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Equilibrium shape of steps and islands on polar CdTe(001) surface: application to the preparation of self organized templates for growth of nanostructures
Thin Solid Films 367 (2000) 48±57 www.elsevier.com/locate/tsf
Equilibrium shape of steps and islands on polar CdTe(001) surface: application to the preparation of self organized templates for growth of nanostructures D. Martrou*, N. Magnea DeÂpartement de Recherche Fondamentale sur la MatieÁre CondenseÂe, SP2M/PS, CEA-Grenoble, France
Abstract Scanning tunneling microscopy studies of (001) CdTe, a partially ionic II±VI compound, show novel surface structures with step and 2D islands edges aligned along the k100l crystallographic directions. This behaviour, which is not observed in covalent material, is interpreted in the framework of a model incorporating electrostatic interactions in the calculation of the energy of charged steps that could explain why the free energy of k100l steps lies below that of the [110] and [11Å0] steps. These results provide new insights about the microscopic growth mode of CdTe especially by atomic layer epitaxy. The energetics of the vicinal surfaces is also strongly in¯uenced by these effects which allows one to organize C-type and A-type surfaces in staircase and checkerboard arrays. These self organized templates are, respectively, used to grow quantum wires and quantum dots. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Scanning tunneling microscopy; Self organization phenomena; Nanotechnology; Quantum dots; Quantum wires; Atomic layer epitaxy
1. Introduction The growth of quantum nanostructures based on semiconductors has raised a strong interest in the comprehension of the growth mechanisms and of the organization of the surfaces during molecular beam epitaxy (MBE). The use of scanning tunneling microscopy (STM) can bring a lot of information for understanding the surface behavior and optimizing the growth conditions. The studies made on the silicon (001) surface with the (2 £ 1) reconstruction show that the `growth shapes' are islands elongated in the k110l directions as a result of the strong preference of atoms to stick at the end of the Si dimer rows rather than at the sides [1]. The `equilibrium shapes' of the islands are made of rectangles with k110l edges and an aspect ratio close to 3, re¯ecting here the free energy ratio between the [110] and the [11Å0] steps [2]. The bond anisotropy accounts also for the surface stress domains, the step roughness and the elastic interactions between steps [3]. On the polar galliumarsenide(001) surface, the most commonly observed reconstruction is (2 £ 4) or c(2 £ 8) involving As dimers. At equilibrium, the islands are anisotropic structures with their long edge in the [11Å0] direction, the 2 £ direction [4,5]. It has * Corresponding author. CEA/DRFMC/SPMM/PSC, 17 Avenue des Martyrs, 38054 Grenoble Cedex 9, France. Tel.: 133-476-885-592; fax: 133-476-885-821. E-mail address: [email protected] (D. Martrou)
been shown that the ionicity of the Ga±As bond (Philips' ionicity fi 0:3) [6], affects only the short range kink interactions [7] and also the step coupling [8] without modifying the surface morphology from that seen on the purely covalent Si surface. Our STM studies, made on the (001) CdTe surface, show that the behavior of this semiconductor with stronger ionicity (fi 0:717) [6] is different of what is commonly observed on the IV±IV or III±V semiconductor surfaces. Either on the Cd terminated surface with the c(2 £ 2) reconstruction or on the Te terminated surface with the (2 £ 1) reconstruction, the step edges are aligned along the k100l directions. This particular arrangement of step edges, showing that the free energy of the k100l steps is lower than that of the k110l steps, can be attributed to the electrostatic interactions along the charged steps. As a consequence, we observe after the growth by MBE and by atomic layer epitaxy (ALE) the formation of isotropic square islands with k100l edges. Furthermore the epitaxial growth on vicinal CdTe surfaces leads to a self organization of steps in a staircase or checkerboard array totally different from anything commonly seen on Si or GaAs. This paper reviews the original experimental results obtained by scanning probe microscopy on epitaxially grown (001) CdTe surfaces. After the experimental setup presented in Section 2, Section 3 is devoted to an extensive description of the CdTe(001) surface, including the smooth-
0040-6090/00/$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S00 40-6090(00)0066 2-3
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ing processes, the surface reconstructions, the islands morphology and the theoretical model explaining the in¯uence of ionic bonding on the surface structures. Section 4 presents the atomic layer epitaxy and the microscopic mechanisms involved in this self-regulated growth technique. Finally, the vicinal surfaces are described in Section 5 as well as the ®rst results on growing organized nanostructures on `staircase' and `checkerboard' steps arrays.
2. Experiments The experiments are performed in a ultra high vacuum system with facilities for epitaxy of II±VI compounds and STM imaging. The layers are principally grown by MBE, in the temperature range T sub 300±3308C. Because of the low bonding energy of II±VI compounds, we consider that at these temperatures, the surface has reached a thermal quasi equilibrium, and that the structures observed by STM have `equilibrium shapes'. To do self-regulated atomic layer epitaxy (ALE), the surface is sequentially exposed to Cd and Te ¯uxes with a dead time of a few seconds between each exposure. In-situ post-annealings with various atmospheres and temperatures are also performed. After cooling down to 2508C, under the thermal beam of Te2 molecules or Cd atoms, the samples are transferred through a gate valve to the STM apparatus. The STM images are obtained at room temperature with electrochemically etched tungsten tips at a voltage of 2±2.5 V and a tunnel current of typically 100 pA. The samples are illuminated with visible light in order to photogenerate carriers in the undoped epilayers and substrate. The borders of the STM images are systematically aligned along the [110] and [11Å0] directions identi®ed by the orientation of cleaved edges and of the (2 £ 1) Te reconstruction.
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3. The CdTe(001) surface 3.1. Preparation and smoothing of the CdTe(001) surface These STM studies are performed on commercial (001) Cd0.96Zn0.04Te substrates. After degreasing, etching in a 1% Bromine-Methanol solution and mounting, the samples are transferred in the UHV chamber and annealed at 3308C under a Cd ¯ux. Fig. 1a shows the morphology of the surface after this ®rst treatment. The STM picture is very fuzzy due to important noise in the tunneling current. Nevertheless the monomolecular terraces are observed with a faint contrast due to the presence of randomly distributed `white' protuberences with an apparent height of 1±2 nm. These `white' defects could be residual oxides (TeO2). In order to eliminate these surface defects, the substrate is treated with an hydrogen plasma in UHV after the chemical etching. This treatment is very ef®cient for removing residual oxides and bromides from the surface [9]. Fig. 1b shows the surface of a substrate after a 2 min H-pretreatment and an annealing at 3308C under a Cd ¯ux. The surface is now very smooth with well de®ned terraces separated by monomolecular steps. All the `white' defects have disappeared leaving only few dispersed monomolecular CdTe islands. Fig. 2a shows the surface obtained after the deposition of 50 nm of CdTe grown at 3008C at 0.2 ML/s and with a Cd/ Te ratio close to two on a substrate not treated with the hydrogen plasma. This surface is rough at the atomic scale with a high density of monomolecular islands with an average size of 10 nm. Smoothing this surface can be obtained by annealing under Cd or Te ¯ux at higher temperature [10]. Fig. 2b,c show the surface after annealing under a Cd ¯ux of 1.5 ML/s at 3608C for the former and under a Te ¯ux of 1 ML/s at 3308C for the later. These surfaces are very smooth with wide monomolecular terraces
Fig. 1. STM pictures of Cd0.96Zn0.04Te substrates after chemical preparation and annealing at 3308C under Cd ¯ux. (a) without the H plasma cleaning process; (b) with 2 nm H pretreatment before annealing.
