JP4065766B2 - Dielectric constant measurement method - Google Patents

Description

【００３１】
ただし、ｘ’_0mはＪ’₀（ｘ’）＝０のｍ番目の解で、特にｍ＝１の時、ｘ’₀₁＝３．８３１７である。Ｊ’₀（ｘ’）は０次の第一種ベッセル関数の微分である。ω＝２πｆ₀は角共振周波数、μ₀＝４π×１０^-7は真空の透磁率である。αは、小林らによるマイクロ波研究会技術報告書ＭＷ７５−７６「平衡形円板共振器による複素誘電率測定法」で開示されているように、Ｓ＝Ｒ／ｄ＞１０のとき、αはほぼ１となる。また、ｃは光速であり、△Ｒは内部円形導体の端での電磁界の外側への広がりを、内部円形導体径の増加として考慮したものである。ｌｎは自然対数を表す。
【００３２】
なお、誘電正接の決定に必要な導体の実効導電率σは、小林らによるマイクロ波研究会技術報告書ＭＷ７５−７６「平衡形円板共振器による複素誘電率測定法」で開示されているように、比誘電率と誘電正接が同じで厚さが異なる誘電体シートにより構成された２種類の平衡形円板共振器のＱｕの差から決定される。あるいは同時焼成導体の実効導電率σは特開２０００−４６７５６号公報に開示された界面導電率の測定法により決定される。
【００３３】
このようにして、第１測定試料１の比誘電率及び／又は誘電正接が予め求められる。尚、特願２００２−２８１９０８号の誘電定数測定法により、第１測定試料１の比誘電率及び／又は誘電正接を求める場合には、表面円形導体と下部導体層で第１測定試料１が挟持された円板共振器と、該円板共振器からの電磁界の漏洩を防ぐシールド体とを設け、該シールド体に設けられた入力用、出力用の励振口を介してＴＭ_0m0モード（ｍ＝１、２・・・）を励振させ、その共振周波数と無負荷Ｑの測定値から、第１測定試料１の比誘電率及び／又は誘電正接が求められる。
【００３４】
このようにして求められた第１測定試料１の比誘電率及び／又は誘電正接と、図１の円板共振器Ａの共振周波数と無負荷Ｑの測定値から、被測定部位である第２測定試料２の比誘電率ε’₂、誘電正接ｔａｎδ₂を計算する。この計算は有限要素法やモードマッチング法等の数値解析によって行う必要がある。
【００３５】
ここでは有限要素法による計算法について述べる。まず共振周波数ｆ₀のε’₂依存性、即ちｆ₀−ε’₂曲線を軸対称有限要素法による解析で求め、次にｆ₀の測定値から、このｆ₀−ε’₂曲線を用いて比誘電率を決定する。
【００３６】
誘電正接ｔａｎδ₂は下記式２を用いて算出される。
【００３７】
【数２】

【００３８】
この式は無負荷Ｑの逆数を、第１測定試料１の誘電正接ｔａｎδ₁と被測定部位である第２測定試料２の誘電正接ｔａｎδ₂と導体３、４、５の表皮抵抗Ｒ_sの項によって表現したものである。Pe１は第１測定試料１に貯えられる電界エネルギーの集中率、Pe2は第２測定試料２に貯えられる電界エネルギーの集中率、Gは形状因子であり、有限要素法により求められる。
【００３９】
図３は、本発明の他の誘電定数測定法を説明するためのものである。図３の円板共振器Ａは支持基板６上に形成されている。即ち、支持基板６上に、第２外部導体５、被測定部位である第２測定試料２、円形内部導体３、第１測定試料１、第１外部導体４を順次積層して構成されており、これらが支持基板６と同時に焼成され、一体となっている。第１、第２測定試料１、２はセラミックス又はガラスセラミックスから構成され、異なる厚みとされている。
【００４０】
共振器Ａの第１、第２測定試料１、２、支持基板６は、配線基板の絶縁層材料と同一で、円形内部導体３、第１、第２外部導体４、５は配線基板の内部配線材料と同一で、同一厚みとされ、焼成などの製法も同一とされている。従って、第１、第２測定試料１、２への円形内部導体３、第１、第２外部導体４、５材料の拡散状態やセラミックス又はガラスセラミックス内の空隙の分布状態は、配線基板と同一と見なすことができる。
【００４１】
このような共振器Ａは、厚い支持基板６上に一体に形成されているため、共振器Ａの第２測定試料２の厚みを２００μｍ以下、特には５０μｍ以下と薄くしても共振器Ａを容易に形成することができ、しかも、支持基板６が形成されていない第１外部導体４に形成された励振口７、８を介して電界により励振することができ、これにより円板共振器Ａの共振周波数と無負荷Ｑを測定でき、上記したように、第１測定試料１の比誘電率と誘電正接、及び円板共振器Ａの共振周波数と無負荷Ｑから、第２測定試料２の比誘電率と誘電正接を算出することができる。
【００４２】
又、支持基板６とその上部を一体基板とみなせるので、基板内の任意深さの位置での比誘電率と誘電正接を測定することができる。
【００４３】
図４は、本発明のさらに他の誘電定数測定法を説明するためのもので、図４の円板共振器Ａは、図３に示した円板共振器Ａと同様に、支持基板６上に、第２外部導体５、被測定部位である第２測定試料２、円形内部導体３、第１測定試料１、第１外部導体４を順次積層して構成されており、これらが支持基板６と同時に焼成され、一体となっている。第１、第２測定試料１、２はセラミックス又はガラスセラミックスから構成され、異なる厚みとされている。
【００４４】
そして、円形内部導体３の半径Ｒに対して、０．４〜０．６倍の半径を有する同心円上の第１外部導体４の位置に２個の励振口７、８を設け、これらの励振口７、８にループアンテナ１９、２０を挿入し、磁界励振によってＴＭ₀₁₀共振モードを励振する。
【００４５】
ＴＭ₀₁₀共振モードの磁界は、図５に示すように、円形内部導体３に対して半径が約１／２の同心円周の位置で強く分布する。これにより、励振口７、８を介して同軸ケーブル９、１０先端のループアンテナ１９、２０で磁界励振すると、ＴＭ₀₁₀共振モードを片面から効率的に励振できる。これを用い、円板共振器Ａの共振周波数と無負荷Ｑを測定し、第２測定試料２の比誘電率と誘電正接を算出することができる。尚、図５では、磁界分布を説明するため、第１、第２測定試料１、２の断面を示す斜線を省略した。
【００４６】
尚、円形内部導体３の半径Ｒに対して、０．２５倍、又は０．７５倍の半径を有する同心円上の第１外部導体４の位置に２個の励振口７、８を設け、これらの励振口７、８にループアンテナ１９、２０を挿入し、磁界励振によってＴＭ₀₂₀共振モードを励振させても良い。
【００４７】
また、円形内部導体３の半径Ｒに対して、１／６倍、又は１／２倍、或いは５／６倍の半径を有する同心円上の第１外部導体４の位置に２個の励振口７、８を設け、これらの励振口７、８にループアンテナ１９、２０を挿入し、磁界励振によってＴＭ₀₃₀共振モードを励振させても良い。
