Patent Publication Number: US-11380974-B2

Title: Superconducting airbridge crossover using superconducting sacrificial material

Description:
DOMESTIC PRIORITY 
     This application is a continuation of U.S. patent application Ser. No. 14/749,143, which is now U.S. Pat. No. 10,170,817, which is a continuation of U.S. patent application Ser. No. 14/700,335, filed Apr. 30, 2015, which is now U.S. Pat. No. 9,614,270, issued on Apr. 4, 2017. The contents of each application are incorporated by reference herein in their entirety. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     This invention was made with Government support under Contract No.: W911NF-10-1-0324 awarded by the Advanced Research Development Agency. The Government has certain rights to this invention. 
    
    
     BACKGROUND 
     The present invention relates to superconducting techniques, and more specifically, to a superconducting airbridge crossover using a superconducting sacrificial material. 
     Quantum computing employs resonant structures called qubits to store information, and resonators (e.g., as a two-dimensional (2D) planar waveguide or as a three-dimensional (3D) microwave cavity) to read out and manipulate the qubits. To date, a major focus has been on improving lifetimes of the qubits in order to allow calculations (i.e., manipulation and readout) to take place before the information is lost to decoherence of the qubits. Currently, qubit coherence times can be as high as 100 microseconds and efforts are being made to increase the coherence times. One area of research with respect to increasing coherence times is focused on eliminating material at the edges of the qubit (i.e., edges) in order to reduce the electric field in that area. The material in proximity to the qubit includes imperfections that support defects known as two-level systems (TLS). 
     SUMMARY 
     According to one embodiment, a method of forming a superconducting airbridge on a structure is provided. The method includes forming a first ground plane, a resonator, and a second ground plane on a substrate, and forming a first lift-off pattern of a first lift-off resist and a first photoresist, where the first photoresist is deposited on the first lift-off resist. The method includes depositing a superconducting sacrificial layer while using the first lift-off pattern, removing the first lift-off pattern, and forming a cross-over lift-off pattern of a second lift-off resist and a second photoresist. The second photoresist is deposited on the second lift-off resist. Also, the method includes depositing a cross-over superconducting material to be formed as the superconducting airbridge while using the cross-over lift-off pattern, removing the cross-over lift-off pattern, and forming the superconducting airbridge connecting the first ground plane and the second ground plane by removing the superconducting sacrificial layer underneath the cross-over superconducting material. The superconducting airbridge crosses over the resonator. 
     According to one embodiment, a method of forming a superconducting airbridge on a structure is provided. The method includes forming a first ground plane, a resonator, and a second ground plane all on a substrate, patterning the substrate to have recessed portions between the first ground plane and the resonator as well as between the resonator and the second ground plane, and forming a protective layer on the recessed portions. The method includes forming a first lift-off pattern of a first lift-off resist and a first photoresist, where the first photoresist is deposited on the first lift-off resist, depositing a superconducting sacrificial layer while using the first lift-off pattern, and removing the first lift-off pattern. Also, the method includes forming a cross-over lift-off pattern of a second lift-off resist and a second photoresist, where the second photoresist is deposited on the second lift-off resist, and depositing a cross-over superconducting material to be utilized as the superconducting airbridge while using the cross-over lift-off pattern. Further, the method includes removing the cross-over lift-off pattern, and forming the superconducting airbridge connecting the first ground plane and the second ground plane by removing the superconducting sacrificial layer underneath the cross-over superconducting material. The superconducting airbridge crosses over the resonator. 
     According to one embodiment, a superconducting microwave structure is provided. The structure includes a first ground plane, a resonator, and a second ground plane formed on a substrate. A superconducting airbridge connects the first ground plane and the second ground plane, and the superconducting airbridge has an airgap underneath from where a superconducting sacrificial layer has been removed. A residual portion of the superconducting sacrificial layer remains on at least one of the first ground plane, the resonator, the second ground plane, and/or the superconducting airbridge. 
