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Modeling halogen chemical vapor deposition for III–V semiconductor compounds
Journal of Crystal Growth 225 (2001) 50–58
Modeling halogen chemical vapor deposition for III–V semiconductor compounds J. Mimila-Arroyoa,*, J. Dı´ az-Reyesb b
a CINVESTAV-IPN, Ing. Electrica-SEES, AP. 14-740, Mexico, D.F. C.P. 07000, Mexico Puebla. Acatlan 63, Col. La Paz, Puebla, Pue. Mexico, CICATA-IPN, Seccion C.P. 72160, Mexico
Received 2 September 2000; accepted 21 February 2001 Communicated by D.W. Shaw
Abstract Halogen chemical vapor deposition is a well-developed technique widely used for growing semiconductors, in which the best growing conditions are obtained on an empirical way. From the theoretical point of view, most of the time the developed models are too complex and not accurate enough to correctly adjust the experimental results. Here, we present a general model to explain the epitaxial growth kinetics of III–V semiconductor materials by halogen chemical vapor deposition. The model considers one reversible chemical reaction between the transporting gas and the III element at its reservoir, and the same reaction at the substrate surface. This means that the reaction producing the volatile compounds that transport the III element from its reservoir to the substrate is active at the substrate surface as well. However, the model considers that the III element might have a different chemical activity at each one of those surfaces. The proposed model correctly explains experimental results reported in the literature on different III–V materials, by different laboratories, over decades. # 2001 Published by Elsevier Science B.V. Keywords: A1. Growth models; A3. Chloride vapor phase epitaxy; B2. Semiconducting III–V materials
1. Introduction The technique of chemical vapor deposition (CVD) using a halogen as transporting gas is very well known and widely used in semiconductors research and industry. This method, with excellent experimental results, has permitted a great development of the physics of semiconductor devices and their industrial production. However, in most of the cases of practical interest the growth control *Corresponding author. E-mail address: [email protected] (J. Mimila-Arroyo).
has been attained empirically. This is because in spite of the great achievement of the CVD halogen process, the different proposed theoretical models do not always correctly explain growth rate experimental data as function of growth conditions. Theoretical models had become too complex, in their effort to fit experimental data, they attempt to consider as many physical processes as possible. They take into account mass transport in the gas phase from the main gas flux to the growing surface, the precursors adsorption phenomena, the density of free and blocked lattice sites, the chemical activity of the species involved in the growth, the chemical reactions, the atomic
0022-0248/01/$ - see front matter # 2001 Published by Elsevier Science B.V. PII: S 0 0 2 2 - 0 2 4 8 ( 0 1 ) 0 1 0 3 2 - 6
J. Mimila-Arroyo, J. Dı´az-Reyes / Journal of Crystal Growth 225 (2001) 50–58
surface diffusion and the final lattice incorporation. Complete theoretical models might need about a hundred equations with countless approximations, and a high number of adjusting parameters that after all, fitting to experimental results is poor [1–3]. Here we propose a model that uses just a reversible reaction between the transporting gas and the III element that occurs at both surfaces; the III source reservoir surface and the substrate growing surface. However, the model considers that the III element might have different chemical activities at each one of those surfaces.
2. Theory Basically, growing a III–V semiconductor by chemical vapor deposition, as by any other vapor phase technique, consists of the ordered incorporation on the growing crystal surface, of III and V columns atoms contained in the gas phase that constitutes the growing atmosphere. Then, the first point to consider is the way in which the III and V elements are introduced in the atmosphere that is, or will be, in contact with the substrate growing surface. Generally, the V column element is introduced in the gas phase as an elemental gas as V2 or V4 or a gaseous compound containing it. The III column element is brought onto the growing surface as a gaseous compound synthesized just besides the substrate through a reversible reaction between the III element and the transporting gas. Both compounds are transported to the substrate place by a carrier gas, usually hydrogen. The volatile compound containing the III element is synthesized by a chemical reaction between the transporting gas and elemental III or the III atoms of a solid compound. This solid compound acting as III atom source is the same solid to be grown but without the required physical properties for the layer to be grown. According to the above description, there are two geometrical possibilities for the way in which the gaseous compound containing the V column element is introduced. Let us call case one, when the V column element is introduced before the site where the reservoir of the III element is located,
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and the carrier gas bring them in contact and then, immediately after, with the substrate. We will call case two when the V element is introduced between the site where the volatile compound containing the III element is synthesized and the substrate. In this case, as the carrier gas flows towards the substrate, the V element never gets in contact with the III column element but at the growing surface. It is well known that in case one and using as source elemental III, a crust of the material to be grown is formed on the III element reservoir surface exposed to the V element flow. Actually, is this already synthesized material which is transported onto the substrate through the corresponding reactions. We will see below, that both cases can be theoretically treated in a similar way. The model that we present here considers just the net rates of the chemical reaction that produces the volatile compound containing the III column element, from here on M, at its reservoir and at the substrate surface, which are at the temperatures T and y, respectively. Then, making the assumption that in steady state both net rates are equal, a simple theoretical law for the growth rate is obtained. Let us consider that M, the V column element to be transported onto the substrate, is at its reservoir at a temperature T, that the substrate surface is at a temperature y, and that the transporting gas is present at a pressure ph . The reaction producing the volatile compound containing the III column element at its reservoir surface can be schematized as M þ hðgÞ $ cðgÞ;
ð1Þ
where h is the transporting gas and c is the volatile compound, formed by the reaction between it and M. Then, the volatile compound c is swept by the carrier gas onto the substrate surface. As the substrate temperature is lower than the source one, the rate of Eq. (1) and the carrier gas impose a c pressure on the substrate surface higher than its equilibrium value. Under this condition the reverse sense of the same reaction becomes dominant, incorporating M onto the substrate. The V element is incorporated from the gas that contains it, through its own reaction.
