ORGANOMETALLIC EPITAXIAL GROWTH OF GaAs1-xPx

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GaAs1-xPx

L. Samuelson, P. Omling, H. Titze, H. Grimmeiss

To cite this version:

L. Samuelson, P. Omling, H. Titze, H. Grimmeiss. ORGANOMETALLIC EPITAXIAL GROWTH OF GaAs1-xPx. Journal de Physique Colloques, 1982, 43 (C5), pp.C5-323-C5-338.

�10.1051/jphyscol:1982538�. �jpa-00222258�

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JOURNAL DE PHYSIQUE

Colloque CS, supplément au n°12, Tome 43, décembre 1982 page C5-323

ORGANOMETALLIC EPITAXIAL GROWTH OF G a AS l_xPx

L. Samuelson, P. Omling, H. Titze and H.G. Grimmeiss

Department of Solid State Physies, University of Lund, Box 725, S-220 07 Lund, Sweden

Résumé.- Nous p r é s e n t o n s l a c r o i s s a n c e de GaAs1 - xP u t i l i s a n t (CH3)3Ga, ASH3 e t PH3. La q u a l i t é des couches é p i t a x i a l e s e s t é v a l u é e à p a r t i r d ' a n a l y s e s en m i c r o s c o p i e é l e c t r o n i q u e à b a l a y a g e e t de c a r a c t é r i s a t i o n o p t i q u e . Une é t u d e s y s t é m a t i q u e des v a r i a - t i o n s de t a u x d ' i n c o r p o r a t i o n d e s é l é m e n t s V (As e t P) a é t é menée. A p a r t i r d ' u n modèle simple d ' i n c o r p o r a t i o n , une é n e r g i e d ' a c t i v a t i o n EA sa 1 eV e s t d é d u i t e du r a p p o r t P/As dans l e s o l i d e . Ce r é s u l t a t e s t d i s c u t é s u r l a b a s e de r é a c t i o n s dans l a phase vapeur e t de p r o c e s s u s a d s o r p t i o n / d ë s o r p t i o n à l ' i n t e r f a c e vapeur - s o l i d e .

Abstract.- Successful epitaxial growth of GaAsi_xP„ using (CI^-jGa, ASH3 and PH3 is reported. The epitaxial layer quality is evaluated from SEM analysis and from optical data. A syste- matic study of variations in the incorporation rates of the group V atoms (As and P) with growth parameters is presented.

From a simple model for the incorporation, an activation energy of.:EA«wl.O eV is deduced for the P/As mixture in the solid. This result is discussed in terms of vapour phase reactions and adsorption/desorption processes at the vapour-solid interface.

1. INTRODUCTION

Metal organic vapour phase epitaxy (MOVPE) is achieving a growing interest for the fabrication of binary and multinary III-V compounds.

This method [1] is suitable for growth on semiconducting as well as insulating substrates and many different device structures have been grown by MOVPE [2,3]. Most of the interest has been focused on the AlGaAs/GaAs system because of its great potential for applications in optical communications. MOVPE growth of GaAs, P , the classical material for light emitting diodes (LED's), has, however, been the subject of only a few reports [4,5].

In spite of the usefulness of MOVPE for growth of many alloys the understanding of the processes leading to epitaxy is still very incomplete.

From e.g. thermodynamical arguments [6] and from measurements of reac- tant profiles in the vapour [7] conclusions have been made about gas phase and suface reactions [8] . Experimentally it is often found that the composition in an epitaxial layer differs strongly from the composition

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982538

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in the gas phase [3,5]. Composition control and, thereby, control of the lattice constant is crucial for most heterostructure devices.

Hence, it is most important to obtain a better understanding of the processes governing the growth of alloys.