     Additional features and advantages are realized through the techniques of the present invention. Other embodiments and aspects of the invention are described in detail herein and are considered a part of the claimed invention. For a better understanding of the invention with the advantages and the features, refer to the description and to the drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The subject matter which is regarded as the invention is particularly pointed out and distinctly claimed in the claims at the conclusion of the specification. The forgoing and other features, and advantages of the invention are apparent from the following detailed description taken in conjunction with the accompanying drawings in which: 
         FIGS. 1A through 1N  illustrate a process of fabricating a superconducting airbridge using a superconducting sacrificial material according to an embodiment, in which: 
         FIG. 1A  is a top-down view of a superconducting microwave structure; 
         FIG. 1B  is a top-down view of an enlarged view of the superconducting microwave structure; 
         FIG. 1C  is a cross-sectional view of the enlarged view of the superconducting microwave structure; 
         FIG. 1D  is a cross-sectional view illustrating a lift-off pattern of bilayers; 
         FIG. 1E  is a cross-sectional view illustrating deposition of a sacrificial superconducting material; 
         FIG. 1F  is a cross-sectional view illustrating that the lift-off process removes the first lift-off pattern; 
         FIG. 1G  is a top-down view of the superconducting microwave structure showing the sacrificial superconducting material; 
         FIG. 1H  is a cross-sectional view illustrating a second lift-off pattern of bilayers; 
         FIG. 1I  is a cross-sectional view illustrating deposition of a cross-over superconducting material that is to form the superconducting airbridge; 
         FIG. 1J  is a cross-sectional view illustrating that the lift-off process removes the second lift-off pattern; 
         FIG. 1K  is a top-down view of the superconducting microwave structure showing the superconducting material crossing over the sacrificial superconducting material; 
         FIG. 1L  is a top-down view illustrating the superconducting material crossing over the sacrificial superconducting material; 
         FIG. 1M  is a top-down view of the superconducting microwave structure showing junction fabrication of a superconducting tunnel junction; and 
         FIG. 1N  is a cross-sectional view illustrating removal of the sacrificial superconducting material to form the superconducting airbridge; 
         FIG. 2  illustrates a cross-sectional view according to another embodiment; 
         FIGS. 3A and 3B  together illustrate a method of forming a superconducting airbridge on a superconducting microwave structure according to an embodiment; 
         FIGS. 4A and 4B  together illustrate a method of forming a superconducting airbridge on a superconducting microwave structure according to another embodiment; and 
         FIG. 5  illustrates an example showing one or more residual portions that may remain after etching the residual sacrificial superconducting material according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     In superconducting cavity quantum electrodynamics (cQED) circuits meant to be operated at microwave frequencies, separate ground planes should be tied together to prevent parasitic resonances which can be a source of decoherence for qubits within the circuit. 
     Most work in superconducting cQED circuits relies on wirebonding to tie together separate ground planes together. In the state-of-the-art, a microfabricated airbridge cross-over structure has been demonstrated which uses resist as a sacrificial material. This process results in lossy resist residue (after the removal process for the sacrificial resist material) which degrades the performance of the device. Another disadvantage to the method is the fact that the sacrificial material removal is not compatible with highly delicate tunnel junctions, and thus suspension (the airbridge) cannot be performed as the last step of device fabrication. (That is, the hardened resist used as a sacrificial material must be removed with processes such as O2 plasma etching, but energetic processes such as O2 plasma etching will break down the highly delicate tunnel junctions.) This leaves suspended structures which must be mechanically robust enough to survive the subsequent mechanically stressful steps such as dicing, lift-off with sonication, or wirebonding. 
     According to an embodiment, disclosed is the fabrication of superconducting airbridge cross-overs using a superconducting sacrificial material. This innovation is beneficial because the use of a superconducting sacrificial material minimizes any dielectric losses associated with residual sacrificial material (e.g., remaining after the removal process of the superconducting sacrificial material). 
     Additionally, embodiments disclose the use of a vapor etch, e.g., such as XeF 2 , for the removal of superconducting sacrificial material under the cross-overs. The removal of superconducting sacrificial material is performed as a final step in the device fabrication, e.g., after all mechanically stressful steps such as dicing, lift-off with sonication, or wirebonding have been completed. 
     Now turning to the figures,  FIGS. 1A through 1N  illustrate a process of fabricating a superconducting airbridge using a superconducting sacrificial material according to an embodiment. 
       FIG. 1A  begins with a starting schematic of a superconducting microwave structure  100  for building the superconducting airbridge.  FIG. 1A  is a top-down view of the superconducting microwave structure  100 . 