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The net rate VðTÞ of reaction (1) at the III source surface at temperature T, is given by the difference between the rates towards the right Vr ðTÞ, and the left Vl ðTÞ, i.e. V ðT Þ ¼ Vr ðT Þ Vl ðT Þ
ð2Þ
rates that are given by Vr ðTÞ ¼ af kr ðTÞFðphf Þ
ð3aÞ
and Vl ðTÞ ¼ kl ðTÞcðpcs Þ;
ð3bÞ
where af is the chemical activity coefficient of M at the source surface, kr;l ðTÞð¼ xr;l expðEr;l =kTÞÞ are the kinetic constants of the reaction towards the right and the left, respectively, xr,l are the preexponential terms, Er;l are the activation energies of the reaction towards the right and the left, respectively, and k is the Boltzman’s constant. F is a function of the transporting gas pressure ph, C is a function of the pressure of the volatile compound c and T is the temperature at which the reactions take place. The kinetic constants are related through the reaction equilibrium constant, i.e. KðTÞ ¼ kr ðTÞ=kl ðTÞ ¼ Z exp ðEr El Þ=kT, where Z ¼ xr =xl is the pre-exponential term of the equilibrium constant. Equivalent relations can be written for the reaction on the substrate surface V ðyÞ ¼ Vl ðyÞ Vr ðyÞ ¼ kl ðyÞCðpcs Þ as kr ðyÞFðphs Þ;
ð4Þ
where as , this time, is the chemical activity coefficient of M at the substrate surface, which might be different from af ; phs is the pressure of the transporting gas on the substrate surface. In Eq. (4), Cðpcs Þ is the same function as in Eq. (3b) but evaluated at pcs , the pressure value of the volatile compound at the substrate surface. The order in Eq. (4) is the reverse of that of Eq. (2) because on this surface the growth takes place. The last right hand term of Eq. (4), Eq. (5) below, gives the rate at which the transporting gas removes the III atoms from the growing surface. Vr ðyÞ ¼ as kr ðyÞFðphs Þ:
ð5Þ
Because of the carrier gas flow it can be assumed that phf ¼ phs as well as that pcf ¼ pcs .
Then, making the additional approximation that VðTÞ ¼ VðyÞ and thus, both of them equal to the growth rate VðT; y; ph Þ (we will discuss the validity of such approximations later). Substituting Eqs. (3a) and (3b) in (2), using the above assumptions and getting Cðpcs Þ from there and using it together with the reaction equilibrium constant in (4), it follows that: V ðT; y; ph Þ ¼ l
af eDH=kT as eDH=ky ; eEl =kT þ eEl =ky
ð6Þ
where l ¼ Fðph Þxr and DH ¼ Er El , all other terms have been defined before. The numerator of Eq. (6), is just the difference between the equilibrium constant values of the transporting reaction at both surfaces, in each case modulated by the chemical activity coefficient of M. As seen, from Eq. (6), the growth rate seems to depend only on three experimental parameters that can be externally and independently fixed: T; y and ph . Let us now discuss the two practical cases mentioned before.
3. Discussion For the case presented as one in the first paragraph of the precedent section, it happens that the reactions (3) take place on the same type of material at the source and at the substrate. Thus, it can be assumed af ¼ as ¼ 1. Let us take some arbitrary values for l; El ; DH, a typical value for T and plot Eq. (6) as a function of y. This is shown in Fig. 1 curve (a; T ¼ 9508C), qualitatively, this curve is identical to those very often obtained experimentally and widely reported [1,4–11]. The growth rate as a function of the substrate temperature presents three regions of clearly different growth rate behavior, for low, intermediate and high y values, roughly shown in the same figure. For discussing this curve is necessary to remark that the values of the experimental parameters, T; ph and the pressure of the reactive providing the V element, are constant throughout the curve. As the processes occurring at the source surface are unchanged by changes on the substrate temperature, the rates
J. Mimila-Arroyo, J. Dı´az-Reyes / Journal of Crystal Growth 225 (2001) 50–58
53
Fig. 1. Theoretical growth rate given by Eq. (6) two source temperatures, T1 ¼ 9508C and T2 ¼ 8508C, using some arbitrary values l; Q; DH and the chemical activities of the III element; af ¼ as ¼ 1:0.
Fig. 2. Evolution of the theoretical growth rate given by Eq. (6) for T ¼ 8508C, as a function of the chemical activity of the III element on the substrate; as .
given by Eqs. (3) are also constant throughout the curve. That means that any point on this curve has been grown, as well, under the same pressure of the compound c. Then, according to our proposition the growth rate is established by the reaction net rate at the substrate surface given by Eq. (4). That is to say that the III element incorporation rate is given by Eq. (3b), at y and the rate at which it is removed from the growing layer, is given by Eq. (5). In the y region, that we called low substrate temperature, the rate given by Eq. (5) is almost negligible, and the growth rate is given only by the III element incorporation rate. For the intermediate y range, as the substrate temperature increases both reaction rates; towards the left and the right increase exponentially. However, the rate toward the right increases in a faster way and its contribution in Eq. (4) becomes no negligible although the growth rate continues to increase. At the substrate temperature indicated as ymax, located in the middle of the intermediate y range, the growth rate reaches its maximum. At this substrate temperature, the rapidity at which the rate of the chemical reaction towards the right increases is such that the growth rate stops increasing and start to decrease. For the high y range the rate given by Eq. (5) continues to increase, and in fact in this y region the growth rate is established by the competition between the reaction that produces the III element incorpora-
tion and that which removes it. Further increase of y will stop the growth, when T ¼ y, or even etching can be produced [10]. The same Fig. 1 curve (b) shows the growth rate for a second source temperature, T ¼ 8508C. The form of the curve is the same, it is just shifted to the right and to lower growth rates. It might be convenient to discuss at this point the assumptions made at obtaining Eq. (6). Actually the approximations that we made; VðTÞ ¼ VðyÞ and phf ¼ phs as well as that pcf ¼ pcs are closely related. Experimental data show that VðyÞ might be smaller than VðTÞ, in fact that means that pcs is slightly smaller than pcf . Now, from Figs. 1 and 2 is clear that a pcs value smaller than the assumed one will just lightly shift down the obtained growth rate curve. Then, such assumptions do not have an important consequence on the qualitative growth rate behavior. Moreover, on the approximation concerning the h and c pressures, once again from Fig. 2 curves c and a, we can see that the maximum growth rate when no M is retaken from the substrate surface, is higher than the experimental maximum growth rate for when as 51. That is, as we will see from the experimental results, the experimental case that is the most frequent one. That means that the growth process consumes a small part of the c vapor produced at the source surface and then that its pressure is not strongly different at both surfaces.
