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The evaluation of growth dynamics in MBE using electron diffraction
Journal of Crystal Growth 99 (1990) 9 17 North-Holland
9
THE EVALUATION OF GROWTH DYNAMICS IN MBE USING ELECTRON DIFFRACTION B.A. JOYCE University of London Interdisciplinary Research Centre for Semiconductor Materials, The Blackett Laboratory, Imperial College, Prince Consort Road, London SW7 2BZ, UK
Reflection high energy electron diffraction (RHEED) has proved to be a very versatile technique for growth and surface studies of epitaxial metal and semiconductor thin films prepared by molecular beam epitaxy (MBE). The combination of the forward scattering geometry of RHEED with the near-normal incidence of the atomic and molecular beams on to the substrate enables diffraction features to be monitored continuously during growth. This paper is concerned with the application of RHEED intensity measurements, especially temporal oscillations, to the study of growth dynamics in MBE, with particular emphasis on III V compound semiconductors.
1. Introduction
2. Observation of intensity oscillations diffraction conditions
One of the many advantages of molecular beam epitaxy (MBE) is the extent to which in-situ diagnostics can be applied. The UHV environment means that many techniques developed for surface science can be used directly. Surface crystallographic [1,2] and electronic [3,4] structure, cornposition [5,6] and surface reaction kinetics [7—10] have all been investigated. Of particular interest for crystal growth is the application of RHEED to studies of dynamic and kinetic processes in epitaxial thin film fonnation. Since the first detailed report [11], the RHEED intensity oscillation technique has received much
Details of intensity measurements have been given in several publications [11,13]. In most cases only a single feature of the diffraction pattern is monitored, usually the specular spot on the 00 rod, but intensity variations over the whole pattern can be followed by TV techniques [14]. Fig. 1 shows oscillations from the specular spot on the 00 rod as a function of polar angle in [110] and [010] azimuths at a primary energy of 12.5 keV. The growing film was GaAs on a GaAs(001)2 X 4 reconstructed surface, maintained at a ternperature of 580°C, a Ga flux of 1 x iO’~atoms cm 2 1 and an arsenic (As 2) flux of 2>< were 1014 2s~’.These growth conditions molecules cm~ invariant so the different oscillation waveforms can only be attributed to diffraction effects. The reasons for this are rather complex and have been dealt with previously in a number of publications [12,13], so here I will only summarize the salient features. The important point is that these effects must be understood sufficiently well that they can be deconvolved from those associated with growth processes. In general terms the waveform variations shown in fig. 1 derive from the many diffraction processes which contribute to the measured intensity. A single scattering kinematic approximation is not
attention (see ref.It [12] a rangewhich of summary and review articles). is a for technique is remarkably simple to apply, but is difficult to interpret correctly and can be misleading in the hands of the unwary. The basic observation is of a periodic intensity variation during growth, the period corresponding precisely to the growth of a single atomic or molecular layer. In this paper I will first discuss the origin of the temporal intensity variations in relation to both growth and diffraction and then indicate how the technique can be applied to studies of growth kinetics and dynamics and the development of process modifications to MBE. 0022-0248/90/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
—
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10
BA. Joyce
/ Evaluation of growth dynamics in MBE using electron diffraction
b
~ 110]
a
r
010
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0
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4
of polar hg. 2. Phase angle relationship for [110],of[0101 RHEED and oscillations [110] azimuths as a function from a growing GaAs(001)-2
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to reach the conditions were second as time for oscillation fig. of a1.complete Phase minimum is period. defined normalized as the timebytaken the
2 6~
so their position remains fixed to the shadow edge
—
Time Fig. 1. RHEED intensity oscillations of the specular spot on the 00 rod in [110] and [010] azimuths from a growing GaAs(001)-2X4 reconstructed surface at different polar angles; primary beam energy 12.5 keV; 7~= 5800 C; Joa = lx 1014 atoms cm 2 s 1, ‘As 2 = 2 x l0~~ molecules cm 2 1
usually adequate and other factors must be included in the analysis of diffracted beam profiles, since all detectors integrate over some region of reciprocal space. Multiple scattering effects frequently occur, especially those related to surface wave resonances and beam emergence conditions resulting from the RHEED geometry [15]. Some thermal diffuse scattering will always be present, although its contribution to the total intensity may be small. This of course is in addition to the normal diffuse intensity due to the existence of finite regions of the surface at different levels (terraces separated by steps). There is also a significant inelastic cornponent of the scattered intensity and in particular strong Kikuchi features can occur [13,16]. They are incoherent with respect to the primary beam
as the polar angle is varied. The variation of intensity with the surface morphology changes which occur during growth is different for the different diffraction processes, so the phase and amplitude of the oscillations will depend on the proportion of each of the processes integrated by the detector for particular diffraction conditions. It is this which leads to the different waveforms. Two points of particular importance can be singled out. The first, illustrated in fig. 2, is that an intensity maximum may not correspond to monolayer completion (in the illustration this is only true for an ordinate value of 1.5) and the second is that double period oscillations can occur purely as the result of diffraction effects in which intensity changes of different processes are out of phase. With this background we will examine the application of the technique to studies of growth dynamics.
3. Growth mode It is now universally accepted that the basic origin of the oscillating intensity behaviour is the changing surface topography (step density) associated with two-dimensional layer-by-layer growth.
B.A. Joyce
/
Evaluation of growth dynamics in MBE using electron diffraction
That the steady state period corresponds precisely to the formation of a monolayer is also without serious question, although the period of the first oscillation may be different, depending both on the diffraction processes being sampled and transient surface reconstruction changes when growth is initiated [17]. It is also important to emphasize that RHEED is sensitive to step density rather than surface coverage because of the multiple and diffuse scattering components in the measured intensity. It is only in the kinematic approximation that coverage is the dominant factor in the intensity variation, In addition to the periodic variation of the intensity, the observed damping of the oscillations also provides valuable information on the growth mode. The simplest interpretation is that is represents a transition from two-dimensional growth to step propagation, the final state of complete damping being reached when the mean terrace width created by 2D growth is equal to the mean surface migration length of an adatom. This defines the initial and final states, but does not explain the gradual decrease in intensity between them. This occurs principally because regions of the surface separated by distances greater than the mean adatom diffusion length, although statistically independent, are nevertheless sampled by the same RHEED beam. Differences in the stage of growth can therefore develop, even though each region still grows in a layer-by-layer mode, The differences lead to a steady state mean intensity produced by an incoherent superpositioning of individual oscillatory step densities and the rate of decay is then an indication of the effective migration length of adatoms, or equivalently, the step density. A final point on growth mode concerns the dependence of the intrinsic quality of material on its growth mode. There has been a definite tendency to associate the presence and persistence of RHEED intensity oscillations with material of higher quality, as judged by its optical and electrical properties, than that grown without oscillations being present. The implicit assumption, therefore, is that layer-by-layer growth produces material superior to that grown by a step propagation mechanism, even though the transition from
11
one mode to the other is quite rapid, especially at high temperatures. There seems to be no justification for this assumption, although where interfaces are concerned their abruptness is likely to be growth mode dependent.
