DE102014106919A1 - Glass ceramic capacitor for high voltage applications - Google Patents

Abstract

Capacitor for high voltage applications with a glass ceramic body (10) as a dielectric and metallization layers (11, 13) as electrodes. Starting from a series of test capacitors, the parameter values of a capacitor to be designed are determined on the basis of formulas.

Description

The invention relates generally to capacitors with glass-ceramic as a dielectric, and more particularly to glass-ceramic capacitors for high voltage applications.

Capacitors with glass ceramic as a dielectric are known. That's how it describes DE 1 951 624 a method for the production of stacked capacitors, which are composed of alternating, by application of pressure and temperature to a compact unit connected layers of a dielectric and metal layers. The dielectric layers are formed from a crystallizable glass in an organic binder, wherein the organic components are driven off by heating and the glass is converted to a glass-ceramic by means of heat treatment. Similarly, the metal layers are sintered from slurries of metal particles during the manufacture of the stacked capacitors. As a result of the manufacturing process, the layers contain a large amount of pores, which has a detrimental effect on high-voltage applications.

The WO 2005/095301 A1 describes a glass-ceramic composition comprising at least one ferrite and at least one glass material containing bismuth oxide in passive electrical component applications. The glass-ceramic composition is present as a powder mixture, also mixed with an organic binder, and can be sintered. The disadvantage is the relatively high percentage of pores.

The DE 10 2008 011 206 A1 describes a glass-ceramic which has ferroelectric crystallites with a maximum diameter of 20 to 100 nm and with a glass ceramic content of more than 50% by volume. The glass ceramic is produced by ceramizing from a starting glass and is extremely low in pores. Such glass ceramics are suitable as part of a capacitor or a high-frequency filter.

The invention is based on the object as glass-ceramic capacitors are to be built sufficiently thin and dimensioned overall, and yet are suitable for high-voltage applications.

Difficulties and concerns are as follows:
Previous glass ceramics for high-performance capacitors contain ceramics such as BST (barium strontium titanate). Capacitors with BaTiO ₃ , a ferroelectric material, have not previously been used for high power electronics because the ferroelectric hysteresis leads to significant, high dielectric losses. Furthermore, the thickness of the glass ceramic would have to be very high, so that the dielectric field strength in the glass ceramic does not exceed 1 to 3 KV / mm. For applications in a voltage range above 10 kV, this would lead to a thickness of the glass-ceramic dielectric in the range of a few cm, which is unreasonable for practical use.

The solution of the problem is achieved on the basis of the teaching of claim 1 and is further developed and designed by the measures of the dependent claims.

The invention is based on the discovery that glass ceramic containing ferroelectric material can then be used for the high voltage applications in capacitors, when the glass ceramic is extremely porous or non-porous and the ferroelectric material is in crystallite form of the order of a few nanometers. A pore fraction in the volume of less than 0.03% is considered within the scope of the invention as "extremely low in pores". The crystallites of the ferroelectric material should be of the order of magnitude of the ferroelectric domains, that is to say lie within limits of 10 nm to 100 nm for the glass-ceramic BaTiO ₃ . This means that the glass-ceramic glass-ceramic must be obtained under stringent manufacturing conditions to produce ferroelectric material which exhibits a narrow hysteresis at the pole reversal and thus provides a tolerable power dissipation to be useful for high voltage applications in capacitors.

Instead of ferroelectric material and paraelectric material can be used. The paraelectric crystallites can be in the order of a few microns. This means crystallite sizes in the range 0.1 microns to 50 microns. Thus, the crystallites are substantially smaller than the thickness of the dielectric glass ceramic body for the production of the capacitors.

The dielectric glass ceramic body forms a disk-shaped substrate whose substrate thickness and substrate radius together with the radius of metallization layers can be determined as electrodes for a capacitor to be designed according to the teachings of the invention.

The inventors take advantage of the fact that the breakdown voltage (voltage to breakdown) of a glass-ceramic capacitor increases as the thickness of the glass-ceramic layer decreases. This is a great help in designing high performance capacitors of small design with high breakdown voltage. When dimensioning the glass-ceramic capacitors, it must finally be taken into account that field flashovers at the edges of the glass-ceramic must be prevented or at least kept within a tolerable range.

