Abstract:
A sensor element for detecting a physical property of a gas includes: a solid electrolyte film; a first end area and a second end area situated diametrically opposite in the longitudinal direction; a functional element in the first end area in the interior which is electrically conductively connected to a contact surface situated in the second end area on the outer surface, the electrically conductive connection having a strip conductor running essentially in the longitudinal direction in the interior of the sensor element; and a reference gas channel running essentially in the longitudinal direction of the sensor element communicating with a reference gas outside of the sensor element via a reference gas opening, the strip conductor and the reference gas channel being situated in such a way that at least a partial overlap occurs between them.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention is directed to known sensor elements, which are used for example as exhaust gas sensors, in particular as lambda sensors, which have gained an extensive prevalence in motor vehicles. The present invention is, however, also applicable in other types of sensor elements, for example in sensors for detecting other gaseous components of exhaust gases and in particle sensors or the like. The present invention relates in particular to a sintered or sinterable ceramic sensor element which is manufactured for example by combining, in particular by stacking, individual, possibly printed, ceramic green sheets. The present invention further relates in particular to a sensor element in the interior of which a reference gas channel is formed. 
     2. Description of the Related Art 
     The sensor element of the type described above further includes in particular at least one electrical, electrochemical, and/or electronic functional element in a first end area of the sensor element generally facing the exhaust gas. An electrical supply to the sensor element is provided in the present case by a contact surface on the outer surface of the sensor element in a second area generally facing away from the exhaust gas. 
     An electrical supply to the sensor element is carried out in this case by an electrical connection of the functional element to the contact surface, which has a strip conductor running essentially in the longitudinal direction of the sensor element in the interior of the sensor element. 
     To prevent distortion due to sintering and to optimize the thermal conduction in the interior of the sensor element during operation, it is attractive to configure the strip conductor to overlap completely or partially (for example at least 10% of the width) with the reference gas channel in a top view of the sensor element. The effects in particular of the low sintering shrinkage and the low thermal conduction of a completely or partially unfilled reference gas channel may hereby be compensated for with respect to the entire sensor element. 
     It is problematic that, due to the aforementioned measures, an edge of the reference gas channel overlaps with the strip conductor in a top view of the sensor element, and thus in the sense of a cutting edge may potentially cause a squeezing of the strip conductor in this area during the manufacturing process. 
     Sensor elements of this type are known for example from German patent document DE 101 57 733 B4. 
     BRIEF SUMMARY OF THE INVENTION 
     Sensor elements according to the present invention have the advantage over the related art that the area, in which an edge of the reference channel overlaps with the strip conductor in a top view of the sensor element, extends relatively far in the longitudinal direction of the sensor element. The potential cutting effect of the edge of the reference gas channel is thus distributed across this broad extension and, as a result, a squeezing of the strip conductor in this area emerges to a disproportionately lesser degree. 
     For this purpose, it is provided according to the present invention that the strip conductor runs at an angle α of not more than 25°, in particular not more than 14°, to the outer side of the sensor element 20° at its end facing away from the first end area of the sensor element. 
     To not unnecessarily reduce the area, in which the strip conductor is configured to completely or partially overlap with the reference gas channel in a top view of the sensor element, in its length and/or width, a lower limit may in particular also be provided for angle α, which it should not fall short of, and which may be for example 2° or 5°. 
     The area in which the strip conductor runs at an angle preferably has a minimum extension in the longitudinal direction, which may be for example 2 mm, 3 mm, or even 4 mm, or may be defined by the width of the strip conductor. 
     The lateral offset, caused by the angle, at the end of the strip conductor facing away from the first end area of the sensor element arises in particular as a product of the extension of the area, in which the strip conductor runs at an angle, and the inverse tangent of angle α. It is preferred that this lateral offset is not less than half or the full width of the overlap between the strip conductor and the reference gas channel. The preferred offset may also be in particular not less than 0.3 mm or not less than 0.5 mm. 