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on the Cd terminated surfaces (Fig. 2a,b) or on the Te terminated surface (Fig. 2c). Furthermore these k100l step edges are also observed after controlled sublimation of the Te surface and after deposition of a fraction monolayer of CdTe by ALE. Fig. 3a has been obtained after annealing under Te ¯ux of 0.35 ML/s at 3208C. In these conditions, the equilibrium between the Te terminated surface and the vapor phase is displaced towards sublimation. The STM image reveals holes with a depth of one CdTe monolayer Ê ) attributed to a local thermal etching of the terraces (3.24 A due to the congruent sublimation of CdTe. The edges of these isotropic holes are also oriented preferentially along the k100l directions. Fig. 3b has been obtained after deposing a fractional monolayer of CdTe on a smoothed CdTe(001) surface by atomic layer epitaxy at T sub 3008C. This growth technique, described in Section 4, induces the formation of isolated monomolecular islands on the surface. The size of the islands increases with the temperature of deposition but they always keep square or rectangular shapes with k100l edges. The similarity of the structures observed either after deposition or after sublimation indicates that we are looking at equilibrium shapes. In order to understand this speci®c orientation of step edges along the k100l directions and not along the k110l direction as expected for tetrahedrally coordinated materials, it will be useful to look at islands with atomic resolution. Fig. 4a shows an island on the Cd terminated surface with the c(2 £ 2) reconstruction. On this image we identify the
Fig. 2. STM pictures of a 50 nm thick epitaxial CdTe(001) layer. (a) after a standard molecular beam deposition at 3008C. (b) same as (a) plus an annealing under a Cd ¯ux (1.5 ML/s) at 3608C. (c) same as (a) plus an annealing under a Te2 ¯ux (1.2 ML/s) at 3308C.
of several tenth of nm. The local misorientations of the (001) surface result in random steps and `giant' kinks. These smoothed surfaces are very interesting for the growth of quantum wells. Indeed with such smooth interfaces between the quantum well and the barrier, the optical spectra exhibit multiple excitonic peaks resulting from quantized thickness ¯uctuations on scale several times larger than the exciton Bohr radius [11]. 3.2. The Cd and the Te terminated CdTe(001) surfaces The peculiar morphology of the CdTe surface after growth appears clearly on Fig. 2. The key point is that the step edges are preferentially oriented along the k100l directions either
Fig. 3. STM pictures of a 50 nm thick epitaxial CdTe(001) layer. (a) after sublimation at 3208C under a low Te2 ¯ux (0.35 ML/s). (b) after depositing half a monolayer of CdTe by atomic layer epitaxy.
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Fig. 4. (a) Atomically resolved STM image of the Cd rich c(2 £ 2) reconstructed surface with a monomolecular island. (b) atomic representation of the c(2 £ 2) reconstruction showing the positions of the Cd and the Te atoms on the surface and on the monomolecular island. The shaded area indicate the (2 £ 1) domain walls.
rows of Cd atoms along the k100l directions, each Cd atom Ê side. This being situated at the corner of a square of 6.48 A two-fold symmetry is reproduced identically on a larger scale to build the square shape of the monomolecular island. The Cd terminated surface with the c(2 £ 2) reconstruction has two important characteristics: 1. The surface coverage is one half monolayer of Cd atoms. These atoms are aligned along the k100l-axis, they are not dimerized and they are in the plane of the Te underlayer as a result of molecular bonding [12]. 2. Two adjacent Te atoms on the [11Å0] direction have s molecular bond as a result of their incorporation in the dimer form Te2. An interesting question is: why does the Cd terminated surface adopt the c(2 £ 2) reconstruction rather than the (2 £ 1) with the same surface coverage of one half? The energy difference between these two reconstructions comes mostly from the electrostatic interactions between the charged atoms of the surface layer. Due to the ionicity of the II±VI compound, the Cd atoms have a positive effective charge of 0.33 electron and the Te atoms a negative
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charge of 20.33 electron [6] The (2 £ 1) reconstruction would induce in®nite rows along the [110] direction of positively charged Cd atoms alternating with two rows of negatively charged Te atoms. This charge con®guration, made of positively and negatively charged rows, have a high Coulomb energy. In the case of the c(2 £ 2) reconstruction the charged atoms are organized in a twofold symmetry similar to a NaCl plane with each Cd atoms having Te atoms for ®rst neighbors atoms. Then the Coulomb energy is lower than for the (2 £ 1) con®guration and electrostatic interactions between the charged atoms on the surface layer stabilize the c(2 £ 2) reconstruction [13]. An atomic representation of the island on the Cd terminated surface is shown on Fig. 4b. The k100l edges of the island correspond to the higher density directions for the Cd atoms. Starting from each corner, we also see stripes made of two rows of Cd which locally adopt the (2 £ 1) reconstruction. These stripes act as antiphase walls between two c(2 £ 2) domains. This is clearly observed in the STM image where the (2 £ 1) structure appears at each intersection of (100) steps. These stripes of (2 £ 1) reconstruction are necessary to build four identical step edges. The model also shows that there is two rows of Cd atoms in the lower level of the k100l edges. These rows offer sites with three or four Cd atoms very reactive for incorporation of the Te2 molecules diffusing on the c(2 £ 2) surface. Then the lateral growth of the island will proceed mainly perpendicular to the k100l edges with the same velocity for the four equivalent k100l directions. The k100l edges of the 2D islands on the Cd terminated surface can be explained by the twofold symmetry of the c(2 £ 2) reconstruction. In the case of the Te terminated surface with the (2 £ 1) reconstruction, the presence of k100l edges can not be induced by the surface symmetry. High resolution images revealing the reconstruction of the Te terminated surfaces and the atomic structure of the monomolecular islands are shown in Fig. 5. For the Te rich surface with the (2 £ 1) reconstruction, we observe on Fig. 5a the Te2 dimer rows parallel to the [110] direction despite the presence of Te2 diatomic molecules physisorbed during cooling down. The STM image is in close agreement with the relaxed structure calculated by ab initio method and shown below Fig. 5a. The result of the calculation con®rms the small outward relaxation, the large surface corrugation of the Te terminated surface and the p -like bonding of the Te2 dimer which explains the dif®culty to observe with STM the two Te atoms in a dimer. The second high resolution image (Fig. 5b) shows that the k100l edges are in fact made of a staggering of elementary kinks aligned along the [110] (B kinks) and the [11Å0] (A kinks)-axis. 3.3. The electrostatic model The main conclusion of this analysis is that k100l steps of the (2 £ 1) Te rich surface of CdTe have a formation energy which is lower than that of [110] (B-step) and [11Å0] (A-step)
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Fig. 5. (a) Atomically resolved STM image of the Te rich (2 £ 1) reconstructed surface. The atomic positions shown below result from an ab-initio calculation of the Te (2 £ 1) surface. (b) Atomically resolved STM image of the edges of a CdTe island on the Te (2 £ 1) surface. The atomic model is shown below with the electrostatic charge at the edges of the island.