The purpose of this paper is therefore to contribute to the knowledge about epitaxial growth of alloys and to stimulate crucial experimental and theoretical work. Epitaxial growth and assessment techniques will be described in Section 2. In Section 3 some properties of GaASj__ P epitaxial layers will be presented. The major part of Section 3 will deal with the problem of the vapour-solid distribution coefficients for the cations. Detailed temperature dependence data will be presented and interpreted in a model which extracts an activation energy for the competition between P and As on the group V sub-lattice. This activation energy will be discussed in terms of vapour phase reactions and the adsorption/desorption balance on the growing surface. Finally, conclusions drawn from our results will be given in Section 4.

2. EXPERIMENTAL 2.1. Epitaxial growth

The equipment used to grow the GaAs.._ P material for this study is a horizontal, RF-heated VPE reactor operating at atmospheric pressure.

The design is similar to that of Bass [9], The details of our equipment have been published previously [10]. The active gases used are AsH- and P H3 diluted to 5 % in H- (from British Oxygen Corp.). These gases are mixed with trimethylgallium (TMG = ( C H3)3 Ga) close to the entrance to the cell. Palladium diffused H_ is used as a carrier gas with a flow of ~ 4 1/min. TMG in the vapour phase is produced by H, bubbled through liquid TMG (from Texas Alkyls) kept at a fixed temperature, 0 °C. The mole fraction of TMG is « 2 > 10 and the sum of

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the mole fractions of the hydrides is kept at » 2 • 10 . The substrates used in this study are n-type GaAs and GaP, oriented in the [100]- orientation (or [100], 2° off towards [110]). In order to study the growth kinetics we have varied the growth temperature between 650 C and 850 °C. To reduce the problems with the misfit between substrate and epitaxial layer, a graded composition layer is grown between the substrate and the final composition layer. For the specific investi- gation (see Section 3.3 below) of the group V composition dependence, on gas mixture and temperature, samples have also been grown with the gas composition varied in steps.

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2.2. Assessment techniques

Grown layers are studied by scanning electron microscope techniques.

For composition control, cleaved samples are investigated by electron beam induced X-ray emission (micro-probe) in the SEM. In some cases the samples are angle lapped to improve the micro-probe resolution.

For electrical characterization, Schottky barriers are prepared by evaporation of Cr contacts. For the optical characterization, p n-

+

diodes have been prepared by zinc diffusion. Injection luminescence spectra are recordedwith current densities between 1-10 ~ / c m ~ and the luminescence is detected with a cooled S1 photomultiplier. For recor- ding of transmission data, layers grown on "transparent" Gap substrates are used and monochromatic light is passed through the sample and detected by a Si solar cell.

3. RESULTS AND DISCUSSION.

3.1. Epitaxial layer properties.

Examples of grown GaAslmxPx layers are shown in Fig. 1. This figure shows SEM images of cleaved samples, Super imposed on each image is the result from micro-probe analysis obtained along a line perpendicular to the surface. The samples shown are for x = 0.13 and 0.5 grown on GaAs and with X = 0.40 and 0.83 grown on Gap. Growth rates are found to vary from 0.2 pm/min for GaAs to 0.1 pm/min for Gap, in fair agreement with lresults from Inoue and Asahi 141. Typical composition gradients are 5 10 %/urn, corresponding to a lattice parameter grading of

-

0.02 A/um. The thickness of the final composition layer is, typi- cally, 5-10 pm. The samples appear smooth and mirrorlike, except for samples with compositions graded over close to the full alloy range, like GaAs on Gap. Carrier concentrations of not intentionally doped

material are found to vary between n = N d - ~ a = 1 . 1 0 ~ ~

-

3-1016 c ~ I - ~ , with the high values observed for the phosphorous rich material.

Distance

Fig. 1. SEM pictures of GaAs -xPx samples grown on GaAs and Gap substrates. Also shown are data from micro-prohe composition analyses, where each dot is a mean va- lue of seveoal measured ppints. The diameter of the dots corresponds to 0.5 um.

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3.2. Optical properties

The electrical and optical behaviour of GaAs and Gap are quite unlike.

