Method for manufacturing a bridge structure, electronic circuit and superconducting qubit including a bridge structure

Abstract

Disclosed is a method for manufacturing a bridge structure (1) which comprises forming a base layer (3) over a substrate (2), depositing a first sacrificial layer (4) on the base layer, patterning the first sacrificial layer into a bridge-like shape (4.1), depositing a second sacrificial layer (5) on the patterned first sacrificial layer and on the base layer, depositing a bridge layer (6, 6.1) on the second sacrificial layer and the base layer, and removing the patterned first sacrificial layer and the second sacrificial layer, thereby leaving a vertical gap (7) between the bridge layer and the base layer, both preferably formed of a superconducting material. The bridge structure may form part of a shunt capacitance of a superconducting qubit, for example.

Description

[0001] METHOD FOR MANUFACTURING A BRIDGE STRUCTURE, ELECTRONIC CIRCUIT AND SUPERCONDUCTING QUBIT INCLUDING A BRIDGE STRUCTURE

[0002] Technical field

[0003] The invention relates to a method for manufacturing a bridge structure, an electronic circuit and a superconducting qubit.

[0004] Background

[0005] Bridge structures such as air bridges are important elements in a large variety of electronic circuits. In particular, in superconducting electronic circuits air bridges can be used to improve the interconnectivity of critical metal structures of superconducting chips that may be used for quantum technology applications such as quantum sensing, quantum simulation or quantum computing. For example, air bridges may be configured to connect to outer ground metal plates in order to improve the grounding of interior metal structures. Moreover, air bridges can be configured as interconnects that cross signal carrying lines such as coplanar waveguide (CPW) structures and thereby enhance and improve planar routing configurations. On the other hand, air bridges may be dedicated to suppressing unwanted electromagnetic modes (e.g., microwave modes) or disturbing crosstalk between adjacent metal lines. Current implementations of superconducting air bridges, however, impose a critical loss channel, thereby considerably reducing the quality of various superconducting circuit elements such as on-chip filters, resonators, parametric amplifiers or superconducting qubits. Furthermore, the manufacturing process of air bridges often relies on critical lift-off process steps that are rather unreliable and may impose defects that could further harm the stability and quality of the air bridge.

[0006] Thus, an object of the invention is to overcome such limitations and provide a a method of manufacturing a bridge structure an electronic circuit and a superconducting qubit that improve upon the available methods and devices.

[0007] Summary

[0008] This object of the invention is achieved by a method for manufacturing a bridge structure, an electronic circuit and a superconducting qubit as described in the appended independent claims. Advantageous developments and embodiments are described in the dependent claims.

[0009] In a first aspect, the invention relates to a method for manufacturing a bridge structure. The method comprises forming a base layer over a substrate, depositing a first sacrificial layer on the base layer, patterning the first sacrificial layer into a bridge-like shape, depositing a second sacrificial layer on the patterned first sacrificial layer and on the base layer, depositing a bridge layer on the second sacrificial layer and on the base layer to obtain the bridge structure, and removing the patterned first sacrificial layer and the second sacrificial layer.

[0010] With the proposed method high-quality bridge structures can be manufactured that are essentially loss-free. Moreover, the depositing of two sacrificial layers, the first and the second sacrificial layer, ensures high flexibility with respect to a selection of materials, the shape and the thickness of the bridge structure as well as the sacrificial structure below the bridge layer that defines the vertical gap between the to-be-manufactured bridge and the underlying base layer and / or substrate. The depositing of a second sacrificial layer on the patterned first sacrificial layer that has already been brought into a bridge-like shape (i.e., on the bridge-like shape) ensures a protective cover for the patterned first sacrificial layer before the bridge layer is being deposited on the second sacrificial layer over the bridge-like shape of the patterned first sacrificial layer. Additionally, the manufacturing method comprises subtractive method steps that render a critical lift-off process obsolete, thereby ensuring CMOS compatibility and improving upon flexibility and scalability of the proposed process.

[0011] Optionally, after the depositing the second sacrificial layer and before depositing the bridge layer the method further comprises patterning the second sacrificial layer to expose at least partially a surface of the base layer. The exposed surface may be next to the patterned first sacrificial layer. The bridge layer can then be deposited on the patterned second sacrificial layer and also on the at least partially exposed surface of the base layer to contact the base layer. Alternatively, when depositing the second sacrificial layer, the base layer may not be covered completely by the second sacrificial layer, so that a surface of the base layer remains exposed and the depositing of the bridge layer comprises depositing the bridge layer also on the exposed surface of the base layer.

[0012] Since the second sacrificial layer can be patterned to expose a surface of the base layer before the bridge layer is being deposited and before the (patterned) first sacrificial layer is being removed, the method enables the realization of a large variety of support / foundation and contact structures for the bridge structure with diverse geometries to contact the base layer, e.g., by using the second sacrificial layer as a mask layer for subsequent processing steps (e.g., during the deposition of the bridge layer on the exposed surface of the base layer).

[0013] Optionally, the substrate may be a semiconductor substrate. The substrate may be a silicon substrate or a sapphire substrate or any other substrate that allows for the forming of the base layer.

[0014] Optionally, the base layer may be made of a superconducting material. The base layer may be a superconducting thin film. For example, the base layer may be a metal or metal-nitride layer. The base layer may be made of or at least comprise Niobium, Tantalum, Niobium-Titanium nitride or any other superconducting material. Advantageously, the base layer should be configured to withstand acids, e.g., a Piranha acid (i.e., a sulfuric acid mixed with hydrogen peroxide) and / or a hydrofluoric acid.

[0015] In this application, the term "superconducting" refers to a characteristic of a device component or material. A device component or material is considered superconducting when a critical temperature exists below which it exhibits superconducting properties. The term "superconducting" is not meant to limit the scope of protection to a certain temperature regime, e.g., below the critical temperature. The term "superconductive" or "superconductor" may also be used instead of the term "superconducting".

[0016] Optionally, the base layer may be formed directly on the substrate. The forming of the base layer may comprise depositing the base layer using commonly known deposition methods. The method may comprise patterning the base layer to form openings (e.g., capacitive gaps) in the base layer. The openings in the base layer may expose an upper surface of the substrate. For example, the openings in the base layer may correspond to horizontal gaps along the upper surface of the substrate between different segments of the base layer. The openings may be configured as vacuum-gap capacitances between the different segments of the base layer. Optionally, the base layer and / or the different segments defined by the openings may form a coplanar waveguide structure. The different segments and / or the coplanar waveguide structure may comprise at least a center portion of the base layer and two contact portions of the base layer. The center portion of the base layer may be positioned between the two contact portions and be (air) gapped and / or horizontally separated by the openings and / or horizontal gaps from the two contact portions.

