Silicon nitride substrate and cooling device

Abstract

This silicon nitride substrate comprises a first surface including a region of 40 mm in length × 40 mm in width. When sinusoidal surface components having a wavelength of 10 mm or more are removed from the uneven shape of the region, the total number of protrusions having a height of 5 μm or more from a reference surface, which is an average height, and recesses having a depth of 5 μm or more from the reference surface is 60 or less.

Description

Silicon nitride substrate and cooling device

[0001] The present disclosure relates to silicon nitride substrates and cooling devices.

[0002] Japanese Patent Application Laid-Open No. 2000-72552 describes a silicon nitride heat dissipating member that prevents a decrease in strength and has high thermal conductivity.

[0003] A silicon nitride substrate according to one embodiment of the present disclosure has a first surface including an area of ​​40 mm length x 40 mm width, and when a sinusoidal curved surface component of 10 mm or more is removed from the uneven shape of said area, the total number of convex portions having an average height of 5 μm or more from a reference plane and concave portions having a depth of 5 μm or more from the reference plane is 60 or less.

[0004] Another aspect of the present disclosure provides a silicon nitride substrate having a first surface including an area measuring 40 mm in length and 40 mm in width, wherein when the center points of all convex portions and all concave portions are extracted as a plurality of center points from the uneven shape of the area, the number of center points among the plurality of center points that satisfy a first condition is 60 or less, and the first condition is such that when a range of a radius of 5 mm from the target center point is called a first section, and a plane that smooths out the unevenness of the first section is called a reference plane, the difference between the maximum height and minimum height of the first section from the reference plane is 10 μm or more.

[0005] A cooling device according to the present disclosure includes the silicon nitride substrate described above, and a heat sink that absorbs heat from the silicon nitride substrate.

[0006] FIG. 1 is a plan view showing a silicon nitride substrate according to an embodiment of the present disclosure. FIG. 2 is a side view showing a silicon nitride substrate according to an embodiment of the present disclosure. FIG. 3 is a diagram explaining a method for counting concaves and convexes in region R1, showing a cross-sectional curve of a partial section of region R1. FIG. 4 is a diagram explaining a method for counting concaves and convexes in region R1, showing a cross-sectional curve of the section after removing a curved surface component of a specific sine wave. FIG. 5 is a diagram explaining a method for counting concaves and convexes in region R1, showing the heights of convex portions and concave portions from a reference plane L1. FIG. 6 is a diagram explaining a method for counting center points in region R1 that satisfy a first condition. FIG. 7 is a diagram explaining a method for counting center points in region R1 that satisfy a first condition. FIG. 8 is a diagram explaining one step for manufacturing a silicon nitride substrate 1 according to an embodiment. FIG. 9 is a diagram showing a comparative example of a step for manufacturing a silicon nitride substrate 1 according to an embodiment. FIG. 10 is a graph showing the relationship between the amount of concaves and convexes of a silicon nitride substrate and cooling performance. FIG. 11 is a diagram showing a configuration for a simulation. FIG. 12 is a diagram showing a cooling device according to an embodiment of the present disclosure.

[0007] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. Figures 1A and 1B are a plan view and a side view showing a silicon nitride substrate according to an embodiment of the present disclosure. In the plan view of Figure 1A, minute irregularities on the first surface 11 are shown by contour lines. The contour lines conceptually show the irregularities and do not correspond to actual irregularities.

[0008] The silicon nitride substrate 1 is made of silicon nitride (Si ３ N ４ ) as the main component. The term "main component" refers to a component having a mass ratio of 80% or more. This configuration achieves high insulation, high strength, and high thermal conductivity. With this configuration, the silicon nitride substrate 1 is positioned between a heat source that passes current, such as a semiconductor element for power control, and a heat sink, thereby enabling a large amount of heat to be conducted from the heat source to the heat sink while maintaining insulation between the heat source and the heat sink.

[0009] The silicon nitride substrate 1 may have a first surface 11 including a region R1 measuring 40 mm long x 40 mm wide. The entire first surface 11 may be region R1. The size of region R1 is such that it can almost completely cover a heat source, such as a semiconductor element for power control, from one side, making it easy to apply to a configuration that receives a large amount of heat from the heat source.