The bandstructures of GaAs and Gap are shown in Fig. 2, and the varia- - tions in the conduction band minima with composition x are drawn con- necting the two binary compound bandstructures [Ill. For x 5 0.45 radiative recombination has a high probability and proceeds without requirement of phonon involvement for momentum conservation (see Fig.3).

Likewise, the absorption edge is steep, reaching values of the absorption coefficient a

-

10 cm-I within less than fifty me" (see Fig. 4). 4 This behaviour is characteristic of the transmission spectra in Fig. 4. In the indirect gap region (x

2

0.45) a major part of the recombination occurs with simultaneous emission of momentum conserving phonons, as observed for higher values of x in Fig. 3. In the indirect gap region the absorption coefficient is small, 1-100 cm-lr for a wide range of photon energies above the absorption edge [I21 (see Fig. 4). For x > 0.6 the

r

conduction band minimum is above the X minimum of Gap

I

Photon energy lev) ---r

I

^Fig.^3. Normalized injection lumi- LO nescence spectra for various alloy

compositions (T=77 K).

Fig. 2. Thin lines show the band Photon energy [eV]

structures for GaAs and Gap. The

variations of the band extrema with Pig. 4. Transmission through % 5 q x are drawn with thick lines. GaAsl-xPx on 350 urn Gap substrates for

various alloy compositions (T=77 K).

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and the transmission is strongly affected by the

--

350 pm thich substrate. In the sample with x = 0.7 the absorption from the

-

^{5pm thick}

epitaxial layer is comparable with that of the substrate. The steep- ness of the Gap absorption edge [12] agrees with a shift of the X minimum

-

0.14 eV. A description of the electronic states involved in luminescence and in deep level transitions (thermal and optical) is published elsewhere [13].

By comparing the injection luminescence efficiency with that of corresponding commercial material we estimate that the efficiencies are comparable, at least within an order of magnitude, although the MOVPE material is not optimized for LED use.

3.3. Relationship between the composition _(x)of GaAsl-xPx and growth conditions

3.3.1. Backqround

-

The problem of two atomic species competing about

--- ---..-

positions on the same sublattice occurs in growth of all ternary and quaternary compounds. For the conventional GaAsl-xPx growth technique, i.e. the halogen transport method [141, thermodynamical calculations for the composition in the solid have been performed by e.g. Mullin and Hurle [151. This system is theoretically complicated since growth is the result of a series of processes occuring in different zones of the equipment with different temperatures and gas mixtures. In prin- ciple, MOVPE growth ought to be a simpler problem. In this case growth is resulting from pyrolyses followed by recombination at or above the surface. Leys and Veenvliet have concluded that for GaAs growth, TMG decomposes in the boundary layer and diffuses towards the substrate either as elemental Ga or as GaAs molecules [71. This would mean that either GaAs molecules are formed in the boundary layer or that Ga and As recombine at or very close to the substrate. In each case growth requires (i) decomposition of the organometallic group I11 molecules and the group V hydrides, followed by (ii) recombination of group I11 and group V atoms in the vapour or at the surface. These should be

(iii) chemisorbed on the surface and incorporated in the lattice. The competing process (iiii) desorption of atoms adsorbed on the surface should also be treated. It is not easy to say which of these steps is rate limiting and, thus, will determine the composition of a mixed crystal, like the admixture of As and P in GaAsl-xPx material. Some data are available on cation incorporation in MOVPE grown GaAslqxPx [4,5]. Inoue and Asahi [4] found a nearly 1:l correspondence between the gas composition, x = pPH3/(pAsH3 + pPH3) and the P mole fraction

g

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in the solid, xs = [P]/([ASI+[P]), for growth between 800 and 850 OC.

Saitoh and Minagawa 151 found a temperature dependent vapour-solid distribution coefficient with a tendency for P incorporation to in- crease with temperature. A critical discussion of the model in which they interpret their data will be given below and it will be shown how a reinterpretation extracts meaningful information and gives good agreement with the data presented in this paper.