【００４８】
尚、磁界を印可して円板共振器Ａを励振する図４の場合に、図１に示したように支持基板６を形成しなくても、図１に示した場合と同様にして、第２測定試料２の比誘電率と誘電正接を測定することができる。
【００４９】
【実施例】
本発明の誘電定数測定法により、アルミナ質基板の内部の比誘電率を測定した。測定基板の構造は図４に示すものであり、アルミナ材料からなるグリーンシートにＣｕ−Ｗ系の導電性ペーストを塗布し、これを複数積層して積層成形体を作製し、この積層成形体を同時焼成し、円板共振器Ａと支持基板６を一体化した。
【００５０】
ここで、支持基板６の厚みを２００μｍ、円形内部導体３、第１、第２外部導体４、５の厚みを１０μｍとし、円形内部導体３の直径を２３．３ｍｍとした。第１、第２測定試料１、２の厚みを変化させた円板共振器Ａを作製した。
【００５１】
又、図４に示す磁界結合を行うため、励振口７、８を１．５ｍｍ径とし、１．２ｍｍ径の同軸ケーブル９、１０先端に作製した約１．５ｍｍ径のループアンテナ１９、２０を挿入し、円板共振器Ａを励振し、円板共振器Ａの共振周波数、無負荷Ｑを求めた。
【００５２】
この後、第１測定試料１の比誘電率を特願２００２−１５１６６５号に記載された方法で測定した。
【００５３】
即ち、円形内部導体を両側から第１測定試料により挟持し、これを第１、第２外部導体で挟持し、第１外部導体の励振口から同軸ケーブルにより電界を印加し電界励振し、円板共振器の共振周波数と無負荷Ｑを測定し、上記式１から第１測定試料１の比誘電率を算出した。
【００５４】
さらに図４の円板共振器Ａの共振周波数を測定し、及び第１測定試料１の誘電率から、第２測定試料の比誘電率を計算した。結果を表１に示す。図６に、試料基板Ｎｏ．２の共振波形を示す。
【００５５】
【表１】

【００５６】
この表１によれば、第２測定試料２の比誘電率は異なった値として測定されている。この違いは円形内部導体、第１、第２外部導体から第２測定試料２への拡散効果、及び基板全体の中での第２測定試料２の深さ（上下方向への位置）に依存したものと考えられる。
【００５７】
【発明の効果】
以上、詳述した通り、本発明の誘電定数測定法によれば、円板共振器を構成する第１外部導体に磁界や電界の入力用、出力用の励振口を形成するため、支持基板の上に導体層と同時焼成あるいは一体成形した円板共振器の誘電定数を測定でき、従来測定が困難であった導体層と同時焼成あるいは一体成形された薄層の測定試料の比誘電率及び／又は誘電正接を容易に求めることができるとともに、異なる誘電体層を有し、誘電体層間に内部配線を有する配線基板等の電子部品において、任意の誘電体層における誘電定数を測定することができ、これにより、現実に近い配線基板等の電子部品の設計を行うことができ、マイクロ波用途の同時焼成用、或いは一体成形用の誘電体材料の開発が容易になるとともに、これらの材料を用いた回路基板や、半導体パッケージの設計がより高精度に行えるようになる。
【図面の簡単な説明】
【図１】本発明の誘電定数測定法に用いられる円板共振器の一例を示すもので、（ａ）は平面図、（ｂ）は概略断面図である。
【図２】図１の円板共振器におけるＴＭ₀₁₀モードの電界分布を説明するもので、（ａ）は平面図、（ｂ）は概略断面図である。
【図３】本発明の誘電定数測定法に用いられる円板共振器の他の例を示すもので、（ａ）は平面図、（ｂ）は概略断面図である。
【図４】本発明の誘電定数測定法に用いられる円板共振器のさらに他の例を示すもので、（ａ）は平面図、（ｂ）は概略断面図である。
【図５】図４の円板共振器におけるＴＭ₀₁₀モードの磁界分布を説明するもので、（ａ）は平面図、（ｂ）は概略断面図である。
【図６】表１の試料基板Ｎｏ．２の誘電定数測定に用いられる共振波形を示す図である。
【図７】従来の誘電定数測定法に用いられる平衡形円板共振器を示すもので、（ａ）は平面図、（ｂ）は概略断面図である。
【符号の説明】
１・・・第１測定試料
２・・・第２測定試料
３・・・円形内部導体
４・・・第１外部導体
５・・・第２外部導体
６・・・支持基板
７、８・・・励振口
９、１０・・・同軸ケーブル
１９、２０・・・ループアンテナ
Ａ・・・円板共振器[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a dielectric constant measurement method, and more particularly to a dielectric constant measurement method for a dielectric substrate used as an electronic component in a high frequency region.
[0002]
[Prior art]
In recent years, with the development and popularization of mobile communication technology, there is a strong demand for a dielectric constant measurement method for dielectric substrates for microwave circuit configuration. Various methods for measuring dielectric constants of microwaves on dielectric substrates have been proposed. Among them, the cavity resonator method is recognized as a high-precision measurement method. This cavity resonator method measures the dielectric constant in the in-plane direction of the substrate, but it is difficult to measure a thin or fragile sample that cannot be self-supported by a measurement sample alone or a dielectric layer formed on the substrate. .
[0003]
