
~
J.B. Mullin, D.T.J. Hurle, Epitaxy of mixed 111-V compounds
179
is not important in calculations where complete equilibrium is involved; AsH3 is generally present in relatively insignificant concentrations. However, in certain special cases where there are rate controlling factors in the decomposition of AsH3 commensurate with the deposition period, the thermochemical properties of the AsH3 become important and must be taken into account to explain the vapour— solidus relationship. An additional problem in the mixed Ill-V compounds, which is absent in the pure binaries, is the presence of the mixed arseno-phosphides mentioned earlier. They have been a subject of mass spectrographic investigations both by Gutbier [21and by Ban [3] in connection with dissociation and pseudo-deposition studies on GaAs(l_x)Px and InAs056P044 respectively. In these studies dimer recombination in the source of the mass spectrometer as reported by Arthur [6] and noted earlier could have effected the measured relative abundances of the species. No attempt has been made therefore to interpret thermodynamic properties from their data. Instead, the thermochemical properties of the mixed compounds have been assessed by taking a linear interpolation of the known equivalent properties of the related monocomponent tetramers As4, P4 and dimers As2, P2. This assessment is consistent with Gutbier’s results. Thus he calculated the dissociation energies of the mixed dimers and tetramers using a linear interpolation of the mono-component species and found good agreement with the experimentally-determined dissociation energies. One further piece of basic data is required in order to predict the solidus composition of the vapour grown layers. This data is the heat of mixing of the ternary compounds. Fortunately, the liquidus-solidus equilibria along the pseudo-binary section of the ternary phase diagrams has been experimentally determined and this enables an estimate to be made of the heats of mixing. We have assumed that the liquid and solid phases form regular solutions and that the standard heat of mixing /~Hmin phase i can be written as: L~JI~ =~21X1(1—Xi),
(1)
where X, is the atom fraction of one of the variable component elements and (1 X1) is the atom fraction of the other; ~ are the atomic interaction parameters. 2~were used as selection parameters to obtain the best fit The values for ~L and & solidus and liquidus curves of the pseudo-binary phase of the theoretically-derived diagram to the experimental curves. The procedure used to derive the theoretical curves involves equating the chemical potentials p5~)of each pseudo-component (InAs and GaAs) in the two phases, where: ,IL_/JOL+RT1nYLXL (2)
(pf
/1~’=~oS
+RTlnySXS.
(3)
1 80
.J.B. Mullin, D.T.J. Hurle, Epitaxy of mixed 111-V compounds
Using regular solutions theory for y RTln~s=&~is(l ~X~)2.
(4)
The quality of the theoretical fit obtainable can be judged from fig. 1, which is the pseudo-binary section of the GaAs-InAs diagram [8}.The scatter in the experimental solidus data provides the biggest uncertainty, but it is estimated that the values of the interaction parameter obtained are probably accurate to within ±0 2 kcal/mole. 2.3. Accuracy of data
In assessing thermodynamic data it is necessary to know, if only approximately, the effect of the accuracy of the data on the predictions. In the reactions involving many species, such as the mixed ternaries, considerable calculation is required to assess the effect of even just one variation in say the enthalpy of a species. However, an approximate estimate of the accuracy required of thermochemical data can be ascertained by analysing a relatively simple system such as the Ga : As : Cl : H in terms of a single reaction (eq. (5)) 2GaCl+~As4+H2 s~2GaAs+2HCl.