At an early stage of this project it was observed that G ~ A S ~ - ~ P ~ deposited on GaAs substrates at T

-

^700-725 ^OC^followed^a^different

vapour-solid distribution curve than material grown on Gap substrates at T

-

⁸⁰⁰^OC.This result is schematically shown in Fig. 5. At 800 OC

on GaAs substrates at T r 7 0 0 ° C

Material deposited on Gap substrates at T.80O0C

Gas composition CASH3

Iv

C A S H ~ ] ~ + [pH3

1,

Fig. 5. Trends observed f o r two growth tempera- t u r e s i n d a t a f o r compo- s i t i o n i n t h e s o l i d a s a f u n c t i o n of t h e composi- t i o n i n t h e vapour.

the composition in the solid roughly correspondstothat of the vapour, but at lower temperatures the incorporation of P seems to be much less efficient than that of As, a result which was partly observed already by Saitoh and Minagawa [51.

3 . 3 . 2 . Model

-

In an attempt to understand the cause for this non-li-

---

nearity a simple model for incorporation of competing atoms will be discussed next. Fig. 6 shows the processes at the growing surface which are taken into account in the model. In the boundary layer above

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Molecules AsH3 pH3 Hp

1.phase vopour{

2

tothers

1

I

^solid

_I

Fig. 6. The processes on

empty site _thegrowing surface inclu-

site with As atom ded in the model (see text).

1

site with P atom

the surface is, except for TMG and its products, a mixture of the entering gases, H2, AsH3 and pH3. Decomposition of AsH3 and pH3 gives simple molecules like As2, Asq, P2 and P4, but also more complicated ones like Asp3, As2P2 and As P as shown by Ban 1161. 3

We denote the total number of sites on the surface for group V atoms by Ns, and the number of these sites occupied by As and P are written as NAs(t) and Np(t) respectively. Hence the number of available sites is Ns-N(t) where N(t)=NAs (t)+Np(t) and we can write the adsorption rate for e.g. As-atoms as kAs-pAsH3.[Ns-N(t)]. With this definition kAs can be called an effective adsorption rate coefficient and includes effects from all steps leading from AsH3 in the vapour to the adsorbed As. The reverse process, desorption of As atoms, is described by a desorption rate coefficient dAs. The set of coupled differential equations describing the covering of a group V atom mono-layer becomes:

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In Appendix A is given the full time dependent solution to these equations. The time dependences of NAs, Np and N are quite complicated, but for the purpose of analysing data on vapour-solid distribution coefficients, it is sufficient to solve for the simple steady state condition when t +

-.

This solution gives for the chemical composition on the cation sub-lattice:

Eq. (5) is written for the composition of a mono-layer, which is ob- viously equal to the bulk composition of group V atoms. For interpretation of composition data for any pair of atoms A and B occuring on the same sub-lattice, Eq. (5) can be expressed as:

In Fig. 7 is plotted the composition of atom A in the solid ([AI~/([AI~+[BI~)) as a function of gas composition [A] J([Alv+[Bl,)

Fig. 7. Graphs of the theoretical expression in Eq. (6) for the com- position in the solid as a function of the composition in the va- pour for different va- lues of alB.

1

.o

n

2,

V)

u 0.8

Am

a

U

0.6 .- '0

- S .-

C

0.4

,- 0

C

--

%

a

8

^0.2

CAI, Gas composition

CAI;CBI,

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for different values of a/$. If a/B M 1, i.e the effective adsorption to desorption ratio is similar for A and B, the incorporation in the solid equals the gas mixture. If, on the other hand, a/$ is a large number, i.e. atom A has a larger effective adsorption to desorption ratio, the solid will contain much more of atom A. It fs, furthermore, easily seen (Eq. (6) ) that for small values of X ~ , ~ = [ A ~ ~ / ( [A]~+[B]~)

,

the curves can be approximated by straight lines with slope a/$ (and with slope $/a for values of xAIv close to 1). By fitting curves like those in Fig. 7 to measured composition data for different growth temperatures, one can thus obtain the temperature dependence of $/a and deduce an activation energy which describes the competition between atoms A and B on the growing surface.