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Let us see now what happens when the pressure of the V column element is increased, keeping all other experimental parameters constant. This will produce at the substrate surface level a more rapid coverage of the III element by the V element, which means a reduction of the as value, resulting in a decrease of the rate of the reaction (5). From Eqs. (4) and (5) we see that decreasing the as value should lead at least to an increase in the growth rate. The effect of such a situation is shown in Fig. 2, for different values of as . As seen, for as 51 the expected increase on the growth rate is clearly observed. At the same time the ‘‘low y range’’ widens towards higher substrate temperatures. The intermediate y range is shifted to the left as well as the y point where the growth stops, allowing the growth at substrate temperatures higher than that of the source, situation often experimentally observed [6]. For the case that we have called two, af and as are different, as in the source there is elemental M and in the substrate M is bonded to a V column atom, then it might occur that as 4af , leading to the same situation discussed before through Fig. 2. Then, both cases are actually equivalent, depending on the experimental conditions. Let us introduce a third case that is experimentally used to avoid the deposition of the growing material on the reactor walls. Here, an additional flow of the transporting gas is added to the growth atmosphere. This is done in such a way that it does not get in contact with the III element reservoir, but it gets in contact with the substrate. Actually, by doing this it is just produced an increases of the rate given by Eq. (5) and this can be made equivalent to an increase of as . This situation is also considered in Fig. 2 curve (d) using, just to illustrate, as ¼ 2. Once again the obtained growth rate curve is qualitatively similar to curve (a) but this time has been shifted, as expected, the contrary way, i.e., towards lower growth rates and the substrate temperature at which the growth rate becomes zero is lower than before. It is also interesting to observe that the obtained law for the growth rate can be used to calculate, for a given set of experimental conditions; T; p and pressure of the V element, the maximal theoretical growth rate as well as the growth chemical efficiency. This is
simply done by obtaining the growth rate for as values approaching to zero, and a reasonable high value for the substrate temperature, Fig. 2 curve (c). Under such growth conditions almost no III atom is retaken from the substrate surface, leading to the maximum theoretical growth rate. The ratio between the maximum of the curve fitting the experimental data, for instance curve (b) of the same figure, and the maximum theoretical growth rate obtained for as 51 gives the growth chemical efficiency for those conditions.
4. Results For testing the model we looked in the literature for results obtained under experimental conditions close to those that have been considered in this model. Several authors have published, for most of the III–V compounds and using a halogen as transporting gas, the CVD growth rate as a function of the substrate temperature [1,4–11]. The most abundant results that we found correspond to what we have called case three, then we will apply the model first to these results [4–7]. D.W. Shaw published in 1968 [4] a study of the growth rate of GaAs as a function of the substrate orientation and temperature using HCl as transporting gas, elemental Ga as III element source and As4 as arsenic source. Of great importance in this case, is an additional HCl flow that was not in contact with the Ga reservoir but that was in contact with the substrate. The author clearly states that the III reservoir temperature was at 9008C. Fig. 3, curves (a, b and c), shows Eq. (6) fitting to Shaw data corresponding to substrate orientations (100, 113A and 115). The fit is extremely good for all the substrate temperature ranges reported by the author including the high substrate temperature range so hard to fit by other models. Experimental data are fitted with different activation energies for each substrate orientation. The best fitting parameters are given in Table 1. For other substrate orientations studied by Shaw, the fit using Eq. (6) was equally good although we do not show it because the number of figures would be too high, nevertheless the fitting parameters are given in Table 1 as well. In a later work
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using the same transporting gas, Shaw studied the effect of the growth atmosphere composition on the growth rate [5]. In one part of that study, the partial pressure of the As4 was increased over a wide range, all other parameters kept constant, included the substrate orientation (0 0 1). The result was a systematic increase of the growth rate as the As4 pressure increased. For fitting these experimental data we proceeded on the following way; first we fitted the data obtained with the lowest As4 pressure used in the study. For the fit we used the El and DH values obtained in the precedent fit for the same substrate orientation and then we just found the values for the preexponential factor l and as using, of course, the authors source temperature. In this case, we preferred to use a linear scale rather than the logarithmic one used by Shaw, as in this way the fitting accuracy can be better seen. Fig. 4 shows the fit, once again it is quite good and behave in
the expected way; increasing the As4 pressure, increases As substrate surface coverage reducing the gallium possibility to react again with the transporting gas and be retaken from this surface. This is considered by the model, as discussed before, by a decrease of the as value, which was exactly the result obtained by the fit, adjusting . et al. parameters are given in Table 2. Later, Putz reported results on the growth rate as a function of the substrate temperature and total pressure in the growth system using HCl and (1 0 0) oriented GaAs [6]. Fig. 5 shows the fit using Eq. (6), as the transporting reaction is the same as for the Shaw’s studies, for the fit we used the El and DH values for this orientation found at Shaw’s results fit, other fitting parameters values are given in Table . 2. Much more recently Gruter et al. [7], reported this type of study, the fit of our model to their data is shown in Fig. 5 too. For this case, we proceeded in the same way using the El and DH values
Fig. 3. Fitting to Shaw’s GaAs growth rate data for different substrate orientations, Ref. [4], using Eq. (6) and source temperature given by the author; 9008C.
Fig. 4. Fitting to Shaw’s GaAs growth rate data as a function of As4 pressure in the growth atmosphere, Ref. [5], using Eq. (6) and source temperature given by the author.