(5)
The main sources of uncertainty derive in this and equivalent Ill-V epitaxial processes principally from inadequate data on the standard enthalpy of formation of the main species present in equilibrium. This would include the binary and ternary Ill-V compounds, the monochlorides and the dimers and tetramers of arsenic and or phosphorus. The effect of errors in the enthalpies in these compounds specifically in connection with eq. (5) may be seen readily in the equilibrium constant K~(eqs. (6) and (7)) K~e~RT
(6)
K’
(7)
~
where L~~G is the standard free energy change for eq. (5) and &AH is the error in the enthalpy of reaction. At l000°Ka 1 kcal mo1e~error (5~H)can lead to a 40% error in K,,. A more useful presentation of the effect of ~ can be seen in fig. 2, where the relationship between Ga/Cl ratio is plotted against temperature for two separate values of ~~1~0298for GaAs differing by 3 kcal. Curves as in fig. 2. can be used for predicting the optimum conditions for epitaxial growth or vapour transport. The 3 kcal difference can cause a maximum error in the deposition curve of’-’lOO°Ca very significant effect. It is evident therefore that one needs to know values to better than 1 kcal rnole~and preferably to better than ~ kcal mole l~
J.B. Mullin, D.T.J. Hurle, Epitdxy of mixed 111-V compounds 1300
I
181
I
T 1°C) ns 200
= ~L~°2
1 2~5K CAL MOLE K CAL MOLE1
-
0
1100
-
£
S
000
-
A A 0 90C
0 InAs
I
0.25
I
05
0.75
1-0 GaAs
Fig. 1. lnAs-GaAs pseudo-binary phase diagram. Thick lines show the theoretical fit to the experimentalliquidus (thin line) and solidus (points). Experimental data taken from [81. 1-0 09
C’S 07 0-6
~o-5
A
B
0-4 03 02 0-I
C700
BOO
I
900 000 TEMPERATURE (°Kl —
1100
1200
Fig. 2. Theoretical variation of the (Ga/Cl) ratio with temperature in the Ga—As—Cl—H system using values of AH° 298for GaAs of A) — 17.7 and B) — 20.7 kcal per mole.
182
J.B. Mullin, D.T.J. Hurle, Epitaxy of mixed III- V compounds
3. Calculation of the equilibrium surfaces 3.]. Variables
The phase rule can be readily applied to the case of a closed system in equilibrium e.g. a solid in contact with a gaseous environment. However, if we wish to apply such a model to an open flow epitaxial system, its relevance must be carefully considered since it is known that under certain conditions the growth rate of the compound can be kinetically-controlled. In an open flow system one may conveniently consider three regions; the input region I, the deposition region D and the post-deposition region PD. Normally a non-equilibrium gaseous mixture is admitted into I and this converts towards equilibrium in the region D, so that a near equilibrium mixture flows out through PD. Provided the gas in D rapidly converts to equilibrium the effect of deposition will only change the relative amounts of solid phase in D and one can treat the region D as a pseudo-equilibrium region. However, in considering the variance of the system it is to be noted that the concentrations of the components of the compound do not remain constant. Thus, in the case of InAsO_x)Px, which we will now treat as an example of a ternary system, the partial pressure of As4 in D will vary as a result of transferring lnAs(1X)PX from the solid to the vapour phase; ~As4 cannot be treated therefore as an independent variable. Nevertheless the relative amounts of the solid and gaseous phases must be independent of the equilibrium situation so that the deposition of IOAS(lx)Px involves a conserved parameter. In the equivalent case of GaAs this was identified as (Ga—As)/H a short hand syinbol for a non-dimensional variable (‘~Ga ~As)/~H, where the n’s refer to the concentrations