JP4530951B2 - Dielectric constant measurement method and open-ended half-wavelength coplanar line resonator - Google Patents

Description

  The present invention relates to a dielectric constant measuring method and a half-wavelength coplanar line having open ends, and particularly suitable for measuring the direct current voltage dependence of the relative dielectric constant of a dielectric thin film in the microwave and millimeter wave regions of 10 GHz or higher. The present invention relates to a measurement method and an open-ended half-wavelength coplanar line resonator.

In recent years, development of high-frequency circuits using the direct current voltage dependence of the relative permittivity of high dielectric constant thin films and the development of thin film dielectric materials therefor have been actively conducted. In order to develop these high-frequency circuits and materials, a technique for measuring the DC voltage dependence of the relative permittivity, dielectric loss tangent, and relative permittivity of a high dielectric constant thin film with a microwave or millimeter wave is required. As a method for measuring the relative dielectric constant and dielectric loss tangent of a high dielectric constant thin film from microwave to millimeter wave, Non-Patent Document 1 describes that a capacitor is composed of a high dielectric constant thin film, and S11 of the capacitor (S parameter indicating the magnitude of reflection) ) To measure the relative dielectric constant and dielectric loss tangent have been reported (see Non-Patent Document 1).
Y. Iwazaki, K. Ohta, T. Suzuki ans S. Sekiguchi; “Elimination of parasitic effects due to measurement conditions of SrTiO3 thin films up to 40 GHz,” MMA2004, O-A27, pp.65, (2004)

  However, in the measurement method of Non-Patent Document 1, the relative permittivity and dielectric constant are determined depending on how the electric parasitic parameter generated between the prober and the high dielectric constant thin film capacitor around the high dielectric constant thin film capacitor is corrected. There is a problem that the measurement result of tangent changes. Further, the direct current voltage dependency of the dielectric constant is usually measured at a frequency of 1 MHz or less, and no measurement method using microwaves or millimeter waves has been reported.

  Accordingly, an object of the present invention is to provide a dielectric constant measuring method and an open-ended half-wavelength coplanar line resonator capable of measuring the dielectric constant of a dielectric constant thin film with high accuracy using microwaves or millimeter waves.

Yuden constant measurement method of the present invention, the dielectric so as to surround the both ends in the longitudinal direction of the arranged linear central conductor on a dielectric substrate, the periphery of said central conductor to open the said central conductor and spacing in at least one hand between the deployed ground conductor on the body substrate, and the measurement sample electrode on both end surfaces in the thickness direction is formed is arranged, is one of the electrodes is connected to said center conductor, a resonator excitation step of the other of said electrodes to excite both end open type half-wavelength coplanar line resonators connected to said ground conductor, said end open type half-wavelength coplanar line resonator of the resonance frequency and / or free a measuring step of measuring the load Q value, characterized by comprising a calculation step of calculating the dielectric constant in the thickness direction of the measurement sample from the measured values of the resonant frequency and / or unloaded Q value.

According to such a dielectric constant measurement method, a parallel plate capacitor can be formed from the measurement sample in the open part of the coplanar line resonator, so the dielectric constant in the direction perpendicular to the surface of the measurement sample (thickness direction) is measured. it can. Furthermore, it is possible to integrally manufactured as planar circuit resonator and a sample for dielectric constant measurement, compared to the case of using the three-dimensional resonator can be suppressed to a minimum measurement errors associated with the resonator formed.

Yuden constant measurement method of the present invention, the dielectric constant of the dielectric constant to be measured, or can be suitably used in the case of a dielectric loss tangent. That is, since the electric field is most strongly distributed in the open part of the coplanar line resonator, the relative permittivity of the measurement sample is effectively reflected in the resonance frequency of the resonator by arranging the measurement sample in the open part. This is because the dielectric loss tangent of the sample can be effectively reflected in the unloaded Q value of the resonator. In addition, since the magnetic field is the weakest at the open part of the coplanar line resonator, even if the measurement sample has magnetic permeability (magnetism), the change in the resonance frequency due to the magnetic permeability is suppressed to the minimum, and the relative dielectric constant is increased. This is because it can be measured with high accuracy.

Yuden constant measurement method of the present invention is particularly effective when the measurement sample is thick 50μm following ceramics, or an organic based dielectric. In general, when the dielectric properties of ceramics, organic dielectrics, or thin films having a thickness of 50 μm or less are measured with a three-dimensional circuit resonator such as a cavity resonator, the measurement sample cannot stand by itself, which makes measurement difficult. In the measurement method of the present invention, the measurement sample and the electrode are integrally formed on the dielectric substrate, and the dielectric constant can be measured. Therefore, the measurement sample can be easily produced.

