Sensor element with four contact surfaces and three plated through holes

By optimizing the position of the plated through holes and the layout of the insulating layer, the problem of insufficient mechanical stress load of ceramic sensor elements was solved, thereby improving the mechanical stability and resistance to external stress of the sensor.

CN115885175BActive Publication Date: 2026-06-30ROBERT BOSCH GMBH

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
ROBERT BOSCH GMBH
Filing Date
2021-06-14
Publication Date
2026-06-30

AI Technical Summary

Technical Problem

Existing ceramic sensor elements have insufficient mechanical stress load capacity in the setting of plated through holes, especially when the plated through holes are close to the sensor end and outer edge, resulting in mechanical weakening.

Method used

By adjusting the position and spacing of the plated through holes to form an isosceles triangular layout in the axial and lateral directions, and reducing the use of insulation layers in the sensor end region, mechanical weakening can be reduced.

Benefits of technology

It improves the mechanical stress load capacity of sensor elements, enhances resistance to external mechanical stress, and reduces stress concentration caused by leverage effect.

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Abstract

This invention relates to a sensor element (10) having four contact surfaces and three plated through-holes, the sensor element being used, for example, as a λ probe. Measures are proposed to improve the load-bearing capacity of the sensor element relative to mechanical stress. These measures particularly relate to the arrangement of the plated through-holes and the design of the insulating layer within the sensor element.
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Description

Background Technology

[0001] Ceramic sensor elements for λ probes are known from the prior art, such as DE 10 2018 206 966 A1, which have the features of the preamble of claim 1. DE 10 2018 206966 A1 is also based on efforts to improve the load-bearing capacity of sensor elements relative to mechanical stress. Summary of the Invention

[0002] The present invention further aims to improve the load-bearing capacity of sensor elements relative to mechanical stress.

[0003] Here, the inventors have first recognized that, in the case of the ceramic sensor element as described in the preamble of claim 1, the mechanical weakening of the sensor element in the end region away from the exhaust gas is caused by the arrangement of the first, second, and third plated through holes.

[0004] Furthermore, the inventors recognized that when the plated through-holes are close to each other, this further weakens the mechanism. In this case, the individual weakening caused by each plated through-hole increases further in total.

[0005] Furthermore, the inventors recognized that when one or more plated through-holes are located close to the outer edge of the sensor element in the lateral direction, this mechanical weakening is further caused. In this case, the sensor element's resistance to mechanical stress from the outer edge of the sensor element is reduced.

[0006] Furthermore, the inventors recognized that when the plated through-holes are spaced relatively far from the axial end of the sensor element away from the exhaust gas, this mechanical weakening is further exacerbated. In this case, a large leverage effect becomes effective in the region of the plated through-holes due to the force acting in the layer direction on the axial end of the sensor away from the exhaust gas, thereby causing high mechanical stress there.

[0007] The inventors also recognized that further, in principle, mechanical weakening could arise from insulating layers disposed between the solid electrolyte layers, partly because these layers, in principle, disrupt the homogeneous layered structure formed by the solid electrolyte layers. Furthermore, the insertion of the insulating layers leads to mechanical stress due to the different sintering properties of the insulating and solid electrolyte layers.

[0008] The inventors recognized that this was especially true when the insulating layer extended in the lateral or axial direction up to the outer edge of the sensor element.

[0009] The inventors then discovered different possibilities on how to reduce or minimize these mechanical weakenings as a whole. Each of these possibilities is effective individually and, in particular, in combination.

[0010] Accordingly, in the case of the sensor element according to the preamble of claim 1, the second and third plated through-holes are both arranged axially on the exhaust gas side of the first plated through-hole, and the first plated through-hole is arranged transversely between the second and third plated through-holes. Compared with arrangements known in the prior art, this method increases the spacing between the plated through-holes without requiring them to be arranged excessively far from the axial end of the sensor element away from the exhaust gas. Furthermore, the spacing between the first plated through-hole and the outer edge of the sensor element is increased transversely.

[0011] When the second and third plated through-holes are arranged at the same axial height, and when the first plated through-hole is arranged laterally at the center between the second and third plated through-holes, such that the first, second, and third plated through-holes are located at the corners of an isosceles triangle, this is particularly applicable when the angle opposite the base of the isosceles triangle is no greater than 90° and no less than 30°. This is preferably, for example, an equilateral triangle.

