Abstract:
A sensor element for detecting a physical property of a gas includes: a first end region and a second end region opposing one another; a functional element in the first end region interior that is electroconductively connected to a contact area disposed in the second end region exterior; the electrically conductive connection between the functional element and the contact area having a conductor in the interior of the sensor element essentially extending in the longitudinal direction, and having a leadthrough that essentially extends orthogonally to the longitudinal direction of the sensor element. The ratio between an electrical resistance of the conductor and an electrical resistance of the leadthrough is between 3 and ⅓.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    The present invention relates to known sensor elements that serve as exhaust-gas sensors, for example, in particular as lambda probes that are widely used in motor vehicles. However, the present invention can also be applied to other types of sensor elements, for example, to sensors for detecting other gaseous components of exhaust gases, and also to particle sensors or the like. In particular, the present invention relates to a sintered or sinterable ceramic sensor element that is produced, for example, by assembling individual, in some instances imprinted ceramic green films, in particular by stacking them one upon the other. 
         [0003]    2. Description of the Related Art 
         [0004]    In particular, the sensor element of the type described above includes at least one electrical, electrochemical and/or electronic functional element in a first end region of the sensor element, generally a first end region facing the exhaust gas. The sensor element&#39;s ability to be electrically powered is provided here by a contact area on the outer surface thereof in a second region, typically one facing away from the exhaust gas. 
         [0005]    The sensor element&#39;s ability to be electrically powered is provided here by an electrical connection of the functional element with the contact area that includes a conductor in the interior of the sensor element that essentially extends in the longitudinal direction of the sensor element and a leadthrough that essentially extends orthogonally to the longitudinal direction of the sensor element, in particular in the vertical direction. Sensor elements of this kind are known, for example, from the German Patent Application DE 10 2006 055 797 A1. 
         [0006]    During operation and manufacture of the sensor element, high temperature and chemical resistances are required for the electrical connection. Therefore, noble metals, such as platinum or the like, are widely used. Since such noble metals are relatively expensive, efforts are generally directed to reducing the quantity of material used. 
         [0007]    This type of miniaturization of the electrical connection is limited in that, at a specified resistance, the total resistance is all the greater, the smaller the particular lead cross sections are. Resulting voltage drops, respectively power losses and/or signal distortions can only be tolerated within predefined limits. 
         [0008]    In particular, such a total resistance limit of this electrical connection of the functional element, in particular of a heating resistor, with the contact area is to be seen within the range here of 1 to 4 ohms at 20° C., in particular within the range of 2 to 3 ohms at 20° C. 
       BRIEF SUMMARY OF THE INVENTION 
       [0009]    On the other hand, inventive sensor elements according to the present invention have the advantage that the quantity of material, for example, of the noble metal used for electrically connecting the functional element to the contact area, may be minimized without exceeding a definable total resistance of the electrical connection. 
         [0010]    Underlying the present invention in the first instance is the consideration that the conductor and the leadthrough are two serially connected sections of the electrical connection. The total resistance of the electrical connection is thus cumulatively derived from the individual resistances. Secondly, underlying the present invention is the consideration that, when the conductive structures are reduced in cross section, the electrical resistance thereof is approximately inversely proportional to the quantity of material used. 
         [0011]    Consequently, a simultaneous optimization of the total resistance of the electrical connection and of the material quantity required for the electrical connection is recognized as present when the ratio between the electrical resistance of the conductor and the electrical resistance of the leadthrough is not greater than 3 and not smaller than ⅓. 
         [0012]    In the case of a different ratio, the material quantity that is altogether required or that is smaller for the section would be disproportionately increased, without the total resistance being significantly reduced. 
         [0013]    Inasmuch as the specific resistance of the materials used is temperature-dependent, it is particularly necessary to assess temperature distributions that occur, respectively that can typically occur during operation of the sensor. Besides a homogeneous temperature distribution, for example, 20° C., which, for example, represents the state at initial start-up of the sensor, the present invention may also be alternatively or additionally realized with respect to inhomogeneous temperature distributions. For example, uniform increases in temperature in the longitudinal direction of 750° C. or even of 1100° C. in the area of the functional element, and of 200° C., 300° C. or even of 400° C. in the area of the leadthrough may each be used as a basis in the resulting combinations. Such temperature distributions exist, for example, on the completely heated sensor, for example, in continuous operation. 
         [0014]    Even at different temperatures and temperature distributions, the electrical resistances of the conductors and leadthroughs are readily available to one skilled in the art, for example, by performing measurements. Also, he/she is easily able to selectively adapt the resistances, for example, by modifying the lead cross sections. 
         [0015]    In particular, the present invention also relates to a sensor element where an electrical connection of the functional element, in particular of a heating resistor with a contact area, has already been miniaturized. In this case, the electrical resistance of the electrical connection of the functional element, in particular of the heating resistor with the contact area, is within the range of 1 to 4 ohms at 20° C., in particular within the range of 2 to 3 ohms at 20° C. 