edges. On Si this is the opposite while the symmetry and the atomic structure of the reconstructed (001) surface are similar. We think that the unusual behaviour of Te based II±VI materials can be found in the large ionicity of the bonding which results in charged steps. From this point of view, the CdTe(001) surface behaves more like MgO or NaCl ionic crystal surfaces where only k100l steps, with edges formed of a line of anions and cations pairs, are stable [14]. In order to elucidate the origin of the forces that stabilize the k100l con®guration, the contribution of the step energy E(n) to the total energy of a CdTe island deposited on a (001) CdTe surface is evaluated as a function of the number n of atoms forming `100' and `110' square islands. Their edge and charge con®gurations are depicted schematically on Fig. 6. Our simpli®ed calculation is based on an extension of the model of Tersoff and Tromp [15] which gives an analytical value of E(n) for a pseudomorphic island, where we add the coulombic
interactions between the charges located at the borders of the islands. We assume that these effective charges arise from the deviation of the electronic distribution at the step from that of the ¯at surface. For the B type steps on the Te rich surface, the Te atom sitting at the edge is coordinated with three Cd atoms instead of four in the bulk. In a purely ionic model, this is equivalent to a net positive charge of (1/4)q * compared to the effective charge q* equal to 0.33 electron in CdTe [6]. For the A-type steps this is the Cd atom which carries a net negative charge of (21/4)q *. Then, the interactions between these static charges lead to the Coulomb energy Ec n Ê is the M nijk q* =42 = 4p10 d110 where d110 4:54 A distance between the charged atoms along the k110l-axis. M(n) ijk is a 2D Madelung factor calculated numerically for the two charge con®gurations shown on Fig. 6. The interactions of these extra charges with the surface and bulk dipolar charges are of second order and thus can be neglected.
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parameters of the substrate (CdTe) and the islands (ZnTe) [16], decreases the energy difference between the two con®gurations but does not change the relative position of the curves of Fig. 6. The same estimate of E(n) made for GaAs by taking a line Ê [16] and q* 0:2 [6] is shown in Fig. tension of 55 meV/A 6. Because GaAs is stiffer and less ionic than CdTe, elasticity is predominant and the k110l steps are always more stable than the k100l. The small Coulomb energy affects only the short range kink-kink interactions [7] but not the overall shape of the islands which mimic more or less the symmetry of the surface reconstruction. For Si, where q* 0, the kink-kink interactions disappear and the line tension plays the major role so that anisotropic islands with [110] and [11Å0] edges are observed. 4. The atomic layer epitaxy
Fig. 6. Variations of the step energy vs. the number of atoms forming an island calculated for CdTe and GaAs. The calculation is made for the `110' and the `100' steps and charges con®gurations depicted above the curves. Black and white circles indicate, respectively, the position of cations and anions on step edges.
The other contributions Eel(n) to the total energy E(n) involves the line tension resulting from the broken bonds at the steps and the elastic relaxation induced by the long range interaction between step edges of the islands [3,15,16]. The relaxation term can be neglected for homoepitaxy of binary compounds due to the absence of domains of different reconstructed phases between adjacent terraces [3]. For heteroepitaxy, it is proportional to the square of the lattice mismatch [15,16]. The line tension energy, supposed to be proportional to the cohesive energy of the bulk mateÊ by scaling with rial, is estimated for CdTe around 27 meV/A the GaAs value [16]. For ideally square islands, which means that we do not consider a possible energy anisotropy p of A and B steps [17], Eel(n) is a factor 2 higher for the `100' than for the `110' con®guration due to the difference in the number of broken bonds. For the `110' con®guration, the corner energy can be disregarded because we only consider elementary kinks of length 2d[110] [18]. The plot of E n Eel n 1 Ec n, represented on Fig. 6, shows that the `100' island con®guration is more stable than the `110' for CdTe. This is because the gain in energy of the `100' con®guration due to the Coulomb interactions (Ec(n) is negative) is greater that the elastic energy cost due to a larger step length. For the `110' con®guration, the step length is shorter but Ec(n) is now positive and increases rapidly with n so that islands with straight k110l steps become unstable for n.30. Adding to Eel(n) the relaxation term, calculated for a mismatch of 7% between the lattice
The common way for growing high quality CdTe quantum structures is MBE and consist of exposing simultaneously the substrate to the ¯ux of Cd atoms and Te2 molecules. The growth is then characterized by the usual growth steps: diffusion of physisorbed atoms, nucleation and growth of islands. The second way of growth called atomic layer epitaxy (ALE) is obtained by exposing sequentially the surface to Cd and Te2 ¯uxes with a dead time of a few seconds between each exposure. Because the CdTe surface can be stabilized under an excess of cations (Cd) or anion (Te), in contrast to GaAs, a self regulated regime de®ned by the surface coverage of the reconstructed surfaces is expected and has been experimentally observed by several groups [19,20]. Each ALE cycle (exposure to Cd, growth interruption, exposure to Te, growth interruption) induces alternatively the c(2 £ 2) Cd and (2 £ 1) Te reconstructed surfaces, with surface coverages, respectively, equal to half a monolayer of Cd atoms and a full monolayer of Te atoms. This should lead to a self-regulated growth rate of 0.5 ML per cycle determined by the surface with the lowest coverage, i.e. the Cd c(2 £ 2) [20]. In order to check this behaviour, we have imaged by STM the surface after each step of a full ALE cycle. The ®rst image (step 1 of Fig. 7) shows a very smooth Cd terminated surface with few steps due to the slight misorientation of the substrate. On the second one (step 2), the surface is now Te terminated and there is a lot of monomolecular islands. The third image (step 3), obtained after Cd exposure, is slightly identical to the later with several islands. On the last one (step 4), the layer has been completed with few holes indicating that the growth rate is not exactly equal to 0.5 ML per cycle. The second and the fourth step show that CdTe material is only deposited after exposing the Cd stabilized surface to a Te2 molecular beam. The growth then proceeds by the formation of small and isolated islands and it is very different from what is obtained after MBE growth (Fig. 2a).
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Fig. 7. Surface morphology after each steps of two ALE cycles leading to the deposition of 1 ML of CdTe.
The islands are formed by the chemical reaction of the impinging Te2 molecules with the Cd atoms forming the c(2 £ 2) reconstruction. To form a CdTe islands needs to move chemisorbed Cd atoms along the [11Å0]-axis. This is very slow because it needs ®rst to break a Cd±Te bond and then a weak Te±Te bond. Moreover, moving Cd atoms along the perpendicular [110]-axis is strongly inhibited by the high energy cost necessary to break two Cd±Te bonds. The consequence of this slow diffusion rate of Cd atoms is an important nucleation rate explaining then the high density of islands. Fig. 8 show three images obtained after one ALE cycle, which corresponds to the deposition of half a monolayer of CdTe, at different substrate temperatures, respectively 280, 300 and 3208C. As expected for a diffusion limited growth model, the size of the islands increases with the substrate temperature while their density decreases. Simultaneously the width of the depleted zone free of islands in the vicinity of the step edges increases as a result of the step advancement. Assuming that the diffusion is anisotropic, the step advancement Dstep is given by the simple relation in the [11Å0] direction between the terrace length Lterrace and the sum of the island lengths on this terrace Lislands Lterrace 2qLislands 12Dstep
1
The factor two re¯ects the surface coverage of one half
monolayer in Cd atoms and the parameter q is a correction factor for tip effects. The images have been digitized and the analysis consists in measuring, on each line parallel to the [11Å0] direction, the length of the terraces and the length of their islands. Fig. 9a show the plot of Lterrace vs. Lislands and the linear ®t giving the value of the step advancement along the [11Å0] direction. One obtains a step advancement of 105 Ê at 2808C, 130 A Ê at 3008C and 155 A Ê at 3208C with an A Ê error of ^10 A. The same analysis made along the [110] direction does not show any simple relation between Lterrace and Lislands, as shown on Fig. 9b. This con®rms that the diffusion of chemisorbed Cd atoms is really anisotropic. If the substrate temperature is lowered below 2508C, the kinetic barriers contributes more to the surface morphology, and then the islands are small square forming long chains along the [110] direction as a result of the diffusion anisotropy of Cd atoms. 5. Growth on (100) vicinal surfaces The large ionicity of the bonding of CdTe has important consequences for the growth on vicinal surfaces where the knowledge acquired on Si and GaAs can not be transferred directly to CdTe(001) surfaces. For thermodynamic parameters favoring a step ¯ow growth mechanism, straight and equally spaced steps are expected on the CdTe C type
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Because of the low energy of formation of k100l steps, macro kinks with [100]-axis are easily excited forming sawtooth structures. However the steps of the A type surface are relatively smooth compared to those of B type which consist of a succession of small triangles with k100l edges. This difference is due to the stripes of (2 £ 1) reconstruction (the domain walls shown on Fig. 4) on the Cd terminated surface which link the corners. On the B type surface, these stripes of (2 £ 1) are perpendicular to the steps and they stabilize a lot of corners while on the A type surface they are parallel to the steps so that few corners are pinned along the steps. If now the growth of CdTe is performed on the A-type vicinal surface at a slow rate (below 0.1 ML/s) and at 3308C, a temperature higher than that commonly used in MBE, a quasi-equilibrium is reached consisting in a self organized checkerboard array of square terraces as shown in Fig. 11a. The formation of the checkerboard can be understood by analogy with the ordering of strained islands. But in the case of CdTe, the step edges interaction is rather coulombic than elastic as in Si [3,22]. The energetics of an array of interacting islands show that the equilibrium con®guration is a 2D periodic square lattice with primitive lattice vector along the direction with the lowest energy [23,24]. Then, for the A-type CdTe surface, the primitive lattice-axis of the surface array are the k100l directions which minimize the
Fig. 8. Evolution of the surface morphology after deposition of half a monolayer of CdTe by ALE as a function of substrate temperature.