3.3.3. Experimental data

-

In order to experimentally investigate this

--- ---

dependence for G ~ A S ~ - ~ P ~ , a set of samples were grown at different temperatures and with the group V gas composition varied in steps. With electron beam induced X-ray emission (micro-probe) the composition of each step can be determined. The result of one such analysis is shown in Fig. 8 where the measured P content is plotted versus the electron beam position on the cleaved sample. The gas composition is given in the figure for each step in the curve. Data like those in Fig. 8 have

F i g . 8 . Micro

-

probe analyses data obtained f o r a layer grown a t 800 OC with the vapour composition (given i n the f i g u r e ) varied i n s t e p s .

Depth position

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0 0.2 0.4 0.6 0.8 Gas composition CAsH31v

CAsH3IV+CPH3IV

Fig. 9. Experimental data of the composition in the solid plotted versus that of the vapour obtained for five growth temperatures from analyses like in Pig. 8. The experimental points have for each temperature been fitted with the theoretical expression given by Eq.

(6). The inserted table lists the Bla values deduced.

been taken for samples grown at T = 650 C, 700 Oc,750 Oc,800 0 OC and 850 OC where, incidentally, it is found that the samples grown at the lower temperatures suffer in crystalline quality. For each of these temperatures the composition in the solid is in Fig. 9 plottet versus the gas composition. The curves in Fig. 9 are fits of the theoretical expression in E q . (6) to the experimental points. A Value of B/a is thus determined for each temperature. The logarithm of B/a is in Fig. 10 plotted versus 1/T. It is found that within the limits of

Fig. 10. Arrhenius plot of B/CL (log(B/a) VS. 1/T) with values of B/a from the fit in Pig. 9. The error bars in the figure correspond to estimated uncertainties in the evaluation of compositions in the solid.

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uncertainty the dependence is linear, which means that $/a can be described by $/a a exp(-EA/kT) with EA=l.O+O,l eV (corresponding to 23

+

3 kcal/mole).

3.3.4. Discussion

-

Before an interpretation of this result is attemp-

---

ted, an explanation will be given for the discrepancy between this result and the conclusions made in the literature by Saitoh and Mina- gawa [51. They concluded that phosphorous incorporation increases linearlywithtemperature, which is quite a different result from that obtained above. They assume that P incorporation has a linear dependence on the pH3 content in the vapour, and using this assumption they keep the gas composition constant (x =[PH31V/([AsH31V+[~H31,)=0.54)

9

and evaluate the slope of this assumed incorporation proportionality factor. They find for the "slopeq' that k,=xs/x =3.7 T-2.9. As

g

discussed above, the linear approximation of Eq. (6) is valid only for x close to zero. However, it is interesting to take their linear

4

function for kp and try to deduce numbers for the temperature dependence of $/a. This can be done according to:

which can be re-written as: $/a =(3.7 -10-3~-2.9)/(5.578-4 . 3 4 3 - 1 0 - ~ ~ )

.

An Arrhenius plot (like in Fig. 10) of this function gives an almost straight line with a slope somewhat less steep than the one given above

(EA=0.75 eV). Considering that this value will suffer from imperfec- tions in the linear fit to the original data, we fitted Eg. (6) direct- ly to the few experimental points given in [5](for two temperatures).

Theseresultsindicates, in fact, an activation energy of -1 eV. The exponential temperature dependence for the P incorporation is a drama- tically different result from what was originally concluded [51. This shows that data like these should be interpreted in a model which has relevance to the experimental situation.

