Method for producing a niobium-based resonator, and resonator

Abstract

The present disclosure relates to a method (200) for manufacturing a resonator comprising a niobium-based enclosure, the method comprising the following successive steps: a) annealing (201) the enclosure at a temperature of at least 400°C for a duration of at least 1 h; and b) exposing (203) the enclosure to the air.

Description

DESCRIPTION TITLE: Manufacturing process for a niobium-based resonator Technical field

[0001] This disclosure relates generally to niobium-based resonators and their manufacturing processes, more particularly to 3D resonators and 2D thin films based on niobium. Prior art

[0002] Niobium-based resonators have been proposed in various application fields, such as particle accelerators, superconducting digital electronics, quantum computing, and quantum sensing. In particular, radiofrequency superconducting resonators implemented in the quantum regime, at temperatures below 1 K, have been integrated into 3D and 2D quantum processing units and used as quantum detectors for dark matter and gravitational wave research.

[0003] Existing niobium-based resonators, for example those based on pure niobium or niobium alloys such as the niobium-tin alloy NbsSn or the niobium-aluminum alloy NbsAl, however, have various drawbacks. In particular, they suffer from a decoherence phenomenon caused by the presence of so-called "two-level systems," or two-state defects, present in oxide layers, which form when the niobium-based superconducting material of the resonator is exposed to air, and at the interface with the superconducting material. These native oxide layers have an amorphous structure and are characterized by a lack of large-scale order in the atomic lattice. Regardless of their chemical composition, solids Amorphous materials all exhibit similar behavior at low temperatures. This behavior is caused by the presence of two-level defects (TLDs) in the material. Due to relatively low energy, these defects are saturated at high temperatures. However, once the niobium-based material is cooled to below a few kelvins to make it superconducting, these additional degrees of freedom become accessible and are a significant source of noise and decoherence in superconducting quantum devices.This particularly concerns 2D and 3D superconducting resonators, whose resonance frequency is in the microwave range. The parasitic coupling of two-level defects with electromagnetic fields present in the resonator constitutes a major source of decoherence and fluctuation, tending to degrade the quality factor of the resonators and to reduce their coherence time. Summary of the invention

[0004] There is a need to overcome all or part of the disadvantages of existing niobium-based resonators. In particular, it would be desirable to be able to manufacture niobium-based resonators with quality factors higher than those of existing resonators.

[0005] For this, one embodiment provides a method for manufacturing a resonator comprising a niobium-based enclosure, the method comprising the following successive steps: a) annealing the enclosure at a temperature of at least 400°C for a duration of at least 1 h; and b) exposing the enclosure to air.

[0006] According to one embodiment, the method further comprises, after step b), a rinsing step c) to the water in the enclosure, preferably at a pressure of the order of several bars or several tens of bars, more preferably equal to approximately 90 bars, and preferably for a duration of at least half an hour.

[0007] According to one embodiment, the temperature is between 400 and 1000°C, preferably between 600 and 700°C, more preferably equal to approximately 650°C.

[0008] According to one embodiment, the duration is between 1 and 24 hours, preferably between 2 and 20 hours, more preferably between 3 and 12 hours, even more preferably equal to approximately 4 or 10 hours.

[0009] According to one embodiment, the annealing is carried out under vacuum, for example at a pressure less than or equal to 10 -2 Pa, preferably less than or equal to 10 -3 Pa.

[0010] According to one embodiment, the annealing is carried out in the presence of an oxygen source.

[0011] According to one embodiment, the method further comprises, prior to step a), a step of coating an internal wall of the enclosure with at least one layer of at least one metal oxide and / or at least one metal nitride and / or at least one metal carbide, preferably with a single layer of a metal oxide, a metal nitride or a metal carbide.

[0012] According to one embodiment, said at least one layer is made of an amorphous material.

[0013] According to one embodiment, said at least one layer is made of a crystalline material.

[0014] According to one embodiment: - the metal oxide is chosen from aluminum oxide, tantalum oxide, yttrium oxide, zirconium oxide and titanium oxide; and - the metal nitride is chosen from nitride of tantalum, zirconium nitride, titanium nitride and niobium nitride.

