Quantitative strain mapping in Si_0.7Ge_0.3/Si/ Si_0.7Ge_0.3 heterostructures for spin qubits

We present laterally resolved maps of the lattice strains around spin qubits housed in Si/SiGe heterostructures and demonstrate that that material related inhomogeneities must be taken into account in the optimization and design for scaled CMOS-compatible quantum processors. 

The Si/SiGe material system is promising for large-scale integration of solid state qubits due to the demonstration of high coherence times and multi-qubit algorithms. One key requirement for realizing large arrays of qubits with shared gate control is a high degree of homogeneity of the lattice strains. Here, we leverage Scanning Xray Diffraction Microscopy (SXDM) at ID01/ESRF to investigate non-destructively the lattice homogeneity in Si/SiGe heterostructures. We map the strain tensor in a 10 nm thick Si QW with a lateral resolution below 50 nm and determine local strain variations larger than 1e-4. Based on the experimental data, we perform Finite Element Method (FEM) thermomechanical simulations to calculate the strain distribution at low temperature. Furthermore, the strain maps are translated into spatially resolved profiles for the energy of the conduction band valley state, the variation of which is found to be of the magnitude as the charging energy of an electrostatic quantum dot of approx. 1 meV