4. Surface migration Irrespective of the model details, significant adatom migration is a necessary condition for layer-by-layer growth. With III V compounds it is cation migration which is the determining factor; changes in the anion surface concentration only influence rates, not mechanisms, at least over the range of growth conditions used in practice [18]. We are simply concerned with the migration of a cation on the substrate surface in a relatively weakly bound precursor state before it is incorporated into a lattice site. Attempts to obtain reliable values for the diffusion parameters have only met with limited success, however. The basic experimental approach [19,20] utilizes growth on a vicinal surface for which the degree of misorientation and consequently the terrace width is known. The diffusion length can then be measured as a function of growth parameters (temperature, flux and flux ratio) by observing the change of growth mode from 2D layer-by-layer on the terraces to step propagation, depending on the presence or absence respectively of RHEED intensity oscillations. The point at which they just disappear as either the flux or temperature changes then gives the diffusion length (which is equated to the terrace width) for those conditions. The principle is illustrated in fig. 3. Although conceptually simple, there are difficult interpretational problems which have not yet been properly solved. An important factor is that the measurements are kinetic, obtained under conditions far from equilibrium, so any values obtained will depend on the particular growth conditions used and should not be considered as fundamental diffusion constants. If it is assumed that surface migration is isotropic, we can write: =
2 D’r,
(1)
12
B.A. Joyce / Evaluation ofgrowth dynamics in MBE using electron diffraction
an upper Nishinaga and Cho [21] proposed an limit. alternative approach based onhave classical critical nuclei appropriate to a thermodynamic nucleation treatment. For theory, typical which MBE therefore conditions, requires however, large the critical nucleus will be a single adatom, so the validity of such a thermodynamic approach must also be questioned. The second limitation concerns the evaluation of energy terms. Even if T is correctly equated with monolayer deposition rate, the activation enpendence D is the sum of the terms shown ergy valueofdetermined from the two temperature de-
T4
Incident beam
XE
t
Incident
beam Fig. 3. Illustration of the principle of the vicinal plane method, showing the change in RHEED information as the growth mode changes from step propagation to 2D nucleation,
where x represents the mean displacement, i.e. terrace width, i• is the surface lifetime in the mobile precursor state and D a temperature dependent diffusion coefficient, If ED is the sitedependent energy barrier to diffusion, then: D = D0 exp( ED/kT), —
(2)
where D0 corresponds to a vibrational frequency. This energy barrier to diffusion is the combination of a surface barrier plus a term representing bonds made to nearest-neighbour atoms, E~: ED
E~+ E~.
(3)
This simple analysis has two major limitations, The first is the choice of r, the surface lifetime, Conventionally [19,20] it has been equated to the monolayer deposition rate: = N/J (4) where N~is the number of surface sites per unit area and J is the cation flux. This is certainly an oversimplification however and at best represents
in eq. (3). For Ga on GaAs(O01)-2 X 4, ED was measured to be 1.3 eV [19], which means that the surface barrier will be significantly smaller. This is reasonable, if only qualitative and helps to confirm the importance of surface migration in 2D growth. In spite of these quantitative difficulties, the basic concept of a layer-by-layer growth mode continuing until the adatom (cation) migration length because less than the mean terrace width, when step propagation becomes the dominant mode, seems established. It can be further substantiated by the growth of beterostructures and we can distinguish two cases: (i) each region is sufficiently thin that oscillations are still present when the interface is grown, i.e. a steady state terrace width distribution has not been attained and (ii) thicker structures, where the oscillation amplitude has damped effectively to zero before the heteroj unction is formed. Case (i) is illustrated in fig. 4a for two different diffraction conditions and with the interface formed at various positions in the monolayer growth cycle, as indicated by the arrows. It is immediately apparent that apart from the change in period attributed to the increased Group III flux in the (Al, Ga)As regions, there is virtually no effect of an interface on oscillation behaviour for this situation. For case (ii), however, illustrated in fig. 4b, where the oscillations in each composition region have damped out, they immediately restart at a GaAs—(Al, Ga)As interface, consistent with the shorter migration distance of Al producing a new, shorter terrace width distribution. At an (Al, Ga)As—GaAs interface, where the migration
BA. Joyce
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Evaluation of growth dynamics in MBE using electron diffraction
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of 104. (a) Fig. andIntensity 1.6 o. Interfaces oscillations formed across Time before ~— GaAs oscillations (Al, Ga)As—GaAs have damped. interfaces;(b)7~ Intensity = 5800 C,oscillations Ti (001) me surfaces, — across [110] GaAs—(Al, azimuth atGa)As polar angles GaAs interfaces; T5—600°Cand 650°C respectively, off [110] azimuth at a polar angle of 10. Interfaces formed when oscillations are almost fully damped.
length of Ga is greater than the mean terrace width on the (Al, Ga)As, oscillations do not restart since the growth mode under such circumstances is dominated by step propagation.
5. Computer simulation of MBE growth dynamics and kinetics The basis of simulation studies is the so-called solid-on-solid (SOS) model of Weeks, Gilmer and Jackson [22],but Madhukar and co-workers [23,24] produced the first calculations directed specifically at the growth of compound semiconductors, They were initially aimed at determining the growth front morphology, i.e. the number of molecular layers over which growth is distributed and then extended to an investigation of the relationship between anion incorporation kinetics and cation migration rates [25,26].Clarke and Vvedensky [27,28] have adopted a simpler approach by assuming that the anion incorporation step is never rate limiting over the usual range of growth condilions, which is almost certainly valid. They then
consider only two events: deposition and surface migration of monatomic species. The growth process is represented by a Monte Carlo simulation, which describes events by rate equations and calculates the probability of their occurrence as the product of a rate equation and a time constant. To compare results of such a simulation with experimental observations of RHEED intensity, the step density of the simulated growth front has been chosen as the optimum parameter. It is evaluated by counting the number of unsaturated nearest neighbour bonds parallel to the surface and shows excellent agreement with recorded RHEED intensity oscillations, especially in damping behaviour and growth on vicinal surfaces [28]. An alternative approach to comparison with experiment is to calculate from the simulation the intensity of the specular RHEED beam within the kinematic approximation [24]. This treatment correctly predicts the oscillation period, but there is no decay towards the mean in the intensities at half-layer completion, contrary to observation. The reason is that even if diffraction conditions could
14
BA. Joyce
/ Evaluation of growth dynamics in MBE using electron diffraction
be chosen such that the kinematic approach were valid, it is only sensitive to surface coverage, not to the arrangement of adatoms on the surface and therefore not to the step density or distribution. Consequently, it fails worst in the high step density regime at half-layer completion.