[0012] Within the framework of this application, the location of the plated through-holes, and consequently the description of their relative positions, can be determined from the position of the centroid of the plated through-hole in a top view of the large surface of the sensor element. In the case of a circular plated through-hole in the top view of the large surface of the sensor, this position is the center of the relevant circle.

[0013] Additionally or alternatively, in the case of the sensor element according to the preamble of claim 1, the first plated through-hole, the second plated through-hole, and the third plated through-hole are completely arranged in the end region of the sensor element away from the exhaust gas, wherein the axial extension dimension of the end region of the sensor element away from the exhaust gas is less than one-fifth of the axial extension dimension of the sensor element. Based on the reduced leverage effect, the force acting in the layer direction at the axial end of the sensor element away from the exhaust gas causes only reduced stress in the region of the plated through-hole.

[0014] It can be proposed that the first plated through-hole is a first hole in the first solid electrolyte layer, the first hole having a first conductive material disposed in the first hole; the second plated through-hole is a second hole in the second solid electrolyte layer, the second hole having a second conductive material disposed in the second hole; and the third plated through-hole is a third hole in the second solid electrolyte layer, the third hole having a third conductive material disposed in the third hole, and the first hole has a first diameter, the second hole has a second diameter, and the third hole has a third diameter.

[0015] The aperture may, for example, be circular in a top view of the sensor element, such that the diameter of the aperture is the diameter of the associated circle. The three diameters referred to herein may, for example, be of the same size.

[0016] It can be proposed that, in a top view of the large surface of the sensor element, the centroid of the second hole and the centroid of the third hole are separated by a spacing scale a.

[0017] If, in the case of the sensor element described in the preamble of claim 1, it is proposed in this respect that the spacing scale a is less than the sum of the second diameter and the third diameter, and / or it is proposed that half of the spacing scale is less than the distance between the centroid of the second hole and the outer edge of the sensor element that is closest in the lateral direction, and / or it is proposed that half of the spacing scale is less than the distance between the centroid of the third hole and the outer edge of the sensor element that is closest in the lateral direction, then the spacing between the second and third plated through holes and each other, and relative to the spacing between the plated through holes and the outer edge of the sensor element, and relative to the hole diameter, is generally balanced and mechanically optimized in this respect.

[0018] If, in the case of a sensor element having the features of the preamble of claim 1, the centroid of the first hole is spaced axially from the first, second, third, and / or fourth contact surfaces at a distance not greater than half the diameter of the first hole, this means that the first hole is arranged axially particularly close to the contact surfaces and thus close to the exhaust-averse end of the sensor element. Based on the reduced leverage effect, the force acting in the layer direction at the exhaust-averse axial end of the sensor element causes only reduced stress in the region of the plated through-hole.

[0019] Alternatively or additionally, it may be proposed that the first contact surface has a concave outer contour facing the first plated through-hole in a top view of the large surface of the sensor element. The first plated through-hole can then be moved particularly far relative to the end of the sensor element away from the exhaust gas without contacting the first contact surface. Specifically, it is proposed that the concave outer contour has a radius equal to half the diameter of the first hole or differing from half the diameter of the first hole by no more than 50%. Alternatively or additionally, the concave outer contours of the first plated through-hole and the first contact surface may also be concentric.

[0020] Additionally or alternatively, in the case of the sensor element described in the preamble of claim 1, it may be proposed that an insulating layer or multiple insulating layers be arranged between the first and second solid electrolyte layers, such that a first electrical composite structure including a second electrode, a second conductor circuit, and a first plated via is electrically insulated relative to a second electrical composite structure through one or more insulating layers, the second electrical composite structure including a resistive heater rail, a third conductor circuit, a fourth conductor circuit, a second plated via, and a third plated via.

[0021] It can be proposed here that one or more insulating layers extend only to the required extent in the top view of the large surface of the sensor element to electrically insulate the first electrical composite structure relative to the second electrical composite structure, and are additionally surrounded by a sealing frame / each of the sealing frames, which are made of a solid electrolyte material. "Only" here can be particularly predicated on the following: one or more insulating layers extend beyond the structure to be insulated in the transverse direction and / or axial direction, determined by manufacturing, for example, by a maximum of 250 μm and / or by a maximum of 5% (but not greater than) the transverse extension scale of the sensor element beyond the structure to be insulated. The mechanical weakening of the sensor element is reduced to the minimum unavoidable for the desired electrical insulation.

