SiGe/Si Vertical Heterostructures: Switching the Dislocation Sign by Substrate Under-Etching

The epitaxial growth of lattice-mismatched semiconductors on silicon has attracted widespread attention for the possibility to exploit superior optical/transport properties of the deposited materials while maintaining compatibility with mainstream Si technology. However, due to the lattice mismatch, elastic energy is accumulated in the deposited film up to a certain critical thickness, beyond which plastic relaxation sets in. The latter can be conveniently controlled by growing graded layers. Such substrates proved to be extremely appealing in terms of reducing the threading-dislocation density (TDD) down to values of the order of 10^6 cm-2. The remarkable reduction of the TDD is of particular importance since those defects have detrimental impacts on the properties of integrated devices. However, continuous shrinking of the devices dimensions calls for a further decrease in the TDD, as even a single defect could be sufficient to severely alter the desired functionality. To address this problem, complex techniques deviating from the standard planar film geometry and aimed at producing dislocation-free materials in selected active areas have been developed, such as 3D heteroepitaxy [2]. This requires the deposition of Ge (or SiGe) onto an ordered array of micrometric, square Si pillars. The combined effect of strong out-of-equilibrium growth conditions and mutual shadowing among neighbouring pillars, leads to the formation of Vertical Heterostructures (VHE), whose upper region can be fully dislocation-free. By combining the 3D heteroepitaxy approach with compositional grading, 100% dislocation-free SiGe crystals were recently demonstrated [3]. Properly grading the layer in VHE allows to release completely the lattice-mismatch strain only by exploiting lateral elastic relaxation. As a result, neither misfit dislocations nor TDs, are introduced. Graded VHEs, however, still need further optimization before being easily exploited in applications. Indeed, 100% dislocation-free crystals can be obtained only by a proper choice of the growth parameters. Narrow crystals, and shallow compositional grading rate, favor the elastic stress relaxation mechanism. The aim of this work is to improve the design of these VHEs by suitably tuning the substrate geometry. Promising results in terms of the reduction of TDD inside the upper active area of the heterostructures are experimentally demonstrated, together with a theoretical interpretation of the main mechanism leading to the observed different distributions of dislocations. 2. Experimental results The experimental characterization was performed on SiGe VHEs grown on two different substrate geometries, one is the standard vertical Si pillar, while the other is an under-etched geometry [4] where the sidewalls of the Si pillars were subjected to an additional isotropic etching step as shown in Fig. 1. Fig. 1. SEM view showing the substrate geometries considered in this work. The standard vertical pillars (a) show dislocations mostly on the upper SiGe film, while for the under-etched Si pillar (b), the dislocations tend to dig into the substrate, piling up along the same {111} glide plane. We looked at the dislocation density (DD) for both cases, by counting the etch-pits extending up to the lateral free surfaces, both in the upper SiGe crystal and both inside the Si substrate underneath. The results [5] show that the dislocation density for the upper part, DDSiGe, is lower in the under-etched case with respect to the vertical one, for all the pillar bases considered. By contrast, the dislocation density in the substrate, DDSi, increases for the under-etched case. 3. Model and comparisons The approach exploited in this work to model the experimental distributions of dislocations is a coupling between a two-dimensional dislocation dynamics code and a Finite Element (FE) solver, in the isotropic linear elasticity framework. The coupling is based on the eigenstrain formalism, implemented following the Discrete-Continuous Model presented in Ref. [6]. In this approach, the motion of dislocations follows the Peach-Koehler force. where is the stress field at the dislocation position obtained by the FE solution, its Burgers vector and the dislocation line. Fig. 2. Energy gain for the introduction of a ‘normal’ (red dashed line) and an ‘opposite’ (blue solid line) dislocation plotted against the thickness of the deposited SiGe crystal. The coupling with the FE solver permitted us to evaluate also the total elastic energy in the system and thus to provide a thermodynamical prediction for the onset of plasticity. This was achieved by probing different positions for the insertion of the dislocation in the system and by taking the energy difference between the configurations with and without the defect. The results, as shown in Fig. 2, demonstrate that, for the under-etched geometry, the kind of defects introduced has the opposite sign of the Burgers vector with respect to dislocations normally introduced in SiGe/Si heteroepitaxy (here named ‘normal’ dislocations). This difference with respect to the vertical geometry for the Si pillars helps to explain the different distribution of dislocations found experimentally. In fact, dislocation dynamics simulations performed on pile-ups of identical dislocations aligned along the same {111} glide plane predicts a different behavior for the two investigated geometries, as reported in Fig. 3. The comparison with the experimental results of Fig. 1 shows a nice qualitative agreement: for the vertical Si pillar the dislocations tend to be concentrated in the SiGe crystal while for the under-etched case the pile-ups are found inside the Si substrate, explaining in this way also the difference in the DD observed [5]. Fig. 3. Hydrostatic stress maps obtained from the final distribution of dislocations simulated by means of dislocation dynamics for the two investigated geometries: vertical Si pillar on the left and under-etched pillar on the right. A further analysis can be performed by looking at the typical number of dislocations per pile-up predicted theoretically by exploiting again an energetic criterion as described above. The results show [5] that a number of 4 dislocation per pile-up corresponds to the minimum energy configuration for our systems, in excellent agreement with the experimental distribution taken on a wide range of pillars, that shows a maximum probability of having a number between 3 and 4 dislocations per pile-up. 4. Conclusions In this work we have presented a combined theoretical and experimental investigation of dislocation distributions in graded SiGe crystals grown on vertical and under-etched Si pillars. As shown, the main role played by under-etching is to effectively invert the sign of the Burgers vectors of the dislocations. The modeling of the typical dislocation positioning leads to nice agreement with experiments both in terms of distribution and in number of defects [5]. This study opens the way for future research, e.g. on optimal shaping of the pillars, with the aim of growing larger dislocation-free SiGe crystals. References [1] E.A. Fitzgerald, Materials Science Report 7, 87 (1991). [2] C. Falub et al., Science 335, 1330 (2012). [3] F. Isa et al., Advanced Materials 28, 884 (2016). [4] F. Isa et al., Applied Physics Letters 109, 182112 (2016). [5] F. Rovaris, et al., Physical Review Material 1, 073602 (2017). [6] A. Jamond, et al., International Journal of Plasticity 80, 19 (2016)