[0015] According to one embodiment, the coating is carried out by atomic layer deposition.

[0016] One embodiment provides a resonator comprising a niobium-based enclosure, an inner wall of which is coated with at least one layer of at least one metal oxide and / or at least one metal nitride and / or at least one metal carbide, or any mixture of at least two of these compounds.

[0017] According to one embodiment, said at least one layer has an amorphous structure.

[0018] According to one embodiment, said at least one layer has a crystalline structure.

[0019] According to one embodiment: - the metal oxide is chosen from aluminum oxide, tantalum oxide, yttrium oxide, zirconium oxide and titanium oxide; and - the metal nitride is chosen from tantalum nitride, zirconium nitride, titanium nitride and niobium nitride.

[0020] According to one embodiment, said at least one layer has a thickness of between 1 and 50 nm, preferably between 1 and 25 nm, more preferably equal to approximately 10 nm. Brief description of the drawings

[0021] These and other features and advantages will be set forth in detail in the following description of particular embodiments given without limitation in relation to the attached figures, among which:

[0022] Figure 1 is a schematic and partial side and sectional view of a niobium-based resonator according to one embodiment;

[0023] Figure 2 is a flowchart illustrating successive steps of a method of manufacturing the resonator of Figure 1 according to one embodiment;

[0024] Figure 3 is a graph of variation of a quality factor of the resonator of Figure 1 as a function of an electric field present in the resonator;

[0025] Figure 4 is a schematic and partial side and sectional view of a niobium-based resonator according to another embodiment;

[0026] Figure 5 is a flowchart illustrating successive steps of a method of manufacturing the resonator of Figure 4 according to one embodiment;

[0027] Figure 6 is a graph of variation of a quality factor of the resonator of Figure 4 as a function of an electric field present in the resonator; and

[0028] Figure 7 is a graph of the variation of a quality factor of the resonator of Figure 4 as a function of an electric field present in the resonator. Description of the embodiments

[0029] The same elements have been designated by the same references in the different figures. In particular, the structural and / or functional elements common to the different embodiments may have the same references and may have identical structural, dimensional and material properties.

[0030] For the sake of clarity, only the steps and elements useful for understanding the described embodiments have been shown and are detailed. In particular, the applications of niobium-based resonators have not been detailed, the embodiments described being compatible with all or most applications of niobium-based resonators and, in general, with all superconducting electronics as well as applications in which particles are accelerated, possibly subject to adaptations within the scope of the person skilled in the art upon reading this description.

[0031] Unless otherwise specified, when referring to two elements connected to each other, this means directly connected without intermediate elements other than conductors, and when referring to two elements connected (in English "coupled") to each other, this means that these two elements can be connected or be connected by means of one or more other elements.

[0032] In the following description, when referring to absolute position qualifiers, such as the terms "front", "back", "top", "bottom", "left", "right", etc., or relative, such as the terms "above", "below", "upper", "lower", etc., or to orientation qualifiers, such as the terms "horizontal", "vertical", etc., reference is made, unless otherwise specified, to the orientation of the figures.

[0033] Unless otherwise specified, the expressions “about”, “approximately”, “substantially”, and “in the order of” mean to within 10%, preferably to within 5%.

[0034] In the following description, the terms "insulator" and "conductor" mean, unless otherwise specified, electrically insulating and electrically conductive respectively.

[0035] Figure 1 is a schematic and partial side and sectional view of a superconducting resonator 100 based on niobium according to one embodiment. The view in Figure 1 illustrates more particularly a niobium-based resonator having a “Tesla” type geometry, or two-cell elliptical. However, the embodiments described are of course not limited to this example of geometry but apply more generally to any type of 2D or 3D superconducting resonator based on niobium.