     In special specific embodiments of the present invention, the reference gas channel is unfilled, thus forming in particular a cavity designed macroscopically in relation to the sensor element and having, for example, a rectangular cross section. In this case, while on the one hand the access of reference air to the sensor element is basically improved, the above-mentioned problem of the potential cutting effect of the edge of the reference gas channel is, however, initially even exacerbated. 
     In special specific embodiments of the present invention, the electrically conductive connection between the functional element and the contact surface has a feedthrough in addition to the strip conductor, with which the feedthrough interacts, and the feedthrough runs essentially perpendicularly to the longitudinal direction of the sensor element. The feedthrough includes in particular a conductive coating of the radial wall of a via hole of the sensor element. The reference gas channel is situated in particular without overlap of the feedthrough, in a top view of the sensor element, which results in the advantage that the breaking strength of the sensor element is only slightly reduced by the feedthrough. 
     Insofar as this concerns a strip conductor, it may in the present case include a feed line and a collar, the collar may be situated on the feed line facing away from the exhaust gas, the feed line may have entirely or at least in its part facing away from the exhaust gas a constant width, and/or the collar may have a ring-shaped, for example an annular, design. 
     The end of the strip conductor facing away from the first end area of the sensor element may also in particular be defined by the end of the feed line facing away from the first end area of the sensor element and/or by the totality formed by the end of the feed line facing away from the first end area of the sensor element plus the collar of the strip conductor. 
     The terms “longitudinal direction,” “transverse direction,” and “vertical direction” are basically used in the context of this application in the sense of a rectangular reference system. In particular, they may, however, additionally be directions which are distinguished by the sensor element, for example, in an in particular ashlar shaped sensor element, the longitudinal direction may be the direction in which the longest side edges of the sensor element point, the vertical direction may be the direction in which the shortest side edges of the sensor element point, and/or the transverse direction may be the direction in which the side edges of the sensor element point which have a middle length. For example, in a rod-shaped sensor element, the longitudinal direction may point in the direction of an axis around which the rod-shaped sensor element is rotationally symmetrical or is essentially rotationally symmetrical. 
     Where reference is only essentially made to a direction, directions are considered, in addition to the direction in the narrow meaning, which deviate slightly from this direction, for example by not more than 15°, and/or directions that are at least not orthogonal to this direction. A direction is also essentially realized by a structure if the affected structure only deviates in a small subarea, which for example does not include more than 10% of the structure. 
     “Length of the sensor element” is understood to mean the extension of the sensor element in the longitudinal direction, “width of the sensor element” is understood to mean the extension of the sensor element in the transverse direction, and “height of the sensor element” is understood to mean the extension of the sensor element in the vertical direction within the context of this application. This direction is also applicable for the top view of the sensor element. 
     The term “end area of the sensor element” is understood to mean basically only a cohesive subarea of the sensor element with respect to a longitudinal direction within the context of this application, and includes the affected end of the sensor and does not amount to more than 50% of the length of the sensor element. In this respect, one end area intersects with a diametrically opposite end area only in a flat expanse, for example. In a somewhat more limited way, an end area of the sensor element may be understood in particular as a cohesive subarea of the sensor element which includes the affected end of the sensor and does not amount to more than one-third or even not more than one-fourth of the length of the sensor element. 
     The term “functional element” is in the present case basically not to be interpreted narrowly. For example, it may be a precious metal electrode or cermet electrode communicating with the exterior space of the sensor element, and/or an electrical resistance heater which has in particular an electrical resistance of a maximum of 30 Ohm at 20° C., and/or the like. 
     In the case of the resistance heater as the functional element, two strip conductors of the presently described specific embodiments may be provided positioned side by side, in particular in mirror symmetry. 
     In the case of the cermet electrode as the functional element, the strip conductor or feed line to this cermet electrode may be situated in particular directly diametrically opposite to the reference gas channel. For this reason, it may be advantageous that this strip conductor or feed line has a width in the area, in which it runs at an angle, and/or in the area in which it intersects an edge of the reference gas channel, in a top view of the sensor element, which is increased with respect to an area of the strip conductor (or feed line) facing the exhaust gas, in particular by at least 25% or by at least 0.1 mm. 
