JP4467418B2 - Dielectric constant measurement method - Google Patents

Description

The present invention relates to a dielectric constant measurement method, and more particularly to a method for measuring a relative dielectric constant and a dielectric loss tangent of a dielectric sample having a thickness of 1 × 10 ⁻⁸ m (10 nm) or more.

  Currently, devices using dielectric thin films and dielectric multilayer substrates are actively developed in the microwave band and the millimeter wave band, and a method for accurately measuring the dielectric constant is required.

2. Description of the Related Art Conventionally, two methods are generally known as dielectric constant measurement methods in the microwave band and the millimeter wave band, such as a dielectric thin film formed on a conductor and a co-fired metallized wiring board. One is a method of obtaining a dielectric constant by configuring a strip line or the like on a dielectric sample and measuring its transmission characteristics, and the other is a ring resonator or the like made of a ring conductor on the dielectric sample. There is a method of configuring and obtaining from the resonance characteristics.
Japanese Patent Laid-Open No. 11-298213

  However, in the above method, since the relative permittivity and dielectric loss tangent are obtained from the transmission characteristics of one resonator, when the resonator is optimal for the relative dielectric constant, it is not suitable for the dielectric loss tangent. When the resonator is optimal for the tangent, there is a problem that it is not suitable for the relative dielectric constant, and it is difficult to accurately obtain the relative dielectric constant and the dielectric loss tangent with one resonator.

  That is, when obtaining from the transmission characteristics of a strip line or the like, there is a problem that it is difficult to accurately obtain the dielectric constant of the dielectric sample, particularly the dielectric loss tangent, by separating the conductor loss of the conductor constituting the strip line. there were.

  Further, even when a ring resonator or the like is used, there is a problem that it is difficult to measure a dielectric constant, particularly a dielectric loss tangent, because the conductor loss is large and the Q value of the resonator is greatly deteriorated.

  Therefore, the present invention provides a dielectric constant measurement method capable of measuring the relative dielectric constant and dielectric loss tangent of a dielectric thin film, a dielectric multilayer substrate, etc. with high accuracy in the microwave band and millimeter wave band, particularly in the frequency band of 1 GHz or higher. It is intended to do.

The dielectric constant measuring method of the present invention includes a first resonator in which a conductor is brought into contact with the electrode of the dielectric sample having electrodes formed on both sides, and the dielectric sample having an electrode formed only on one surface. the non-electrode portion of the dielectric sample the electrodes, and the electrodes are not formed, with a second resonator comprising contacting the conductors, respectively, the dielectric sample from the resonance frequency of the first co-vibrator It obtains the relative dielectric constant of, and obtains the dielectric loss tangent of the dielectric sample from the resonance frequency and the unloaded Q of the second co-vibrator. The dielectric constant measuring method of the present invention includes a first resonator in which a conductor is brought into contact with each electrode of a dielectric sample having electrodes formed on both sides, and a dielectric sample having no electrode formed thereon. Using a second resonator in which a conductor is in contact with each non-electrode portion, the relative permittivity of the dielectric sample is obtained from the resonance frequency of the first resonator, and the resonance frequency of the second resonator The dielectric loss tangent of the dielectric sample is obtained from the load Q. In such a dielectric constant measuring method, because determine the specific dielectric constant with a first co-vibrator suitable for measuring the dielectric constant of the dielectric specimen, highly accurately the contact area between the dielectric sample and the center conductor in can be determined, it is possible to determine the dielectric constant of such dielectric thin film or a dielectric multi-layer substrate with high accuracy, and using the second co-oscillator suitable for measuring the dielectric loss tangent of the dielectric sample dielectric to determine the tangent, reduce the contact resistance between the electrode and the center conductor, or can be eliminated entirely, it can be determined Yuden tangent such as dielectric thin film or a dielectric multi-layer substrate with high accuracy.

The dielectric constant measurement method of the present invention obtains an effective contact area between the dielectric sample of the non-electrode part and the conductor from the resonance frequency (f _0B ), and determines the effective contact area and the second resonator. A dielectric loss tangent of the dielectric sample is obtained using a load Q. In such a dielectric constant measurement method, since the ratio of the electric field energy accumulated in the dielectric sample can be determined with high accuracy, the dielectric loss tangent of the dielectric thin film or dielectric multilayer substrate can be obtained with high accuracy. Can do.