6. Surface relaxation and growth technique modifications Several modifications to conventional MBE growth have recently been proposed for growing more perfect” interfaces in heterostructures, quantum wells and superlattices. Perfection in this context is defined as maximizing areas of single composition in the interface plane, or minimizing the number of molecular layers normal to the plane in which compositional variations occur. The aim may also be to obtain useful properties from structures grown at lower temperatures than could be achieved by conventional growth. The modifications include growth interruption [29,30], atomic layer epitaxy ALE [31] and migration en hanced epitaxy MEE [32,33]. They all depend to a greater or lesser extent on the relaxation of the surface when one or other of the beam fluxes is interrupted so we will first examine that process in some detail.
with the rapid initial stage, possibly related to Ga As bond dissociation at step edges. From their Monte Carlo simulation, Clarke et al, [35] have proposed that during the fast stage, two-dimensional islands lose any “dendritic” structure acquired from the non-steady state growth phase by dissociation from sites with the lowest coordination. The slow step then results from adatom clusters evolving to form the maximum number of nearest neighbour bonds. The microscopic recovery process is dominated by the movement of atoms from surface clusters to depressions. The development of the final surface morphology achieved by relaxation will depend critically on the stage in the monolayer deposition at which growth is stopped. In studying the phenomenon using RHEED, therefore, it is clearly essential to choose diffraction conditions correctly [36]. We can demonstrate this by plotting recovery curves under fixed growth conditions and from the same termination point in the oscillation waveform, but with changing diffraction condilions, Typical results are shown in fig. 5 for growth of GaAs-(001)-2 x 4 followed by relaxation, using the [010] azimuth and varying the polar angle. It is immediately apparent that the recovery time con-
0 56
If growth is stopped by shutting off the Group temperature and Group V flux, the commonly observed III flux whilst effectmaintaining [11] is forconstant the intensity the substrate of the specular spot in the RHEED pattern to “recover” almost to its pre-growth value in a manner dependent on the precise point in the intensity oscillation at which the shutter is closed [34]. The
crease. In general terms the been “recovery” or relaxa“smoothing” increasing intensity of the surface, has i.e. terrace equated width with intion occurs in two stages (fast and slow) and obeys an expression of the form: A0 + A~exp( t/’r1) + A2 exp( t/T2), (5) where r 1 and of 1~2 the are fast the temperature dependent time constants and slow stages respectively. For GaAs(001)-2 x 4, Neave et al. [11] reported an activation energy of 2 eV associated I
=
—
—
________________________
T)me 4 atoms cm 2 Fig. 5. Intensity oscillations and recovery curves for constant growth conditions14(T5molecules 580°C; Jo~—lX10’ cm 2 S 1) as a function of polar angle 2A10 for [010] azimuth, GaAs(00l)-2x4 surface, E~— S ~As2~ Ga 12.5~, keV. beam terminated at positions marked by arrows, i.e. at approximately the same point in the oscillation for each polar angle.
B.A. Joyce
/ Evaluation of growth dynamics in MBE using electron diffraction
stants are substantially different, since as a result of the phase effect illustrated in fig. 2 similar points in the oscillation waveforms do not necessarily correspond to similar positions in the layer growth sequence. To obtain reproducible results, conditions must be specified so that an oscillation maximum occurs at monolayer completion. Fig. 5 illustrates a second very important factor in relation to surface relaxation; the amount and rate of any surface smoothing is critically dependent on the extent of monolayer completion when growth is interrupted. The nearer to perfect monolayer formation, the more rapid and more complete is the relaxation. Termination of the cation flux for periods of up to 60 s while maintaining the substrate at the growth temperature in the presence of the cation flux is known as interrupted growth [29,30] and certainly results in a lower step density and consequently smoother interfaces when it is applied to the growth of quantum wells and superlattices. It is more successful for lower binding energy, faster diffusing species, so, for example a lower temperature is required for GaAs than for AlAs or (Al, Ga)As. Tanaka and Sakaki [37] therefore used a temperature switching technique to obtain smooth top and bottom heterointerfaces in GaAs—AlAs quantum wells. The only disadvantages of the method appear to be the potential accumulation of impurities on the surface during the interruption phase and the risk of surface roughening if too high a temperature is used for the relaxation, Both ALE and MEE involve periodic interruptions of fluxes during growth. ALE is based on an alternate supply of constituent elements to the substrate surface, regulated so that a single complete layer is provided with each pulse. This is not a problem for the Group V species, since their adsorption is self-regulated by the available Group III atoms in the surface [9,10]. This is not so for the Group III atoms, however and an excess can accumulate as the free element on the surface if the amount per pulse is too large. This can be obviated by the use of RHEED, and provided correct diffraction conditions are used, exact monolayer quantities can be supplied. The results appear to indicate that “high quality material” (as
15
judged by its optical properties) can be prepared at rather lower temperatures than by conventional growth, but it should be remembered that the overall growth rate is low in ALE and it would be more valid to make a comparison with material grown conventionally at this rate and temperature. This information is not yet available. The basic mechanism seems to be a rapid relaxation process as the result of briefly interrupting growth very close to monolayer completion. The MEE process also involves the alternating supply of cation and anion fluxes and it is claimed that by reducing the surface concentration of the Group V element during the impingement of the Group III atoms, the latter’s surface migration rate is enhanced, resulting in smoother, higher quality growth at low temperatures. A better description would probably be that only very short relaxation times are required near monolayer cornpletion and the alternating supply allows this to happen. We need to consider the diffraction effects involved in MEE in rather more detail, however. It has been clearly demonstrated [32,33] that virtually undamped RHEED intensity oscillations persist throughout the entire growth period, even for relatively thick films. This is claimed to be an indication of high quality growth, in contradistinction to conventional MBE, where oscillations tend to damp relatively quickly. There is no doubt that high optical quantum wells and superlattices can be grown at significantly lower temperatures by MBE than by normal MBE, but it is essential to realize that the origin of the RHEED oscillations is quite different in the two cases. In conventional growth the oscillations are a manifestation of the changing surface morphology (step density) and the damping is indicative of a change of growth mode from two-dimensional to step propagation. In MEE the oscillations occur simply because there is a transient change in surface reconstruction from a Group III stable form to a Group V stable form with each alternate pulse and specular intensity is a strong function of surface reconstruction [38]. Growth modifications provide an interesting approach to producing smoother interfaces and lower temperature growth. The mechanisms of ALE and MEE probably relate more to enhanced
16
BA. Joyce
/ Evaluation of growth dynamics in MBE using electron diffraction
relaxation from near-complete monolayers than to
70
7. Growth of quantum well wires (QWWs)
65
Quantum well wires are low-dimensional structures with quantum confinement in two dimensions and most attempts to fabricate them have relied on high resolution lithography. The lateral dimensions achieved have been rather too large to produce significant separation of sub-band energies, however. A new approach has been made possible by control of the growth mode on vicinal planes, following the principles discussed in section 4. By restricting growth to the step propagation mode and growing alternate fractional monolayers of, say, GaAs and AlAs on a GaAs(001) substrate tilted typically 20 towards [110], vertical columns of GaAs and AlAs can be grown on the terraces which are 80 A in width. There is already evidence [39,40]of some success in the growth of these structures, although it is clear that as yet they are far from ideal. A very recent Monte Carlo simulation study [41] has indicated the possible reasons for this. In this simulation, wire quality was defined as the percentage of one cation within the wire region, ideality being represented by 100%. The optimum quality factor achieved was approximately 70% and in fig. 6 the quality is shown as a function of growth temperature for two fluxes (the actual temperature is not important, it is simply related to the chosen values of the energy terms previously discussed). These curves indicate that there is an optimum diffusion barrier for a particular temperature and flux, which highlights the intrinsic kinetic limitations of QWW growth for two cations having different mobilities. Poor quality at low temperatures results from a significant amount of two-dimensional cluster formation, whilst high temperature degradation is due to enhanced thermal fluctuations in the step edge structure. Tilted, as opposed to vertical columns [42] result when the sum of the fractional
I
~ T
ticular the adatom RHEEDmigration intensity and oscillations enhanced in MEEare inassoparciated with reconstruction effects, not the growth mode.