Thus, according to the invention, glass-ceramic capacitors are made available that are of spatially small dimension, but in which breakdowns of the electric field occur only to a tolerable level or can be virtually ruled out. Furthermore, corresponding capacitors can be produced inexpensively.

According to the invention, a capacitor is provided for applications between 3 kV and 100 kV, in particular between 5 kV and 60 kV, at high breakdown field strengths, comprising as a dielectric a glass ceramic dielectric body of liquid glass phase extremely low pore or non-porous with a content of ferroelectric material in crystallite form of the order less nanometer or on paraelectric material in crystallite form of the order of a few microns and containing glass formers has been produced and forms a disk-shaped substrate having a substrate thickness (d), a substrate radius (r ₁ ) and a wafer top, a disk underside and having a disk edge. The extent of the absence of pores is indicated by means of the so-called volume filling. The latter is at least 99.97% for the dielectric glass-ceramic body of the capacitor according to the invention. In practice, a volume filling of 99.9999% is achieved.

High breakdown field strengths are considered to be in the range of 10 kV / mm to 100 kV / mm and above.

• a) eine tolerable Durchschlagswahrscheinlichkeit (p),
• b) ein Substratradius (r_1n),
• c) eine Substratdicke (d_n),
• d) ein Radius Metallisierungsschicht (r_2n),
• e) Weibull-Gütekennwerte (b_n, E_0n),
• f) empirisch ermittelte Zahlenwerte (α = 0,189, β = 0,958, γ = 2/3), woraus
• g) das maximale elektrische Feld (E_max, ₀) der Serie von Test-Kondensatoren und eine Vergleichsdicke (d₀) ermittelt werden, woraus wiederum
• h) die maximal erlaubte Spannung (Û), das maximal erlaubte elektrische Feld (Ê₀) und das maximale elektrische Feld (E_max) des zu entwerfenden Kondensators bei einer Kondensatorsubstratdicke (d), gemessen in mm, wie folgt berechnet werden:

Further, the capacitor includes a first electrode, a first metalization layer having Metallisierungsradius (r ₂₎ that the disc top side to form a first metallization edge and leaving an upper disc edge area covered, as well as a second electrode, a second metallization layer having Metallisierungsradius (r _2), which the disc lower side covered with the formation of a second metallization edge and leaving a lower edge area of the disc, the first metallization edge and the second metallization edge facing each other on both sides of the glass ceramic body, which is the point of greatest breakdown risk with a maximum electric field (E _max ) for a homogeneous inner field (E ₀ ). forms in the space between the first and second metallization, wherein for determining the electrical and geometric values of a capacitor to be designed first by a series of test capacitors with predetermined, definie geometry whose breakdown strengths are measured for a Weibull statistic, using values as follows:

• a) a tolerable breakdown probability (p),
• b) a substrate radius (r _1n ),
• c) a substrate thickness (d _n ),
• d) a radius metallization layer (r _2n ),
• e) Weibull quality characteristics (b _n , E _0n ),
• f) empirically determined numerical values (α = 0.189, β = 0.958, γ = 2/3), from which
• g) the maximum electric field (E _max , ₀ ) of the series of test capacitors and a comparison thickness (d ₀ ) are determined, which in turn
• h) the maximum permissible voltage (Û), the maximum permissible electric field (Ê ₀ ) and the maximum electric field (E _max ) of the capacitor to be designed at a capacitor substrate thickness (d), measured in mm, are calculated as follows:

If ferroelectric material in crystallite form is used for the glass ceramic body of the capacitor, the glass ceramic body in a preferred embodiment has the following composition in wt%: component SiO ₂ B ₂ O ₃ BaO CaO Al ₂ O ₃ TiO ₂ CeO ₂ wt% 10,012 0.933 53.889 1,074 6,444 27.317 0.33

In this case, at least BaTiO _{3 is present} as a crystallized out ferroelectric phase, wherein the glass formation is the partial replacement of Ba by Ce or La results.

