Uniform and ordered self-assembled Ge dots on patterned Si substrates with selectively epitaxial growth technique

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1 Journal of Crystal Growth (2001) Uniform and ordered self-assembled Ge dots on patterned Si substrates with selectively epitaxial growth technique G. Jin*, J. Wan, Y.H. Luo, J.L. Liu, K.L. Wang Device Research Laboratory, Department of Electrical Engineering, University of California at Los Angeles, Los Angeles, CA , USA Abstract In this work, we report the controlled growth of one-dimensional (1D) and two-dimensional uniform, well-arranged self-assembled Ge dots grown on patterned Si (0 0 1) substrates. Selectively epitaxial growth (SEG) of Si mesas was first performed in an MBE system equipped with a gas source of Si 2 H 6 and a Knudsen cell of Ge. Self-assembled Ge dots on one-dimensional Si SEG stripe mesas demonstrate the periodic arrangement with uniform size, which is different from the bi-modal distribution as normally seen. This cooperative arrangement is attributed to the nature of self-regulation of the self-assembled system with the assistance of the spatial confinement. A systematic study of the one-dimensional arrangement will be discussed. The atomic force microscopic results of two-dimensional arrays show that there are several kinds of the arrangement configurations, indicating the possibility of the controlling the placement of selfassembled Ge dots. Finally, we will discuss the mechanisms of the cooperative arrangements and the possibility to control freely spontaneous growth of Ge dots on pre-grown Si mesas. # 2001 Published by Elsevier Science B.V. PACS: Hi; g; Jk; Ux Keywords: A1. Nanostructures; A3. Selective epitaxy; B1. Nanomaterials 1. Introduction Self-assembly of heterostructure growth has attracted a great interest in nanostructure studies since it offers a low-cost nanofabrication technique. In addition, there are a great number of potential applications [1,2], such as quantum dot based laser, single electron transistor and quantum computer. Uniform dots with ordered arrangement are desirable for further pragmatic applications. However, there are two main problems. *Corresponding author. Tel.: ; fax: address: gjin@ee.ucla.edu (G. Jin). First, previous studies [3 6] showed that selfassembled Ge dots on Si (0 0 1) had a bi- (or even multi-) modal size distribution, which was an obstacle for accomplishing uniform dots. A few studies on the formation of uniform dots have been carried out [7]. Secondly, the self-assembled Ge dots usually have a random spatial distribution due to the spontaneous nature of self-assembled growth. In order to control spatial distribution and form ordered quantum dot arrays, many efforts have been devoted using a variety of techniques, such as growth on miscut substrates with surface steps [8,9] and on relaxed templates with dislocation networks [10 12] and stacking growth of multi-layers of Ge dots [13 15] and /01/$ - see front matter # 2001 Published by Elsevier Science B.V. PII: S (01)

2 G. Jin et al. / Journal of Crystal Growth (2001) others [16]. Among them, one of the efficient approaches to control the spatial distribution is using the post-growth of Ge dots on Si SEG mesas. Kamins study [17] showed 1D ordered arrangement of Ge dots along the edges of the Si stripe mesas, formed in patterned windows prepared by conventional lithography. However, it is far away from the true control of the dot positioning for practical applications. In this paper, we will report our successful control of one- and two-dimensional uniform, well-arranged self-assembled Ge dots grown on patterned Si (0 0 1) substrates with selective epitaxial growth technique. In addition, we will also demonstrate the control of a single self-assembled Ge dot on each square Si mesa and discuss possible mechanisms associated with the cooperative arrangements. 2. Experimental methods The samples used in this study were patterned Si (0 0 1) substrates, which were first thermally oxidized to form about 400-nm-thick SiO 2, and then Si windows were opened to form patterned substrates with their edges aligned along h110i directions by using conventional photolithography. For sample growth, the Si (0 0 1) substrates were chemically cleaned and dipped in a diluted HF solution to form the hydrogen-terminated surface before being loaded into a vacuum chamber. The growths were carried out in a molecular beam epitaxy system with a Si 2 H 6 gas source and a Ge Knudsen cell source. The base pressure of the growth chamber was about Torr and the main residual gas was hydrogen. After thermal cleaning, Si was selectively grown in the exposed Si windows at 6608C with the Si 2 H 6 gas flow rate of 3.0 sccm, resulting in the formation of Si mesas with facets. The Si growth rate under these conditions was about 0.1 nm/s. Details on the facet formation in the selective epitaxial growth (SEG) process can be found in the previous publications [18,19]. After the Si growth, Ge was deposited at a growth temperature with a typical growth rate of about 0.01 nm/s. The samples were taken from the vacuum and the silicon oxide was etched away for atomic force microscopic (AFM) study. The morphology of Ge dots did not show any significant change with the etching process. All the AFM scanning was parallel to the cleaved edge of substrates, the [1 1 0] direction, in a contact mode. 3. Results and discussion Fig. 1 shows a typical AFM result of Si selective growth in a patterned stripe window. It is noted that the silicon dioxide layer has been removed for the AFM measurement. One can see the morphology of the Si mesa formed by SEG process. The sidewall facet angle is about 258 with the thickness of 120 nm, corresponding to the {1 1 3} facets. This facet formation is due to the anisotropy of the growth rate in the SEG process. The sidewall facets are formed on patterned Si (0 0 1) and evolved from the dominance of the {1 1 3} facets at the early stage of the Si selective growth to the dominance of the {1 1 1} facets at larger Si thickness. In this particular case, the {1 1 3}- sidewall facets dominate the mesa sides at the Si thickness of about 120 nm. It was also found that Fig. 1. Typical AFM image of a Si stripe mesa after selective epitaxial growth on a patterned Si (0 0 1) substrate with the window oriented along the h110i directions. The 1D ridge is formed after full reduction of the topplateau. The height of the mesa is about 120 nm and the sidewall facet is {1 1 3}.