i t~
60
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II
I
I
________________________________
/00
/10
720
730
740
750
760
770
780
790
T (K) Fig. 6. Plots of QWW quality as a function of temperature for two cation fluxes.
layer coverage of each cation is not exactly one monolayer. Acknowledgements I am indebted to my colleagues Jim Neave, Jing Zhang, Pete Dobson, Dimitri Vvedensky, Shaun Clarke, and Karl Hugill for their contributions to the work reported here. References [1] A.Y. Cho, J. Appl. Phys. 42 (1971) 2074. [2] J.H. Neave and B.A. Joyce, J. Crystal Growth 44 (1978) 387. [3] P.K. Larsen, J.F. van der Veen, A. Mazur, J. Pollmann, J.H. Neave and B.A. Joyce, Phys. Rev. B26 (1982) 3222. [4] P.K. Larsen, J.H. Neave, J.F. van der Veen, P.J. Dobson and B.A. Joyce, Phys. Rev. B27 (1983) 4966. [5] J. Massies, P. Etienne, F. Dezaly and N.T. Linh, Surface Sci. 99 (1980) 121. [61 Joyce, iF. van derState Veen, P.K. Larsen, J.H.659. Neave and B.A. Solid Commun. 49 (1984) [7] JR. Arthur, J. Appl. Phys. 39 (1968) 4032. [8] J.R. Arthur, Surface Sci. 43 (1974) 449. [9] C.T. Foxon and B.A. Joyce, Surface Sci. 50 (1975) 434. [10] C.T. Foxon and BA. Joyce, Surface Sci. 64 (1977) 293. [11] J.H. Neave, B.A. Joyce, P.J. Dobson and N. Norton, Appl. Phys. A31 (1983) 1. [12] P.K. Larsen and P.J. Dobson, E41s., Reflection High Energy Electron Diffraction and Reflection Electron Imaging of Surfaces (Plenum, New York, 1988).
B.A. Joyce
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Evaluation of growth dynamics in MBE using electron diffraction
[13] J. Zhang, J.H. Neave, P.J. Dobson and B.A. Joyce, Appl. Phys. A42 (1987) 317. [14] B. Bolger and P.K. Larsen, Rev. Sci. Instr. 57 (1986) 1363. [15] P.K. Larsen, P.J. Dobson, J.H. Neave, B.A. Joyce, B. Bolger and J. Zhang, Surface Sci. 169 (1986) 176. [16] P.K. Larsen, G. Meyer-Ehmsen, B. Bölger and A.J. Hoeven, J. Vacuum Sci. Technol. AS (1987) 611. [17] B.A. Joyce, P.J. Dobson, J.H. Neave and J. Zhang, in: Two-Dimensional Systems: Physics and New Devices, Springer Series Solid State Sciences 67, Eds. G. Bauer, F. Kuchar and H. Heinrich (Springer, Berlin, 1986) p. 42. [18] 5. Clarke and D.D. Vvedensky, J. Appl. Phys. 63 (1988) 2272. [19] J.H. Neave, P.J. Dobson, B.A. Joyce and J. Zhang, Appl. Phys. Letters 47 (1985) 100. [20] J.M. Van Hove and P.1. Cohen, J. Crystal Growth 81 (1987) 13. [21] T. Nishinaga and K. Cho, Japan. J. Appl. Phys. 27 (1988) L12. [22] J.D. Weeks, G.H. Gilmer and K.A. Jackson, J. Chem. Phys. 65 (1976) 71. [23] A. Madhukar, Surface Sci. 132 (1983) 344. [24] J. Singh and A. Madhukar, J. Vacuum Sci. Technol. B3 (1985) 540. [25] S.V. Ghaisas and A. Madhukar, J. Vacuum Sci. Technol. B3 (1985) 540. [26] S.V. Ghaisas and A. Madhukar, Phys. Rev. Letters 56 (1986) 1066. [27] S. Clarke and D.D. Vvedensky, Phys. Rev. Letters 58 (1987) 2235. [28] 5. Clarke and D.D. Vvedensky, J. Appl. Phys. 63 (1988) 2272.
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[29] A. Madhukar, T.C. Lee, M.Y. Yen, P. Chen, J.Y. Kim, S.V. Ghaisas and PG. Newman, Appl. Phys. Letters 46 (1985) 1148. [30] H. Sakaki, M. Tanaka and J. Yoshino, Japan. J. Appl. Phys. 24 (1985) L417. [31] F. Briones, L. Gonzalez, M. Recio and M. Vaquez, Japan. J. Appl. Phys. 26 (1987) L1125. [32] Y. Horikoshi, M. Kawashima and H. Yamaguchi, Japan. J. Appl. Phys. 25 (1986) L868. [33] Y. Horikoshi, M. Kawashima and H. Yamaguchi, Japan. J. Appi. Phys. 27 (1988) 169. [34] B.F. Lewis, F.J. Grunthaner, A. Madhukar, T.C. Lee and R. Fernandez, J. Vacuum Sci. Technol. B3 (1985) 1317. [35] 5. Clarke, D.D. Vvedensky and M.W. Ricketts, J. Crystal Growth 95 (1989) 28. [36] B.A. Joyce, J. Zhang, J.H. Neave and P.J. Dobson. Appl. Phys. A45 (1988) 255. [37] M. Tanaka and H. Sakaki, Superlattices Microstruct. 4 (1988) 237. [38] P.K. Larsen, PJ. Dobson, J.H. Neave, B.A. Joyce, B. Bolger and J. Zhang, Surface Sci. 169 (1986) 176. [39] M. Tanaka and H. Sakaki, Japan. J. Appl. Phys. 27 (1988) L2025. [40] M. Tsuchiya, J.M. Gaines, R.H. Yan, R.J. Simes, P.O. Holtz, L.A. Coldren and P.M. Petroff, Phys. Rev. Letters 62 (1989) 466. [41] K.J. Hugill, S. Clarke, D.D. Vvedensky and B.A. Joyce, J. Appl. Phys. 66 (1989) 3415. [42] J.M. Gaines, P.M. Petroff, H. Kroemer, R.J. Simes and J.H. English, J. Vacuum Sci. Technol. B6 (1988) 1378.