On the other hand, a balanced disk resonator method is known as a dielectric constant measuring method perpendicular to the substrate. In many cases, the excitation of the balanced disk resonator method is performed from the side surface of the disk-shaped inner conductor by a strip line. In this balanced disk resonator method, it is necessary to set the characteristic impedance of the stripline to 50Ω in order to obtain consistency with the measurement system, but in order to realize the impedance of 50Ω on the thin dielectric substrate, the stripline line is required. Needs to be extremely thin.
[0004]
For example, in order to realize a stripline line having an impedance of 50Ω by simultaneous firing, a dielectric layer having a thickness of 200 μm is the limit. If the resonator is excited by a strip line having an impedance deviating from 50Ω, reflection occurs at the connector or the like, and there is a problem that the measurement accuracy of the resonance characteristics, and hence the measurement accuracy of the dielectric characteristics, deteriorates.
[0005]
In order to solve such problems, in recent years, a method has been proposed in which the resonator is excited by a coaxial cable from the center of the upper and lower surfaces of the balanced disk resonator. FIG. 7 shows this dielectric constant measurement method. A circular inner conductor 31 is sandwiched between measurement samples 33 made of an organic resin, and outer conductors 35 are formed on the surfaces of these measurement samples 33, respectively. A is formed, excitation ports are respectively formed in the outer conductors 35 corresponding to the center of the circular inner conductor 31, coaxial cables 37 are inserted into these excitation ports, and the resonator A is excited by an electric field. The relative dielectric constant and dielectric loss tangent of the measurement sample 33 were obtained from the measured values of the resonance frequency and the no-load Q (see Non-Patent Document 1).
[0006]
[Non-Patent Document 1]
“Electronic Information and Communication Technology Research Report, Science Technology Vol. 91-17, No. 52” The Institute of Electronics, Information and Communication Engineers, May 23, 1991, p. 17-22
[0007]
[Problems to be solved by the invention]
However, in the dielectric constant measurement method shown in FIG. 7, it is necessary to insert the coaxial cable 37 into the excitation ports on both sides of the balanced disk resonator A and perform measurement. Therefore, the balanced disk resonator is placed on the support substrate. In the measurement of a ceramic sample that cannot be manufactured A and is a very thin dielectric layer and co-fired with a conductor layer, or a dielectric sample that is a very thin dielectric layer and is integrally molded, there is no warping of the sample. Since it occurs or breaks, there is a problem that it is substantially difficult to prepare a thin layer sample.