[0022] A similar technical effect is caused by the following measure: the lateral extension of the sealing frame / all sealing frames, measured from the outer edge of the sensor element in the region away from the exhaust gas, is always greater than 1 / 10 of the lateral extension of the sensor element.

[0023] As with the case of materials used in solid electrolyte layers, the solid electrolyte material can be YSZ or similar materials.

[0024] Advantageously, a first insulating layer and a second insulating layer can be provided simultaneously, wherein, viewed from the second insulating layer, the first insulating layer is located on the side pointing towards the first solid electrolyte layer and the first electro-composite structure in the layer direction, and viewed from the first insulating layer, the second insulating layer is located on the side pointing towards the second solid electrolyte layer and the second electro-composite structure in the layer direction.

[0025] This can be configured such that a first insulating layer covers the second conductor circuit and the first, second, and third plated vias in a top view of the large surface of the sensor element, wherein the first insulating layer is widened laterally in the axial height of the second and third plated vias, and / or the second insulating layer wraps around the second electrical composite structure in a top view of the large surface of the sensor element and additionally covers the first plated via, wherein the second insulating layer is narrowed laterally in the axial height of the first plated via. In these cases, the desired electrical insulation effect is achieved with minimal mechanical weakening of the sensor element, i.e., while maintaining optimized mechanical stability of the sensor element. Attached Figure Description

[0026] Figure 1 The outline of the ceramic sensor element is schematically shown.

[0027] Figure 2 shows Figure 1 The layer plane of the ceramic sensor element in the process. Detailed Implementation

[0028] Figure 1 The basic shape of a planar ceramic sensor element is schematically shown. The sensor element has an axial end region 101 facing the exhaust gas, and an axial end region 102 facing away from the exhaust gas. The sensor element has a basic cuboid shape with two minimum sides 103 and two maximum sides 104 (also referred to as large faces 104), wherein the minimum sides 103 are oriented perpendicular to the axial direction 201, and the maximum sides 104 are oriented perpendicular to the layer direction 202. The transverse direction 203 is oriented perpendicular to both the axial direction 201 and the layer direction 202. The extension dimension of the sensor element in the transverse direction 203 is, for example, 5 mm.

[0029] In Figure 2, a single layer is shown in part af. Figure 1 The sensor element 10 shown is composed of the single layer. This schematic diagram is always in a top view of the largest side 104, corresponding to... Figure 1 The line of sight from top to bottom.

[0030] In part a of Figure 2, it is shown that... Figure 1 The first solid electrolyte layer 21 is arranged on the uppermost side of the first solid electrolyte layer 21. In the end region 102 away from the exhaust gas, on the upper side of the first solid electrolyte layer 21, the first contact surface 31 and the second contact surface 32 are arranged side by side in the lateral direction at the same axial height.

[0031] The first contact surface 31 is connected to the first electrode 61 via the first conductor circuit 51 on the upper side of the first solid electrolyte layer 21. The first electrode is arranged in the exhaust gas-facing end region 101 of the sensor element 10.

[0032] The second contact surface 32 is electrically connected to the first plated through-hole 41, which is centrally arranged in the lateral direction with respect to the sensor element 10, having a small axial distance from the first and second contact surfaces 31, 32. The first plated through-hole 41 is, for example, a cylindrical first hole 41' passing through the first solid electrolyte layer 21, which has a first conductive material 41" inside (possibly electrically insulating towards the first solid electrolyte layer 21). The diameter D of the first hole is, for example, 1 mm.

[0033] The first plated through hole 41 is, for example, 5 mm away from the end of the sensor element 10 away from the exhaust gas in the axial direction 201.

[0034] The corner of the first contact surface 31 facing the first plated through-hole 41 is designed as a rounded notch, giving the first contact surface 31 a concave outer contour 31k. The concave outer contour 31k is designed as an arc, in this example as a 90° arc with a radius of curvature of 0.5 mm. Therefore, even if the accurate arrangement of the structural components fluctuates due to manufacturing constraints, an electrical short circuit between the first plated through-hole 41 and the first contact surface 31 is eliminated.