         [0016]    Within the scope of this application, the terms “longitudinal direction” “transverse direction,” and “vertical direction” are generally merely used in the sense of a rectangular reference system. Moreover, directions may, in particular, be concerned that are characterized by the sensor element. Namely in the case of a cuboidal sensor element, for example, the longitudinal direction may be the direction in which the longest lateral edges of the sensor element point; the vertical direction may be the direction in which the shortest lateral edges of the sensor element point; and/or the transverse direction may be the direction in which the medium-length lateral edges of the sensor element point. For example, in the case of a rod-shaped sensor element, the longitudinal direction may point in the direction of an axis about which the rod-shaped sensor element is axially symmetric, respectively essentially axially symmetric. 
         [0017]    Where reference is essentially made to only one direction, besides the direction in the narrow sense, directions also come under consideration that deviate slightly from this direction, for example, by not more than 15° and/or directions that are at least not orthogonal to this direction. Additionally, a direction is also realized by a structure essentially when the structure in question deviates in only one small portion, for example, by not more than 10% of the structure. 
         [0018]    Within the scope of this application, “length of the sensor element” is understood to be the longitudinal extent of the sensor element; “width of the sensor element” is understood to be the transverse extent of the sensor element; and “height of the sensor element” is understood to be the vertical extent of the sensor element. This direction is also consequential for the plan view of the sensor element. 
         [0019]    Within the scope of this application and with reference to a longitudinal direction, the term “end region of the sensor element” is generally understood to be merely a cohesive portion of the sensor element that includes the particular end of the sensor and does not represent more than 50% of the length of the sensor element. In this respect, one end region and one opposite end region overlap merely in one area, for example. “Somewhat limited” may be understood as an end region of the sensor element, in particular also as a cohesive portion of the sensor element that includes the particular end of the sensor and no longer represents one third or even no longer one fourth of the length of the sensor element. 
         [0020]    In the present case, the term “functional element” is generally not to be narrowly interpreted. For example, it may be a question of a noble metal electrode or cermet electrode that communicates with the exterior of the sensor element and/or of an electrical resistance heater that, in particular, has an electrical resistance of maximally 30 ohms at 20° C. and/or the like. 
         [0021]    If the resistance heater is a functional element, two electrical connections of the specific embodiments described here may be provided adjacently, in particular mirror symmetrically. 
         [0022]    Advantageous embodiments of the present invention provide that the ratio between the electrical resistance of the conductor and the electrical resistance of the leadthrough be limited to an even greater extent within the range of 1. The electrical resistance of the conductor and the electrical resistance of the leadthrough are then equal or at least approximately equal, for example, with a ratio within the range of 2 to 1/2 or within the range of 3/2 to 2/3 or within the range of 110% to 90%. 
         [0023]    One further refinement of the present invention, which is especially beneficial from a production engineering standpoint, is provided in that, at the end thereof facing away from the end region of the sensor element, the conductor is laterally angled, the conductor extending off-center, in particular in the transverse direction of the sensor element and, at the end thereof facing away from end region ( 201 ) of the sensor element, is angled toward the outer face of the sensor element. Two conductors of this kind may also be provided that are disposed in opposition to one another, in particular symmetrically, in particular off-center in the transverse direction of the sensor element and, at the end thereof facing away from the end region of the sensor element, are angled toward the particular outer face of the sensor element. The advantage of these specific embodiments is that, in the transverse direction, the conductor may extend relatively centrally in that, in one region of the sensor element, it may be manufactured very reliably. On the other hand, the leadthroughs must not fall below a certain minimum mutual distance since, otherwise, the breaking strength of the sensor element, in particular, would be reduced. Overall, therefore, the amount of material used and the functionality may be thereby further optimized. 
         [0024]    In special specific embodiments of the present invention, the leadthrough is made of a conductive coating of the radial wall of a plated-through hole of the sensor element or of a conductive filling of a plated-through hole of the sensor element. 
         [0025]    Additionally or alternatively, the conductor may include a lead and a collar, the lead or an end region of the lead facing away from the exhaust gas having, in particular, a constant or an essentially constant lead width B and being routed from the functional element into the region of the leadthrough; and, in a plan view of the sensor element, the collar being annularly disposed, in particular, around the plated-through hole, and effecting the electrical connection between the leadthrough and the lead; the annular ring having an annular ring width b, measured radially in a plan view of the plated-through hole. 
         [0026]    In particular, the functional element may be an electrical resistance heater that, in particular, has an electrical resistance of maximally 30 ohms at 20° C. In this case, during operation, the electrical connection is a conductor of substantial currents. To avoid unwanted losses, respectively waste heat, adequate dimensioning is to be provided, in particular of the lead of the conductor that is directly adjacent to the resistance heater. On the other hand, the region of the collar may be more sparingly designed. In particular, an optimization has revealed that a width ratio, annular ring width divided by the lead width, resides within the range of from 0.1 to 0.4, preferably within the range of from 0.22 to 0.32. Overall, therefore, the quantity of material used and the functionality may be thereby further optimized. 