Further, the dielectric constant measuring method of the present invention, by using the resonant frequency and the unloaded Q of the resonance mode generated an electric field toward one said conductors or al the other of said conductor opposing the ratio of the dielectric sample It is characterized by obtaining a dielectric constant and a dielectric loss tangent. In such a dielectric constant measurement method, it is particularly important to determine the contact area between the dielectric sample and the central conductor with high accuracy, in order to obtain the relative dielectric constant of the dielectric thin film, dielectric multilayer substrate, etc. with high accuracy. Therefore, the relative permittivity and dielectric loss tangent of the dielectric thin film, the dielectric multilayer substrate, etc. can be obtained with high accuracy by using the above measurement method.

  The dielectric constant measuring method of the present invention is characterized in that the first and second resonators have an axisymmetric structure. Such a dielectric constant measurement method can suppress disturbance of electromagnetic waves, and can determine the relative dielectric constant and dielectric loss tangent of a dielectric thin film, a dielectric multilayer substrate, etc. with higher accuracy.

  Furthermore, in the dielectric constant measuring method of the present invention, the first and second resonators include a cylindrical conductor, a central conductor provided in the axial direction in the cylindrical conductor, and openings on both sides of the cylindrical conductor. A semi-coaxial resonator comprising a dielectric sample interposed between the central conductor and one of the short-circuit conductors. In such a dielectric constant measurement method, the ratio of the electric field energy accumulated in the dielectric sample to the entire resonator and the Q value can be increased, and the relative dielectric constant and dielectric constant of the dielectric thin film, dielectric multilayer substrate, etc. can be increased. The tangent can be obtained with higher accuracy.

  Further, the dielectric constant measuring method of the present invention includes a semi-coaxial resonator between a dielectric sample sandwiched between a center conductor and one short-circuit conductor, and a cylindrical conductor and one or both short-circuit conductors. And a sandwiched second dielectric. In such a dielectric constant measurement method, the capacitance formed equivalently in the resonator can be reduced. Therefore, in the microwave band and the millimeter wave band, the relative dielectric constant of a dielectric thin film, a dielectric multilayer substrate, etc. And the dielectric loss tangent can be obtained with higher accuracy. Here, it is desirable to measure the relative dielectric constant and the dielectric loss tangent from the resonance frequency and the no-load Q in the resonance mode in which the dielectric sample and the second dielectric operate in series connection.

  In the dielectric constant measurement method of the present invention, the semi-coaxial resonator includes a dielectric sample sandwiched between the center conductor and one short-circuit conductor, and the tip of the center conductor has a tapered shape. desirable. In such a dielectric constant measurement method, the capacitance formed equivalently in the resonator can be reduced. Therefore, in the microwave band and the millimeter wave band, the relative dielectric constant of a dielectric thin film, a dielectric multilayer substrate, etc. And the dielectric loss tangent can be obtained with higher accuracy. Here, the tip of the central conductor may constitute a part of a sphere, and the tip of the sphere may be in contact with the dielectric sample.

  In the dielectric constant measuring method of the present invention, the dielectric sample sandwiched between the center conductor and one short-circuit conductor, and the second sample sandwiched between the cylindrical conductor and one or both short-circuit conductors. A dielectric sample is measured from the first semi-coaxial resonator characterized by comprising a dielectric, and a dielectric sample sandwiched between a center conductor and one short-circuited conductor is provided. It is desirable to measure the dielectric loss tangent of the dielectric sample from the second semi-coaxial resonator, wherein the tip of the central conductor has a tapered shape.

  In the first semi-coaxial resonator, the presence of the second dielectric allows measurement at 1 GHz or more even if the electrode area formed on the dielectric sample is relatively large. If the resonance space is reduced or the thickness of the second dielectric is thin and the area is not widened, the ratio of the electric field energy accumulated in the dielectric sample to the entire resonator is reduced. It is disadvantageous.

  On the other hand, the second semi-coaxial resonator is advantageous in that the Q value is increased because the ratio of the electric field energy accumulated in the dielectric sample to the entire resonator is large even if the resonance space is increased. If the area of the electrode formed on the dielectric sample is not made relatively small, measurement at 1 GHz or more becomes difficult.