or number densities of the components. In the case of InAs()_x)Px, (ln—As-—P)/H is used as the conserved parameter. (ln—As-—P)/H is a linear combination of the prime independent variables [(l—x) In—As] /H and [x In—P] /H and is a more convenient choice since it is independent of x and permits the latter variable to be treated as an independent parameter. Apart from pressure, P and temperature, Ta further independent variable will be Cl/H, since the amount of Cl and H remains constant in the gas phase if the relative amounts of the solid and gas phase are changed. The dependent variables are selected in order to characterise the deposition process. Thus both As/H and P/H are necessary in order to determine the. gaseous parameter P/(P + As). 3.2. Variance
The system (In—As—P—Cl—-H) has five components, a gaseous phase and a single solid phase of variable composition which is characterised by the parameter x, the mole fraction of InP in the compound InAs(l x)Px. In order to determine the dependence of the equilibrium one can relate the dependent variables As/H and P/H
J.B. Mullin, D.T.J. Hurle, Epitdxy of mixed 1II-Vcompounds
183
in terms of the five independent variables, P, T, Cl/H, (In—As—P)/H, and x. In doing so one considers the deposition of the InAs and InP as separate species which combine to form a solid solution in which the activities of these species in the InAs(lx)Px are less than unity. We can consider their activity coefficients to be respectively 7i and ~ 3.3. Procedure
The equilibrium conditions may therefore be represented by the equations In—As—P fl(P,T,x,~H
Cl As ,-~,-~-)=0
and In—As—P ~Cl P
~
The variables of interest in the system are the partial pressures of the eighteen vapour species. Following the general procedure [1], the independent variables P,T,x,
In—As—P CI H ‘H
and the dependent variables As/H, P/H can be formulated in terms of the partial pressures of the chemical species. Thus: ‘~InCl+ ~InCl
=
1~HCl+ ~Cl 3 +
+PPC13
+P
As4
2 + ~H2 + ~A~l
+PP4 +PAs2 +PP2 +PCl +PPH3 +PAsH3 +PAsP +PAs2P2
+PAP+PAsP
(8)
~InCl+
~ ~h~Cl3 + 2 ~Cl2+ ~ ~AsCl3 + ~Cl 2P+ ~HCI 3Ppfl+3PAH PHC1+ 11+
Cl]
—[lifT-
[In—As—P][~~InCl+ ~InCl H +
—
—
—
~AsCl3
—
2 4P~4 P HC1 +2P H2 +3PP1-I3 +3P AsH3 4— ~AsCl3
—
3AsH 2~AsP— 4’~As 41~As 3PPH 2p2 3PAsH ‘ PHCI+2PH 3 — — 3p 2 + 3 + 3
4PA [As] [H]
2~As
4~As 3
+
+2PA
—
—
—
~PCI3
—
2P~1
4~ASP 1 3
(10)
+PA~ +PASP+2PAP +3PAS 3P+PAsP (11) 2PH+3PpH+3PAH P~l+
184
.J.B. Mu/un, D.T.J. Hurle, Epitaxy ofmixed 111-V compounds
[P]
T1’lT
~PCl
3
+4PP4 +2Pp+Ppfl+PAsP+2PAP+PAP+3P 3
3
3~ASH
~PH
~HCi~~I-I2~
=
AsP
3
3 +
(12)
—.
The relationships between the partial pressures are given by: —l
lnCl3
InCl
H2+C12
Cl-,
+
s~2HCl
k6
=
k
2-P
3 Cl2 +-~As4
k8
2PC13
3 Cl2
k
+~ P4
=
2 As2
k 10
=
Cl
pCl23
-
pAs 2 pA~il3 —2
(15)
p
.
p
(16)
~
As4
1-P
P 1-ICI
2AsC13
~
3 Cl2
~.
As22
--2 PCI3
P As4 ~
-
2P2
2p ~ k 11 =PP2 P4
Cl2
~2Cl
k
=P
p
~.
P4
P4
12
(13) (14)
~InC1 ~C12 ~InCl,
(17) (18) (19)
2-P1~Cm —~ ~Cl 2 2
‘3C1
~ 2
-2
As
(20)
2lnCl+~As4s~2InAs+Cl2
k13
2InCl+~P4 s~2lnP+Cl2
k14y~(x)
3 H2
+
P2
2 PH3
k 15
=
pPH32 p P3—1 ~~2 —3
(22)
3 H2
+
As2
2 AsH3
k 16
=
pAsH32
(23)
2AsP
k 17
=
pAsP 2
2 AsP
As2 P2
k18
=
‘~As2P
AsP + As2
As3P
=
~As,P P
As2
+
P2
AsP+P2
AsP3
y~(l—x)
4 mCI
2PCl .p-~ P p
2 .
-2
.
-
.
2
-
‘
—~ -
As2
(21)
InCl
P H2
—~
P As2 ~ P P2 1
(24)
pAsP —2
(25)
-
—1. P —I As AsP
k2oPAsP~P
AsP
1
-P
—1 P2
(26) (27)
where the ks’s are given by the formulae k~=_~i/~~T
(28)
J.B. Mu/un, D.T.J. Hurle, Epitaxy of mixed 111-V compounds
185
The ~Gt’sare given by temperature dependent functions of the enthalpy entropy and specific heat changes for the i reactions: T
~G~=L~H98+f
T~C
~c~dT_Tzxs;98_Tf
dT.
