Gradient phononic crystal resonator based on two-dimensional material

Abstract

The invention discloses a gradient phononic crystal resonator based on a two-dimensional material. The gradient phononic crystal resonator comprises a substrate and a gradient phononic crystal beam made of the two-dimensional material, the gradient phononic crystal beam comprises a fixed area in contact with the substrate and a suspension area not in contact with the substrate, the suspension area comprises bilaterally symmetrical forbidden band phononic crystals and a middle phononic crystal defect, each forbidden band phononic crystal is composed of a plurality of unit primitive cells, and each unit primitive cell is composed of a plurality of unit primitive cells. And the width of each unit primitive cell is gradually reduced from the two ends to the middle defect area so as to realize co-positioning of stress and a displacement field. According to the scheme of the gradient phononic crystal resonator based on the two-dimensional material, the problem that due to the positive correlation of mechanical wave loss and frequency, the ultrahigh quality factor and the resonance frequency of a mechanical resonator are generally difficult to obtain at the same time is solved, and soft clamping and strain engineering technologies are applied to the phononic crystal based on the two-dimensional material; and the ultra-high quality factor mechanical resonator of GHz or even higher frequency band is realized.

Description

Technical Field

[0001] The invention belongs to the technical field of resonators and relates to a gradient phononic crystal resonator based on two-dimensional materials. Background Art

[0002] In recent years, micromechanical resonators have been maturely used in various fields, such as filtering in microwave radio frequency circuits, various sensors (including pressure, inertia and acceleration, etc.) and biomolecule detection. At the same time, micromechanical resonators have a remarkable development prospect in quantum computing as a carrier of quantum information processing, storage and transmission.

[0003] At present, optomechanical coupling of micromechanical resonators or piezoelectric coupling with superconducting quantum bits have shown many novel quantum phenomena in experiments, including ground state cooling of mechanical resonators, optomechanical compression, entanglement between microwaves and mechanical resonators, and entanglement between multiple mechanical resonators. In order to meet the needs of long-lived quantum states, pursuing a higher quality factor (Q value) of the resonator in the optomechanical frequency band (GHz) and the superconducting bit frequency band (GHz) has become an important research goal. Improving the Q value mainly includes two mechanisms: one is to reduce losses, and the other is to increase the total energy stored in the resonator.

[0004] Due to the positive correlation between mechanical wave loss and frequency, it is usually difficult to achieve both ultra-high quality factor and resonant frequency of mechanical resonators. In the prior art, there are one-dimensional phononic crystal beam resonators designed using a soft clamping method, which can effectively reduce clamping losses. There are also trampoline-type thin film resonators that use topology optimization and binary tree-type mechanical resonators that use hierarchical structure design to further improve the Q value. The use of two-dimensional materials with excellent properties of high elastic strength, ultra-low mass and single-atomic layer flat structure is expected to achieve higher Q values ​​at higher frequencies. However, the existing two-dimensional material resonator structure is relatively simple, the clamping loss has not been effectively suppressed, and the Q value is always low. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a gradient phononic crystal resonator based on two-dimensional materials.

[0006] Technical solution: The present invention provides a gradient phononic crystal resonator based on two-dimensional materials, comprising: a substrate and a gradient phononic crystal beam made of two-dimensional materials; the gradient phononic crystal beam comprises a fixed area in contact with the substrate, and a suspended area not in contact with the substrate, the suspended area comprises a bilaterally symmetrical bandgap phononic crystal and a phononic crystal defect in the middle, the bandgap phononic crystal is composed of a plurality of unit cells, the width of each unit cell gradually decreases from both ends to the middle defect area to achieve co-localization of stress and displacement fields.

[0007] Furthermore, the width of the primitive cell of each unit follows the Gaussian envelope curve:

[0008]

[0009] Where i represents the unit number, i from the inner layer to the outer layer of the defect of the gradient phononic crystal beam are is the total number of units; w max (i) and w min (i) respectively represent the maximum and minimum values ​​of the width of the i-th unit structure; the α w =0.16~0.3, said i0=3~12.

[0010] Furthermore, the α w =0.16~0.22, said i0=5~9.

[0011] Furthermore, L c (i) is the length of the primitive cell of the i-th unit, L d is the length of the middle phononic crystal defect, L d =(1~3)L c (0).

[0012] Furthermore, the lengths of the wider and narrower structures of the primitive cell of each unit are L wide and L narrow , the L wide (i) = L narrow (i) = Lc(i) / 2.