Table 1 Best fitting parameters to growth rate data on different GaAs substrate orientations, Ref. [4] and showed in Fig. 3, using Eq. (6) Orientation
100
111A
112B
115
113B
113A
112A
19
1.0 2.5 1.6 2.4
13.2 2.2 2.1 4.5
3.3 2.1 2.2 5.3
7.3 1.9 2.5 4.05
2.7 1.7 2.6 6.6
2.7 1.75 2.5 4.2
1.5 0.9 3.4 8
l (10 mm/min) El (eV) H(eV) as
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Table 2 Best fitting parameters to (1 0 0) GaAs growth rate data of Figs. 4 and 5, Refs. [5,6 and 7] using the Eq. (6), with El ¼ 2:5 eV, and DH ¼ 1:6 eV pAs4 (103 Atm) 19
l (10 mm/min) as
5.88
2.21
1.33
0.73
0.59
. Putz
. Putz
. Gruter
7.7 3.5
6.65 3.9
6.3 4.3
6 4.9
6 5.6
1.3 0.13
5.5 0.13
500 0.28
Fig. 5. Fitting to GaAs growth rate data of Refs. [6–7], using Eq. (6) and source temperature given by the authors and indicated in the figure.
corresponding for the same GaAs orientation used for Shaw’s data, other values of the fitting parameters are also given in Table 2, once again the fit is excellent. The same halogen CVD system has been successfully used to grow InP [1,8–10]. Hales used HCl as transporting gas, elemental In as III element source and PCl3 as phosphorous source [8]. In the same way as in the precedent case of GaAs, PCl3 bypassed the III source. Here Hales studied the behavior of the growth rate for three different values of the source material temperature; 7508C, 7008C and 6508C, as a function of the substrate temperature. Fig. 6, curves (a, b, and c), shows the fit of Eq. (6) to his data, as seen the fit is excellent for the source temperature of 7508C and reasonably good for the other source temperatures. The fitting parameters are given in Table 3. Susa and Yamauchi reported an equivalent study [9], Fig. 6 curve (d), shows the fit with Eq. (6) using the same energy values found in the precedent fit. As seen, the agreement between the experimental
Fig. 6. Fitting to InP growth rate data of Refs. [1,8,9], using Eq. (6) and source temperature given by the authors, also shown in the figure.
Table 3 Best fitting parameters to InP growth rate data, shown in Fig. 6 using the Eq. (6) for InP, with values for El ¼ 1:57 eV, DH ¼ 0:73 eV l ( 1011 mm/min)
as
References
4.8 24.2 20 1.24 85
1.13 1.33 1.3 1.6 1.0
[8] [8] [8] [9] [1]
data and the model is excellent. Fitting parameters are given in Table 3. Much more recently, . Jurgensen et al. published a similar study including a quite complete theoretical model [1]. Our fitting to their data is shown the same Fig. 6 curve (e), the fitting parameters are given in Table 3. More recently Buckley et al. [11], reported similar results on InP too, however, as the authors did not provide the source temperature the fitting of their
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Fig. 7. Fitting to GaAs, GaP, InP and InAs growth rate data of Ref. [10] using Eq. (6) and source temperature given by the authors, 8508C, 9308C, 9308C and 8008C, respectively, for curves (a), (b); (c) and (d).
experimental data was possible only through proposing of a value for the source temperature that results to be quite reasonable. However, because this missing source temperature we do not show here the obtained theoretical fit. For what we have called case 1, the closest situation that we found in the literature was the study made by Mizuno [10] where he reported the growth rate as a function of the substrate temperature for several III–V compounds. In their study the author used polycrystalline GaAs, GaP, InP and InAs as III element source and AsCl3 and PCl3 as V element source. In that study the authors explored the effect of the growth atmosphere composition and substrate temperature. Each material was grown at its particular source
temperature of 8508C, 9508C, 8008C and 7508C, respectively. Fig. 7 curves (a, b, c, and d, respectively) shows the fit obtained using Eq. (6) for the data obtained on those materials. Table 4 gives the parameters values that gave the best fit. It is interesting to remark that for GaAs and GaP the element to be transported is in both cases the gallium and the involved reaction energies result to be the same for both materials as well. This situation repeats again for the case of InP and InAs. Obviously the as values are, as expected, quite close to 1. Using the obtained fitting parameters for all the data here before discussed we found that the growth conditions leading to the highest growth chemical efficiency are for . [6] and Shaw [4] for GaAs(1 1 2)A with a Putz
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Table 4 Best fitting parameters to growth rate data of Fig. 7(a, b, c and d), using the Eq. (6) and values for El and DH already given values for transporting Ga and In using HCl and (1 0 0) substrates GaAs 3
PH2 (10 Atm) l (1010 mm/min) as
0.2 0.013 1.03
GaP 0.6 0.025 1.05
1 0.04 1.06
0.2 0.008 1.09
InP 0.4 0.016 1.07
chemical efficiency 0.6. The lowest is for InP where systematically the chemical efficiency is 0.2.
1 0.013 1.07
0.2 80 2.1
InAs 0.6 135 1.44
1 220 1.3
0.2 8 1.15
0.6 15 1.15
1 25 1.15
Acknowledgements The authors would like to acknowledge the significant contribution from our collaborator Ruben Huerta Cantillo.
5. Conclusions We have proposed a theoretical model to explain the epitaxial growth rate in the halogen chemical vapor deposition system. It assumes that one reversible reaction rules all the process and that the growth rate is given by the net rate of this transporting reaction at the source surface and at substrate surface as well. That means that the reaction that produces the volatile compounds that transport the III element from its reservoir to the substrate is active at the substrate as well. The obtained growth rate law contains just four adjusting parameters. The model explains in a reasonable way experimental data obtained on different III–V compounds grown under quite different thermodynamic conditions. For the same material and using the same transporting gas, systematically the same activation energies of the reactions were found. The model explains data from different laboratories obtained over decades.
References . [1] H. Jurgensen, J. Korec, M. Heyen, P. Balk, J. Crystal Growth 66 (1984) 73. [2] K.A. Jones, J. Crystal Growth 60 (1982) 313. [3] D.W. Shaw, in: C.H.L. Goodman (Ed.), Crystal Growth: Theory & Techniques, Plenum Press, London-New York, 1974. [4] D.W. Shaw, J. Electrochem. Soc. 115 (1968) 405. [5] D.W. Shaw, J. Electrochem. Soc. 117 (1970) 683. . . [6] N. Putz, E. Veuhoff, K.H. Bachem, P. Balk, H. Luth, J. Electrochem. Soc. 128 (1981) 2202. . . [7] K. Gruter, M. Deschler, H. Jurgensen, R. Beccard, P. Balk, J. Crystal Growth 94 (1989) 607. [8] M.C. Hales, J. Electron. Mater. 9 (1980) 355. [9] N. Susa, Y. Yamauchi, J. Crystal Growth 51 (1981) 518. [10] O. Mizuno, H. Watanabe, J. Crystal Growth 30 (1975) 240. [11] D.N. Buckley, J.R.C. Filipe, F.R. Lineman, K.W. Wang, K.M. Lee, A.A. Westphal, S.M. Mc Ewan, J. Electrochem. Soc. 139 (1992) 1185.