—~
298
(29)
298
The procedure used for solving these equations involves setting values for the independent parameters and then with the aid of approximate values for the partial pressures of the vapour species, using an iterative computer technique to obtain the accurate partial pressures. Thus for a fixed P, T, Cl/H and (In—As—P)/H one can obtain a plot of x against P/(P + As).
4. Comparison of results The theoretical plots of the vapour parameters P/(P + As) and Ga/(Ga + In) against x for the respective ternaries InAs(l x)Px and Gaxln(l_x)As are shown in figs. 3 and 4. The full lines have been calculated using the procedure outlined in section 3. The points are experimentally-determined values. In the case of IC
I
I
I
.
In As11_51P5 0-75
(J.J.TIETJEN et ol I
—
-
S
x0•5-
.
-
S
025
-
-
. S
0
0.25
0-5
0-75
0
MOLE RATIO PH3/(PH3+AsH3)
Fig. 3. Comparison of the theoretical dependence — full line — of the mole fraction of InP in 3, IflAs(l_x)Pxas a function of the vapour parameter P/(P + As) with the equivalent experimental data points taken (ln—As—P)/H = —1.0 fromX [91. 10~. Theoretical parametersPl atm, T~1000°K, C1/H2.0 X i0
186
J.B. Mu//in, D.T.J. Hur/e, Epitaxy of mixed 111-V compounds c I
I
As I R.W CONRAD et oil 0-75
.
-
-
$
x 05-
•
-
. 0-25
-4•1
-
S
0-25
0-5
Go FLOW I
0.175
0
Ga FLOW + In FLOW I
Fig. 4. Comparison of the theoretical dependence -- full line — with the mole fraction of GaAs in GaxIn 0 _x)’~~ as a function of the vapour parameter Ga/(Ga + In) with the equivalent experimental data2,(In — points 1111. Theoretical parameters, P = 1 atns, T = 1023°K, + Ga——taken As)/Hfrom = 5 X i0’. Cl/H 1.0 X 10
lflA5U_x)Px these points were taken from the paper of Tietjen, Maruska and Clough [9]. They deposited epitaxial layers of the ternary compound on InAs in the temperature range 675 725°C.The agreement between theory and experiment is well within the limits of experimental error. The shape of the theoretical curve shows a slight inflexion; it differs in this respect to the relationship drawn through the points by Tietjen et al. The inflexion is probably caused by the role of dimers and tetramers in the deposition reaction. Allen and Mehl [10] have carried out a similar experimental study to that of Tietjen et al. They also reacted AsH 3 and PH3 gaseous mixtures with InCI depositing the InAsU_X)PX in the temperature range 630 750°C.However the deposition was carried out on GaAs substrates. Their results closely parallel those of Tietjen et al., the experimental curve being very slightly to the right of the currently-calculated theoretical curve. The variables temperature and chlorine to hydrogen ratio will of course both effect the shape of the curve, and the fact that the former was not held constant throughout the range of investigation from x 0 to x 1 could well account for the slight divergence of the curves. However, from the theoretical prediction viewpoint the agreement between theory and experiment is remarkably good. —
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The result for GaxIn(l_x)As a mixed group III ternary is shown in fig. 4. Again, the full line is theoretical. It represents the variation of the mole fraction of GaAs in the solid as a function of the Ga mole fraction of the group III bearing species in the vapour. The experimental points are replotted from Conrad et al. [11]. They transported HCI over separate sources of Ga and In and reacted the chlorides of these elements with arsenic vapour, the Gaxln(l_x)As being deposited at 745 750°Con GaAs substrates. The agreement between theory and experiment is good. The preferential deposition of GaAs is particularly marked. In an earlier study by Minden [121the same compound was deposited from the gaseous mixture resulting from flowing H2 and HC1 firstly over a boat of solid arsenic and sub—
sequently over a boat of liquid Ga/In. His results are not strictly comparable with the present theory since he plots the mole percentage of GaAs in the deposit as a function of mole percentage Ga in the source. If the source was converted to a solid of average composition equivalent to that of the liquid then the pick up of Ga and In would be in proportion to the initial Ga/In ratio in the liquid. In fact one could infer reasonable agreement with Minden’s curve. But, since both the liquid and segregated solid in the source region must play a part in the process one is uncertain as to the applicability of the present theory. Enstrom et al. [13] have also investigated the deposition of Gaxln(lx)As using arsine and separate Ga and In sources. Their results have been checked by plotting a curve similar to fig. 4. The points fit well and show good agreement with theory the maximum deviation being of the order + 0.1 in x in the region of 0.2—0.3 