[0013] Furthermore, in order to ensure that the gradient phononic crystal beam structure has a consistent phononic crystal bandgap, the length L of each unit cell is c The maximum value of the width w max Follow this formula:

[0014]

[0015] Furthermore, the two-dimensional material is graphene.

[0016] Furthermore, the gradient phononic crystal beam comprises 36 to 84 primitive cells.

[0017] Furthermore, the base comprises a Si substrate and a SiO2 epitaxial layer on the surface thereof.

[0018] Furthermore, metal is deposited on a substrate at the bottom of the suspension region of the gradient phononic crystal beam to form a gate, the gate is externally connected to a DC power supply with adjustable voltage, and the metal is one of aluminum, gold, silver and copper.

[0019] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: 1. The present invention combines dissipative dilution and strain engineering design theory with two-dimensional materials with extremely high mechanical strength to achieve ultra-high-quality mechanical resonators in the GHz or even higher frequency bands. The width of each unit cell in the bandgap phononic crystal is gradually reduced from the two ends to the middle defect area to achieve co-localization of stress and displacement fields, and dissipative dilution is further improved, so that the Q value of the resonator at the same frequency reaches 6.8×10 8 , breaking through the theoretical limit of soft clamping technology. This design scheme with the combined effect of dissipative dilution and strain engineering can also achieve more advantageous Q×f in a higher operating frequency band, promoting the improvement of the operating frequency of high-quality resonators;

[0020] 2. The present invention forms a gate by depositing metal on the substrate at the bottom of the suspension area of ​​the gradient phononic crystal beam. The gate is externally connected to a DC power supply with adjustable voltage, and has good frequency adjustability when the gate voltage is applied. The increase in the stress of the two-dimensional material caused by the gate voltage further increases the resonator frequency and Q value by several times. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a schematic diagram of the structure of a gradient phononic crystal resonator;

[0022] Figure 2 Schematic diagram of the two-dimensional structure of the gradient phononic crystal beam;

[0023] Figure 3 Schematic diagram of the phononic crystal primitive cell structure of the gradient phononic crystal beam structure;

[0024] Figure 4 (a) is a schematic diagram of the two-dimensional structure of a uniform phononic crystal beam; Figure 4 (b) Schematic diagram of the phononic crystal unit cell structure with a uniform phononic crystal beam structure;

[0025] Figure 5 The energy band diagram corresponding to each unit in the gradient phononic crystal beam as a primitive cell;

[0026] Figure 6 (a) Out-of-plane displacement distribution of defect mode of gradient phononic crystal resonator; Figure 6 (b) is the stress distribution of the defect mode of the gradient phononic crystal resonator; Figure 6 (c) is the characteristic frequency spectrum of the resonator out-of-plane mode;

[0027] Figure 7 D of Comparative Example 1 and Comparative Example 2 Q and Q-value spectrum diagram;

[0028] Figure 8 D of Example 1 and Comparative Example 1 Q and Q-value spectrum diagram;

[0029] Fig. 9 (a) is a uniform phononic crystal resonator with 6 units in comparative example 3 and its defect mode out-of-plane displacement distribution; Fig. 9 (b) is a uniform phononic crystal resonator with 84 units in Comparative Example 3 and its defect mode out-of-plane displacement distribution;

[0030] Fig. 9 (c) is a gradient phononic crystal resonator with 36 units in Example 2 and its defect mode out-of-plane displacement distribution; Fig. 9 (d) is a gradient phononic crystal resonator with 84 units in Example 2 and its defect mode out-of-plane displacement distribution;

[0031] Fig.10 D is the resonant mode corresponding to the uniform (unit number 6 to 84) and gradient phononic crystal (unit number 36 to 84) resonators with different unit numbers. Q and Q value;

[0032] Fig.11 D is the resonant mode corresponding to the uniform (unit number 6 to 84) and gradient phononic crystal (unit number 36 to 84) resonators with different unit numbers. Q ×f and Q×f;

[0033] Fig.12 The phononic crystal beam structure and corresponding stress distribution of representative parameter combinations in the performance optimization strategy of gradient phononic crystal resonator;

[0034] Fig.13 is the D of all gradient phononic crystal resonators in the optimization strategy Q ;

[0035] Fig.14 Schematic diagram of the structure of an electrically tunable graphene phononic crystal resonator with applied gate voltage;