     In conjunction with the present invention, a specific material selection for strip conductors, feed lines, feedthroughs, and contact surfaces may be additionally constructive. Basically, materials with a precious metal proportion of 83 wt. % or more are hereby preferred, so that predefined ohmic resistances may be achieved at minimized use of precious metals. For at least one feed line to the heating device, even precious metal proportions of 95 wt. % or more, for example 98 wt. %, are preferred. A proportion of at least 1 wt. % of Al2O3, even better at least 1.5 wt. % of Al2O3, preferably a maximum of 2.5 wt. % of Al2O3, has been proven as favorable for the precise adjustability of the electrical resistance of these structures. 
     At least one feed line to the heating device may be configured integrally with the heating device and made from the same material. 
     In addition or alternatively, a lower precious metal proportion, than is provided for the at least one feed line to the heating device, is provided for the feed line to the cermet electrode and/or for at least one contact surface, preferably for example 83 wt. % through 87 wt. %, in particular a proportion of ZrO2 and Y2O3 together of 12 wt. % through 16 wt. % being provided in the feed line to the cermet electrode. 
     It is advantageous that the feed line to the cermet electrode may be manufactured together with the cermet electrode in one process step and made from the same material. For the feed line to the cermet electrode or for the cermet electrode, a proportion of Al2O3 of preferably 0.2 wt. % through 1 wt. % is also advantageous. 
     In addition or alternatively, a lower precious metal proportion, than is provided for the at least one feed line to the heating device, is provided for the at least one feed through, preferably for example 83 wt. % through 87 wt. %, a proportion of ZrO2 and Y2O3 together of 3 wt. % through 8 wt. % and additionally a proportion of Nb2O5 of 6 wt. % through 12 wt. % being provided in the feedthrough. It is advantageous that the feedthroughs are easier to manage handle during the manufacturing process. In particular, corresponding pastes have better rheological characteristics and enable a better ceramic linking of the feedthroughs within the sensor element. In conjunction with sensor elements, which are made predominantly from YSZ, a reduced oxygen ion conductivity is moreover formed in the border areas of the feedthroughs, which improves the functionality of the sensor elements. 
     The above-mentioned precious metal proportions may include in particular platinum. Alternatively, in particular with respect to at least one feedthrough, proportions of rhodium may be included to stabilize the metal phase, preferably 0.2 wt. % through 0.8 wt. % relative to the total composition of the materials, and/or proportions of palladium, preferably 0.2 wt. % through 1 wt. % relative to the total composition of the materials, may be included. 
     Additional proportions of precious metals may always be provided. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows a sensor element according to the present invention perspectively and schematically in an exploded view. 
         FIG. 2  shows second end area  202  of sensor element  20  facing away from the exhaust gas in a top view of third solid electrolyte film  23 . 
         FIG. 3  shows second end area  202  of sensor element  20  facing away from the exhaust gas in a bottom view to below first solid electrolyte film  21  facing downward in  FIG. 1 . 
         FIG. 4  shows second end area  202  of sensor element  20  facing away from the exhaust gas in a top view of first solid electrolyte film  21 , from above in  FIG. 1 . 
         FIG. 4 a    shows as a variant a sensor element  20  with slightly modified feed lines  323 ,  325 . 
         FIG. 5  shows second end area  202  of sensor element  20  facing away from the exhaust gas in a bottom view to below first solid electrolyte film  23  from below in  FIG. 3 . 
         FIG. 5 a    shows as a variant a sensor element  20  with slightly modified feed line  328 . 
         FIG. 6  shows a purely schematic section through sensor element  20  shown in the preceding  FIGS. 1 through 5 , in a plane perpendicular to the longitudinal direction of sensor element  20  through feedthroughs  501 ,  502 ,  503 . 
