Nanoscale Mapping of Strain Variations in Vicinity of Si/Sige Spin Qubit Devices By Scanning X-Ray Diffraction Microscopy

Richter, Carsten

Strain engineering is one of the main routes to tune the electronic and optical properties of semiconductor devices. Today, it is still a challenge to measure strain in epitaxial systems in a non-destructive manner which becomes especially important for devices that are subjected to intense stress. Here, we demonstrate the quantitative imaging of all components of lattice strain and rotation by means of scanning X-ray diffraction microscopy (SXDM). Based on a nano-focused X-ray beam as it is available at modern synchrotron radiation sources, the technique provides the opportunity to investigate buried layers, devices in operation or materials in complex environments.

We use this approach to study strain variations in Si/SiGe heterostructures, which regained strong attention as a CMOS compatible material system that allows large-scale integration of electron spin qubits. These qubits rely on a quantum well (QW) that forms in a Si layer that is biaxially strained by two adjacent, mismatched SiGe layers. Metal gate electrodes on top of the layer stack then provide lateral confinement resulting in a quantum dot where the electron spin state can be determined and manipulated.

Lattice strain variations in the quantum well translates into electron potential fluctuations that can cause excitation and decoherence of the electron. Furthermore, realizing a large architecture of qubits requires coherent shuttling of qubits over several microns [1,2] and high degree of homogeneity of the QW strain state to allow shared gate control. Therefore, a precise strain measurement with resolution corresponding to the size of the qubit is vital to optimize the material system. Sources of strain variations can be intrinsic, such as dislocations or alloy fluctuations [3], or caused by stress introduced during the post-growth fabrication, such as the deposited gate electrodes [4].

We present SXDM data on the lattice homogeneity in a qubit device based on a Si/SiGe heterostructure. We quantify all components of the strain and rotation tensors and observe fluctuations that are caused by dislocation bunching and the thermal contraction of top gate electrodes. This can be seen if form of a significant in-plane strain as well as a tilt of the lattice planes. The data is compared to thermomechanical simulations showing a complex depth profile of elastic interaction. Calculations indicate that the resulting variations of the electron band structure would be on the same order of magnitude as the typical charging energy of an electrostatic quantum dot, showing that structural inhomogeneities must be considered in the development of SiGe-based qubit architectures for quantum computing.

Fig. 1 exemplarily shows the X-ray diffraction contrast image of the QW layer below a QuBus structure with a 15um x 15um field of view.

References

[1] I. Seidler et al., arXiv:2108.00879 [cond-mat, physics:quant-ph] (2021) (http://arxiv.org/abs/2108.00879).

[2] V. Langrock et al., arXiv:2202.11793 [cond-mat] (2022) (available at http://arxiv.org/abs/2202.11793).

[3] B. P. Wuetz et al., arXiv:2112.09606 [cond-mat] (2021) (http://arxiv.org/abs/2112.09606).

[4] C. Corley-Wiciak, C. Richter, M. H. Zoellner, K. Anand, I. Zaitsev, C. Manganelli, Y. Yamamoto, E. Zatterin, T. Schuelli, L. Schreiber, W. Langheinrich, W. M. Klesse, G. Capellini, „Mapping of the 3D strain tensor by Scanning Nanoprobe X-Ray Diffraction in a Ge/Si_0.2Ge_0.8 heterostructure housing two functional hole spin qubits”, in preparation