[0017] The first sacrificial layer may be a soft mask (layer) or a soft (photo-) resist layer. The patterning of the first sacrificial layer into a bridge-like shape may define, at least approximately, the shape, width and / or length of the to-be- manufactured bridge structure. The patterning of the first sacrificial layer into a bridge-like shape may comprise bringing a middle portion of the first sacrificial layer into a curved and / or an arched shape and / or removing outer portions of the first sacrificial layer away from the center portion of the first sacrificial layer from the upper surface of the base layer.

[0018] The patterning of the first sacrificial layer into a bridge-like shape may comprise a reflow resist process. For example, the patterning of the first sacrificial layer may comprise heating the deposited first sacrificial layer to its reflow temperature. Additionally, or alternatively, the patterning of the first sacrificial layer into a bridge-like shape may comprise a lithography process, e.g., an optical lithography process or an electron beam lithography process.

[0019] Optionally, the patterning of the first sacrificial layer into a bridge-like shape comprises first applying a lithography process to define a rectangular shape of the first sacrificial layer (in a cross-sectional view) and to apply the reflow resist process in order for the reflow to bring the rectangular shape into the shape of an arch, thereby defining the bridge-like shape.

[0020] Optionally, the patterning of the first sacrificial layer may comprise a grayscale lithography process. Advantageously, the form and / or mechanical stability of the bridge-like shape may be defined or improved by varying the light intensity or electron dose across the length of the bridge-like shape. Optionally, the patterning of the first sacrificial layer comprises a combination of a reflow resist process and a grayscale process.

[0021] The thickness of the deposited first sacrificial layer before the patterning of the first sacrificial layer into a bridge-like shape may be, at least approximately, a homogeneous thickness along / across the upper surface of the substrate. The (e.g., homogeneous and / or maximal) thickness of the deposited first sacrificial layer before the patterning into the bridge-like shape may be between 300 Nanometer and 20 Micrometer, optionally between 500 Nanometer and 10 Micrometer, preferably between 1 Micrometer and 5 Micrometer. The maximal thickness of the bridge-like shape may be at least approximately identical to the thickness of the first sacrificial layer before the patterning into the bridge-like shape. The second sacrificial layer may be made of a different material than the first sacrificial layer. The second sacrificial layer may be harder than the first sacrificial layer. Optionally, the second sacrificial layer is a hard mask or a hard mask layer. For example, the second sacrificial layer may be made of or at least comprise aluminum or gold (e.g., evaporated aluminum or gold).

[0022] Advantageously, the second sacrificial layer may function as a cover and / or protective layer for the patterned first sacrificial layer and / or the base layer.

[0023] Moreover, the second sacrificial layer may be configured to prevent intermixing of the patterned first sacrificial layer and the (to-be-deposited) bridge layer during and / or after the depositing of the bridge layer. For example, the second sacrificial layer may serve / f unction as a cover to protect the underlying first sacrificial layer from ion implantation during the depositing of the bridge layer. The second sacrificial layer may also be configured to be selectively removable with respect to the base layer, i.e., being removable without necessarily removing the underlying base layer.

[0024] The (e.g. homogeneous and / or maximal) thickness of the second sacrificial layer can be smaller than the (e.g., homogeneous and / or maximal) thickness of the first sacrificial layer before the patterning of the first sacrificial layer into a bridge-like shape and / or smaller than the maximal thickness of the bridge-like shape. The thickness of the second sacrificial layer may be smaller than 300 Nanometer. The thickness of the second sacrificial layer may be larger than 3 Nanometer. Optionally, the thickness of the second sacrificial layer ranges between 10 Nanometer and 200 Nanometer, or between 30 Nanometer and 100 Nanometer.

[0025] The bridge layer may be made of or at least comprise a metal and / or a superconducting material. For example, the bridge layer may be made of or at least comprise Niobium, Tantalum, Niobium-Titanium nitride or any other superconducting material. Optionally, the bridge layer may be made of the same material as the base layer. The bridge layer may be made of a different material as the second sacrificial layer. Advantageously, the bridge layer should be configured to withstand acids, e.g., a Piranha acid (i.e., a sulfuric acid mixed with hydrogen peroxide) and / or a hydrofluoric acid. The bridge layer may be deposited using sputtering, thermal evaporation and / or electron beam evaporation. The second sacrificial layer may act as a protective layer for the (patterned) first sacrificial layer during the depositing of the bridge layer, thereby enabling the usage of deposition processes for the bridge layer with high kinetic energies and high temperatures without suffering from intermixing between the deposited bridge layer and the first sacrificial layer.

[0026] The thickness of the bridge layer may be larger than the thickness of the second sacrificial layer. The thickness of the bridge layer may be between 50 Nanometer and 5 Micrometer, or between 300 Nanometer and 1 Micrometer. The length and width of the bridge structure may depend on the application. The length of the bridge structure along the upper surface of the substrate may be between 500 Nanometers and 200 Micrometers. The width of the bridge structure (in a direction perpendicular to the length dimension but along the upper surface of the substrate, e.g., corresponding to the length of the tunnel formed between the base layer and the bridge structure) may be larger than 500 Nanometer.

[0027] Optionally, the patterning of the second sacrificial layer to expose at least partially a surface of the base layer (next to the patterned first sacrificial layer) comprises forming openings into the second sacrificial layer to locally expose the surface of the base layer. The openings may be formed by etching.

[0028] Optionally, the depositing a bridge layer on the patterned second sacrificial layer and on at least a part of the exposed surface of the base layer then also comprises depositing the bridge layer into the openings of the patterned second sacrificial layer to contact the base layer. hTe bridge layer may be deposited into the openings to form the foundations / support of the to-be-manufac- tured bridge structure. Optionally, the bridge layer may be deposited into the openings to form pillars of the bridge structure in the openings. The pillars may contact the base layer in the openings, e.g., to form galvanic connec- tions / contacts. For example, the pillars may contact the contact portions of the base layer.

[0029] The dimensions of the foundations and / or the pillars of the bridge structure can be chosen flexibly and largely independent of the overall dimensions of the bridge structure, e.g., independent of the length and / or width of the bridge structure and / or independent of the dimensions of the capping portions over and on top of the pillars that connect the pillars with a middle portion of the bridge structure.

[0030] Optionally, the depth of an opening and / or the height of a pillar is smaller than the thickness of the bridge layer. The height of a / each pillar can correspond to the depth of an / each opening. The height of a / each pillar and / or the depth of an / each opening can correspond to the thickness of the second sacrificial layer.

[0031] Optionally, the lateral dimension of an opening, foundation and / or a pillar in a direction along the length of the bridge-like shape and / or the (to-be-manufac- tured) bridge structure is smaller than 1 Micrometer, smaller than 500 Nanometer. The bottom surface of each pillar that contacts the base layer may have a rectangular or quadratic shape.

[0032] Optionally, and before depositing the bridge layer into the openings, the method further comprises removing oxides from inside the openings and / or from the exposed surface of the base layer using ion milling, e.g., for an improved galvanic connection / contact between base layer and bridge structure or pillar. Here, the second sacrificial layer may also act as protective layer for the first sacrificial layer during the ion milling process.