         FIG. 7  shows a purely schematic profile section through sensor element  20  shown in the preceding  FIGS. 1 through 5 , in a plane perpendicular to the longitudinal direction of sensor element  20  approximately in the area of half of the longitudinal extension of sensor element  20 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  shows, as an exemplary embodiment of the present invention, a general view of a sensor element  20 , which may be situated in a housing of a gas sensor (not shown) which is used for determining the oxygen concentration in an exhaust gas of an internal combustion engine (not shown). Provided with corresponding functional elements, the present invention is of course also suited for sensor elements in other sensors, for example sensors for particle measurement. 
     The sensor element extends in  FIG. 1  in the longitudinal direction from left to right, a first end area  201  of sensor element  20  being mapped on the right and a second end area  202  of sensor element  20  being mapped on the left. In intended installation and operation, first end area  201  of sensor  20  faces an exhaust gas and second end area  202  of sensor element  20  faces away from the exhaust gas. 
     Sensor element  20  in  FIG. 1  additionally extends in the transverse direction from front to back and in the vertical direction from bottom to top. 
     Sensor element  20  is constructed from printed ceramic layers which are formed in this example as a first, second, and third solid electrolyte film  21 ,  22 ,  23  and contain zirconium oxide stabilized by yttrium oxide (yttria-stabilized zirconia, YSZ). Solid electrolyte films  21 ,  22 ,  23  have, prior to a sintering process in the example, a length of 72 mm, a width of 5 mm, and a height of 540 μm. Films of a sintered sensor element  20  have an edge length reduced by 20%. 
     First solid electrolyte film  21  is provided on its large surface facing outward, downward from the perspective of sensor element  20  in  FIG. 1 , in second end area  202  of sensor element  20  with a contact surface  43  and an additional contact surface  44 , printed in this case; see also  FIG. 3 . 
     First solid electrolyte film  21  is provided on its large surface facing inward, upward from the perspective of sensor element  20  in  FIG. 1 , in first end area  201  of sensor element  20  with a meander-shaped heating device  311  as a functional element  31  which is used for heating first end area  201  of sensor element  20 . In a continuation of meander-shaped heating device  311 , a strip conductor  321 ,  322  is connected to its respective ends, the transition from heating device  311  to strip conductor  321 ,  322  being characterized by an increase in the structural width and/or height or by a reduction of the electrical resistance per length. 
     Strip conductors  321 ,  322  have on the exhaust gas side a section, designated as feed line  323 ,  325  which in the present case has a constant width. Strip conductors  321 ,  322  additionally have a section facing away from the exhaust gas designated as collar  324 ,  326 , which in the present case has a ring-shaped design; see also  FIG. 4 . 
     First solid electrolyte film  21  is additionally provided on its large surface facing inward, upward from the perspective of sensor element  20  in  FIG. 1 , with insulation layers  330  and a sealing frame  331 , and also a film binder layer  333 , printed in this case. 
     First solid electrolyte film  21  has in second end area  202  two feedthroughs  501 ,  502  which extend in the vertical direction through first solid electrolyte film  21  and each electrically conductively connect a contact surface  43 ,  44  to a collar  324 ,  326  of a strip conductor  321 ,  322 ; see  FIG. 6 . 
     Second solid electrolyte film  22  is provided on both sides with a film binder layer  333 ; second solid electrolyte film  22  additionally has a reference gas channel  35  which extends longitudinally from a reference gas opening  351  situated facing away from the exhaust gas to first end area  201  of sensor element  20  and thereby runs centrically in the transverse direction. Reference gas channel  35  is designed as unfilled, in particular no porous fillings are provided in it. 
     Third solid electrolyte film  23  is provided on its large surface facing inward, downward from the perspective of sensor element  20  in  FIG. 1 , with a cermet electrode  312  as functional element  31  for measuring an oxygen concentration diametrically opposite to reference gas channel  35 . In a continuation of cermet electrode  312 , a strip conductor  328  is connected to the end of cermet electrode  312 , the transition from the cermet electrode to strip conductor  328  being characterized by a reduction of the structural width. 
