Physical amount detection device and method for manufacturing substrate
By irradiating excitation light from the opposite side of the substrate to avoid waveguide obstruction, the device enhances detection sensitivity by aligning emission state measurement with maximum microwave intensity, addressing the issue of reduced sensitivity in existing devices.
Patent Information
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- KK TOYOTA CHUO KENKYUSHO
- Filing Date
- 2025-11-05
- Publication Date
- 2026-07-23
AI Technical Summary
The detection sensitivity of physical quantity detection devices using color centers in solids is reduced due to insufficient microwave intensity, leading to a deteriorated signal-to-noise ratio when the microwave irradiation is not strong enough.
The device irradiates excitation light from the opposite side of the substrate, allowing detection of the emission state of color centers from the second surface, avoiding the waveguide obstruction and maximizing microwave intensity at the center of the waveguide, thus enhancing detection sensitivity.
This configuration enables increased detection sensitivity by aligning the emission state measurement with the maximum microwave intensity, improving the signal-to-noise ratio and sensitivity of the physical quantity detection.
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Figure JP2025038824_23072026_PF_FP_ABST
Abstract
Description
Physical Quantity Detection Device and Method for Manufacturing a Substrate
[0001] This application claims priority based on Japanese Patent Application No. 2025-008012 filed on January 20, 2025. All the contents of that application are incorporated herein by reference. This specification relates to a physical quantity detection device and a method for manufacturing a substrate.
[0002] Conventionally, a physical quantity detection device has been proposed that uses a substrate having color centers (spin defects) in a solid to detect physical quantities such as magnetic fields, temperatures, and electric fields. Detection of a physical quantity is performed by measuring the amount of change in the emission intensity when microwaves are irradiated onto the color centers. Related technology is disclosed in Japanese Patent Application Laid-Open No. 2020-054860.
[0003] If the intensity of the microwaves irradiated onto the color centers is not sufficiently strong, the change in the emission intensity becomes small. Since the signal-to-noise ratio deteriorates, the detection sensitivity of the physical quantity detection device decreases.
[0004] The physical quantity detection device disclosed in this specification includes a substrate having a plurality of color centers. The physical quantity detection device is disposed on a first surface of the substrate and includes a waveguide irradiated with microwaves. The physical quantity detection device includes an irradiation unit that irradiates excitation light from a second surface located on the opposite side of the first surface of the substrate. The physical quantity detection device includes a detection unit that detects the emission state of the color centers from the second surface side. The waveguide is composed of a conductor film. The waveguide extends in the longitudinal direction and has a width direction orthogonal to the longitudinal direction. The irradiation unit is configured to be able to irradiate excitation light at a central position in the width direction of the waveguide.
[0005] In the above configuration, a microwave waveguide is formed by a conductive film arranged on the first surface of the substrate. The inventors have found that in this configuration, the position where the microwave intensity is maximum is sometimes directly below the waveguide and at the center in the width direction of the waveguide. However, at the position directly below the waveguide and at the center in the width direction, the waveguide itself acts as an obstruction, making it difficult to irradiate with excitation light or detect the emission state. Therefore, in the above configuration, excitation light is irradiated from a second surface located on the opposite side of the first surface, and the emission state of the color center is detected from the second surface side. This makes it possible to avoid the waveguide, so that excitation light can be irradiated and the emission state can be detected at the position directly below the waveguide and at the center in the width direction. Since the emission state of the color center can be measured at the position where the microwave intensity is maximum, the detection sensitivity of the physical quantity detection device can be increased.
[0006] This is a schematic diagram of the physical quantity detection device 1. This is a schematic diagram of the substrate 10 and waveguide 11. This is a diagram illustrating the flow for forming the waveguide 11. This is a diagram illustrating a modified example of the mask. This is a schematic diagram of the substrate 10 and waveguide 11 in Example 2. This is a schematic diagram of the physical quantity detection device 101 according to a modified example.
[0007] (Overview of Physical Quantity Detection Device 1) Figure 1 is a schematic diagram showing the general configuration of a physical quantity detection device 1 according to one embodiment. The physical quantity detection device 1 is a solid-state quantum sensor system that can measure magnetic fields, electric fields, temperature, etc., of a target with high sensitivity. The physical quantity detection device 1 mainly comprises a substrate 10, a waveguide 11, an excitation light irradiation unit 20, a microwave oscillation unit 30, a photodetection unit 40, a static magnetic field application unit 50, a control unit 60, and a lens 70.