         [0027]    The selection of this width ratio is, in fact, not only to be exclusively seen in synergic cooperation. Accordingly, the following is an alternative object of the present invention to which the further embodiments discussed in other respects may nevertheless be applied: 
         [0028]    A sensor element, in particular for detecting a physical property of a gas, in particular for detecting the concentration of a gas component or the temperature or a solid component or a liquid component of an exhaust gas of a combustion engine; in the longitudinal direction thereof, the sensor element having a first end region and second end region that oppose one another; in the first end region, the sensor element, in the interior thereof, having a functional element that is electroconductively connected to a contact area disposed in the second end region on the outer face of the sensor element; the electrically conductive connection between the functional element and the contact area having a conductor in the interior of the sensor element that essentially extends in the longitudinal direction and having a leadthrough that essentially extends orthogonally to the longitudinal direction of the sensor element; the leadthrough being made of a conductive coating of the radial wall of a plated-through hole of the sensor element or of a conductive filling of the plated-through hole, and the conductor including a lead and a collar; the lead or an end region of the lead facing away from the exhaust gas having a constant or an essentially constant lead width B and being routed from the functional element into the region of the leadthrough; and, in a plan view of the sensor element, the collar being annularly disposed around the plated-through hole and effecting the electrical connection between the leadthrough and the lead; the annular ring having a width b, measured radially in a plan view of the plated-through hole; the functional element being an electrical resistance heater, which, in particular, has an electrical resistance of maximally 30 ohms at 20° C. and a width ratio, annular ring width b divided by lead width B, within the range of from 0.1 to 0.4, preferably within the range of from 0.22 to 0.32. 
         [0029]    In particular, the diameter of the plated-through hole plus twice the annular ring width may be identical or approximately identical to the lead width. At the end thereof in the area of the leadthrough, the conductor is then not made thicker by the collar, so that material is saved without causing any appreciable functional disadvantages. 
         [0030]    In particular, in the case of a sintered sensor element, lead width B may reside within the range of from 0.72 to 1.12 mm; and/or annular ring width b may be within the range of from 0.2 to 0.28 mm; and/or the diameter of plated-through hole D may be within the range of from 0.4 to 0.56 mm. For unsintered sensor elements, dimensions are to be added that are 25% larger in each case than those indicated for sintered sensor elements. 
         [0031]    In particular, the functional element may be a cermet electrode having a flat design that communicates, in particular, with the exterior of the sensor element. 
         [0032]    In this case, the electrical connection is only traversed during operation by the flow of low currents. To economize material, the lead of the conductor may be realized with a relatively small width. On the other hand, it is not possible for the region of the collar and of the leadthrough to be similarly scaled, since, otherwise, a reliable contacting would no longer be feasible under all circumstances from a standpoint of production engineering. In particular, an optimization has revealed that a width ratio—the annular ring width divided by the lead width—resides within the range of from 0.6 to 1.08, preferably with the range of from 0.7 to 0.9. 
         [0033]    Overall, therefore, the amount of material used and the functionality may be thereby further optimized. 
         [0034]    The selection of this width ratio is, in fact, not only to be exclusively seen in synergic cooperation. Accordingly, the following is an alternative object of the present invention to which the further embodiments discussed in other respects may nevertheless be applied: 
         [0035]    A sensor element, in particular for detecting a physical property of a gas, in particular for detecting the concentration of a gas component or the temperature or a solid component or a liquid component of an exhaust gas of a combustion engine; in the longitudinal direction thereof, the sensor element having a first end region and a second end region that oppose one another; outside of the second end region, in particular in the first end region, the sensor element, in the interior thereof, having a functional element that is electroconductively connected to a contact area disposed in the second end region on the outer face of the sensor element; the electrically conductive connection between the functional element and the contact area having a conductor in the interior of the sensor element that essentially extends in the longitudinal direction and has a leadthrough that essentially extends orthogonally to the longitudinal direction of the sensor element; the leadthrough being made of a conductive coating of the radial wall of a plated-through hole of the sensor element or of a conductive filling of the plated-through hole, and the conductor including a lead and a collar; the lead or an end region of the lead facing away from the exhaust gas having a constant or an essentially constant lead width B and being routed from the functional element into the region of the leadthrough; and, in a plan view of the sensor element, the collar being annularly disposed around the plated-through hole and effecting the electrical connection between the leadthrough and the lead; the annular ring having a width b, measured radially in a plan view of the plated-through hole; the functional element being a cermet electrode having a flat design that communicates, in particular, with the exterior of the sensor element, and a width ratio, annular ring width b divided by lead width B within the range of from 0.6 to 1.08, preferably within the range of from 0.7 to 0.9. 