If paraelectric material in crystallite form is used for the glass ceramic body of the capacitor, the glass ceramic body in a preferred embodiment has the following composition in wt%: component SiO ₂ Al ₂ O ₃ BaO La ₂ O ₃ TiO ₂ ZrO ₂ wt% 3,607 9.184 34.528 6,114 37.897 (8,671

Here, at least Ba ₄ Al ₂ Ti ₁₀ O _{27 is present} as a crystallized paraelectric phase, resulting in the glass formation of the partial replacement of Ba by La and the partial replacement of Ti by Zr.

In a preferred embodiment, the capacitor according to the invention each has an annular zone with increased resistivity in comparison to the specific resistance of the metallization layers between the first metallization edge and the upper disk edge region, or between the second metallization edge and the lower disk edge region.

The geometry of the capacitor is described by the ratio of the diameter (2r ₂ ) of the metallization to the substrate thickness (d). This ratio is in a range between 10 and 300, preferably in a range between 15 and 200.

The ferroelectric material of the capacitor has a relative permittivity in the range between 100 and 600, preferably in the range between 200 and 500.

It should be noted that "relative permittivity" is the standard term for the dielectric constant or the dielectric constant. The relative permittivity is a measure of the permeability of a material for electric fields. It results as the ratio of the permittivity of the respective material to the electric field constant.

The dielectric material of the capacitor has a relative permittivity in the range between 15 and 70, preferably in the range between 25 and 50.

In a further preferred embodiment of the capacitor according to the invention, the thickness of the glass ceramic body in the region of the opposing metallization edges is increased. As a result, the course of the electric field lines is "distributed", that is, the density of the field lines decreases at the critical edge point. This increases the breakdown voltage.

The wafer edge of the glass ceramic body of the capacitor may alternatively be rounded, which also increases the breakdown voltage.

In a further embodiment, the capacitor has a glass ceramic body which is constructed from individual disks stacked on one another as a disk package with additional inner metallization layers on the individual disks.

This embodiment of the capacitor according to the invention can be modified such that the inner metallization layers occupy a larger area than the first or second metallization layer. In this way it is exploited that the breakdown voltage is higher for thin glass ceramic layers than for thicker layers.

Furthermore, the individual disks of the disk package of the capacitor may have an increasing disk thickness toward the center of the disk package.

In the following, the invention will be described in more detail with reference to the accompanying drawings, wherein like reference numerals refer to like parts.

Show it:

1 a perspective section through a first embodiment of the invention,

2 for the embodiment according to 1 in a diagram, the dependence of the maximum electric field strength with respect to the electric field strength in the interior of the ratio of the metallization radius to the substrate thickness,

3 a perspective section through a second embodiment of the invention,

4 in a diagram, the dependence of the maximum electric field strength with respect to the electric field strength in the interior of the resistivity of the additional annular zone of the embodiment according to 3 when applying a DC voltage,

5 in a diagram, the dependence of the maximum electric field strength with respect to the electric field strength in the interior of the resistivity of the additional annular zone of the embodiment according to 3 when applying an alternating voltage,

6 an equivalent circuit diagram for the embodiment of the invention according to 3 .

7 a perspective section through a third embodiment of the invention,

8th a perspective section through a fourth embodiment of the invention.

With reference to 1 Now, a first embodiment of a capacitor according to the invention 1 described. 1 is a perspective section through such a capacitor 1 , This comprises a glass ceramic body 10 as a dielectric.

The dielectric glass ceramic body 10 forms a disk-shaped substrate with a substrate thickness d, a substrate radius r ₁ , as well as a disk top, a disk bottom and a disk edge.

The glass ceramic body 10 was produced with extremely low pores or without pores from a liquid glass phase. The degree of freedom from pores is specified by means of the volume filling. This is in practice 99.9999%. The porosity should not exceed 0.03% in any case. The glass ceramic body has a content of ferroelectric material in crystallite form of the order of a few nanometers (in the range of 10 nm to 100 nm) or on paraelectric material in crystallite form of the order of magnitude of a few μm (in the range of 0.1 μm to 50 μm ). In practice, crystallite sizes in the range of 30 nm to 50 nm are measured for the glass-ceramic BaTiO ₃ . Thus, the order of magnitude of the crystallites in the order of magnitude of the ferroelectric domains of this glass ceramic of about 10 nm. For the glass-ceramic Ba ₄ Al ₂ Ti ₁₀ O ₂₇ crystallite sizes have been measured in the range 1 .mu.m to 10 .mu.m. The thickness of glass ceramic bodies for purposes of the invention is about 1 mm. Thus, the crystallites are much smaller than the thickness of such glass ceramic body for capacitors and the structure of the capacitors appears microscopically homogeneous to the outside. It should be noted that the glass ceramic 10 contains a residual glass phase in which the crystallites are embedded.