  Therefore, in the dielectric constant measurement method of the present invention, the relative permittivity of a dielectric sample having electrodes formed on both surfaces is measured from the first semi-coaxial resonator, and the dielectric sample is measured from the second semi-coaxial resonator. It is desirable to measure the dielectric loss tangent.

In the dielectric constant measuring method of the present invention, it is desirable that the resonance frequencies f _0A and f _0B are 1 GHz or more. The resonance frequency f _0A is 0.5 to 1.5 times the resonance frequency f _0B . In order to obtain the dielectric loss tangent of the dielectric sample using the second resonator from the relative dielectric constant of the dielectric sample obtained using the first resonator, the relative dielectric constant of the dielectric sample in the second resonator is used. Is the same as the dielectric constant of the first resonator. In general, since the frequency dependence of the relative permittivity of a dielectric thin film, a dielectric multilayer substrate, or the like that needs to measure the dielectric loss tangent with high accuracy in a frequency band of 1 GHz or higher is small, the resonance frequency f _{0A is set} to the resonance frequency f _0B . By setting 0.5 to 1.5 times, it can be assumed that the dielectric constant of the dielectric sample in the second resonator is the same as the dielectric constant of the first resonator.

In the dielectric constant measuring method of the present invention, the thickness of the dielectric sample is preferably 10 ⁻⁸ m or more. This is because by setting the thickness of the dielectric sample to 10 ⁻⁸ m or more, the resonance frequency f _0A and f _{0B is set} to 1 GHz or more while increasing the ratio of the electric field energy accumulated in the dielectric sample to the entire resonator. It becomes possible.

Hereinafter, the dielectric constant measuring method of the present invention will be described. As the dielectric sample, for example, a dielectric thin film formed on a conductor and having a thickness of 10 ⁻⁸ m or more, a simultaneously fired metallized wiring board, or the like is assumed.

  FIG. 1 is a cross-sectional view for explaining a relative dielectric constant measuring step in the dielectric constant measuring method of the present invention.

  In the first resonator shown in FIG. 1, the lower electrode 3 is formed by simultaneous firing on the lower surface of the dielectric sample A1 (co-fired metallized wiring board), and the upper electrode (conductor bump) 2 is formed on the upper surface. This structure is sandwiched between an upper conductor (center conductor) 4 and a lower conductor 5 connected by a cylindrical outer conductor 6.

  As a method for forming the conductor bump 2 bonded to the dielectric sample A1, any method can be used as long as it can be formed at a temperature equal to or lower than the simultaneous firing temperature of the metallized wiring board. For example, plating, vapor deposition, printing, etching, reflow and the like can be mentioned. Moreover, the method which combined these may be used. Furthermore, the material of the conductor bump 2 may be anything such as gold, silver, copper, or solder. In particular, gold, silver, copper, and the like are desirable from the viewpoint of low electrical resistance, and solder is desirable from the viewpoint of a low melting point.

  FIG. 2 is a cross-sectional view for explaining a dielectric loss tangent measurement step in the dielectric constant measurement method of the present invention.

  In the second resonator shown in FIG. 2, the lower electrode 3 is formed by simultaneous firing on the lower surface of the dielectric sample B1 (co-fired metallized wiring board), and the upper conductor connected by the cylindrical outer conductor 6 The structure is sandwiched between the (center conductor) 4 and the lower conductor 5.

  In these first and second resonators, the area of the upper electrode (conductor bump) 2 or the contact area between the dielectric sample B1 and the upper conductor (center conductor) 4 is reduced to make it equivalent in the resonator. Thus, the capacitance formed in the capacitor can be reduced, and the resonance frequency can be prevented from lowering.

  In such a case, in the first resonator, the contact resistance between the upper electrode (conductor bump) 2 and the upper conductor (center conductor) 4 is increased, or the dielectric sample B1 and the upper conductor (center conductor) 4 Ensuring the reproducibility of the effective contact area due to the gaps between them is a problem. In contrast, in this measurement method, the first resonator shown in FIG. 1 performs relative permittivity measurement in which an increase in contact resistance between the upper electrode (conductor bump) 2 and the upper conductor (center conductor) 4 is not a problem. From this result, in order to measure the effective contact area and the dielectric loss tangent between the dielectric sample B1 and the upper conductor (center conductor) 4 by the second resonator shown in FIG. It can be obtained with higher accuracy.