     Strip conductor  328  has a section on the exhaust gas side designated as feed line  327  which in the present case has a constant width. Strip conductor  328  additionally has a section facing away from the exhaust gas designated as collar  329  which has a ring-shaped design in the present case; see also  FIG. 5 . A film binder layer  333  is provided on this side of third solid electrolyte film  23 , at least where it is otherwise plain. 
     Third solid electrolyte film  23  is provided on its large surface facing outward, upward from the perspective of sensor element  20  in  FIG. 1 , in second end area  202  of sensor element  20  with a contact surface  45  and an additional contact surface  46 , printed in the present case; see also  FIG. 2 . 
     A strip conductor  320 , with for example a constant width, connects to additional contact surface  46  and extends to an additional cermet electrode  313  situated in first end area  201  of sensor element  20 . Strip conductor  320  is covered for example with a dense cover layer  361 ; additional cermet electrode  313  is provided with porous layers  362  so that a communication between the exterior space and additional cermet electrode  313  is ensured. 
     Third solid electrolyte film  23  has in the second end area a feedthrough  503  which extends in the vertical direction through third solid electrolyte film  23  and electrically conductively connects contact surface  45  to collar  329 ; see  FIG. 6 . 
       FIG. 2  shows second end area  202  of sensor element  20  facing away from the exhaust gas in a top view of third solid electrolyte film  23 . Contact surface  45  is situated on the left there when viewed toward first end area  201  of sensor  20  facing the exhaust gas. 
     Contact surface  45  is composed of three subareas, namely a trunk area  451 , a head area  452 , and a neck area  453 . Trunk area  451  is situated on the side of contact surface  45  facing away from the exhaust gas. It has an elongated base shape which arises from a rectangle with equal length and width through maximum rounding of the corners, i.e., through a rounding at a radius of curvature R which corresponds to half of the width of trunk area  451  or contact surface  45 . In this way, semicircular end areas of trunk area  451  or contact surface  45  are thus created on the side of contact surface  45  facing away from the exhaust gas. 
     Based on an unsintered sensor element  20  (sintered: −20%), the length of trunk area  451  in this example is 2.5 mm or more; the width or trunk area  451  is 1.5 mm or more. Trunk area  451  is spaced at a distance of 0.4 mm or less from the left outer edge of sensor element  20  and is spaced at a distance of 1.3 mm or less from the front outer edge of sensor element  20 . 
     Head area  452  is situated on the side of contact surface  45  facing the exhaust gas. Head area  452  has, for example, a ring-shaped design with an inner diameter of 0.5 mm or less and an outer diameter of 1 mm or more based on an unsintered sensor element  20  (sintered: −20%). 
     Neck area  453  is formed between trunk area  451  and head area  452 . It forms a constriction of contact surface  45  with respect to trunk area  451  and head area  452  and has a minimum width in the example of 0.3 mm and a length of 0.3 mm based on an unsintered sensor element  20  (sintered: −20%). 
     Trunk area  451  in the example has a mirror symmetry with respect to an axis which points in the longitudinal direction of sensor element  20 . Head area  452  and neck area  453  likewise have a mirror symmetry; however, with respect to an axis which is rotated by 9° in the mathematically negative direction of rotation in a top view of sensor element  20  with respect to the longitudinal axis of sensor element  20  so that head area  452  and neck area  453  are, as a whole, slightly tilted toward the center of the sensor. 
     Head area  452  of contact surface  45  interacts electrically conductively with a feedthrough  503  through third solid electrolyte film  23 . 
     Moreover, additional contact surface  46  is situated to the right adjacent to contact surface  45  in  FIG. 2  when viewed toward first end area  201  of sensor element  20  facing the exhaust gas. The arrangement and the size of additional contact surface  46  correspond in this sense, i.e., by interchanging left and right, to the arrangement and the size of trunk area  451  of contact surface  45  providing that a distance of at least 0.6 mm exists between contact surface  45  and additional contact surface  46 , based on an unsintered sensor element  20  (sintered: −20%). 