[0008]
In addition, it is known that a wiring board made of ceramics has a distribution such as porosity in the thickness direction of the substrate during firing, and the dielectric constant may change in the thickness direction. In the constant measurement method, the average dielectric constant of the dielectric substrate is measured due to the structure, and the change of the dielectric constant in the thickness direction of the dielectric substrate cannot be measured.
[0009]
An object of the present invention is to provide a dielectric constant measurement method capable of measuring a dielectric constant of a thin layer measurement sample and measuring a dielectric constant of a dielectric layer having an arbitrary thickness at an arbitrary depth of the measurement sample. To do.
[0010]
[Means for Solving the Problems]
In the dielectric constant measurement method of the present invention, a circular inner conductor is sandwiched between a first measurement sample and a second measurement sample having different thicknesses, and first and second outer conductors are formed on the surfaces of the first and second measurement samples, respectively. Ri greens and, said first disc resonator Ru der than 200μm thickness of the measurement sample, and excitation Fukuchi provided at a position of the first outer conductor corresponding to the center position of the circular inner conductor, A coaxial cable is inserted into the excitation port provided at the position of the first outer conductor corresponding to the position of the end of the circular inner conductor, and the TM _0m0 mode (m = 1, 2,...) _Is excited by an electric field. , Measuring the resonance frequency and no-load Q, and from the measured values of the resonance frequency and no-load Q of the disc resonator, and the relative dielectric constant and / or dielectric loss tangent of the first measurement sample measured in advance, A dielectric constant of the second measurement sample is obtained.
Further, the circular inner conductor is sandwiched between the first measurement sample and the second measurement sample having different thicknesses, and the first and second outer conductors are formed on the surfaces of the first and second measurement samples, respectively. A disk resonator having a measurement sample thickness of 200 μm or more is inserted in a loop antenna into at least two excitation openings provided at positions of the first outer conductor corresponding to concentric circles of the circular inner conductor, and a magnetic field is applied. The TM _0m0 mode (m = 1, 2,...) _Was excited, its resonance frequency and unloaded Q were measured, and the measured values of the resonance frequency and unloaded Q of the disk resonator were measured in advance. A dielectric constant of the second measurement sample is obtained from a relative dielectric constant and / or a dielectric loss tangent of the first measurement sample.
[0011]
In such a dielectric constant measurement method, an excitation port for input and output of a magnetic field and an electric field is formed on one outer conductor constituting a disk resonator, so that it is simultaneously fired or integrated with a conductor layer on a support substrate. Dielectric constant of molded disk resonator can be measured, and dielectric constants such as relative permittivity and / or dielectric loss tangent of thin layer measurement sample co-fired or integrally formed with conductor layer, which was difficult to measure conventionally, are easy Can be requested.
[0012]
Further, in the present invention, since the disk resonator can be excited by applying a magnetic field or an electric field from one side of the disk resonator and the dielectric constant of the measurement sample can be measured, for example, the disk resonator is placed on a flat part. It is possible to measure the dielectric constant by placing it, and it is not necessary to pay attention to holding for applying an electric field from both sides of the disk resonator, such as measuring with a disk resonator standing up like before, Even if the plate resonator is thinned, it is easy to handle by forming the disc resonator on the support substrate.
[0013]
Furthermore, in the dielectric constant measurement method of the present invention, the thicknesses of the measurement samples above and below the circular inner conductor of the disk resonator can be set to different thicknesses without being the same thickness. In an electronic component such as a wiring board having internal wiring between dielectric layers, the dielectric constant in an arbitrary dielectric layer can be measured.
[0014]
That is, in an actual electronic component such as a wiring board, a dielectric layer made of ceramics or glass ceramics and internal wiring are fired at the same time, and the dielectric layer is affected by its thickness, internal wiring material, etc. It is known that the dielectric layers have different dielectric constants depending on the formation depth), but the dielectric constants of the dielectric layers in the portions having different dielectric layers between the internal wirings are measured. If this is desired, a disk resonator modeled on that part can be produced, and the dielectric constant of each dielectric layer can be measured. Therefore, it is possible to design an electronic component such as a wiring board that is more realistic.
[0015]
In addition, by using the excitation port provided at a position where the electric field strength is zero or small, the disk resonator is excited by a magnetic field, so that even if the measurement sample is thin, it is not affected by the excitation port and is measured with high accuracy. it can.
[0016]
The dielectric constant measurement method of the present invention is characterized in that the thickness of the second measurement sample of the disk resonator formed on the support substrate is 0.2 mm or less. Further, the first and second measurement samples are made of ceramics or glass ceramics, and the support substrate and the disk resonator are simultaneously fired and integrated.
[0017]
In general, if the dielectric constant of the insulating layer of the wiring board used in the microwave region can be confirmed, it can be utilized for the design of the wiring board. By the way, in a wiring board formed by simultaneously firing an insulating layer made of ceramics or glass ceramics and internal wiring, the metal material forming the internal wiring can diffuse into the insulating layer during firing and the dielectric constant of the insulating layer can change. Sex is pointed out. By confirming the dielectric constant of such an actual insulating layer, it is possible to make the most of the circuit design.
