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Germanium Quantum Technology

01 /What can CMOS technology do for quantum computing? 02 /Semiconductor devices and scaling with industrial approach 03 /Semiconductor foundry facilities: the good and the bad for qubits 04 /IMEC's latest qubit developments 05 /Summary and outlook 06 /Semiconductors for spin qubits 07 /Germanium quantum wells on silicon 08 /Germanium quantum wells on silicon-germanium 09 /Growth methods 10 /Characterization techniques 11 /Electrical characterization of germanium quantum wells 12 /Fabrication of H-FET 13 /Semiconductor qubits: vision and challenges 14 /Quantum materials 15 /Quantum dot qubits and their operation 16 /Types of quantum dot qubits 17 /Qubit Readout 18 /Qubit Control 19 /Qubit Coherence and Fidelity 20 /Multi-qubit control and quantum algorithms 21 /Quantum links and scaling 22 /Physics of holes 23 /Hole spin qubits 24 /Introduction to electronics for quantum computing 25 /Room temperature electronics 26 /Cryogenic qubit chip carriers 27 /Contribution to IGNITE 28 /Quantum Control Stack for Spin Qubits 29 /Auto-tuning a quantum computer 30 /Tuning and operation of arrays 31 /Finding operation points example 32 /What is auto-tuning? 33 /Neural network tuning 34 /Navigating charge stability diagrams 35 /Experimental implementation 36 /Towards universal quantum algorithms 37 /Classical error correction 38 /Quantum error correction 39 /Progress and challenges 40 /Introduction to quantum algorithms 41 /The first algorithms 42 /Quantum annealing 43 /Quantum Machine Learning

Characterization techniques

Composition and strain of the buffer layer, and the thickness of the QW, are routinely measured by high-resolution x-ray diffraction (XRD). The X-ray wavelength is similar to the spacing between the atoms in the crystal, and Ge makes this spacing larger, so a precise measurement of the diffraction angle gives the germanium content of the SiGe alloy. For a thin (< 150 nm) QW and cap, XRD is effectively a Fourier transform of the structure, so by comparing with simulations we find the thicknesses of the QW and cap layer. While XRD can also give some indications as to the quality of the material, defects in the structure can instead be seen by transmission electron microscopy (TEM) which can also map strain and composition at the atomic scale. Secondary-ion mass spectrometry is used to quantify the presence of impurity atoms which may degrade the qubit performance. 

Prerequisite knowledge

  • Hooke’s law, stress and strain 
  • Bragg’s law of diffraction 
  • Fourier transform 
  • Some facility with reciprocal space is useful for understanding the presentation of the x-ray results

Main takeaways

  •  X-ray diffraction gives the composition and strain state of thick layers, and can be routinely performed on every wafer. 
  • Diffraction of thin coherent layers corresponds to a Fourier transform of the structure, so that the QW and barrier thicknesses can be found. 
  • Transmission electron microscopy would directly show if there are any defects in the QW, and can be used to see the atomic composition and strain directly but on a very small scale. 
  • Secondary-ion mass spectrometry can be used to directly look for impurity atoms in the grown layers, as well as to check the QW profile against the other methods.  

Further thinking

True or False: Geometrical Phase Analysis (GPA) carried out in TEM measurements of the Ge QW with respect to a reference point in the SiGe barrier indicates an in-plane strain close to 0. This means that the QW is fully relaxed.

Solution

Further reading

Günther Bauer et al., X-ray reciprocal space mapping of Si/Si1xGex heterostructures. J. Cryst. Growth 157 (1--4) 61--67 (1995) http://dx.doi.org/10.1016/S0022-0248(95)00372-X
https://doi.org/10.1016/0022-0248(95)00372-X 

The data in this presentation are also presented in Daniel Jirovec et al., A singlet triplet hole spin qubit in planar Ge. Nature Mater. 20 (8) 1106--1112 (2021) https://www.nature.com/articles/s41563-021-01022-2

Dynamical simulations were made using the free open source python package “xrayutilities”: D. Kriegner et al., xrayutilities: a versatile tool for reciprocal space conversion of scattering data recorded with linear and area detectors. J. Appl. Cryst. 46 (4) 1162--1170 (2013) 
http://dx.doi.org/10.1107/S0021889813017214
https://xrayutilities.sourceforge.io/