for the vapour parameter Ga/(Ga + In). The results are again not strictly comparable to the theoretical prediction since their Cl/H values varied from a factor of 6 less up to the currently-used value of 1.0 X 10—2. Nagai et a). [14] have recently made a theoretical and experimental study of the Ga—In—As—Cl—H system. They have not however explicitly deduced the relationship between the vapour parameter Ga/(Ga + In) and the mole fraction of GaAs in the solid compound Gaxln(l_x)As. Their results are calculated for a value of Cl/H of 2.05 X 10—2. This is twice the value which is relevant to Conrad et al.’s study and the present authors’ computation. One can deduce a composition relationship from their results similar to those investigated here but it does not give good agreement with Conrad et al.’s experimental results. The comparison between their theory and Conrad et al.’s results however may not be strictly valid since the equilibria could be quite sensitive to the value of the parameter Cl/H.
5. Discussion In addition to the currently-discussed systems the P/(P + As) versus x relationship for GaAs(l_x)Px and the Ga/(Ga + In) versusx relationship for Gaxln(l_x)P have also been completed. Very good agreement has been obtained between the theoretical predictions and published experimental work. In achieving this agreement
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a preferential selection was made for certain values of ~H~98 notably for GaP and InP. The justification for this was that the same set of values successfully predicted the vapour solidus curves for all four systems InAs(l x)Px, GaAs(l_X)PX, In(l_x)GaxAs and In(l_x)GaxP. The derivation and existence of a self-consistent set of values provides in itself additional evidence on the reliability of the data. The justification for the use of equilibrium theory is that it can predict experimental results as in the present paper. However, one can criticise the use of equilibrium theory in that it does not predict or explain, for example, the experimentally-determined temperature-dependence in growth rate found in GaAs [15, 16] and GaAs(lx)Px [17]. Equilibrium theory would normally predict a con~ tinuously increasing growth rate with decreasing temperature using constant input conditions. In the case of GaAs, Shaw [15, 16] has found that growth rates increase with decreasing temperature to a maximum at ~780°— ~720°C depending on the exact As4 or GaC1 concentration in the system and then subsequently fall with further decrease in temperature. A similar behaviour has been found in GaAs(l_x)Px by Ban et a). [17]. Shaw explained the reduction in growth rate at temperatures below those giving a peak growth rate as the consequence of a heterogeneous kinetically-controlled surface reaction which had an activation energy of 49 kcal per mole. It is evident then that in GaAs, GaAs(l_x)Px and probably other 1lI-V’s, the optimum conditions for compound deposition which are currently used occur in a kinetically-controlled growth regime. In effect equilibrium theory is predicting the consequences of non-equilibrium growth. Qualitatively one may appreciate that this is a consequence of growth behaviour involving atom incorporation which is dominated by bulk equilibrium energy considerations but that the velocity is dominated by surface phenomena involving a rate transfer mechanism. Equally in the case of melt and solution growth of mixed Ill-V’s there is evidence that the solidus composition is representative of equilibrium thus enabling one, as has been done here, to construct pseudo-binary phase diagrams. Further evidence that the incorporation of the mixed group III’s or group V’s in the ternaries is controlled by bulk properties can be inferred from the experimental observations of Nagai et al. [14]. They found that the composition of Gaxln(lx)As was independent of the chemical nature of the substrate surface e.g. quartz, GaAs, InAs etc. Of course once nucleation occurs growth continues on GaxIn(l_x)As of some composition. However, differently orientated substrates also produced Gaxln(l_x)As deposits of the same composition. In conclusion it is clear that equilibrium theory can predict important experimental information and that it should help in elucidating further the mechanism of epitaxial growth. Additionally it should give greater impetus to establishing more accurate thermochemical data. Acknowledgements The authors gratefully acknowledge useful discussions with their colleagues in
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particular with the late Dr. B.D. Joyce. They also appreciate the skilful help of Mr. S. Benn for computing the results shown in fig. 2. Contributed by permission of the Director RRE. Copyright controlled HBMSO.