9
THE EVALUATION OF GROWTH DYNAMICS IN MBE USING ELECTRON DIFFRACTION B.A. JOYCE University of London Interdisciplinary Research Centre for Semiconductor Materials, The Blackett Laboratory, Imperial College, Prince Consort Road, London SW7 2BZ, UK
Reflection high energy electron diffraction (RHEED) has proved to be a very versatile technique for growth and surface studies of epitaxial metal and semiconductor thin films prepared by molecular beam epitaxy (MBE). The combination of the forward scattering geometry of RHEED with the near-normal incidence of the atomic and molecular beams on to the substrate enables diffraction features to be monitored continuously during growth. This paper is concerned with the application of RHEED intensity measurements, especially temporal oscillations, to the study of growth dynamics in MBE, with particular emphasis on III V compound semiconductors.
1. Introduction
2. Observation of intensity oscillations diffraction conditions
One of the many advantages of molecular beam epitaxy (MBE) is the extent to which in-situ diagnostics can be applied. The UHV environment means that many techniques developed for surface science can be used directly. Surface crystallographic [1,2] and electronic [3,4] structure, cornposition [5,6] and surface reaction kinetics [7—10] have all been investigated. Of particular interest for crystal growth is the application of RHEED to studies of dynamic and kinetic processes in epitaxial thin film fonnation. Since the first detailed report [11], the RHEED intensity oscillation technique has received much
Details of intensity measurements have been given in several publications [11,13]. In most cases only a single feature of the diffraction pattern is monitored, usually the specular spot on the 00 rod, but intensity variations over the whole pattern can be followed by TV techniques [14]. Fig. 1 shows oscillations from the specular spot on the 00 rod as a function of polar angle in [110] and [010] azimuths at a primary energy of 12.5 keV. The growing film was GaAs on a GaAs(001)2 X 4 reconstructed surface, maintained at a ternperature of 580°C, a Ga flux of 1 x iO’~atoms cm 2 1 and an arsenic (As 2) flux of 2>< were 1014 2s~’.These growth conditions molecules cm~ invariant so the different oscillation waveforms can only be attributed to diffraction effects. The reasons for this are rather complex and have been dealt with previously in a number of publications [12,13], so here I will only summarize the salient features. The important point is that these effects must be understood sufficiently well that they can be deconvolved from those associated with growth processes. In general terms the waveform variations shown in fig. 1 derive from the many diffraction processes which contribute to the measured intensity. A single scattering kinematic approximation is not
attention (see ref.It [12] a rangewhich of summary and review articles). is a for technique is remarkably simple to apply, but is difficult to interpret correctly and can be misleading in the hands of the unwary. The basic observation is of a periodic intensity variation during growth, the period corresponding precisely to the growth of a single atomic or molecular layer. In this paper I will first discuss the origin of the temporal intensity variations in relation to both growth and diffraction and then indicate how the technique can be applied to studies of growth kinetics and dynamics and the development of process modifications to MBE. 0022-0248/90/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
—
effect of
10
BA. Joyce
/ Evaluation of growth dynamics in MBE using electron diffraction
b
~ 110]
a
r
010
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0
1 Angl,
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2 tin pd,nce beg
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4
of polar hg. 2. Phase angle relationship for [110],of[0101 RHEED and oscillations [110] azimuths as a function from a growing GaAs(001)-2
x4
reconstructed surface. The growth
to reach the conditions were second as time for oscillation fig. of a1.complete Phase minimum is period. defined normalized as the timebytaken the
2 6~
so their position remains fixed to the shadow edge
—
Time Fig. 1. RHEED intensity oscillations of the specular spot on the 00 rod in [110] and [010] azimuths from a growing GaAs(001)-2X4 reconstructed surface at different polar angles; primary beam energy 12.5 keV; 7~= 5800 C; Joa = lx 1014 atoms cm 2 s 1, ‘As 2 = 2 x l0~~ molecules cm 2 1
usually adequate and other factors must be included in the analysis of diffracted beam profiles, since all detectors integrate over some region of reciprocal space. Multiple scattering effects frequently occur, especially those related to surface wave resonances and beam emergence conditions resulting from the RHEED geometry [15]. Some thermal diffuse scattering will always be present, although its contribution to the total intensity may be small. This of course is in addition to the normal diffuse intensity due to the existence of finite regions of the surface at different levels (terraces separated by steps). There is also a significant inelastic cornponent of the scattered intensity and in particular strong Kikuchi features can occur [13,16]. They are incoherent with respect to the primary beam
as the polar angle is varied. The variation of intensity with the surface morphology changes which occur during growth is different for the different diffraction processes, so the phase and amplitude of the oscillations will depend on the proportion of each of the processes integrated by the detector for particular diffraction conditions. It is this which leads to the different waveforms. Two points of particular importance can be singled out. The first, illustrated in fig. 2, is that an intensity maximum may not correspond to monolayer completion (in the illustration this is only true for an ordinate value of 1.5) and the second is that double period oscillations can occur purely as the result of diffraction effects in which intensity changes of different processes are out of phase. With this background we will examine the application of the technique to studies of growth dynamics.
3. Growth mode It is now universally accepted that the basic origin of the oscillating intensity behaviour is the changing surface topography (step density) associated with two-dimensional layer-by-layer growth.
B.A. Joyce
/
Evaluation of growth dynamics in MBE using electron diffraction
That the steady state period corresponds precisely to the formation of a monolayer is also without serious question, although the period of the first oscillation may be different, depending both on the diffraction processes being sampled and transient surface reconstruction changes when growth is initiated [17]. It is also important to emphasize that RHEED is sensitive to step density rather than surface coverage because of the multiple and diffuse scattering components in the measured intensity. It is only in the kinematic approximation that coverage is the dominant factor in the intensity variation, In addition to the periodic variation of the intensity, the observed damping of the oscillations also provides valuable information on the growth mode. The simplest interpretation is that is represents a transition from two-dimensional growth to step propagation, the final state of complete damping being reached when the mean terrace width created by 2D growth is equal to the mean surface migration length of an adatom. This defines the initial and final states, but does not explain the gradual decrease in intensity between them. This occurs principally because regions of the surface separated by distances greater than the mean adatom diffusion length, although statistically independent, are nevertheless sampled by the same RHEED beam. Differences in the stage of growth can therefore develop, even though each region still grows in a layer-by-layer mode, The differences lead to a steady state mean intensity produced by an incoherent superpositioning of individual oscillatory step densities and the rate of decay is then an indication of the effective migration length of adatoms, or equivalently, the step density. A final point on growth mode concerns the dependence of the intrinsic quality of material on its growth mode. There has been a definite tendency to associate the presence and persistence of RHEED intensity oscillations with material of higher quality, as judged by its optical and electrical properties, than that grown without oscillations being present. The implicit assumption, therefore, is that layer-by-layer growth produces material superior to that grown by a step propagation mechanism, even though the transition from
11
one mode to the other is quite rapid, especially at high temperatures. There seems to be no justification for this assumption, although where interfaces are concerned their abruptness is likely to be growth mode dependent.