surface with the surface normal tilted towards [100], instead of the A type surface tilted towards [110] as in GaAs [21]. This is demonstrated on Fig. 10a showing, after epitaxy, an STM image of a C type surface of CdTe with a miscut angle of 18. The k100l steps are parallel and regularly spaced with only microroughness corresponding to atomic kinks. This surface has been used to grow quantum wires and vertical superlattices by depositing fractional monolayer of CdTe and ZnTe or MgTe. Preliminary spectroscopic experiments have already shown optical properties characteristic of 1D structures. For A or B type CdTe surface, the k110l miscut-axis does not correspond to the energetically most favorable steps. Thus, the steps and terraces are extremely disordered as shown on Fig. 10b,c obtained on a A type and B type surface after the deposition of 50 nm of CdTe grown at 3008C at 0.2 ML/s followed by an annealing at 3608C index Cd excess.
Fig. 9. (a) plot of the terraces length (Lterraces) vs. the total length of the islands (Lislands) along the [11Å0] direction deduced from Fig. 8b. The linear ®t gives with the help of relation (IV-1) a measurement of the step advancement. (b) same as (a) along the [110] direction.
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6. Conclusions The STM studies of the polar (001) surface of CdTe have shown novel step con®gurations and island shapes in fourfold coordinated semiconductors with an atomic bonding dominated by ionic interactions. The 2D islands are isotropic with k100l edges and do not necessarily reproduce the symmetry of the surface reconstruction as in covalent materials. We suggest that in partially ionic II±VI compounds, the lowering of the free energy of k100l steps compared to that of the k110l steps results from the electrostatic interaction between the charges lying at the steps edges. This is con®rmed by a simpli®ed model incorporating these Coulomb interaction in the calculation of the total energy of the steps of square islands. The epitaxy of thin ®lms is also strongly affected by the peculiarity of the CdTe(001) surface, especially the atomic layer epitaxy. We show that this growth method is able to produce isolated and well de®ned monomolecular islands of any telluride compounds on a smooth surface. The size and
Fig. 10. STM pictures of CdTe(001) 18 vicinal surfaces after depositing 30 nm of CdTe by MBE and annealing. (a) C-type vicinal surface miscut towards [100]. (b) A-type vicinal surface miscut towards [110]. (c) Btype miscut towards [11Å0].
electrostatic contributions. Convoluted with the miscut towards [110], this results in a checkerboard arrangement of the monomolecular terraces. When half a monolayer of CdTe or ZnTe is deposited by ALE on the checkerboard at 3008C, square `quantum dots' made of a one monolayer high island, are observed as shown on Fig. 11b. The checkerboard organization is affected by the steps advancement but the `dots' tend to grow at the center of the terraces. This is a direct consequence of the mechanism of ALE described in the previous section. The obtaining of a single dot per terrace depends on the balance between nucleation on the terrace and incorporation of the Te2 molecules at step edges. If the temperature is too high, the step advancement dominates and no dots are observed. If the temperature is too low, several islands nucleate on the terraces.
Fig. 11. (a) STM picture of a checkerboard array obtained on the Te terminated A-type vicinal surface. (b) STM picture obtained after the deposition of half a monolayer of CdTe by ALE on the checkerboard shown in (a).
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the distribution of islands is de®ned by the strong anisotropic diffusion of chemisorbed Cd atoms. All these results have been used to ®nd out and to prepare the vicinal surfaces of CdTe suitable for growing self organized quantum nanostructures. This is the C-type vicinal surface, miscut towards [100], which organizes in a regular staircase array of monomolecular steps. This surface is shown to be the best template for growing telluride based quantum wires. Contrary to the C-type surface, the steps are very rough on A and B-type vicinal surfaces. This is because the [110] and [11Å0] miscut-axis differ from the energetically most favorable steps direction, i.e. the k100l-axis. But if the growth conditions are modi®ed in order to deposit the telluride layers as close as possible to the thermodynamic equilibrium (very low growth rate and high substrate temperature), the A-type surface can be organized in a checkerboard array of square terraces. This surface is shown to be the template for growing self assembled and self organized quantum `dots'. Acknowledgements The authors specially thanks P. Gentile for its skillful technical assistance, J. Eymery for the ab-initio calculations of the reconstructed surfaces of CdTe and very fruitful discussions, L. Besombes and V. Huard for the optical spectroscopy data. This work was made possible with the constant support of J.L. Pautrat.
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References [1] Y.W. Mo, M.G. Lagally, Surf. Sci. 248 (1991) 313. [2] Y.W. Mo, et al., Phys. Rev. Lett. 63 (1989) 2392. [3] O.L. Alerhand, D. Vanderbilt, R.D. Meade, J.D. Joannopoulos, Phys. Rev. Lett. 61 (1988) 1973. [4] M.D. Pashley, K.W. Haberern, J.M. Gaines, Appl. Phys. Lett. 58 (1991) 406. [5] M.D. Pashley, Phys. Rev. B 40 (1989) 10481. [6] J.C. Philips, Bonds and Bands in Semiconductors, Academic Press, New York, 1973. [7] E.J. Heller, M.G. Lagally, Phys. Rev. Lett. 71 (1993) 743. [8] F. Lelarge, Z.Z. Wang, A. Cavanna, F. Laruelle, B. Etienne, EuroPhys. Lett. 39 (1997) 97. [9] E. Picard, P. Gentile, D. Martrou, N. Magnea, Appl. Phys. Lett. 75 (5) (1999) 677. [10] D. Martou, et al., J. Cryst. Growth 184 (1998) 203. [11] L. Besombes, et al., Phys. Rev. B. Submitted for publication. [12] M.B. Veron, et al., Appl. Phys. Lett. 67 (1995) 155. [13] C. Noguera, Physics and Chemistry of Oxide Surface, Cambridge University Press, Cambridge, 1996. [14] Y.W. Tsang, L.M. Falicov, Phys. Rev. B 12 (1975) 2441. [15] J. Tersoff, R.M. Tromp, Phys. Rev. Lett. 70 (1993) 2782. [16] C. Priester, M. Lannoo, Phys. Rev. Lett. 75 (1995) 93. [17] D.J. Chadi, Phys. Rev. Lett. 59 (1987) 1691. [18] H.J.W. Zandvliet, et al., Phys. Rev. 45 (1992) 5965. [19] B. Daudin, S. Tatarenko, D. Brun-Le, Cunff, Phys. Rev. B 52 (1995) 7822. [20] W. Fashinger, et al., Mater. Sci. Eng. B 16 (1993) 79. [21] P.R. Pukite, et al., J. Cryst. Growth 95 (1989) 269. [22] C. Ebner, D.E. Jones, J.P. Pelz, Phys. Rev. B 56 (1997) 1581. [23] P. Zeppenfeld, et al., Phys. Rev. Lett. 72 (1994) 2737. [24] V.A. Shchukin, et al., Phys. Rev. Lett. 75 (1995) 2968.