[0008] The substrate 10 comprises a surface 10f and a back surface 10b located opposite the surface 10f. The substrate 10 is made of a material containing a plurality of color centers 12. Examples of materials containing color centers include SiC, diamond, GaN single crystal, and hBN. In this embodiment, the material of the substrate 10 is 4H-SiC. 4H-SiC contains silicon vacancy color centers 12. In Figure 1, the color centers 12 are shown as black dots. The same applies in subsequent figures.
[0009] The waveguide 11 is located on the surface 10f of the substrate 10. Microwaves MW are irradiated onto the waveguide 11 from the microwave oscillation unit 30. The specific details of the waveguide 11 will be described later.
[0010] The microwave oscillator 30 is the part that generates microwave MW. The microwave MW is used to manipulate the spin qubits of the color center 12. The microwave oscillator 30 is connected to the waveguide 11. The microwave oscillator 30 generates microwave MW of a specific frequency in response to driving and control by the control unit 60. The microwave MW is irradiated onto the substrate 10 via the waveguide 11.
[0011] The excitation light irradiation unit 20 is located on the back surface 10b side of the substrate 10. The excitation light irradiation unit 20 is the part that generates excitation light EL and irradiates the back surface 10b. The excitation light irradiation unit 20 may include a light source such as a light-emitting diode or laser diode, a filter, a mirror, a lens, etc. The excitation light irradiation unit 20 may also include an acousto-optic modulator for digital modulation, etc., as needed.
[0012] The light detection unit 40 is located on the back surface 10b side of the substrate 10. The light detection unit 40 is the part that detects the light-emitting LU of the color center 12 from the back surface 10b side. The light detection unit 40 may include photoelectric conversion elements such as PD (photodiode) or APD (avalanche photodiode), or imaging sensors such as CCD or CMOS sensors. The light detection unit 40 may also include one or more of the following: a lens, a beam splitter, a diffraction grating, an optical filter, or a mirror.
[0013] The lens 70 is positioned between the excitation light irradiation unit 20 and the photodetection unit 40 and the substrate 10. The lens 70 may be, for example, an objective lens. The static magnetic field application unit 50 is positioned near the substrate 10 and applies a known static magnetic field to the substrate 10. The static magnetic field application unit 50 may be, for example, a permanent magnet or an electromagnet.
[0014] The control unit 60 is a component configured to control the operation of the excitation light irradiation unit 20, the microwave oscillation unit 30, the photodetection unit 40, and other components. Various information terminal devices, such as a known general-purpose computer, can be used as the control unit 60.
[0015] (Configuration of substrate 10 and waveguide 11) Figure 2(A) shows a schematic configuration diagram of the substrate 10 and waveguide 11. The substrate 10 is provided with a plurality of color centers 12. The plurality of color centers 12 are formed by ion implantation from the surface 10f, as will be described later. Therefore, the plurality of color centers 12 are located in the vicinity of the surface 10f.
[0016] The waveguide 11 is arranged on the surface 10f of the substrate 10. The waveguide 11 extends in the longitudinal direction (y direction). The waveguide 11 also has a width W1 in the width direction (x direction), which is perpendicular to the longitudinal direction. The waveguide 11 has an end 11e1 in the -x direction and an end 11e2 in the +x direction. Note that the planar shape of the waveguide 11 is not limited to a straight line, and may include a loop or a coil.
[0017] The waveguide 11 is composed of a conductive film. In this embodiment, the waveguide 11 is an Au film. The thickness T1 and width W1 of the waveguide 11 can be various values. In this embodiment, the thickness T1 was set to 600 nm and the width W1 to 300 μm.
[0018] Waveguide 11 may be a planar waveguide, such as a microstrip line or a coplanar line. If waveguide 11 is a microstrip line, it may include a first grounding conductor (not shown). The first grounding conductor may be positioned opposite waveguide 11 with a dielectric in between. If waveguide 11 is a coplanar line, it may include a second grounding conductor (not shown). The second grounding conductor may be positioned parallel to waveguide 11 on both sides of waveguide 11.
