Strong and periodic 1D in-plane modulation obtained by MBE on (001) GaAs vicinal surfaces

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applied

surface science ELSEVIER

Applied Surface Science 113/l

14 (1997) 66-72

Strong and periodic 1D in-plane modulation obtained by MBE on ( 001) GaAs vicinal surfaces B. Etienne

*, F. Lelarge, Z.Z. Wang, F. Laruelle

Laboratoire de Microstructures et de MicroClectronique (LZMI C.N.R.S.. B.P. 107, 92225 Bagneux Cedex. France

Abstract The lateral atomic organization of group III atoms (here Ga and Al) by atomic steps on GaAs substrates slightly misoriented with respect to (001) is far from being perfect. Nevertheless low-disordered in-plane potential modulation of large amplitude (IO-50 meV) and short periodicity ( < 40 nm) can be obtained. The electronic properties observed in quantum structures with a lateral potential modulation will be shortly reviewed. Before this, different growth phenomena limiting the organization are discussed and some post-growth AFM studies of the step array are presented. The terrace distribution is analyzed using thermodynamical equilibrium models on one hand and Monte Carlo simulation of the crystal growth on the other hand. An anisotropic Schwoebel barrier at the step edge is considered in order to best explain the measurements. PAC.? 68.55.Eg;

68.35.B~: 61.16.Ch;

Keywords: Epitaxy; Vicinal surfaces:

61.20.Ja AFM; Monte-Carlo

1. Introduction Fabricating high quality quantum structures of dimensionality lower than 2 directly by epitaxy on free (i.e. not masked) substrate surfaces is quite attractive. Techniques such as cleaved edge overgrowth [l] and growth in V grooves [2] or on mesa [3] for 1D structures, quantum dots [4] in strained material systems for OD structures have proven to be of great interest. Making use of the step flow growth mode in order to get lateral atomic organization on a misoriented substrates could be even easier: the terraces can have

* Corresponding author. Tel.: + 33.142317378; 1423 17378; e-mail: [email protected]. 0169-4332/97/$17.00 Copyright PII SO169-4332(96)00862-8

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the most widely used (001) crystal orientation, misoriented substrates are sold by many companies, lattice matched material system such as GaAs/AlAs can be used as well. After a first attempt [5], pioneering results using MOCVD [6] and MBE [7] have demonstrated the potential interest of this technique for the growth of lateral superlattices (LSL’s). Our efforts have been aimed at developing cross studies of the optimization of the growth [S] using RHEED and more recently AFM [9] (with an analysis based on a Monte-Carlo simulation of the surface kinetics) on one hand and of their electronic properties (investigated by low temperature band gap spectroscopy [lb], by transport and magneto-transport [ 1 l] and by far infra-red magneto-optics [ 121) on the other hand.

0 1997 Elsevier Science B.V. All rights reserved.

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2. Concepts and problems It is obvious that the atomic steps of a crystal surface (and also the kinks along these steps) are preferential sites for further growth (as described for nearly thermodynamical equilibrium in Ref. [13]). In molecular beam epitaxy (MBE) the impinging adatoms have a 2D diffusion on the surface and these sites offer an additional lateral binding energy .E, for incorporation (which adds to the substrate vertical binding energy E._). When the diffusion length L, is larger than the mean terrace length L of a vicinal surface (L = u/tan (Y where (Y is the misorientation angle and a the lattice parameter, in GaAs (Y= 0.5” gives L = 32 nm), island nucleation on the terraces will be negligible and the step flow growth mode will indeed be reached. This regime is identified in MBE by the non-observation of RHEED (reflective high energy electron diffraction) oscillations and by instantaneous recovery of the intensity of the e-beam specular spot when a group III element shutter is open and closed (this is easily observed for GaAs growth but much more difficult and not so clear cut for AlAs). Some claims have been made however that the onset of these features does not correspond actually to a full step flow growth mode 1141 i.e. some island nucleation remains (Fig. 1). But the surface diffusion can be enhanced further using MEE (migration enhanced epitaxy) i.e. alternating fluxes for cations (Ga, Al) and anions (As), a technique initially proposed to reduce the growth temperature [15]. In MEE the step flow growth mode can be easily identified by RHEED in a similar way 1161. We use MEE at a high temperature to really get diffusion lengths as large as possible. But it has been shown that it is of paramount importance to avoid a transition of the (2 X 4) surface reconstruction to-

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a) p =1

Fig. 2. Sketch of a GaAs/AIAs (X = 0.5) LSL (with perfect lateral atomic ordering) for a coverage ratio p = 1 (a) or larger than 1 (b). The drawing is not to scale: the tilt angle p is usually much larger than the misorientation angle (Y.