         [0036]    In particular, in the case of a sintered sensor element, lead width B may reside within the range of from 0.3 to 0.6 mm; and/or annular ring width b may be within the range of from 0.22 to 0.36 mm; and/or the diameter of plated-through hole D may be within the range of from 0.4 to 0.56 mm. For unsintered sensor elements, dimensions are to be added that are 25% larger in each case than those indicated for sintered sensor elements. 
         [0037]    In the context of the present invention, it may still be expedient for specific material to be selected for conductors, leads, leadthroughs and contact areas. Materials may be generally preferred here having a noble metal content of 83% by weight or more, making it possible for predefined ohmic resistances to be achieved with a minimized noble metal application. Noble metal contents of 95% by weight or more, for example, 98% by weight are even preferred for at least one lead to the heating device. A content of at least 1% by weight of AI203, optimally of even at least 1.5% by weight of AI203, preferably of maximally 2.5% by weight of AI203, turns out to be beneficial for precise adjustability of the electrical resistance of these structures. At least one lead to the heating device, together with the heating device, may be made in one piece and of the same material. 
         [0038]    Additionally or alternatively, for the lead to the cermet electrode and/or for at least one contact area, a lower noble metal content than for the at least one lead to the heating device is provided, preferably, for example, of 83% by weight to 87% by weight; in particular, in the lead to the cermet electrode, a content of ZrO2 and Y203 of together 12% by weight to 16% by weight being provided. It is advantageous that the lead to the cermet electrode, together with the cermet electrode, may be manufactured in one process step and from the same material. An AI203 content, preferably 0.2% by weight to 1% by weight is also advantageous for the lead to the cermet electrode, respectively for the cermet electrode. 
         [0039]    Additionally or alternatively, for at least one leadthrough, a lower noble metal content is provided than for the at least one lead to the heating device, preferably, for example, of 83% by weight to 87% by weight; a content of ZrO2 and Y203 of, together 3% by weight to 8% by weight and, additionally, a content of Nb205 of 6% by weight to 12% by weight being provided in the leadthrough. It is advantageous that the leadthroughs are able to be more effectively handled during the manufacturing process. In particular, appropriate compounds have more effective rheologic properties and make possible a more effective ceramic binding of the leadthroughs within the sensor elements. Moreover, in connection with sensor elements that are predominantly composed of YSZ, a reduced oxygen ion conductivity thereby results in the peripheral regions of the leadthroughs, which improves the functionality of the sensor elements. 
         [0040]    The noble metal contents mentioned above may, in particular, be made of platinum. Alternatively, in particular relative to at least one leadthrough, contents, preferably 0.2% by weight to 0.8% by weight, relative to the total composition of the materials, may be made of rhodium to stabilize the metal phase; and/or contents, preferably 0.2% by weight to 1% by weight, relative to the total composition of the materials, may be made of palladium. 
         [0041]    Other noble metal contents may always be provided. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0042]      FIG. 1  shows a sensor element according to the present invention. 
           [0043]      FIG. 2  shows, in a plan view of third solid electrolyte foil  23 , a second end region  202  of sensor element  20  facing away from the exhaust gas. 
           [0044]      FIG. 3  shows second end region  202  of sensor element  20  facing away from the exhaust gas in a bottom view below first solid electrolyte foil  21  pointing downwardly in  FIG. 1 . 
           [0045]      FIG. 4  shows second end region  202  of sensor element  20  facing away from the exhaust gas in a plan view of first solid electrolyte foil  21 , from above in  FIG. 1 . 
           [0046]      FIG. 4 a    shows a sensor element  20  having slightly modified leads  323 ,  325 , in comparison to the configuration shown in  FIG. 4 . 
           [0047]      FIG. 5  shows second end region  202  of sensor element  20  facing away from the exhaust gas in a bottom view below third solid electrolyte foil  23 , pointing downwardly in  FIG. 3 . 
           [0048]      FIG. 5 a    shows a sensor element  20  having a slightly modified lead  328 , in comparison to the configuration shown in  FIG. 5 . 
           [0049]      FIG. 6  shows, purely schematically, a sectional view through sensor element  20  shown in preceding  FIG. 1 through 5 , in a plane perpendicular to the longitudinal direction of sensor element  20  through leadthroughs  501 ,  502 ,  503 . 
           [0050]      FIG. 7  shows, purely schematically, a sectional view through sensor element  20  shown in preceding  FIG. 1 through 5 , in a plane orthogonal to the longitudinal direction of sensor element  20  approximately in the area of half of the longitudinal extent of sensor element  20 . 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0051]    As an exemplary embodiment of the present invention,  FIG. 1  shows an overall view of a sensor element  20 , which may be mounted in a housing of a gas sensor (not shown) that is used for determining the oxygen concentration in an exhaust gas of a combustion engine (not shown). If appropriate functional elements are provided, it is self-evident that the present invention is also suited for other sensors, such as sensors used for measuring particulate matter. 