[0036] In the example shown, the resonator 100 comprises a niobium-based enclosure 101, the enclosure 101 being for example essentially made of niobium. The enclosure 101 is for example essentially made of solid niobium, or of a niobium film, or of a niobium alloy such as the niobium-tin alloy NbsSn or the niobium-aluminum alloy NbsAl. The enclosure 101 comprises for example at least one resonant cavity 103, or cell. In the example illustrated, the enclosure 101 delimits two resonant cavities 103. This example is however not limiting, the resonator 100 being able, as a variant, to comprise a number of resonant cavities 103 other than two. Each resonant cavity 103 has for example an elliptical section. The resonator 100 has, for example, a symmetry of revolution around a horizontal axis, in the orientation of figure 1.For example, the resonant cavities 103 of the resonator 100 have dimensions and shapes adapted to a type of particles to be accelerated and to a desired speed for these particles.

[0037] Although this has not been detailed in figure 1, the enclosure 101 is for example coated, on its internal wall, with a first layer of native niobium oxide of chemical formula NbO x with 0 < x < 2.5 and having an amorphous or crystalline structure. The first layer may further comprise at least one oxide of an element other than niobium, for example aluminum oxide A10 x with 1 < x < 1.5 in the case where the enclosure 101 is made of niobium-aluminium alloy NbsAl, or tin oxide SnO xwith 1 < x < 2 in the case where the enclosure 101 is made of niobium-tin alloy NbsSn. In the present description, the expression “internal wall” of the enclosure 101 designates the face or wall of the enclosure 101 delimiting or bordering the resonant cavity(ies) 103 of the resonator 100. The first layer of niobium oxide is for example more precisely located on and in contact with the internal wall of the enclosure 101. The first layer has for example a crystalline structure. For example, the first layer of niobium oxide has a thickness of the order of a few nanometers. The first layer is for example made of an oxide of chemical formula NbO or NbCy. As a variant, the first layer is made of Nb2O5, or more generally has a chemical formula of the type Nb x O y Most of these oxides are amorphous, but some of them, such as NbO, can have a crystalline structure.

[0038] The enclosure 101 is for example further coated, on its outer face or wall, opposite the inner wall of the enclosure 101, with a second layer of niobium oxide. The second layer of niobium oxide is for example more precisely located on and in contact with the outer wall of the enclosure 101. By way of example, the second layer of niobium oxide has a thickness and a structure identical or similar to those of the first layer of niobium oxide.

[0039] The superconducting resonator 100 is for example intended to be implemented at operating frequencies between 0.08 and 12 GHz, for example of the order of 1.3 GHz.

[0040] Figure 2 is a flowchart illustrating successive steps of a method 200 for manufacturing the resonator 100 of Figure 1 according to one embodiment.

[0041] In the example shown, the method 200 for manufacturing the resonator 100 comprises a step 201 (ANNEALING) for annealing the enclosure 101. For this purpose, the enclosure 101 is for example previously introduced into a chamber comprising a heating device, for example a furnace. When it is introduced into the chamber, the enclosure 101 is for example coated with a layer of native oxide.

[0042] According to one embodiment, the annealing of the enclosure 101 is carried out at a temperature of at least 400°C for a duration of at least 1 hour.

[0043] The annealing temperature is for example between 400 and 1000 °C, for example between 600 and 700 °C. For example, the annealing temperature is approximately 650 °C.

[0044] Furthermore, the annealing time is, for example, between 1 and 24 hours, for example, between 2 and 20 hours, for example, between 3 and 12 hours. For example, the annealing time is approximately 4 or 10 hours.

[0045] Annealing is for example carried out under vacuum, for example at a pressure less than or equal to 10 -2 Pa, for example less than or equal to 10 -3 Pa. For this purpose, the chamber into which the enclosure 101 is introduced is for example connected to a vacuum pump.

[0046] Alternatively, the annealing may be carried out in a controlled atmosphere, for example in an atmosphere comprising a source of oxygen in gaseous form without hydrogen or carbon, for example pure dioxygen (O2), dry air or ozone. For example, the partial pressure of this oxygen source is in this case less than or equal to 1 Pa. The annealing temperature is for example at least 100°C and the annealing time is for example at least half an hour.