       FIG. 1A  shows a linear part  105  and a non-linear part  107 . Superconducting material  10  is deposited on a substrate  5 . The superconducting material  10  is patterned into various features including resonator layer  10 A, ground plane layers  10 B, and pad layers (paddles)  10 C. The substrate  5  may be a material intended not to conduct electricity (e.g., intentionally without doping so as not to be conductive) in one case. In one implementation, the substrate  5  may be sapphire. In another implementation, the substrate may be high purity silicon. The superconducting material  10  forming the resonator layer  10 A, ground plane layers  10 B, and paddles  10 C may be aluminum, titanium nitride, or any other superconducting material which is robust to endure the etch used to remove the sacrificial material. The superconducting material  10  is intended not to be etched away during the etching of the superconducting sacrificial layer discussed further below. 
     Superconducting material may be defined as a material that can conduct electricity or transport electrons from one atom to another with no resistance when the superconducting material has reached “critical temperature” (Tc), or the temperature at which the material becomes superconductive. Conducting electricity or transporting electrons from one atom to another with no resistance means that no heat, sound, or any other form of energy would be released from the material as understood by one skilled in the art. 
     Also, a circle is designated in  FIG. 1A  to illustrate an enlarged view  110  that is discussed below.  FIG. 1B  is a top-down view illustrating a breakout of the enlarged view  110  of the superconducting microwave structure  100 .  FIG. 1B  shows the resonator  10 A separated from the ground planes  10 B by the substrate  5 . The width of the resonator  10 A in the x-axis may range from about 10 nanometers (nm) to 100 micrometers (μm). The width of the ground planes in the x-axis may range from about three times the resonator width to an “infinite” ground plane which extends across the entire substrate surface. It is understood that the resonator  10 A and ground planes  10 B meander along the superconducting microwave structure  100  and their widths may not always be along the x-axis. 
       FIG. 1C  is a cross-sectional view of the enlarged view  110  of the superconducting microwave structure  100  with the resonator  10 A and ground planes  10 B. The cross-sectional view is taken along line A-A of the enlarged view  110  in  FIG. 1B . The thickness of the superconducting material  10  may range from 1 nm to 1 μm, typically between 40 nm and 300 nm. 
       FIG. 1D  is a cross-sectional view illustrating a first lift-off pattern  25  of bilayers in preparation for sacrificial material lithography. The bilayers of the lift-off pattern  25  include a lift-off resist layer  15  patterned on top of the ground planes  10 B and a photoresist layer  20  patterned on top of the lift-off resist  15 . The height of the lift-off resist  15  may range from about 300 nm to 1 μm. The height of the photoresist  20  may range from about 50 to 300 nm. In one implementation the height in the z-axis of the lift-off resist  15  may be 800 nanometers (nm). In a lift-off process, the photoresist forms a mold, into which the desired material is deposited. The desired features are completed when photoresist under unwanted areas is dissolved and when the unwanted material is “lifted off”. The reentrant profile  25  can be obtained by using an underlayer  15  which develops away faster than the optically patterned layer  20 . Alternately, layer  20  may be a deposited hard mask such as germanium (Ge), which is patterned using lithography and etching. 
       FIG. 1E  is a cross-sectional view illustrating deposition of the sacrificial superconducting material  30 . The sacrificial superconducting material  30  is deposited on top of the resonator  10 A, substrate  5 , and ground planes  10 B within the mold of the pattern  25 . Additionally, sacrificial superconducting material  30  is deposited on top of the photoresist layer  20 . The sacrificial superconducting material  30  may be, e.g., niobium and/or tantalum. The thickness in the z-axis of the sacrificial superconducting material  30  may range from 40 to 300 nm. The sacrificial superconducting material  30  may be deposited by, e.g., e-beam evaporation or any other directional deposition method. The deposition of the sacrificial superconducting material  30  forms in the center of the opening in the lift-off pattern  25  without completely filling the mold due to the directionality of the deposition. 
