Hydrostatic strain enhancement in laterally confined SiGe nanostripes

Strain engineering in SiGe nanostructures is fundamental for the design of optoelectronic devices at the nanoscale. Here we explore a new strategy, where SiGe structures are laterally confined by the Si substrate, to obtain high tensile strain yet avoid the use of external stressors, thus improving the scalability. Spectromicroscopy techniques, finite element method simulations, and ab initio calculations are used to investigate the strain state of laterally confined Ge-rich SiGe nanostripes. Strain information is obtained by tip-enhanced Raman spectroscopy with an unprecedented lateral resolution of ∼30 nm. The nanostripes exhibit a large tensile hydrostatic strain component, which is maximal at the center of the top free surface and becomes very small at the edges. The maximum lattice deformation is larger than the typical values of thermally relaxed Ge/Si(001) layers. This strain enhancement originates from a frustrated relaxation in the out-of-plane direction, resulting from the combination of the lateral confinement induced by the substrate side walls and the plastic relaxation of the misfit strain in the (001) plane at the SiGe/Si interface. The effect of this tensile lattice deformation at the stripe surface is probed by work function mapping, which is performed with a spatial resolution better than 100 nm using x-ray photoelectron emission microscopy. The nanostripes exhibit a positive work function shift with respect to a bulk SiGe alloy, quantitatively confirmed by electronic structure calculations of tensile-strained configurations. The present results have a potential impact on the design of optoelectronic devices at a nanometer-length scale.

Figure 1

Laterally confined SiGe nanostripes. (a) Top-view SEM image of the periodic array of nanostripes. (b) Cross-section SEM image of a single nanostripe after FIB processing. During FIB processing, the ion beam hits the sample surface with an incidence angle of 52° with respect to the normal direction. In this condition, the cross-section profile of the nanostripe can be distinguished by possible ion-induced artifacts due to the amorphization of the cross-section surface, which could appear only along the 52° tilted direction.

Figure 2

Sample cleaning for XPEEM experiment. (a) Auger spectra monitoring the surface contamination during the different steps of the cleaning procedure on a Si test sample: precleaning (bottom), post-UV-ozone treatment (center), and postsputtering (top). (b) Photoemission spectrum of the Ge 3$d$ core level measured on the nanostripes after the cleaning procedure. The absence of any shifted structure at the low kinetic energy side indicates the absence of germanium oxide.

Figure 3

TERS data. (a) Schematic representation of the TERS experiment; incident light has a $p$ polarization, and the scattering plane is represented by the $yz$ plane. (b) STM image of a single SiGe nanostripe. The dotted blue line represents the path over which the tip is scanned and Raman spectra were acquired. STM cross-section profile across the nanostripe (inset). (c) Baseline-corrected TERS spectra measured with the STM tip in tunneling on the SiGe nanostripe (blue line) and on the Si substrate (black line). Qualitative schematics of the experimental geometry for the spectra shown in the main panels (inset); the far-field and the near-field interaction volumes within the sample are qualitatively represented by the blue and green areas, respectively; the electric field polarization ($E$) and the scattering directions are defined by the red and black arrows, respectively. (d) and (e) Background-subtracted intensity profiles of the Ge-Ge 2TO and the Si-Ge first-order peaks, respectively, as derived by TERS spectra monitored as a function of the position across a single nanostripe along two scan lines of the tip acquired at two different position along the stripe axis. (f) Raman frequency profiles of the SiGe mode as a function of the position across the stripe for the two scan lines shown in (d) and (e).

Figure 4

Ge concentration mapping. (a) and (b) Background-subtracted Ge 3$d$ and Si 2$p$ core level XPEEM images (FoV is ∼12 μm) of the nanostripe array; Ge 3$d$ and Si 2$p$ photoemission spectra extracted on a single nanostripe (black squares) fitted with Voigt line shape components (solid lines; insets). In the case of the Ge 3$d$ spectrum, two spin-orbit split structures separated by $0.6\pm 0.1$ eV and with a branching ratio of ∼1.5 have been considered. The weak component at the high-binding-energy side within the Si 2$p$ spectrum is consistent with a 1$+$ ionization state. (c) Spatial map of the Ge concentration as obtained by monitoring the pixel-by-pixel Ge 3$d$ and Si 2$p$ peak peaks and fitting their intensities with a standard quantification model.