[0036] Fig.15 (a) The band gap and defect mode of the phononic crystal corresponding to the unit in the resonator change with the applied gate voltage;

[0037] Fig.15 (b) is the D of the resonator of Example 4 and Comparative Example 4 Q and Q value with gate voltage, the inset is the D Q ratio. DETAILED DESCRIPTION

[0038] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0039] like Figure 1-3As shown, the gradient phononic crystal resonator based on two-dimensional materials of this embodiment includes: a substrate and a gradient phononic crystal beam 3 made of two-dimensional materials, the substrate includes a Si substrate 1 and a SiO2 epitaxial layer 2 on its surface; the gradient phononic crystal beam 3 includes a fixed area in contact with the substrate, and a suspended area not in contact with the substrate, the suspended area includes a bilaterally symmetrical bandgap phononic crystal 31 and a phononic crystal defect 32 in the middle, the bandgap phononic crystal 31 is composed of a plurality of unit cells, and the bandgap phononic crystal 31 plays a role in isolating the energy of the resonant cavity from leaking outward, as shown in FIG. Figure 2 The width of each unit cell gradually decreases from both ends to the middle defect region to achieve co-localization of stress and displacement fields. In a specific embodiment, the total number of cells is 36 to 84.

[0040] Combined with Figure 3 , W max and W min are the widths of the wider and narrower structures of the primitive cell of each unit, L wide and L narrow are the lengths of the wider and narrower structures of the primitive cell of each unit, L d is the length of the middle phononic crystal defect, L c is the length of the primitive cell of each unit.

[0041] In order to better achieve the co-localization of stress and displacement fields, the width of each unit cell should follow the Gaussian envelope curve:

[0042]

[0043] Where i represents the unit number, i from the inner layer to the outer layer of the defect of the gradient phononic crystal beam are

[0044] n is the total number of units; w max (i) and w min (i) represents the maximum and minimum width of the i-th unit structure; α w and i0 approximately represent the width ratio of the structure at both ends and the center area of ​​the beam and the rate of geometric gradient, α w Approximately represents the width ratio of the beam ends and the center area structure (approximately equal to i0 directly affects the rate of geometric gradient from the ends of the beam to the center area. w The values ​​of and i0 are: w =0.16~0.3, i0=3~12. L c (i) is the length of the i-th unit, L d is the length of the middle phononic crystal defect, L d =(1~3)L c(0). The lengths of the wider and narrower structures of the primitive cell of the i-th unit are L wide (i) and L narrow (i), L wide (i) = L narrow (i) = Lc(i) / 2.

[0045] In order to ensure that the gradient phononic crystal beam structure has a consistent phononic crystal bandgap, the length L of each unit cell in the gradient phononic crystal beam is c With W max Follow this formula:

[0046]

[0047] like Figure 5 As shown in the figure, it can be seen that in the gradient beam structure designed according to formula (2), the representative unit is used as the primitive cell (W min =20nm, 64nm, 108nm, 152nm, 196nm, 240nm) and the corresponding phononic crystal energy bands are as follows Figure 5 As shown, it can be seen that the band gaps corresponding to each unit in the gradient phononic crystal beam as the original cell are the same.

[0048] Example 1

[0049] Graphene is selected to prepare a resonator with a gradient phononic crystal beam structure. The thickness h of the graphene resonator is 0.335 nm and the density ρ is 2.267 g / cm 3 , Young's modulus E is 1TPa, Poisson's ratio is 0.165, and prestress is 2GPa. The total length of the structure is L = 120μm, including 36 primitive cells, L d =1.3L c . Select α w = 0.2, i0 = 8 to construct a graphene gradient phononic crystal resonator. Figure 6 (a) and Figure 6 (b) shows the out-of-plane displacement and stress distribution of the defect mode of the gradient phononic crystal resonator. As the width of the gradient phononic crystal beam gradually shrinks from both ends to the center, the stress is concentrated at the central defect, and the magnitude gradually decreases towards the two ends of the beam in an exponential trend. The downward trend of the out-of-plane displacement is basically consistent with the stress, which indicates the successful realization of the co-localization of the two. Figure 6 (c) is the characteristic frequency spectrum of the out-of-plane mode in the gradient phononic crystal resonator, which further confirms the 3.1-3.8 GHz band gap of the gradient phononic crystal beam structure. The defect mode with highly localized energy is located at 3.3 GHz in the band gap, which is the resonant frequency of this mechanical resonator.