[0047] The treatment under oxygen under the conditions described above allows a self-limiting growth of a layer of niobium oxides NbO and Nb2O with a maximum thickness equal to approximately 5 nm. The niobium oxides NbO and Nb2O are conductive and allow surface passivation by limiting or even preventing the subsequent growth of a niobium oxide having an oxidation state greater than one, for example NbO2 or Nb2Os. At so-called "cryogenic" temperatures, typically less than or equal to 9.2 K, the NbO layer becomes superconducting by proximity effect with the underlying metallic niobium. This protective layer of NbO is passivating and in particular allows re-exposure of the electronic device to air or water without altering the superconducting performance of the device at temperatures less than or equal to 2 K.In particular, this method allows the suppression of defects such as two-level systems and can be applied to any type of superconducting niobium-based electronic device in the quantum regime.

[0048] In the example shown, the method for manufacturing the resonator 100 further comprises a step 203 (EXPOSURE TO AIR), subsequent to step 201, during which the enclosure 101 is exposed to air. For this, the enclosure 101 is for example removed from the chamber previously used during the annealing step 201.

[0049] Although this has not been detailed in figure 2, the step 203 of exposing the enclosure 101 to air is for example followed by a step of rinsing, for example with water, the enclosure 101 of the resonator 100. By way of example, the rinsing is carried out under high water pressure, for example of the order of several bars or several tens of bars, for example equal to approximately 90 bar, and for a duration of at least half an hour. Alternatively, the rinsing step can be omitted.

[0050] In the method 200, the annealing step 201 is not preceded by any step of coating the inner wall of the enclosure 101 other than a step of depositing the superconducting material, in the case where the superconducting material forms a 2D film. In particular, in this method, the inner wall of the enclosure 101 made of niobium-based superconducting material does not comprise, prior to step 201, any coating layer other than a possible native oxide layer forming spontaneously in contact with air after manufacture of the enclosure 101, and possibly the film of the superconducting material in the case where the superconducting material forms a 2D film previously deposited on the inner wall of the enclosure 101.

[0051] Surprisingly, the inventors have found that carrying out step 201 of annealing the enclosure 101 at a temperature of at least 400°C for a duration of at least 1 h, followed by step 203 of exposing the enclosure 101 to air and / or high-pressure rinsing with water, allows for more efficient rearrangement of the native oxide layer(s) coating the walls of the enclosure 101. As explained in more detail below in relation to FIG. 3, this advantageously allows the resonator 100 to have a quality factor Q higher than that which would be exhibited by a resonator similar to the resonator 100 but which had not undergone the steps 201 and 203 previously described.

[0052] In particular, unlike the process outlined in the 2021 publication by D. Bafia, A. Grassellino, and A. Romanenko entitled “Magnetic Suboxides as a Source of Two-Level System Losses in Superconducting Niobium” (arXiv: 2108.13352) and in which a niobium-based resonator is annealed for 5 h under ultra-high vacuum at a temperature of approximately 340°C and then maintained under vacuum in order to prevent reoxidation of the niobium, the method proposed by the inventors takes advantage of the annealing steps 201 and exposure to air 203 to allow the resonator 100 to have a quality factor Q at low fields (E < 0.05 MV / m) higher than those described in the aforementioned publication, despite the exposure to air and the high-pressure rinsing with water of the enclosure 101.

[0053] Figure 3 is a graph 300 of variation of the quality factor Q of the resonator 100 of Figure 1 as a function of an electric field E, expressed in megavolts per meter (MV / m), present in the resonator 100 at a temperature equal to approximately 1.4 K. The graph of Figure 3 corresponds more particularly to the case of annealing of the enclosure 101 under high vacuum, for example at a pressure less than or equal to 10 -3 Pa, at a temperature equal to approximately 650°C for a duration equal to approximately 10 h.

[0054] Graph 300 of Figure 3 illustrates, by a curve 301, a variation of the quality factor Q of the resonator 100 when the electric field E is in a range between 1 x 10 -4MV / m and 10 MV / m. The abscissa axis, representing the variation of the electric field E, is graduated in logarithmic scale in the illustrated example. Within this range of electric field E, the quality factor Q of the resonator 100 is greater than or equal to approximately 9 x 10 10 .