3 1102 G. Jin et al. / Journal of Crystal Growth (2001) the top(0 0 1) surface had been fully reduced to form a ridge in the exposed Si windows having a base width of 40.5 mm. Fig. 2 illustrates an AFM image of 1D cooperative arrangement of self-assembled Ge dots on an h110i-oriented Si stripe mesa, selectively formed in an exposed Si stripe window with a window width of 0.55 mm and a pitch of 0.1 mm. Perfectly aligned and cooperatively arranged 1D array of Ge dots can be seen on the ridge of the Si stripe mesa after the deposition of 1.6 nm Ge at 6008C. The average height and base size of the dots are about 24 and 95 nm, respectively. Moreover, the cooperatively arranged array shows excellent periodicity with a constant period of about 110 nm. The perfect alignment of the dots on the Si stripe mesa arises from the energetically preferential nucleation on top of the 1D ridge and is also assisted by the formation of the 1D ridge during SEG process [20]. The periodic arrangement is attributed to the minimization of the total energy [20 22]. We have carefully examined the Ge dots on the ridges of Si stripe mesas over a large region. It is interesting to find that all the dots are domeshaped and have a close size of nm. A similar result was reported on high index facets of SEG mesas [23], in contrast with the results usually obtained on bare Si (0 0 1) substrates, where a bior multi-modal distribution of the Ge dots was evident. The mono-modal distribution of Ge dots in our case may be attributed to the preferential nucleation and the elastic interaction [21,22,24] between the neighboring dots. The influence of the amount of Ge deposited on the cooperative arrangement has been studied. At the low Ge deposition of 0.4 nm, very few Ge dots were seen and the growth is believed to be in the layer-by-layer mode. As the deposition was increased to 0.8 nm, pronounced Ge dots were observed, indicating a 3D growth mode. Therefore, for Ge growth on Si stripe mesas, the growth was in the Stranski Krastanov growth mode. We estimated the critical thickness to be nm for Ge growth on Si stripe mesas, which is consistent with the value of 3 ML on a planar Si (0 0 1) surface. Fig. 3 shows the statistically Fig. 2. Two-dimensional (top) and three-dimensional (bottom) AFM images of self-assembled Ge dots on an h110i-oriented Si stripe mesa with a base width of 0.55 mm and the length on the order of 1 mm. One-dimensional cooperative arrangement of Ge dots is formed on the ridge of the Si mesa after the deposition of 1.6 nm Ge at a growth temperature of 6008C. The sidewall facets of the mesa are {1 1 3}. The base size (along the [1 1 0] ridge direction) and the height of the Ge dots are about 95 and 24 nm, respectively. Fig. 3. The statistical results of dot spacing R versus the amount of deposited Ge or equivalent Ge thickness. The error bars are the standard deviation values. The growth is in a 2D (layer-by-layer) mode as the equivalent thickness is less than 0.5 nm, which becomes the 3D (islanding) mode as the thickness is larger than 0.5 nm.