[0019] Here, we consider the waveguide region WR, which is the region obtained by perpendicularly projecting the waveguide 11 onto the surface 10f. Figure 2(B) shows the density distribution CD of the color center 12 within the waveguide region WR. The density distribution CD of the color center 12 is higher towards the center in the width direction than towards the edges in the width direction. The density distribution CD has a maximum value CDmax at the center position CP in the width direction.
[0020] (Physical quantity detection operation) Microwaves MW generated by the microwave oscillation unit 30 are irradiated onto the back surface 10b of the substrate 10 via the waveguide 11. Excitation light EL generated by the excitation light irradiation unit 20 is irradiated onto the back surface 10b of the substrate 10 via the lens 70. The irradiation width and position of the excitation light EL can be controlled using the lens 70. That is, the irradiation width of the excitation light EL can be made sufficiently small compared to the width W1 of the waveguide 11. The irradiation position of the excitation light EL can be freely set within the range of the width W1. In other words, the excitation light irradiation unit 20 is configured to irradiate the excitation light EL to the center position CP in the width direction of the waveguide 11. The light emission LU of the color center 12 is measured by the light detection unit 40 via the lens 70. The amount of change in the light emission intensity of the color center 12 becomes the sensor signal.
[0021] Figure 2(A) shows the spatial distribution SD of microwave intensity when microwaves MW are irradiated onto the waveguide 11. The spatial distribution SD is formed radially from the center position CP of the waveguide 11. The spatial distribution SD is also formed directly below the waveguide 11.
[0022] Figure 2(C) shows the electric field strength distribution ED for the microwave MW. The electric field strength distribution ED reaches its maximum value EDmax at the center position CP of the waveguide 11 and its minimum value at the ends 11e1 and 11e2. In other words, the profile of the electric field strength distribution ED is approximately identical to the profile of the spatial distribution SD.
[0023] Figure 2(D) shows the signal intensity distribution DD of the sensor signal. The signal intensity distribution DD can be obtained by moving the sensor signal acquisition position from end 11e1 to 11e2 of the waveguide 11. The intensity of the sensor signal is minimum at ends 11e1 and 11e2 of the waveguide 11. It can be seen that the intensity of the sensor signal increases as you approach the center position CP from ends 11e1 and 11e2. From the above, it can be seen that a more sensitive quantum sensor can be realized by using a color center 12 located near the center position CP.
[0024] (Effects) In the physical quantity detection device 1 of this embodiment, a waveguide 11 for microwaves MW is formed by a conductive film arranged on the surface 10f of the substrate 10. The inventors have found that in such a waveguide 11 configuration, the position where the microwave electric field strength is maximum is directly below the waveguide 11 and may also be the center position CP in the width direction of the waveguide 11. However, the waveguide 11 itself is an obstacle at the position directly below and at the center of the waveguide 11. Therefore, it was difficult to irradiate this position with excitation light EL or to detect the emission state at this position. In the technology described herein, excitation light EL is irradiated from the back surface 10b located on the opposite side of the surface 10f, and the emission LU of the color center 12 is detected from the back surface 10b side. As a result, the waveguide 11 can be avoided, making it possible to irradiate the center position CP directly below the waveguide 11 with excitation light EL and to detect the emission LU. Since the emission state of the color center 12 can be measured at the position where the electric field strength of the microwave MW is maximum, it is possible to increase the detection sensitivity of the physical quantity detection device 1.
[0025] The electric field strength distribution ED of the microwave MW is higher towards the center of the waveguide 11 in the width direction than towards the ends in the width direction (see Figure 2(C)). In the technology described herein, the density distribution CD of the color center 12 is also higher towards the center of the waveguide 11 in the width direction than towards the ends in the width direction (see Figure 2(B)). This makes it possible to match the trend of the electric field strength distribution ED of the microwave MW with the trend of the density distribution CD of the color center 12. Therefore, it is possible to irradiate more color centers 12 with stronger microwave MW, thereby increasing the amount of change in emission intensity. Thus, it is possible to increase the detection sensitivity of the physical quantity detection device 1.
[0026] (Manufacturing method for substrate 10 and waveguide 11) The process for forming the waveguide 11 on a substrate 10 equipped with a color center 12 will be explained using Figure 3. As an example, the case in which the color center 12 is formed to have the density distribution CD shown in Figure 2(B) will be explained.
