Superconducting microwave filters and filter elements for quantum devices
A superconducting device is described wherein the device comprises a substrate; a capacitor structure ( 604 ) and a superconducting inductor structure ( 602 ) disposed on the substrate, the capacitor structure an the superconducting inductor structure forming a superconducting microwave filter structure, in particular a low-pass filter, the superconducting inductor structure including a plurality of nanowires of a superconducting material, each of the plurality of nanowires being galvanically connected to one of a plurality of capacitor electrodes ( 608 ) forming the capacitor structure, wherein the cross-sectional dimensions of the plurality of nanowires are selected such that the kinetic inductance of each of the one or more nanowires is larger, preferably substantially larger, than the geometrical inductance of the nanowire.
1 . A superconducting device comprising:
a substrate;
at least one superconducting inductor structure between a first terminal and a second terminal disposed on the substrate,
at least one capacitor structure for connecting the second terminal of the superconductor structure to a ground;
the at least one capacitor structure and the at least one superconducting inductor structure forming a low-pass microwave filter structure,
the at least one superconducting inductor structure including one or more nanowires of a superconducting material, and
the at least one capacitor structure comprising one or more first capacitor electrodes and one or more second capacitor electrodes,
wherein one end of each of the one or more nanowires is galvanically connected to one of the one or more first capacitor electrodes and
cross-sectional dimensions of each of the one or more nanowires is selected such that each of the one or more nanowires has a kinetic inductance that is larger than a geometrical inductance of each of the one or more nanowires.
2 . The superconducting device according to claim 1 ,
wherein the one or more first capacitor electrodes are made of a superconducting material.
3 . The superconducting device according to claim 1 wherein at least one of the one or more first capacitor electrodes and at least one of the one or more second capacitor electrodes form a thin-film interdigitated capacitor.
4 . The superconducting device according to claim 1 wherein at least one of the one or more first capacitor electrodes and at least one of the one or more second capacitor electrodes form a thin-film overlap capacitor.
5 . The superconducting device according to claim 1 , wherein the one or more first capacitor electrodes includes at least a first thin-film capacitor electrode disposed over the substrate and the one or more second capacitor electrodes includes at least a second thin-film capacitor electrode disposed over the first thin-film capacitor electrode, the superconducting device further comprising a dielectric disposed between the first and second thin-film capacitor electrode.
6 . The superconducting device according to claim 5 wherein the one or more first thin film capacitor electrodes or the one or more second thin-film capacitor electrodes are made of the same superconducting material as the superconducting material of the one or more nanowires.
7 . The superconducting device according to claim 1 , wherein the at least one capacitor structure comprises a plurality of first capacitor electrodes and at least one second capacitor electrode, and the superconducting device further comprises a thin-film dielectric layer disposed over the plurality of first capacitor electrodes and a thin-film metal layer disposed over the dielectric thin-film layer, and the thin-film metal layer forming the at least one second electrode of the at least one capacitor structure.
8 . The superconducting device according to claim 1 , wherein the cross-sectional dimensions of each of the one or more nanowires are selected such that the kinetic inductance of each of the one or more nanowires is at least 10 times larger than the geometrical inductance of each of the one or more nanowires.
9 . The superconducting device according to claim 1 wherein the cross-sectional dimensions of each of the one or more nanowires includes a width and a thickness, the width is selected between 10 nm and 800 nm and the thickness is selected between 3 nm and 200 nm.
10 . The superconducting device according to claim 1 , wherein the superconducting material of the one or more nanowires is selected from the group consisting of NbTiN, NbTi, TiN, NbN, NbSn and Nb.
11 . The superconducting device according to claim 1 , wherein the cutoff frequency of the low-pass microwave filter structure is selected to be below a frequency selected between 1 GHz and 10 GHz.
12 . The superconducting device according to claim 1 , further comprising:
at least one quantum dot structure disposed on or in the substrate, and
a plurality of gate electrodes disposed over the substrate to control the quantum dot structure,
wherein each of the plurality of the gate electrodes includes a nanowire section and a width of the gate electrode is reduced to form at least one of the plurality of nanowires of the inductor structure.
13 . The superconducting device according to claim 12 wherein the at least one quantum dot structure is a silicon-based quantum dot structure selected from the group consisting of a SiGe quantum dot structure and a silicon-silicon oxide quantum dot structure.
14 . The superconducting device according to claim 12 further comprising:
a superconducting resonator structure connected to the at least one quantum dot structure.
15 . The superconducting device according to claim 1 , wherein the superconducting inductor structure is located at a first area of the substrate and the at least a capacitor structure is located at a second area of the substrate; and/or the low-pass microwave filter structure is a thin-film lumped element filter.
16 . The superconducting device according to claim 1 , wherein
the one or more first capacitor electrodes are made of a same superconducting material as the one or more nanowires,
the dielectric of the superconducting device is a thin-film dielectric layer,
the cross-sectional dimensions of each of the one or more nanowires are selected such that the kinetic inductance of each of the one or more nanowires is at least 1000 times larger than the geometrical inductance of each of the one or more nanowires,
the width of the one or more nanowires is selected between 50 nm and 300 nm and the thickness of the one or more nanowires is selected between 6 nm and 50 nm, and
the cutoff frequency of the low-pass microwave filter structure is selected to be below a frequency selected between 2 GHz and 8 GHz.
17 . A solid-state quantum device comprising:
one or more quantum devices formed on or in a semiconductor substrate;
one or more electrodes connecting bonding pads on the substrate to the one or more quantum devices;
wherein each of the one or more electrodes includes at least one low-pass microwave filter, each said low-pass microwave filter comprising a superconducting inductor structure and a capacitor structure for connecting an electrode of one of the one or more quantum devices to a ground;
the at least one superconducting inductor structure including one or more nanowires of a superconducting material,
the at least one capacitor structure comprising one or more first capacitor electrodes and one or more second capacitor electrodes,
one end of each of the one or more nanowires is galvanically connected to one of the one or more first capacitor electrodes, and
the cross-sectional dimensions of each of the one or more nanowires are selected such that a kinetic inductance of each of the one or more nanowires is larger, than a geometrical inductance of each of the one or more nanowires.
18 . The superconducting device according to claim 17 wherein a cut-off frequency of the low-pass microwave filter structure is selected to be below a frequency selected between 1 GHz and 10 GHZ and/or wherein the low-pass microwave filter structure is a thin-film lumped element filter.
19 . The superconducting device according to claim 17 , wherein the at least one low-pass microwave filter is integrated in an electrode of one of the one or more quantum devices.
20 . A method of fabricating a quantum device comprising:
forming a thin-film heterostructure over a substrate;
forming a superconducting layer over the thin-film heterostructure to form a thin-film stack provided on the substrate;
forming a first patterned resist layer over the thin-film stack, the first patterned resist layer including a capacitor pattern, an inductor pattern, a connection pattern connecting the capacitor and inductor pattern and quantum device pattern, the inductor pattern including a nanowire pattern;
forming a capacitor structure, an inductor structure, a connection structure galvanically connecting the inductor structure with the capacitor structure and a quantum device structure in the thin-film stack using an etching step;
forming a second patterned resist layer over the capacitor structure exposing the top surface of the capacitor structure; and,
forming a thin-film capacitor, the forming of the thin-film capacitor including forming a dielectric layer and a metal layer over the second patterned resist layer and removing the second patterned resist layer,
wherein a width of the nanowire and a thickness of the superconducting layer are selected such that a kinetic inductance of the nanowire structure is larger than a geometrical inductance of the nanowire structure.