[0010] The silicon nitride substrate 1 may have a second surface 12 on the opposite side of the first surface 11, and may have a thin plate thickness from the first surface 11 to the second surface 12. The plate thickness may be selected to be thin enough to reduce thermal resistance without losing the desired strength and insulating properties. For example, the plate thickness may be 0.1 mm to 10 mm.

[0011] The region R1 of the silicon nitride substrate 1 may have minute irregularities.

[0012] <Details of Irregularities 1-1> The irregularities in region R1 may be configured to satisfy the following requirement 1. [Requirement 1] When curved surface components of a sine wave having a wavelength of 10 mm or more are removed from the irregularity shape of region R1, the total number of convex portions 21ex having an average height of 5 μm or more from reference plane L1 and concave portions 23ex having an average depth of 5 μm or more from reference plane L1 is 60 or less.

[0013] 2A to 2C are diagrams illustrating an example of a method for counting the convex portions 21ex and concave portions 23ex. FIG. 2A shows the cross-sectional curve of one section of the original uneven surface of region R1, and FIG. 2B shows the cross-sectional curve of the same section after removing the curved surface component of the sine wave f1 with a wavelength of 10 mm or more. FIG. 2A shows the sine wave f1 with a wavelength of 10 mm. FIG. 2C shows the heights h21 and h23 of the convex portions 21 and concave portions 23 from the reference plane L1. The cross-sectional curves in FIGS. 2A to 2C are conceptually shown for the purpose of explaining the above-described counting method and do not correspond to the actual convex and concave portions of the silicon nitride substrate 1. Furthermore, the aspect ratios are altered to make the convex and concave portions more noticeable. The cross-sectional curves in FIGS. 2A to 2C are not cross-sections along a straight cross-sectional line, but rather cross-sections along a curved cross-sectional line that passes through the centers of several convex portions 21 and concave portions 23 included in region R1. The reference plane L1 in FIG. 2C is a plane that is substantially along the irregular surface after removing the sinusoidal curved surface component of 10 mm or more, and may be, for example, a regression plane of the irregular surface.

[0014] 2A to 2C show the unevenness on one cross-sectional curve and the processing for that cross-sectional curve. However, in practice, by measuring and analyzing the two-dimensional curved surface of region R1, it is possible to similarly remove the curved surface components of a sine wave f1 with a wavelength of 10 mm or more from the two-dimensional curved surface and calculate the reference plane L1. Removing the curved surface components of the sine wave means removing all of the curved surface components if the curved surface components are sine waves with a wavelength of 10 mm or more and include multiple curved surface components. Once the uneven surface and reference plane L1 are determined as shown in FIG. 2C, the heights h21 and h23 of each convex portion 21 and each concave portion 23 from the reference plane L1 can be calculated to count the convex portions 21ex and concave portions 23ex required by requirement 1.

[0015] Gentle unevenness, such as a sinusoidal curve with a wavelength of 10 mm or more, can be reduced by pressing the silicon nitride substrate 1 against a heat source. Furthermore, even if the silicon nitride substrate 1 is pressed against the heat source to reduce the gentle unevenness, stress concentration on the silicon nitride substrate 1 is unlikely. On the other hand, it is difficult to reduce steep unevenness with sinusoidal curve components with a wavelength of 10 mm or less by pressing the silicon nitride substrate 1 against the heat source to avoid stress concentration. The remaining unevenness creates a gap between the heat source and the silicon nitride substrate 1. The gap can be filled with, for example, thermally conductive grease, but if the gap is large, the thermal conductive grease becomes thicker, increasing thermal resistance. Therefore, a configuration that satisfies requirement 1 can suppress the increase in thermal resistance due to unevenness and achieve the desired cooling performance of the heat source.

[0016] <Details of Irregularities 1-2> The irregularities in the region R1 may be configured to satisfy the following requirement 2 in addition to requirement 1: [Requirement 2] The total number of the above-mentioned convex portions 21ex and concave portions 23ex is 10 or more.

[0017] In general, it is convenient to store a plurality of silicon nitride substrates 1 in a stacked state prior to assembly of a device using the silicon nitride substrates 1. However, if the flatness of region R1 is too high, the silicon nitride substrates 1 will adhere to each other when multiple substrates are stacked, creating the problem that the silicon nitride substrates 1 cannot be easily removed one by one. On the other hand, by satisfying requirement 2, it becomes possible to easily remove the silicon nitride substrates 1 one by one from a stacked state.