Figure 5

(a) Experimental spatial profiles (black and green squares) of the hydrostatic strain ${\varepsilon }_h$ obtained by combining TERS and XPEEM data. The blue solid line represents the computed ${\varepsilon }_h$ profile as obtained by FEM simulations (see text). The red dashed line is the hydrostatic strain value in the case of a 2D thin film. (b) Spatial map of the hydrostatic deformation in the $xz$ plane obtained by FEM simulations. A strain field is created by two 90° dislocations at the interface between the SiGe stripe and the Si substrate (inset).

Figure 6

FDTD simulation of TERS experiment. Spatial map of the Raman signal (proportional to the fourth power of the electric field) in a Si${}_{0.1}$Ge${}_{0.9}$ alloy in the $xz$ plane during the interaction between the laser beam and a gold tip that has a radius of 30 nm and is separated 0.7 nm from the $z$ $=$ 0 plane (the (001) plane), calculated with a FDTD solver. The electromagnetic radiation from the laser is coming from the left side. Transversal (top inset) and longitudinal (left inset) profiles of the Raman intensity.

Figure 7

Work function mapping. XPEEM images of the nanostripes’ array acquired with soft x-ray excitation at $h\nu$ $=$ 90 eV using secondary electrons of 4.6 eV (a) and 4.9 eV (b). The FoV is ∼15 μm. (c) Local work function map obtained from the experimental photoemission threshold spectra taken pixel by pixel and least-square fitted to the secondary electron distribution described by Henke et al.'s model (Ref. 57; see Appendix ).

Figure 8

DFT-LDA: work function calculation. Calculated band structure of the Ge(001)$b(2\times 1)$ surface using DFT in LDA under different tensile strain conditions. In all panels, the magenta crosses represent the unstrained band structure, while the black circles describe the effect of the applied tensile strain. The dashed line defines the Fermi level. (a) Unstrained surface, where the size of points is proportional to the bulk partial weight of those bands states. Thin states are surface bands. (b) ${\varepsilon }_{xx}=0.01$, ${\varepsilon }_{yy}=0$, and ${\varepsilon }_{zz}=0$. (c) ${\varepsilon }_{xx}=0$, ${\varepsilon }_{yy}=0.01$, and ${\varepsilon }_{zz}=0$. (d) ${\varepsilon }_{xx}=0$, ${\varepsilon }_{yy}=0$, and ${\varepsilon }_{zz}=0.01$. When in contact with $n+$ silicon, the Fermi energy of the Ge stripe moves up to pin the bulk states near $-$4 eV. (e) Calculated work function shift ΔΦ as a function of the hydrostatic strain ${\varepsilon }_h$ inside the nanostripes (see text for details). The comparison of the experimentally measured work function change (black dashed line) with the calculated values gives an estimation of the strain state of the nanostripe (gray region). The dashed green line represents the strain value as measured by TERS (∼0.53$\%$).

Figure 9

Experimental secondary electron energy distributions (open squares and circles) as a function of $E$−$E_F$ for the Si bulk and the SiGe nanostripes, respectively. The red curves represent the best least-square fitting of the experimental data using Henke et al.'s model (Ref. 57).

Figure 10

Sensitivity analysis of FEM simulations. Simulated hydrostatic strain maps as obtained by FEM for different relaxation conditions, stripe shapes, and interface profiles: (a) both elastic and plastic (formation of dislocation) relaxation mechanisms for a rectangular stripe shape, (b) a rectangular shape with only elastic relaxation, (c) and (d) elastic relaxation for polygonal shape profiles (closer to the experimental shape reported in Fig. 1 of the main text), (e) elastic relaxation on a fully rounded shape, and (f) elastic relaxation for the case of a wavy interface profile.