Modeling halogen chemical vapor deposition for III–V semiconductor compounds J. Mimila-Arroyoa,*, J. Dı´ az-Reyesb b
a CINVESTAV-IPN, Ing. Electrica-SEES, AP. 14-740, Mexico, D.F. C.P. 07000, Mexico Puebla. Acatlan 63, Col. La Paz, Puebla, Pue. Mexico, CICATA-IPN, Seccion C.P. 72160, Mexico
Received 2 September 2000; accepted 21 February 2001 Communicated by D.W. Shaw
Abstract Halogen chemical vapor deposition is a well-developed technique widely used for growing semiconductors, in which the best growing conditions are obtained on an empirical way. From the theoretical point of view, most of the time the developed models are too complex and not accurate enough to correctly adjust the experimental results. Here, we present a general model to explain the epitaxial growth kinetics of III–V semiconductor materials by halogen chemical vapor deposition. The model considers one reversible chemical reaction between the transporting gas and the III element at its reservoir, and the same reaction at the substrate surface. This means that the reaction producing the volatile compounds that transport the III element from its reservoir to the substrate is active at the substrate surface as well. However, the model considers that the III element might have a different chemical activity at each one of those surfaces. The proposed model correctly explains experimental results reported in the literature on different III–V materials, by different laboratories, over decades. # 2001 Published by Elsevier Science B.V. Keywords: A1. Growth models; A3. Chloride vapor phase epitaxy; B2. Semiconducting III–V materials
1. Introduction The technique of chemical vapor deposition (CVD) using a halogen as transporting gas is very well known and widely used in semiconductors research and industry. This method, with excellent experimental results, has permitted a great development of the physics of semiconductor devices and their industrial production. However, in most of the cases of practical interest the growth control *Corresponding author. E-mail address: [email protected] (J. Mimila-Arroyo).
has been attained empirically. This is because in spite of the great achievement of the CVD halogen process, the different proposed theoretical models do not always correctly explain growth rate experimental data as function of growth conditions. Theoretical models had become too complex, in their effort to fit experimental data, they attempt to consider as many physical processes as possible. They take into account mass transport in the gas phase from the main gas flux to the growing surface, the precursors adsorption phenomena, the density of free and blocked lattice sites, the chemical activity of the species involved in the growth, the chemical reactions, the atomic
0022-0248/01/$ - see front matter # 2001 Published by Elsevier Science B.V. PII: S 0 0 2 2 - 0 2 4 8 ( 0 1 ) 0 1 0 3 2 - 6
J. Mimila-Arroyo, J. Dı´az-Reyes / Journal of Crystal Growth 225 (2001) 50–58
surface diffusion and the final lattice incorporation. Complete theoretical models might need about a hundred equations with countless approximations, and a high number of adjusting parameters that after all, fitting to experimental results is poor [1–3]. Here we propose a model that uses just a reversible reaction between the transporting gas and the III element that occurs at both surfaces; the III source reservoir surface and the substrate growing surface. However, the model considers that the III element might have different chemical activities at each one of those surfaces.
2. Theory Basically, growing a III–V semiconductor by chemical vapor deposition, as by any other vapor phase technique, consists of the ordered incorporation on the growing crystal surface, of III and V columns atoms contained in the gas phase that constitutes the growing atmosphere. Then, the first point to consider is the way in which the III and V elements are introduced in the atmosphere that is, or will be, in contact with the substrate growing surface. Generally, the V column element is introduced in the gas phase as an elemental gas as V2 or V4 or a gaseous compound containing it. The III column element is brought onto the growing surface as a gaseous compound synthesized just besides the substrate through a reversible reaction between the III element and the transporting gas. Both compounds are transported to the substrate place by a carrier gas, usually hydrogen. The volatile compound containing the III element is synthesized by a chemical reaction between the transporting gas and elemental III or the III atoms of a solid compound. This solid compound acting as III atom source is the same solid to be grown but without the required physical properties for the layer to be grown. According to the above description, there are two geometrical possibilities for the way in which the gaseous compound containing the V column element is introduced. Let us call case one, when the V column element is introduced before the site where the reservoir of the III element is located,
51
and the carrier gas bring them in contact and then, immediately after, with the substrate. We will call case two when the V element is introduced between the site where the volatile compound containing the III element is synthesized and the substrate. In this case, as the carrier gas flows towards the substrate, the V element never gets in contact with the III column element but at the growing surface. It is well known that in case one and using as source elemental III, a crust of the material to be grown is formed on the III element reservoir surface exposed to the V element flow. Actually, is this already synthesized material which is transported onto the substrate through the corresponding reactions. We will see below, that both cases can be theoretically treated in a similar way. The model that we present here considers just the net rates of the chemical reaction that produces the volatile compound containing the III column element, from here on M, at its reservoir and at the substrate surface, which are at the temperatures T and y, respectively. Then, making the assumption that in steady state both net rates are equal, a simple theoretical law for the growth rate is obtained. Let us consider that M, the V column element to be transported onto the substrate, is at its reservoir at a temperature T, that the substrate surface is at a temperature y, and that the transporting gas is present at a pressure ph . The reaction producing the volatile compound containing the III column element at its reservoir surface can be schematized as M þ hðgÞ $ cðgÞ;
ð1Þ
where h is the transporting gas and c is the volatile compound, formed by the reaction between it and M. Then, the volatile compound c is swept by the carrier gas onto the substrate surface. As the substrate temperature is lower than the source one, the rate of Eq. (1) and the carrier gas impose a c pressure on the substrate surface higher than its equilibrium value. Under this condition the reverse sense of the same reaction becomes dominant, incorporating M onto the substrate. The V element is incorporated from the gas that contains it, through its own reaction.