Equilibrium shape of steps and islands on polar CdTe(001) surface: application to the preparation of self organized templates for growth of nanostructures D. Martrou*, N. Magnea DeÂpartement de Recherche Fondamentale sur la MatieÁre CondenseÂe, SP2M/PS, CEA-Grenoble, France
Abstract Scanning tunneling microscopy studies of (001) CdTe, a partially ionic II±VI compound, show novel surface structures with step and 2D islands edges aligned along the k100l crystallographic directions. This behaviour, which is not observed in covalent material, is interpreted in the framework of a model incorporating electrostatic interactions in the calculation of the energy of charged steps that could explain why the free energy of k100l steps lies below that of the [110] and [11Å0] steps. These results provide new insights about the microscopic growth mode of CdTe especially by atomic layer epitaxy. The energetics of the vicinal surfaces is also strongly in¯uenced by these effects which allows one to organize C-type and A-type surfaces in staircase and checkerboard arrays. These self organized templates are, respectively, used to grow quantum wires and quantum dots. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Scanning tunneling microscopy; Self organization phenomena; Nanotechnology; Quantum dots; Quantum wires; Atomic layer epitaxy
1. Introduction The growth of quantum nanostructures based on semiconductors has raised a strong interest in the comprehension of the growth mechanisms and of the organization of the surfaces during molecular beam epitaxy (MBE). The use of scanning tunneling microscopy (STM) can bring a lot of information for understanding the surface behavior and optimizing the growth conditions. The studies made on the silicon (001) surface with the (2 £ 1) reconstruction show that the `growth shapes' are islands elongated in the k110l directions as a result of the strong preference of atoms to stick at the end of the Si dimer rows rather than at the sides [1]. The `equilibrium shapes' of the islands are made of rectangles with k110l edges and an aspect ratio close to 3, re¯ecting here the free energy ratio between the [110] and the [11Å0] steps [2]. The bond anisotropy accounts also for the surface stress domains, the step roughness and the elastic interactions between steps [3]. On the polar galliumarsenide(001) surface, the most commonly observed reconstruction is (2 £ 4) or c(2 £ 8) involving As dimers. At equilibrium, the islands are anisotropic structures with their long edge in the [11Å0] direction, the 2 £ direction [4,5]. It has * Corresponding author. CEA/DRFMC/SPMM/PSC, 17 Avenue des Martyrs, 38054 Grenoble Cedex 9, France. Tel.: 133-476-885-592; fax: 133-476-885-821. E-mail address: [email protected] (D. Martrou)
been shown that the ionicity of the Ga±As bond (Philips' ionicity fi 0:3) [6], affects only the short range kink interactions [7] and also the step coupling [8] without modifying the surface morphology from that seen on the purely covalent Si surface. Our STM studies, made on the (001) CdTe surface, show that the behavior of this semiconductor with stronger ionicity (fi 0:717) [6] is different of what is commonly observed on the IV±IV or III±V semiconductor surfaces. Either on the Cd terminated surface with the c(2 £ 2) reconstruction or on the Te terminated surface with the (2 £ 1) reconstruction, the step edges are aligned along the k100l directions. This particular arrangement of step edges, showing that the free energy of the k100l steps is lower than that of the k110l steps, can be attributed to the electrostatic interactions along the charged steps. As a consequence, we observe after the growth by MBE and by atomic layer epitaxy (ALE) the formation of isotropic square islands with k100l edges. Furthermore the epitaxial growth on vicinal CdTe surfaces leads to a self organization of steps in a staircase or checkerboard array totally different from anything commonly seen on Si or GaAs. This paper reviews the original experimental results obtained by scanning probe microscopy on epitaxially grown (001) CdTe surfaces. After the experimental setup presented in Section 2, Section 3 is devoted to an extensive description of the CdTe(001) surface, including the smooth-
0040-6090/00/$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S00 40-6090(00)0066 2-3
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ing processes, the surface reconstructions, the islands morphology and the theoretical model explaining the in¯uence of ionic bonding on the surface structures. Section 4 presents the atomic layer epitaxy and the microscopic mechanisms involved in this self-regulated growth technique. Finally, the vicinal surfaces are described in Section 5 as well as the ®rst results on growing organized nanostructures on `staircase' and `checkerboard' steps arrays.
2. Experiments The experiments are performed in a ultra high vacuum system with facilities for epitaxy of II±VI compounds and STM imaging. The layers are principally grown by MBE, in the temperature range T sub 300±3308C. Because of the low bonding energy of II±VI compounds, we consider that at these temperatures, the surface has reached a thermal quasi equilibrium, and that the structures observed by STM have `equilibrium shapes'. To do self-regulated atomic layer epitaxy (ALE), the surface is sequentially exposed to Cd and Te ¯uxes with a dead time of a few seconds between each exposure. In-situ post-annealings with various atmospheres and temperatures are also performed. After cooling down to 2508C, under the thermal beam of Te2 molecules or Cd atoms, the samples are transferred through a gate valve to the STM apparatus. The STM images are obtained at room temperature with electrochemically etched tungsten tips at a voltage of 2±2.5 V and a tunnel current of typically 100 pA. The samples are illuminated with visible light in order to photogenerate carriers in the undoped epilayers and substrate. The borders of the STM images are systematically aligned along the [110] and [11Å0] directions identi®ed by the orientation of cleaved edges and of the (2 £ 1) Te reconstruction.