Indicates the glass ceramic body 10 a ferroelectric phase, such as BaTiO ₃ , the following composition in wt% is preferred: component SiO ₂ B ₂ O ₃ BaO CaO Al ₂ O ₃ TiO ₂ CeO ₂ wt% 10,012 0.933 53.889 1,074 6,444 27.317 0.33

In the case of this composition, the glass formation results in the partial replacement of Ba by Ce or La.

The ferroelectric material of the glass ceramic body 10 has a relative permittivity in the range between 100 and 600, preferably in the range between 200 and 500.

, The glass-ceramic body paraelectric phase such as Ba ₄ Al ₂ Ti ₁₀ O _27, La ₄ Ti ₉ SiO ₂ or La ₂ Ti ₂ SiO _9, the following composition is preferred in wt%: component SiO ₂ Al ₂ O ₃ BaO La ₂ O ₃ TiO ₂ ZrO ₂ wt% 3,607 9.184 34.528 6,114 37.897 (8,671

Glass formation in the case of this composition results in partial replacement of Ba by La and partial replacement of Ti by Zr.

The paraelectric material of the glass ceramic body 10 has a relative permittivity in the range between 15 and 70, preferably in the range between 25 and 50.

On top of the glass ceramic body is a first metallization layer 11 applied. This layer covers the top of the glass ceramic body 10 such that an upper disc edge area 12 is released. The boundary between the first metallization layer 11 and upper disk edge area 12 is formed by a metallization edge. The first metallization area 11 has a radius r ₂ .

Mirrored to the top, the capacitor 1 on its underside a second metallization area 13 with a second metallization edge and a lower edge of the disc 14 on. The second metallization area 13 also has a radius r ₂ .

Together form the first metallization area 11 and the second metallization region 13 the two electrodes of the capacitor 1 ,

The first metallization edge on the top of the glass ceramic body 10 and the second metallization edge on the underside of the glass ceramic body 10 stand opposite each other. The point at which the two metallization edges face each other forms the point of highest breakdown risk with a maximum electric field E _max for a homogeneous electric field of field strength E ₀ in the space between the first and second metallization layers.

The dependence of the maximum electric field strength E _max / E ₀ on the field strength E ₀ , on the ratio of radius r _{2 of} the two metallization layers 11 . 13 and substrate thickness d is in 2 shown. The lower curve shows this course in the event that to the capacitor 1 an AC voltage with a frequency of 100 Hz is applied, the upper curve is the case of an applied DC voltage. Both curves show that the maximum electric field E _max decreases as the ratio r ₁ / d increases. This implies the surprising fact that the field increase, the maximum electric field E _max , decreases at the point of greatest strike-through risk, the smaller the ratio r ₁ / d or r ₂ / d, that is, the thinner the glass ceramic body 10 is.

Against the background of this knowledge, the inventors now have a scaling rule for determining the electrical and geometric parameters of a capacitor according to the invention to be designed 1 developed.

First, certain values are assumed for a series of test capacitors with parameter values similar to the capacitor to be designed, but with a certain, defined geometry. For this series, the breakdown strengths are measured to provide Weibull statistics and to determine the maximum electric field (E _{max, 0} ). This forms the basis for the design rules of the new condenser to be designed, which may have changed geometries.

• a) Eine tolerable Durchschlagswahrscheinlichkeit p,
• b) einen Substratradius r_1n in mm,
• c) eine Substratdicke d in mm,
• d) einen Radius r_2n der beiden Metallisierungsschichten,
• e) Weibull-Gütekennwerte b_n, E_on für die Beschreibung der Verteilung der Ausfallwahrscheinlichkeit der Testkondensatoren und
• f) empirisch ermittelte Zahlenwerte (α = 0,189, β = 0,958, γ = 2/3), die sich durch Fitten bei numerischen Simulationen ergeben.