[0027] In step S10, a mask 80 is formed on the surface 10f of the substrate 10 (see Figure 3(A)). The mask 80 can be formed by known photolithography techniques. The mask 80 has an aperture OP corresponding to the waveguide 11. A plurality of line patterns 80L are arranged within the aperture OP. Each of the plurality of line patterns 80L extends in the longitudinal direction (y direction) and is adjacent to others with space between them in the width direction (x direction).
[0028] The coverage of the multiple line patterns 10L is adjusted so that the coverage is lower towards the center in the width direction than towards the edges in the width direction. There are various methods for adjusting the coverage of the line patterns 10L. For example, methods include changing the space width, changing the line width, or a combination thereof. In this embodiment, the coverage at the edges is increased by making the width of the line patterns 10L larger towards the edges than towards the center. In addition, the coverage at the center is reduced by making the space width SW1 at the center position CP of the waveguide 11 larger than the space width SW2 at the edges.
[0029] In step S20, ions are implanted into the surface 10f of the substrate 10 through the opening OP of the mask 80. Silicon vacancies (color centers 12) can be formed in the ion-implanted areas. As described above, the coverage of the line pattern 10L is lower towards the center in the width direction than towards the edges in the width direction. Therefore, the concentration distribution ID of the ion implantation amount is higher towards the center in the width direction than towards the edges in the width direction (see Figure 3(B)). This makes it possible to make the concentration distribution of the color centers 12 higher towards the center in the width direction than towards the edges in the width direction (see Figure 2(B)). Note that any type of ion capable of forming color centers 12 may be used for implantation. For example, helium ions may be used.
[0030] In step S30, the mask 80 is removed. In step S40, a conductive film is formed in the ion-implanted region. In this embodiment, a 600 nm thick Au thin film was formed as the conductive film. This completes the structure shown in Figure 2(A).
[0031] (Modification) Figure 3 illustrates a method of controlling the concentration distribution of ion implantation by changing the pattern coverage of the mask 80, but the method is not limited to this. For example, as shown in Figure 4, it is also possible to control the concentration distribution of ion implantation by changing the thickness of the mask 80. Parts common to Figures 3 and 4 are given the same reference numerals, and their explanation is omitted.
[0032] As shown in Figure 4(A), a line pattern 80La is arranged within the opening OP. The line pattern 80La extends in the longitudinal direction (y-direction). The mask 80 has a thickness MT1. The line pattern 80La has a thickness MT2. Thickness MT2 is smaller than thickness MT1. Such a line pattern 80La can be fabricated by using a grayscale mask and varying the exposure dose between the space region SP and the line pattern 80La. Furthermore, the coverage of the line pattern 80La is adjusted so that the coverage is lower towards the center in the width direction than towards the edges in the width direction. In this embodiment, the coverage towards the center is reduced by placing the space region SP at the center position CP.
[0033] Figure 4(B) shows the concentration distribution ID2 of the ion implantation amount by the ion implantation process (step S20). The implantation concentration in the space region SP is higher than the implantation concentration in the line pattern 80La. This is because in the region where the space region SP is formed, all of the irradiated ions are implanted into the surface 10f, but in the region where the line pattern 80La is formed, only a portion of the irradiated ions are implanted into the surface 10f. This makes it possible to set the concentration distribution of the color center 12 so that the center side in the width direction is higher than the edge side in the width direction (see Figure 2(B)).
[0034] Example 2 describes a configuration in which the density distribution of the color center 12 is lower towards the center in the width direction than towards the edges in the width direction. Parts common to Examples 1 and 2 are given the same reference numerals, and their explanation is omitted.
[0035] Figure 5(B) shows the density distribution CD2 of the color center 12 within the waveguide region WR. The density distribution CD2 of the color center 12 is lower towards the center in the width direction than towards the edges in the width direction. The density distribution CD2 reaches its maximum value CDmax near the edges 11e1 and 11e2. Figure 5(D) shows the signal intensity distribution DD2 of the sensor signal. The intensity of the sensor signal is approximately constant throughout the width direction of the waveguide 11.