     Additional contact surface  46  includes only one part corresponding to trunk area  451  of contact surface  45 , thus has neither head- nor neck area. It also does not interact with a feedthrough; instead, it is directly contacted to strip conductor  328  which leads to additional cermet electrode  313 . A center axis of strip conductor  328  is displaced transversely inward in the longitudinal direction, with respect to a center axis of additional contact surface  46 , by 0.1 mm to 0.4 mm, in the example by 0.2 mm, based on an unsintered sensor element  20  (sintered: −20%). 
     Contact surfaces  45 ,  46  have a precious metal proportion of 83 wt. % through 87 wt. %, and a proportion of ZrO2 and Y2O3 together of 12 wt. % through 16 wt. %. 
       FIG. 3  shows second end area  202  of sensor element  20  facing away from the exhaust gas in a bottom view to below first solid electrolyte film  21  facing downward in  FIG. 1 . Contact surface  43  is situated on the left there when viewed toward first end area  201  of sensor element  20  facing the exhaust gas. 
     Contact surface  43  is composed of three subareas, namely a trunk area  431 , a head area  432 , and a neck area  433 . Trunk area  431  is situated on the side of contact surface  43  facing away from the exhaust gas. It has an elongated base shape which arises from a rectangle with equal length and width through maximum rounding of the corners, i.e., through a rounding at a radius of curvature R which corresponds to half of the width of trunk area  431  or contact surface  43 . In this way, semicircular end areas of trunk area  431  or contact surface  43  are thus created on the side of contact surface  43  facing away from the exhaust gas. 
     Based on an unsintered sensor element  20  (sintered: −20%), the length of trunk area  431  in this example is 2.5 mm or more; the width or trunk area  431  is 1.5 mm or more. Trunk area  431  is spaced at a distance of 0.4 mm or less from the left outer edge of sensor element  20  and is spaced at a distance of 1.3 mm or less from the front outer edge of sensor element  20 . 
     Head area  432  is situated on the side of contact surface  43  facing the exhaust gas. Head area  432  has a ring-shaped design, for example, with an inner diameter of 0.5 mm or less and an outer diameter of 1 mm or more based on an unsintered sensor element  20  (sintered: −20%). 
     Neck area  433  is formed between trunk area  431  and head area  432 . It forms a constriction of contact surface  43  with respect to trunk area  431  and head area  432  and has a minimum width in the example of 0.9 mm and a length of 0.3 mm based on an unsintered sensor element  20  (sintered: −20%). 
     Neck area  433  of contact surface  43  is substantially wider, in this case by a factor of 2, than neck area  451  of contact surface  45  in  FIG. 2 . The background is that high currents are supplied to heating device  311  via contact surface  43 , whereas only comparatively low currents are supplied to cermet electrode  312  via contact surface  45 . Contact surface  43  is consequently provided with a reduced ohmic resistance or a widened neck area  433 . 
     Trunk area  431  in the example has a mirror symmetry with respect to an axis which points in the longitudinal direction of sensor element  20 . Head area  432  and neck area  433  likewise have a mirror symmetry; however, with respect to an axis which is rotated by 9° in the mathematically negative direction of rotation in a top view of sensor element  20  with respect to the longitudinal axis of sensor element  20  so that head area  432  and neck area  433  are, as a whole, slightly tilted toward the center of the sensor. 
     Head area  432  of contact surface  43  interacts electrically conductively with a feedthrough  501  through first solid electrolyte film  21 . 
     Moreover, additional contact surface  44  is situated to the right adjacent to contact surface  43  in  FIG. 3  when viewed toward first end area  201  of sensor element  20  facing the exhaust gas. The arrangement and the size of additional contact surface  46  correspond in this sense, i.e., by interchanging left and right and positive direction of rotation with negative direction of rotation, to the arrangement and the size of contact surface  43  providing that a distance of at least 0.6 mm exists between contact surface  43  and additional contact surface  44 , based on an unsintered sensor element  20  (sintered: −20%). 