         [0052]    In  FIG. 1 , the sensor element extends in the longitudinal direction from left to right, a first end region  201  of sensor element  20  being shown on the right, and a second end region  202  of sensor element  20  on the left. If sensor element  20  is installed and operated as intended, first end region  201  thereof faces an exhaust gas, and second end region  202  thereof faces away from the exhaust gas. 
         [0053]    In addition, in  FIG. 1 , sensor element  20  extends in the transverse direction from front to back and in the vertical direction from bottom to top. 
         [0054]    Sensor element  20  is assembled from imprinted ceramic layers that are formed in this example as a first, second and third solid electrolyte foil  21 ,  22 ,  23  and contain yttrium-oxide stabilized zirconium oxide (YSZ). In the example, prior to a sintering process, solid electrolyte foils  21 ,  22 ,  23  have a length of 72 mm, a width of 5 mm, and a height of 540 μm. Foils of a sintered sensor element  20  have edge lengths diminished by 20%. 
         [0055]    On the large surface area thereof that is outwardly pointing from sensor element  20 , on the bottom of  FIG. 1 , first solid electrolyte foil  21  is provided in second end region  202  of sensor element  20  with a contact area  43  and a further contact area  44 , here imprinted; see also  FIG. 3 . 
         [0056]    On the large surface area thereof, pointing inwardly from sensor element  20 , in the top of  FIG. 1 , first solid electrolyte foil  21  is provided in first end region  201  of sensor element  20  with a meander-shaped heating device  311  as a functional element  31  that is used for heating first end region  201  of sensor element  20 . In a continuation of meander-shaped heating device  311 , a conductor  321 ,  322  is connected in each case at the ends thereof, the transition from heating device  311  to conductor  321 ,  322  being characterized by an increase of the structure width and/or height, respectively by a decrease in the electrical resistance per length. 
         [0057]    On the exhaust gas side, conductors  321 ,  322  have a section denoted as lead  323 ,  325 , which, in the present case, has a constant width. In addition, facing away from the exhaust gas, conductors  321 ,  322  have a section denoted as a collar  324 ,  326 , which is annular here; see also  FIG. 4 . 
         [0058]    On the large surface area thereof that points inwardly from sensor element  20 , on the top of  FIG. 1 , first solid electrolyte foil  21  is also provided with insulation layers  330  and a sealing frame  331 , as well as with a foil binder layer  333 , in this case imprinted. 
         [0059]    In second end region  202 , first solid electrolyte foil  21  has two leadthroughs  501 ,  502  that extend orthogonally through first solid electrolyte foil  21  and, in each case, electroconductively connect a contact area  43 ,  44  to a collar  324 ,  326  of a conductor  321 ,  322 ; see  FIG. 6 . 
         [0060]    Second solid electrolyte foil  22  is provided on each of both sides with a foil binder layer  333 ; in addition, second solid electrolyte foil  22  features a reference gas channel  35  that extends along a reference gas channel  351 , which faces away from the exhaust gas, into first end region  201  of sensor element  20 , and thereby extends centrally in the transverse direction. Reference gas channel  35  is configured to be unfilled; in particular no porous fillings are provided therein. 
         [0061]    At the bottom in  FIG. 1 , opposite reference gas channel  35 , on large surface area thereof, which is inwardly pointing from the point of view of sensor element  20 , third solid electrolyte foil  23  is provided with a cermet electrode  312  as a functional element  31  for measuring an oxygen concentration. In a continuation of cermet electrode  312 , a conductor  328  is connected at the end thereof, the transition from the cermet electrode to conductor  328  is characterized by a decrease in the structure width. 
         [0062]    On the exhaust gas side, conductor  328  has a section denoted as lead  327 , which has a constant width here. In addition, facing away from the exhaust gas, conductor  328  features a section denoted as a collar  329 , which is annular here; see also  FIG. 5 . Provided on this side of third solid electrolyte layer  23 , at least where otherwise unprinted, is a foil binder layer  333 . 
         [0063]    At the top of  FIG. 1 , on the large surface area thereof that points outwardly from sensor element  20 , third solid electrolyte foil  23  is provided in second end region  202  of sensor element  20  with a contact area  45  and a further contact area  46 , here imprinted; see also  FIG. 2 . 
         [0064]    Adjoining further contact area  46  is a conductor  320  having a constant width, for example, that extends to a further cermet electrode  313  disposed in first end region  201  of sensor element  20 . Conductor  320  is covered with a, for example, impervious cover layer  361 ; further cermet electrode  313  is provided with porous layers  362 , thereby ensuring a communication between the exterior and further cermet electrode  313 . 
         [0065]    In the second end region, third solid electrolyte foil  23  features a leadthrough  503  that extends orthogonally through third solid electrolyte foil  23  and electroconductively connects contact area  45  with collar  329 ; see  FIG. 6 . 