[0018]
However, in recent years, the thickness of the wiring board has been reduced, and the actual thickness of the insulating layer has been reduced to 0.2 mm or less, particularly 0.05 mm or less. The dielectric constant of the insulating layer of such a wiring board has been measured. Therefore, when an attempt is made to produce a resonator as shown in FIG. 7 that reflects the actual thickness, the measurement sample is thin, making it difficult to measure.
[0019]
In the present invention, the first and second measurement samples are made of ceramics or glass ceramics, and the support substrate and the disk resonator are simultaneously fired and integrated, and the disk resonator is formed on the support substrate. Even if the measurement sample of the resonator is thinned, the strength of the resonator can be improved by the support substrate, so that the resonator can be easily formed, and the dielectric constant can be measured using the excitation port of the first outer conductor. Even when the thickness of the measurement sample is as thin as 0.2 mm or less, the dielectric constant can be easily measured.
[0021]
DETAILED DESCRIPTION OF THE INVENTION
The dielectric constant measurement method of the present invention will be described with reference to FIG. First, the disk resonator A used for measurement is produced.
[0022]
The disk resonator A includes a first measurement sample (upper dielectric layer) 1 having a different thickness and a second measurement sample (lower dielectric layer) 2 that is a part to be measured. The first and second circular inner conductors 3 having a smaller area than the second measurement samples 1 and 2 are disposed outside the first and second measurement samples 1 and 2. The outer conductors 4 and 5 are respectively arranged. That is, the disc resonator A sandwiches the circular inner conductor 3 between the first and second measurement samples 1 and 2 having different thicknesses, and the first and second measurement samples 1 and 2 have first and second surfaces respectively. The second outer conductors 4 and 5 are formed.
[0023]
The circular inner conductor 3 and the outer conductors 4 and 5 may be formed of a conductor material. In particular, the electromagnetic field is not transmitted between the two first and second measurement samples 1 and 2 and the electromagnetic field is radiated. From the viewpoint of preventing this, it is desirable that the thickness of the circular inner conductor 3 and the outer conductors 4 and 5 is at least 5 μm or more, particularly 10 μm or more.
[0024]
The first and second measurement samples 1 and 2 are made of an insulating material such as ceramics, glass ceramics, or organic resin. In particular, the first and second measurement samples 1 and 2 are easy to form. 1. The thickness of the second measurement samples 1 and 2 is desirably 200 μm or more .
[0025]
When the first and second measurement samples 1 and 2 are ceramics and glass ceramics, the disk resonator A has the first and second measurement samples 1 and 2, the circular inner conductor 3, and the first and second outer conductors 4. When the first and second measurement samples 1 and 2 are organic resins, the disc resonator A has the first and second measurement samples 1 and 2 and a circular shape. The inner conductor 3 and the first and second outer conductors 4 and 5 are formed by bonding or pressure bonding.
[0026]
One excitation port 7 is formed at the position of the first outer conductor 4 corresponding to the center of the circular inner conductor 3, and one is provided at the position of the first outer conductor 4 corresponding to the end of the circular inner conductor 3. The excitation opening 8 is formed. Coaxial cables 9 and 10 are inserted into the excitation ports 7 and 8 so that the TM _0m0 resonance mode (m = 1, 2,...) Is excited. The distance R between the excitation ports 7 and 8 is ½ of the diameter D of the circular inner conductor 3.
[0027]
When an electric field is applied through the coaxial cable 9 from the excitation port 7 of the resonator A configured as described above, the resonator A is excited by the electric field, and the TM _0m0 resonance mode (m = 1, 2,...) In particular, the TM ₀₁₀ resonance mode can be excited efficiently from one side. The electric field of the TM ₀₁₀ resonance mode is strongly distributed at the center of the circular inner conductor 3 and the circumferential portion at the end of the circular inner conductor 3 as shown in FIG. Then, an electric field is taken out from the excitation port 8 through the coaxial cable 10, whereby the resonance frequency and the no-load Q of the disk resonator A are measured. An electric field may be applied from the excitation port 8 and taken out from the excitation port 7. In FIG. 2, the hatched lines indicating the cross sections of the first and second measurement samples 1 and 2 are omitted in order to clarify the electric field distribution.
[0028]
Next, the relative dielectric constant and / or the dielectric loss tangent of the first measurement sample 1 are obtained in advance by, for example, the dielectric constant measurement method described in Japanese Patent Application Nos. 2002-151665 and 2002-281908. The relative dielectric constant and / or dielectric loss tangent of the first measurement sample 1 may be obtained by other measurement methods. Of course, the relative dielectric constant and / or the dielectric loss tangent of the first measurement sample 1 may be performed before measuring the resonance frequency and no-load Q of the disk resonator A.