[0036] Let's explain the effects. The electric field strength distribution ED of the microwave MW is higher towards the center in the width direction of the waveguide 11 than towards the ends in the width direction (see Figure 5(C)). In the technology of Example 2, the density distribution CD2 of the color center 12 is lower towards the center in the width direction of the waveguide 11 than towards the ends in the width direction (see Figure 5(B)). This makes it possible to reverse the trend of the electric field strength distribution ED of the microwave MW and the trend of the density distribution CD2 of the color center 12. Therefore, the density of the color center 12 can be increased in regions where the microwave MW intensity is weak. As a result, the intensity of the sensor signal (change in emission intensity) can be made substantially uniform across the entire width direction. Even when the irradiation position of the excitation light EL changes within the width W1 of the waveguide 11, the intensity of the sensor signal can be kept substantially constant. Therefore, it is possible to stabilize the detection sensitivity of the physical quantity detection device 1.
[0037] Although specific examples of the present invention have been described in detail above, these are merely illustrative and do not limit the scope of the claims. The technologies described in the claims include various modifications and changes to the specific examples illustrated above. Furthermore, the technical elements described in this specification or drawings exhibit technical usefulness individually or in various combinations, and are not limited to the combinations described in the claims at the time of filing. In addition, the technologies illustrated in this specification or drawings can achieve multiple objectives simultaneously, and achieving even one of these objectives itself constitutes technical usefulness.
[0038] (Modified Version) Figure 6 shows a modified physical quantity detection device 101. The modified physical quantity detection device 101 further includes a spectroscopic unit 90 compared to the physical quantity detection device 1 of this embodiment. The spectroscopic unit 90 is a part that spectrally separates the excitation light EL and the emission light LU. The spectroscopic unit 90 may be, for example, a dichroic mirror or a beam splitter. The excitation light EL output from the excitation light irradiation unit 20 passes through the spectroscopic unit 90 and irradiates the substrate 10. The emission light LU output from the color center 12 is reflected by the spectroscopic unit 90 and input to the photodetector 40. This makes it possible to make the paths of the excitation light EL and the emission light LU different, thereby increasing the degree of freedom in the layout of the excitation light irradiation unit 20 and the photodetector 40. The spectroscopic unit 90 is located between the excitation light irradiation unit 20 and the lens 70.
[0039] The physical quantity detection devices 1 and 101 do not necessarily need to be equipped with a lens 70.
[0040] In this embodiment, SiC was used as the substrate with color centers, but the embodiment is not limited to this, and various substrates can be used. For example, the substrate may be diamond, GaN single crystal, hBN, etc.
[0041] In this embodiment, the case in which silicon vacancies of 4H-SiC are used as color centers has been described, but the embodiment is not limited to this, and various color centers can be used. For example, Frenkel defects of 6H-SiC may be used as color centers.
[0042] The following are embodiments of the present technology. [Embodiment 1] A physical quantity detection device comprising: a substrate having a plurality of color centers; a waveguide disposed on a first surface of the substrate and irradiated with microwaves; an irradiation unit that irradiates excitation light from a second surface located opposite to the first surface of the substrate; and a detection unit that detects the emission state of the color centers from the second surface side, wherein the waveguide is made of a conductive film, the waveguide extends in a longitudinal direction and has a width direction perpendicular to the longitudinal direction, and the irradiation unit is configured to irradiate excitation light to the center position in the width direction of the waveguide. [Embodiment 2] The physical quantity detection device according to Embodiment 1, wherein the waveguide is a metal film. [Embodiment 3] The physical quantity detection device according to Embodiment 1 or 2, wherein in a region perpendicularly projected of the waveguide onto the first surface of the substrate, the density distribution of the color centers is higher on the center side in the width direction than on the end side in the width direction. [Aspect 4] The physical quantity detection device according to aspect 1 or 2, wherein in a region where the waveguide is projected perpendicularly onto the first surface of the substrate, the density distribution of the color center is lower on the center side in the width direction than on the edge side in the width direction. [Aspect 5] The physical quantity detection device according to any one of aspects 1 to 4, further comprising a lens disposed between the irradiation unit and the substrate, wherein the lens is configured to control the irradiation position of the excitation light output from the irradiation unit to the center position of the waveguide. [Aspect 6] The physical quantity detection device according to any one of aspects 1 to 5, further comprising an oscillation unit connected to the waveguide and configured to generate microwaves. [Aspect 7] The physical quantity detection device according to any one of aspects 1 to 6, wherein the substrate is one of SiC, diamond, or GaN single crystal.