Further, by setting the bonding area between the upper electrode (conductor bump) 2 and the dielectric sample A1 and the effective contact area between the dielectric sample B1 and the upper conductor (center conductor) 4 to the same size. The resonance frequencies f _0A and f _0B can be matched within a range of 50% (0.5f _0B ≦ f _0A ≦ 1.5f _0B ).

  The calculation method for obtaining the relative permittivity using the first resonator of FIG. 1 and obtaining the dielectric loss tangent using the second resonator of FIG. 2 includes a mode matching method, a finite element method, a lumped constant equivalent circuit method. Etc.

  FIG. 3 is a cross-sectional view of a first resonator for explaining a relative dielectric constant measurement step in another dielectric constant measurement method of the present invention.

  In the first resonator shown in FIG. 3, the upper electrode 2 and the lower electrode 3 are formed by simultaneous firing on the upper and lower surfaces of the dielectric sample A1 (simultaneously fired metallized wiring board), and the upper conductor connected thereto 4 and the lower conductor 5.

  FIG. 4 is a cross-sectional view of the second resonator for explaining the dielectric loss tangent measurement step. In the second resonator shown in FIG. 4, the electrodes of the metallized wiring board formed by simultaneous firing are peeled off from the upper and lower surfaces of the dielectric sample B1, and the upper conductor 4 and the lower conductor 5 to which the electrodes are connected are separated. It has a sandwiched structure. That is, the upper conductor 4 and the lower conductor 5 are in contact with the surface of the dielectric sample B1.

Also in these resonators, the first resonator shown in FIG. 3 performs relative permittivity measurement in which an increase in contact resistance between the upper electrode 2 and the upper conductor 4 and an increase in contact resistance between the lower electrode 3 and the lower conductor 5 is not a problem. In order to measure the effective contact area and dielectric loss tangent between the dielectric sample B1 and the upper conductor 4 and the dielectric sample B1 and the lower conductor 5 by the second resonator shown in FIG. The dielectric constant and dielectric loss tangent can be measured with higher accuracy. Further, the area of the upper electrode 2, the effective contact area between the dielectric sample B1 and the upper conductor 4, the area of the lower electrode 3, and the effective contact area between the dielectric sample B1 and the lower conductor 5, respectively. By setting the same size, the resonance frequencies f _0A and f _0B can be matched within a range of 50%.

  As a calculation method for obtaining a relative dielectric constant using the first resonator of FIG. 3 and obtaining a dielectric loss tangent using the second resonator of FIG. 4, a mode matching method, a finite element method, a lumped constant equivalent circuit method are available. Etc.

  FIG. 5 is a cross-sectional view of the first resonator for explaining the relative dielectric constant measurement step in the dielectric constant measurement method of the present invention using another resonator (semi-coaxial resonator).

  In the semi-coaxial resonator (first resonator) shown in FIG. 5, the upper electrode 2 is formed on the upper surface of the dielectric thin film sample A1 formed on the lower electrode 3 that also functions as the lower conductor 5 (conductor). Dielectric thin film sample A1) is sandwiched between a central conductor 4 and a lower conductor 5 connected via a cylindrical outer conductor 6 and an air layer 7 as a second dielectric. It has a structure. The lower conductor 5 is formed on the support substrate 8. The support substrate 8 may be made of any material such as metal, semiconductor, dielectric, etc. In particular, silicon, sapphire, Glass or the like is desirable.

Further, in this semi-coaxial resonator, the radiation of the electromagnetic wave from the air layer 7 slightly affects the resonance frequency _f0A , which is prevented by the shielding conductor 9. Two through holes are formed in the shield conductor 9 and the central conductor 4, and a pair of coaxial cables 10 are inserted from the outside to the inside. A pair of loop antennas 11 for excitation and detection are provided at the inner ends of the through holes. Is provided. The insertion depth of the loop antenna 11 into the resonator is adjusted so that the insertion loss at the resonance frequency f _0A of the target resonance mode is about 40 dB. The direction of the electric field in this resonance mode is indicated by an arrow.