     Contact surfaces  43 ,  44  have a precious metal proportion of 83 wt. % through 87 wt. %, and a proportion of ZrO2 and Y2O3 together of 12 wt. % through 16 wt. %. 
       FIG. 4  shows second end area  202  of sensor element  20  facing away from the exhaust gas in a top view of first solid electrolyte film  21 , from above in  FIG. 1 . Strip conductor  322  is situated to the right when viewed toward first end area  201  of sensor element  20  facing the exhaust gas. Strip conductor  322  is composed of two subareas, namely a feed line  325  and a collar  326 . 
     Feed line  325  forms the exhaust gas side part of strip conductor  322  and extends from heating device  311  on the exhaust gas side to collar  326  situated on feed line  325  facing away from the exhaust gas. In the present case, feed line  325  has a width B of 1.2 mm and runs on the exhaust gas side with a spacing in the transverse direction of 0.25 mm from the central longitudinal axis of sensor element  20 , respectively based on an unsintered sensor element  20  (sintered: −20%). In an end area facing away from the exhaust gas, feed line  325  is angled toward the right, i.e., toward the outside, at an angle of 18°. 
     Collar  326  has a ring-shaped design and describes in the present case an arc of 180°, the outer diameter of which is identical to width B of feed line  325  and its inner diameter is 0.4 mm. A width of the collar is thus 0.3 mm, each based on an unsintered sensor element  20  (sintered: −20%). A width ratio of collar width b to feed line width B is 0.33. 
     The electrical resistance of feedthrough  501  is the same or approximately the same as the electrical resistance of strip conductor  322 , relative to a temperature distribution which may occur or may typically occur during operation of the sensor. In addition to a homogeneous temperature distribution, for example 20° C., alternative temperature distributions which are inhomogeneous are also conceivable here. For example, uniform temperature increases in the longitudinal direction of 1100° C. in the area of heating device  311  and 200° C., 300° C., or even 400° C. in the area of feedthrough  501  may be taken as a basis. 
     The electrical resistance of the electrical connection of the functional element, in particular heating device  311 , to contact surface  43 , is in the range of 2.5 Ohms at 20° C., for example. 
     Moreover, strip conductor  321  is situated symmetrically to strip conductor  322  relative to the central longitudinal axis in  FIG. 4  when viewed toward first end area  201  of sensor element  20  facing the exhaust gas. The arrangement and the size of strip conductor  321  correspond in this sense, i.e., by interchanging left and right, to the arrangement and the size of strip conductor  322 . 
     Feed lines  325 ,  323  have a precious metal proportion of more than 95 wt. %, for example 98 wt. %, and at least 1 wt. % of Al2O3. 
     The electrical resistance of feedthrough  502  is the same or approximately the same as the electrical resistance of strip conductor  321 , relative to a temperature distribution which may occur or may typically occur during operation of the sensor. In addition to a homogeneous temperature distribution, for example 20° C., alternative temperature distributions which are inhomogeneous are also conceivable here. For example, uniform temperature increases in the longitudinal direction of 1100° C. in the area of heating device  311  and 200° C., 300° C., or even 400° C. in the area of feedthrough  501  may be taken as a basis. 
       FIG. 4 a    shows as a variant a sensor element  20  with slightly modified feed lines  323 ,  325 , the modification consisting merely in that width B of feed lines  323 ,  225  is only 1.08 mm instead of 1.2 mm, thus slightly (10%) reduced in comparison to collar  324 ,  326 . The metric dimensions are based on an unsintered sensor element  20  (sintered: −20%). 
       FIG. 5  shows second end area  202  of sensor element  20  facing away from the exhaust gas in a bottom view to below first solid electrolyte film  23  from below in  FIG. 3 . Strip conductor  322  is situated to the right when viewed toward first end area  201  of sensor element  20  facing the exhaust gas. Strip conductor  322  is composed of two subareas, namely a feed line  327  and a collar  329 . 