[0033] Optionally, during the deposition of the bridge layer outer portions of the second sacrificial layer positioned away from the bridge-like shape of the patterned first sacrificial layer can be masked by a lift-off mask to prevent the deposition of the bridge layer on the outer portions of the second sacrificial layer. This may also define a length and / or width of the bridge structure.

[0034] Optionally, the method may also comprise patterning the bridge layer. The patterning of the bridge layer may comprise a lithography process and / or etching the bridge layer. For example, the patterning of the bridge layer may comprise removing outer portions of the bridge layer (as seen from the bridge-like shape or middle portion of the bridge structure) from an upper surface of the (patterned) second sacrificial layer. Here, the second sacrificial layer may act or be configured as an etch stopper (thus mitigating over-etching into the base layer). For example, this can be achieved with a sulfur hexafluoride based reactive ion etching process and a hard mask as a second sacrificial layer being made of aluminum or gold. The patterning of the bridge layer may define a length and / or width of the bridge structure

[0035] More specifically, after depositing the bridge layer and / or after forming the foundations or pillars and before removing the patterned second sacrificial layer, the method may additionally comprise removing outer portions of the bridge layer away from the bridge-like shape of the patterned first sacrificial layer from a top surface of the patterned second sacrificial layer.

[0036] Preferably, the patterning of the bridge layer leaves the bridge layer inside the openings of the second sacrificial layer such that the openings remain filled completely with the bridge layer and / or the capping portions remain on the pillar and remain extending beyond the pillar.

[0037] Preferably, after the patterning of the bridge layer, the remaining capping portions of the bridge layer (outside the openings) are extending and hanging over the pillar in a (lateral / horizontal) direction parallel to the upper surface of the substrate and / or away from the bridge-like shape such that the capping portions also remain on the upper surface of the (patterned) second sacrificial layer (at least until the second sacrificial layer is removed).

[0038] More specifically, the method may comprise forming capping portions of the bridge structure on top of the pillars by patterning the bridge layer. Each capping portion may connect a pillar with the (e.g. curved or arch-shaped) middle portion of the bridge structure. Each capping portion may also overlap and / or extend beyond a pillar in a direction away from the middle portion. Each capping portion may have a bottom surface substantially parallel to and gapped from the upper surface of the base layer. The bottom surface of each capping portion may (at least partially) directly contact the patterned second sacrificial layer (before the second sacrificial layer is removed).

[0039] The area of the planar bottom surface of each capping portion may be larger than the area of the planar bottom surface of the pillar contacting the base layer. The vertical gap between the upper surface of the base layer and the bottom surface of the capping portion may correspond to the thickness of the second sacrificial layer and / or the height of the pillars and / or the depth of the openings. Preferably, the removing of the patterned second sacrificial layer may comprise removing the second sacrificial layer completely from the surface of the base layer and / or the patterned first sacrificial layer. In particular, the removing of the patterned second sacrificial layer may comprise selectively removing the patterned second sacrificial layer from all areas / volumes below the bridge structure without removing and / or affecting the base layer and / or the bridge layer.

[0040] Optionally, the removing of the patterned second sacrificial layer is achieved by using a wet chemistry process configured to selectively remove the second sacrificial layer. Optionally, the wet chemistry process may comprise applying Aqua Regia to remove the patterned second sacrificial layer, e.g., when the second sacrificial layer comprises and / or is made of gold. Optionally, the wet chemistry process may comprise applying an acetic, nitric or phosphoric acid or a combination thereof to remove the patterned second sacrificial layer, e.g., when the second sacrificial layer comprises and / or is made of aluminum.

[0041] The removing of the first sacrificial layer may comprise removing the first sacrificial layer completely from the upper surface of the base layer and / or the substrate. This can be achieved using wet chemistry, an oxygen plasma or a combination of both processes.

[0042] Optionally, the method further comprises cleaning the bridge structure and / or the base layer with an acid, e.g., with a Piranha and / or hydrofluoric acid, to further reduce losses of the bridge structure, e.g., at the metal-air interface.

[0043] Electronic circuit

[0044] In a second aspect, the invention also relates to an electronic circuit. The electronic circuit comprises a substrate, a base layer over the substrate, and at least one bridge structure on the base layer. Each bridge structure of the at least one bridge structure comprises a middle portion connecting two end portions on opposite sides of the middle portion, wherein the middle portion is gapped from the base layer by a vertical gap in a direction perpendicular to an upper surface of the substrate. Each first end portion comprises a pillar, wherein each pillar has a bottom surface galvanically contacting the base layer. Optionally, each pillar contacts a contacting portion of the base layer.

[0045] Optionally, the electronic circuit may be a superconducting electronic circuit. The vertical gap may be an air gap. Each one of the at least one bridge structure may be an air bridge structure. The base layer may be made of a metal and / or a superconducting material. Each one of the at least one bridge structure may be made of a metal and / or a superconducting material.

[0046] Optionally, each end portion of the bridge structure additionally comprises a capping portion. Each capping portion may be on top of and on a pillar. Each capping portion may be connecting the middle portion and a pillar. Each capping portion may have a bottom surface substantially planar and parallel to the upper surface of the base layer (e.g., as seen from the substrate).

[0047] The bottom surface of the capping portion may be gapped by a second vertical gap from the upper surface of the base layer. The second vertical gap between the bottom surface of the capping portion and the upper surface of the base layer may correspond to the height of the pillar. The second vertical gap may correspond to the thickness of the second sacrificial layer as described in relation to the first aspect (see ranges of thicknesses as described above).

[0048] The area of the bottom surface of the capping portion maybe larger than the area of the bottom surface of the pillar contacting the base layer and / or the contact portion, and the pillar may be positioned below the capping portion. An inner portion of the capping section may be directly on the pillar. An outer portion of the capping portion that is completely or at least partially surrounding or encapsulating the inner portion may be air gapped from the upper surface of the base layer. The thickness of the outer portion of the capping portion may correspond to the sum of the thickness of the inner portion of the capping portion and the height of the pillar such that inner portion of the capping portion is vertically recessed with respect to the outer portion.

[0049] Each capping portion may extend beyond the pillar that is directly below the (inner portion of the) capping portion in a direction pointing away from the middle portion of the bridge structure (to form the outer portion of the capping portion). Optionally, each capping portion may extend beyond the pillar along said direction by more than 100 Nanometers, 500 Nanometers or even by more than 1 Micrometer.

[0050] The substrate, the base layer, the bridge structure, the middle portion, the end portion, the pillar, the capping portion, the center portion and / or the contact portion may be configured as described in the context of the first aspect of the invention.

[0051] Superconducting qubit

[0052] In a third aspect, the invention relates to superconducting qubit.

[0053] The superconducting qubit comprises a substrate, a base layer over the substrate and at least one bridge structure on the base layer. Each bridge structure of the at least one bridge structure comprises a middle portion connecting two end portions on opposite sides of the middle portion, wherein the middle portion is gapped from the base layer and / or a center portion of the base layer by a vertical gap in a direction perpendicular to an upper surface of the substrate. Each end portion galvanically contacts the base layer and / or a contact portion of the base layer, wherein a shunt capacitance of the superconducting qubit comprises each middle portion of the at least one bridge structure and the center portion of the base layer.