By injecting a frequency-swept signal from an oscillator, for example, a synthesized sweeper, from one coaxial cable through a loop antenna to a resonator, an electromagnetic field of a target resonance mode is excited. Through the coaxial cable from the other loop antenna, transmission signal of the resonator by input to the measuring instrument such as a network analyzer to measure the resonance frequency f _0A of the semi-coaxial resonator.

  FIG. 6 is a cross-sectional view for explaining a dielectric loss tangent measurement step in the dielectric constant measurement method of the present invention using another resonator (semi-coaxial resonator).

  In the semi-coaxial resonator (second resonator) shown in FIG. 6, the dielectric thin film sample B1 (dielectric thin film formed on the conductor) formed on the lower electrode 3 that also functions as the lower conductor 5 is The structure is sandwiched between a center conductor 4 and a lower conductor 5 having a tapered tip connected by a cylindrical outer conductor 6. The lower conductor 5 is formed on the support substrate 8. The support substrate 8 may be made of any material such as metal, semiconductor, dielectric, etc. In particular, silicon, sapphire, Glass or the like is desirable.

Further, in this semi-coaxial resonator, the radiation of the electromagnetic wave due to the skin effect from the lower conductor 5 slightly affects the no-load Q, which is prevented by the shielding conductor 9. Two through holes are formed in the shielding conductor 9 and the cylindrical outer conductor 6, and a pair of coaxial cables 10 are inserted from the outside to the inside, and a pair of loop antennas 11 for excitation and detection are provided at the tips. Is formed. The insertion depth of the loop antenna 11 into the resonator is adjusted so that the insertion loss at the resonance frequency f _0B of the target resonance mode is about 40 dB. The direction of the electric field in this resonance mode is indicated by an arrow.

By injecting a frequency-swept signal from an oscillator, for example, a synthesized sweeper, from one coaxial cable through a loop antenna to a resonator, an electromagnetic field of a target resonance mode is excited. The resonance signal f _0B and the no-load Q of this semi-coaxial resonator are measured by inputting the transmitted signal of the resonator from the other loop antenna through the coaxial cable to a measuring device such as a network analyzer.

When a dielectric thin film formed on a conductor is used as the dielectric sample, the capacitance formed equivalently in the resonator tends to be particularly high, so that the resonance frequency is lowered. In the first resonator shown in FIG. 5, a decrease in the resonance frequency is prevented by inserting an air layer 7 in series with the dielectric sample A1, and in the second resonator shown in FIG. Reduction of the resonance frequency is prevented by using a tapered tip. Further, in the first resonator shown in FIG. 5, the resonance frequency can be controlled by changing the thickness of the air layer 7 formed between the cylindrical outer conductor 6 and the lower conductor 5, and FIG. In the second resonator shown, since the resonance frequency can be controlled by changing the size of the resonance space determined by the cylindrical outer conductor 6, the resonance frequencies f _0A and f _0B are matched within a range of 50%. Can be made.

  Further, in these resonators, the relative dielectric constant measurement in which the increase in contact resistance between the upper electrode 2 and the central conductor 4 does not become a problem is performed by the first resonator shown in FIG. Since the effective contact area and dielectric loss tangent between the dielectric sample B1 and the central conductor 4 are measured by the second resonator shown, the relative permittivity and dielectric loss tangent can be measured with higher accuracy.

Furthermore, in order to accurately measure the relative permittivity by the first resonator shown in FIG. 5, the thickness G of the air layer 7 formed in advance between the cylindrical outer conductor 6 and the lower conductor 5 is accurately measured. (Air layer thickness measurement step). This is measured from the resonance frequency f _0S when the center conductor 4 is brought into direct contact with the surface of the lower conductor 5 where the dielectric thin film sample A1 does not exist.