       FIG. 1F  is a cross-sectional view illustrating that the lift-off process removes the first lift-off pattern  25 . The lift-off process etches off the lift-off resist layer  15 , along with any layers on top such as the photoresist layer  20  and sacrificial superconducting material  30 . However, the sacrificial superconducting material  30  deposited directly on top of the resonator  10 A, substrate  5 , and ground planes  10 B remains, and is not lifted off. The etchant (wet and/or dry) used during the lift-off process is designed to selectively attack the lift-off resist layer  15  (same analogy for lift-off resist layer  17  discussed below) such that the lift-off resist layer  15  is selectively dissolved. Consequently, dissolving the lift-off resist layer  15  causes any layers on top to be lifted off along with the lift-off resist layer  15 . Alternately, feature  30  could be obtained using subtractive patterning, where a blanket layer of material is deposited and then unwanted portions are etched away using lithography and wet or dry etching. 
       FIG. 1G  is a top-down view of the superconducting microwave structure  100  showing the sacrificial superconducting material  30  deposited directly deposited on top of the resonator  10 A, substrate  5 , and ground planes  10 B. In  FIG. 1G , the sacrificial superconducting material  30  is outlined as a rectangular shape so as not to obscure the figure. 
       FIG. 1H  is a cross-sectional view illustrating a second lift-off pattern  27  (i.e., cross-over lift-off pattern) of bilayers in preparation for cross-over lithography. The bilayers of the second lift-off pattern  27  include a lift-off resist layer  17  patterned on top of the ground planes  10 B and a photoresist layer  22  patterned on top of the lift-off resist  17 . The photoresist layers  20  and  22  may be of the same materials, such as for example, positive resist or negative resist layers. The photoresist layers  20  and  22  are light sensitive such that they can be imaged with light and etched as desired without affecting other layers. The lift-off resist layer  15  and  17  may be of the same materials, such that the materials are dissolvable by the etchant during the lift-off process. 
       FIG. 1I  is a cross-sectional view illustrating deposition of cross-over superconducting material  35  that is to form the superconducting airbridge. The cross-over superconducting material  35  is deposited on top of the sacrificial superconducting material  30  and ground planes  10 B within the mold of the cross-over lift-off pattern  27 . Additionally, cross-over superconducting material  35  is deposited on top of the photoresist layer  22 . The thickness in the z-axis of the cross-over superconducting material  35  (to form the superconducting airbridge) may range from 40 to 300 nm. In one implementation, the cross-over superconducting material  35  may be aluminum. In another implementation, the cross-over superconducting material  35  may be titanium nitride. Alternately, feature  35  could be obtained using subtractive patterning, where a blanket layer of material is deposited and then unwanted portions are etched away using lithography and wet or dry etch. 
       FIG. 1J  is a cross-sectional view illustrating that the lift-off process removes the second lift-off pattern  27 . The lift-off process etches off the lift-off resist layer  17 , along with any layers on top such as the photoresist layer  20  and superconducting material  35 . However, after lift-off, the cross-over superconducting material  35  deposited directly on top of the sacrificial superconducting material  30  and on top of the ground planes  10 B remains. 
       FIG. 1K  is a top-down view of the superconducting microwave structure  100  showing the superconducting material  35  crossing over the sacrificial superconducting material  30  while contacting the ground planes  10 B on both sides of the resonator  10 A.  FIG. 1K  also shows the sacrificial superconducting material  30  deposited directly on top of the resonator  10 A, the substrate  5 , and the ground planes  10 B. In  FIG. 1K , both the superconducting material  35  (future airbridge) and the sacrificial superconducting material  30  are outlined as rectangular shapes so as not to obscure the figure. 
       FIG. 1L  is a top-down view illustrating the enlarged view  110  of the superconducting microwave structure  100 . Illustrated as a dashed line rectangular shape so as not to obscure the underlying layers,  FIG. 1L  shows the superconducting material  35  crossing over the sacrificial superconducting material  30  while contacting the grounds planes  10 B on both sides of the resonator  10 A. Also, illustrated as a dashed line rectangular shape so as not to obscure underlying layer,  FIG. 1L  shows the sacrificial superconducting material  30  directly on top of the resonator  10 A, the substrate  5 , and the ground planes  10 B. 
       FIG. 1M  is a top-down view of the superconducting microwave structure  100  showing junction fabrication of a superconducting tunnel junction  40  in contact with paddles  10 C. The process of fabricating the superconducting tunnel junction  40  is understood by one skilled in the art. The superconducting tunnel junction (STJ), also known as a superconductor-insulator-superconductor tunnel junction (SIS), is an electronic device consisting of two superconductors separated by a very thin layer of insulating material. Current passes through the junction via the process of quantum tunneling. The STJ is a type of Josephson junction and is an important part of the qubit. 