wards a (4 X 2) Ga rich surface. This requires using temperature below the congruent sublimation temperature (taken by us as T,, = 595°C) and to deposit only a fraction of monolayer in each MEE cycle [ 171. Our growth conditions on vicinal substrates (type ‘A’: Ga atom terminated steps) used in order to get high quality GaAs/AlAs LSL’s have been described elsewhere [81. The ideal structure is shown in Fig. 2a. But this would require perfect Ga and Al flux calibrations and negligible lateral gradients of the atomic beams. In practice LSL’s are tilted [5] over most of the substrate (Fig. 2b). It is possible to determine by optical measurements [lo] the region where the coverage ratio p (ratio of the real amount of matter deposited per nominal monolayer) is close to 1 (with 10-j accuracy). This corresponds to a narrow region (w 1 mm wide) around a curved line crossing the center of the substrate provided the flux calibrations have been accurate enough. Observation of the LSL’s by TEM (transmission electron microscopy) reveals that the lateral atomic modulation is far from being perfect [181. This is the result of a

Vertical atomic

Fig. 1. Different phenomena, occurring during the growth on a vicinal surface, are detrimental to a perfect lateral atomic ordering. those indicated in italics can be avoided (step bunching) or reduced (step pinning, island nucleation).

Only

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0.25 0.50 FL.9 MEAN ALUMINIUM CONTENT

Fig. 3. Variation of the lateral ordering parameter I,, as of the LSL mean aluminium content ?. Black dots and correspond to the results of the indicated experiments line is a guide to the eye) while the light lines are the calculation (based on the model of Ref. [22]) in which diffusion of the Al atoms is taken into account.

a function error bars (the dark result of a no lateral

very efficient vertical Ga/Al exchange process (Ga atoms come up, see Fig. 1) [19] which is well known to limit the sharpness of quantum well interfaces

DO]. Therefore the LSL is actually rather an AlGaAs alloy with a periodic in-plane modulation of its composition: xA,( y) = X{l + h,,(X) cos(27ry/L) + . . . ), F being the mean Al content of the FLS and y is the direction of misorientation. The parameter A,,, describing the atomic lateral ordering, depends on X as shown in Fig. 3 but not significantly on L or on the tilt angle. These values are reached when the LSL is at least 10 ML’s (monolayer) thick, as shown by post growth measurements of the photoluminescence linear polarization [21]. A steady state atomic lateral organization is indeed not reached immediately, a possible reason being the strong competition between attachment of adatoms at step edges and in the vicinity of previous exchange sites [8]. As a result thinner LSL’s or say fractional layers (a 1 ML thick LSL) have a composition modulation which is nearly independent of L. A Monte Carlo simulation which includes this effect, occurring when different species are on the surface, is currently under development. This should allow a quantitative understanding of the value of A,,(?). A simpler model [22] which supposes that Al atoms impinging on the surface are exchanged immediately with Ga atoms

underneath is predicting values significantly lower than the measurements (Fig. 3). The above formula for x,,(y) is assuming a perfectly periodic step array with very straight ledges. In reality terrace disorder and kinks (Fig. 1) could be additional factors limiting h,,(x), the value of which is averaged out over the probed area in any measurement. In order to assess this, the surface morphology has been investigated by post growth AFM measurements discussed in the next part. The results of Fig. 3 correspond to growth conditions giving the lowest step disorder.

3. AFM measurements and equilibrium models The AFM measurements are performed ex situ in a dry box filled with NZ (the applied force is less than 10 nN) [9]. First, the substrate has been studied before the growth, after the sublimation of the oxide and a 5 min thermal annealing at 650°C under As, flux. Our results are consistent with others [23]. We find that the surface is very rough, with holes elongated along [liO], which can be as large as 5 nm deep, 100 nm wide and 500 nm long. Aft$r GaAs growth at 620°C for 60 s at a speed of 2 A/s, the RHEED pattern in the direction of the misorientation exhibit a splitting of the streaks [24] which reveals that the step periodicity has already recover somehow. Because the calculation of the RHEED intensity is quite involved, no quantitative information on the terrace distribution can be deduced from the pattern (we can only check with f 0.1” accuracy that the misorientation angle is close to the nominal one). Our experience is that it is quite hazardous to draw conclusions from RHEED observations on the respective efficiency of GaAs and AlAs to get a surface with a low disordered array of steps: RHEED gives the feeling that GaAs is good to give a smooth surface and that AlAs is better to improve step periodicity. This could be easily understood using a simple 1D kinetic model [25] taking into account the Schwoebel barrier [26]. The first point is well known to be true but the second point has however appeared to us to be completely erroneous. Only vicinal substrates with Ga atom terminated steps (‘type A’ steps along [ liO]) have low disor-