[0054] In the proposed superconducting qubit at least one bridge structure is thus implemented and used as a shunting (bridge) capacitance that can be scaled up in a flexible and stable manner. Importantly, through this three-dimensional design the superconducting qubit exhibits extremely low loss properties. Alternatively, or additionally, the superconducting qubit and its components may be configured as described according the first or second aspect. The superconducting qubit may be considered as an electronic circuit.

[0055] Optionally, the superconducting qubit comprises a shunt capacitance element with a lower capacitive plate separated from an upper capacitive plate. The lower capacitive plate can comprise a center portion of the base layer arranged between and horizontally gapped from the two contact portions of the base layer. The upper capacitive plate can comprise the middle portion of the bridge structure. The middle portion can be overlapping and vertically gapped by the vertical gap from the center portion of the base layer. In this application, the term "superconducting qubit" refers to a device or device component comprising superconducting circuitry that can be repre- sented / described by at least two discrete energy levels or states whose properties (occupation, i.e., excitation and / or deexcitation) can be controlled by external circuitry. The at least two discrete energy levels may represent a computational subspace used, e.g., for quantum computing or quantum simulation. The at least two discrete energy levels may also be used for quantum sensing or metrology or other quantum-technological application.

[0056] Thereby, the shunt capacitance defines the energy-level spacing in the energy level spectrum of the superconducting qubit. The superconducting qubit may be a charge qubit, a transmon qubit or a fluxonium qubit.

[0057] Optionally, the electronic circuit and / or the superconducting qubit may comprise a plurality of bridge structures, e.g., as described according to the first or second aspect. In particular, the at least one bridge structure may comprise a plurality of bridge structures. The plurality of bridge structures may be connected in series. The upper capacitive plate may comprise the plurality of middle portions of the plurality of bridge structures.

[0058] The base layer may comprise a plurality of center portions. Each center portion may be positioned between two contact portions of the base layer. Each middle portion of a bridge structure may overlap and may be gapped by the vertical gap from a different center portion of the base layer. The lower capacitive plate may comprise the plurality of center portions of the base layer.

[0059] Optionally, when the superconducting qubit comprises a plurality of bridge structures, the shunt capacitance of the superconducting qubit may comprise all middle portions of the bridge structures and center portions of the base layer, wherein each middle portion overlaps a center portion and the shunt capacitance is formed by their total overlap area. Each center portion of the base layer may overlap and / or be positioned below a middle portion of a bridge structure.

[0060] In particular, by the use of a plurality of bridge structures, the shunting capacitance can be scaled up considerably to more than 100 Pico-Farad (pF). The shunting capacitance may be several hundred Pico-Farad. Preferably, two neighboring bridge structures in the series of the plurality of bridge structures may share a same pillar (e.g. to contact a same contact portion of the base layer) and / or share a same capping portion. In that case the same capping portion and / or pillar may be arranged between and / or connect the two (different) middle portions of the two neighboring bridge structures. Also, the two neighboring bridge structures may galvanically contact the same contact portion of the bridge layer through the same pillar.

[0061] The superconducting qubit can comprise a nonlinear circuit element to induce an anharmonicity in the energy-level spectrum of the superconducting qubit. The nonlinear circuit element can be electrically connected to the at least one bridge structure. The nonlinear circuit element can electrically couple the lower capacitive plate and the upper capacitive plate. Optionally, the nonlinear circuit element can electrically connect a contact portion and a center portion of the base layer.

[0062] The nonlinear circuit element can comprise or correspond to at least one Josephson element. The Josephson element may comprise a Josephson junction, an array of Josephson junctions (in a parallel or series configuration), a SQUID (superconducting quantum interference device) and / or a combination thereof.

[0063] In conclusion, the invention discloses a fabrication process for a low-loss bridge structure. In particular, methods that would just use a thick hard mask lack the flexibility to control the shape of the bridge. Methods that only use a soft mask result in air bridge structures with high losses at least partially stemming from the intermixing between the soft mask and the air bridge material during fabrication. Additionally, the second sacrificial layer according to the invention may act as an etch stopper and as such the proposed process contains subtractive manufacturing steps that may be used to get rid of any detrimental lift-off procedures when fabricating an air bridge. Moreover, the proposed steps of the method can be considered subtractive and as such are CMOS compatible and scalable.

[0064] It is also noted that lift-off processes require a face-to-face deposition, wherein the deposition source needs to be directed in a normal direction with respect to the upper surface of the substrate. Otherwise the deposited film would establish a physical connection between the substrate and the top of the resist. The proposed method is not constrained in this way and thus improves the flexibility of the manufacturing process.

[0065] The invention also facilitates the realization of efficient means for grounding and interconnect structures in planar routing configurations, as well as vacuum gap capacitances in various superconducting elements such as superconducting qubits. In contrast to planar capacitances, a large proportion of the electric field can be shifted from the substrate, which is prone to losses, into loss-free vacuum. Since superconducting qubits and resonators are susceptible to two-level system losses, it is crucial that a capacitor, e.g., an air bridge, is as loss-free as possible. This is ensured by the proposed manufacturing process in a particular reliable and flexible manner.

[0066] Detailed Description

[0067] Exemplary embodiments of the invention are illustrated in the drawings and will now be described with reference to figures 1 to 4.

[0068] In the figures:

[0069] Fig. 1 shows an embodiment of a process flow according to the method of manufacturing a bridge structure,

[0070] Fig. 2 shows an embodiment of an electronic circuit comprising a bridge structure,

[0071] Fig. 3 shows embodiments and use cases of a bridge structure,

[0072] Fig. 4 shows an embodiment of an electronic circuit comprising a plurality of bridge structures.

[0073] Figure 1 shows an embodiment of a process flow according to the method for manufacturing a bridge structure 1.

[0074] The method comprises forming a base layer 3 on a substrate 2 and depositing a first sacrificial layer 4 on the base layer 3. The result of these method steps is shown in Panel (a) of Figure 1. The substrate 2 is a Silicon substrate and the base layer 3 is made of the superconducting material Niobium. Here, the method additionally comprises patterning the base layer 3 by defining openings (horizontal vacuum-gap capacitances) in the base layer 3 through etching before the depositing of the first sacrificial layer 4 on the base layer 3. The openings in the base layer 3 then define a center portion 3.1 of the base layer 3 arranged and positioned between two contact portions 3.2.1, 3.2.2 of the base layer 3 (see also figure 2). In other words, the center portion 3.1 is horizontally air-gapped from the two contact portions 3.2.1, 3.2.2. In another embodiment, the material of the center portion 3.1 may also be different from the material of the two contact portions 3.2.1, 3.2.2.