[Aspect 8] A method for manufacturing a substrate having a plurality of color centers, comprising: a step of forming a mask on a first surface of the substrate having an opening corresponding to a waveguide to which microwaves are irradiated; an implantation step of implanting ions into the first surface of the substrate through the mask; and a step of forming a conductive film in a region of the first surface to which the ions were implanted by the implantation step, wherein the opening extends in the longitudinal direction and has a width direction perpendicular to the longitudinal direction, and the concentration distribution of the amount of ions implanted in the implantation step is higher on the center side in the width direction than on the edge side in the width direction, or lower on the center side in the width direction than on the edge side in the width direction. [Aspect 9] The method for manufacturing a substrate according to aspect 8, wherein the mask has a plurality of line patterns arranged in the opening, each of the plurality of line patterns extends in the longitudinal direction and is adjacent to the width direction with space between them, and the coverage of the plurality of line patterns is lower on the center side in the width direction than on the edge side in the width direction, or higher on the center side in the width direction than on the edge side in the width direction. [Aspect 10] The method for manufacturing a substrate according to aspect 8, wherein the mask is provided with a line pattern disposed within the opening, the line pattern extends in the longitudinal direction, the thickness of the line pattern is less than the thickness of the mask, and the coverage of the line pattern is lower on the center side in the width direction than on the edge side in the width direction, or higher on the center side in the width direction than on the edge side in the width direction.
Claims
1. A physical quantity detection device comprising: a substrate having a plurality of color centers; a waveguide disposed on a first surface of the substrate and irradiated with microwaves; an irradiation unit that irradiates excitation light from a second surface located opposite to the first surface of the substrate; and a detection unit that detects the light emission state of the color centers from the second surface side, wherein the waveguide is made of a conductive film, the waveguide extends in a longitudinal direction and has a width direction perpendicular to the longitudinal direction, and the irradiation unit is configured to irradiate excitation light to the central position in the width direction of the waveguide.
2. The physical quantity detection device according to claim 1, wherein the waveguide is a metal film.
3. The physical quantity detection device according to claim 1, wherein, in a region where the waveguide is projected perpendicularly onto the first surface of the substrate, the density distribution of the color center is higher towards the center in the width direction than towards the edges in the width direction.
4. The physical quantity detection device according to claim 1, wherein, in the region obtained by projecting the waveguide perpendicularly onto the first surface of the substrate, the density distribution of the color center is lower towards the center in the width direction than towards the edges in the width direction.
5. The physical quantity detection device according to any one of claims 1 to 4, further comprising a lens disposed between the irradiation unit and the substrate, wherein the lens is configured to control the irradiation position of the excitation light output from the irradiation unit to the center position of the waveguide.
6. The physical quantity detection device according to claim 1, further comprising an oscillator connected to the waveguide and configured to generate microwaves.
7. The physical quantity detection device according to claim 1, wherein the substrate is one of SiC, diamond, or GaN single crystal.
8. A method for manufacturing a substrate having a plurality of color centers, comprising: a step of forming a mask on a first surface of the substrate having an opening corresponding to a waveguide to which microwaves are irradiated; an implantation step of implanting ions into the first surface of the substrate through the mask; and a step of forming a conductive film in a region of the first surface into which the ions were implanted by the implantation step, wherein the opening extends in the longitudinal direction and has a width direction perpendicular to the longitudinal direction, and the concentration distribution of the amount of ions implanted in the implantation step is higher on the center side in the width direction than on the edge side in the width direction, or lower on the center side in the width direction than on the edge side in the width direction.
9. The method for manufacturing a substrate according to claim 8, wherein the mask comprises a plurality of line patterns arranged within the opening, each of the plurality of line patterns extending in the longitudinal direction and adjacent to each other with space in the width direction, and the coverage of the plurality of line patterns is lower on the center side in the width direction than on the edge side in the width direction, or higher on the center side in the width direction than on the edge side in the width direction.
10. The method for manufacturing a substrate according to claim 8, wherein the mask comprises a line pattern disposed within the opening, the line pattern extends in the longitudinal direction, the thickness of the line pattern is less than the thickness of the mask, and the coverage of the line pattern is lower on the center side in the width direction than on the edge side in the width direction, or higher on the center side in the width direction than on the edge side in the width direction.