[0050] Comparative Example 1

[0051] A resonator comprising a uniform phononic crystal beam. The difference from Example 1 is that the structure of each phononic crystal unit cell is the same. Figure 4 (a) is a schematic diagram of the two-dimensional structure of a uniform phononic crystal beam. Figure 4 (b) The structure of a single phononic crystal unit cell is shown in the figure. The total length of the structure is L = 139 μm, which contains 36 units. Except for the central defect, the length of each unit cell is L c =3.73μm. The length of the central defect L d 1.3L c The width of the primitive cell at its widest point is W max =152nm, the narrowest width W min =76nm, L wide =L narrow =L c / 2.

[0052] Comparative Example 2

[0053] A resonator that does not contain a uniform or graded phononic crystal beam structure.

[0054] Figure 7 is D of Comparative Example 1 and Comparative Example 2 Q And Q value spectrum, where blue is comparative example 1, red is comparative example 2, the blue solid line is the theoretical limit of soft clamping, and the gray solid line is the strength limit of graphene. In the resonator of comparative example 2, D Q The Q value decreases slowly with the increase of frequency. In the resonator of comparative example 1 including a uniform phononic crystal beam structure, that is, under the soft clamping scheme, D Q The Q value is significantly improved in the phononic crystal band gap, D Q Up to 2×10 5 , approaching the clamping loss limit obtained by theoretical calculation.

[0055] Figure 8 is D of Example 1 and Comparative Example 2 Q and Q value spectrum, where blue is Example 1, red is Comparative Example 2, the blue solid line is the theoretical limit of soft clamping, and the gray solid line is the strength limit of graphene. In the resonator of Comparative Example 2, D Q The Q value decreases slowly with increasing frequency. In the resonator of Example 1 including the gradient phononic crystal beam, that is, the soft clamping scheme supported by strain engineering, the theoretical dilution coefficient D of the resonator is Q Up to 5×10 5 This value not only far exceeds the D of the uniform beam resonator Q, breaking through the theoretical limit of soft clamping technology and getting closer to the theoretical limit of dissipative dilution determined by the yield strength of graphene. Specifically, compared with a uniform phononic crystal resonator using only soft clamping, the strain-engineered gradient phononic crystal resonator achieves a Q value improvement of about 260%.

[0056] Example 2

[0057] While keeping the total length of the gradient phononic crystal beam structure of Example 1 unchanged, we changed the number of units of its primitive cell to 36 and 84.

[0058] Comparative Example 3

[0059] While keeping the total length of the uniform phononic crystal beam structure of Comparative Example 2 unchanged, we changed the number of units of its primitive cell to 6 and 84.

[0060] The number of primitive cells directly makes L c The changes affect the operating frequency of the resonator. Fig. 9 (a) and Fig. 9 (b) is the out-of-plane displacement distribution of the defect mode in the uniform phononic crystal resonator when the number of units is 6 and 84. The resonant frequencies of the two are 0.63 GHz and 7.59 GHz respectively. Fig. 9 (c) Fig. 9 (d) is the out-of-plane displacement distribution of the defect mode in the gradient phononic crystal resonator when the number of units is 36 and 84. The resonant frequencies of the two are 3.30 GHz and 7.47 GHz, respectively. As the number of units increases, the resonant frequency of the resonator increases monotonically, and the volume of the resonant mode decreases, and the localization increases.

[0061] Fig.10 The D of the resonance modes corresponding to different uniform beams, uniform phononic crystal resonators (with the number of units ranging from 6 to 84) and gradient phononic crystal resonators (with the number of units ranging from 36 to 84) Q and Q value. It can be seen that as the operating frequency of the resonator increases, the D Q For a uniform phononic crystal resonator of a certain length, the resonator has an optimal operating frequency (i.e., the number of units) with the highest D Q The reason is that the uniform phononic crystal resonator is limited by the theoretical limit of the soft clamping technology. Q Both the D and Q values ​​of the gradient phononic crystal resonator exceed the theoretical limit of soft clamping. Q The decrease rates of the Q value and the Q value are significantly lower than the decrease rate of the theoretical limit of the soft clamping technology.