It should be noted that the breakdown field strengths are highly dependent on the geometry of the capacitors. Normally values are around 60kv / mm to 80kV / mm. For very thin glass ceramics (thicknesses less than 0.1 mm), values greater than 100 kV / mm are expected. In detail, the following values are used:

• a) A tolerable breakdown probability p,
• b) a substrate radius r _1n in mm,
• c) a substrate thickness d in mm,
• d) a radius r _{2n of} the two metallization layers,
• e) Weibull quality characteristics b _n , E _on for the description of the distribution of the probability of failure of the test capacitors and
• f) empirically determined numerical values (α = 0.189, β = 0.958, γ = 2/3), which result from fits in numerical simulations.

From these values, the maximum electric field E _{max, 0 of} the test capacitors and a comparison thickness d ₀ in mm are calculated.

On the basis of these values, in turn, the maximum permissible voltage Û and the maximum electric field E _{max of} the capacitor to be designed for the case of a given substrate thickness d in mm are calculated as follows.

Referring now to 3 In the following, a second embodiment of a capacitor according to the invention will be described. 3 shows a perspective section through such a second embodiment. Shown is a capacitor 2 with a glass ceramic body 10 , for the geometry and composition of the corresponding statements to the first embodiment according to 1 be valid. On top of the glass ceramic body 10 is a first metallization layer 11 with a first metallization edge, on the underside a second metallization layer 13 attached with a second metallization edge. The capacitor 2 also has an upper disc rim area 12 and a lower disk edge area 14 on. In the embodiment according to 3 is between the first metallization edge and the upper disk edge area 12 and between the second metallization edge and the lower disk edge region 14 each an additional annular zone 21 with a specific resistance to the glass ceramic body 10 applied by coating. The specific resistance of this annular zone 21 is higher than the resistivity of the two metallization layers.

As already stated, occurs without such an annular zone 21 the peak value of the electric field at the metallization edge. When such an annular zone is applied, in the case of a highly conductive ring, this corresponds only to an increase in the radius of the metallization layer and results in the peak electric field occurring closer to the perimeter of the glass ceramic body, which is undesirable. With high specific resistance of the zone 21 it remains at the peak of the electric field at the original metallization edge. By varying the specific resistance of the annular zone, it is thus possible to find the resistance value for which the peak value of the electric field is minimal for a given geometry and operating frequency. The exiting edge field lines are distributed over the ring zone 21 and do not stay focused on the metallization edge.

The results of such investigations will be published in 4 shown. 4 shows in a diagram the dependence of the maximum electric field strength E _max with respect to the field strength E _{0 of} the homogeneous field inside the capacitor 2 the resistivity ρ _L [Ωm] of the annular zone 21 when applying a DC voltage. The investigations were carried out for comparison reasons for a capacitor according to the invention with a glass ceramic body as a dielectric and for a capacitor of the same geometry, but with oil as a dielectric. For both dielectrics considered, the result is almost the same favorable value for the specific resistance of the annular zone 21 in the range 1 × 10 ⁸ to 1 × 10 ¹⁰ Ωm and an optimum at 1 × 10 ⁹ Ωm.

5 shows in a diagram the dependence of the maximum electric field strength E _max with respect to the field strength E _{0 of} the homogeneous field inside the capacitor 2 the resistivity ρ _L [Ωm] of the annular zone 21 when applying an alternating voltage with a frequency of 100 Hz. The investigations were carried out for comparison reasons for a capacitor according to the invention with a glass ceramic body as a dielectric and for a capacitor of the same geometry, but with oil as a dielectric. Out 5 it follows that there is an optimum for the dielectric loss at which the dielectric strength is maximum. However, the frequency requirement must still be considered in the design (equivalent circuit diagram).