Furthermore, when measuring the dielectric properties of ceramics, organic dielectrics, or thin films with a thickness of 50 μm or less with a resonator of a planar circuit, the conductor loss increases and the unloaded Q value decreases, making measurement difficult. . However, according to the measuring method of Yuden constants of the present invention, the distance between the center conductor and the ground conductor in the central portion of the resonator in which a current flows most strongly, and the strip line resonator, spread compared to the microstrip line resonator Therefore, conductor loss can be suppressed. As a result, it is possible to suppress the decrease in the unloaded Q of the resonator due to the conductor loss, and it is possible to improve the measurement accuracy.

Yuden constant measurement method of the present invention will become more effective when the measurement sample is less dielectric film thickness 5 [mu] m. In general, it is known that the dielectric properties of a dielectric thin film change under the influence of a substrate. Furthermore, when a dielectric thin film is used in an electric circuit, opposing electrodes (for example, comb electrodes) are formed on the same surface of the substrate to form a capacitor, and electrodes are formed above and below the dielectric thin film. It may be used as a parallel plate capacitor. In the former case, the dielectric properties in the surface direction of the dielectric thin film formed on the dielectric substrate are important. In the latter case, the dielectric film is perpendicular to the surface of the dielectric thin film formed on the conductor (on the lower electrode). The dielectric properties in the direction (thickness direction) are important.

If the Yuden constant measuring method of the present invention is applied to the dielectric thin film, and the dielectric characteristics in a direction perpendicular to the plane of the dielectric thin film formed on the conductor (the lower electrode), its voltage dependence of the measurement Is possible.

Calculation of the dielectric constant of the present invention measures the resonance frequency f ₀ and the unloaded Q value Q _u of the open ends form a half-wavelength coplanar line resonator, using these data, FEM (finite element method) Through the numerical analysis, it is possible to calculate the dielectric constant such as the relative dielectric constant and dielectric loss tangent of the measurement sample.

In order to calculate the relative permittivity of the measurement sample, the relationship between the relative permittivity and the resonance frequency is obtained by numerical analysis such as FEM (finite element method) within an assumed range, and this relationship is approximated by an appropriate function. and to calculate the dielectric constant from the measured values of the resonance frequency f ₀ and the approximate function. In order to calculate the dielectric loss tangent, the resonator form factor G and the electric field energy concentration rate Pe of each of the measurement sample and the dielectric substrate are calculated by FEM, and the sample is calculated from the measured values of G, Pe and Qu. Is calculated.

An open-ended half-wavelength coplanar line resonator according to the present invention has both ends in the length direction of a linear center conductor disposed on a dielectric substrate, and a periphery of the center conductor spaced from the center conductor. at least one hand, and the measurement sample electrode on both end surfaces in the thickness direction is formed is arranged, one of the electrodes is the center between the dielectric substrate on the arranged ground conductor so as to surround is connected to the conductor, the other of said electrodes, characterized in Tei Rukoto connected to the ground conductor.

  In such an open-ended half-wavelength coplanar line resonator, not only can it be used effectively in the measurement method described above, but also a resonance that is the basic structure of electronic parts such as filters using ceramic thin layers and dielectric thin films. It is also effective as a vessel.

  Such a double-ended open half-wavelength coplanar line resonator can increase the capacitance at both ends compared to a normal open-ended half-wavelength coplanar line resonator, and is therefore effective for downsizing filters and the like. . In addition, the conductor loss can be reduced as compared with a normal open-ended half-wavelength coplanar line resonator, which is effective in reducing the loss.

According to the dielectric constant measuring method of the present invention, the dielectric constant of the measurement perpendicular to the plane of the constant sample (dielectric thin film) (thickness direction), it is possible that voltage dependence of the measurement.

(Dielectric constant measurement method in the surface direction of the measurement sample)
A method for measuring the dielectric constant in the plane direction will be described with reference to FIG. 1, taking as an example the case where the measurement sample is a thin film.

  In order to measure the dielectric properties in the plane direction of the dielectric thin film formed on the dielectric substrate and the voltage dependence thereof, the open-ended half-wavelength coplanar line resonator A1 shown in FIG. 1 is fabricated. This open-ended half-wavelength coplanar line resonator includes a dielectric substrate 1, a central conductor 2, a ground conductor 3, and a measurement sample 4.