[0029]
When the relative permittivity and / or dielectric loss tangent of the first measurement sample 1 is measured in Japanese Patent Application No. 2002-151665, for example, the thicknesses of the first and second measurement samples 1 and 2 in FIG. The thickness of the sample 1 is set, that is, the circular inner conductor 3 is sandwiched by the first measurement sample 1, and an electric field is applied from the excitation port 7 of the resonator A by the coaxial cable 9 to excite the electric field. Measure the resonance frequency and no-load Q. When the ratio of the radius R of the circular inner conductor 3 to the thickness d of the measurement samples 1 and 2 is 10 or more, that is, R / d> 10, the resonance frequency f ₀ of the TM _0m0 mode of this balanced disk resonator A is _obtained. From the unloaded Q (Qu), the relative dielectric constant ε ′ and the dielectric loss tangent tan δ of the measurement samples 1 and 2 can be calculated by the following equations.
[0030]
[Expression 1]

[0031]
However, x ′ _0m is the m-th solution of J ′ ₀ (x ′) = 0, and particularly when m = 1, x ′ ₀₁ = 3.8317. J ′ ₀ (x ′) is the derivative of the zeroth-order first-order Bessel function. ω = 2πf ₀ is the angular resonance frequency, and μ ₀ = 4π × 10 ⁻⁷ is the vacuum permeability. α is disclosed by Kobayashi et al. in the microwave research group technical report MW 75-76 “Measuring complex permittivity using balanced disk resonator”, when S = R / d> 10, α is It becomes almost 1. In addition, c is the speed of light, and ΔR is a consideration of the outward spread of the electromagnetic field at the end of the inner circular conductor as an increase in the inner circular conductor diameter. In represents a natural logarithm.
[0032]
Note that the effective conductivity σ of the conductor necessary for determining the dielectric loss tangent is disclosed in Kobayashi et al., Microwave Study Group Technical Report MW 75-76, “Complex Dielectric Constant Measurement Method Using Balanced Disk Resonator”. In addition, it is determined from the difference in Qu of two types of balanced disk resonators composed of dielectric sheets having the same relative dielectric constant and dielectric loss tangent and different thicknesses. Alternatively, the effective conductivity σ of the co-fired conductor is determined by the interface conductivity measurement method disclosed in Japanese Patent Application Laid-Open No. 2000-46756.
[0033]
In this way, the relative dielectric constant and / or the dielectric loss tangent of the first measurement sample 1 is obtained in advance. When the relative dielectric constant and / or dielectric loss tangent of the first measurement sample 1 is obtained by the dielectric constant measurement method of Japanese Patent Application No. 2002-281908, the first measurement sample 1 is sandwiched between the surface circular conductor and the lower conductor layer. A disc resonator and a shield body that prevents leakage of an electromagnetic field from the disc resonator, and a TM _0m0 mode (m) via an input / output excitation port provided in the shield body. = 1, 2,...), And the relative dielectric constant and / or dielectric loss tangent of the first measurement sample 1 is obtained from the measured values of the resonance frequency and the unloaded Q.
[0034]
From the relative dielectric constant and / or dielectric loss tangent of the first measurement sample 1 thus obtained, and the measured values of the resonance frequency and no-load Q of the disk resonator A in FIG. The relative dielectric constant ε ′ ₂ and the dielectric loss tangent tan δ ₂ of the measurement sample 2 are calculated. This calculation must be performed by numerical analysis such as a finite element method or a mode matching method.
[0035]
Here, the calculation method by the finite element method is described. First epsilon _'2 dependent, i.e. f _0-epsilon' of the resonance frequency f ₀ determined _two curves analysis by axisymmetric finite element method, and then the measured value of f _0, using the f _{0-epsilon '2} curve To determine the dielectric constant.
[0036]
The dielectric loss tangent tan δ ₂ is calculated using the following equation 2.
[0037]
[Expression 2]

[0038]
Term of this equation free the reciprocal of the load Q, skin resistance R _s of the first measurement specimen 1 of the dielectric loss tangent tan [delta ₁ and the second measurement sample 2 is a measurement site dielectric loss tangent tan [delta ₂ and conductors 3, 4 and 5 It is expressed by. Pe1 is the concentration ratio of the electric field energy stored in the first measurement sample 1, Pe2 is the concentration ratio of the electric field energy stored in the second measurement sample 2, and G is a shape factor, which is obtained by the finite element method.
[0039]
FIG. 3 is a view for explaining another dielectric constant measuring method of the present invention. The disc resonator A in FIG. 3 is formed on the support substrate 6. That is, the second outer conductor 5, the second measurement sample 2, the circular inner conductor 3, the first measurement sample 1, and the first outer conductor 4 are sequentially stacked on the support substrate 6. These are fired at the same time as the support substrate 6 and are integrated. The first and second measurement samples 1 and 2 are made of ceramics or glass ceramics and have different thicknesses.
[0040]
The first and second measurement samples 1 and 2 and the support substrate 6 of the resonator A are the same as the insulating layer material of the wiring board, and the circular inner conductor 3, the first and second outer conductors 4 and 5 are the inner parts of the wiring board. It is the same as the wiring material, has the same thickness, and has the same manufacturing method such as firing. Accordingly, the diffusion state of the circular inner conductor 3, the first and second outer conductors 4, 5 and the distribution of the voids in the ceramic or glass ceramic to the first and second measurement samples 1 and 2 are the same as the wiring board. Can be considered.