[0075] The first sacrificial layer 4 is a soft mask. Specifically, the first sacrificial layer 4 is a soft (photo-)resist layer. The thickness of the first sacrificial layer 4 shown in Panel (a) of Figure 1 is 3 Micrometers.

[0076] The method further comprises patterning the first sacrificial layer 4 into a bridge-like shape 4.1. The result of this method step is shown in Panel (b) of Figure 1.

[0077] The patterning of the first sacrificial layer 4 into the bridge-like shape 4.1 comprises a lithography step and a subsequent reflow resist process. The lithography step comprises patterning the first sacrificial layer 4 into a rectangular shape as seen in the cross-sectional view of Figure 1, wherein the lateral length of the rectangle at least approximately defines the length of the to-be- manufactured bridge structure 1. After the lithography step, the method comprises a reflow resist process. The reflow resist process comprises heating up the first sacrificial layer 4 in the shape of the rectangle to the reflow temperature of the resist so that the reflow changes the rectangular shape into an arch defining the bridge-like shape 4.1. In alternative embodiments, the reflow resist process may also be replaced or combined with a grayscale lithography process in order to define the length of the bridge-like shape 4.1.

[0078] The method further comprises depositing a second sacrificial layer 5 on the patterned first sacrificial layer 4, 4.1 and on the base layer 3. The second sacrificial layer 5 is deposited on the base layer 3 on portions of the upper surface of the baser layer 3, where the first sacrificial layer 4 has been removed, e.g., by lithography, during the step of patterning the first sacrificial layer 4 into the bridge-like shape 4.1. The result of this method step is shown in Panel (c) of Figure 1.

[0079] The second sacrificial layer 5 is a hard mask. Specifically, the second sacrificial layer 5 is made of aluminum. The thickness of the second sacrificial layer 5 is 50 Nanometers.

[0080] The method further comprises patterning the second sacrificial layer 5 to expose at least partially a surface of the base layer 3 next to the patterned first sacrificial layer 4, 4.1. The result of this method step is shown in Panel (d) of Figure 1.

[0081] The patterning of the second sacrificial layer 5 to expose at least partially a surface of the base layer 3 next to the patterned first sacrificial layer with the bridge-like shape 4.1 comprises etching openings 5.1 into the second sacrificial layer 5 to locally expose the surface of the base layer 3 in the openings

[0082] 5.1. The etching of the openings 5.1 into the second sacrificial layer 5 comprises first defining the positions of the openings 5.1 on the second sacrificial layer 5 by lithography and then dry etching or wet-chemical etching these openings 5.1 until the upper surface of the base layer 3 is locally exposed. Specifically, the openings 5.1 are etched locally above the contact portions

[0083] 3.2.1, 3.2.2 of the base layer 3, but not above the center portion 3.1, such that only (parts of) the upper surface of these contact portions 3.2.1, 3.2.2 is exposed. The depth of the openings 5.1 corresponds to the thickness of the second sacrificial layer 5 of 50 Nanometers.

[0084] The method further comprises removing oxides from inside the openings 5.1 at the exposed surface of the base layer 3 using ion milling (not shown). This ensures a higher quality galvanic connection between the base layer 3 and the to-be-manufactured bridge structure 1. Here, the second sacrificial layer 5 as a hard mask acts also as a protective cover to protect the underlying patterned first sacrificial layer 4, 4.1 from ion implantation during the ion milling process.

[0085] The method further comprises depositing a bridge layer 6 on the patterned second sacrificial layer 5 and on the exposed surface of the base layer 3 to contact the base layer 3. The result of this method step is shown in Panel (e) of Figure 1. The bridge layer 6 is made of a superconducting material. Specifically, the bridge layer 6 is made of Niobium. The thickness of the bridge layer is 500 Nanometers. The bridge layer 6 is deposited using sputtering. In alternative embodiments, the bridge layer 6 may also be deposited using thermal or electron beam evaporation. Here, the second sacrificial layer 5 acts as a protective layer for the patterned first sacrificial layer 4, 4.1 with the bridge-like shape

[0086] 4.1 during the deposition of the bridge layer 6, thereby preventing an intermixing of the patterned first sacrificial layer 4, 4.1 with the bridge layer 6. This enables the usage of high kinetic energies and high temperatures during the deposition / sputtering process.

[0087] The depositing of a bridge layer 6 on the patterned second sacrificial layer 5 and on the exposed surface of the base layer 3 comprises depositing the bridge layer 6 into the openings 5.1 to form pillars 1.3.1, 1.3.2 of the to-be- manufactured bridge structure 1. The pillars 1.3.1, 1.3.2 are contacting the base layer 3 (see also Figure 2). The height of each pillar 1.3.1, 1.3.2 corresponds to the thickness of the second sacrificial layer 5 of 50 Nanometer.

[0088] The method further comprises patterning the deposited bridge layer 6, thereby obtaining the bridge structure 1. The patterning of the bridge layer 6 comprises removing outer portions of the bridge layer 6 from a top (upper) surface of the patterned second sacrificial layer 5 away from the bridge-like shape 4.1 of the patterned first sacrificial layer 4, 4.1 (or away from the middle portion 1.1 of the bridge layer, see Figure 2). The result of this method step is shown in panel (f) of Figure 1.

[0089] The patterned bridge layer 6.1 still completely fills and covers the openings

[0090] 5.1 such that capping portions 1.2.1,1.2.2 of the bridge structure (see Figure 2 and description further below) overlap the pillars 1.3.1,1.3.2 extending beyond the pillars 1.3.1,1.3.2 in a direction away from the bridge-like shape 4.1 of the patterned first sacrificial layer 4, 4.1. Thus, in said direction the patterned bridge layer 6.1 extends beyond the pillars 1.3.1,1.3.2 and there also contacts and is on the upper surface of the patterned second sacrificial layer 5.

[0091] The patterning of the deposited bridge layer 6 is achieved by a lithography process and subsequent etching of the bridge layer 6 (to define the capping portions 1.2.1, 1.2.2 discussed further below in relation to Figure 2). The patterning of the bridge layer 6 then defines the lateral dimensions of the bridge structure 1, i.e., the length and width of the bridge structure 1. Here, the patterned second sacrificial layer 5 acts as an etch stopper, thus mitigating overetching into the base layer 3. This is achieved by using a sulfur hexafluoride based reactive ion etching process when etching the bridge layer 6.

[0092] The method further comprises removing completely the patterned first 4, 4.1 and the patterned second sacrificial layer 5 (from the substrate 2 and the base layer 3) to form a vertical air gap 7 between the base layer 3 and the bridge layer 6, 6.1. The result of this method step is shown in Panel (g) of Figure 1.

[0093] Here, the vertical air gap 7 corresponds at least approximately to the sum of the thickness of the first sacrificial layer 4 and the second sacrificial layer 5. In the embodiment shown in panel (g) of Figure 1, the vertical air gap 7 corresponds to the maximal vertical distance between the upper surface of the base layer 3, i.e., the center portion 3.1 of the base layer 3, and the bottom surface of the bridge structure 1, i.e., the center of the bottom surface of the arch-shaped middle portion 1.1 of the bridge structure 1 (see also Figure 2). Thus, the bridge structure 1 forms an air bridge over the center portion 3.1 of the base layer 3.