  A center conductor 2 and a ground conductor 3 are formed on the upper surface of the dielectric substrate 1, and a dielectric thin film measurement sample 4 is provided so as to partially cover the center conductor 2 and the ground conductor 3 on both open portions. Form. That is, a rectangular frame-shaped ground conductor 3 having an opening inside is formed on the upper surface of the dielectric substrate 1, and a linear center conductor 2 is formed on the dielectric substrate 1 in the opening. Both ends of the center conductor 2 and the ground conductor 3 are separated from each other, and a measurement sample 4 is filled in the open portions at these two locations. In other words, the measurement sample 4 is filled between both ends of the center conductor 2 and the ground conductor 3, and the measurement sample 4 is also laminated on the central conductor 2 and the ground conductor 3 around the release portion.

  The dielectric substrate 1 is preferably a sapphire substrate or the like. A central thin film conductor 2 such as Au or Pt and a ground thin film conductor 3 are formed on the upper surface of the dielectric substrate 1 by sputtering or the like. A measurement sample 4 made of a dielectric thin film is formed by sputtering or the like so as to partially cover.

Next, the measurement process will be described. Exciting the resonator A1 with the loop antenna 7 formed at the tip of one of the coaxial cable 6, and detected by the other of the loop antenna 7, the unloaded Q value Q _u and the resonance frequency f ₀ in the measuring instrument such as a network analyzer taking measurement. The relative dielectric constant epsilon 'of the measurement sample 4 than the resonance frequency f _0, to calculate the dielectric loss tangent tanδ of the measurement sample 4 from the unloaded Q value Q _u. If the dielectric constant epsilon 'and obtains the DC voltage dependence of the dielectric loss tangent tan [delta, the central conductor 2 and the DC voltage dependence of the resonance frequency f ₀ by applying a DC voltage between the ground conductor 3 and the unloaded Q value Q _u And the DC voltage dependence of the relative dielectric constant ε ′ and the dielectric loss tangent tan δ is calculated.

(Dielectric constant measurement method in the thickness direction of the measurement sample)
The dielectric constant measuring method of the present invention will be described with reference to FIG. 2, taking as an example the case where the measurement sample is a thin film.

  When measuring dielectric characteristics in the direction perpendicular to the surface of the measurement sample (thickness direction) and voltage dependency thereof, the open-ended half-wavelength coplanar line resonator A2 shown in FIG. 2 is fabricated. This open both-end half-wavelength coplanar line resonator A2 includes a dielectric substrate 1, a center conductor 2, a ground conductor 3, a measurement sample 14, and an upper electrode 5.

  A center conductor 2 and a ground conductor 3 are formed on the upper surface of the dielectric substrate 1, and a dielectric thin film measurement sample 14 is formed so as to partially cover the center conductor 2 on both open portions. . An upper electrode 5 is disposed between the measurement sample 14 and the ground conductor 3. The upper electrode 5 is also formed on the upper surface of the ground conductor 3 and the upper surface of the measurement sample 14, and the measurement sample 14 has a lower surface. The upper electrode 5 is formed on the upper surface of the electrode that is a part of the central conductor 2, and the upper electrode 5 is connected to the ground conductor 3.

In the measurement process, similarly to the above, the resonator is excited by the loop antenna 7 formed at the tip of one coaxial cable 6, detected by the other loop antenna 7, and the resonance frequency f _{0 by} a measuring instrument such as a network analyzer. and to measure the no-load Q value _{Q u.}

  When the radiation loss of the open-ended half-wavelength coplanar line resonator shown in FIGS. 1 and 2 cannot be ignored, it is desirable to install a shielding conductor 9 surrounding the resonator as shown in FIG. The shield conductor 9 is configured to surround the entire resonator, and a hollow rectangular structure or the like is preferable.

Next, a method for calculating the dielectric constant will be described. First, the relative dielectric constant ε ′ of the measurement sample 4 is obtained from the measured value of the resonance frequency f ₀ of the resonator by numerical analysis such as a finite element method (FEM) or a mode matching method. Here, the case where the finite element method is used will be described. The resonance frequency f ₀ of the open-ended half-wavelength coplanar line resonator shown in FIG. 1 is the relative permittivity ε ′, width W, length L, thickness t of the measurement sample 4, and the relative dielectric constant of the dielectric substrate 1. It is a function of the ratio ε ′s, the thickness tc of the central conductor 2 and the ground 3, the width Wc and the length Lc of the central conductor 2, and the distance d between the both ends of the central conductor 2 and the ground conductor 3. Accordingly, W, L, t, ε ′s, tc, Wc, Lc, d are fixed to measured values or design values, and the relative permittivity ε ′ of the measurement sample 4 is set to several points within an expected range. The corresponding resonance frequency f ₀ is calculated by the finite element method. From these calculation results, the relationship between the resonance frequency f ₀ and the relative dielectric constant ε ′ is approximated by an appropriate function, and ε ′ is calculated from this approximate expression and the measured value of f ₀ .