References [1] D.T.J. Hurle and J.B. Mullin, I. Phys. Chem. Solids — Supplement, International Conference on Crystal Growth, Boston 1966 (1967) 241. [21 H. Gutbier, Z. Naturforsch. 16a, no. 11(1961)268. [31 V.S. Ban, I. Electrochem. Soc. 118 (1971) 1473. [41 A.W. Laubengayer and F.B. Schirmer, I. Am. Chem. Soc. 62 (1940) 1578. [5] D.T.J. Hurle and J.B. Mullin, to be published. [6] J.R. Arthur, I. Phys. Chem. Solids 28 (1967) 2257. [7] D.D. Wagman, W.H. Evans, V.B. Parker, I. Halow, S.M. Bailey and R.H. Schumm, National Bureau of Standards (USA) Technical Note 270-3 (1968). [81 J. Steininger, J. Appl. Phys., 41, (1970) 2713. [9] 1.1. Tietjen, H.P. Maruska and R.B. Clough, I. Electrochem. Soc. 116 (1969) 492. [10] H.A. Allen and E.W. Mehal, I. Electrochem. Soc. 117 (1970) 1081. [111 R.W. Conrad, P.L. Hoyt and D.D. Martin, I. Electrochem. Soc. 114 (1967) 164. [121 H.T. Minden, I. Electrochem. Soc. 112 (1965) 300. [131 RE. Enstrom, D. Richman, M.S. Abrahams, J.R. Appert, D.G. Fisher, A.H. Sommer and B.F. Williams, in: Proceedings Internationa/ Symposium on Ga//ium Arsenide and re/ated compounds, Aachen (]970)(lnstitute of Physics and the Physical Society, London) 30. [14]H. Nagai, T. Shibata and H. Okamoto, lap. J. Appl. Phys. 10 (1971) 1337. [151 D.W. Shaw, I. Electrochem. Soc. 115 (1968) 405. [16] D.W. Shaw, I. Electrochem. Soc. 117 (1970) 683. [171 VS. Ban, HF. Gossenberger and J.J. Tietjen, I. Appl. Phys. 43 (1972) 2471.
Discussion F. Williams: You have shown important relations between the vapor and the average composition at the growing surface, using equilibrium thermodynamics. My question concerns subsequent processes which may occur in the solid leading to inhomogeneities, graded and without phase boundaries. This is relevant to a remark you made during the panel discussion on small gap semiconductor devices. Specifically, I am interested in whether these systems are expected to exhibit spinoidal separation and whether there is experimental evidence for its occurrence in these ternary systems. If the Gibbs free energy versus composition has a spinoid (convex maximum) at the temperature of preparation, then the system will be stable in favor of graded inhomogeneities and the kinetics then may lead to globular graded inhomogeneities on a scale of the order of a few hundred ângstroms (see works of J. Cahn). We have considered the effects on electronic and optical properties for such graded inhomogeneities, relevant to amorphous semiconductors (see Inglis and Williams, Phys. Rev. Letters (1970), 1. Non-Cryst. Sol. (1971); Martens and Williams, Warsaw Semiconductor Conf. (1971)). Do you have experimental evidence for or against spinoidal separation in the ternaries investigated? The evidence could be : (1) an Urbach tail in optical absorption due to the effective microfields of the inhomogeneities, (2) a temperature-dependent mobility arising from interglobule electronic transport, (3) annealing effects, (4) dependence of the electronic properties on the substrate temperature, and (5) actual phase separation during the final stages of spinoidal decomposition.