[0041]
Since such a resonator A is integrally formed on the thick support substrate 6, even if the thickness of the second measurement sample 2 of the resonator A is reduced to 200 μm or less, particularly 50 μm or less, the resonator A is formed. It can be easily formed, and can be excited by an electric field through the excitation ports 7 and 8 formed in the first outer conductor 4 on which the support substrate 6 is not formed. The resonance frequency and no-load Q of the second measurement sample 2 can be measured from the relative permittivity and dielectric loss tangent of the first measurement sample 1 and the resonance frequency and no-load Q of the disk resonator A as described above. The relative dielectric constant and dielectric loss tangent can be calculated.
[0042]
Further, since the support substrate 6 and the upper part thereof can be regarded as an integrated substrate, the relative dielectric constant and the dielectric loss tangent at an arbitrary depth in the substrate can be measured.
[0043]
FIG. 4 is a view for explaining still another dielectric constant measuring method of the present invention. The disk resonator A of FIG. 4 is formed on the support substrate 6 in the same manner as the disk resonator A shown in FIG. In addition, a second outer conductor 5, a second measurement sample 2, which is a part to be measured, a circular inner conductor 3, a first measurement sample 1, and a first outer conductor 4 are sequentially stacked, and these are configured as a support substrate 6. At the same time, it is fired and integrated. The first and second measurement samples 1 and 2 are made of ceramics or glass ceramics and have different thicknesses.
[0044]
Then, two excitation ports 7 and 8 are provided at the position of the first outer conductor 4 on a concentric circle having a radius 0.4 to 0.6 times the radius R of the circular inner conductor 3, and these excitations are provided. Loop antennas 19 and 20 are inserted into the mouths 7 and 8, and the TM ₀₁₀ resonance mode is excited by magnetic field excitation.
[0045]
As shown in FIG. 5, the magnetic field of the TM ₀₁₀ resonance mode is strongly distributed at a position of a concentric circumference having a radius of about ½ with respect to the circular inner conductor 3. Thus, when the magnetic field excitation is performed by the loop antennas 19 and 20 at the tips of the coaxial cables 9 and 10 through the excitation ports 7 and 8, the TM ₀₁₀ resonance mode can be efficiently excited from one side. Using this, the resonance frequency and the no-load Q of the disk resonator A can be measured, and the relative dielectric constant and dielectric loss tangent of the second measurement sample 2 can be calculated. In FIG. 5, the oblique lines indicating the cross sections of the first and second measurement samples 1 and 2 are omitted in order to explain the magnetic field distribution.
[0046]
Two excitation ports 7 and 8 are provided at the position of the first outer conductor 4 on a concentric circle having a radius 0.25 or 0.75 times the radius R of the circular inner conductor 3. The loop antennas 19 and 20 may be inserted into the excitation ports 7 and 8 to excite the TM ₀₂₀ resonance mode by magnetic field excitation.
[0047]
In addition, two excitation ports 7 are arranged at the position of the first outer conductor 4 on a concentric circle having a radius of 1/6, 1/2, or 5/6 times the radius R of the circular inner conductor 3. 8 may be provided, and loop antennas 19 and 20 may be inserted into the excitation ports 7 and 8 to excite the _TM030 resonance mode by magnetic field excitation.
[0048]
In the case of FIG. 4 in which the magnetic field is applied to excite the disk resonator A, the first support substrate 6 is not formed as shown in FIG. 2 The relative dielectric constant and dielectric loss tangent of the measurement sample 2 can be measured.
[0049]
【Example】
The dielectric constant inside the alumina substrate was measured by the dielectric constant measurement method of the present invention. The structure of the measurement substrate is as shown in FIG. 4. A Cu-W conductive paste is applied to a green sheet made of an alumina material, and a plurality of these are laminated to produce a laminated molded body. At the same time, the disk resonator A and the support substrate 6 were integrated.
[0050]
Here, the thickness of the support substrate 6 is 200 μm, the thickness of the circular inner conductor 3, the first and second outer conductors 4 and 5 is 10 μm, and the diameter of the circular inner conductor 3 is 23.3 mm. Disk resonators A in which the thicknesses of the first and second measurement samples 1 and 2 were changed were produced.
[0051]
Further, in order to perform the magnetic field coupling shown in FIG. 4, the excitation openings 7 and 8 have a diameter of 1.5 mm, and the coaxial cables 9 and 10 having a diameter of 1.2 mm have loop antennas 19 and 20 having a diameter of about 1.5 mm. The disk resonator A was inserted, and the resonance frequency and no-load Q of the disk resonator A were determined.
[0052]
Thereafter, the relative dielectric constant of the first measurement sample 1 was measured by the method described in Japanese Patent Application No. 2002-151665.
[0053]
That is, the circular inner conductor is sandwiched between the first measurement samples from both sides, and is sandwiched between the first and second outer conductors, and an electric field is applied through a coaxial cable from the excitation port of the first outer conductor to excite the electric field. The resonance frequency and no-load Q of the resonator were measured, and the relative dielectric constant of the first measurement sample 1 was calculated from the above equation 1.