[0055] For comparison, existing niobium-based resonators, for example the resonator in the aforementioned publication, have quality factors Q between 1 x 10 10 and 2 x 10 10 in this electric field range E. In other words, the quality factor Q of the resonator 100 is approximately five to ten times higher than that of existing analogous resonators despite exposure to air, and possibly with water during high pressure rinsing of the enclosure 101 after annealing, which is not the case for existing resonators whose spontaneous oxidation of the surface by exposure to air and / or water degrades the quality factor Q.

[0056] Figure 4 is a schematic and partial side and sectional view of a niobium-based resonator 400 according to another embodiment.

[0057] The resonator 400 of Figure 4 comprises elements in common with the resonator 100 of Figure 1. These common elements will not be detailed again below. The resonator 400 of Figure 4 differs from the resonator 100 of Figure 1 in that the enclosure 101 is, in the case of the resonator 400, coated with at least one layer of at least one metal oxide and / or at least one metal nitride and / or at least one metal carbide, or any mixture of at least two of these compounds. In the case of the resonator 400, the metal oxide is other than niobium oxide.

[0058] Figure 4 illustrates more particularly a case in which the enclosure 101 is coated with a single layer 401 of a metal oxide, a metal nitride or a metal carbide. In the example illustrated, the layer 401 coats the internal face or wall of the enclosure 101. The layer 401 is for example more precisely located on and in contact with the internal wall of the enclosure 101 made of niobium. Furthermore, although this has not been shown in Figure 4 so as not to overload the drawing, a layer identical or similar to the layer 401 can coat the external face or wall, opposite the internal wall, of the enclosure 101.

[0059] The layer 401 has, for example, an amorphous structure. For example, the layer 401 is made of a metal oxide, for example chosen from aluminum oxide, tantalum oxide, yttrium oxide, zirconium oxide. and titanium oxide, or a mixture of at least two of these oxides. Alternatively, the layer 401 may be made of a metal nitride, for example chosen from tantalum nitride, zirconium nitride, titanium nitride and niobium nitride, or a mixture of at least two of these nitrides.

[0060] As a variant, the layer 401 may have a crystalline structure. For example, the layer 401 is made of a metal oxide, for example chosen from the aforementioned metal oxides, or a mixture of at least two of these oxides. In this case, each oxide is for example chosen from the oxides of empirical formulas AI2O3, Ta2O5, Y2O3, ZrCy and TiCy. As a variant, the layer 401 may be made of a metal nitride, for example chosen from the aforementioned metal nitrides, or a mixture of at least two of these nitrides. In this case, each nitride is for example chosen from the nitrides of empirical formulas TaN, ZrN, TiN and NbN.

[0061] The layer 401 has, for example, a thickness of the order of a few nanometers or a few tens of nanometers. For example, the thickness of the layer 401 is between 1 and 50 nm, for example between 1 and 25 nm, for example equal to approximately 10 nm.

[0062] Figure 5 is a flowchart illustrating successive steps of a method 500 for manufacturing the resonator 400 of Figure 4 according to one embodiment. The method 500 of Figure 5 comprises steps in common with the method 200 of Figure 2. These common steps will not be detailed again below.

[0063] The method 500 of Figure 5 differs from the method 200 of Figure 2 in that the method 500 further comprises, prior to the step 201 of annealing the enclosure 101, a step 501 (COATING) of coating the internal wall of the enclosure 101 with the layer 401.

[0064] For example, the coating of the enclosure 101 is carried out, during step 501, by atomic layer deposition (ALD).

[0065] Implementing the method 500 of Figure 5 provides advantages identical or similar to those provided by implementing the method 200 of Figure 2. In particular, the method 500 enables the resonator 400 to exhibit a quality factor Q higher than those of existing niobium-based resonators after exposure to air and water.