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dered ledges in MBE. The surface has been analyzed by AFM after the growth of a 200 nm buffer on surfaces misoriented by an angle (Y ranging from N 0.5 to u 2” (kinks are not resolved, the lateral resolution being _ 4 nm) [9]. In our best growth conditions using a pure GaAs buffer (there is no improvement including a GaAs/AlAs superlattice), this distribution is, as shown in Fig. 4, a Gaussian (the ratio of the standard deviation AL with L is equal, respectively, to 0.22, 0.24, 0.29 for L = 27.4, 17.0, 8.4 nm). These good results contradict reports by others [27]. Using an AlAs buffer covered by 20 A GaAs (in order to avoid AlAs oxidation before AFM measurements) makes a much more disordered surface, in contradiction with the feeling given by a stronger splitting of the RHEED specular spot during the growth. We note that the mean terrace length is always within the uncertainty of the nominal desorientation and that we do not observe any step bunching [28] (Fig. 1) or mounds [23] unless we are using much lower growth temperature (540°C). In order to explain these results, we considered 4 equilibrium models based on: (i) straight non-interacting steps, (ii) single steps meandering between

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fixed walls, (iii) terrace-step-kink (TSK) model to take into account only entropic repulsion and (iv) entropic and energetic step-step repulsion. The exponential distribution expected for a sequence of straight non-interacting steps (dotted line in Fig. 4) is obviously not observed. The distribution, obtained for a single step confined between two rigid walls separated by 2L [29], already captures most of the physics because the entropic repulsion drastically reduces the probability of finding small terraces. For purely entropic interactions, the distribution obeys to the ‘universal law’ calculated by Joos et al. in the one-dimensional free fermion model [30]. If entropic and energetic repulsion coexists, the distribution is narrow and obeys to a Gaussian law when energetic repulsion outweighs the entropic one. An energetic repulsion with a L-’ decay, as in the last model, is needed to explain the linear relationship between the standard deviation and the mean value of the Gaussian. Our results appear to be in fact very similar to vicinal Si( 1 11) where it was found that AL = 0.25L [31]. This close similarity with Si is really surprising if we consider the very different conditions used in the two material systems.

TERRACE

WIDTH (nm)

Fig. 4. Post-growth AFM measurements of the terrace distribution on a GaAs vicinal surface (dots). Equilibrium models (see text): dots (model (i)), short dashes (model (ii)), long dashes (model (iii)), plain line (model (iv)). L is the mean terrace length and AL is the standard deviation.

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4. Monte-Carlo simulation and kinetics It is indeed quite dubious that the terrace distribution of a GaAs vicinal surface be determined by thermodynamics only. On the contrary the kinetics should play a major role in the building up of the periodicity because of the much lower temperature (N 600°C here versus N 900°C in Si) and of the much shorter time scale (200 nm grown at 0.5-l ML/s here versus N 10 h thermal annealing for Si> used for the surface preparation. We have tried to explain the AFM results using a Monte-Carlo simulation, which is very similar to that developed by D. Vvedensky et al. [32]. Very few parameters are introduced: the binding energy to the substrate Es (N 1.58 eV>, the binding energy to in-plane nearest neighbour En (E,” - 0.32 eV along 110 and Et 0.16 eV along [ 1 lo]) and a Schwoebel barrier E, [26]. With these values for Es, E,” and E,” an ‘atom’ (actually a GaAs ‘molecule’) on the surface makes N 100 hops at 600°C for a growth speed of 1 ML/s (a 50°C higher temperature increases the number of hops by a factor of 3). The anisotropy E:/Ei is determined by the shape of the islands which nucle-

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ate on the terraces [33]. We do not use additional rule such as the instantaneous selection by impinging atoms of the most favourable site (in a small area> because this destroys at once any roughness at any temperature. This does not correspond to reality. The Schwoebel barrier reflects the fact that an atom hopping across a step becomes loosened from the substrate. It has to be taken into account in order to explain the formation of the mounds observed at low growth temperature [34]. The anisotropy of these mounds (elongated again along [liO]) should be indicative of an anisotropy of the Schwoebel barrier (with Et > IT:). We have found that EF should be very small in order to recover a smooth surface after the growth of a buffer layer on a rough surface (we take therefore E: = 0 and Et = 175 meV). We have done a calculation on a 100 X 100 array (i.e. 40 X 40 nm) with periodic boundary conditions in order to study the ordering of the steps on a surface 2” off (001). The initial conditions are 5 steps which are bunched together (4 nm apart from each other) and separated by a large terrace (24 nm wide) (Fig. 5, insert, left). The growth conditions of the simulation are 650°C and 0.1 ML/s. The step length reaches in

I

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30

!