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The net rate VðTÞ of reaction (1) at the III source surface at temperature T, is given by the difference between the rates towards the right Vr ðTÞ, and the left Vl ðTÞ, i.e. V ðT Þ ¼ Vr ðT Þ Vl ðT Þ
ð2Þ
rates that are given by Vr ðTÞ ¼ af kr ðTÞFðphf Þ
ð3aÞ
and Vl ðTÞ ¼ kl ðTÞcðpcs Þ;
ð3bÞ
where af is the chemical activity coefficient of M at the source surface, kr;l ðTÞð¼ xr;l expðEr;l =kTÞÞ are the kinetic constants of the reaction towards the right and the left, respectively, xr,l are the preexponential terms, Er;l are the activation energies of the reaction towards the right and the left, respectively, and k is the Boltzman’s constant. F is a function of the transporting gas pressure ph, C is a function of the pressure of the volatile compound c and T is the temperature at which the reactions take place. The kinetic constants are related through the reaction equilibrium constant, i.e. KðTÞ ¼ kr ðTÞ=kl ðTÞ ¼ Z exp ðEr El Þ=kT, where Z ¼ xr =xl is the pre-exponential term of the equilibrium constant. Equivalent relations can be written for the reaction on the substrate surface V ðyÞ ¼ Vl ðyÞ Vr ðyÞ ¼ kl ðyÞCðpcs Þ as kr ðyÞFðphs Þ;
ð4Þ
where as , this time, is the chemical activity coefficient of M at the substrate surface, which might be different from af ; phs is the pressure of the transporting gas on the substrate surface. In Eq. (4), Cðpcs Þ is the same function as in Eq. (3b) but evaluated at pcs , the pressure value of the volatile compound at the substrate surface. The order in Eq. (4) is the reverse of that of Eq. (2) because on this surface the growth takes place. The last right hand term of Eq. (4), Eq. (5) below, gives the rate at which the transporting gas removes the III atoms from the growing surface. Vr ðyÞ ¼ as kr ðyÞFðphs Þ:
ð5Þ
Because of the carrier gas flow it can be assumed that phf ¼ phs as well as that pcf ¼ pcs .
Then, making the additional approximation that VðTÞ ¼ VðyÞ and thus, both of them equal to the growth rate VðT; y; ph Þ (we will discuss the validity of such approximations later). Substituting Eqs. (3a) and (3b) in (2), using the above assumptions and getting Cðpcs Þ from there and using it together with the reaction equilibrium constant in (4), it follows that: V ðT; y; ph Þ ¼ l
af eDH=kT as eDH=ky ; eEl =kT þ eEl =ky
ð6Þ
where l ¼ Fðph Þxr and DH ¼ Er El , all other terms have been defined before. The numerator of Eq. (6), is just the difference between the equilibrium constant values of the transporting reaction at both surfaces, in each case modulated by the chemical activity coefficient of M. As seen, from Eq. (6), the growth rate seems to depend only on three experimental parameters that can be externally and independently fixed: T; y and ph . Let us now discuss the two practical cases mentioned before.
3. Discussion For the case presented as one in the first paragraph of the precedent section, it happens that the reactions (3) take place on the same type of material at the source and at the substrate. Thus, it can be assumed af ¼ as ¼ 1. Let us take some arbitrary values for l; El ; DH, a typical value for T and plot Eq. (6) as a function of y. This is shown in Fig. 1 curve (a; T ¼ 9508C), qualitatively, this curve is identical to those very often obtained experimentally and widely reported [1,4–11]. The growth rate as a function of the substrate temperature presents three regions of clearly different growth rate behavior, for low, intermediate and high y values, roughly shown in the same figure. For discussing this curve is necessary to remark that the values of the experimental parameters, T; ph and the pressure of the reactive providing the V element, are constant throughout the curve. As the processes occurring at the source surface are unchanged by changes on the substrate temperature, the rates
J. Mimila-Arroyo, J. Dı´az-Reyes / Journal of Crystal Growth 225 (2001) 50–58
53
Fig. 1. Theoretical growth rate given by Eq. (6) two source temperatures, T1 ¼ 9508C and T2 ¼ 8508C, using some arbitrary values l; Q; DH and the chemical activities of the III element; af ¼ as ¼ 1:0.
Fig. 2. Evolution of the theoretical growth rate given by Eq. (6) for T ¼ 8508C, as a function of the chemical activity of the III element on the substrate; as .
given by Eqs. (3) are also constant throughout the curve. That means that any point on this curve has been grown, as well, under the same pressure of the compound c. Then, according to our proposition the growth rate is established by the reaction net rate at the substrate surface given by Eq. (4). That is to say that the III element incorporation rate is given by Eq. (3b), at y and the rate at which it is removed from the growing layer, is given by Eq. (5). In the y region, that we called low substrate temperature, the rate given by Eq. (5) is almost negligible, and the growth rate is given only by the III element incorporation rate. For the intermediate y range, as the substrate temperature increases both reaction rates; towards the left and the right increase exponentially. However, the rate toward the right increases in a faster way and its contribution in Eq. (4) becomes no negligible although the growth rate continues to increase. At the substrate temperature indicated as ymax, located in the middle of the intermediate y range, the growth rate reaches its maximum. At this substrate temperature, the rapidity at which the rate of the chemical reaction towards the right increases is such that the growth rate stops increasing and start to decrease. For the high y range the rate given by Eq. (5) continues to increase, and in fact in this y region the growth rate is established by the competition between the reaction that produces the III element incorpora-
tion and that which removes it. Further increase of y will stop the growth, when T ¼ y, or even etching can be produced [10]. The same Fig. 1 curve (b) shows the growth rate for a second source temperature, T ¼ 8508C. The form of the curve is the same, it is just shifted to the right and to lower growth rates. It might be convenient to discuss at this point the assumptions made at obtaining Eq. (6). Actually the approximations that we made; VðTÞ ¼ VðyÞ and phf ¼ phs as well as that pcf ¼ pcs are closely related. Experimental data show that VðyÞ might be smaller than VðTÞ, in fact that means that pcs is slightly smaller than pcf . Now, from Figs. 1 and 2 is clear that a pcs value smaller than the assumed one will just lightly shift down the obtained growth rate curve. Then, such assumptions do not have an important consequence on the qualitative growth rate behavior. Moreover, on the approximation concerning the h and c pressures, once again from Fig. 2 curves c and a, we can see that the maximum growth rate when no M is retaken from the substrate surface, is higher than the experimental maximum growth rate for when as 51. That is, as we will see from the experimental results, the experimental case that is the most frequent one. That means that the growth process consumes a small part of the c vapor produced at the source surface and then that its pressure is not strongly different at both surfaces.