[0066] The vacuum annealing process of the layers deposited on the niobium-based superconducting material allows the removal of all or part of the niobium oxides and, where applicable, the oxides of other elements present in the niobium-based superconducting material such as AlOx or SnOx. For the highest annealing temperatures, i.e. annealing temperatures above 750 °C, annealing also allows the reduction of the nitride or oxide layers deposited in their metallic form. For example, this allows the reduction of Ta2Os to Ta and / or Y2O3 to Y. These metals partially reoxidize after exposure to air and / or water. The amount of oxide present after this reoxidation step is less than that present before annealing. In addition, the niobium oxide is removed.Regardless of the annealing temperature between 400 and 1000 °C, the new structure and the nature of the native oxide stabilize the resonator performance in the quantum regime in air. This process allows in particular to obtain coherence times (or a quality factor) better than niobium-based resonators without deposition or annealing at temperatures below 1 K and electric fields below 0.05 MV / m. The thin-film deposition and annealing process applies exclusively to previously oxidized niobium-based superconducting materials. This. The process therefore differs from the process outlined in the 2023 paper by M. Bal et al. entitled “Systematic Improvements in Transmon Qubit Coherence Enabled by Niobium Surface Encapsulation” (arXiv: 2304.13257) in which 10 nm coatings of tantalum, aluminum, and titanium nitride were deposited without a subsequent annealing step.

[0067] Figure 6 is a graph of variation of the quality factor Q of the resonator 400 of Figure 4 as a function of the electric field E, expressed in megavolts per meter (MV / m), present in the resonator 400 at a temperature equal to approximately 1.4 K. The graph of Figure 6 corresponds more particularly to the case where the layer 401 coating the internal wall of the enclosure 101 is a layer of alumina (AI2O3) having a thickness equal to approximately 10 nm, and where the annealing is carried out under high vacuum, for example at a pressure less than or equal to 10 -4 Pa, at a temperature equal to approximately 650°C for a duration equal to approximately 4 h.

[0068] The graph in Figure 6 illustrates, by a curve 601 in solid line, a variation of the quality factor Q of the resonator 400 when the electric field E is in a range between 1 x 10 -4MV / m and 10 MV / m. The abscissa axis, reflecting the variation of the electric field E, is graduated on a logarithmic scale in the illustrated example.

[0069] For comparison, the graph of figure 6 further illustrates, by a dotted curve 603, a variation in the quality factor Q of a niobium-based resonator which has not undergone either the coating step 501 or the annealing step 201.

[0070] In the example shown, the quality factor Q of the resonator 400 is, over the entire range of variation of the electric field E, at least 1.7 times greater than the quality factor Q of the resonator which has not undergone either the coating step 501 or the annealing step 201.

[0071] Figure 7 is a graph of variation of the quality factor Q of the resonator 400 of Figure 4 as a function of the electric field E, expressed in megavolts per meter (MV / m), present in the resonator 400 at a temperature equal to approximately 1.5 K. The graph of Figure 7 corresponds more particularly to the case where the layer 401 coating the internal wall of the enclosure 101 is a layer of alumina (AI2O3) having a thickness equal to approximately 10 nm, and where the annealing is carried out under high vacuum, for example at a pressure less than or equal to 10 -4 Pa, at a temperature equal to approximately 650°C for a duration equal to approximately 10 h.

[0072] The graph in Figure 7 illustrates, by a curve 701 in solid line, a variation of the quality factor Q of the resonator 400 when the electric field E is in a range between 1 x 10“ 4MV / m and 10 MV / m. The abscissa axis, reflecting the variation of the electric field E, is graduated on a logarithmic scale in the illustrated example.

[0073] For comparison, the graph of figure 7 further illustrates, by a dotted curve 703, a variation in the quality factor Q of a niobium-based resonator which has not undergone either the coating step 501 or the annealing step 201. Curve 703 is for example identical or analogous to curve 603.

[0074] In the example shown, the quality factor Q of the resonator 400 is, over the entire range of variation of the electric field E, at least twice as high as the quality factor Q of the resonator which has not undergone either the coating step 501 or the annealing step 201.

[0075] The resonator 400 of Figure 4 therefore exhibits superior performance, notably lower losses, than existing niobium-based resonators.

