Perfect crystals grown from imperfect interfaces

Abstract The fabrication of advanced devices increasingly requires materials with different properties to be combined in the form of monolithic heterostructures. In practice this means growing epitaxial semiconductor layers on substrates often greatly differing in lattice parameters and thermal expansion coefficients. With increasing layer thickness the relaxation of misfit and thermal strains may cause dislocations, substrate bowing and even layer cracking. Minimizing these drawbacks is therefore essential for heterostructures based on thick layers to be of any use for device fabrication. Here we prove by scanning X-ray nanodiffraction that mismatched Ge crystals epitaxially grown on deeply patterned Si substrates evolve into perfect structures away from the heavily dislocated interface. We show that relaxing thermal and misfit strains result just in lattice bending and tiny crystal tilts. We may thus expect a new concept in which continuous layers are replaced by quasi-continuous crystal arrays to lead to dramatically improved physical properties. Introduction Epitaxial heterostructures and nanostructures have become of immense interest in past decades because of their unique mechanical, electrical and optical properties. Traditionally, destructive techniques based on transmission electron microscopy (TEM) have been the methods of choice to analyse their crystal perfection, composition and strain1,2,3. With the advent of nanofocused X-ray beams4,5,6,7,8,9,10 and advanced X-ray diffraction (XRD) imaging techniques11,12,13,14,15,16 available at third-generation synchrotrons it has become possible to address individual crystals down to the nanoscale non-destructively. The role of strain induced by lattice misfit in determining the properties of epitaxial heterostructures and nanostructures can hardly be overemphasized. Its effects on the structural, optical and transport properties have been studied for decades17,18,19,20,21,22,23,24,25,26. Here we show by scanning X-ray nanodiffraction how misfit and thermal strain of a highly mismatched layer-substrate system may evolve when the substrate is deeply patterned at a micron scale. We show that space-filling arrays of highly perfect single crystals can grow from heavily dislocated interfaces, provided that epitaxial growth conditions and substrate patterns are carefully matched as described in detail elsewhere27. As a prototypical case we take germanium epitaxially grown onto tall pillars a few microns in width, obtained by etching Si(001) substrates to much larger depths. For this system, the lattice mismatch between Si and Ge amounts to 4.2%28, while the difference of thermal expansion coefficients is 130% at 300 K29. The Report is separated into three parts. First, we demonstrate how elastic relaxation of the thermal strain leads to diminishing lattice bending as the crystals gain in height. Second, we evaluate the net tilts of individual crystals emerging during the plastic relaxation of the misfit strain. Finally, by mapping the crystal quality on a nanometre scale, we provide evidence for perfect epitaxial single crystal growth from a heavily disordered interface. We believe that the concept developed here may be the key to device applications heretofore simultaneously hampered by crystal defects, wafer bowing and layer cracks. Such applications may comprise X-ray detectors made from many tens of microns tall Ge crystals grown directly onto Si readout electronics; multiple-junction solar cells from III/V semiconductors stacked on a Ge bottom cell on top of a Si substrate; or power transistors, for example from cubic SiC grown on suitably patterned Si substrates. Results The Ge crystals forming the object of the present study were grown on deeply patterned Si(001) substrates under conditions favouring vertical over later growth (Methods, Supplementary Information S1). In the top view scanning electron microscopy (SEM) images of Fig. 1a, b and c, and the corresponding perspective views of Fig. 1d, e and f we show how such a Ge/Si heterostructure evolves with increasing deposition time. For low coverage (Fig. 1a and d) the separation of epitaxial Ge crystals is defined by the substrate geometry. The crystals then expand both laterally and vertically (Fig. 1b and e), but eventually lateral growth stops, leaving a quasi-continuous layer of Ge crystals separated by gaps which are just a few tens of nanometres wide (Fig. 1c and f; see also Supplementary Information S1). Figure 1: Scanning X-ray nanodiffraction of arrays of epitaxial Ge crystals. Top- and perspective-view SEM micrographs of 1.2 μm (a, d), 3.1 μm (b, e), and 7.3 μm (c, f) tall Ge crystals on patterned Si(001) wafer with 8-μm-tall and 2-μm-wide Si pillars, spaced by 1 μm. The insets in (a, b, c) show the total intensity for four crystals collected around the Ge(115) peak for all incidence angles. (g), Experimental setup at the ID01 beamline (ESRF). The primary beam (vector K0, incidence angle ω), focused down to ~ 300 × 500 nm by means of Fresnel zone plates, is moved across the Ge crystals array by a high-precision piezo-stage. The scattered beam (vector Ks) was collected by a 2D X-ray pixel detector. Full size image We have previously studied such an array of closely spaced Ge crystals by laboratory high-resolution XRD measurements27. The information gained on strain and crystal quality was, however, obscured by averaging over thousands of crystals because of the large size of the X-ray beam, e.g. full-width-at-half-maximum (FWHM) ~ 1 mm (a brief summary can be found in Supplementary Information S2). Here we shall discuss crystal quality and strain mapping at a microscopic scale as obtained by scanning X-ray nanodiffraction. A schematic of the scattering geometry is shown in Fig. 1g. The scattering plane with reciprocal space directions (Qx,Qz) is defined by the vectors K0 and Ks, forming the axes of the cones of incident and scattered X-ray beams, respectively. As a result of the beam focusing and the use of a two-dimensional (2D) detector, the scattered X-rays provide simultaneous information in all three directions Qx, Qy and Qz of reciprocal space (Supplementary Information S3-A). Individual Ge crystals were localized by recording the total intensity of an asymmetrical Ge(115) Bragg peak during sample translation in the (x,y) plane defined in Fig. 1g (Supplementary Information S3-B). The resulting intensity patterns are shown in the insets of Fig. 1a, b and c. They indicate that with increasing height, and therefore smaller gaps, the Ge crystals become more and more difficult to resolve. Lattice bending close to the interface Let us first focus on the elastic relaxation of the strain induced by the mismatch of thermal expansion parameters. As we shall see, it manifests itself most clearly for the thinnest sample with 1.2-μm-tall crystals of Fig. 1a and d. Figure 2a–d shows for such a sample the three-dimensional (3D) reciprocal sp (...truncated)