       FIG. 1N  is a cross-sectional view of the enlarged view  110  of the superconducting microwave structure  100  illustrating removal of the sacrificial superconducting material  30 . In  FIG. 1N , the superconducting material  35  is an airbridge from one ground plane  10 B to the other ground plane  10 B, all while crossing over the resonator  10 A. The airbridge of superconducting material  35  is suspended over the airgap  45 . 
     To form the airbridge of superconducting material  35 , the sacrificial superconducting material  30  may be etched using a dry etch such as vapor etching or a wet etch. In one implementation, the vapor etchant may be XeF 2  and the sacrificial superconducting material  30  may be niobium. In another implementation, the sacrificial superconducting material  30  may be tantalum. The vapor etchant dissolves the sacrificial superconducting material  30  while leaving the substrate  5 , the airbridge of superconducting material  35 , the tunnel junction  40  (e.g., qubit), and the superconducting material  10  (e.g., resonator  10 A, ground planes  10 B, paddles  10 C) all undamaged. 
     Etching the sacrificial superconducting material  30  does not negatively impact the previously formed tunnel junction  40 . The superconducting materials of the airbridge of superconducting material  35 , tunnel junction  40 , and superconducting material layer  10  are different from the sacrificial superconducting material  30 . For example, when the sacrificial superconducting material  30  is niobium, the superconducting materials of the airbridge of superconducting material  35 , tunnel junction  40 , and superconducting material layer  10  may be aluminum that is not etched away by the vapor etchant. 
     In one case, if there happens to be a little residual sacrificial superconducting material  30  remaining on, e.g., the resonator  10 A, ground planes  10 B, paddles  10 C, and/or the airbridge of superconducting material  35 , the residual sacrificial superconducting material  30  (if any) does not include any lossy resist residue (after the removal process for the sacrificial resist material in the state-of-the-art) because no sacrificial resist material is utilized to form the airbridge of superconducting material  35 . Additionally, the residual sacrificial superconducting material  30  does not degrade the performance of the superconducting microwave structure  100 . According to an embodiment,  FIG. 5  illustrates an example showing one or more residual portions  30 A that may remain after etching the residual sacrificial superconducting material  30 . However, these example residual portions  30 A of sacrificial superconducting material  30  do not cause losses to the energy in tunnel junction  40  (qubit energy) because the residual sacrificial superconducting material  30  (i.e., residual portions  30 A) is superconducting material. 
     In contrast, the state-the-art may have residual sacrificial resist material, and the leftover resist can drain the excitation energy from the qubit thus degrading the performance of the superconducting microwave structure. 
     The removal of the sacrificial superconducting material  30  using a vapor etch such as XeF 2  is compatible with highly delicate tunnel junctions  40 , and thus suspension (i.e., creation of the airbridge of superconducting material  35 ) can be performed as the last step of device fabrication (e.g., after formation of the tunnel junction  40 ). XeF 2  is a room temperature, non-energetic etchant which has been shown not to affect Al—Al x O y —Al tunnel junctions. Although not shown for the sake of conciseness, all mechanically stressful steps such as dicing, lift-off with sonication, or wirebonding are performed before removal of the sacrificial superconducting material  30 . Therefore, none of the mechanical stress associated with dicing, lift-off with sonication, or wirebonding is passed on to the superconducting airbridge  35  because the superconducting airbridge  35  has not been formed yet. 
       FIG. 2  illustrates a cross-sectional view of the enlarged view  110  according to another embodiment.  FIG. 2  may include the fabrication process discussed in  FIG. 1  along with additional operations discussed below. In this case, the superconducting material  10  may be titanium nitride, and the substrate  5  may be silicon. Unlike the description in  FIG. 1 , the substrate  5  (e.g., wafer) is annealed in N 2  or O 2  gas after patterning the superconducting material  10  (e.g., titanium nitride) into the resonator  10 A, ground planes  10 B, and paddles  10 C. Also, the substrate  5  may be recessed between the resonator  10 A and ground planes  10 B. The N 2  or O 2  gas forms a protective layer  210  in recesses  205 . The protective layer  210  extends upward to be formed partially along the sides of the resonator  10 A and the ground planes  10 B. The protective layer  210  may be silicon nitride or silicon dioxide depending on the gas utilized during annealing, and may be patterned as needed. These additional fabrication processes occur before proceeding with the cross-over fabrication. For example, these additional fabrication processes occur after  FIG. 1C  but before  FIG. 1D . The protective layer is needed in the case of XeF 2  etch and silicon substrates, since XeF 2  attacks silicon; the protective layer  210  protects the silicon substrate during etching. However, in the case of sapphire substrates, the protective layer  210  is not needed since XeF 2  does not attack sapphire. 