[0035] In part b of Figure 2, it is shown that... Figure 1 The first solid electrolyte layer 21 is arranged on the lower side of the uppermost layer. A plated through-hole 41 extending from the upper side of the first solid electrolyte layer 21 leads into the plane of this layer. The plated through-hole is electrically connected to the second electrode 62 on the lower side via the second conductor circuit 52. The second electrode is arranged inside the sensor element 10 in the exhaust gas-facing end region 101 of the sensor element 10.

[0036] The first electrode 61 exposed to the exhaust gas, together with the first solid electrolyte layer 21 and the second electrode 62 not exposed to the exhaust gas, forms an electrochemical Nernst cell. With the aid of this electrochemical Nernst cell (assuming corresponding heating, see below), based on the Nernst voltage generated on the electrochemical Nernst cell that can be measured between the first and second contact surfaces 31, 32, it can be determined whether the exhaust gas is generated by combustion with excess oxygen (“lean combustion”), combustion with excess fuel (“fett combustion”), or combustion in which oxygen and fuel are in stoichiometric equilibrium.

[0037] In part f of Figure 2, it is shown that... Figure 1 The first solid electrolyte layer 22 is located below the second solid electrolyte layer 22. In the end region 102 away from the exhaust gas, the third contact surface 33 and the fourth contact surface 34 are arranged side by side with each other in the lateral direction on the lower side of the first solid electrolyte layer 22. The third contact surface 33 and the fourth contact surface 34 are arranged at the same axial height of the sensor element 10 relative to the first contact surface 31 and the second contact surface 32.

[0038] The third contact surface 33 is electrically connected to the second plated through-hole 42, which is arranged, for example, with a spacing of 7.2 mm from the end of the sensor element 10 facing away from the exhaust gas. The second plated through-hole 42 is arranged, for example, eccentrically in the lateral direction by 0.95 mm (in part f of FIG2: on the right). That is, the distance between the second plated through-hole and the outer edge of the sensor element 10 in the lateral direction 203 is 1.55 mm.

[0039] In contrast, the fourth contact surface 34 is electrically connected to the third plated through hole 43, which is arranged at the same axial height as the second plated through hole 42 and is also eccentrically arranged in the lateral direction (but on the left side instead of the right side).

[0040] The second and third plated through-holes 42 and 43 are, for example, cylindrical second and third holes 42' and 43' passing through the second solid electrolyte layer 22, and the second and third holes have second and third conductive materials 42" and 43" inside them (possibly electrically insulating towards the second solid electrolyte layer 22). In both cases, the diameter D of these holes is, for example, 1 mm.

[0041] In part e of Figure 2, it is shown that... Figure 1 The second solid electrolyte layer 22 is arranged on the upper side of the bottommost layer. Plated through holes 42 and 43 extending from the lower side of the second solid electrolyte layer 22 lead into the plane of this layer. The plated through holes on the upper side are electrically connected to the two ends 63a and 63o of the resistance heater track 63 via a third conductor circuit 53 and a fourth conductor circuit 54. The resistance heater track is arranged in the exhaust gas-facing end region 101 of the sensor element 10.

[0042] By applying voltage between the third and fourth contact surfaces 33 and 34, the resistance heater track 63 is heated so that the Nernst cell has the operating temperature required for the measurement function of the sensor element 10.

[0043] To prevent unwanted electrical crosstalk between the heating function and the measurement function of the sensor element 10, a first insulating layer 23 and a second insulating layer 24 are arranged between the first solid electrolyte layer 21 and the second solid electrolyte layer 22. Here, the first insulating layer 23 is placed flat on the lower side of the first solid electrolyte layer 21, and the second solid electrolyte layer is placed flat on the upper side of the second solid electrolyte layer 22.

[0044] The insulating layers 23 and 24 are composed of, for example, Al2O3, and their extension scale in the layer direction 202 is, for example, smaller than the extension scale of the solid electrolyte layers 21 and 22. For example, the insulating layers 23 and 24 are screen-printed layers, while the solid electrolyte layers 21 and 22 are, for example, based on a green ceramic thin film.