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MONOLAYERS Fig. 5. Decay of the error function f(r) (see text) used to estimate the terrace ordering as a function of the number of deposited monolayers. The initial and a typical final surface are shown in the insert.

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where N is the number of steps (i.e. 5) and I,, is the mean distance between two neighbouring steps (f(f) is 0 for a perfectly ordered surface). With our initial conditions f(O) is close to 1 and f(t) should become smaller than AL/L. (0.29 for this misorientation). With our choice of parameters, we succeed this in less than 60 ML as shown in Fig. 5. This is not the case without any Schwoebel barrier although the two cases are very similar for the first 40 ML. Some of the terrace width fluctuations observed in the simulation could be reduced taking into account the repulsive step-step interaction. We hope that this type of calculation will allow an understanding of the optimization of the surface morphology and, in a next step, of the lateral atomic organization. This should provide a knowledge of the atomic disorder, a quantity which is of paramount importance in order to understand the electronic properties of the structures.

A EF (A E is the GaAs/AlAs I’ band offset for the conduction or the valence band). Another consequence of this effect is that substrates with a too short lateral periodicity L would lead to a 2D pseudo-alloy rather than to a lower dimensional structure. We are therefore now growing structures on substrates with a nominal misorientation (Y= 0.5” (L = 32 nm) for the optical and electrical measurements but we also used 1” (16 nm) and 2” (8 nm> in preliminary studies. The peak-to-peak potential amplitude is 2A Ex A,,( X) (40 meV in the conduction band with X = 0.1 and A,, = 0.2). We will now give a summary of the main results. Valuable information to optimize the growth is given by measurements of the low temperature photoluminescence (PL) linear polarization ratio [lo]. To be sure that there is no artefact in the experimental set-up we checked that the PL of the same structures grown at 520°C (L, < L) is not polarized. Our best samples are grown at 590°C sending l/4 ML GaAs per MEE cycle (or less to get the correct Al composition). The polarization reaches a maximum (20%) in the region where the coverage ratio p = 1. In modulation doped structures, a strong Fermi edge singularity is observed, which reaches a maximum in a region with p - 1/N (N is the number of ML in the LSL), where the tilt provides the largest coupling between the electrical subbands of the structures

5. Electronic

[%I. With quantum

less than l/20 ML a nearly stationary value in the range (1.35 k 0.05) X 40 nm (discarding the case of island incorporation, which gives a much longer step for a short time). In order to get a quick quantitative estimation of the ordering, we consider the following error function:

,f( t) =

(c (L,

i

-

L)‘j’yN

properties

We have studied GaAs/AlAs LSL’s inserted in quantum wells or in selectively doped heterojunctions. All the layers with the exception of the LSL are grown by conventional MBE and are supposed to be laterally unmodulated. In particular we do not believe in the claim of a lateral organization of Si (the n-type dopant used the AlGaAs barrier) [35]. Even if it were true the potential modulation would be much weakened by the set-back distance z between impurities and electrons (the Fourier component q is reduced by exp( - 2rrqz/L) and we have z - L). We have studied structures with LSL of mean Al content between 0.05 and 0.10. The reason is that the lateral atomic ordering parameter A,,(?) being < 1 (Fig. 3) the effective barrier height determining the confinement or the charge is reduced by

L - 32 nm and X = 0.05, we get coupled wires [S]. The electrical resistivity anisotropy is - 20% at 300 K and gets through a strong maximum (- 20) around 20 K then decreases again slightly. This is interpreted as evidence for the opening of a band gap (- 5 meV) in the lateral minibands 1111. Another proof for this gap is the strong positive magnetoresistance (followed by magnetic breakdown) observed at low temperature when the current is flowing in the direction orthogonal to the step edges and a magnetic field is applied in the direction orthogonal to the surfaces [ 1 I]. At a higher magnetic field, in the quantum limit, the amplitude of the Shubnikov-de Haas oscillations for both directions of current (perpendicular and parallel to the steps) is in a ratio equal to the electrical anisotropy at zero magnetic field [37]. At a still higher field we observed a first order transition of the spin polarization of the Landau bands due to a competition

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between the exchange electron-electron interaction and the potential gradients. All these effects can be analyzed to get independent and consistent values for the lateral ordering parameter h,,(x) (see Fig. 3).

6. Conclusion The epitaxy and the physics of low dimensionality quantum structures grown on vicinal surfaces are now rather well understood. This method of fabrication, in spite of its limitations, allows formation of very convenient structures which exhibit a range of new properties. This should open the way to explore in the near future their usefulness for new devices.

Acknowledgements It is a pleasure to thank J. Bloch, A. Cavanna, M. Hayne, S. Huant, T. MClin, F. Petit and L. Sfaxi for their essential contributions to this work.

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