4 G. Jin et al. / Journal of Crystal Growth (2001) Fig. 4. One-dimensional fast Fourier transforms (FFT) of the corresponding AFM images, showing the spatial periodicity and also showing the peak shift with the Ge thickness. average results of dot spacing R versus the amount of deposited Ge. Meanwhile, we studied the onedimensional fast Fourier transform (FFT) of the AFM images, showing the decrease of the dot spacing with Ge amount in Fig. 4. The dot spacing reduces as the equivalent thickness y of deposited Ge increases. Moreover, the dot base size becomes smaller with the increase of the Ge amount at large Ge thickness. However, the dot height increases slightly. Therefore, we examined the dot volumes and found that the volume decreases with the Ge amount [24]. In general, in a non-correlated growth, the deposited amount increases, the dot size becomes larger, or the dot density increases while the size remains constant. In our case, however, the dots are correlated and the volume changes with the amount of deposited Ge. The possible evolution of the dots with Ge thickness is described as follows. Before the formation of Ge dots, Ge growth on Si stripe mesas occurs in a layer-by-layer mode to form a wetting layer. After the onset of 3D growth, Ge dots are formed. At the earlier stage of the formation of Ge dots, the nucleation is rather random and the interactions between dots are very weak due to the very low dot density. Once a Ge dot is formed, the dot grows fast and saturates at a certain size (about 200 nm in the base at the growth temperature of 6008C). The size saturation may arise from a kinetically self-limited mechanism; for example, large strain suppresses the further increase of the dot size [25]. In our case, the 1D stripe mesas may also suppress the growth of the dots in the direction cross the mesas. The morphology of dots tends to be symmetric, however, the growth across the ridge is suppressed due to the morphologic anisotropy. This may lead to the suppression of the pyramid formation in 1D case. Meanwhile, the Ge dots are metastable and the interchange of Ge atoms between the neighboring dots takes place via diffusion, attachment and detachment processes. Further deposition increases additional nucleation sites and the dot density, then the interactions [20 22] between dots become stronger. Contrast to the Ostwald ripening process, the new dots grow at the expense of wellgrown dots according to the energetic preference, leading to the size decrease with the increase of Ge thickness. This self-regulation of the dot size and position may be driven by the minimization of the total energy, promoting this cooperative arrangement on the 1D ridges. Fig. 5 shows an AFM image of 2D arrangement of the self-assembled Ge dots on the SEG Si mesas. The bright regions are Si mesa network, which were formed after the selective epitaxial growth. The dark regions correspond to the original SiO 2 mask regions, which have been removed for AFM inspection. It is interesting to note that the original Si windows are oriented in [1 1 0] direction, but the baselines of the sidewalls of the Si mesas after SEG process are oriented in [1 0 0] direction rather than in [1 1 0] directions. The change of the baseline orientation may be attributed to the result of the competitive growth on different facets [18,19]. A 0.8-nm-thick Ge was deposited at a temperature of 6008C, resulting in pyramid-shaped Ge dots with an average height of 12 nm (Fig. 5a). It is interesting to note that there are four Ge dots on each unit cell of the Si mesas and the arrangement of Ge dots shows ordered 2D

5 1104 G. Jin et al. / Journal of Crystal Growth (2001) Fig. 5. AFM images with a scanning area of 4 mm 4 mm, showing the dependence of the 2D arrangement of Ge dots on Ge thickness. Several configurations of arrangement can be seen with different Ge thickness. The Ge thickness deposited is equivalent to (a) 0.8 nm and (b) 1.3 nm. arrays. The four Ge dots are located at the corners of each Si mesa and the central region is free of Ge dots. Upon careful examination, we see that the base squares of the dots are oriented in h100i directions. The formation of Ge dots at the corners is due to the energetically preferential nucleation [26], similar to that along the edges. The growth of Ge on Si SEG square mesas is also in Stranski Krastanov growth mode, and the critical thickness is estimated to be about nm on Si SEG mesas. With the increase of the Ge deposition thickness, several configurations of arrangement can be seen [26]. Fig. 5b shows two sets of Ge dots, domes at the corners and pyramids at the edges of a unit cell. The first set of dots at the corners form at the initial stage of the growth due to the energetic preference, and then the dots grow from the pyramid to the dome shape. Due to the increase of strain energy at the corners, the dots at edges appear. The second set of Ge dots observed are square-based pyramids, different from the dome dots at the corners, as they are still at the early stage of their evolution, i.e. that they have not undergone the shape transformation. In order to understand the effect of temperature on 2D arrangement of Ge dots, we investigated the dependence of 2D arrangement on growth temperature. Fig. 6 shows the AFM image of the sample with the growth temperatures of 7008C and 1.6 nm Ge. One can see that only one dot on each Si mesa is formed on each Si mesa at 7008C. The formation of single dot on a unit square Si mesa is attributed to the reduction of the top(0 0 1) facet and the larger Ge dots. During the Si SEG process, the top(0 0 1) facet of Si mesas becomes smaller due to the stronger mass transfer from the sidewalls of Si mesas, leading to the increase of the height and the reduction of the mesa tops (0 0 1) (to 0.3 mm 0.3 mm vs. original 0.8 mm 0.8 mm). At 7008C, the Ge dots are larger compared with those at 6008C [27]. Therefore, only one dot can be formed on a square mesa. This result shows the possibility of controlling the positioning of a single self-assembled Ge dot on Si SEG mesas. Other variations of patterns of dots are possible.