[0045] The first insulating layer 23 is shown in part c of Figure 2. The first insulating layer is shaped such that it just covers the second conductor circuit 52 and the first, second, and third plated vias 41, 42, and 43, without protruding laterally over these components to a degree greater than necessary for manufacturing purposes. For this purpose, the first insulating layer 23 is widened laterally in the lateral direction 203 in the axial height of the second and third plated vias 42 and 43.

[0046] The second insulating layer 24 is shown in part d of FIG2. The second insulating layer 24 is shaped such that it just covers the resistance heater track 63, the third and fourth conductor circuits 53, 54, and the first, second, and third plated through-holes 41, 42, 43, without protruding laterally over these components to a degree greater than necessary in terms of manufacturing technology. For this purpose, the second insulating layer 24 is narrowed laterally in the lateral direction 203 at the axial height of the first plated through-hole 41.

Claims

1. A planar ceramic sensor element (10) for use with a λ probe, wherein, The sensor element (10) has an axial end region (101) facing the exhaust gas and an axially opposed end region (102) facing away from the exhaust gas. The sensor element (10) has a basic cuboid shape with two minimum sides (103) and two maximum sides (104). The minimum sides (103) are oriented perpendicular to the axial direction (201), and the maximum sides (104) are oriented perpendicular to the layer direction (202). The transverse direction (203) is oriented perpendicular to both the axial direction (201) and the layer direction (202). The ceramic sensor element (10) has ceramic layers (21, 22, 2...). 3, 24), the ceramic layers are arranged in a stacked manner in the layer direction (202), wherein the ceramic layers (21, 22, 23, 24) include at least one first and second solid electrolyte layers (21, 22), wherein the ceramic sensor element (10) has a first electrode (61) exposed to the exhaust gas in an axial end region (101) facing the exhaust gas, wherein the ceramic sensor element (10) has a second electrode (62) separated from the exhaust gas in the interior of the sensor element in the axial end region (101) facing the exhaust gas, wherein the first electrode (61) and the second electrode (62) together with the first solid electrolyte layer (21) form an electrochemical cell. In the axial end region (101) facing the exhaust gas, a resistance heater track (63) is arranged inside the ceramic sensor element (10). The resistance heater track has a first end (63a) and a second end (63o). In the axial end region (101) away from the exhaust gas, exactly two contact surfaces (31, 32, 33, 34) are arranged on each of the two largest sides (104) for external electrical contact with the sensor element (10). The first contact surface (31) of the contact surfaces (31, 32, 33, 34) is connected to the first electrode (61) via a first conductor circuit (51). The second contact surface (32) of the contact surfaces (31, 32, 33, 34) is connected to the second electrode (62) via a first plated through-hole (41) through the first solid electrolyte layer (21) and via a second conductor circuit (52), the second conductor circuit being arranged inside the sensor element (10). The third contact surface (33) of the contact surfaces (31, 32, 33, 34) is connected to the first end (63a) of the resistance heater track (63) via a second plated through-hole (42) through the second solid electrolyte layer (22) and via a third conductor circuit (53), the third conductor circuit being arranged inside the sensor element (10).The fourth contact surface (34) of the sensor element (10) is connected to the second end (63o) of the resistance heater track (63) via a third plated through-hole (43) passing through the second solid electrolyte layer (22) and via a fourth conductor circuit (54), the fourth conductor circuit being arranged inside the sensor element (10). The second plated through-hole (42) and the third plated through-hole (43) are both arranged in the axial direction (201) on the exhaust side of the first plated through-hole (41), and the first plated through-hole (41) is arranged in the transverse direction (203) between the second plated through-hole (42) and the third plated through-hole (43).

2. The sensor element according to claim 1, characterized in that, The first plated through hole (41), the second plated through hole (42) and the third plated through hole (43) are completely arranged in the end region (102) of the sensor element (10) away from the exhaust gas, wherein the extension dimension of the end region (102) of the sensor element (10) away from the exhaust gas in the axial direction is less than one-fifth of the extension dimension of the sensor element (10) in the axial direction (201).

3. The sensor element according to claim 1 or 2, characterized in that, The second plated through hole (42) and the third plated through hole (43) are arranged at the same axial height, and the first plated through hole (41) is centrally arranged between the second plated through hole (42) and the third plated through hole (43) in the transverse direction (203), such that the first, second and third plated through holes (41, 42, 43) are located at the corner points of an isosceles triangle.