[0094] More specifically, the patterned second sacrificial layer 5 is selectively removed from the upper surface of the base layer 3 without removing or attacking the base layer 3, the patterned bridge layer 6.1 and thus the bridge structure 1. This is achieved by using a mixture of acetic, nitric and phosphoric acid in a wet chemical process when removing the second sacrificial layer.

[0095] The patterned first sacrificial layer 4, 4.1 is then removed with a wet chemistry process. In a different embodiment, the patterned first sacrificial layer 4, 4.1 can also be removed using an oxygen plasma process or a combination of both processes.

[0096] In a further step, the method comprises cleaning the bridge structure 1 with a Piranha and hydrofluoric acid to further reduce losses in the metal-air interface. The resulting air bridge is essentially loss-free. This has been measured using the process described in the following:

[0097] A characterization of the properties of the air bridge as obtained from the proposed method can be achieved by probing the air bridge with coplanar waveguide resonators in the single photon regime. The internal quality factor of the resonator is being measured at cryogenic temperatures and low applied signal powers (down to less than one photon per average in the resonator). By measuring a varying number of air bridges on top of a resonator, statistics can be obtained and the loss per air bridge can be extracted. Typical values for the loss per air bridge (obtained from the inverse of the quality factor of the resonator, wherein the loss per air bridge is obtained by dividing the total loss of the resonator, i.e., the inverse of the quality factor of the resonator, by the number of air bridges over said resonator) as manufactured by known methods vary between 2e-8 to 4e-9. With the proposed method, the loss per air bridge can be suppressed below 4e-10.

[0098] In summary, the proposed method enables the fabrication of air bridges with a significantly lower loss compared to state of the art implementations.

[0099] Recurring features are provided in the following figures with identical reference signs as in Figure 1.

[0100] Figure 2 shows an embodiment of an electronic circuit 10. The electronic circuit 10 is a superconducting electronic circuit and has been manufactured using the method as described with respect to Figure 1.

[0101] The electronic circuit comprises the substrate 2, the base layer 3 over and on the substrate 2, and the bridge structure 1 on the base layer 3. The bridge structure 1 comprises a middle portion 1.1 connecting two end portions on opposite sides of the middle portion 1.1, wherein the middle portion 1.1 is gapped from the base layer 3 by a vertical air gap 7 in a direction perpendicular to an upper surface of the substrate 2.

[0102] Each first end portion of the first bridge structure 1 comprises a pillar 1.3.1, 1.3.2, wherein each pillar 1.3.1, 1.3.2 has a bottom surface galvanically contacting an upper surface of a contact portion 3.2.1, 3.2.2 of the base layer 3. The bottom surface of each pillar 1.3.1, 1.3.2 that establishes a galvanic contact to a contact portion 3.2.1, 3.2.2 has the shape of a square.

[0103] Each end portion of the bridge structure 1 additionally comprises a capping portion 1.2.1, 1.2.2. Each capping portion 1.2.1, 1.2.2 is on (top of) a pillar

[0104] 1.3.1, 1.3.2. Each capping portion 1.2.1, 1.2.2 is connecting the middle portion 1.1 with a pillar 1.3.1, 1.3.2. Each capping portion 1.2.1, 1.2.2 has a bottom surface A substantially planar and parallel to the upper surface of the base layer 3 (as seen from the substrate 2).

[0105] The middle portion 1.1 has a bottom surface (facing the substrate 2) with an arched shape, wherein the arch extends outwards as seen from the substrate 2. The middle portion 1.1 ends where the arch-shaped bottom surface of the middle portion 1.1 forms a corner with the planar bottom surface A of the capping portions 1.2.1, 1.2.2.

[0106] The base layer 3 is patterned and comprises a center portion 3.1 vertically airgapped below the middle portion 1.1 of the bridge structure 1. The center portion 3.1 is positioned between and horizontally air-gapped from the two contact portions 3.2.1, 3.2.2 of the base layer 3. The vertical air gap 7 corresponds to the maximal distance in a direction perpendicular to the upper surface of the substrate 2 between the center portion 3.1 and the bottom surface of the middle portion 1.1. The center portion 3.1 together with the contact portions 3.2.1, 3.2.2 form a coplanar waveguide (CPW) structure.

[0107] The bottom surface A of the capping portions 1.2.1, 1.2.2 facing the substrate 2 is air gapped by a second vertical gap from the upper surface of the base layer 3, i.e., the upper surface of the contact portions 3.2.1, 3.2.2. The second vertical air gap between the bottom surface A of the capping portions 1.2.1, 1.2.2 and the upper surface of the base layer 3 corresponds to the height of the pillars 1.3.1, 1.3.2. The second vertical air gap also corresponds to the thickness of the second sacrificial layer 5 as described with respect to Figure 1.

[0108] The area of the bottom surface A of each capping portion 1.2.1, 1.2.2 is larger than the (contact) area of the bottom surface of each pillar 1.3.1, 1.3.2 contacting a contact portion 3.2.1, 3.2.2 of the base layer 3 and being positioned below the capping portion 1.2.1, 1.2.2. In other words, each capping portion

[0109] 1.2.1, 1.2.2 extends beyond the pillar 1.3.1, 1.3.2 that contacts said capping portion 1.2.1, 1.2.2 in a lateral direction pointing away from the middle portion 1.1 (along the length of the bridge structure 1) by more than 50 Nanometers such that said capping portion 1.2.1, 1.2.2 is air-gapped by the second vertical gap from the contact portion 3.2.1, 3.2.2 of the base layer 3 that contacts said pillar 1.3.1, 1.3.

[0110] Since the material of the pillars 1.3.1, 1.3.2 and the capping portions 1.2.1, 1.2.2 has been deposited during the deposition of the bridge layer 6, the sum of the thickness of a pillar 1.3.1, 1.3.2 and the thickness of the capping portion 1.2.1, 1.2.2 in the area above and overlapping the pillar 1.3.1, 1.3.2 corresponds to the (total) thickness of the bridge layer 6 of 500 Nanometer. The thickness of the part of the capping portion 1.2.1, 1.2.2 that is extending beyond and is not overlapping the pillar 1.3.1, 1.3.2 also corresponds to the thickness of the bridge layer 6 of 500 Nanometer. Thus, the (inner) part of the capping portion 1.2.1, 1.2.2 above the pillar 1.3.1, 1.3.2 is vertically recessed (has a smaller thickness) with respect to the (outer) part of the capping portion 1.2.1, 1.2.2 extending beyond and not overlapping the pillar 1.3.1, 1.3.2. The height of the vertical recess corresponds to the thickness of the second sacrificial layer 5 and the height of the pillars 1.3.1,1.3.2. The area of the vertical recess corresponds to the exposed surface area of the opening 5.1 and thus the area of the bottom surface of the pillar 1.3.1, 1.3.2.