         [0066]    In a plan view of third solid electrolyte foil  23 ,  FIG. 2  shows second end region  202  of sensor element  20  facing away from the exhaust gas. From a perspective there of first end region  201  of sensor element  20  facing the exhaust gas, contact area  45  is configured to the left. 
         [0067]    Contact area  45  is composed of three portions, namely of a trunk portion  451 , a head portion  452 , and of a neck portion  453 . Trunk portion  451  is disposed on the side of contact area  45  facing away from the exhaust gas. It has a basic oblong form that results from a rectangle of the same length and width by a maximum rounding of the corners, thus by a rounding with a radius of curvature R that corresponds to half of the width of trunk portion  451 , respectively of contact area  45 . Thus, in this manner, semicircular end regions of trunk portion  451 , respectively of contact area  45  are formed on the side of contact area  45  facing away from the exhaust gas. 
         [0068]    Relative to an unsintered sensor element  20  (sintered: −20%), the length of trunk portion  451  in this example is 2.5 mm or more; the width of trunk portion  451  is 1.5 mm or more. Trunk portion  451  is spaced apart from the left outer edge of sensor element  20  by 0.4 mm or less and from the front outer edge of sensor element  20  by 1.3 mm or less. 
         [0069]    Head portion  452  is disposed on the side of contact area  45  facing the exhaust gas. Head portion  452  is annular, for example, having an inner diameter of 0.5 mm or less and an outer diameter of 1 mm or more, relative to an unsintered sensor element  20  (sintered: −20%). 
         [0070]    Neck portion  453  is configured between trunk portion  451  and head portion  452 . In comparison with trunk portion  451  and head portion  452 , it forms a constricted region of contact area  45  having a minimal width of 0.3 mm in the example and a length of 0.3 mm relative to an unsintered sensor element  20  (sintered: −20%). 
         [0071]    In the example, trunk portion  451  features a mirror symmetry relative to an axis that points in the longitudinal direction of sensor element  20 . Head portion  452  and neck portion  453  likewise have a mirror symmetry; however, relative to an axis that is rotated relative to the longitudinal axis of sensor element  20  by 9° in a plan view of sensor element  20  in the mathematically negative direction of rotation, so that head portion  452  and neck portion  453  are altogether slightly tilted toward the middle of the sensor. 
         [0072]    Head portion  452  of contact area  45  cooperates electroconductively together with a leadthrough  503  through third solid electrolyte layer  23 . 
         [0073]    Moreover, from a perspective of first end region  201  of sensor element  20  facing the exhaust gas, further contact area  46  is configured to the right next to contact area  45  in  FIG. 2 . In this sense, thus transposing left and right, the configuration and size of further contact area  46  correspond to that of trunk portion  451  of contact area  45  under the condition that there be a spacing of at least 0.6 mm, relative to an unsintered sensor element  20  (sintered: −20%) between contact area  45  and further contact area  46 . 
         [0074]    Further contact area  46  is merely composed of a portion corresponding to trunk portion  451  of contact area  45 , thus has neither a head portion nor a neck portion. It also does not cooperate with a leadthrough; instead, it is directly contacted by conductor  328  that leads to further cermet electrode  313 . Relative to a central axis of further contact area  46 , a central axis of conductor  328  is transversely inwardly offset, in the longitudinal direction by 0.1 mm to 0.4 mm, in the example by 0.2 mm, relative to an unsintered sensor element  20  (sintered: −20%). 
         [0075]    Contact areas  45 ,  46  have a noble metal content of 83% by weight to 87% by weight, and a content of ZrO2 and Y203, together, of 12% by weight to 16% by weight. 
         [0076]      FIG. 3  shows second end region  202  of sensor element  20  facing away from the exhaust gas in a bottom view below first solid electrolyte foil  21  pointing downwardly in  FIG. 1 . From a perspective there of first end region  201  of sensor element  20  facing the exhaust gas, contact area  43  is configured there to the left. 
         [0077]    Contact area  43  is composed of three portions, namely of a trunk portion  431 , a head portion  432 , and of a neck portion  433 . Trunk portion  431  is disposed on the side of contact area  43  facing away from the exhaust gas. It has a basic oblong form that results from a rectangle of the same length and width by a maximum rounding of the corners, thus by a rounding with a radius of curvature R that corresponds to half of the width of trunk portion  431 , respectively of contact area  43 . Thus, in this manner, semicircular end regions of trunk portion  431 , respectively of contact area  43  are formed on the side of contact area  43  facing away from the exhaust gas. 
         [0078]    Relative to an unsintered sensor element  20  (sintered: −20%), the length of trunk portion  431  in this example is 2.5 mm or more; the width of trunk portion  431  is 1.5 mm or more. Trunk portion  431  is spaced apart from the left outer edge of sensor element  20  by 0.4 mm or less and from the front outer edge of sensor element  20  by 1.3 mm or less. 
         [0079]    Head portion  432  is disposed on the side of contact area  43  facing the exhaust gas. Head portion  432  is configured to be annular, for example, having an inner diameter of 0.5 mm or less and an outer diameter of 1 mm or more, relative to an unsintered sensor element  20  (sintered: −20%). 