[0062] The Q value of a resonator is closely related to its operating frequency. Due to the positive correlation between various losses and frequency, the Q value always decreases as the frequency increases. Therefore, in the evaluation of a resonator, the Q value multiplied by the operating frequency (Q×f) is often a more valuable indicator. For example, when measuring the quantum coherence of a resonator, Q×f needs to reach 6.62×10 12 Threshold in Hz. Fig.11 Shows the Fig.10 The vertical axis is replaced with the result of DQ×f and Q×f. For uniform phononic crystal resonators, their Q×f decreases significantly with increasing frequency in the higher frequency band. This means that high frequency and high Q value cannot be achieved at the same time. However, it is advantageous that in resonators containing gradient phononic crystal beam structures, their Q×f decreases relatively slowly with increasing frequency. This means that even for higher frequencies, there is hope for ultra-high performance mechanical resonators.

[0063] Example 3

[0064] In a gradient phononic crystal beam, the stress concentration in the central area will lead to the relaxation of stress at both ends, thus reducing the overall average stress of the beam to a certain extent. w and i0 are closely related to the redistribution of stress in the beam structure, which determines the optimal solution for improving the resonator Q value by enhancing local stress and reducing average stress. Fig.12 As shown, it contains representative α w The phononic crystal beam structure and corresponding stress distribution under the combination of and i0. When the total length of the gradient phononic crystal beam is constant, the total number of units is 36, and the W of the outermost unit is constant. min (18) is fixed at 200 nm, thus maintaining the operating frequency of the resonator at 3.3 GHz. Fig.12 (1) Medium α w =0.3, i0=12 as the starting point, along the positive direction of the X axis in the figure, at α w When i0 is reduced to 3(2), Fig.12 It can be seen from (1) and (2) that, geometrically, the beam gradually changes from the widest part on both sides to the narrowest part in the center, and the curvature of the Gaussian envelope function increases; in terms of stress, the stress concentration in the center area of ​​the beam increases. Along the positive direction of the Y axis in the figure, when i0 remains unchanged, α w Reduced to 0.16(3), from Fig.12 It can be seen from (1) and (3) that geometrically, the variation trend of the width of the gradient phononic crystal beam is basically the same. However, as α w The decrease of α reduces the width of the defect at the center of the beam. This change mainly affects the stress magnitude in the stress concentration area. wWhen it is less than 0.16, due to the large mutation of the geometric scale of adjacent units, the evolution of the gradient phononic crystal beam is no longer adiabatic, and it is difficult to form a defect mode in the center of the gradient beam. w =0.16, i0=3 as the end point of optimization, such as Fig.12 (4). At this time, the minimum geometric scale W of the gradient phononic crystal min It is 32nm.

[0065] like Fig.13 As shown, it shows the starting point: α w =0.3, i0=12 to the end point: α w =0.16, i0=3, and α w D of all gradient phononic crystal resonators with interval 0.02 and i0 interval 1 Q The results show that when α w When i0 increases, D Q The overall trend is to increase first and then decrease. w When D increases Q The overall trend is downward. w =0.16, i0=7, D Q The maximum value is 5.54×10 5 Therefore, when designing the resonator, α can be minimized. w , and i0 should take a moderate value. Too large or too small will lead to a decrease in device performance. It can be seen that when α w =0.16~0.22, i0=5~9, DQ is as high as 4×10 5 ~5.54×10 5 The value of .

[0066] Example 4

[0067] like Fig.14 As shown, the gradient phononic crystal resonator (α w =0.2, i0=7) as an example, metal 4 is deposited on the substrate at the bottom of the suspended graphene to form a gate, and the gate is externally connected to a DC power supply with adjustable voltage to introduce additional electrostatic stress in the monolayer graphene.

[0068]

[0069] P es is the additional electrostatic stress, in N / m; ε0 is the vacuum dielectric constant; d is the distance between the gate and the resonator, which is set to 200nm; the resonator out-of-plane displacement u is much smaller than the distance d and can be ignored; V g is the gate voltage.

[0070] Gradient phononic crystal resonator (α w=0.2, i0=7) as an example, Fig.15 (a) shows the change of the phononic crystal band gap and the defect mode therein with the applied gate voltage. The blue dotted solid line in the figure represents the upper and lower edges of the band gap. The red dotted solid line represents the defect mode located in the band gap. The additional stress brought by the gate changes the equivalent elastic modulus and density of graphene, thereby affecting the frequency position and width of the band gap. In a specific phononic crystal resonator, as the gate voltage and stress are modulated, the relative position of the defect mode in the band gap remains unchanged. This result proves the monotonic, precise and efficient electrical tunability of the resonator.