On the other hand, in order to accurately perform the dielectric loss tangent measurement by the second resonator shown in FIG. 6, it is necessary to accurately measure in advance the specific conductivity σr of the central conductor 4 where the current is concentrated (the central conductor of the central conductor 4). Specific conductivity measurement step). This is measured together with the effective contact area S _S between the standard sample and the central conductor 4 from the resonance frequency f _0S and no load Q when the standard sample is inserted instead of the dielectric thin film sample B 1. This standard sample is accumulated in the dielectric thin film sample B1 with respect to the entire resonator during measurement of the dielectric thin film sample B1 and the ratio of the electric field energy accumulated in the standard sample with respect to the entire resonator during measurement of the standard sample. The ratio of the electric field energy is selected to be equal. Thereby, the systematic error of the effective conductivity at the time of measuring the dielectric thin film sample caused by the difference in current distribution between the measurement of the standard sample and the measurement of the dielectric thin film sample B1 can be suppressed.

As a calculation method for obtaining the relative dielectric constant using the first resonator of FIG. 5 and obtaining the dielectric loss tangent using the second resonator of FIG. 6, there are a finite element method, a lumped constant equivalent circuit method, and the like. . In particular, since the axially symmetric finite element method can be used for the axially symmetric semi-coaxial resonators shown in FIGS. 5 and 6, the resonant electromagnetic field distribution is determined from the dimensions, relative permittivity, dielectric loss tangent, and the like. The resonance frequency, no-load Q, etc. can be calculated with high accuracy and in a short time. Therefore, if this is applied, based on the resonance frequency and no-load Q, the dielectric constant and dielectric loss tangent of a dielectric thin film having a thickness of 10 ⁻⁸ m or more formed on the conductor or a co-fired metallized wiring board, etc. Can be requested.

More specific calculation methods include the following methods. First, the resonance frequency f ₀ when the relative permittivity ε ′ of the dielectric sample A1 in the relative permittivity measurement step is changed by at least three points is calculated by the axially symmetric finite element method. Calculated value of the resonance frequency f ₀ obtained at this time is preferably a degree of variation between the measured value of the resonance frequency. Next, a linear approximation formula of resonance frequency f ₀ and relative permittivity ε ′, coefficients a and b of f ₀ = a × ε ′ + b are obtained by the linear least square method. Thereby, the relative dielectric constant ε ′ can be calculated from the measured value f _0A of the resonance frequency f ₀ .

Subsequently, the resonance frequency f ₀ when the contact area S between the dielectric sample B1 and the conductor in the dielectric loss tangent measurement step is changed by at least three points is calculated by the axially symmetric finite element method. Calculated value of the resonance frequency f ₀ obtained at this time is preferably a degree of variation between the measured value of the resonance frequency. Next, a linear approximation formula of resonance frequency f ₀ and contact area S, coefficients c and d of f ₀ = c × S + d are obtained by the linear least square method. Thereby, the contact area S can be calculated from the measured value f _0B of the resonance frequency f ₀ .

Further, by using the calculated value of the contact area S, the conductor Q (Qc) and the electric field energy ratio (Pe) accumulated in the dielectric sample are calculated by the axially symmetric finite element method. A relational expression of Qu ⁻¹ = Qc ⁻¹ + Pe × tan δ is established between the calculated values of Qc and Pe obtained at this time, the unloaded Q (Qu), and the dielectric loss tangent tan δ. Therefore, the dielectric loss tangent can be calculated by substituting the measured value of no-load Q into this equation.

  The present invention is not limited to the above embodiment, and various modifications can be made within the scope of the present invention.

Three kinds of high dielectric constant dielectric thin film samples A1 (HQ, MQ, LQ) having a thickness of 3 × 10 ⁻⁷ m on which the measurement jig in the relative dielectric constant measurement step of the present invention shown in FIG. ), These high dielectric constant dielectric thin film samples A1 are set on the lower electrode 3 of the measurement jig to form a first resonator, and the high dielectric constant dielectric thin film samples A1 are 2 GHz and 5 GHz. The relative dielectric constant of was evaluated. The lower electrode 3 was made of Pt, and the support substrate 8 was made of sapphire.

  In evaluating the relative dielectric constant, first, the dimensions of the measurement jig were evaluated 10 times each using a shape measuring microscope and a micrometer. The thicknesses of the high dielectric constant dielectric thin film sample A1 and the upper electrode 2 are design values managed based on the data of a scanning electron microscope (SEM), and the expected variation coefficient of measurement uncertainty is 5%. The results are shown in Table 1.