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Reply:I have no evidence for spinoidal separation in the ternary systems discussed. This was the reason I asked a similar question of CALAWA. One could, however, expect that spinoidal separation would be thermodynamically feasible in the case of solid solutions where the pseudobinary interaction constant was large, for example in the Ga/In compounds. The condition for spinoidal separation would not necessarily occur at the growth temperature but at some temperature below this. Clearly one could take a crystal rapidly through the critical temperature T~for spinoidal separation into a region of metastability. However, subsequent fabrication techniques in the region below T~,but where diffusion is significant, could bring about separation of new sohd phase. A.T. Vink: (1) The composition curve for Inq x)GaxP deviates rather drastically from the others shown. This clearly tends to make the material technologically a difficult one. Can this behaviour of the curve be simply explained? (2) Can these calculations be easily extended to quaternaries like the Ga 0 _x)lnxAsyPo —y) system mentioned here by Onton? (3) Can the theory be applied to doping of the Ill-V compounds, e.g. the isoelectronic centre N or donors like S, Sc, Te in GaP? For these donors it is known that the incorporation is not an equilibrium process and that an “orientation effect” is present for incorporation: when growing on (111)-Ga or (111)-P faces different doping levels are found under the same conditions. Are such effects within the scope of such a theory?
Reply: (1) The “difficulty” in incorporating Ga into In0 _x)GaxP is a fundamental one associated with the chemistry of Ga in lnP. One can identify the difficulty in the pseudo-binary solid/ hquid phase diagram where the interaction constants between the InP and GaP in the liquid and solid are large. The interaction constants are small in the arsenide-phosphide systems and it is “equally” easy to incorporate phosporus or arsenic into the In or Ga ternary. (2) In principle it would be possible to apply the analysis to the quaternaries but it would be necessary to know the thermochemical properties of the quaternary compound. (3) Again, in connection with your third question it should be possible to apply the analysis to the incorporation of impurities in these compounds. However, in those specific cases where one has a significant orientation effect such as the facet effect (B.D. Joyce and J.B. Mullin, Solid State Commun. (1969)) the theory would not predict quantitatively the impurity incorporation on or close to the low index planes. Away from the low index planes there is a greater probabihty of equilibrium incorporation. H. Signiund: You are dealing with an open flow system; this means that the pressure is constant, but also that some changes in the volume of the reaction gases may occur. Could you comment about this point especially for what concerns computing growth rates? Reply: The theory which has been developed applies specifically to the equilibrium between a ternary and a gas phase immediately adjacent to the surface of the ternary. Transport effects in the vapour have not been considered. The analysis has not been carried out at constant volume but at constant pressure. In so far as the experimental conditions conform to constant pressure then the analysis will apply. In any case the potential error of considering the analysis at constant pressure when the experimental conditions may be tending to constant volume is very small, possibly a few percent. M. Bleicher: (1) Could you observe a remarkable change of the results by omitting species which occur only in minor concentrations ~ i0~ atm) such as AsH3, Cl2, Cl, PC13 or AsCl3? (2) Did the polycrystalline material deposited on the holder differ in its composition x from the monocrystalline layer? (3) In what direction does a temperature variation of the substrate shift the composition x and how strong is the influence of this temperature variation?
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Reply:
(1) These species will not have a significant effect on the equilibrium situation since they are present in very low concentrations (at equilibrium). (2) We have not studied the experimental composition of the deposits. Nagai et al. (Jap. J. AppI. Phys. 10 (1971)1331) as noted in the paper found the same composition of In( 1 _x)GaxAs in deposits formed on differently orientated substrates and various surfaces in the same growth run. (3) The temperature-dependence of x has not been examined. One would probably expect x to increase with temperature with all other conditions kept constant.(assuming x refers to the mole fraction of the pseudo component having the smaller absolute value of ~~H°295). We have no quantitative results for x versus Tat the moment.