[0054]
Further, the resonance frequency of the disk resonator A in FIG. 4 was measured, and the relative dielectric constant of the second measurement sample was calculated from the dielectric constant of the first measurement sample 1. The results are shown in Table 1. In FIG. 2 shows a resonance waveform.
[0055]
[Table 1]

[0056]
According to Table 1, the relative permittivity of the second measurement sample 2 is measured as a different value. This difference depends on the diffusion effect from the circular inner conductor, the first and second outer conductors to the second measurement sample 2, and the depth (position in the vertical direction) of the second measurement sample 2 in the entire substrate. It is considered a thing.
[0057]
【The invention's effect】
As described above in detail, according to the dielectric constant measurement method of the present invention, in order to form excitation ports for input and output of magnetic field and electric field in the first outer conductor constituting the disk resonator, The dielectric constant of a disk resonator that is simultaneously fired or integrally molded with a conductor layer can be measured. Alternatively, the dielectric loss tangent can be easily determined, and the dielectric constant of an arbitrary dielectric layer can be measured in an electronic component such as a wiring board having different dielectric layers and having internal wiring between the dielectric layers. This makes it possible to design electronic parts such as wiring boards that are close to reality, and facilitates the development of dielectric materials for simultaneous firing or integral molding for microwave applications. Circuit board , The design of the semiconductor package is allow more accurately.
[Brief description of the drawings]
1A and 1B show an example of a disk resonator used in a dielectric constant measurement method of the present invention, in which FIG. 1A is a plan view and FIG. 1B is a schematic cross-sectional view.
FIGS. 2A and 2B are diagrams for explaining the electric field distribution of the TM ₀₁₀ mode in the disk resonator of FIG. 1, wherein FIG. 2A is a plan view and FIG. 2B is a schematic cross-sectional view.
3A and 3B show another example of a disk resonator used in the dielectric constant measurement method of the present invention, where FIG. 3A is a plan view and FIG. 3B is a schematic cross-sectional view.
4A and 4B show still another example of a disk resonator used in the dielectric constant measurement method of the present invention, in which FIG. 4A is a plan view and FIG. 4B is a schematic cross-sectional view.
FIGS. 5A and 5B are diagrams for explaining the magnetic field distribution of the TM ₀₁₀ mode in the disk resonator of FIG. 4, wherein FIG. 5A is a plan view and FIG. 5B is a schematic cross-sectional view.
6 is a sample substrate No. in Table 1. It is a figure which shows the resonance waveform used for the dielectric constant measurement of 2. FIG.
7A and 7B show a balanced disk resonator used in a conventional dielectric constant measurement method, in which FIG. 7A is a plan view and FIG. 7B is a schematic cross-sectional view.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 ... 1st measurement sample 2 ... 2nd measurement sample 3 ... Circular inner conductor 4 ... First outer conductor 5 ... Second outer conductor 6 ... Support substrate 7, 8, ... Excitation ports 9, 10 ... Coaxial cables 19, 20 ... Loop antenna A ... Disc resonator

Claims (5)

Sandwiching a circular inner conductor in the first measurement specimen and the second measurement sample different thicknesses, the first, first each surface of the second measurement sample, Ri Na to form a second outer conductor, the first measurement samples of the thickness of the disc resonator Ru der least 200 [mu] m, and excitation Fukuchi provided at a position of the first outer conductor corresponding to the center position of the circular inner conductor, the position of the edge of the circular inner conductor A coaxial cable is inserted into the corresponding excitation port provided at the position of the first outer conductor, and the TM _0m0 mode (m = 1, 2,...) _Is excited by an electric field. The dielectric constant of the second measurement sample is determined from the measured values of the resonance frequency and no-load Q of the disk resonator, and the relative dielectric constant and / or dielectric loss tangent of the first measurement sample measured in advance. A dielectric constant measurement method characterized by being obtained. A circular inner conductor is sandwiched between a first measurement sample and a second measurement sample having different thicknesses, and first and second outer conductors are formed on the surfaces of the first and second measurement samples, respectively. A disc resonator having a thickness of 200 μm or more is inserted into a loop antenna into at least two excitation openings provided at positions of the first outer conductor corresponding to concentric circles of the circular inner conductor, and TM is applied by a magnetic field. _0m0 The mode (m = 1, 2,...) Is excited, the resonance frequency and the no-load Q are measured, the measured values of the resonance frequency and the no-load Q of the disc resonator, and the previously measured first A dielectric constant measurement method, wherein a dielectric constant of the second measurement sample is obtained from a relative dielectric constant and / or a dielectric loss tangent of the measurement sample. 3. The dielectric constant measuring method according to claim 1, wherein the disk resonator is formed on a support substrate. The dielectric constant measurement method according to claim 3, wherein the thickness of the second measurement sample is 0.2 mm or less. It said first, second measurement sample is made of ceramic or glass ceramic, the support substrate and the disc resonator is co-fired dielectric constant measurement according to claim 3 or 4, wherein that are integrated Law.

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