[0111] The length L of the bridge structure 1 corresponds to a dimension in a direction parallel to the upper surface of the substrate 2 (as seen from the cross- sectional view of Figure 2), wherein the length corresponds to the distance between outer sidewalls of the capping portions 1.2.1, 1.2.2 (as seen from the middle portion 1.1). The length L of the bridge structure 1 in Figure 2 is 60 Micrometer. The width of the bridge structure 1 corresponds to a dimension in a direction parallel to the upper surface of the substrate 2 and perpendicular to the length L of the bridge structure 1. The width of the bridge structure 1 also corresponds to the length of the tunnel formed by the vertical air gap 7 below the middle portion 1.1. The width of the bridge structure 1 is 10 Micrometer.

[0112] The area of the bridge structure 1 is defined as the length times the width. The overlap area of the bridge structure 1 with the center portion 3.1 of the base layer 3 can be scaled up such that the length and / or width of the overlap area and / or of the bridge structure 1 reach several Millimeters. The area of the bridge structure 1 typically depends on the capacitance that needs to be achieved, e.g., when the bridge structure 1 is used as a vacuum-gap capacitance and / or shunting capacitance. The overlap area and thus the capacitance can be scaled up considerably in a stable manner by implementing a plurality of (connected) bridge structures 1 as shown in Figure 4 (for details see description further below). A plurality of bridge structures 1 forms a large connected structure (e.g., an upper capacitive plate 9.2, see Figure 4 and the description further below) that is supported by the plurality of pillars 1.3.1,1.3.2 ensuring stability.

[0113] Figure 3 shows top views of embodiments of an electronic circuit 10 with at least one bridge structure 1 as manufactured with the method described with respect to figure 1.

[0114] Top panel (a) of Figure 3 shows a bridge structure 1 over a coplanar waveguide structure. The coplanar waveguide structure comprises the center portion 3.1 of the base layer 3 as a signal line between the two contact portions 3.2.1, 3.2.2 of the base layer 3. The bridge structure 1 is configured to contact and connect the two contact portions 3.2.1, 3.2.2 to ensure grounding of the contact portions 3.2.1, 3.2.2. The bridge structure 1 bridges over but does not contact the center portion 3.1 of the base layer 3.

[0115] Middle panel (b) of Figure 3 shows a first bridge structure 1 configured to connect a first signal line interrupted by a second signal line. The first signal line comprises two first contact portions 3.2.1, 3.2.2 of the base layer 3. The second signal line comprises a first center portion 3.1 of the base layer 3. The first bridge structure 1 bridges over but does not contact the first center portion 3.1 and thus the second signal line. The first and second signal line run perpendicular to each other and parallel to the upper surface of the substrate 2. The first and second signal line are also horizontally separated and air-gapped from each other.

[0116] Panel (b) also shows a second bridge structure 1 configured to connect and contact two second contact portions 3.2.1, 3.2.2 of the base layer 3. The second bridge structure 1 is configured to ground the second contact portions 3.2.1, 3.2.2.

[0117] Panel (b) also shows a third bridge structure 1 configured to connect and contact two third contact portions 3.2.1, 3.2.2 of the base layer 3. The third bridge structure 1 is configured to ground the third contact portions 3.2.1, 3.2.2.

[0118] The first, second and third bridge structures 1 are arranged in parallel to each other and spatially separated from each other in a direction along the second signal line. The lengths of the first, second and third bridge structures 1 is identical and extends in a direction along the first signal line. The first bridge structure 1 is arranged between the second and the third bridge structure 1.

[0119] Panel (c) of Figure 3 shows a superconducting qubit 20 with at least one bridge structure 1 configured and used as a vacuum-gap capacitance between a center portion 3.1 of the base layer 3 and the middle portion 1.1 of the bridge structure 1.

[0120] The superconducting qubit 20 comprises a shunt capacitance element with a lower capacitive plate 9.2 (spatially) separated from an upper capacitive plate 9.1. The lower capacitive plate 9.2 comprises a center portion 3.1 of the base layer 3 arranged between and horizontally gapped from the two contact portions 3.2.1, 3.2.2 of the base layer 3. The upper capacitive plate 9.1 comprises the middle portion 1.1 of the bridge structure 1. The middle portion 1.1 is overlapping and vertically air-gapped by the vertical gap 7 from the center portion 3.1 of the base layer 3. In another embodiment, the superconducting qubit 20 may comprise a plurality of bridge structures 1 that are connected with each other similar to the configuration shown in Figure 4.

[0121] The superconducting qubit 20 also comprises a Josephson element 8 connecting one 3.2.1 of the two contact portions 3.2.1, 3.2.2 of the base layer 3 with the center portion 3.1 of the base layer 3. The lower capacitive plate 9.2 and the upper capacitive plate 9.1 of the shunting capacitance are electrically coupled by the Josephson element 8. The Josephson element 8 comprises a Josephson junction.

[0122] The superconducting qubit 20 shown in panel (c) of Figure 3 is configured as a transmon qubit. In alternative embodiments, the superconducting qubit 10 could also be configured as a charge qubit, fluxonium qubit or zero-pi qubit.

[0123] Figure 4 shows another embodiment of an electronic circuit 10 that could also be used as a superconducting qubit 20. The electronic circuit 10 comprises a plurality of bridge structures 1 connected in series to increase the capacitance. Multiple series of bridge structures 1 are arranged in parallel resulting in a two-dimensional array of bridge structures 1 with rows and columns, each row and column comprising a plurality of bridge structures 1. The plurality of bridge structures 1 can also be considered as a single large bridge structure lwith additional support elements in the form of additional pillars 1.3.1, 1.3.2 that establish additional connections and contacts between the large bridge structure 1 and the base layer 3.

[0124] Panel (a) of Figure 4 shows a top view of the electronic circuit 10 in the direction of the upper surface of the substrate 2. The circles on the upper capacitive plate 9.1 show the positions of pillars 1.3.1, 1.3.2 overlapped by and below the upper capacitive plate 9.1. Panel (b) of Figure 4 shows a cross section along the line B-B, i.e., through the pillars 1.3.1, 1.3.2. Panel (c) shows a cross section along the line C-C running between the pillars 1.3.1, 1.3.2.

[0125] Each one of the bridge structures 1 is configured similar to the configurations described with respect to Figures 1 and 2. However, here the patterning of the bridge layer 6 comprises removing only one outer portion of the bridge layer 6 from each one of the two bridge structures 1 forming the end of a row (and column) of the array.

[0126] The upper capacitive plate 9.1 comprises the plurality of middle portions 1.1 of the plurality of bridge structures 1 connected in series. The lower capacitive plate 9.2 comprises the plurality of center portions 3.1 of the base layer 3.

[0127] Each center portion 3.1 is arranged between two contact portions 3.2.1, 3.2.2 of the base layer 3 and is horizontally air gapped from the two contact portions 3.2.1, 3.2.2.