[0076] Various embodiments and variations have been described. Those skilled in the art will understand that certain features of these various embodiments and variations could be combined, and other variations will occur to those skilled in the art. In particular, those skilled in the art are able, based on the indications of the present description, to adapt the method 500 set forth in relation to FIG. 5 to the case where the internal wall of the enclosure 101 is coated with more than one layer.

[0077] Furthermore, the person skilled in the art is able, based on the indications of the present description, to adapt the method 500 of FIG. 5 to the case where each layer coating the internal wall of the enclosure 101 is made of a mixture of at least two materials.

[0078] Finally, the practical implementation of the embodiments and variants described is within the reach of the person skilled in the art from the functional indications given above. In particular, the person skilled in the art is capable, from the indications of the present description, of choosing the coating material(s) of the internal wall of the enclosure 101 and / or the temperature and duration of the annealing step 201 according to the application, for example according to the value of the quality factor Q targeted.

Claims

CLAIMS 1. Method (200; 500) for manufacturing a resonator (100; 400) comprising a niobium-based enclosure (101), the method comprising the following successive steps: a) carrying out an annealing (201) of the enclosure at a temperature of at least 400°C for a duration of at least 1 h; and b) exposing (203) the enclosure to air.

2. Method (200; 500) according to claim 1, further comprising, after step b), a step c) of rinsing the enclosure (101) with water, preferably at a pressure of the order of several bars or several tens of bars, more preferably equal to approximately 90 bars, and preferably for a duration of at least half an hour.

3. Method (200; 500) according to claim 1 or 2, wherein the temperature is between 400 and 1000°C, preferably between 600 and 700°C, more preferably equal to approximately 650°C.

4. Method (200; 500) according to claim 1, 2 or 3, in which the duration is between 1 and 24 h, preferably between 2 and 20 h, more preferably between 3 and 12 h, even more preferably equal to approximately 4 or 10 h.

5. Method (200; 500) according to any one of claims 1 to 4, in which the annealing (201) is carried out under vacuum, for example at a pressure less than or equal to 10 -2 Pa, preferably less than or equal to IO' 3 Pa.

6. Method (200; 500) according to any one of claims 1 to 4, in which the annealing (201) is carried out in the presence of an oxygen source.

7. Method (500) according to any one of claims 1 to 6, further comprising, prior to step a), a step of coating (501) an internal wall of the enclosure (101) with at least one layer (401) of at least one metal oxide and / or at least one metal nitride and / or at least one metal carbide, preferably with a single layer of a metal oxide, a metal nitride or a metal carbide.

8. Method (500) according to claim 7, wherein said at least one layer (401) is made of an amorphous material.

9. Method (500) according to claim 7, wherein said at least one layer (401) is made of a crystalline material.

10. Method (500) according to claim 7, 8 or 9, wherein: - the metal oxide is chosen from aluminum oxide, tantalum oxide, yttrium oxide, zirconium oxide and titanium oxide; and - the metal nitride is chosen from tantalum nitride, zirconium nitride, titanium nitride and niobium nitride.

11. Method (500) according to any one of claims 7 to 10, in which the coating (501) is carried out by atomic layer deposition.

12. Resonator (100; 400) comprising a niobium-based enclosure (101) of which an internal wall is coated with at least one layer (401) of at least one metal oxide and / or at least one metal nitride and / or at least a metallic carbide, or any mixture of at least two of these compounds.

13. Resonator (100; 400) according to claim 12, wherein said at least one layer (401) has an amorphous structure.

14. Resonator (100; 400) according to claim 12, wherein said at least one layer (401) has a crystalline structure.

15. Resonator (100; 400) according to claim 12, 13 or 14, in which: - the metal oxide is chosen from aluminum oxide, tantalum oxide, yttrium oxide, zirconium oxide and titanium oxide; and - the metal nitride is chosen from tantalum nitride, zirconium nitride, titanium nitride and niobium nitride.

16. Resonator (100; 400) according to any one of claims 12 to 15, wherein said at least one layer (401) has a thickness of between 1 and 50 nm, preferably of between 1 and 25 nm, more preferably equal to approximately 10 nm.

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