[0018] <Details of unevenness 1-3> The unevenness of region R1 may be configured to satisfy the following requirement 3 in addition to requirement 1. Furthermore, the unevenness of region R1 may be configured to satisfy the following requirement 3 in addition to requirements 1 and 2. [Requirement 3] When the curved surface component of a sine wave having a wavelength of 10 mm or more is removed, the difference between the maximum height of the convex portion 21 and the minimum height of the concave portion 23 is 30 μm or less.

[0019] Generally, when the flat surface of a heat source is pressed against region R1, stress may concentrate in areas where the difference in unevenness between the convex and concave portions is steep and large. However, if the size of the convex and concave portions satisfies requirement 3, the above-mentioned stress concentration can be reduced. Furthermore, because stress concentration can be reduced, the thickness of silicon nitride substrate 1 can be reduced while maintaining its fracture resistance.

[0020] <Details of Irregularities 2-1> The irregularities of region R1 may be configured to satisfy the following requirement 4. Requirement 4 may be substituted for the above-mentioned requirement 1. [Requirement 4] When the central points p1, p2... (see FIG. 3A) of all convex portions 21 and the central points n1, n2... (see FIG. 3A) of all concave portions 23 are extracted as a plurality of central points p1, p2..., n1, n2... from the irregular shape of region R1, the number of central points p1, p2..., n1, n2... that satisfy the following first condition is 60 or less among the plurality of central points p1, p2..., n1, n2...

[0021] First condition: When the range of 5 mm radius from the center point of the object (center point n1 in the example of Figure 3A) is called the first section R11, and the plane that smooths out the unevenness of the first section R11 is called the reference plane L11, the difference Δh between the maximum height hmax and the minimum height hmin from the reference plane L11 in the first section R11 is 10 μm or more.

[0022] 3A and 3B show an example of a method for counting the central points under requirement 4. FIG. 3A is an explanatory diagram that associates the positions of a plan view of a first section R11, which is within a 5 mm radius from the central point n1 included in region R1, with the cross-sectional curve along line A-A of the plan view. FIG. 3B shows the cross-sectional curve of FIG. 3A when the reference plane L11 is horizontal. Line A-A is set so as to pass near the central points p1 and p2 of several convex portions 21 included in first section R11 and the central points n1 to n3 of the concave portions 23.

[0023] Next, an example of a method for counting the center points in the above requirement 4 will be described. First, the two-dimensional curved surface of region R1 in FIG. 1B is measured and analyzed, and points where the gradient in the X direction and the gradient in the Y direction are approximately zero are extracted as center points p1, p2, ..., n1, n2, ... (see the plan view in the upper part of FIG. 3A). Next, one of the center points p1, p2, ..., n1, n2, ... is selected as the center point of the object. FIG. 3A shows an example in which center point n1 is selected as the center point of the object. After selection, a first section R11 with a radius of 5 mm and centered on the center point n1 of the object is set. Next, a reference plane L11 is set on the two-dimensional curved surface of first section R11, as shown in the cross-sectional curve in the lower part of FIG. 3A. The reference plane L11 is a plane that approximately follows the uneven surface of first section R11 and may be, for example, a regression plane of the uneven surface. If the first section R11 has an overall slope, the reference plane L11 will be a plane with an inclination. After the reference plane L11 is set, as shown in FIG. 3B , the uneven surface of the first section R11 is re-analyzed as an uneven surface when the reference plane L11 is horizontal. The point with the maximum height hmax and the point with the minimum height hmin are determined, and the height difference Δh between these two points is calculated. If the difference Δh is 10 μm or greater, the target center point n1 is counted as a center point that satisfies the first condition. This counting is then performed in the same manner for each of the center points p1, p2, ..., n1, n2, ..., to determine the number of center points that satisfy the first condition in requirement 4.

[0024] Height differences occurring in an area larger than one first section R11 correspond to height differences due to gentle unevenness. On the other hand, height differences occurring within one first section R11 correspond to height differences due to steep unevenness. Gentle unevenness can be reduced by pressing the silicon nitride substrate 1 against the heat source without concentrating stress. On the other hand, it is difficult to reduce steep unevenness by pressing in the manner described above. If the unevenness remaining between the silicon nitride substrate 1 and the heat source is large, thermal resistance increases. Therefore, by a configuration that satisfies requirement 4, the number of large steep unevennesses is 60 or less, suppressing the increase in thermal resistance due to unevenness and achieving the desired cooling performance of the heat source.