         [0080]    Neck portion  433  is configured between trunk portion  431  and head portion  432 . In comparison with trunk portion  431  and head portion  432 , it forms a constricted region of contact area  43  having a minimal width of 0.9 mm in the example and a length of 0.3 mm relative to an unsintered sensor element  20  (sintered: −20%). 
         [0081]    Neck portion  433  of contact area  43  is substantially wider, in this case larger by a factor greater than two than neck portion  451  of contact face  45  in  FIG. 2 . The background is that high currents are fed via contact area  43  of heating device  311 , while only comparatively low currents are fed via contact area  45  of cermet electrode  312 . Contact area  43  is consequently configured with a reduced ohmic resistance, respectively widened neck region  433 . 
         [0082]    In the example, trunk portion  431  features a mirror symmetry relative to an axis that points in the longitudinal direction of sensor element  20 . Head portion  432  and neck portion  433  likewise have a mirror symmetry, however, relative to an axis that is rotated relative to the longitudinal axis of sensor element  20  by 9° in a plan view of sensor element  20  in the mathematically negative direction of rotation, so that head portion  432  and neck portion  433  are altogether slightly tilted toward the middle of the sensor. 
         [0083]    Head portion  432  of contact area  43  cooperates electroconductively with a leadthrough  501  through first solid electrolyte layer  21 . 
         [0084]    Moreover, from a perspective of first end region  201  of sensor element  20  facing the exhaust gas, further contact area  44  is configured to the right next to contact area  43  in  FIG. 3 . In this sense, thus transposing left and right and the positive direction of rotation with the negative direction of rotation, the configuration and size of further contact area  46  correspond to the configuration and size of contact area  43  under the condition that there be a spacing of at least 0.6 mm, relative to an unsintered sensor element  20  (sintered: −20%) between contact area  43  and further contact area  44 . 
         [0085]    Contact areas  43 ,  44  have a noble metal content of 83% by weight to 87% by weight, and a content of ZrO2 and Y203, together, of 12% by weight to 16% by weight. 
         [0086]      FIG. 4  shows second end region  202  of sensor element  20  facing away from the exhaust gas in a plan view of first solid electrolyte foil  21 , from above in  FIG. 1 . From a perspective there of first end region  201  of sensor element  20  facing the exhaust gas, conductor  322  is configured to the right. Conductor  322  is composed of two portions, namely of a lead  325  and of a collar  326 . 
         [0087]    Lead  325  forms the exhaust gas-side section of conductor  322  and extends from heating device  311  on the exhaust gas-side to collar  326  that is disposed to face away from the exhaust gas side thereof. In the present case, lead  325  has a width B of 1.2 mm and extends on the exhaust gas-side at a spacing in the transverse direction of 0.25 mm to the central longitudinal axis of sensor element  20 , in each case relative to an unsintered sensor element  20  (sintered: −20%). In an end region facing away from the exhaust gas, lead  325  is angled 18° to the right, thus outwardly. 
         [0088]    Collar  326  is annular in form and, in the present case, describes an arc of 180°, whose outer diameter is identical to width B of lead  325  and whose inner diameter is 0.4 mm. In each case, relative to an unsintered sensor element  20  (sintered: −20%), a width of the collar is thus 0.3 mm. A ratio of collar width b to lead width B is 0.33. 
         [0089]    The electrical resistance of leadthrough  501  is equal or approximately equal to that of conductor  322  relative to a temperature distribution that may, respectively may typically occur during operation of the sensor. Besides a homogeneous temperature distribution, for example, 20° C., inhomogeneous temperature distributions may also be alternatively excluded here. For example, uniform increases in temperature in the longitudinal direction of 1100° C. within the range of heating device  311  and of 200° C., 300° C. or even of 400° C. within the range of leadthrough  501  may also be used as a basis. 
         [0090]    The electrical resistance of the electrical connection of the functional element, in particular of heating device  311  with contact area  43  is within the range of 2.5 ohms at 20° C., for example. 
         [0091]    Moreover, in  FIG. 4 , from a perspective of first end region  201  of sensor element  20  facing the exhaust gas, conductor  321  is symmetrically disposed relative to the central longitudinal axis of conductor  322 . In this sense, the configuration and size of conductor  321  correspond to that of conductor  322 , thus, with transposition of left and right. 
         [0092]    Leads  325 ,  323  feature a noble metal content of more than 95% by weight, for example, of 98% by weight and of at least 1% by weight of AI203. 
         [0093]    The electrical resistance of leadthrough  502  is equal or approximately equal to that of conductor  321  relative to a temperature distribution that may, respectively may typically occur during operation of the sensor. Besides a homogeneous temperature distribution, for example, 20° C., inhomogeneous temperature distributions may also be alternatively excluded here. For example, uniform increases in temperature in the longitudinal direction of 1100° C. within the range of heating device  311  and of 200° C., 300° C. or even of 400° C. within the range of leadthrough  501  may also be used as a basis. 
