Fabrication, characterization, and mechanical loading of Si/Si-Ge membranes for spin-qubit devices

<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>Si</a:mi> </a:math> / <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mi>Si</c:mi> <c:mi>Ge</c:mi> </c:mrow> </c:math> heterostructures on bulk <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>Si</e:mi> </e:math> substrates have been shown to host high-fidelity electron spin qubits. Building a scalable quantum processor would, however, benefit from further improvement of critical material properties such as the valley-splitting landscape. Flexible control of the strain field and the out-of-plane electric field <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mrow> <g:mi mathvariant="script">E</g:mi> </g:mrow> <g:mi>z</g:mi> </g:msub> </g:math> may be decisive for valley-splitting enhancement in the presence of alloy disorder. We envision the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi>Si</j:mi> </j:math> / <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mrow> <l:mi>Si</l:mi> <l:mi>Ge</l:mi> </l:mrow> </l:math> membrane as a versatile scientific platform for investigating intervalley scattering mechanisms which have thus far remained elusive in conventional <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>Si</n:mi> </n:math> / <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mrow> <p:mi>Si</p:mi> <p:mi>Ge</p:mi> </p:mrow> </p:math> heterostructures and have the potential to yield favorable valley-splitting distributions. Here, we report the fabrication of locally etched, suspended <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mrow> <r:mi>Si</r:mi> <r:mi>Ge</r:mi> </r:mrow> </r:math> / <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mi>Si</t:mi> </t:math> / <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:mrow> <v:mi>Si</v:mi> <v:mi>Ge</v:mi> </v:mrow> </v:math> membranes from two different heterostructures and apply the process to realize a spin-qubit shuttling device on a membrane for future valley mapping experiments. The membranes have a thickness in the micrometer range and can be metallized to form a back-gate contact for extended control over the electric field. To probe their elastic properties, the membranes are stressed by loading with a profilometer stylus at room temperature. We distinguish between linear elastic and buckling modes, each offering mechanisms through which strain can be coupled to spin qubits.