[0025] <Details of the Concave and Convex Shapes 2-2> The concave and concave shapes of the region R1 may be configured to satisfy the following requirement 5 in addition to requirement 4: [Requirement 5] The number of center points that satisfy the above-mentioned condition 1 is 10 or more.

[0026] The configuration that satisfies requirement 5 can reduce adhesion between a plurality of stacked silicon nitride substrates 1. This makes it possible to easily remove the silicon nitride substrates 1 one by one from a stack of multiple substrates, which is convenient when assembling devices that use silicon nitride substrates 1 as components.

[0027] <Details of unevenness 2-3> The unevenness of region R1 may be configured to satisfy the following requirement 6 in addition to requirement 4. Furthermore, the unevenness of region R1 may be configured to satisfy the following requirement 6 in addition to requirements 4 and 5. [Requirement 6] The maximum value of the difference Δh between the maximum height hmax and the minimum height hmin from the reference plane L11 in the first section R11 is 30 μm or less.

[0028] If the size of the unevenness satisfies requirement 6, it is possible to reduce the concentration of stress that occurs at the unevenness when the flat portion of the heat source is pressed against region R1, which in turn allows the thickness of silicon nitride substrate 1 to be reduced while maintaining its fracture resistance.

[0029] The unevenness of the region R1 in the above requirements 1 to 6 can be measured using a three-dimensional measuring device VR-6000 manufactured by Keyence Corporation.

[0030] <Method of manufacturing silicon nitride substrate 1> Fig. 4A is a diagram illustrating one step for manufacturing the silicon nitride substrate 1 of the embodiment. Fig. 4B is a diagram illustrating a comparative example of the step. Figs. 4A and 4B show the state of the silicon nitride substrate 1 of the embodiment and the silicon nitride substrate of the comparative example during firing.

[0031] The silicon nitride substrate 1 can be manufactured, for example, by the following process. First, various powders of ceramic materials are mixed with a liquid to form a slurry, and the slurry is molded into a tape-shaped ceramic green tape. Next, the ceramic green tape is cut into small ceramic green tapes 40, and multiple ceramic green tapes 40 are coated with an undercoat and then stacked together.

[0032] In the powder coating, as shown in FIG. 4A, spherical powder 51 having an average particle size of more than 20 μm and not more than 30 μm may be used. In this powder coating, spherical powder 51 having a ratio of minor axis to diameter (minor axis / diameter) of 0.5 to 1 may be used. When a scaly powder 85 is used, as in the comparative example of FIG. 4B, protrusions may occur in some parts of the powder, resulting in steep and large irregularities on the ceramic green tape 40. However, by using the above-described powder 51, the size of the irregularities on the surface of the ceramic green tape 40 can be reduced.

[0033] Next, the stacked ceramic green tapes 40 are degreased and fired to produce a plurality of ceramic plates, which are then separated into individual pieces, cleaned, and divided into a plurality of pieces according to the dimensions of the individual silicon nitride substrates 1.

[0034] The individual silicon nitride substrates 1 are inspected for shape and electrical properties, and then packed and shipped in a stacked state as a plurality of silicon nitride substrates 1. In inspecting the shape, an inspection of unevenness may be performed to determine whether the above-mentioned requirements 1 to 3 or requirements 4 to 6 are satisfied.

[0035] It should be noted that each step of the above manufacturing method is not essential for manufacturing the silicon nitride substrate 1 of the embodiment, and the silicon nitride substrate 1 of the embodiment can also be manufactured by applying various other steps.

[0036] In addition, when inspecting the unevenness of requirement 1, the following alternative method may be applied instead of the calculation process of removing the curved surface component of the sine wave f1 with a wavelength of 10 mm or more from the original uneven surface of the region R1. ２ Alternatively, the surface may be divided into a plurality of areas, each of which has an average height, and a reference plane having an average height for each area may be set. The number of convex portions and concave portions each of which has an average height of 5 μm or more from the reference plane may then be counted. The total number of counts for all areas may then be regarded as the total number for requirement 1.