6 G. Jin et al. / Journal of Crystal Growth (2001) References Fig. 6. AFM image of 2D arrangement of Ge dots with 1.6 nm Ge at growth temperature of 7008C. Only one Ge dot is placed on each unit of Si mesas. The scanning area is 10 mm 10 mm. The inset shows the 2D array of Ge dots by adjusting the height bar in AFM image for only showing the Ge dots. Before the Ge deposition, the mesa size is 0.8 mm 0.8 mm, and the size shrinks to 0.3 mm 0.3 mm after Ge deposition. 4. Conclusions In summary, we have demonstrated and studied the 1D and 2D cooperative arrangements of selfassembled Ge dots (CASAD) on patterned Si substrates with selective epitaxial growth Si mesas. The growth of Ge on Si SEG ridges and square mesas (with the lateral size less than 0.5 mm) occurs in the Stranski Krastanov growth mode. The control of single self-assembled Ge dot on a Si SEG mesa has been demonstrated. This promising growth technique can be extended to other heterogeneous system. This work illustrates the possibilities of constructing controlled dot patterns beyond today s lithographic size limit. This technique may find important applications for new multi-functional devices. Acknowledgements This work was in part supported by Semiconductor Research Corporation (SRC) and Army Research Office (ARO). [1] P.M. Tersoff, G. Mederios-Riberio, Mater. Res. Bull. 21 (1996) 50, and references therein. [2] A. Balandin, K.L. Wang, Superlatt. Microstruct. 25 (1999) 509, and references therein. [3] D.J. Eaglesham, M. Cerullo, Phys. Rev. Lett. 64 (1990) [4] Y.W. Mo, D.E. Savage, B.S. Swartzentruber, M.G. Lagally, Phys. Rev. Lett. 65 (1990) [5] T.I. Kamins, E.C. Carr, R.S. Williams, S.J. Rosner, J. Appl. Phys. 81 (1997) 211. [6] F.M. Ross, R.M. Tromp, M.C. Reuter, Science 286 (1999) [7] X. Wang, Z.-M. Jiang, H.-J. Zhu, F. Lu, D. Huang, X. Liu, C.-W. Hu, Y. Chen, Z. Zhu, T. Yao, Appl. Phys. Lett. 71 (1997) [8] K. Sakamoto, H. Matsuhata, M.O. Tanner, D. Wang, K.L. Wang, Thin Solid Films 321 (1998) 55. [9] J.-H. Zhu, K. Brunner, G. Abstreiter, Appl. Phys. Lett. 73 (1998) 620. [10] Y.H. Xie, S.B. Samavedam, M. Bulsara, T.A. Langdo, E.A. Fitzgerald, Appl. Phys. Lett. 71 (1997) [11] S.Y. Shiryaev, V.E. Pedersen, F. Jensen, W.J. Petersen, L.J. Hansen, N.A. Larsen, Thin Solid Films 294 (1997) 311. [12] C. Lee, A.-L. Barabasi, Appl. Phys. Lett. 73 (1998) [13] C. Teichert, M.G. Lagally, L.J. Peticolas, J.C. Bean, Tersoff, J. Phys. Rev. B 53 (1996) [14] E. Mateeva, P. Sutter, J.C. Bean, M.G. Lagally, Appl. Phys. Lett. 71 (1997) [15] O.G. Schmidt, K. Eberl, Phys. Rev. B 61 (2000) [16] E.S. Kim, N. Usami, Y. Shiraki, Appl. Phys. Lett. 72 (1998) [17] T.I. Kamins, R.S. Williams, Appl. Phys. Lett. 71 (1997) [18] A. Madhukar, Thin Solid Films 231 (1993) 8. [19] Q. Xiang, S. Li, D. Wang, K.L. Wang, J.G. Couillard, H.G. Craighead, J. Vac. Sci. Technol. B 14 (1996) [20] G. Jin, J.L. Liu, S.G. Thomas, Y.H. Luo, K.L. Wang, B.- Y. Nguyen, Appl. Phys. Lett. 75 (1999) [21] M. Zinke-Allmang, L.C. Feldman, M.H. Grabow, Surf. Sci. Rep. 16 (1992) 377. [22] V.A. Shchukin, N.N. Ledentsov, P.S. Kopev, D. Bimberg, Phys. Rev. Lett. 75 (1995) [23] L. Vascan, Phantom Newslett. 16 (1999) 1. [24] G. Jin, K.L. Wang, Phys. Rev. Lett., submitted for publication. [25] Y. Chen, J. Washburn, Phys. Rev. Lett. 77 (1996) [26] G. Jin, J.L. Liu, K.L. Wang, Appl. Phys. Lett. 76 (2000) [27] S.A. Chaparro, Y. Zhang, J. Drucker, D. Chandrasekhar, D.J.J. Smith, Appl. Phys. 87 (2000) 2245.