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Let us see now what happens when the pressure of the V column element is increased, keeping all other experimental parameters constant. This will produce at the substrate surface level a more rapid coverage of the III element by the V element, which means a reduction of the as value, resulting in a decrease of the rate of the reaction (5). From Eqs. (4) and (5) we see that decreasing the as value should lead at least to an increase in the growth rate. The effect of such a situation is shown in Fig. 2, for different values of as . As seen, for as 51 the expected increase on the growth rate is clearly observed. At the same time the ‘‘low y range’’ widens towards higher substrate temperatures. The intermediate y range is shifted to the left as well as the y point where the growth stops, allowing the growth at substrate temperatures higher than that of the source, situation often experimentally observed [6]. For the case that we have called two, af and as are different, as in the source there is elemental M and in the substrate M is bonded to a V column atom, then it might occur that as 4af , leading to the same situation discussed before through Fig. 2. Then, both cases are actually equivalent, depending on the experimental conditions. Let us introduce a third case that is experimentally used to avoid the deposition of the growing material on the reactor walls. Here, an additional flow of the transporting gas is added to the growth atmosphere. This is done in such a way that it does not get in contact with the III element reservoir, but it gets in contact with the substrate. Actually, by doing this it is just produced an increases of the rate given by Eq. (5) and this can be made equivalent to an increase of as . This situation is also considered in Fig. 2 curve (d) using, just to illustrate, as ¼ 2. Once again the obtained growth rate curve is qualitatively similar to curve (a) but this time has been shifted, as expected, the contrary way, i.e., towards lower growth rates and the substrate temperature at which the growth rate becomes zero is lower than before. It is also interesting to observe that the obtained law for the growth rate can be used to calculate, for a given set of experimental conditions; T; p and pressure of the V element, the maximal theoretical growth rate as well as the growth chemical efficiency. This is
simply done by obtaining the growth rate for as values approaching to zero, and a reasonable high value for the substrate temperature, Fig. 2 curve (c). Under such growth conditions almost no III atom is retaken from the substrate surface, leading to the maximum theoretical growth rate. The ratio between the maximum of the curve fitting the experimental data, for instance curve (b) of the same figure, and the maximum theoretical growth rate obtained for as 51 gives the growth chemical efficiency for those conditions.
4. Results For testing the model we looked in the literature for results obtained under experimental conditions close to those that have been considered in this model. Several authors have published, for most of the III–V compounds and using a halogen as transporting gas, the CVD growth rate as a function of the substrate temperature [1,4–11]. The most abundant results that we found correspond to what we have called case three, then we will apply the model first to these results [4–7]. D.W. Shaw published in 1968 [4] a study of the growth rate of GaAs as a function of the substrate orientation and temperature using HCl as transporting gas, elemental Ga as III element source and As4 as arsenic source. Of great importance in this case, is an additional HCl flow that was not in contact with the Ga reservoir but that was in contact with the substrate. The author clearly states that the III reservoir temperature was at 9008C. Fig. 3, curves (a, b and c), shows Eq. (6) fitting to Shaw data corresponding to substrate orientations (100, 113A and 115). The fit is extremely good for all the substrate temperature ranges reported by the author including the high substrate temperature range so hard to fit by other models. Experimental data are fitted with different activation energies for each substrate orientation. The best fitting parameters are given in Table 1. For other substrate orientations studied by Shaw, the fit using Eq. (6) was equally good although we do not show it because the number of figures would be too high, nevertheless the fitting parameters are given in Table 1 as well. In a later work
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using the same transporting gas, Shaw studied the effect of the growth atmosphere composition on the growth rate [5]. In one part of that study, the partial pressure of the As4 was increased over a wide range, all other parameters kept constant, included the substrate orientation (0 0 1). The result was a systematic increase of the growth rate as the As4 pressure increased. For fitting these experimental data we proceeded on the following way; first we fitted the data obtained with the lowest As4 pressure used in the study. For the fit we used the El and DH values obtained in the precedent fit for the same substrate orientation and then we just found the values for the preexponential factor l and as using, of course, the authors source temperature. In this case, we preferred to use a linear scale rather than the logarithmic one used by Shaw, as in this way the fitting accuracy can be better seen. Fig. 4 shows the fit, once again it is quite good and behave in
the expected way; increasing the As4 pressure, increases As substrate surface coverage reducing the gallium possibility to react again with the transporting gas and be retaken from this surface. This is considered by the model, as discussed before, by a decrease of the as value, which was exactly the result obtained by the fit, adjusting . et al. parameters are given in Table 2. Later, Putz reported results on the growth rate as a function of the substrate temperature and total pressure in the growth system using HCl and (1 0 0) oriented GaAs [6]. Fig. 5 shows the fit using Eq. (6), as the transporting reaction is the same as for the Shaw’s studies, for the fit we used the El and DH values for this orientation found at Shaw’s results fit, other fitting parameters values are given in Table . 2. Much more recently Gruter et al. [7], reported this type of study, the fit of our model to their data is shown in Fig. 5 too. For this case, we proceeded in the same way using the El and DH values
Fig. 3. Fitting to Shaw’s GaAs growth rate data for different substrate orientations, Ref. [4], using Eq. (6) and source temperature given by the author; 9008C.
Fig. 4. Fitting to Shaw’s GaAs growth rate data as a function of As4 pressure in the growth atmosphere, Ref. [5], using Eq. (6) and source temperature given by the author.
Table 1 Best fitting parameters to growth rate data on different GaAs substrate orientations, Ref. [4] and showed in Fig. 3, using Eq. (6) Orientation
100
111A
112B
115
113B
113A
112A
19
1.0 2.5 1.6 2.4
13.2 2.2 2.1 4.5
3.3 2.1 2.2 5.3
7.3 1.9 2.5 4.05
2.7 1.7 2.6 6.6
2.7 1.75 2.5 4.2
1.5 0.9 3.4 8
l (10 mm/min) El (eV) H(eV) as
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Table 2 Best fitting parameters to (1 0 0) GaAs growth rate data of Figs. 4 and 5, Refs. [5,6 and 7] using the Eq. (6), with El ¼ 2:5 eV, and DH ¼ 1:6 eV pAs4 (103 Atm) 19
l (10 mm/min) as
5.88
2.21
1.33
0.73
0.59
. Putz
. Putz
. Gruter
7.7 3.5
6.65 3.9
6.3 4.3
6 4.9
6 5.6
1.3 0.13
5.5 0.13
500 0.28
Fig. 5. Fitting to GaAs growth rate data of Refs. [6–7], using Eq. (6) and source temperature given by the authors and indicated in the figure.