4. The sensor element according to claim 3, characterized in that, In the isosceles triangle, the angle opposite the base is no greater than 90° and no less than 30°.

5. The sensor element according to claim 1 or 2, characterized in that, The first plated through-hole (41) is constructed as a first hole (41') in the first solid electrolyte layer (21), the first hole having a first conductive material (41") disposed in the first hole (41'), the second plated through-hole (42) is constructed as a second hole (42') in the second solid electrolyte layer (22), the second hole having a second conductive material (42") disposed in the second hole (42'), the third plated through-hole (43) is constructed as a third hole (43') in the second solid electrolyte layer (22), the third hole having a third conductive material (43") disposed in the third hole (43'), and the first hole (41') has a first diameter, the second hole (42') has a second diameter, the third hole (43') has a third diameter, and in the top view of the large surface (104) of the sensor element (10), the centroid of the second hole (42') and the centroid of the third hole (43') are spaced apart by a spacing scale (a).

6. The sensor element according to claim 5, characterized in that, The spacing scale (a) is smaller than the sum of the second diameter and the third diameter.

7. The sensor element according to claim 5, characterized in that, Half of the spacing scale (a) is less than the distance between the centroid of the second hole (42') and the outer edge of the sensor element (10) that is closest to it in the lateral direction, and half of the spacing scale (a) is less than the distance between the centroid of the third hole (43') and the outer edge of the sensor element (10) that is closest to it in the lateral direction.

8. The sensor element according to claim 5, characterized in that, The distance between the centroid of the first hole (41') and the first, second, third and / or fourth contact surfaces (31, 32, 33, 34) in the axial direction (201) is no greater than half the diameter of the first hole (41').

9. The sensor element according to claim 5, characterized in that, The first contact surface (31) has a concave outer contour (31k) facing the first plated through hole (41) in a top view of the large surface (104) of the sensor element (10).

10. The sensor element according to claim 9, characterized in that, The concave outer contour (31k) has a radius equal to half the diameter of the first hole (41').

11. The sensor element according to claim 1 or 2, characterized in that, An insulating layer (23, 24) or multiple insulating layers (23, 24) are arranged between the first and second solid electrolyte layers (21, 22) such that the first electrical composite structure, including the second electrode (62), the second conductor circuit (52) and the first plated via (41), is electrically insulated from the second electrical composite structure by the one or more insulating layers (23, 24), the second electrical composite structure including the resistive heater track (63), the third conductor circuit (53), the fourth conductor circuit (54), the second plated via (42) and the third plated via (43).

12. The sensor element according to claim 11, characterized in that, The one or more insulating layers (23, 24) extend only in the top view of the large surface (104) of the sensor element to insulate the first electrical composite structure relative to the second electrical composite structure, and are additionally surrounded by a sealing frame (23', 24') / each surrounded by a sealing frame (23', 24') made of a solid electrolyte material.

13. The sensor element according to claim 12, characterized in that, The extension dimension of the sealing frame (23', 24') / all sealing frames (23', 24') in the lateral direction (203), measured from the outer edge of the sensor element (10) in the end region (102) of the sensor element (10) away from the exhaust gas, is always greater than 1 / 10 of the extension dimension of the sensor element (10) in the lateral direction (203).

14. The sensor element according to claim 11, characterized in that, A first insulating layer (23) and a second insulating layer (24) are provided, wherein, viewed from the second insulating layer (24), the first insulating layer (23) is located on the side pointing towards the first solid electrolyte layer (21) and the first electro-composite structure in the layer direction (202), and viewed from the first insulating layer (23), the second insulating layer (24) is located on the side pointing towards the second solid electrolyte layer (22) and the second electro-composite structure in the layer direction (202).

15. The sensor element according to claim 14, characterized in that, The first insulating layer (23) covers the second conductor circuit (52) and the first, second and third plated through holes (41, 42, 43) in a top view of the large surface (104) of the sensor element, wherein the first insulating layer (23) is widened in the lateral direction (203) at the axial height of the second and third plated through holes (42, 43).

16. The sensor element according to claim 14 or 15, characterized in that, The second insulating layer (24) wraps the second electrical composite structure in a top view of the large surface (104) of the sensor element (10) and additionally covers the first plated through hole (41) in such a way that the second insulating layer (24) is narrowed in the lateral direction (203) at the axial height of the first plated through hole (41).