Next, the dielectric loss tangent tan δ of the measurement sample 4 is obtained from the measured value of the no-load Q value Qu by the following formula 1.

In Equation 1, μ is the magnetic permeability of the conductor, and for a nonmagnetic conductor, μ is equal to the vacuum magnetic permeability μ ₀ = 4π × 10 ⁻⁷ H / m. P _e is concentration ratios of electric field energy in the sample 4, P _es the concentration ratios of electric field energy in the dielectric substrate 1, G is a shape factor of the resonator, non-patent document 2 "J. Krupka, K. Derzakowski, A. Abramowicz, ME Tobar and RG Geyer, “Use of whispering-gallery modes for complex permittivity determinations of ultra-low-loss dielectric materials,” IEEE Trans. Microwave Theory Tech., Vol. 47, pp.752-759 , June 1999 ”. tan δs is the dielectric loss tangent of the dielectric substrate.

The concentration ratio of the electric field energy is defined as a fraction of the electric field energy stored in each part with respect to the electric field energy stored in the resonator. _Pe and _Pes are given by the following equation 2.

G in Equation 1 indicates the form factor of the ring resonator, and is given by Equation 4 below.

  Equations 2, 3, and 4 are obtained by a numerical analysis method such as a finite element method (FEM) or a mode matching method.

Calculated P _{e, P es,} and _G, measurements or literature value of the conductivity σ by alternative, yet substituting the measured values or the literature values for tan [delta _s by alternative to Formula 1, obtaining the tan [delta.

Another method for obtaining σ is “A. Nakayama, Y. Terashi, H. Uchimura and, A. Fukuura,“ Conductivity measurement at the interface between the sintered conductor and dielectric substrate at microwave frequencies, ”IEEE Trans. Microwave Theory Tech. , vol. MTT-50, No.7, pp. 1665-1674, July 2002. " As another method for obtaining the tanδ _s JIS-R1641: 2002 it is preferable.

2A and 2B show an open-ended half-wavelength coplanar line resonator used in a method for measuring a dielectric constant in a plane direction , wherein (a) is a plan view and (b) is a cross-sectional view. The other end open type half wavelength coplanar line resonator used for the measuring method of this invention is shown, (a) is a top view, (b) is sectional drawing. It is explanatory drawing for demonstrating the structure which provided the shielding conductor in the both ends open type | mold half wavelength coplanar line resonator.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Board | substrate 2 ... Center conductor 3 ... Ground conductor 4, 14 ... Measurement sample 5 ... Upper electrode A1, A2 ... Both ends open type half wavelength coplanar line resonator

Claims (3)

Both ends in the length direction of a linear center conductor disposed on the dielectric substrate, and a ground conductor disposed on the dielectric substrate so as to surround the center conductor with a space from the center conductor. in at least one way between, the measurement sample electrode on both end surfaces in the thickness direction is formed is placed, the electrode of the hand is connected to the center conductor, the electrode of the other side is the ground conductor a resonator excitation step for exciting the connected ends open type half-wavelength coplanar line resonator, a measurement step of measuring the resonant frequency and / or unloaded Q value of the open-ended type half-wavelength coplanar line resonator the dielectric constant measuring method characterized by comprising a calculation step of calculating the dielectric constant in the thickness direction of the measurement sample from the measured values of the resonant frequency and / or unloaded Q value. A DC voltage is applied between the center conductor and the ground conductor of the open ends form a half-wavelength coplanar line resonator, No placement claim 1 Symbol and measuring the DC voltage dependence of the dielectric constant Dielectric constant measurement method. Both ends in the length direction of a linear center conductor disposed on the dielectric substrate, and a ground conductor disposed on the dielectric substrate so as to surround the center conductor with a space from the center conductor. in at least one way between, the measurement sample electrode on both end surfaces in the thickness direction is formed is placed, the electrode of the hand is connected to the center conductor, the electrode of the other side is the ground conductor open-ended type half-wavelength coplanar line resonator, characterized in that it is connected to.

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