Recalling that $/a = (kp-dAs)/(dpakAs) a few candidates for the origin of the measured temperature dependence of B/u can be selected.

ki (i=As or P) includes formation of reactive species in the gas phase, their grrival to the surface and the gidfiggpglgq of atom i. Unfortu- nately, the available data in the literature for AsH3 and pH3 decomposition is incomplete. It is, furthermore, not clear if thermodynamical equilibrium is reached in the gas phase or if our growth conditions favour homogeneous or heterogeneous hydride decomposition 17,17,181. If one assumes that decomposition activation energies

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for AsH3 and pH3 are similar for each mechanism, the observed activation energy can be interpreted as a difference in decomposition mechanisms, i.e. AsH3 decomposition being heterogeneous and pH3 homogeneous Gas phase reactions leading to formation of GaAs and/or Gap molecules

[ 7 1 are not unlikely to involve activation energies (and differences in activation energies) of the magnitude observed. However, neither the process of diffusion through the boundary layer, nor physisorption are likely to cause the observed strongly activated temperature dependence. For chemisorption and incorporation on lattice sites of As and P atoms on GaAs and Gap it is hard to find data in the literature.

However, a difference in barrier heights for chemisorption of As and P as large as 1 eV (or 23 kcal/mole) seems unrealistic.

The part of the expression for p / a which remains to be treated is the ratio of desorptions of As and P. Petzke et a1 [ 6 1 have interpreted the reduction in the growth rate of GaAs above 800 C 0 as As losses from the surface with a desorption activation energy of 2 6 * 5 kcal/

mole. Even if this As desorption only affects the growth rate in this high temperature regime where the reaction rate becomes second order, it could affect the balance for As to P incorporation even for much lower temperatures. Unfortunately, it is hard to find a corresponding P desorption activation energy in the literature, but it can be concluded from Eq. (6) that if P desorption is not very temperature sen- sitive (i.e. has a small activation energy) such a difference in dAs and dp is sufficient to explain the strong temperature dependence for As and P incorporation in G ~ A S ~ - ~ P ~ .

From this discussion it is clear that it would be most interesting to have access to detailed data for, especially, gas phase reactions, homogeneous and heterogeneous hydride decomposition and desorption activation energies for As and P adsorbed on GaAs and Gap surfaces. Such data would together with the experimental data reported here improve the understanding of, not only MOVPE of G ~ A S ~ - ~ P ~ , but of the basic mechanisms involved in vapour phase epitaxial growth.

4. CONCLUSIONS

It has been shown that MOVPE is able to produce high quality GaAsl-xPx material with optical properties comparable with co~ventional LED ma-

terial. Incorporation of the group V atoms has been interpreted in a model which allows extraction of numbers for physically meaningful quantities. A thus deduced activation energy of EA%l eV has been dis-

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chssed in terms of gas phase reactions and adsorption/desorption processes on the surface.

ACKNOWLEDGEMENTS

The authors acknowledge assistance from M. Ahlstrom in SEM investiga- tions and S. Nilsson in optical measurements. This project has been supported by the Swedish Board for Technical Development.

APPENDIX

In this appendix will be shown how the equations corresponding to a model involving both absorption (ki) and desorption (di) can be sol- ved (se section 3.3.2). The equations written for atom A and B are:

For definitions see Section 3.3.2. These coupled differentialequations with constant coefficients can be converted to simultaneous linear al- gebraic equations by applying the Laplace transform operator

L

^[191.

Transforming ( N ( S ) = L ( N ( ~ ) ) , N ~ ( S ) = L ( N ~ ( ~ ) ) ,

...