       FIGS. 3A and 3B  illustrate a method  300  of forming a superconducting airbridge on a structure  100  according to an embodiment. 
     At block  305 , the first ground plane  10 B, a resonator  10 A, and a second ground plane  10 B are all formed on the substrate  5 . There are two ground planes  10 B on both sides of the resonator  10 A, as shown in  FIGS. 1A, 1B, 1C . 
     At block  310 , the first lift-off pattern  25  is formed of a first lift-off resist  15  and a first photoresist  20 . An example is shown in  FIG. 1D . 
     At block  315 , the superconducting sacrificial layer  30  is deposited while using the first lift-off pattern  25  as a mold. An example is shown in  FIG. 1E . 
     At block  320 , the first lift-off pattern  25  is removed, such that the desired pattern of the superconducting sacrificial layer  30  remains, as shown in  FIGS. 1F, 1G . 
     At block  325 , a cross-over lift-off pattern  27  is formed of a second lift-off resist  17  and a second photoresist  22 . An example is shown in  FIG. 1H . 
     At block  330 , the cross-over superconducting material  35  is deposited to be utilized as the superconducting airbridge  35  while using the cross-over lift-off pattern  27  as a mold. An example is shown in  FIG. 1I . 
     At block  335 , the cross-over lift-off pattern  27  is removed. The layers remaining after performing lift-off are illustrated in  FIG. 1J, 1K, 1L . 
     At block  340 , the superconducting airbridge  35  connecting the first ground plane  10 B and the second ground plane  10 B is formed by removing the superconducting sacrificial layer  30  underneath the cross-over superconducting material  35 , where the superconducting airbridge  35  crosses over the resonator  10 A. For example,  FIG. 1N  shows the superconducting airbridge  35  with the airgap  45  underneath. 
     The first lift-off resist  15  is formed on top of the first ground plane  10 B (e.g., to the left of the resonator  10 A) and the second ground plane  10 B (e.g., to the right of the resonator  10 A). The first photoresist  20  is formed on top of the first lift-off resist  15 . Reference can be made to  FIG. 1D . 
     The second lift-off resist  17  is formed on top of the first ground plane  10 B (e.g., to the left of the resonator  10 A) and the second ground plane  10 B (e.g., to the right of the resonator  10 A). The second photoresist  22  is formed on top of the second lift-off resist  17 . Reference can be made to  FIG. 1H . 
     Removing the superconducting sacrificial layer  30  underneath the cross-over superconducting material  35  to thereby form the superconducting airbridge  35  is performed by vapor etching utilizing a vapor etchant. The vapor etchant has a high selectivity for etching the superconducting sacrificial layer  30  (e.g., niobium), while not etching the first ground plane  10 B, the resonator  10 A, the second ground plane  10 B, and the substrate  5  (along with the paddles  10 C and tunnel junction  40 ). Since the vapor etchant has a high selectivity for etching the superconducting sacrificial layer  30 , all other layers on the superconducting microwave structure  100  remain unaffected by the vapor etching. 
     In one implementation, the superconducting sacrificial layer  30  is niobium. In another implementation, the superconducting sacrificial layer  30  is tantalum. The substrate  5  includes sapphire. The first ground plane  10 B, the resonator  10 A, and the second ground plane  10 B are a superconducting material not etched by the vapor etchant. In one case, the substrate  5  includes silicon. 
     The tunnel junction  40  is formed on the substrate  5  connecting first paddle  10 C (e.g., in front of the tunnel junction  40 ) to the second paddle  10 C (e.g., behind the tunnel junction  40 ), as illustrated in  FIG. 1M . The tunnel junction  40  is a qubit. The resonator  10 A is a readout resonator configured to read a state of the qubit. 
     Removing the superconducting sacrificial layer  30  underneath the cross-over superconducting material  35  to thereby form the superconducting airbridge  35  is performed by wet etching. 
