Strain Imaging of Nanoscale Semiconductor Heterostructures with X-Ray Bragg Projection Ptychography

We report the imaging of nanoscale distributions of lattice strain and rotation in complementary components of lithographically engineered epitaxial thin film semiconductor heterostructures using synchrotron x-ray Bragg projection ptychography (BPP). We introduce a new analysis method that enables lattice rotation and out-of-plane strain to be determined independently from a single BPP phase reconstruction, and we apply it to two laterally adjacent, multiaxially stressed materials in a prototype channel device. These results quantitatively agree with mechanical modeling and demonstrate the ability of BPP to map out-of-plane lattice dilatation, a parameter critical to the performance of electronic materials.

Figure 1

Schematic of the experimental scattering geometry—materials as labeled are the embedded silicon germanium (eSiGe) stressor region, the silicon-on-insulator (SOI) channel region, and the buried oxide (BOX) region. The diffraction plane is in the $y-z$ plane, oriented normal to the channel direction. Coherent x-ray diffraction patterns were collected at two separate scattering conditions (SiGe 004, SOI 004) allowing for ptychographic lattice visualization of both stressor and strained materials across a nanoscale heteromaterial interface.

Figure 2

(a) Cross sectional, scanning electron microscopy (SEM) image of the semiconductor channel region. Representative nanofocused coherent x-ray diffraction patterns are shown taken from both the eSiGe stressor region (b)–(d) and strained SOI region (e)–(f). Differences are evident in the intensity distribution of diffraction images taken from the edges of the regions (c), (d), (e), (g) compared to the center of the regions (b), (f) due to lattice perturbations near the lithographically defined interface.

Figure 3

Results of Bragg projection ptychography (BPP) analysis showing an iteratively reconstructed image of both the complex amplitude (a), (b) and phase (c), (d) of the diffracting sample. The $x/y$ gradients in the phase image were interpreted using methods described in the text to estimate the lattice strain (e), (f) and rotation (g), (h) as a function of position transverse to the channel direction. These results are found to be quantitatively consistent with lattice strain and rotation predicted by linear elastic mechanical modeling [solid lines (e)–(h)].

Figure 4

(a) Model system of a 65 nm thick continuous silicon film with two simple lattice perturbations introduced as a function of position along $x$—the first is a constant lattice strain along the out-of-plane ($z$) lattice vector, and the second is an out-of-plane lattice tilt. The strain perturbation leads to a $q_y$ displacement in the coherent diffraction pattern (c) and the tilt perturbation leads to a $q_x$ displacement (d) when comparing to the ideal lattice coherent diffraction pattern (b). The magnitude of this displacement allows us to calculate the linear relationship between BPP phase gradients in the $x$ direction and lattice tilt, and phase gradients in the $y$ direction and lattice strain.