         [0094]    As a variant,  FIG. 4 a    shows a sensor element  20  having slightly modified leads  323 ,  325 , the modification residing merely in that width B of leads  323 ,  225  is only 1.08 mm instead of 1.2 mm, thus, slightly reduced (10%) in comparison to collar  324 ,  326 . The metric dimensions are based on an unsintered sensor element  20  (sintered: −20%). 
         [0095]      FIG. 5  shows second end region  202  of sensor element  20  facing away from the exhaust gas in a bottom view below third solid electrolyte foil  23 , pointing downwardly in  FIG. 3 . From a perspective there of first end region  201  of sensor element  20  facing the exhaust gas, conductor  322  is configured to the right. Conductor  322  is composed of two portions, namely of a lead  327  and of a collar  329 . 
         [0096]    Lead  327  forms the exhaust gas-side section of the conductor and extends from cermet electrode  312  on the exhaust gas-side to collar  329  disposed to face away from the exhaust gas side of lead  327 . In the present case, the lead has a width B of 0.4 mm (unsintered; sintered: −20%) and extends on the exhaust gas side in such a way that it is disposed within reference gas channel  35  in a perpendicular projection in a plan view of sensor element  20 . Thus, this section of lead  327  is substantially protected from squeezing during the production process. 
         [0097]    In an end region facing away from the exhaust gas, lead  327  is angled by not more than 25°, here 8° to the right, thus outwardly. In this end region facing away from the exhaust gas, the lead intersects with the edge of reference gas channel  35  in a perpendicular projection in a plan view of sensor element  20 . The comparatively small angle of intersection results in a long overlap zone between conductor  328  and the edge of reference gas channel  35  and, thus, in turn, in an effective protection against squeezing of lead  327  during the production process. 
         [0098]    Collar  329  has an annular design. Relative to an unsintered sensor element  20  (sintered: −20%), a width of collar b is 0.3 mm. A ratio of collar width b to lead width B is 0.75. 
         [0099]    Lead  327  has a noble metal content of 83% by weight to 87% by weight, and a content of ZrO2 and Y203, together, of 12% by weight to 16% by weight. 
         [0100]    The electrical resistance of leadthrough  503  is equal or approximately equal to that of conductor  328  relative to a temperature distribution that may, respectively may typically occur during operation of the sensor. Besides a homogeneous temperature distribution, for example, 20° C., inhomogeneous temperature distributions may also be alternatively excluded here. For example, uniform increases in temperature in the longitudinal direction of 750° C. within the range of cermet electrode  312  and of 200° C., 300° C. or even of 400° C. within the range of leadthrough  503  may also be used as a basis. 
         [0101]    As a variant,  FIG. 5 a    shows a sensor element  20  having a slightly modified lead  328 ; the modification residing merely in that width B of lead  328  is increased in the end region facing away from the exhaust gas relative to the region of lead  328  facing the exhaust gas by 50%, by 0.4 mm to 0.6 mm. The metric dimensions are based on an unsintered sensor element  20  (sintered: −20%). 
         [0102]      FIG. 6  shows, purely schematically, a sectional view through sensor element  20  shown in preceding  FIG. 1 through 5 , in a plane perpendicular to the longitudinal direction of sensor element  20  through leadthroughs  501 ,  502 ,  503 . 
         [0103]    Leadthroughs  501 ,  502 ,  503  are made as a conductive coating of the radial wall of a plated-through hole  601 ,  602 ,  603  of sensor element  20 . In the example, the diameter of plated-through holes  601 ,  602 ,  603  is 0.6 mm in relation to an unsintered sensor element  20  (sintered: −20%, thus 0.48 mm). 
         [0104]    It is readily apparent that leadthroughs  501 ,  502 ,  503 , together with reference gas channel  35 , are each configured to be overlap-free in a plan view of sensor element  20 . 
         [0105]    Leadthroughs  501 ,  502 ,  503  have a noble metal content of 83% by weight to 87% by weight, and a content of ZrO2 and Y203 of, together, 3% by weight to 8% by weight and, additionally, a content of Nb205 of 6% by weight and of 12% by weight. 
         [0106]      FIG. 7  shows, purely schematically, a sectional view through sensor element  20  shown in preceding  FIG. 1 through 5 , in a plane orthogonal to the longitudinal direction of sensor element  20  approximately in the area of half of the longitudinal extent of sensor element  20 . 
         [0107]    A plan view of sensor element  20  reveals that conductor  328 , respectively lead  327 , which is routed to cermet electrode  312 , comes to overlap  703  over the full width thereof with reference channel  35 . In addition, conductors  321 ,  322 , respectively leads  323 ,  325 , which are routed to the resistance heater, come to overlap  701 ,  702 , in each case over approximately 10% of the width thereof, with reference channel  35 .