49
3. The CdTe(001) surface 3.1. Preparation and smoothing of the CdTe(001) surface These STM studies are performed on commercial (001) Cd0.96Zn0.04Te substrates. After degreasing, etching in a 1% Bromine-Methanol solution and mounting, the samples are transferred in the UHV chamber and annealed at 3308C under a Cd ¯ux. Fig. 1a shows the morphology of the surface after this ®rst treatment. The STM picture is very fuzzy due to important noise in the tunneling current. Nevertheless the monomolecular terraces are observed with a faint contrast due to the presence of randomly distributed `white' protuberences with an apparent height of 1±2 nm. These `white' defects could be residual oxides (TeO2). In order to eliminate these surface defects, the substrate is treated with an hydrogen plasma in UHV after the chemical etching. This treatment is very ef®cient for removing residual oxides and bromides from the surface [9]. Fig. 1b shows the surface of a substrate after a 2 min H-pretreatment and an annealing at 3308C under a Cd ¯ux. The surface is now very smooth with well de®ned terraces separated by monomolecular steps. All the `white' defects have disappeared leaving only few dispersed monomolecular CdTe islands. Fig. 2a shows the surface obtained after the deposition of 50 nm of CdTe grown at 3008C at 0.2 ML/s and with a Cd/ Te ratio close to two on a substrate not treated with the hydrogen plasma. This surface is rough at the atomic scale with a high density of monomolecular islands with an average size of 10 nm. Smoothing this surface can be obtained by annealing under Cd or Te ¯ux at higher temperature [10]. Fig. 2b,c show the surface after annealing under a Cd ¯ux of 1.5 ML/s at 3608C for the former and under a Te ¯ux of 1 ML/s at 3308C for the later. These surfaces are very smooth with wide monomolecular terraces
Fig. 1. STM pictures of Cd0.96Zn0.04Te substrates after chemical preparation and annealing at 3308C under Cd ¯ux. (a) without the H plasma cleaning process; (b) with 2 nm H pretreatment before annealing.
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D. Martrou, N. Magnea / Thin Solid Films 367 (2000) 48±57
on the Cd terminated surfaces (Fig. 2a,b) or on the Te terminated surface (Fig. 2c). Furthermore these k100l step edges are also observed after controlled sublimation of the Te surface and after deposition of a fraction monolayer of CdTe by ALE. Fig. 3a has been obtained after annealing under Te ¯ux of 0.35 ML/s at 3208C. In these conditions, the equilibrium between the Te terminated surface and the vapor phase is displaced towards sublimation. The STM image reveals holes with a depth of one CdTe monolayer Ê ) attributed to a local thermal etching of the terraces (3.24 A due to the congruent sublimation of CdTe. The edges of these isotropic holes are also oriented preferentially along the k100l directions. Fig. 3b has been obtained after deposing a fractional monolayer of CdTe on a smoothed CdTe(001) surface by atomic layer epitaxy at T sub 3008C. This growth technique, described in Section 4, induces the formation of isolated monomolecular islands on the surface. The size of the islands increases with the temperature of deposition but they always keep square or rectangular shapes with k100l edges. The similarity of the structures observed either after deposition or after sublimation indicates that we are looking at equilibrium shapes. In order to understand this speci®c orientation of step edges along the k100l directions and not along the k110l direction as expected for tetrahedrally coordinated materials, it will be useful to look at islands with atomic resolution. Fig. 4a shows an island on the Cd terminated surface with the c(2 £ 2) reconstruction. On this image we identify the
Fig. 2. STM pictures of a 50 nm thick epitaxial CdTe(001) layer. (a) after a standard molecular beam deposition at 3008C. (b) same as (a) plus an annealing under a Cd ¯ux (1.5 ML/s) at 3608C. (c) same as (a) plus an annealing under a Te2 ¯ux (1.2 ML/s) at 3308C.
of several tenth of nm. The local misorientations of the (001) surface result in random steps and `giant' kinks. These smoothed surfaces are very interesting for the growth of quantum wells. Indeed with such smooth interfaces between the quantum well and the barrier, the optical spectra exhibit multiple excitonic peaks resulting from quantized thickness ¯uctuations on scale several times larger than the exciton Bohr radius [11]. 3.2. The Cd and the Te terminated CdTe(001) surfaces The peculiar morphology of the CdTe surface after growth appears clearly on Fig. 2. The key point is that the step edges are preferentially oriented along the k100l directions either
Fig. 3. STM pictures of a 50 nm thick epitaxial CdTe(001) layer. (a) after sublimation at 3208C under a low Te2 ¯ux (0.35 ML/s). (b) after depositing half a monolayer of CdTe by atomic layer epitaxy.
D. Martrou, N. Magnea / Thin Solid Films 367 (2000) 48±57
Fig. 4. (a) Atomically resolved STM image of the Cd rich c(2 £ 2) reconstructed surface with a monomolecular island. (b) atomic representation of the c(2 £ 2) reconstruction showing the positions of the Cd and the Te atoms on the surface and on the monomolecular island. The shaded area indicate the (2 £ 1) domain walls.
rows of Cd atoms along the k100l directions, each Cd atom Ê side. This being situated at the corner of a square of 6.48 A two-fold symmetry is reproduced identically on a larger scale to build the square shape of the monomolecular island. The Cd terminated surface with the c(2 £ 2) reconstruction has two important characteristics: 1. The surface coverage is one half monolayer of Cd atoms. These atoms are aligned along the k100l-axis, they are not dimerized and they are in the plane of the Te underlayer as a result of molecular bonding [12]. 2. Two adjacent Te atoms on the [11Å0] direction have s molecular bond as a result of their incorporation in the dimer form Te2. An interesting question is: why does the Cd terminated surface adopt the c(2 £ 2) reconstruction rather than the (2 £ 1) with the same surface coverage of one half? The energy difference between these two reconstructions comes mostly from the electrostatic interactions between the charged atoms of the surface layer. Due to the ionicity of the II±VI compound, the Cd atoms have a positive effective charge of 0.33 electron and the Te atoms a negative
51
charge of 20.33 electron [6] The (2 £ 1) reconstruction would induce in®nite rows along the [110] direction of positively charged Cd atoms alternating with two rows of negatively charged Te atoms. This charge con®guration, made of positively and negatively charged rows, have a high Coulomb energy. In the case of the c(2 £ 2) reconstruction the charged atoms are organized in a twofold symmetry similar to a NaCl plane with each Cd atoms having Te atoms for ®rst neighbors atoms. Then the Coulomb energy is lower than for the (2 £ 1) con®guration and electrostatic interactions between the charged atoms on the surface layer stabilize the c(2 £ 2) reconstruction [13]. An atomic representation of the island on the Cd terminated surface is shown on Fig. 4b. The k100l edges of the island correspond to the higher density directions for the Cd atoms. Starting from each corner, we also see stripes made of two rows of Cd which locally adopt the (2 £ 1) reconstruction. These stripes act as antiphase walls between two c(2 £ 2) domains. This is clearly observed in the STM image where the (2 £ 1) structure appears at each intersection of (100) steps. These stripes of (2 £ 1) reconstruction are necessary to build four identical step edges. The model also shows that there is two rows of Cd atoms in the lower level of the k100l edges. These rows offer sites with three or four Cd atoms very reactive for incorporation of the Te2 molecules diffusing on the c(2 £ 2) surface. Then the lateral growth of the island will proceed mainly perpendicular to the k100l edges with the same velocity for the four equivalent k100l directions. The k100l edges of the 2D islands on the Cd terminated surface can be explained by the twofold symmetry of the c(2 £ 2) reconstruction. In the case of the Te terminated surface with the (2 £ 1) reconstruction, the presence of k100l edges can not be induced by the surface symmetry. High resolution images revealing the reconstruction of the Te terminated surfaces and the atomic structure of the monomolecular islands are shown in Fig. 5. For the Te rich surface with the (2 £ 1) reconstruction, we observe on Fig. 5a the Te2 dimer rows parallel to the [110] direction despite the presence of Te2 diatomic molecules physisorbed during cooling down. The STM image is in close agreement with the relaxed structure calculated by ab initio method and shown below Fig. 5a. The result of the calculation con®rms the small outward relaxation, the large surface corrugation of the Te terminated surface and the p -like bonding of the Te2 dimer which explains the dif®culty to observe with STM the two Te atoms in a dimer. The second high resolution image (Fig. 5b) shows that the k100l edges are in fact made of a staggering of elementary kinks aligned along the [110] (B kinks) and the [11Å0] (A kinks)-axis. 3.3. The electrostatic model The main conclusion of this analysis is that k100l steps of the (2 £ 1) Te rich surface of CdTe have a formation energy which is lower than that of [110] (B-step) and [11Å0] (A-step)
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Fig. 5. (a) Atomically resolved STM image of the Te rich (2 £ 1) reconstructed surface. The atomic positions shown below result from an ab-initio calculation of the Te (2 £ 1) surface. (b) Atomically resolved STM image of the edges of a CdTe island on the Te (2 £ 1) surface. The atomic model is shown below with the electrostatic charge at the edges of the island.