6 is an equivalent circuit diagram for the embodiment according to 3 , The annular zone forms an RC series element with ohmic resistance R ₂ and capacitance C _{2 in} addition to the RC parallel element with ohmic resistance R ₁ and capacitance C ₁ . If a capacitor according to 3 is designed, it is checked whether the target cutoff frequency or cutoff frequency f _{c is} complied with in accordance with known engineering rules.

example

To obtain a scaling rule for the resistivity of an annular zone for a capacitor intended for operating frequencies below 1 kHz, a capacitor was set with the following values:
Rated capacity: 5.5 nF
Rated voltage: 30 kV

When using glass-ceramic with a relative permittivity ε of the dielectric of 220, the following values were determined:
Electrical field constant: 8.85 x 10 ^-12 As / Vm
Thickness of the dielectric: 1 mm
Radius r _{2 of} the metallization layer: 30 mm
Total radius r ₃ of metallization layer and annular zone: 34 mm
Capacity of the annular zone C ₂ : 1.56 · 10 ^-9 F
Height or thickness of the annular zone h: 5 · 10 ^-3 mm
electrical resistance R _{2 of} the annular zone: 102 kΩ
Cutoff frequency f _c : 1000 Hz
Specific resistance ρ of the material for the annular zone: 2 kΩm

In order to obtain a cutoff frequency f _c of 1000 Hz, the material of the annular zone must be suitably chosen, where:

A material with a specific resistance ρ of 2 kΩm in a thickness of 5 microns fulfills this condition and can be applied as a paste by coating on the glass ceramic body.

The embodiments according to the 1 and 3 can be varied in two ways.

On the one hand, the thickness of the glass-ceramic body can be increased in the region of the metallization edges which are in mirror image. The resulting shape of the glass ceramic body is also referred to as the Rogowski profile.

On the other hand, the disc edge of the glass ceramic body can be rounded.

These two developments lead to the course of the electric field in the edge region of the capacitor is flattened, resulting in a higher breakdown voltage, that is, the electrical breakdown occurs only at a higher voltage relative to the case without the training.

Referring now to 7 a third embodiment of the capacitor according to the invention will be described. 7 is a perspective section through a capacitor 3 standing at its top with a metallization layer 11 is provided. This layer 11 does not cover the entire surface, but leaves a border area 12 left. Instead of the glass ceramic body 10 of the two embodiments described above, the capacitor 3 a glass ceramic body 30 on, made of individual glass ceramic panes 30a with metallization layers between them 31 consists. The capacitor 3 is thus constructed as a disk package. The capacitor 3 consists of series-connected single capacitors, whereby the total voltage of the capacitor 3 compared to the embodiments according to the 1 or 3 is increased. At the same time, the dielectric strength increases significantly as the capacitor becomes thinner for the same area. at 7 If several individual capacitors are connected in series, the high dielectric strength can be harnessed for high voltages.

Will be an odd number of metallization layers 31 planned, the middle layer can be omitted for symmetry reasons, as in 8th shown.

In a not shown embodiment of the embodiment according to 7 or 8th take the metallization layers inside the glass ceramic body 30 a larger area (have a slightly larger radius), as the first and the second metallization layer on the top and the bottom of the glass ceramic body. In order to obtain a significant effect on the field distribution at the critical location, the marginal edge of the metallization layer, the degree of enlargement of the metallization layers must be increased 31 in the interior of the glass ceramic body in the order of the thicknesses of the individual glass ceramic panes 30a be. If such glass ceramic discs are 1 mm thick, the inner metallization layers should 31 have a radius larger by about 1 mm than the first or second metallization layer 11 . 13 ,

Referring now to 8th a fourth embodiment of the capacitor according to the invention will be described. 8th is a perspective section through a capacitor 4 , which is the same structure with respect to the layer sequence of glass ceramic discs and metallization layers as the capacitor 3 in 7 , However, the individual disks have a thickness increasing toward the middle of the disk package.

LIST OF REFERENCE NUMBERS

1

capacitor

2

capacitor

3

capacitor

4

capacitor

10

Ceramic body

11

first metallization layer

12

upper disk edge area

13

second metallization layer

14

lower pane edge area

21

annular zone

30

Ceramic body

30a

 Ceramic discs

31

metallization

40

Ceramic body

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• DE 1951624 [0002]
• WO 2005/095301 A1 [0003]
• DE 102008011206 A1 [0004]

Claims (12)