     Feed line  327  forms the exhaust gas side part of the strip conductor and extends from cermet electrode  312  on the exhaust gas side to collar  329  situated on feed line  327  facing away from the exhaust gas. In the present case, the feed line has a width B of 0.4 mm (unsintered; sintered: −20%) and runs on the exhaust gas side so that it is situated within reference gas channel  35  in a vertical projection in a top view of sensor element  20 . This part of feed line  327  is thus largely protected from squeezing during the manufacturing process. 
     In an end area facing away from the exhaust gas, feed line  327  is angled toward the right, i.e., toward the outside, at an angle of not more than 25°, here 8°. In this end area facing away from the exhaust gas, the feed line intersects with the edge of reference gas channel  35  in a vertical projection in a top view of sensor element  20 . Due to the comparatively small intersecting angle, a large overlapping zone results between strip conductor  328  and the edge of reference gas channel  35 , and thus in turn a good protection from squeezing feed line  327  during the manufacturing process. 
     Collar  329  has a ring-shaped design. A width of the collar b is 0.3 mm, based on an unsintered sensor element  20  (sintered: −20%). A width ratio of collar width b to feed line width B is 0.75. 
     Feed line  327  has a precious metal proportion of 83 wt. % through 87 wt. %, and a proportion of ZrO2 and Y2O3 together of 12 wt. % through 16 wt. %. 
     The electrical resistance of feedthrough  503  is the same or approximately the same as the electrical resistance of strip conductor  328 , relative to a temperature distribution which may occur or may typically occur during operation of the sensor. In addition to a homogeneous temperature distribution, for example 20° C., alternative temperature distributions which are inhomogeneous are also conceivable here. For example, uniform temperature increases in the longitudinal direction of 750° C. in the area of cermet electrode  312  and 200° C., 300° C., or even 400° C. in the area of feedthrough  503  may be taken as a basis. 
       FIG. 5 a    shows as a variant a sensor element  20  with slightly modified feed line  328 , the modification consisting merely in that width B of feed line  328  is increased by 50%, from 0.4 mm to 0.6 mm, in the end area facing away from the exhaust gas with respect to the area of feed line  328  facing the exhaust gas. The metric dimensions are based on an unsintered sensor element  20  (sintered: −20%). 
       FIG. 6  shows a purely schematic section through sensor element  20  shown in the preceding  FIGS. 1 through 5 , in a plane perpendicular to the longitudinal direction of sensor element  20  through feedthroughs  501 ,  502 ,  503 . 
     Feedthroughs  501 ,  502 ,  503  are designed as a conductive coating of the radial wall of a via hole  601 ,  602 ,  603  of sensor element  20 . The diameter of via holes  601 ,  602 ,  603  is 0.6 mm in the example based on an unsintered sensor element  20  (sintered: −20%, i.e., 0.48 mm). 
     Each of feedthroughs  501 ,  502 ,  503  is apparently designed to be without overlap with reference gas channel  35  in a top view of sensor element  20 . 
     Feedthroughs  501 ,  502 ,  503  have a precious metal proportion of 83 wt. % through 87 wt. %, and a proportion of ZrO2 and Y2O3 together of 3 wt. % through 8 wt. % and additionally a proportion of Nb2O5 of 6 wt. % through 12 wt. %. 
       FIG. 7  shows a purely schematic profile section through sensor element  20  shown in the preceding  FIGS. 1 through 5 , in a plane perpendicular to the longitudinal direction of sensor element  20  approximately in the area of half of the longitudinal extension of sensor element  20 . 
     As is apparent, in a top view of sensor element  20 , strip conductor  328  and feed line  327 , which lead to cermet electrode  312 , have an overlap  703  across its full width with reference channel  35 . Additionally, strip conductors  321 ,  322  and feed lines  323 ,  325 , which lead to the resistance heater, have an overlap  701 ,  702  across approximately 10% of their respective widths with reference channel  35 .