[0128] Each middle portion 3.1 of a bridge structure 1 of the plurality of bridge structure 1 in the series overlaps and is air gapped by the same vertical gap 7 from a different center portion 3.1 of the base layer 3.

[0129] Two (nearest) neighboring bridge structures 1 of the plurality of bridge structures 1 in the series share a same pillar 1.3.1, 1.3.2 and a same capping portion 1.2.1, 1.2.2. The same capping portion 1.2.1, 1.2.2 and the same pillar 1.3.1, 1.3.2 are arranged between and connect two different middle portions 1.1 of the two neighboring bridge structures 1. Thus, the two neighboring bridge structures 1 galvanically contact the same contact portion 3.2.1, 3.2.2 of the base layer 3 through the same pillar 1.3.1, 1.3.2.

[0130] In particular, by manufacturing a plurality of bridge structures 1 connected in series, the shunting capacitance can be scaled up considerably from up to 1 Pico-Farad with a single air bridge (with an overlap area of about 1 square Micrometer) to multiple 100 Pico-Farad (pF) with a plurality of air bridges 1 (with a total overlap area of the upper capacitive plate of about 1 to 10 square Millimeter).

[0131] Since the plurality of bridge structures 1 are manufactured using the method described with respect to Figure 1, they constitute extremely low-loss air bridges 1 and are thus configured to provide small footprint capacitances in quantum circuits such as superconducting qubits and other electrical circuits.

[0132] Features of the different embodiments which are merely disclosed in the exemplary embodiments as a matter of course can be combined with one an- other and can also be claimed individually.

Claims

Claims1. A method for manufacturing a bridge structure (1), the method comprising: forming a base layer (3) over a substrate (2); depositing a first sacrificial layer (4) on the base layer (3); patterning the first sacrificial layer (4) into a bridge-like shape (4.1); depositing a second sacrificial layer (5) on the patterned first sacrificial layer (4, 4.1) and on the base layer (3); depositing a bridge layer (6, 6.1) on the second sacrificial layer (5) and on the base layer (3) to obtain the bridge structure (1); removing the patterned first sacrificial layer (4, 4.1) and the second sacrificial layer (5).

2. Method according to claim 1, wherein the first sacrificial layer (4) is a soft resist layer and / or the patterning of the first sacrificial layer (4) into a bridge-like shape (4.1) comprises a reflow resist process.

3. Method according to any of the preceding claims, wherein the second sacrificial layer (5) is a hard mask layer and / or the second sacrificial layer (5) functions as a protective layer for the patterned first sacrificial layer (4, 4.1) and / or the second sacrificial layer (5) is configured to prevent intermixing of the patterned first sacrificial layer (4, 4.1) and the bridge layer (6, 6.1).

4. Method according to any of the preceding claims, wherein a thickness of the second sacrificial layer (5) is smaller than a thickness of the first sacrificial layer (4) before the patterning of the first sacrificial layer (4) into the bridge-like shape (4.1).

5. Method according to any of the preceding claims, wherein the thickness of the second sacrificial layer (5) is between 10 Nanometer and 200 Nanometer.

6. Method according to any of the preceding claims, wherein after the depositing the second sacrificial layer (5) and before depositing the bridge layer (6), the method further comprises patterning the second sacrificial layer (5) to expose at least partially a surface of the base layer (3) next to the patterned first sacrificial layer (4, 4.1);7. Method according to claim 6, wherein the patterning the second sacrificial layer (5) to expose at least partially a surface of the base layer (3) next to the patterned first sacrificial layer (4.1) comprises forming openings (5.1) into the second sacrificial layer (5) to locally expose the surface of the base layer (3); and the depositing a bridge layer (6, 6.1) on the second sacrificial layer (5) and the base layer (3) comprises depositing the bridge layer (6, 6.1) into the openings (5.1) to contact the base layer (3).

8. Method according to claim 7, wherein the thickness of the second sacrificial layer (5) and / or the depth of an opening (5.1)is smaller than the thickness of the bridge layer (6).

9. Method according to claim 7 or 8, wherein before depositing the bridge layer (6) into the openings (5.1), the method further comprises removing oxides from inside the openings (5.1) using ion milling.

10. Method according to any of the preceding claims, wherein during the depositing of the bridge layer (6) outer portions of the second sacrificial layer (5) positioned away from the bridge-like shape (4.1) of the patterned first sacrificial layer (4, 4.1) are masked by a lift-off mask to prevent the deposition of the bridge layer (6) on the outer portions of the second sacrificial layer (5); or before removing the second sacrificial layer (5), the method further comprises patterning the bridge layer (6) by removing outer portions of the bridge layer (6) away from the bridge-like shape (4.1) of the patterned first sacrificial layer (4, 4.1).

11. An electronic circuit (10) comprising: a substrate (2);a base layer (3) over the substrate (2); at least one bridge structure (1) on the base layer (3); wherein each bridge structure (1) of the at least one bridge structure (1) comprises: a middle portion (1.1) connecting two end portions on opposite sides of the middle portion (1.1), wherein the middle portion (1.1) is gapped from the base layer (3) by a vertical gap (7) in a direction perpendicular to an upper surface of the substrate (2); and each first end portion comprises a pillar (1.3.1, 1.3.2), wherein each pillar (1.3.1, 1.3.2) has a bottom surface galvanically contacting the base layer (3).

12. An electronic circuit (10) according to claim 11, wherein each end portion additionally comprises a capping portion (1.2.1, 1.2.2) connecting the middle portion (1.1) and a pillar (1.3.1, 1.3.2), wherein each capping portion (1.2.1, 1.2.2) has a bottom surface (A) substantially parallel to the upper surface of the base layer (3), wherein the area of the bottom surface (A) of the capping portion (1.2.1, 1.2.2) is larger than the area of the bottom surface of the pillar (1.3.1, 1.3.2) contacting the base layer (3).

13. Electronic circuit (10) according to claim 11 or 12, wherein the at least one bridge structure (1) comprises a plurality of bridge structures (1) connected in series.

14. Electronic circuit (10) according to claim 13, wherein two neighboring bridge structures (1) in the plurality of bridge structures (1) connected in series share a same pillar (1.3.1, 1.3.2) to contact a same contact portion (3.2.1, 3.2.2) of the base layer (3).

15. A superconducting qubit (20) comprising a substrate (2); a base layer (3) over the substrate (2);at least one bridge structure (1) on the base layer (3); wherein each bridge structure (1) of the at least one bridge structure (1) comprises: a middle portion (1.1) connecting two end portions on opposite sides of the middle portion (1.1), wherein the middle portion (1.1) is gapped from a center portion (3.1) of the base layer (3) by a vertical gap (7) in a direction perpendicular to an upper surface of the substrate (2); and each end portion galvanically contacts a contact portion (3.2.1, 3.2.2) of the base layer (3), wherein a shunt capacitance of the superconducting qubit (20) comprises each middle portion (1.1) of the at least one bridge structure (1) and the center portion (3.1) of the base layer (3).

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