Next, the resonance frequency f _0S when the center conductor 4 is brought into direct contact with the surface of the lower conductor 5 where the high dielectric constant dielectric thin film sample A1 does not exist is measured five times, and between the cylindrical outer conductor 6 and the lower conductor 5 is measured. The thickness G of the air layer 7 formed in the above was obtained by an axially symmetric finite element method. The results are shown in Table 2.

Finally, the resonance frequency f _0A was measured five times, and ε ′ of the high dielectric constant dielectric thin film sample A1 was obtained by the axially symmetric finite element method. The results are shown in Table 3.

The uncertainty of ε ′ was calculated by the following equation (1). Uncertainty is represented by measurement variation (standard deviation) by repeated measurement. However, f ₀ is the resonant frequency, m _i denotes the dimensions of such measurement jig.

  From Table 3, it was found that the uncertainty coefficient of variation (standard deviation / average value of relative dielectric constant) was less than 10% for any sample and frequency. In addition, as the controlling factors of the uncertainty at this time, the thickness uncertainty of the high dielectric constant dielectric thin film sample A1 (5%), the measurement uncertainty of the radius of the upper electrode, the uncertainty of the thickness of the upper electrode (5%) The result that it was large in order of was obtained.

Three types of 3 × 10 ⁻⁷ m high dielectric constant dielectric thin film samples B1 (HQ, MQ, LQ) in which the measurement jig and the upper electrode are not formed in the dielectric loss tangent measurement process of the present invention shown in FIG. Then, these high dielectric constant dielectric thin film samples B1 are set on the lower electrode 3 of the measuring jig to constitute a second resonator, and the dielectric loss tangent of the high dielectric constant dielectric thin film samples B1 at 2 GHz and 5 GHz. Evaluated. The support substrate 8 was made of sapphire, and the blocking conductor 9 was made of oxygen-free Cu.

  In evaluating the dielectric loss tangent, first, the dimensions of the measuring jig were evaluated 10 times each using a shape measuring microscope and a micrometer. The thicknesses of the high dielectric constant dielectric thin film sample B1 and the lower electrode 3 are designed values managed based on SEM data, and the expected variation coefficient of measurement uncertainty is 5%. The results are shown in Table 4.

Next, the resonance frequency f _0S and the no-load Q when the standard sample (ε ′ = 313, Qf = 10 ⁴ GHz) shown in Table 4 is inserted instead of the high dielectric constant dielectric thin film sample B1 are measured five times. measured, and the specific conductivity σr of the effective contact area S _S and the central conductor 4 of the standard sample and the central conductor 4 calculated by the finite element method axisymmetric. The specific conductivity of the lower electrode 3 is 61379.56 × π ² × f ₀ × t ² % using the resonance frequency f ₀ (GHz) and the thickness t (mm) of the lower electrode 3, and the cylindrical outer conductor 6 The specific conductivity of was 6.4.6375%. The results are shown in Table 5.

Finally, the resonance frequency f _0B and the no-load Q are measured five times, and the effective contact area S between the high dielectric constant dielectric thin film sample B1 and the central conductor 4 and the tan δ of the high dielectric constant dielectric thin film sample B1 are calculated. Obtained by axisymmetric finite element method. The specific conductivity of the lower electrode 3 and the cylindrical outer conductor 6 is as described above. As the specific conductivity of the center conductor 4, results of 1.7 GHz and 3.3 GHz (weighted average value) were used for 2 GHz measurement, and results of 3.3 GHz and 8 GHz (weighted average value) were used for 5 GHz measurement. Further, as the ε ′ data of the high dielectric constant dielectric thin film sample B1, the measurement result of the high dielectric constant dielectric thin film sample A1 was used. The results are shown in Table 6.

The uncertainty of tan δ was calculated by equation (2). However, Qu is unloaded Q, Qd is the dielectric Q, .sigma.r _i the lower electrode 3, the central conductor 4, represents the specific conductivity of the conductor of the cylindrical outer conductor 6.

  From Table 6, it was found that the coefficient of uncertainty fluctuation was less than 10% for any sample and frequency. In addition, as a controlling factor of uncertainties at this time, it was found that the measurement uncertainties of the unloaded Q, the uncertainties of the specific conductivity of the lower conductor, and the uncertainties of the specific conductivity of the center conductor increase in this order.