[0037] <Cooling Performance> Fig. 5 is a graph showing the relationship between the amount of unevenness on a silicon nitride substrate and cooling performance. The graph in Fig. 5 was obtained by simulation. Fig. 6 is a diagram showing the configuration for the simulation. In the simulation, a configuration was adopted in which a heat source 61, a copper (Cu) plate 62, grease 63, a silicon nitride substrate 64, grease 65, and an aluminum (Al) plate 66 were stacked in this order. Furthermore, in the heat source 61, the heat generation rate was set to 40 W / mm ３ The dimensions of the heat source 61 were 2 mm x 2 mm x 0.5 mm (t denotes thickness), and the heat generation rate per unit time was 80 W. The length and width of the other components were 40 mm x 40 mm, with thicknesses of 0.5 mm for the copper plate 62, 0.05 mm for the greases 63 and 65, 0.3 mm for the silicon nitride substrate 64, and 2.0 mm for the aluminum plate 66. The temperature of one end surface S66 of the aluminum plate 66 (i.e., the end surface S66 opposite the heat source 61) was fixed at 25°C. The thermal conductivity of each component was 168 W / mK, the same as that of silicon, for the heat source 61, 400 W / mK for the copper plate 62, 4 W / mK for the greases 63 and 65, 70.5 W / mK for the silicon nitride substrate 64, and 210 W / mK for the aluminum plate 66.

[0038] In the simulation, the saturation temperature of the heat source 61 was calculated for multiple cases in which multiple silicon nitride substrates 64 with different amounts of surface roughness were used. Recesses 645, each 3 mm in diameter and 5 μm thick, were provided on the first surface 641 of the silicon nitride substrate 64 at uniform intervals, while the number of recesses 645 on one surface was varied to 36, 44, 64, 79, and 100. The second surface 642 was the same as the first surface 641. The horizontal axis of the graph in Figure 5 represents the number of recesses 645 on one surface.

[0039] As shown in the graph of FIG. 5, by setting the number of recesses 645 to 60 or less, the result was that the junction temperature did not greatly exceed 150° C., which is specified as the maximum rating of the junction temperature in many semiconductor products.

[0040] The configuration applied to the simulation in Fig. 6 reproduces the same cooling conditions as those of a configuration for cooling semiconductor components for power control. The simulation results in Fig. 5 show that the desired cooling performance for semiconductor components for power control can be obtained by applying a silicon nitride substrate 1 that satisfies the above-mentioned requirement 1 or requirement 4.

[0041] (Cooling Device) FIG. 7 is a diagram illustrating a cooling device 100 according to an embodiment of the present disclosure. The cooling device 100 of this embodiment includes a silicon nitride substrate 1 according to the embodiment and a heat sink 110 that absorbs heat through the silicon nitride substrate 1. The heat sink 110 has a flow path 111 through which a coolant flows, but may be configured to dissipate heat in any manner, such as by being air-cooled with fins or the like. The silicon nitride substrate 1 may have a first surface 11 in contact with the heat source 200 and a second surface 12 in contact with the heat sink 110. Contact includes contact via thermally conductive grease. While FIG. 7 illustrates a configuration in which the silicon nitride substrate 1 and the heat sink 110 are located on one side of the heat source 200, a configuration may also be adopted in which multiple sets of silicon nitride substrates 1 and heat sinks 110 are provided, and the heat source 200 is sandwiched between the multiple sets of silicon nitride substrates 1 and heat sinks 110. In this case as well, a configuration may be adopted in which each silicon nitride substrate 1 is in contact with the heat source 200 and the heat sink 110 is located on the side of each silicon nitride substrate 1 opposite to the heat source 200 .

[0042] According to the cooling device 100 of this embodiment, it is easy to remove individual silicon nitride substrates 1 during assembly, thereby improving the efficiency of the manufacturing process. Furthermore, by having the unevenness on the first surface 11 or the second surface 12 of the silicon nitride substrate 1 satisfy requirement 1 or requirement 4, it is possible to improve the adhesion between the heat source 200 or the silicon nitride substrate 1 and the heat source 200, or between the silicon nitride substrate 1 and the heat sink 110, while maintaining the fracture resistance of the silicon nitride substrate 1. The improved adhesion allows the intervening thermally conductive grease to be thinner, thereby reducing the thermal resistance in the heat conduction path from the heat source 200 to the heat sink 110 and achieving the desired cooling performance.