[0071] Comparative Example 4

[0072] Taking the resonator including the uniform phononic crystal beam in comparative example 2 as an example, metal 4 is also deposited on the substrate at the bottom of the suspended graphene to form a gate, and the gate is externally connected to a DC power supply with adjustable voltage.

[0073] like Fig.15 (b) shows D of Example 4 and Comparative Example 4 Q and Q value with gate voltage / stress. It can be seen that the D of the resonator containing uniform and gradient phononic crystal beam structures Q Both are proportional to the gate voltage. The illustration is the D Q The ratio of Q to dissipation dilution is basically constant at about 260% with the change of gate voltage. This shows that under a certain resonator design scheme, the improvement of dissipation dilution effect by strain engineering is not affected by stress changes. In fact, the reason why the Q value changes with stress is different for uniform and gradient phononic crystal resonators. The former only comes from dissipation dilution itself; while the latter also includes the additional gain of strain engineering for dissipation dilution. In either scheme, a gate voltage of 60mV achieves an improvement of the resonator Q value by nearly 60%.

[0074] The gradient phononic crystal resonator based on two-dimensional materials of the present invention is prepared by the following steps:

[0075] Step 1: Using methods such as CVD, a single layer of two-dimensional material is deposited on the SiO2 epitaxial layer on the surface of a Si substrate;

[0076] Step 2: patterning the phononic crystal on the two-dimensional material layer using photolithography and etching processes;

[0077] Step 3: Etch the SiO2 or Si substrate at the bottom of the patterned phononic crystal to achieve suspension of the two-dimensional material phononic crystal.

[0078] The above is an exemplary description of the embodiments of the present invention. However, the protection scope of the present invention is not limited to the above embodiments. Any modification, equivalent substitution, improvement, etc. made by those skilled in the art within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A gradient phononic crystal resonator based on two-dimensional materials, characterized in that: include: A substrate and a gradient phononic crystal beam made of a two-dimensional material; the gradient phononic crystal beam includes a fixed area in contact with the substrate and a suspended area not in contact with the substrate, the suspended area includes a bilaterally symmetrical bandgap phononic crystal and a phononic crystal defect in the middle, the bandgap phononic crystal is composed of a plurality of unit primitive cells, and the width of each unit primitive cell gradually decreases from both ends to the position of the middle defect area.

2. The gradient phononic crystal resonator based on two-dimensional materials according to claim 1 is characterized in that: The width of each unit cell follows the Gaussian envelope curve: Where i represents the unit number, i from the inner layer to the outer layer of the defect of the gradient phononic crystal beam are is the total number of units; w max (i) and w min (i) respectively represent the maximum and minimum values ​​of the width of the i-th unit structure; the α w =0.16~0.3, said i0=3~12.

3. The gradient phononic crystal resonator based on two-dimensional materials according to claim 2 is characterized in that: The α w =0.16~0.22, said i0=5~9.

4. The gradient phononic crystal resonator based on two-dimensional materials according to claim 2 is characterized in that: L c (i) is the length of the primitive cell of the i-th unit, L d is the length of the middle phononic crystal defect, L d =(1~3)L c (0).

5. The gradient phononic crystal resonator based on two-dimensional materials according to claim 4 is characterized in that: The lengths of the wider and narrower structures of the primitive cell of each unit are L wide and L narrow , the L wide (i) = L narrow (i) = Lc(i) / 2.

6. The gradient phononic crystal resonator based on two-dimensional materials according to claim 1 is characterized in that: The length of each primitive cell is L c The maximum value of the width w max Follow this formula:

7. The gradient phononic crystal resonator based on two-dimensional materials according to claim 1 is characterized in that: The two-dimensional material is graphene.

8. The gradient phononic crystal resonator based on two-dimensional materials according to claim 1 is characterized in that: The gradient phononic crystal beam comprises 36 to 84 primitive cells.

9. The gradient phononic crystal resonator based on two-dimensional materials according to claim 1, characterized in that: The base comprises a Si substrate and a SiO2 epitaxial layer on the surface thereof.

10. The gradient phononic crystal resonator based on two-dimensional materials according to any one of claims 1 to 9, characterized in that: A metal is deposited on a substrate at the bottom of the suspension region of the gradient phononic crystal beam to form a gate, the gate is externally connected to a DC power supply with adjustable voltage, and the metal is one of aluminum, gold, silver and copper.

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