edges. On Si this is the opposite while the symmetry and the atomic structure of the reconstructed (001) surface are similar. We think that the unusual behaviour of Te based II±VI materials can be found in the large ionicity of the bonding which results in charged steps. From this point of view, the CdTe(001) surface behaves more like MgO or NaCl ionic crystal surfaces where only k100l steps, with edges formed of a line of anions and cations pairs, are stable [14]. In order to elucidate the origin of the forces that stabilize the k100l con®guration, the contribution of the step energy E(n) to the total energy of a CdTe island deposited on a (001) CdTe surface is evaluated as a function of the number n of atoms forming `100' and `110' square islands. Their edge and charge con®gurations are depicted schematically on Fig. 6. Our simpli®ed calculation is based on an extension of the model of Tersoff and Tromp [15] which gives an analytical value of E(n) for a pseudomorphic island, where we add the coulombic
interactions between the charges located at the borders of the islands. We assume that these effective charges arise from the deviation of the electronic distribution at the step from that of the ¯at surface. For the B type steps on the Te rich surface, the Te atom sitting at the edge is coordinated with three Cd atoms instead of four in the bulk. In a purely ionic model, this is equivalent to a net positive charge of (1/4)q * compared to the effective charge q* equal to 0.33 electron in CdTe [6]. For the A-type steps this is the Cd atom which carries a net negative charge of (21/4)q *. Then, the interactions between these static charges lead to the Coulomb energy Ec n Ê is the M nijk q* =42 = 4p10 d110 where d110 4:54 A distance between the charged atoms along the k110l-axis. M(n) ijk is a 2D Madelung factor calculated numerically for the two charge con®gurations shown on Fig. 6. The interactions of these extra charges with the surface and bulk dipolar charges are of second order and thus can be neglected.
D. Martrou, N. Magnea / Thin Solid Films 367 (2000) 48±57
53
parameters of the substrate (CdTe) and the islands (ZnTe) [16], decreases the energy difference between the two con®gurations but does not change the relative position of the curves of Fig. 6. The same estimate of E(n) made for GaAs by taking a line Ê [16] and q* 0:2 [6] is shown in Fig. tension of 55 meV/A 6. Because GaAs is stiffer and less ionic than CdTe, elasticity is predominant and the k110l steps are always more stable than the k100l. The small Coulomb energy affects only the short range kink-kink interactions [7] but not the overall shape of the islands which mimic more or less the symmetry of the surface reconstruction. For Si, where q* 0, the kink-kink interactions disappear and the line tension plays the major role so that anisotropic islands with [110] and [11Å0] edges are observed. 4. The atomic layer epitaxy
Fig. 6. Variations of the step energy vs. the number of atoms forming an island calculated for CdTe and GaAs. The calculation is made for the `110' and the `100' steps and charges con®gurations depicted above the curves. Black and white circles indicate, respectively, the position of cations and anions on step edges.
The other contributions Eel(n) to the total energy E(n) involves the line tension resulting from the broken bonds at the steps and the elastic relaxation induced by the long range interaction between step edges of the islands [3,15,16]. The relaxation term can be neglected for homoepitaxy of binary compounds due to the absence of domains of different reconstructed phases between adjacent terraces [3]. For heteroepitaxy, it is proportional to the square of the lattice mismatch [15,16]. The line tension energy, supposed to be proportional to the cohesive energy of the bulk mateÊ by scaling with rial, is estimated for CdTe around 27 meV/A the GaAs value [16]. For ideally square islands, which means that we do not consider a possible energy anisotropy p of A and B steps [17], Eel(n) is a factor 2 higher for the `100' than for the `110' con®guration due to the difference in the number of broken bonds. For the `110' con®guration, the corner energy can be disregarded because we only consider elementary kinks of length 2d[110] [18]. The plot of E n Eel n 1 Ec n, represented on Fig. 6, shows that the `100' island con®guration is more stable than the `110' for CdTe. This is because the gain in energy of the `100' con®guration due to the Coulomb interactions (Ec(n) is negative) is greater that the elastic energy cost due to a larger step length. For the `110' con®guration, the step length is shorter but Ec(n) is now positive and increases rapidly with n so that islands with straight k110l steps become unstable for n.30. Adding to Eel(n) the relaxation term, calculated for a mismatch of 7% between the lattice
The common way for growing high quality CdTe quantum structures is MBE and consist of exposing simultaneously the substrate to the ¯ux of Cd atoms and Te2 molecules. The growth is then characterized by the usual growth steps: diffusion of physisorbed atoms, nucleation and growth of islands. The second way of growth called atomic layer epitaxy (ALE) is obtained by exposing sequentially the surface to Cd and Te2 ¯uxes with a dead time of a few seconds between each exposure. Because the CdTe surface can be stabilized under an excess of cations (Cd) or anion (Te), in contrast to GaAs, a self regulated regime de®ned by the surface coverage of the reconstructed surfaces is expected and has been experimentally observed by several groups [19,20]. Each ALE cycle (exposure to Cd, growth interruption, exposure to Te, growth interruption) induces alternatively the c(2 £ 2) Cd and (2 £ 1) Te reconstructed surfaces, with surface coverages, respectively, equal to half a monolayer of Cd atoms and a full monolayer of Te atoms. This should lead to a self-regulated growth rate of 0.5 ML per cycle determined by the surface with the lowest coverage, i.e. the Cd c(2 £ 2) [20]. In order to check this behaviour, we have imaged by STM the surface after each step of a full ALE cycle. The ®rst image (step 1 of Fig. 7) shows a very smooth Cd terminated surface with few steps due to the slight misorientation of the substrate. On the second one (step 2), the surface is now Te terminated and there is a lot of monomolecular islands. The third image (step 3), obtained after Cd exposure, is slightly identical to the later with several islands. On the last one (step 4), the layer has been completed with few holes indicating that the growth rate is not exactly equal to 0.5 ML per cycle. The second and the fourth step show that CdTe material is only deposited after exposing the Cd stabilized surface to a Te2 molecular beam. The growth then proceeds by the formation of small and isolated islands and it is very different from what is obtained after MBE growth (Fig. 2a).
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Fig. 7. Surface morphology after each steps of two ALE cycles leading to the deposition of 1 ML of CdTe.