  The electric field energy ratio Pe stored in the standard sample given by the above equation (3) is 54% to 87%, and 87% of the electric field energy ratio Pe stored in the high dielectric constant dielectric thin film sample B1. It was a value close to ~ 94%. For this reason, it is considered that the systematic error of the effective conductivity caused by the difference in current distribution between the measurement of the standard sample and the measurement of the high dielectric constant dielectric thin film sample B1 is small.

It is sectional drawing of the 1st resonator for demonstrating the dielectric constant measurement process in the dielectric constant measuring method of this invention. It is sectional drawing of the 2nd resonator for demonstrating the dielectric loss tangent measurement process in the dielectric constant measuring method of this invention. It is sectional drawing of the 1st resonator for demonstrating the dielectric constant measurement process in the other dielectric constant measuring method of this invention. It is sectional drawing of the 2nd resonator for demonstrating the dielectric loss tangent measurement process in the other dielectric constant measuring method of this invention. It is sectional drawing of the 1st resonator for demonstrating the dielectric constant measurement process in the further another dielectric constant measuring method of this invention. It is sectional drawing of the 2nd resonator for demonstrating the dielectric loss tangent measurement process in the further another dielectric constant measuring method of this invention.

Explanation of symbols

A1, B1 Dielectric sample 2 Upper electrode (conductor bump)
3 Lower electrode 4 Upper conductor (center conductor)
5 Lower conductor 6 Cylindrical outer conductor 7 Air layer (second dielectric)
8 Support substrate 9 Shielding conductor 10 Coaxial cable 11 Loop antenna

Claims (8)

A first resonator in which a conductor is brought into contact with each electrode of a dielectric sample having electrodes formed on both surfaces, the electrode of the dielectric sample having electrodes formed only on one surface, and the electrodes are formed. the non-electrode portion of the dielectric specimen not using a second resonator comprising contacting the conductors, respectively, determine the dielectric constant of the dielectric sample from the resonance frequency of the first co-vibrator, wherein said dielectric constant measuring method according to claim from the resonant frequency and the unloaded Q of 2 co-oscillator to determine the dielectric loss tangent of the dielectric sample.   A conductor is brought into contact with a first resonator in which a conductor is brought into contact with the electrode of the dielectric sample having electrodes formed on both surfaces, and a non-electrode portion of the dielectric sample with no electrode formed therein. The dielectric constant of the dielectric sample is obtained from the resonance frequency of the first resonator, and the dielectric loss tangent of the dielectric sample is determined from the resonance frequency of the second resonator and the unloaded Q. A method for measuring a dielectric constant, characterized in that: Seeking an effective contact area between the conductor and the dielectric sample of the non-electrode portions from the resonance frequency (f _0B), with no-load Q of the effective contact area and the second resonator, wherein dielectric constant measuring method according to claim 1, wherein the determination of the dielectric loss tangent of the dielectric sample. Using the resonance frequency and the unloaded Q of the resonance mode generated an electric field towards the opposite one the conductors or al the other of said conductors, and wherein the determination of the dielectric constant and dielectric loss tangent of the dielectric sample The dielectric constant measuring method according to any one of claims 1 to 3 . The first, the dielectric constant measuring method according to any one of claims 1 to 4 second resonator and having an axisymmetric structure. It said first, second resonator, comprising: a cylindrical conductor, a central conductor disposed in the axial direction within the tubular conductor, and a short-circuit conductor provided on both sides openings of the tubular conductor as well as, the center conductor and the dielectric constant measuring method according to claim 5, wherein the dielectric sample formed by interposing a is a semi-coaxial resonator between one of the shorting conductors. The semi-coaxial resonators, the center conductor and one and of the short-circuit conductor the dielectric sample sandwiched between the second sandwiched between said tubular conductor and one or both of the shorting conductors The dielectric constant measuring method according to claim 6 , further comprising: Claims, characterized in that the and the dielectric sample and the second dielectric from the resonance frequency and the unloaded Q of the resonance mode which operates as a serial connection, to measure the dielectric constant and dielectric loss tangent of the dielectric sample 8. The dielectric constant measuring method according to 7 .

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