[0043] The embodiments of the present disclosure have been described above. However, the silicon nitride substrate and cooling device of the present disclosure are not limited to the silicon nitride substrate 1 and cooling device 100 shown in the embodiments, and can be modified as appropriate without departing from the spirit of the invention. For example, in the above embodiment, the first surface 11 and the second surface 12 of the silicon nitride substrate 1 have the same configuration, but the second surface 12 may have different unevenness conditions from the first surface 11.

[0044] In one embodiment, (1) a silicon nitride substrate has a first surface including an area of ​​40 mm length x 40 mm width, and when a curved surface component of a sine wave having a wavelength of 10 mm or more is removed from the uneven shape of the area, the total number of convex portions having an average height of 5 μm or more from a reference plane and concave portions having a depth of 5 μm or more from the reference plane is 60 or less.

[0045] (2) In the silicon nitride substrate of (1) above, the total number of the convex portions and concave portions is 10 or more.

[0046] (3) In the silicon nitride substrate of (1) or (2) above, the difference between the maximum height and the minimum height when the curved surface component of a sine wave having a wavelength of 10 mm or more is removed from the uneven shape of the region is 30 μm or less.

[0047] (4) A silicon nitride substrate has a first surface including an area of ​​40 mm length x 40 mm width, and when the center points of all convex portions and all concave portions are extracted as a plurality of center points from the uneven shape of the area, the number of center points among the plurality of center points that satisfy a first condition is 60 or less, and the first condition is that when a range of a radius of 5 mm from the target center point is called a first section, and a plane that smooths out the unevenness of the first section is called a reference plane, the difference between the maximum height and the minimum height of the first section from the reference plane is 10 μm or more.

[0048] (5) In the silicon nitride substrate of (4) above, the number of the central points that satisfy the first condition is 10 or more.

[0049] (6) In the silicon nitride substrate of (4) or (5) above, the maximum difference between the maximum height and the minimum height from the reference plane in the first section is 30 μm or less.

[0050] (7) A cooling device includes: the silicon nitride substrate according to any one of (1) to (6) above; and a heat sink that absorbs heat through the silicon nitride substrate.

[0051] The present disclosure can be used in silicon nitride substrates and cooling devices.

[0052] REFERENCE SIGNS LIST 1 silicon nitride substrate 11 first surface 12 second surface 21, 21ex convex portion 23, 23ex concave portion 40 ceramic green tape 51 powder spread 100 cooling device 110 heat sink 111 flow path 200 heat source L1, L11 reference surface p1, p2, n1, n2, n3 center point R1 region R11 first section

Claims

1. A silicon nitride substrate having a first surface including an area of ​​40 mm length x 40 mm width, wherein when the curved surface component of a sine wave with a wavelength of 10 mm or more is removed from the uneven shape of said area, the total number of convex portions whose height from a reference plane (average height) is 5 μm or more and concave portions whose depth from the reference plane is 5 μm or more is 60 or less.

2. The silicon nitride substrate according to claim 1, wherein the total number of said projections and recesses is 10 or more.

3. A silicon nitride substrate according to claim 1 or 2, wherein the difference between the maximum height and the minimum height when a sinusoidal curved surface component having a wavelength of 10 mm or more is removed from the uneven shape of said region is 30 μm or less.

4. A silicon nitride substrate having a first surface including an area of ​​40 mm length x 40 mm width, wherein when the center points of all convex portions and all concave portions are extracted as multiple center points from the uneven shape of said area, the number of center points among said multiple center points that satisfy a first condition is 60 or less, and said first condition is that when a range of 5 mm radius from said target center point is called a first section, and a plane that smooths out the unevenness of said first section is called a reference plane, the difference between the maximum height and minimum height of said first section from said reference plane is 10 μm or more.

5. The silicon nitride substrate according to claim 4, wherein the number of said central points that satisfy said first condition is 10 or more.

6. A silicon nitride substrate according to claim 4 or claim 5, wherein the maximum difference between the maximum height and the minimum height from the reference plane in said first section is 30 μm or less.

7. A cooling device comprising: a silicon nitride substrate according to any one of claims 1 to 6; and a heat sink that absorbs heat through the silicon nitride substrate.

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