4. Surface migration Irrespective of the model details, significant adatom migration is a necessary condition for layer-by-layer growth. With III V compounds it is cation migration which is the determining factor; changes in the anion surface concentration only influence rates, not mechanisms, at least over the range of growth conditions used in practice [18]. We are simply concerned with the migration of a cation on the substrate surface in a relatively weakly bound precursor state before it is incorporated into a lattice site. Attempts to obtain reliable values for the diffusion parameters have only met with limited success, however. The basic experimental approach [19,20] utilizes growth on a vicinal surface for which the degree of misorientation and consequently the terrace width is known. The diffusion length can then be measured as a function of growth parameters (temperature, flux and flux ratio) by observing the change of growth mode from 2D layer-by-layer on the terraces to step propagation, depending on the presence or absence respectively of RHEED intensity oscillations. The point at which they just disappear as either the flux or temperature changes then gives the diffusion length (which is equated to the terrace width) for those conditions. The principle is illustrated in fig. 3. Although conceptually simple, there are difficult interpretational problems which have not yet been properly solved. An important factor is that the measurements are kinetic, obtained under conditions far from equilibrium, so any values obtained will depend on the particular growth conditions used and should not be considered as fundamental diffusion constants. If it is assumed that surface migration is isotropic, we can write: =
2 D’r,
(1)
12
B.A. Joyce / Evaluation ofgrowth dynamics in MBE using electron diffraction
an upper Nishinaga and Cho [21] proposed an limit. alternative approach based onhave classical critical nuclei appropriate to a thermodynamic nucleation treatment. For theory, typical which MBE therefore conditions, requires however, large the critical nucleus will be a single adatom, so the validity of such a thermodynamic approach must also be questioned. The second limitation concerns the evaluation of energy terms. Even if T is correctly equated with monolayer deposition rate, the activation enpendence D is the sum of the terms shown ergy valueofdetermined from the two temperature de-
T4
Incident beam
XE
t
Incident
beam Fig. 3. Illustration of the principle of the vicinal plane method, showing the change in RHEED information as the growth mode changes from step propagation to 2D nucleation,
where x represents the mean displacement, i.e. terrace width, i• is the surface lifetime in the mobile precursor state and D a temperature dependent diffusion coefficient, If ED is the sitedependent energy barrier to diffusion, then: D = D0 exp( ED/kT), —
(2)
where D0 corresponds to a vibrational frequency. This energy barrier to diffusion is the combination of a surface barrier plus a term representing bonds made to nearest-neighbour atoms, E~: ED
E~+ E~.
(3)
This simple analysis has two major limitations, The first is the choice of r, the surface lifetime, Conventionally [19,20] it has been equated to the monolayer deposition rate: = N/J (4) where N~is the number of surface sites per unit area and J is the cation flux. This is certainly an oversimplification however and at best represents
in eq. (3). For Ga on GaAs(O01)-2 X 4, ED was measured to be 1.3 eV [19], which means that the surface barrier will be significantly smaller. This is reasonable, if only qualitative and helps to confirm the importance of surface migration in 2D growth. In spite of these quantitative difficulties, the basic concept of a layer-by-layer growth mode continuing until the adatom (cation) migration length because less than the mean terrace width, when step propagation becomes the dominant mode, seems established. It can be further substantiated by the growth of beterostructures and we can distinguish two cases: (i) each region is sufficiently thin that oscillations are still present when the interface is grown, i.e. a steady state terrace width distribution has not been attained and (ii) thicker structures, where the oscillation amplitude has damped effectively to zero before the heteroj unction is formed. Case (i) is illustrated in fig. 4a for two different diffraction conditions and with the interface formed at various positions in the monolayer growth cycle, as indicated by the arrows. It is immediately apparent that apart from the change in period attributed to the increased Group III flux in the (Al, Ga)As regions, there is virtually no effect of an interface on oscillation behaviour for this situation. For case (ii), however, illustrated in fig. 4b, where the oscillations in each composition region have damped out, they immediately restart at a GaAs—(Al, Ga)As interface, consistent with the shorter migration distance of Al producing a new, shorter terrace width distribution. At an (Al, Ga)As—GaAs interface, where the migration
BA. Joyce
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Evaluation of growth dynamics in MBE using electron diffraction
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03G~07As
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of 104. (a) Fig. andIntensity 1.6 o. Interfaces oscillations formed across Time before ~— GaAs oscillations (Al, Ga)As—GaAs have damped. interfaces;(b)7~ Intensity = 5800 C,oscillations Ti (001) me surfaces, — across [110] GaAs—(Al, azimuth atGa)As polar angles GaAs interfaces; T5—600°Cand 650°C respectively, off [110] azimuth at a polar angle of 10. Interfaces formed when oscillations are almost fully damped.
length of Ga is greater than the mean terrace width on the (Al, Ga)As, oscillations do not restart since the growth mode under such circumstances is dominated by step propagation.
5. Computer simulation of MBE growth dynamics and kinetics The basis of simulation studies is the so-called solid-on-solid (SOS) model of Weeks, Gilmer and Jackson [22],but Madhukar and co-workers [23,24] produced the first calculations directed specifically at the growth of compound semiconductors, They were initially aimed at determining the growth front morphology, i.e. the number of molecular layers over which growth is distributed and then extended to an investigation of the relationship between anion incorporation kinetics and cation migration rates [25,26].Clarke and Vvedensky [27,28] have adopted a simpler approach by assuming that the anion incorporation step is never rate limiting over the usual range of growth condilions, which is almost certainly valid. They then
consider only two events: deposition and surface migration of monatomic species. The growth process is represented by a Monte Carlo simulation, which describes events by rate equations and calculates the probability of their occurrence as the product of a rate equation and a time constant. To compare results of such a simulation with experimental observations of RHEED intensity, the step density of the simulated growth front has been chosen as the optimum parameter. It is evaluated by counting the number of unsaturated nearest neighbour bonds parallel to the surface and shows excellent agreement with recorded RHEED intensity oscillations, especially in damping behaviour and growth on vicinal surfaces [28]. An alternative approach to comparison with experiment is to calculate from the simulation the intensity of the specular RHEED beam within the kinematic approximation [24]. This treatment correctly predicts the oscillation period, but there is no decay towards the mean in the intensities at half-layer completion, contrary to observation. The reason is that even if diffraction conditions could
14
BA. Joyce
/ Evaluation of growth dynamics in MBE using electron diffraction
be chosen such that the kinematic approach were valid, it is only sensitive to surface coverage, not to the arrangement of adatoms on the surface and therefore not to the step density or distribution. Consequently, it fails worst in the high step density regime at half-layer completion.
6. Surface relaxation and growth technique modifications Several modifications to conventional MBE growth have recently been proposed for growing more perfect” interfaces in heterostructures, quantum wells and superlattices. Perfection in this context is defined as maximizing areas of single composition in the interface plane, or minimizing the number of molecular layers normal to the plane in which compositional variations occur. The aim may also be to obtain useful properties from structures grown at lower temperatures than could be achieved by conventional growth. The modifications include growth interruption [29,30], atomic layer epitaxy ALE [31] and migration en hanced epitaxy MEE [32,33]. They all depend to a greater or lesser extent on the relaxation of the surface when one or other of the beam fluxes is interrupted so we will first examine that process in some detail.
with the rapid initial stage, possibly related to Ga As bond dissociation at step edges. From their Monte Carlo simulation, Clarke et al, [35] have proposed that during the fast stage, two-dimensional islands lose any “dendritic” structure acquired from the non-steady state growth phase by dissociation from sites with the lowest coordination. The slow step then results from adatom clusters evolving to form the maximum number of nearest neighbour bonds. The microscopic recovery process is dominated by the movement of atoms from surface clusters to depressions. The development of the final surface morphology achieved by relaxation will depend critically on the stage in the monolayer deposition at which growth is stopped. In studying the phenomenon using RHEED, therefore, it is clearly essential to choose diffraction conditions correctly [36]. We can demonstrate this by plotting recovery curves under fixed growth conditions and from the same termination point in the oscillation waveform, but with changing diffraction condilions, Typical results are shown in fig. 5 for growth of GaAs-(001)-2 x 4 followed by relaxation, using the [010] azimuth and varying the polar angle. It is immediately apparent that the recovery time con-
0 56
If growth is stopped by shutting off the Group temperature and Group V flux, the commonly observed III flux whilst effectmaintaining [11] is forconstant the intensity the substrate of the specular spot in the RHEED pattern to “recover” almost to its pre-growth value in a manner dependent on the precise point in the intensity oscillation at which the shutter is closed [34]. The
crease. In general terms the been “recovery” or relaxa“smoothing” increasing intensity of the surface, has i.e. terrace equated width with intion occurs in two stages (fast and slow) and obeys an expression of the form: A0 + A~exp( t/’r1) + A2 exp( t/T2), (5) where r 1 and of 1~2 the are fast the temperature dependent time constants and slow stages respectively. For GaAs(001)-2 x 4, Neave et al. [11] reported an activation energy of 2 eV associated I
=
—
—
________________________
T)me 4 atoms cm 2 Fig. 5. Intensity oscillations and recovery curves for constant growth conditions14(T5molecules 580°C; Jo~—lX10’ cm 2 S 1) as a function of polar angle 2A10 for [010] azimuth, GaAs(00l)-2x4 surface, E~— S ~As2~ Ga 12.5~, keV. beam terminated at positions marked by arrows, i.e. at approximately the same point in the oscillation for each polar angle.
B.A. Joyce
/ Evaluation of growth dynamics in MBE using electron diffraction
stants are substantially different, since as a result of the phase effect illustrated in fig. 2 similar points in the oscillation waveforms do not necessarily correspond to similar positions in the layer growth sequence. To obtain reproducible results, conditions must be specified so that an oscillation maximum occurs at monolayer completion. Fig. 5 illustrates a second very important factor in relation to surface relaxation; the amount and rate of any surface smoothing is critically dependent on the extent of monolayer completion when growth is interrupted. The nearer to perfect monolayer formation, the more rapid and more complete is the relaxation. Termination of the cation flux for periods of up to 60 s while maintaining the substrate at the growth temperature in the presence of the cation flux is known as interrupted growth [29,30] and certainly results in a lower step density and consequently smoother interfaces when it is applied to the growth of quantum wells and superlattices. It is more successful for lower binding energy, faster diffusing species, so, for example a lower temperature is required for GaAs than for AlAs or (Al, Ga)As. Tanaka and Sakaki [37] therefore used a temperature switching technique to obtain smooth top and bottom heterointerfaces in GaAs—AlAs quantum wells. The only disadvantages of the method appear to be the potential accumulation of impurities on the surface during the interruption phase and the risk of surface roughening if too high a temperature is used for the relaxation, Both ALE and MEE involve periodic interruptions of fluxes during growth. ALE is based on an alternate supply of constituent elements to the substrate surface, regulated so that a single complete layer is provided with each pulse. This is not a problem for the Group V species, since their adsorption is self-regulated by the available Group III atoms in the surface [9,10]. This is not so for the Group III atoms, however and an excess can accumulate as the free element on the surface if the amount per pulse is too large. This can be obviated by the use of RHEED, and provided correct diffraction conditions are used, exact monolayer quantities can be supplied. The results appear to indicate that “high quality material” (as
15
judged by its optical properties) can be prepared at rather lower temperatures than by conventional growth, but it should be remembered that the overall growth rate is low in ALE and it would be more valid to make a comparison with material grown conventionally at this rate and temperature. This information is not yet available. The basic mechanism seems to be a rapid relaxation process as the result of briefly interrupting growth very close to monolayer completion. The MEE process also involves the alternating supply of cation and anion fluxes and it is claimed that by reducing the surface concentration of the Group V element during the impingement of the Group III atoms, the latter’s surface migration rate is enhanced, resulting in smoother, higher quality growth at low temperatures. A better description would probably be that only very short relaxation times are required near monolayer cornpletion and the alternating supply allows this to happen. We need to consider the diffraction effects involved in MEE in rather more detail, however. It has been clearly demonstrated [32,33] that virtually undamped RHEED intensity oscillations persist throughout the entire growth period, even for relatively thick films. This is claimed to be an indication of high quality growth, in contradistinction to conventional MBE, where oscillations tend to damp relatively quickly. There is no doubt that high optical quantum wells and superlattices can be grown at significantly lower temperatures by MBE than by normal MBE, but it is essential to realize that the origin of the RHEED oscillations is quite different in the two cases. In conventional growth the oscillations are a manifestation of the changing surface morphology (step density) and the damping is indicative of a change of growth mode from two-dimensional to step propagation. In MEE the oscillations occur simply because there is a transient change in surface reconstruction from a Group III stable form to a Group V stable form with each alternate pulse and specular intensity is a strong function of surface reconstruction [38]. Growth modifications provide an interesting approach to producing smoother interfaces and lower temperature growth. The mechanisms of ALE and MEE probably relate more to enhanced
16
BA. Joyce
/ Evaluation of growth dynamics in MBE using electron diffraction
relaxation from near-complete monolayers than to
70
7. Growth of quantum well wires (QWWs)
65
Quantum well wires are low-dimensional structures with quantum confinement in two dimensions and most attempts to fabricate them have relied on high resolution lithography. The lateral dimensions achieved have been rather too large to produce significant separation of sub-band energies, however. A new approach has been made possible by control of the growth mode on vicinal planes, following the principles discussed in section 4. By restricting growth to the step propagation mode and growing alternate fractional monolayers of, say, GaAs and AlAs on a GaAs(001) substrate tilted typically 20 towards [110], vertical columns of GaAs and AlAs can be grown on the terraces which are 80 A in width. There is already evidence [39,40]of some success in the growth of these structures, although it is clear that as yet they are far from ideal. A very recent Monte Carlo simulation study [41] has indicated the possible reasons for this. In this simulation, wire quality was defined as the percentage of one cation within the wire region, ideality being represented by 100%. The optimum quality factor achieved was approximately 70% and in fig. 6 the quality is shown as a function of growth temperature for two fluxes (the actual temperature is not important, it is simply related to the chosen values of the energy terms previously discussed). These curves indicate that there is an optimum diffusion barrier for a particular temperature and flux, which highlights the intrinsic kinetic limitations of QWW growth for two cations having different mobilities. Poor quality at low temperatures results from a significant amount of two-dimensional cluster formation, whilst high temperature degradation is due to enhanced thermal fluctuations in the step edge structure. Tilted, as opposed to vertical columns [42] result when the sum of the fractional
I
~ T
ticular the adatom RHEEDmigration intensity and oscillations enhanced in MEEare inassoparciated with reconstruction effects, not the growth mode.
i t~
60
I ç5
•
F=0.4ML/s F—Q.6ML/s
II
I
I
________________________________
/00
/10
720
730
740
750
760
770
780
790
T (K) Fig. 6. Plots of QWW quality as a function of temperature for two cation fluxes.
layer coverage of each cation is not exactly one monolayer. Acknowledgements I am indebted to my colleagues Jim Neave, Jing Zhang, Pete Dobson, Dimitri Vvedensky, Shaun Clarke, and Karl Hugill for their contributions to the work reported here. References [1] A.Y. Cho, J. Appl. Phys. 42 (1971) 2074. [2] J.H. Neave and B.A. Joyce, J. Crystal Growth 44 (1978) 387. [3] P.K. Larsen, J.F. van der Veen, A. Mazur, J. Pollmann, J.H. Neave and B.A. Joyce, Phys. Rev. B26 (1982) 3222. [4] P.K. Larsen, J.H. Neave, J.F. van der Veen, P.J. Dobson and B.A. Joyce, Phys. Rev. B27 (1983) 4966. [5] J. Massies, P. Etienne, F. Dezaly and N.T. Linh, Surface Sci. 99 (1980) 121. [61 Joyce, iF. van derState Veen, P.K. Larsen, J.H.659. Neave and B.A. Solid Commun. 49 (1984) [7] JR. Arthur, J. Appl. Phys. 39 (1968) 4032. [8] J.R. Arthur, Surface Sci. 43 (1974) 449. [9] C.T. Foxon and B.A. Joyce, Surface Sci. 50 (1975) 434. [10] C.T. Foxon and BA. Joyce, Surface Sci. 64 (1977) 293. [11] J.H. Neave, B.A. Joyce, P.J. Dobson and N. Norton, Appl. Phys. A31 (1983) 1. [12] P.K. Larsen and P.J. Dobson, E41s., Reflection High Energy Electron Diffraction and Reflection Electron Imaging of Surfaces (Plenum, New York, 1988).
B.A. Joyce
/
Evaluation of growth dynamics in MBE using electron diffraction
[13] J. Zhang, J.H. Neave, P.J. Dobson and B.A. Joyce, Appl. Phys. A42 (1987) 317. [14] B. Bolger and P.K. Larsen, Rev. Sci. Instr. 57 (1986) 1363. [15] P.K. Larsen, P.J. Dobson, J.H. Neave, B.A. Joyce, B. Bolger and J. Zhang, Surface Sci. 169 (1986) 176. [16] P.K. Larsen, G. Meyer-Ehmsen, B. Bölger and A.J. Hoeven, J. Vacuum Sci. Technol. AS (1987) 611. [17] B.A. Joyce, P.J. Dobson, J.H. Neave and J. Zhang, in: Two-Dimensional Systems: Physics and New Devices, Springer Series Solid State Sciences 67, Eds. G. Bauer, F. Kuchar and H. Heinrich (Springer, Berlin, 1986) p. 42. [18] 5. Clarke and D.D. Vvedensky, J. Appl. Phys. 63 (1988) 2272. [19] J.H. Neave, P.J. Dobson, B.A. Joyce and J. Zhang, Appl. Phys. Letters 47 (1985) 100. [20] J.M. Van Hove and P.1. Cohen, J. Crystal Growth 81 (1987) 13. [21] T. Nishinaga and K. Cho, Japan. J. Appl. Phys. 27 (1988) L12. [22] J.D. Weeks, G.H. Gilmer and K.A. Jackson, J. Chem. Phys. 65 (1976) 71. [23] A. Madhukar, Surface Sci. 132 (1983) 344. [24] J. Singh and A. Madhukar, J. Vacuum Sci. Technol. B3 (1985) 540. [25] S.V. Ghaisas and A. Madhukar, J. Vacuum Sci. Technol. B3 (1985) 540. [26] S.V. Ghaisas and A. Madhukar, Phys. Rev. Letters 56 (1986) 1066. [27] S. Clarke and D.D. Vvedensky, Phys. Rev. Letters 58 (1987) 2235. [28] 5. Clarke and D.D. Vvedensky, J. Appl. Phys. 63 (1988) 2272.
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[29] A. Madhukar, T.C. Lee, M.Y. Yen, P. Chen, J.Y. Kim, S.V. Ghaisas and PG. Newman, Appl. Phys. Letters 46 (1985) 1148. [30] H. Sakaki, M. Tanaka and J. Yoshino, Japan. J. Appl. Phys. 24 (1985) L417. [31] F. Briones, L. Gonzalez, M. Recio and M. Vaquez, Japan. J. Appl. Phys. 26 (1987) L1125. [32] Y. Horikoshi, M. Kawashima and H. Yamaguchi, Japan. J. Appl. Phys. 25 (1986) L868. [33] Y. Horikoshi, M. Kawashima and H. Yamaguchi, Japan. J. Appi. Phys. 27 (1988) 169. [34] B.F. Lewis, F.J. Grunthaner, A. Madhukar, T.C. Lee and R. Fernandez, J. Vacuum Sci. Technol. B3 (1985) 1317. [35] 5. Clarke, D.D. Vvedensky and M.W. Ricketts, J. Crystal Growth 95 (1989) 28. [36] B.A. Joyce, J. Zhang, J.H. Neave and P.J. Dobson. Appl. Phys. A45 (1988) 255. [37] M. Tanaka and H. Sakaki, Superlattices Microstruct. 4 (1988) 237. [38] P.K. Larsen, PJ. Dobson, J.H. Neave, B.A. Joyce, B. Bolger and J. Zhang, Surface Sci. 169 (1986) 176. [39] M. Tanaka and H. Sakaki, Japan. J. Appl. Phys. 27 (1988) L2025. [40] M. Tsuchiya, J.M. Gaines, R.H. Yan, R.J. Simes, P.O. Holtz, L.A. Coldren and P.M. Petroff, Phys. Rev. Letters 62 (1989) 466. [41] K.J. Hugill, S. Clarke, D.D. Vvedensky and B.A. Joyce, J. Appl. Phys. 66 (1989) 3415. [42] J.M. Gaines, P.M. Petroff, H. Kroemer, R.J. Simes and J.H. English, J. Vacuum Sci. Technol. B6 (1988) 1378.