Capacitor for high voltage applications between 3kV and 100kV, comprising: - a dielectric glass ceramic body ( 10 ), which has been produced from liquid glass phase with extremely low pores or without pores under a content of ferroelectric material in crystallite form of the order of a few nanometers or paraelectric material in crystallite form of the order of a few μm and containing glass former, and a disk-shaped substrate having a substrate thickness (d), a substrate radius (r ₁ ) and a wafer top, a wafer bottom and a wafer edge, - a first metallization layer ( 11 metallization radius (r ₂ ), which forms the wafer top to form a first metallization edge and leaving an upper wafer edge region ( 12 ), a second metallization layer having a metallization radius (r ₂ ), which forms the underside of the disk to form a second metallization edge and leaving a lower edge area of the disk ( 14 ), wherein the first metallization edge and the second metallization edge extend on both sides of the glass ceramic body ( 10 ), which forms the site of the greatest breakdown risk with a maximum electric field (E _max ) for a homogeneous inner field (E ₀ ) in the space between the first and second metallization layer, - wherein for determining the electrical and geometric values of a capacitor to be designed first of a series of test capacitors having a predetermined, defined geometry is used, the breakdown strengths of which are measured for a Weibull statistic using values as follows: a) a tolerable breakdown probability (p), b) a substrate radius (r _1n ), c) a substrate thickness (d _n ), d) a radius of the metallization layer (r _2n ), e) Weibull quality characteristics (b _n , E _0n ), f) empirically determined numerical values (α = 0.189, β = 0.958, γ = 2/3 ), from which g) the maximum electric field (E _max , ₀ ) of the series of test capacitors and a comparison thickness (d ₀ ) are determined, from which in turn h) the maximum permissible bte voltage (Û), the maximum permissible electric field (Ê ₀ ) and the maximum electric field (E _max ) of the capacitor to be designed at a capacitor substrate thickness (d) in mm are calculated as follows:

Capacitor ( 1 ) according to claim 1, wherein the glass ceramic body ( 10 ) has the following composition in wt%: component SiO ₂ B ₂ O ₃ BaO CaO Al ₂ O ₃ TiO ₂ CeO ₂ wt% 10,012 0.933 53.889 1,074 6,444 27.317 0.33 and at least BaTiO _{3 is present} as a crystallized ferroelectric phase, wherein the glass formation results in the partial replacement of Ba by Ce or La. Capacitor ( 1 ) according to claim 1, wherein the glass ceramic body ( 10 ) has the following composition in wt%: component SiO ₂ Al ₂ O ₃ BaO La ₂ O ₃ TiO ₂ ZrO ₂ wt% 3,607 9.184 34.528 6,114 37.897 (8,671 and at least Ba ₄ Al ₂ Ti ₁₀ O _{27 is present} as a crystallized paraelectric phase, the glass formation resulting in the partial replacement of Ba by La and the partial replacement of Ti by Zr. A capacitor according to any one of claims 1 to 3, wherein each one annular zone ( 21 ) with increased specific resistance in comparison to the specific resistance of the metallization layers between the first metallization edge and the upper edge region ( 12 ), or between the second metallization edge and the lower edge area of the disc, are mounted. A capacitor according to any one of claims 1 to 4, wherein the ratio of the diameter (2r ₂ ) of the metallization ( 11 ) to the substrate thickness (d) in a range between 10 and 300, preferably in a range between 15 and 200.  A capacitor according to any one of claims 1, 2 and 4, 5, wherein the ferroelectric material has a relative permittivity in the range between 100 and 600, preferably in the range between 200 and 500.  A capacitor according to any one of claims 1 and 3 to 5, wherein the dielectric material has a relative permittivity in the range between 15 and 70, preferably in the range between 25 and 50.  Capacitor according to one of claims 1 to 7, wherein the thickness of the glass ceramic body is increased in the region of the opposing metallization edges. Capacitor according to one of claims 1 to 8, wherein the disk edge of the glass ceramic body ( 10 ) is rounded. A capacitor according to any one of claims 1 to 9, wherein the glass ceramic body ( 30 ) of individual disks ( 30a ) as a disk package with additional inner metallization layers ( 31 ) on the individual discs ( 30a ) is constructed. The capacitor of claim 10, wherein the inner metallization layers have a larger area than the first or second metallization layer (10). 11 . 13 ).  A capacitor according to claim 10 or 11, wherein the individual disks of the disk package have increasing disk thickness towards the center of the disk package.

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