       FIGS. 4A and 4B  illustrate a method  400  of forming a superconducting airbridge on a structure  100 . 
     At block  405 , the first ground plane  10 B, the resonator  10 A, and the second ground plane  10 B are all formed the substrate  5 . Reference can be made to  FIGS. 1A, 1B, 1C . 
     At block  410 , the substrate  5  is patterned to have to have recessed portions  205  between the first ground plane  10 B (e.g., to the left of the resonator  10 A) and the resonator  10 A as well as between the resonator  10 A and the second ground plane  10 B (e.g., to the right of the resonator  10 A). Reference can be made to  FIG. 2 . 
     At block  415 , the protective layer  210  is formed on the recessed portions  205 . An example is illustrated in  FIG. 2 . 
     At block  420 , the first lift-off pattern  25  is formed of a first lift-off resist  15  and a first photoresist  15 . An example is shown in  FIG. 1D  with the modification of having the recessed portions  205  and protective layer  210  from  FIG. 2 . 
     At block  425 , the superconducting sacrificial layer  30  is deposited while using the first lift-off pattern  25  as a mold. Reference can be made to  FIG. 1E  while taking into account changes made in  FIG. 2 . 
     At block  430 , the first lift-off pattern  25  is removed, such that the desired pattern of the superconducting sacrificial layer  30  remains, as shown in  FIGS. 1F, 1G  in view of changes made in  FIG. 2 . 
     At block  435 , a cross-over lift-off pattern  27  is formed of a second lift-off resist  17  and a second photoresist  22 . Reference is made to  FIG. 1H  in view of changes made in  FIG. 2 . 
     At block  440 , the cross-over superconducting material  35  is deposited to be utilized as the superconducting airbridge  35  while using the cross-over lift-off pattern  27  as a mold. An example is shown in  FIG. 1I  in view of the changes made in  FIG. 2 . 
     At block  445 , the cross-over lift-off pattern  27  is removed. The layers remaining after performing lift-off are illustrated in  FIG. 1J, 1K, 1L  in view of the modifications made in  FIG. 2   
     At block  450 , the superconducting airbridge  35  connecting the first ground plane  10 B and the second ground plane  10 B is formed by removing the superconducting sacrificial layer  30  underneath the cross-over superconducting material  35 , where the superconducting airbridge  35  crosses over the resonator  10 A. As an example,  FIG. 2  shows the superconducting airbridge  35  with the airgap  45  underneath, along with the protective layer  210  and recessed portions  205 . 
     The protective layer  210  is at least one of a nitride layer and/or an oxide layer. The substrate  5  is silicon. The first ground plane  10 B, the resonator  10 A, and the second ground plane  10 B are a superconducting material different from the superconducting sacrificial layer  30 . The superconducting material of the first ground plane  10 B, the resonator  10 A, and the second ground plane  10 B (along with the tunnel junction  40  and paddles  10 C) includes titanium nitride. 
     It will be noted that various semiconductor device fabrication methods may be utilized to fabricate the components/elements discussed herein as understood by one skilled in the art. In semiconductor device fabrication, the various processing steps fall into four general categories: deposition, removal, patterning, and modification of electrical properties. 
     Deposition is any process that grows, coats, or otherwise transfers a material onto the wafer. Available technologies include physical vapor deposition (PVD), chemical vapor deposition (CVD), electrochemical deposition (ECD), molecular beam epitaxy (MBE) and more recently, atomic layer deposition (ALD) among others. 
     Removal is any process that removes material from the wafer: examples include etch processes (either wet or dry), and chemical-mechanical planarization (CMP), etc. 
     Patterning is the shaping or altering of deposited materials, and is generally referred to as lithography. For example, in conventional lithography, the wafer is coated with a chemical called a photoresist; then, a machine called a stepper focuses, aligns, and moves a mask, exposing select portions of the wafer below to short wavelength light; the exposed regions are washed away by a developer solution. After etching or other processing, the remaining photoresist is removed. Patterning also includes electron-beam lithography. 
     Modification of electrical properties may include doping, such as doping transistor sources and drains, generally by diffusion and/or by ion implantation. These doping processes are followed by furnace annealing or by rapid thermal annealing (RTA). Annealing serves to activate the implanted dopants. 
     The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions.