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Current understanding and applications of the RHEED intensity oscillation technique
Journal of Crystal Growth 81(1987)1—8 North-Holland, Amsterdam
1
CURRENT UNDERSTANDING AND APPLICATIONS OF ThE RHEED INTENSITY OSCILLATION TECHNIQUE P.J. DOBSON, B.A. JOYCE and J.H. NEAVE Philips Research Laboratories, Redhill, Surrey RHI 5HA, UK
and J. ZHANG Physics Department, Imperial College, Prince Consort Road, London S W7 2BZ, UK
The problem of reflection high energy electron diffraction (RHEED) and electron scattering from smooth and growing surface is briefly reviewed. Evidence is given that strong electron beam penetration and multiple scattering effects are present under the conditions used to observe intensity oscillations in RHEED during growth by molecular beam epitaxy (MBE). A survey is made of the predominant RHEED oscillation features, i.e. damping, increases in amplitude, transient behaviour, phase differences and the appearance of harmonics. These features can be related to growth and diffraction processes.
1. Introduction Reflection high energy electron diffraction (RHEED) has become the standard technique for monitoring the structure of layers grown by molecular beam epitaxy (MBE) because the geometry of the technique is ideally suited to MBE and because the diffraction patterns contain a wealth of useful information which can be related to the structure of the layers. For example, in addition to the surface unit cell dimensions, the presence of roughness, steps, facets and disorder due to antiphase boundaries, etc. can be determined. One of the most significant and exciting observations of recent years is that when growth is initiated, the intensity of RHEED features shows an oscillatory behaviour which is directly related to the growth rate [1—5].This has now become routinely used to calibrate beam fluxes and control alloy composition and the thickness of quantum wells and superlattice layers [6—8].Data relating to surface diffusion [9] and crystal growth mechanisms [10—12]and dopant incorporation [13] have also been obtained from studies of RHEED intensity oscillations.
It is now becoming apparent that there are important differences in the interpretations of these intensity oscillations being offered by different research groups. These differences need to be resolved if we are to optimise the use of this phenomenon. Here, we will first of all briefly survey the electron diffraction and scattering aspect of the problem, before proceeding to specific details of RHEED intensity oscillations which can be related to crystal growth.
2. Electron diffraction and scattering In the situations which are usually employed in MBE a high energy beam of electrons in the range 5 to 40 keY is directed at a low angle (1°to 3°)to the surface. the de Broglie wavelength is therefore in the range 0.17 to 0.06 A and the penetration of the beam into the surface is low, being restricted to the outermost few atomic layers. Most geometrical aspects of the diffraction pattern can be interpreted on the basis of a limited penetration kinematic scattering model [14—16].A detailed analysis of the diffracted beam intensity, particu-
0022-0248/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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RHEED intensity oscillation technique
larly the way in which this changes with incident angle, should in principle permit us to determine the complete structure of the surface unit cell. Whilst this has not yet been achieved for a reconstructed semiconductor surface, sets of data for GaAs (001) have recently been published [17] and the theoretical treatment now exists [18]. One fact is already very clear from this work, i.e. the incident beam does penetrate the solid and very strong multiple scattering (i.e. dynamical in the diffraction sense) effects dominate the diffraction process. This is best illustrated by reference to fig. 1 which shows how the specular beam intensity varies with incident angle for three different azimuths of the GaAs (001) 2 x 4 arsenic stable surface. If the scattering was a simple kinematic process the results for the three azimuths would all be similar and show maxima only at the Bragg conditions for the (001) set of crystal planes.
A similar conclusion that the scattering was dynamical in origin was reached in an earlier study of the azimuthal variation in the intensity of static and growing surfaces [19]. These dynamical or multiple scattering processes transfer the scattered intensity between beams, e.g. between the fractional order beams and the specular beam or between the surface resonances and specular beam. There are also strong enhancements of intensity probably of dynamical origin at the positions in diffraction patterns where Kikuchi lines cross other diffraction features. These dynamical effects mean that we have to be cautious in our interpretation of the intensity and apparent width of diffracted features. The limited penetration of electron beams also means that we have to take account of refraction effects in our estimates of the Bragg conditions and the position of Kikuchi lines. This is most conveniently done by using the relationship between angles outside the solid 0~to angles inside 0~,measured with respect to the surface: /2
cos 00
_______
01 10
io2 C r
4
10
(1— V0/E)’ cos where V~is a negative quantity termed the “inner potential” which represents the gain in potential energy that an electron of kinetic energy E undergoes when it enters the solid. For most of the Group —11 IY and semiconductors lies in the range to III—Y 15 eY and refractionV0 effects are =
—
>,
very significant angles of less than of 5°.the term There is an at unfortunate misuse “Bragg condition” which has developed with re-
-0
0 ________
~Ca) In ios
1io~ 0
a) > 02
t 10 ~0l 10 I • I I 1 2 3 4 Angle of incidence ldegrees) Fig. 1. Specular beam intensity as a function of angle of incidence for the GaAs (001) 2 X 4 surface for the three principal azimuths. Primary beam energy = 12.5 keV [17].
spect toand RHEED and MBE. Cohen and[10—12]use co-workers tive [20.21] the term interference to Madhukar meanfor the electrons condition and co-workers scattered at which construcby adjacent step terraces occurs. Under such circumstances it is not necessary to use any refraction correction it is assumedofcontrary to expectations that since no penetration the beam occurs. However, this condition is not strictly the Bragg condition familiar to crystallography and use of the term should be discouraged. This is also the problem which is central to the description of RHEED intensity oscillations. We have on the one hand the intuitively simple picture of Lent and Cohen [20], in which the varia-
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RHEED intensity oscillation technique
tion of intensity results from the interference of beams reflected from step terraces. On the other hand we have the more complicated picture of strong multiple scattering effects modifying the changes in scattering from a varying sted edge density. We believe firmly in the latter and dispute whether there is any firm evidence for the two-layer interference model. We have sought conditions to provide such evidence [22] but out results were contrary to the expectations of two-layer interference. Furthermore, at the low angles of mcidence employed, one expects that steps 2.83 A in height will strongly scatter electrons of de Broglie wavelength 0.1 A. We therefore adopt the view that RHEED intensity oscillations result from step edge scattering, and can therefore give some indication of the step density. The variations which occur with changes of angle of incidence and azimuth must result from a combination of multiple scattering effects and possibly the preferred step directions. A rigorous multiple scattering calculation for RHEED intensities from surfaces with varying step densities has predicted oscillations [38]. Further evidence for the multiple scattering nature of the problem comes from the observation that the oscillations of intensity of different beams in a diffraction pattern often exhibit a complex phase relationship, i.e. the oscillation of the specular beam is often ~r out of phase with the oscillation of other beams. This aspect of the problem will be dealt with in more detail in a forthcoming publication [23]. —
•
3
reached when oscillations become less apparent or absent. In a recent study, Neave et al. [9] used the disappearance of RHEED oscillations to obtain a measurement of the surface diffusion length of gallium on a terraced GaAs (001) 2 X 4 reconstructed surface. The electron beam was directed parallel to the step edges. If the substrate temperature and incident fluxes were such that the surface diffusion length was less than the mean terrace length, then new growth centres appear on the terraces and these are accompanied by the customary periodic changes of RHEED intensity. The substrate temperature was increased until oscillations ceased, as shown in fig. 2. From these results a surface diffusion energy of 1.3 ±0.1 eV was obtained. Note, however, that at T~>5900 C in this particular experiment, whilst growth occurs it does not result in RHEED oscillations. Under these conditions, growth proceeds by the addition of atoms to the step edges. Absence of RHEED oscillations when growing material may indeed be a desirable situation from the standpoint of electrical and optical quality, since it implies that growth is occurring at step edges and would give
—
2.3~~10atom cn-c i~(°C) 598 596
590°C
588
3. Growth effects and RHEED oscillations Some of the important features that are seen in studies of RHEED intensity oscillations will now be described and discussed.
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.
~
560
550 540
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3.1. Absence of oscillations The occurrence of variations in the intensity with growth has become so familiar that it is timely to examine the conditions under which no such oscillations are seen. Generally, when the substrate temperature is increased, a condition is
Time
—
Fig. 2. An example of the transition from oscillations to a constant response as a function of substrate temperature, with constant gallium flux 19].
P.J. Dobson et a!. / RHEED intensity oscillation technique
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fewer imperfections than for essentially random nucleation on terraces. These remarks only apply for the situation where layer growth occurs. The other situation in which RHEED oscillations are not seen is when gross three-dimensional growth occurs and this is easily determined by the spotty pseudo-transmission nature of the RHEED patterns. 3.2. Damping of oscillations In the step edge scattering model we associate changes in RHEED intensity with changes in the step edge density. The familiar damping of oscillations therefore implies that some equilibrium step density is being achieved, i.e. some equilibrium terrace length which will be governed by the surface diffusion length under the prevalent growth conditions will be attained. Generally, the damping is most rapid for higher substrate temperatures at which the equilibrium terrace length will be reached most quickly. However, there are other factors which affect the damping, the most important of which is the variation of growth rate across the part of the substrate which is sampled by the incident RHEED beam. this can give rise to complicated “beating” of oscillations (see, for example, ref. [24]). It is important to emphasise that the conditions under which oscillations are observed should be noted and recorded. 3.3. Increase of oscillation amplitude The oscillation amplitude can increase when a dopant beam is turned on [4]. This implies that the fluctuations in step density have increased and it would be consistent with ideas that preferential nucleation is occurring on the terraces in the presence of dopant atoms. limura and Kawabe [13] have recently published RHEED oscillation data for beryllium doping in which they demonstrate such behaviour, i.e. the beryllium surface concentration even when 0.02% of a monolayer, controls the growth front morphology. It is also a generally known fact that if GaAs has been grown for several layers such that oscillations are well damped and very small, large ampli-~
tude oscillations will be seen when an aluminium source shutter is opened. This may in part be due to the change in group Ill/V flux ratio, but it is probably most influenced by the change in the mean surface diffusion length due to the presence of aluminium. On the basis of the relative cohesive energies of AlAs and GaAs we expect the activation energy for surface diffusion of Alto be higher than Ga on GaAs. This will lead to a shorter diffusion length and therefore shorter terrace lengths accompanied by an increase in the step density. A note of caution is necessary here. The actual change in the intensity when the aluminium shutter is opened must also be influenced by the diffraction conditions. The surface reconstructions are different for AlAs and GaAs and very little is known about intermediate A1GaAs alloy surface reconstructions. It therefore may be premature to offer a detailed interpretation of the behaviour observed by Yen et al. [25] when growing GaAs/AlAs superlattices, although their general conclusions about interface quality, which they infer from the decay of oscillations, may be valid. 3.4. Recovery effects When growth is terminated by closing the Group III source shutter the intensity of the specular RHEED beam recovers to its original value prior to growth. This has been widely interpreted as a recovery of flatness following cessation of the growth [4,5,19].This has resulted in the concept of the “growth interrupt” to improve the interfacial quality of multiquantum well structures. There is some evidence that such growth interrupts do result in significant narrowing of the low temperature photoluminescence linewidths and hence, it is inferred, and improvement in the interface flatness [26—28].We remark here however that superior low temperature photoluminescence linewidths have been achieved without resorting to the use of growth interrupts [29]. The recovery period is not simple and it can usually be separated into fast and slow processes [19,30]. Lewis et al. [10] have studied the recovery behaviour for a wide range of conditions, including the effect of terminating growth at different points on the oscillation cycle. They have interpre-
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RHEED intensity oscillation technique
[1101
____________________________________
6 10 20 30 40 50s Fig. 3. The effect of termination of growth on the RHEED specular intensity oscillations for a GaAs (001) 2 x 4 surface; [110] azimuth; 1.49° angle of incidence; 00 beam at 12.5 keV 4 molecules primary beam energy; 7 = 580°C; JA, 1.5 )< iO’ cm2 s~, j ~~1X10~ molecules cz2n2 s~. Growth was terminated, i.e. the Ga shutter was closed, at the positions indicated. Note the initial rapid decrease in the intensity [31]. ted the fast process as a rapid smoothing of the growth front profile and the slow process as a recovery of long range order, i.e. re-arrangement of terraces and/or the reduction of one-dimensional disorder. We have also recently shown that the recovery behaviour depends on the point on the intensity oscillation at which growth was terminated [31]. Fig. 3 shows a set of data for which the fact initial stage is a reduction of the intensity, followed by a slow increase. In this particular instance, which has much in common with transient effects at the initiation of growth to be discussed in the next section, we associate the fast process with a change of the surface reconstruction and the slow change is the re-arrangement of the terraces, etc. This particular form of recovery in fig. 3 is most noticeable for the [110] azimuth which has the highest sensitivity to changes in surface reconstruction because of strong multiple scattering associated with the ~ order beams for the static arsenic stable (2 X 4) surface. 3.5. Initial transient There are many examples of published RHEED oscillations which show an initial abrupt increase
5
subsequent series of regular oscillations [5,32]. Briones et a!. [32] suggested that this transient increase is caused by an initial smoothing of steps already present on the GaAs (001) 2 x 4 surface. They observed the effect under well-defined conof ditions intensity along which the does [110] not andalways [010] fit azimuths, in with but the could not record any effect along the [110] direction. They also presented some optical scattering evidence for steps running parallel to the [110] direction and showed that the transient behaviour depends on the arsenic flux. Their explanation has much to commend it and it may be consistent with the model proposed by Däweritz [33,34] for steps along the [110] being responsible for the stability of the (2 x 4) reconstruction. We have examined the transient behaviour for several azimuths under controlled fluxes of galhum and arsenic and we observe a strong dependence on the diffraction condition, i.e. the angles of incidence and azimuth. Contrary to Briones et al., we observe the transient most clearly along the [110] azimuth, as shown in fig. 4. In view of this
-~
C
.E
1.0 30
6 0 a)
0.81°
a) 0.
I 0
I 10
I
I
20
30
I
40s
Fig. 4. Some examples of the initial transient behaviour for RHEED oscillations observed for the specular 00 beam along the [110] azimuth at the angles of incidence indicated. Primary beam energy = 12.5 keV.
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RHEED intensity oscillation technique
strong dependence on the diffraction condition, we reject models which are based on step smoothing, and we favour a model based on a transient
For the Ill—V semiconductors the usual oscillation period corresponds to the growth of a single molecular (Ga + As) layer, i.e. a0/2 for the (001)
change of surface reconstruction. When the galhum shutter is opened, the surface stoichiometry will be instantaneously changed and we expect the surface to adjust its reconstruction from the (2 X 4) towards the rather ill-defined (3 x 1) structure. Such a change produces quite dramatic changes in the specular beam rocking curve [17]. The [110] azimuth is the direction most sensitive to changes in reconstruction since the strength of the ~ order features is considerably weakened and the multiple scattering contribution to the specular beam intensity is changed. We therefore associate this transient with a change in reconstruction. We also expect the effect to be present to some extent along other azimuths. From the practical point of view, the most important point is to appreciate that this transient behaviour is significant if RHEED oscillations are to be used to control the shutters or beam fluxes during MBE growth. We recommend that a diffraction condition is chosen such that this effect is absent, e.g. choose the [010] with angle of mcidence 10 at 10—12 keY primary beam energy.
oriented surface, where a0 is the lattice parameter. However, under certain diffraction conditions oscillations corresponding to periods which are apparently a0/4 can be observed [22], as shown in fig. 5. At first sight it is tempting to attribute this behaviour to the completion of successive layers of gallium and arsenic rather than complete GaAs layers. However, because of the specific diffraction condition dependence of this behaviour we do not believe this explanation is correct, and we have suggested [22] that the second harmonic results from a superposition of the elastic specular scattered intensity and the diffuse scattering, as shown in fig. 6. The diffuse scattering is generally increased if the step edge density increases, whilst the specular intensity is reduced. Diffuse scattering in this sense refers to directional scattering of electrons that form Kikuchi bands or diffuse Bragg
[010]
4. Frequency doubling in RHIEED oscillations 1.88°
There are several examples in the literature of the appearance of harmonics in the oscillations [7,22,35,36]. Sakamoto et a!. [35] showed that for the growth of Si on Si (001) when the beam is along the [110] azimuth, oscillations corresponding to bi-atomic layer growth occurs, whereas other azimuths showed monoatomic layer growth. More recently, the same group [36] has suggested that this can be explained by the growth of alternating layers of (2 x 1) and (1 x 2) reconstruction the reconstruction features exhibiting maxima every bi-atomic layer. In order to establish this, it was necessary to prepare a Si (001) surface which exhibited a single (2 x 1) domain structure. Aarts et al. [37] did not detect any such bi-layer oscillations and it may be that the presence or absence of the effect depends on the original substrate preparation.
1 76°
~.
1.67°
~-
—
I
I
I
I
I
0 10 20 Fig. 5 The appearance of harmonics in the oscillations in the specular beam for different angles of incidence. Primary beam along the [0101azimuth of GaAs (001) 2 x4 at 12.5 keV.
P.J. Dobson et al.
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RHEED intensity oscillation technique
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~/
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~.
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~
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Fig. 6. Schematic diagram showing how the measured intensity variations are the result of the summation of specularly reflected electrons and those diffusely scattered by topographic features. The latter are superimposed on a background which is set by thermal diffuse scattering.
features. The latter usually result from the participation of phonons in the scattering (i.e. thermal diffuse scattering), but scattering by surface irregularities can also provide the parallel momenturn or wavevector for a directional diffuse component. Diffuse scattering is very difficult to quantify at present, but we can say with certainty that it is diffraction condition dependent. Another very important point arises from this argument. if conditions are chosen such that the diffuse scattering completely dominates over elastic specular scattering then we have an explanation of why, under some diffraction conditions, the RHEED intensity shows an increase in the intensity for the first half period and the peaks are apparently 180° out of phase with the more familiar case. This is nicely illustrated in fig. 5 if we compare the behaviour for angles of incidence of 1.67° and 1.88°. The angle of 1.67°does correspond to a deep minimum of intensity on the [010] rocking curve, so we expect the elastic specular intensity to be very low. 5. Conclusions RHEED intensity oscillations provide a convenient method of determining the thickness of
7
layers or beam fluxes used in MBE provided that the conditions for their observation are carefully selected. The RHEED oscillations also provide a means of studying the mechanisms of crystal growth and for determining the kinetics of surface diffusion under the conditions of MBE. However, some care is necessary in the interpretation and in this survey we have emphasised the need to specify the diffraction conditions which are used.
References [1] J.J. Harris, B.A. Joyce and P.J. Dobson, Surface Sci. 103 (1981) L90. [2] C.E.C. Wood, Surface Sci. 108 (1981) L441. [3] J.J. Harris, B.A. Joyce and P.J. Dobson, Surface Sci. 108 (1981) L444. [4] J.H. Neave, B.A. Joyce, P.J. Dobson and N. Norton, Appl. Phys. A31 (1983) 1. [5] J.M. Van Hove, C.S. Lent, P.R. Pukite and P.1. Cohen, J. Vacuum Sci. Technol. Bi (1983) 741. [6] T. Sakamoto, H. Funabashi, K. Ohta, T. Nakagawa, N.J. Kawai and T. Kojima, Japan. J. Appl. Phys. 23 (1984) L657. [7] B.A. Joyce, P.J. Dobson, J.H. Neave, K. Woodbridge, J. Zhang, P.K. Larsen and B. Bolger, Surface Sci. 168 (1986) 423. [8] C.T. Foxon, J. Vacuum Sci. Technol., to be published. [9] J.H. Neave, P.J. Dobson, B.A. Joyce and J. Zhang, Appl. Phys. Letters 47 (1985) 400. [10] B.F. Lewis, F.J. Grunthaner, A. Madhukar, T.C. Lee and R. Fernandez, J. Vacuum Sci. Technol. B3 (1985) 1317. [11] P. Chen, A Madhukar, J.Y. Kim and T.C. Lee, Appi. Phys. Letters 48 (1986) 650. [12] A. Madhukar, S.V. Ghaisas, T.C. Lee, M.Y. Chen, P. Chen, J.Y. Kim and P.G. Newman, Proc. SPIE 524 (1985) 78. [13] Y. limura and M. Kawabe, Japan. J. AppI. Phys. 25 (1986) L81. [14] E. Ba~uer,in: techniques of Metals Research, Ed. R.F. Bunshah (Wiley—Interscience, New York, 1969) p. 501. [15] S. mo, Japan. J. Appi. Phys. 16 (1977) 891. [16] B.A. Joyce, J.h. Neave, P.J. Dobson and P.K. Larsen, Phys. Rev. B29 (1984) 814. [17] P.K. Larsen, P.J. Dobson, J.H. Neave, B.A. Joyce, B. Bolger and J. Zhang, Surface Sci. 169 (1986) 176. [18] P.A. Maksym and J.L. Beeby, Surface Sci. 110 (1981) 423. [19] J.H. Neave, B.A. Joyce and P.J. Dobson, Appl. Phys. A34 (1984) 179. [20] C.S. Lent and P.1. Cohen, Surface Sci. 139 (1984) 121. [21] P.R. Pukite, CS. Lent and P.1. Cohen, Surface Sci. 161 (1985) 39. [22] B.A. Joyce, P.J. Dobson, J.H. Neave and J. Zhang, in: Two-Dimensional Systems: Physics and New Devices,
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[23] [24] [25] [26]
[27] [28] [29] [30]
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RHEED intensity oscillation technique
Eds. G. Bauer, F. Kuchar and H. Heinrich (Springer, Berlin, 1986) p. 42. J. Zhang, BA. Joyce, J.H. Neave and P.J. Dobson, to be published. J.M. Van Hove, P.R. Pukite and P.1. Cohen, J. Vacuum Sci. Technol. B3 (1985) 563. M.Y. Yen, T.C. Lee, P. Chen and A. Madhukar, J. Vacuum Sci. Technol. B4 (1986) 590. T. Hayakawa, T. Suyama. K. Takahashi, K. Kondo, S. Yamamoto, S. Yano and T. Hijikata, AppI. Phys. Letters 47 (1985) 952. H. Sakaki, M. Tanaka and J. Yoshino, Japan. J. AppI. Phys. 24 (1985) L417. D. Bimberg. D. Mars, J.N. Miller, R. Bauer and D. Oertel, J. Vacuum Sci. Technol., to be published. C.T. Foxon, private communication, 1985. F.-Y. Juang, P.K. Bhattacharya and J. Singh, AppI. Phys. Letters 48 (1986) 290.
[31] BA. Joyce, P.J. Dobson, J.H. Neave and J. Zhang, in: Proc. 8th European Conf. on Surface Science (ECOSS-8), JOlich, 1986 [Surface Sci. 178 (1986) 110]. [32] F. Briones, D. Golmayo, L. Gonzalez and J.L. Dc Miguel, Japan. J. AppI. Phys. 24 (1985) L478. [33] L. Däweritz, Surface Sci. 118 (1982) 585. [34] L. DSweritz, Surface Sci. 160 (1985) 171. [35] T. Sakamoto, N.J. Kawai, 1. Nakagawa, K. Ohta and T. Kojima, AppI. Phys. Letters 47 (1985) 167. [36] T. Sakamoto, T. Kawamura and G. Hashiguchi, AppI. Phys. Letters 48 (1986) 1612. [37] J. Aarts, W.M. Gerits and P.K. Larsen, Appl. Phys. Letters 48 (1986) 931. [38] T. Kawamura and PA. Maksym, Surface Sci. 161 (1985) 12.
1
CURRENT UNDERSTANDING AND APPLICATIONS OF ThE RHEED INTENSITY OSCILLATION TECHNIQUE P.J. DOBSON, B.A. JOYCE and J.H. NEAVE Philips Research Laboratories, Redhill, Surrey RHI 5HA, UK
and J. ZHANG Physics Department, Imperial College, Prince Consort Road, London S W7 2BZ, UK
The problem of reflection high energy electron diffraction (RHEED) and electron scattering from smooth and growing surface is briefly reviewed. Evidence is given that strong electron beam penetration and multiple scattering effects are present under the conditions used to observe intensity oscillations in RHEED during growth by molecular beam epitaxy (MBE). A survey is made of the predominant RHEED oscillation features, i.e. damping, increases in amplitude, transient behaviour, phase differences and the appearance of harmonics. These features can be related to growth and diffraction processes.
1. Introduction Reflection high energy electron diffraction (RHEED) has become the standard technique for monitoring the structure of layers grown by molecular beam epitaxy (MBE) because the geometry of the technique is ideally suited to MBE and because the diffraction patterns contain a wealth of useful information which can be related to the structure of the layers. For example, in addition to the surface unit cell dimensions, the presence of roughness, steps, facets and disorder due to antiphase boundaries, etc. can be determined. One of the most significant and exciting observations of recent years is that when growth is initiated, the intensity of RHEED features shows an oscillatory behaviour which is directly related to the growth rate [1—5].This has now become routinely used to calibrate beam fluxes and control alloy composition and the thickness of quantum wells and superlattice layers [6—8].Data relating to surface diffusion [9] and crystal growth mechanisms [10—12]and dopant incorporation [13] have also been obtained from studies of RHEED intensity oscillations.
It is now becoming apparent that there are important differences in the interpretations of these intensity oscillations being offered by different research groups. These differences need to be resolved if we are to optimise the use of this phenomenon. Here, we will first of all briefly survey the electron diffraction and scattering aspect of the problem, before proceeding to specific details of RHEED intensity oscillations which can be related to crystal growth.
2. Electron diffraction and scattering In the situations which are usually employed in MBE a high energy beam of electrons in the range 5 to 40 keY is directed at a low angle (1°to 3°)to the surface. the de Broglie wavelength is therefore in the range 0.17 to 0.06 A and the penetration of the beam into the surface is low, being restricted to the outermost few atomic layers. Most geometrical aspects of the diffraction pattern can be interpreted on the basis of a limited penetration kinematic scattering model [14—16].A detailed analysis of the diffracted beam intensity, particu-
0022-0248/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
2
P.1 Dobson et at
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RHEED intensity oscillation technique
larly the way in which this changes with incident angle, should in principle permit us to determine the complete structure of the surface unit cell. Whilst this has not yet been achieved for a reconstructed semiconductor surface, sets of data for GaAs (001) have recently been published [17] and the theoretical treatment now exists [18]. One fact is already very clear from this work, i.e. the incident beam does penetrate the solid and very strong multiple scattering (i.e. dynamical in the diffraction sense) effects dominate the diffraction process. This is best illustrated by reference to fig. 1 which shows how the specular beam intensity varies with incident angle for three different azimuths of the GaAs (001) 2 x 4 arsenic stable surface. If the scattering was a simple kinematic process the results for the three azimuths would all be similar and show maxima only at the Bragg conditions for the (001) set of crystal planes.
A similar conclusion that the scattering was dynamical in origin was reached in an earlier study of the azimuthal variation in the intensity of static and growing surfaces [19]. These dynamical or multiple scattering processes transfer the scattered intensity between beams, e.g. between the fractional order beams and the specular beam or between the surface resonances and specular beam. There are also strong enhancements of intensity probably of dynamical origin at the positions in diffraction patterns where Kikuchi lines cross other diffraction features. These dynamical effects mean that we have to be cautious in our interpretation of the intensity and apparent width of diffracted features. The limited penetration of electron beams also means that we have to take account of refraction effects in our estimates of the Bragg conditions and the position of Kikuchi lines. This is most conveniently done by using the relationship between angles outside the solid 0~to angles inside 0~,measured with respect to the surface: /2
cos 00
_______
01 10
io2 C r
4
10
(1— V0/E)’ cos where V~is a negative quantity termed the “inner potential” which represents the gain in potential energy that an electron of kinetic energy E undergoes when it enters the solid. For most of the Group —11 IY and semiconductors lies in the range to III—Y 15 eY and refractionV0 effects are =
—
>,
very significant angles of less than of 5°.the term There is an at unfortunate misuse “Bragg condition” which has developed with re-
-0
0 ________
~Ca) In ios
1io~ 0
a) > 02
t 10 ~0l 10 I • I I 1 2 3 4 Angle of incidence ldegrees) Fig. 1. Specular beam intensity as a function of angle of incidence for the GaAs (001) 2 X 4 surface for the three principal azimuths. Primary beam energy = 12.5 keV [17].
spect toand RHEED and MBE. Cohen and[10—12]use co-workers tive [20.21] the term interference to Madhukar meanfor the electrons condition and co-workers scattered at which construcby adjacent step terraces occurs. Under such circumstances it is not necessary to use any refraction correction it is assumedofcontrary to expectations that since no penetration the beam occurs. However, this condition is not strictly the Bragg condition familiar to crystallography and use of the term should be discouraged. This is also the problem which is central to the description of RHEED intensity oscillations. We have on the one hand the intuitively simple picture of Lent and Cohen [20], in which the varia-
P.J. Dobson et al.
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RHEED intensity oscillation technique
tion of intensity results from the interference of beams reflected from step terraces. On the other hand we have the more complicated picture of strong multiple scattering effects modifying the changes in scattering from a varying sted edge density. We believe firmly in the latter and dispute whether there is any firm evidence for the two-layer interference model. We have sought conditions to provide such evidence [22] but out results were contrary to the expectations of two-layer interference. Furthermore, at the low angles of mcidence employed, one expects that steps 2.83 A in height will strongly scatter electrons of de Broglie wavelength 0.1 A. We therefore adopt the view that RHEED intensity oscillations result from step edge scattering, and can therefore give some indication of the step density. The variations which occur with changes of angle of incidence and azimuth must result from a combination of multiple scattering effects and possibly the preferred step directions. A rigorous multiple scattering calculation for RHEED intensities from surfaces with varying step densities has predicted oscillations [38]. Further evidence for the multiple scattering nature of the problem comes from the observation that the oscillations of intensity of different beams in a diffraction pattern often exhibit a complex phase relationship, i.e. the oscillation of the specular beam is often ~r out of phase with the oscillation of other beams. This aspect of the problem will be dealt with in more detail in a forthcoming publication [23]. —
•
3
reached when oscillations become less apparent or absent. In a recent study, Neave et al. [9] used the disappearance of RHEED oscillations to obtain a measurement of the surface diffusion length of gallium on a terraced GaAs (001) 2 X 4 reconstructed surface. The electron beam was directed parallel to the step edges. If the substrate temperature and incident fluxes were such that the surface diffusion length was less than the mean terrace length, then new growth centres appear on the terraces and these are accompanied by the customary periodic changes of RHEED intensity. The substrate temperature was increased until oscillations ceased, as shown in fig. 2. From these results a surface diffusion energy of 1.3 ±0.1 eV was obtained. Note, however, that at T~>5900 C in this particular experiment, whilst growth occurs it does not result in RHEED oscillations. Under these conditions, growth proceeds by the addition of atoms to the step edges. Absence of RHEED oscillations when growing material may indeed be a desirable situation from the standpoint of electrical and optical quality, since it implies that growth is occurring at step edges and would give
—
2.3~~10atom cn-c i~(°C) 598 596
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3. Growth effects and RHEED oscillations Some of the important features that are seen in studies of RHEED intensity oscillations will now be described and discussed.
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.
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3.1. Absence of oscillations The occurrence of variations in the intensity with growth has become so familiar that it is timely to examine the conditions under which no such oscillations are seen. Generally, when the substrate temperature is increased, a condition is
Time
—
Fig. 2. An example of the transition from oscillations to a constant response as a function of substrate temperature, with constant gallium flux 19].
P.J. Dobson et a!. / RHEED intensity oscillation technique
4
fewer imperfections than for essentially random nucleation on terraces. These remarks only apply for the situation where layer growth occurs. The other situation in which RHEED oscillations are not seen is when gross three-dimensional growth occurs and this is easily determined by the spotty pseudo-transmission nature of the RHEED patterns. 3.2. Damping of oscillations In the step edge scattering model we associate changes in RHEED intensity with changes in the step edge density. The familiar damping of oscillations therefore implies that some equilibrium step density is being achieved, i.e. some equilibrium terrace length which will be governed by the surface diffusion length under the prevalent growth conditions will be attained. Generally, the damping is most rapid for higher substrate temperatures at which the equilibrium terrace length will be reached most quickly. However, there are other factors which affect the damping, the most important of which is the variation of growth rate across the part of the substrate which is sampled by the incident RHEED beam. this can give rise to complicated “beating” of oscillations (see, for example, ref. [24]). It is important to emphasise that the conditions under which oscillations are observed should be noted and recorded. 3.3. Increase of oscillation amplitude The oscillation amplitude can increase when a dopant beam is turned on [4]. This implies that the fluctuations in step density have increased and it would be consistent with ideas that preferential nucleation is occurring on the terraces in the presence of dopant atoms. limura and Kawabe [13] have recently published RHEED oscillation data for beryllium doping in which they demonstrate such behaviour, i.e. the beryllium surface concentration even when 0.02% of a monolayer, controls the growth front morphology. It is also a generally known fact that if GaAs has been grown for several layers such that oscillations are well damped and very small, large ampli-~
tude oscillations will be seen when an aluminium source shutter is opened. This may in part be due to the change in group Ill/V flux ratio, but it is probably most influenced by the change in the mean surface diffusion length due to the presence of aluminium. On the basis of the relative cohesive energies of AlAs and GaAs we expect the activation energy for surface diffusion of Alto be higher than Ga on GaAs. This will lead to a shorter diffusion length and therefore shorter terrace lengths accompanied by an increase in the step density. A note of caution is necessary here. The actual change in the intensity when the aluminium shutter is opened must also be influenced by the diffraction conditions. The surface reconstructions are different for AlAs and GaAs and very little is known about intermediate A1GaAs alloy surface reconstructions. It therefore may be premature to offer a detailed interpretation of the behaviour observed by Yen et al. [25] when growing GaAs/AlAs superlattices, although their general conclusions about interface quality, which they infer from the decay of oscillations, may be valid. 3.4. Recovery effects When growth is terminated by closing the Group III source shutter the intensity of the specular RHEED beam recovers to its original value prior to growth. This has been widely interpreted as a recovery of flatness following cessation of the growth [4,5,19].This has resulted in the concept of the “growth interrupt” to improve the interfacial quality of multiquantum well structures. There is some evidence that such growth interrupts do result in significant narrowing of the low temperature photoluminescence linewidths and hence, it is inferred, and improvement in the interface flatness [26—28].We remark here however that superior low temperature photoluminescence linewidths have been achieved without resorting to the use of growth interrupts [29]. The recovery period is not simple and it can usually be separated into fast and slow processes [19,30]. Lewis et al. [10] have studied the recovery behaviour for a wide range of conditions, including the effect of terminating growth at different points on the oscillation cycle. They have interpre-
P.J. Dobson et a!.
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RHEED intensity oscillation technique
[1101
____________________________________
6 10 20 30 40 50s Fig. 3. The effect of termination of growth on the RHEED specular intensity oscillations for a GaAs (001) 2 x 4 surface; [110] azimuth; 1.49° angle of incidence; 00 beam at 12.5 keV 4 molecules primary beam energy; 7 = 580°C; JA, 1.5 )< iO’ cm2 s~, j ~~1X10~ molecules cz2n2 s~. Growth was terminated, i.e. the Ga shutter was closed, at the positions indicated. Note the initial rapid decrease in the intensity [31]. ted the fast process as a rapid smoothing of the growth front profile and the slow process as a recovery of long range order, i.e. re-arrangement of terraces and/or the reduction of one-dimensional disorder. We have also recently shown that the recovery behaviour depends on the point on the intensity oscillation at which growth was terminated [31]. Fig. 3 shows a set of data for which the fact initial stage is a reduction of the intensity, followed by a slow increase. In this particular instance, which has much in common with transient effects at the initiation of growth to be discussed in the next section, we associate the fast process with a change of the surface reconstruction and the slow change is the re-arrangement of the terraces, etc. This particular form of recovery in fig. 3 is most noticeable for the [110] azimuth which has the highest sensitivity to changes in surface reconstruction because of strong multiple scattering associated with the ~ order beams for the static arsenic stable (2 X 4) surface. 3.5. Initial transient There are many examples of published RHEED oscillations which show an initial abrupt increase
5
subsequent series of regular oscillations [5,32]. Briones et a!. [32] suggested that this transient increase is caused by an initial smoothing of steps already present on the GaAs (001) 2 x 4 surface. They observed the effect under well-defined conof ditions intensity along which the does [110] not andalways [010] fit azimuths, in with but the could not record any effect along the [110] direction. They also presented some optical scattering evidence for steps running parallel to the [110] direction and showed that the transient behaviour depends on the arsenic flux. Their explanation has much to commend it and it may be consistent with the model proposed by Däweritz [33,34] for steps along the [110] being responsible for the stability of the (2 x 4) reconstruction. We have examined the transient behaviour for several azimuths under controlled fluxes of galhum and arsenic and we observe a strong dependence on the diffraction condition, i.e. the angles of incidence and azimuth. Contrary to Briones et al., we observe the transient most clearly along the [110] azimuth, as shown in fig. 4. In view of this
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Fig. 4. Some examples of the initial transient behaviour for RHEED oscillations observed for the specular 00 beam along the [110] azimuth at the angles of incidence indicated. Primary beam energy = 12.5 keV.
6
P.J. Dobson et al.
/
RHEED intensity oscillation technique
strong dependence on the diffraction condition, we reject models which are based on step smoothing, and we favour a model based on a transient
For the Ill—V semiconductors the usual oscillation period corresponds to the growth of a single molecular (Ga + As) layer, i.e. a0/2 for the (001)
change of surface reconstruction. When the galhum shutter is opened, the surface stoichiometry will be instantaneously changed and we expect the surface to adjust its reconstruction from the (2 X 4) towards the rather ill-defined (3 x 1) structure. Such a change produces quite dramatic changes in the specular beam rocking curve [17]. The [110] azimuth is the direction most sensitive to changes in reconstruction since the strength of the ~ order features is considerably weakened and the multiple scattering contribution to the specular beam intensity is changed. We therefore associate this transient with a change in reconstruction. We also expect the effect to be present to some extent along other azimuths. From the practical point of view, the most important point is to appreciate that this transient behaviour is significant if RHEED oscillations are to be used to control the shutters or beam fluxes during MBE growth. We recommend that a diffraction condition is chosen such that this effect is absent, e.g. choose the [010] with angle of mcidence 10 at 10—12 keY primary beam energy.
oriented surface, where a0 is the lattice parameter. However, under certain diffraction conditions oscillations corresponding to periods which are apparently a0/4 can be observed [22], as shown in fig. 5. At first sight it is tempting to attribute this behaviour to the completion of successive layers of gallium and arsenic rather than complete GaAs layers. However, because of the specific diffraction condition dependence of this behaviour we do not believe this explanation is correct, and we have suggested [22] that the second harmonic results from a superposition of the elastic specular scattered intensity and the diffuse scattering, as shown in fig. 6. The diffuse scattering is generally increased if the step edge density increases, whilst the specular intensity is reduced. Diffuse scattering in this sense refers to directional scattering of electrons that form Kikuchi bands or diffuse Bragg
[010]
4. Frequency doubling in RHIEED oscillations 1.88°
There are several examples in the literature of the appearance of harmonics in the oscillations [7,22,35,36]. Sakamoto et a!. [35] showed that for the growth of Si on Si (001) when the beam is along the [110] azimuth, oscillations corresponding to bi-atomic layer growth occurs, whereas other azimuths showed monoatomic layer growth. More recently, the same group [36] has suggested that this can be explained by the growth of alternating layers of (2 x 1) and (1 x 2) reconstruction the reconstruction features exhibiting maxima every bi-atomic layer. In order to establish this, it was necessary to prepare a Si (001) surface which exhibited a single (2 x 1) domain structure. Aarts et al. [37] did not detect any such bi-layer oscillations and it may be that the presence or absence of the effect depends on the original substrate preparation.
1 76°
~.
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0 10 20 Fig. 5 The appearance of harmonics in the oscillations in the specular beam for different angles of incidence. Primary beam along the [0101azimuth of GaAs (001) 2 x4 at 12.5 keV.
P.J. Dobson et al.
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Fig. 6. Schematic diagram showing how the measured intensity variations are the result of the summation of specularly reflected electrons and those diffusely scattered by topographic features. The latter are superimposed on a background which is set by thermal diffuse scattering.
features. The latter usually result from the participation of phonons in the scattering (i.e. thermal diffuse scattering), but scattering by surface irregularities can also provide the parallel momenturn or wavevector for a directional diffuse component. Diffuse scattering is very difficult to quantify at present, but we can say with certainty that it is diffraction condition dependent. Another very important point arises from this argument. if conditions are chosen such that the diffuse scattering completely dominates over elastic specular scattering then we have an explanation of why, under some diffraction conditions, the RHEED intensity shows an increase in the intensity for the first half period and the peaks are apparently 180° out of phase with the more familiar case. This is nicely illustrated in fig. 5 if we compare the behaviour for angles of incidence of 1.67° and 1.88°. The angle of 1.67°does correspond to a deep minimum of intensity on the [010] rocking curve, so we expect the elastic specular intensity to be very low. 5. Conclusions RHEED intensity oscillations provide a convenient method of determining the thickness of
7
layers or beam fluxes used in MBE provided that the conditions for their observation are carefully selected. The RHEED oscillations also provide a means of studying the mechanisms of crystal growth and for determining the kinetics of surface diffusion under the conditions of MBE. However, some care is necessary in the interpretation and in this survey we have emphasised the need to specify the diffraction conditions which are used.
References [1] J.J. Harris, B.A. Joyce and P.J. Dobson, Surface Sci. 103 (1981) L90. [2] C.E.C. Wood, Surface Sci. 108 (1981) L441. [3] J.J. Harris, B.A. Joyce and P.J. Dobson, Surface Sci. 108 (1981) L444. [4] J.H. Neave, B.A. Joyce, P.J. Dobson and N. Norton, Appl. Phys. A31 (1983) 1. [5] J.M. Van Hove, C.S. Lent, P.R. Pukite and P.1. Cohen, J. Vacuum Sci. Technol. Bi (1983) 741. [6] T. Sakamoto, H. Funabashi, K. Ohta, T. Nakagawa, N.J. Kawai and T. Kojima, Japan. J. Appl. Phys. 23 (1984) L657. [7] B.A. Joyce, P.J. Dobson, J.H. Neave, K. Woodbridge, J. Zhang, P.K. Larsen and B. Bolger, Surface Sci. 168 (1986) 423. [8] C.T. Foxon, J. Vacuum Sci. Technol., to be published. [9] J.H. Neave, P.J. Dobson, B.A. Joyce and J. Zhang, Appl. Phys. Letters 47 (1985) 400. [10] B.F. Lewis, F.J. Grunthaner, A. Madhukar, T.C. Lee and R. Fernandez, J. Vacuum Sci. Technol. B3 (1985) 1317. [11] P. Chen, A Madhukar, J.Y. Kim and T.C. Lee, Appi. Phys. Letters 48 (1986) 650. [12] A. Madhukar, S.V. Ghaisas, T.C. Lee, M.Y. Chen, P. Chen, J.Y. Kim and P.G. Newman, Proc. SPIE 524 (1985) 78. [13] Y. limura and M. Kawabe, Japan. J. AppI. Phys. 25 (1986) L81. [14] E. Ba~uer,in: techniques of Metals Research, Ed. R.F. Bunshah (Wiley—Interscience, New York, 1969) p. 501. [15] S. mo, Japan. J. Appi. Phys. 16 (1977) 891. [16] B.A. Joyce, J.h. Neave, P.J. Dobson and P.K. Larsen, Phys. Rev. B29 (1984) 814. [17] P.K. Larsen, P.J. Dobson, J.H. Neave, B.A. Joyce, B. Bolger and J. Zhang, Surface Sci. 169 (1986) 176. [18] P.A. Maksym and J.L. Beeby, Surface Sci. 110 (1981) 423. [19] J.H. Neave, B.A. Joyce and P.J. Dobson, Appl. Phys. A34 (1984) 179. [20] C.S. Lent and P.1. Cohen, Surface Sci. 139 (1984) 121. [21] P.R. Pukite, CS. Lent and P.1. Cohen, Surface Sci. 161 (1985) 39. [22] B.A. Joyce, P.J. Dobson, J.H. Neave and J. Zhang, in: Two-Dimensional Systems: Physics and New Devices,
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[23] [24] [25] [26]
[27] [28] [29] [30]
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RHEED intensity oscillation technique
Eds. G. Bauer, F. Kuchar and H. Heinrich (Springer, Berlin, 1986) p. 42. J. Zhang, BA. Joyce, J.H. Neave and P.J. Dobson, to be published. J.M. Van Hove, P.R. Pukite and P.1. Cohen, J. Vacuum Sci. Technol. B3 (1985) 563. M.Y. Yen, T.C. Lee, P. Chen and A. Madhukar, J. Vacuum Sci. Technol. B4 (1986) 590. T. Hayakawa, T. Suyama. K. Takahashi, K. Kondo, S. Yamamoto, S. Yano and T. Hijikata, AppI. Phys. Letters 47 (1985) 952. H. Sakaki, M. Tanaka and J. Yoshino, Japan. J. AppI. Phys. 24 (1985) L417. D. Bimberg. D. Mars, J.N. Miller, R. Bauer and D. Oertel, J. Vacuum Sci. Technol., to be published. C.T. Foxon, private communication, 1985. F.-Y. Juang, P.K. Bhattacharya and J. Singh, AppI. Phys. Letters 48 (1986) 290.
[31] BA. Joyce, P.J. Dobson, J.H. Neave and J. Zhang, in: Proc. 8th European Conf. on Surface Science (ECOSS-8), JOlich, 1986 [Surface Sci. 178 (1986) 110]. [32] F. Briones, D. Golmayo, L. Gonzalez and J.L. Dc Miguel, Japan. J. AppI. Phys. 24 (1985) L478. [33] L. Däweritz, Surface Sci. 118 (1982) 585. [34] L. DSweritz, Surface Sci. 160 (1985) 171. [35] T. Sakamoto, N.J. Kawai, 1. Nakagawa, K. Ohta and T. Kojima, AppI. Phys. Letters 47 (1985) 167. [36] T. Sakamoto, T. Kawamura and G. Hashiguchi, AppI. Phys. Letters 48 (1986) 1612. [37] J. Aarts, W.M. Gerits and P.K. Larsen, Appl. Phys. Letters 48 (1986) 931. [38] T. Kawamura and PA. Maksym, Surface Sci. 161 (1985) 12.