The islands are formed by the chemical reaction of the impinging Te2 molecules with the Cd atoms forming the c(2 £ 2) reconstruction. To form a CdTe islands needs to move chemisorbed Cd atoms along the [11Å0]-axis. This is very slow because it needs ®rst to break a Cd±Te bond and then a weak Te±Te bond. Moreover, moving Cd atoms along the perpendicular [110]-axis is strongly inhibited by the high energy cost necessary to break two Cd±Te bonds. The consequence of this slow diffusion rate of Cd atoms is an important nucleation rate explaining then the high density of islands. Fig. 8 show three images obtained after one ALE cycle, which corresponds to the deposition of half a monolayer of CdTe, at different substrate temperatures, respectively 280, 300 and 3208C. As expected for a diffusion limited growth model, the size of the islands increases with the substrate temperature while their density decreases. Simultaneously the width of the depleted zone free of islands in the vicinity of the step edges increases as a result of the step advancement. Assuming that the diffusion is anisotropic, the step advancement Dstep is given by the simple relation in the [11Å0] direction between the terrace length Lterrace and the sum of the island lengths on this terrace Lislands Lterrace 2qLislands 12Dstep
1
The factor two re¯ects the surface coverage of one half
monolayer in Cd atoms and the parameter q is a correction factor for tip effects. The images have been digitized and the analysis consists in measuring, on each line parallel to the [11Å0] direction, the length of the terraces and the length of their islands. Fig. 9a show the plot of Lterrace vs. Lislands and the linear ®t giving the value of the step advancement along the [11Å0] direction. One obtains a step advancement of 105 Ê at 2808C, 130 A Ê at 3008C and 155 A Ê at 3208C with an A Ê error of ^10 A. The same analysis made along the [110] direction does not show any simple relation between Lterrace and Lislands, as shown on Fig. 9b. This con®rms that the diffusion of chemisorbed Cd atoms is really anisotropic. If the substrate temperature is lowered below 2508C, the kinetic barriers contributes more to the surface morphology, and then the islands are small square forming long chains along the [110] direction as a result of the diffusion anisotropy of Cd atoms. 5. Growth on (100) vicinal surfaces The large ionicity of the bonding of CdTe has important consequences for the growth on vicinal surfaces where the knowledge acquired on Si and GaAs can not be transferred directly to CdTe(001) surfaces. For thermodynamic parameters favoring a step ¯ow growth mechanism, straight and equally spaced steps are expected on the CdTe C type
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Because of the low energy of formation of k100l steps, macro kinks with [100]-axis are easily excited forming sawtooth structures. However the steps of the A type surface are relatively smooth compared to those of B type which consist of a succession of small triangles with k100l edges. This difference is due to the stripes of (2 £ 1) reconstruction (the domain walls shown on Fig. 4) on the Cd terminated surface which link the corners. On the B type surface, these stripes of (2 £ 1) are perpendicular to the steps and they stabilize a lot of corners while on the A type surface they are parallel to the steps so that few corners are pinned along the steps. If now the growth of CdTe is performed on the A-type vicinal surface at a slow rate (below 0.1 ML/s) and at 3308C, a temperature higher than that commonly used in MBE, a quasi-equilibrium is reached consisting in a self organized checkerboard array of square terraces as shown in Fig. 11a. The formation of the checkerboard can be understood by analogy with the ordering of strained islands. But in the case of CdTe, the step edges interaction is rather coulombic than elastic as in Si [3,22]. The energetics of an array of interacting islands show that the equilibrium con®guration is a 2D periodic square lattice with primitive lattice vector along the direction with the lowest energy [23,24]. Then, for the A-type CdTe surface, the primitive lattice-axis of the surface array are the k100l directions which minimize the
Fig. 8. Evolution of the surface morphology after deposition of half a monolayer of CdTe by ALE as a function of substrate temperature.
surface with the surface normal tilted towards [100], instead of the A type surface tilted towards [110] as in GaAs [21]. This is demonstrated on Fig. 10a showing, after epitaxy, an STM image of a C type surface of CdTe with a miscut angle of 18. The k100l steps are parallel and regularly spaced with only microroughness corresponding to atomic kinks. This surface has been used to grow quantum wires and vertical superlattices by depositing fractional monolayer of CdTe and ZnTe or MgTe. Preliminary spectroscopic experiments have already shown optical properties characteristic of 1D structures. For A or B type CdTe surface, the k110l miscut-axis does not correspond to the energetically most favorable steps. Thus, the steps and terraces are extremely disordered as shown on Fig. 10b,c obtained on a A type and B type surface after the deposition of 50 nm of CdTe grown at 3008C at 0.2 ML/s followed by an annealing at 3608C index Cd excess.
Fig. 9. (a) plot of the terraces length (Lterraces) vs. the total length of the islands (Lislands) along the [11Å0] direction deduced from Fig. 8b. The linear ®t gives with the help of relation (IV-1) a measurement of the step advancement. (b) same as (a) along the [110] direction.
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6. Conclusions The STM studies of the polar (001) surface of CdTe have shown novel step con®gurations and island shapes in fourfold coordinated semiconductors with an atomic bonding dominated by ionic interactions. The 2D islands are isotropic with k100l edges and do not necessarily reproduce the symmetry of the surface reconstruction as in covalent materials. We suggest that in partially ionic II±VI compounds, the lowering of the free energy of k100l steps compared to that of the k110l steps results from the electrostatic interaction between the charges lying at the steps edges. This is con®rmed by a simpli®ed model incorporating these Coulomb interaction in the calculation of the total energy of the steps of square islands. The epitaxy of thin ®lms is also strongly affected by the peculiarity of the CdTe(001) surface, especially the atomic layer epitaxy. We show that this growth method is able to produce isolated and well de®ned monomolecular islands of any telluride compounds on a smooth surface. The size and
Fig. 10. STM pictures of CdTe(001) 18 vicinal surfaces after depositing 30 nm of CdTe by MBE and annealing. (a) C-type vicinal surface miscut towards [100]. (b) A-type vicinal surface miscut towards [110]. (c) Btype miscut towards [11Å0].
electrostatic contributions. Convoluted with the miscut towards [110], this results in a checkerboard arrangement of the monomolecular terraces. When half a monolayer of CdTe or ZnTe is deposited by ALE on the checkerboard at 3008C, square `quantum dots' made of a one monolayer high island, are observed as shown on Fig. 11b. The checkerboard organization is affected by the steps advancement but the `dots' tend to grow at the center of the terraces. This is a direct consequence of the mechanism of ALE described in the previous section. The obtaining of a single dot per terrace depends on the balance between nucleation on the terrace and incorporation of the Te2 molecules at step edges. If the temperature is too high, the step advancement dominates and no dots are observed. If the temperature is too low, several islands nucleate on the terraces.
Fig. 11. (a) STM picture of a checkerboard array obtained on the Te terminated A-type vicinal surface. (b) STM picture obtained after the deposition of half a monolayer of CdTe by ALE on the checkerboard shown in (a).
D. Martrou, N. Magnea / Thin Solid Films 367 (2000) 48±57
the distribution of islands is de®ned by the strong anisotropic diffusion of chemisorbed Cd atoms. All these results have been used to ®nd out and to prepare the vicinal surfaces of CdTe suitable for growing self organized quantum nanostructures. This is the C-type vicinal surface, miscut towards [100], which organizes in a regular staircase array of monomolecular steps. This surface is shown to be the best template for growing telluride based quantum wires. Contrary to the C-type surface, the steps are very rough on A and B-type vicinal surfaces. This is because the [110] and [11Å0] miscut-axis differ from the energetically most favorable steps direction, i.e. the k100l-axis. But if the growth conditions are modi®ed in order to deposit the telluride layers as close as possible to the thermodynamic equilibrium (very low growth rate and high substrate temperature), the A-type surface can be organized in a checkerboard array of square terraces. This surface is shown to be the template for growing self assembled and self organized quantum `dots'. Acknowledgements The authors specially thanks P. Gentile for its skillful technical assistance, J. Eymery for the ab-initio calculations of the reconstructed surfaces of CdTe and very fruitful discussions, L. Besombes and V. Huard for the optical spectroscopy data. This work was made possible with the constant support of J.L. Pautrat.
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