corresponding for the same GaAs orientation used for Shaw’s data, other values of the fitting parameters are also given in Table 2, once again the fit is excellent. The same halogen CVD system has been successfully used to grow InP [1,8–10]. Hales used HCl as transporting gas, elemental In as III element source and PCl3 as phosphorous source [8]. In the same way as in the precedent case of GaAs, PCl3 bypassed the III source. Here Hales studied the behavior of the growth rate for three different values of the source material temperature; 7508C, 7008C and 6508C, as a function of the substrate temperature. Fig. 6, curves (a, b, and c), shows the fit of Eq. (6) to his data, as seen the fit is excellent for the source temperature of 7508C and reasonably good for the other source temperatures. The fitting parameters are given in Table 3. Susa and Yamauchi reported an equivalent study [9], Fig. 6 curve (d), shows the fit with Eq. (6) using the same energy values found in the precedent fit. As seen, the agreement between the experimental
Fig. 6. Fitting to InP growth rate data of Refs. [1,8,9], using Eq. (6) and source temperature given by the authors, also shown in the figure.
Table 3 Best fitting parameters to InP growth rate data, shown in Fig. 6 using the Eq. (6) for InP, with values for El ¼ 1:57 eV, DH ¼ 0:73 eV l ( 1011 mm/min)
as
References
4.8 24.2 20 1.24 85
1.13 1.33 1.3 1.6 1.0
[8] [8] [8] [9] [1]
data and the model is excellent. Fitting parameters are given in Table 3. Much more recently, . Jurgensen et al. published a similar study including a quite complete theoretical model [1]. Our fitting to their data is shown the same Fig. 6 curve (e), the fitting parameters are given in Table 3. More recently Buckley et al. [11], reported similar results on InP too, however, as the authors did not provide the source temperature the fitting of their
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57
Fig. 7. Fitting to GaAs, GaP, InP and InAs growth rate data of Ref. [10] using Eq. (6) and source temperature given by the authors, 8508C, 9308C, 9308C and 8008C, respectively, for curves (a), (b); (c) and (d).
experimental data was possible only through proposing of a value for the source temperature that results to be quite reasonable. However, because this missing source temperature we do not show here the obtained theoretical fit. For what we have called case 1, the closest situation that we found in the literature was the study made by Mizuno [10] where he reported the growth rate as a function of the substrate temperature for several III–V compounds. In their study the author used polycrystalline GaAs, GaP, InP and InAs as III element source and AsCl3 and PCl3 as V element source. In that study the authors explored the effect of the growth atmosphere composition and substrate temperature. Each material was grown at its particular source
temperature of 8508C, 9508C, 8008C and 7508C, respectively. Fig. 7 curves (a, b, c, and d, respectively) shows the fit obtained using Eq. (6) for the data obtained on those materials. Table 4 gives the parameters values that gave the best fit. It is interesting to remark that for GaAs and GaP the element to be transported is in both cases the gallium and the involved reaction energies result to be the same for both materials as well. This situation repeats again for the case of InP and InAs. Obviously the as values are, as expected, quite close to 1. Using the obtained fitting parameters for all the data here before discussed we found that the growth conditions leading to the highest growth chemical efficiency are for . [6] and Shaw [4] for GaAs(1 1 2)A with a Putz
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Table 4 Best fitting parameters to growth rate data of Fig. 7(a, b, c and d), using the Eq. (6) and values for El and DH already given values for transporting Ga and In using HCl and (1 0 0) substrates GaAs 3
PH2 (10 Atm) l (1010 mm/min) as
0.2 0.013 1.03
GaP 0.6 0.025 1.05
1 0.04 1.06
0.2 0.008 1.09
InP 0.4 0.016 1.07
chemical efficiency 0.6. The lowest is for InP where systematically the chemical efficiency is 0.2.
1 0.013 1.07
0.2 80 2.1
InAs 0.6 135 1.44
1 220 1.3
0.2 8 1.15
0.6 15 1.15
1 25 1.15
Acknowledgements The authors would like to acknowledge the significant contribution from our collaborator Ruben Huerta Cantillo.
5. Conclusions We have proposed a theoretical model to explain the epitaxial growth rate in the halogen chemical vapor deposition system. It assumes that one reversible reaction rules all the process and that the growth rate is given by the net rate of this transporting reaction at the source surface and at substrate surface as well. That means that the reaction that produces the volatile compounds that transport the III element from its reservoir to the substrate is active at the substrate as well. The obtained growth rate law contains just four adjusting parameters. The model explains in a reasonable way experimental data obtained on different III–V compounds grown under quite different thermodynamic conditions. For the same material and using the same transporting gas, systematically the same activation energies of the reactions were found. The model explains data from different laboratories obtained over decades.
References . [1] H. Jurgensen, J. Korec, M. Heyen, P. Balk, J. Crystal Growth 66 (1984) 73. [2] K.A. Jones, J. Crystal Growth 60 (1982) 313. [3] D.W. Shaw, in: C.H.L. Goodman (Ed.), Crystal Growth: Theory & Techniques, Plenum Press, London-New York, 1974. [4] D.W. Shaw, J. Electrochem. Soc. 115 (1968) 405. [5] D.W. Shaw, J. Electrochem. Soc. 117 (1970) 683. . . [6] N. Putz, E. Veuhoff, K.H. Bachem, P. Balk, H. Luth, J. Electrochem. Soc. 128 (1981) 2202. . . [7] K. Gruter, M. Deschler, H. Jurgensen, R. Beccard, P. Balk, J. Crystal Growth 94 (1989) 607. [8] M.C. Hales, J. Electron. Mater. 9 (1980) 355. [9] N. Susa, Y. Yamauchi, J. Crystal Growth 51 (1981) 518. [10] O. Mizuno, H. Watanabe, J. Crystal Growth 30 (1975) 240. [11] D.N. Buckley, J.R.C. Filipe, F.R. Lineman, K.W. Wang, K.M. Lee, A.A. Westphal, S.M. Mc Ewan, J. Electrochem. Soc. 139 (1992) 1185.