⁾ ^{we get}

Solving these, using partial fraction expansion, and finally by using inverse Laplace transforms we obtain:

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NB(t)= aB + BBwexp(- (a-b) *t)

+

yB*exp(-(a+b) *t) Here a, b, ai, 6 . and yi are given by

I

k * p +k * p +d +d a = A A B B A B

2

Eq. A9-All can be simulated by varying A(=kA=pA)

,

^B(=kB B ^{* p}1, dA anddB If one assume a physically reasonable situation for epitaxy, like

dA, dB << A

,

^B ^{and NA}

⁺

^NB= N,the solution can be divided into four different classes. In the figur-esbelow we have in Fig. A1 the special

1

.o

^l ¹ ^l Î Î Î ⁴

-

^{B / a}

t -

^0.1

1 0.2

z V) j ~ , , ( t )

.c 0

1 ^-

^0.5

.- 0.5

-

V

^- -

^1.0

LL

e

.: 0.5

NB (t)

I -

^0.20.1

0 0 0.5 O 1 0.5 l ' l ' a 1 .O

Time units [.lo4] Time units L.10~1

F i g . A l . F i g . A2.

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0.5 1 .O

Time units [.lo4 1 0 ~ ' " " " ' " 0.5 1.0 Time units C . I O ~ I

Fig. A3. Fig. A4.

Fig. A1-A4. Time dependence simulation for the surface coverage of two competing species A and B for various cases of adsorption and desorption and for various B/a.

For details, see text.

case where A = B = const. (=I)

,

^d⁼const. (=lo -3 ) and dA is varied to B

give B/a = 1.0, 0.5, 0.2 and 0.1 (roughly the range covered by the G ~ A S ~ - ~ P ~ data shown in Section 3 . 3 ) . In Fig. A2 the more general case where A and B are constant but not equal ( A =1, B =0.2) and dB=

with dA varied to give the same @/a as above. Pig. A3 is for d =d =loe3, A- 3B A=1 and, hence, B is varied, and in Fig. A4 is dA=2.1~-4, dg=10 (i-e.

dA

*

dB), A=l and B is varied. From an inspection of these curves it is clear that one can easily distinguish between cases where a variation in B/a originates from adsorption or from desorption processes.

If one has the possibility to monitor the surface coverage of atom A and/or atom B as a function of time during a slow growth process, it would be possible to fit the data to obtain values of ki and di.

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121 DUPUIS R.D. and DAPKUS P.D., IEEE J. Quantum Electron.g(1979)128.

[3] DUCHEMIN J.P., HIRTZ J.P., RAZEGHI M., BONNET M. and HERSEE S.D., J. Crystal Growth 55, (1981) 64.

[41 INOUE M. and ASAHI K., Jpn. J. Appl. Phys.,g(1972)919.

[ 5 1 SAITOH T. and MINAGAlJA S., J. Electrochem. Soc.z(1973)656.

/61 PETZKE W.-H., GOTTSCHALCH V., BUTTER E., Kristall und Technik 2(1974)763.

[71 LEYS M.R. and VEENVLIET H., J. Crystal Growth z(19811145.

[ 8 1 STRINGFELLOW G.B., Rep. Prog. Phys. %(1982)469.

[9] BASS S.J., J. Crystal Growth =(1975)172.

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[lo] SAMUELSON L., OMLING P., TITZE H. and GRIMMEISS H.G., J. Crystal Growth E(1981) 164.

1111 CRAFORD M. G., SHAW R.W., HERZOG A.H. and GROVES W.O., J. Appl. Phys. %(1972)4075.

1121 DEAN P.J. and THOMAS D.G., Phys. Rev. =(1966)690.

1131 OMLING P., SAMUELSON L., TITZE H. and GRIMMEISS H .G.,

roc.

5th~nt.

Conf. on ternary and multinary compounds ( I 1 Nuovo Cirnento,D)(1982) 1141 TIETJEN J.J. and AMICK J.A., J. Electrochem. Soc. g(19661724.

[ 1 5 1 MULLIN J.B. and HURLE D.T.J., J. Luminesc. 1(1973)176.

1161 BAN V.S., J. Electrochem. Soc. =(1971)1473.

[I71 TAMARU K., J. Phys. Chem. %(1955)777.

[181 "GMELIN Handbook", Springer-Verlag, Berlin, Band P [C1(1952)p.32.

[19] See e.g. ARFKEN G., "Mathematical methods for physicists", Academic Press, New York (1970).