JP7743266B2 - Strain gauge and its manufacturing method - Google Patents

Description

The present invention relates to a strain gauge that is attached to the surface of a strain-generating structure to be measured.

Cr-N thin film is a new strain sensor material characterized by a large gauge factor of approximately 14, which indicates sensitivity to strain; the temperature coefficient of resistance (TCR) can be reduced to near zero (<±50 ppm/°C) by adding a small amount of nitrogen and performing heat treatment; and high resistance of several tens of kΩ is possible (see Patent Document 1).

Conventional strain gauges (adhesive-type strain sensor elements) are constructed by attaching the sensor material, a metal foil made of a CuNi or NiCr alloy, formed into a grid pattern, to a base (substrate) made of resin such as polyimide. When used to measure strain and various mechanical quantities, they are further adhered to the surface of the strain-generating structure to be measured. In this case, the base is required to provide electrical insulation and ease of handling, including shape retention. It is also important that the base transmits strain correctly, which requires a material with a low Young's modulus and high elongation; resin is commonly used today.

When using a strain sensor thin film as a mechanical quantity sensor, it is possible to form the sensor element directly on the strain-sensitive structure without using a base (via an insulating film if the strain-sensitive structure is a conductor such as metal). With conventional strain gauges, the "bonding" is done manually, which makes it prone to misalignment, and there are also concerns about the effects of creep due to the base or adhesive. However, with a thin film formed directly on the object to be measured, these issues do not need to be considered. However, when installing a strain sensor in a location where thin film formation is not possible due to the structure of the object to be measured, such as deep inside a hole, pipe, or complex shape, an adhesive method must be used. Therefore, investigation was conducted into base substrate materials for Cr-N thin film in order to develop an element that can be used with the adhesive method.

The polyimide used in conventional strain gauges has the highest heat resistance of all resin films, but has a larger thermal expansion coefficient and thermal shrinkage than inorganic materials. As a result, when polyimide is used as a substrate, the effects of localized stress on the substrate become more pronounced, making it prone to cracking. Research into this issue has revealed that reducing the deposition gas pressure, which strengthens the thin film itself by densifying the Cr-N thin film structure (film quality), is effective in reducing cracking. However, the thermal effects of polyimide have not been completely eliminated, and the fabricated elements are prone to substrate warping and partial deformation of the substrate around the thin film, posing problems with regard to its characteristics and stability.

The study focused on zirconia as a freestanding thin plate material that has a thermal expansion coefficient similar to that of Cr-N thin films, excellent heat resistance with no thermal shrinkage, sufficient strength and high insulation, and can be thinned to provide strain transmission. The results of prototyping and evaluating strain gauges using this as the substrate revealed that, if the substrate thickness is 80 μm or less, it is possible to provide highly sensitive strain gauges that can be bonded and used while maintaining functionality roughly equivalent to conventional ones (see Patent Document 2).

Patent No. 6159613 Patent No. 6022881

When using a Cr-N thin-film strain gauge as an adhesive, the zirconia substrate element is very strong against bending, but is weak against linear tension or compression in the in-plane direction of the substrate, making it prone to breakage. Conventional resin materials are cited as a substrate material that is less likely to break. Therefore, we re-examined resin materials, and found that polyimide, which has the highest heat resistance, would be effective because heat treatment is required in the film formation process. However, when using conventional polyimide as a substrate, there were still problems with film formation yield and uniformity of characteristics.

When using strain gauges, a Wheatstone bridge structure is used as the measurement circuit. However, if there is variation in the characteristics of the four strain gauge elements used, for example, the zero balance of the midpoint potential of the current line will be disrupted, making accurate measurements impossible. It can also cause problems such as increased output drift due to external factors such as temperature. For this reason, it is extremely important that the multiple (large number) strain gauge elements manufactured each have uniform characteristics without variation. Therefore, the present invention aims to provide a strain gauge and a manufacturing method thereof that can improve film formation yield and uniformity of characteristics when using a resin substrate.

The present inventors have conducted extensive research to solve the above problems and have found that a bonded strain gauge comprising a resin substrate having predetermined properties and a Cr-N thin film having predetermined composition and properties, as well as a film-forming method and manufacturing method involving heat treatment at a predetermined temperature, can improve the film-forming yield and the uniformity of properties. The strain gauge of the present invention comprises a substrate made of a resin having a stiffness ratio of 227.5 x 103 ^Pa ·m to 682.5 x ¹⁰³ Pa·m and a thermal expansion coefficient of 3 ppm/°C to 27 ppm/°C, and a thin film element formed on the substrate, the thin film element being made of a Cr-N thin film having a nitrogen (N) content of 2.09 at% to 4.20 at% , a temperature coefficient of resistance (TCR) of -186.1 ppm/°C to 370.1 ppm/°C , and a gauge factor of 16.6 to 19.0 .

The method for manufacturing the strain gauge of the present invention described above includes the steps of forming a thin -film element ^made of a Cr-N thin film, the thin-film element being arranged in a specified manner on the main surface of a substrate made of a resin having a stiffness ratio in the range of 227.5 x ¹⁰³ Pa·m to 682.5 x 103 Pa·m and a thermal expansion coefficient in the range of 3 ppm/°C to 27 ppm/°C, and heat-treating the thin-film element at a temperature in the range of 180 to 200°C.

The present invention provides a bonded strain gauge and a manufacturing method thereof that can improve film formation yield and uniformity of characteristics when using a resin substrate.

FIG. 1 is an explanatory diagram relating to a method for reducing the heat treatment temperature in sputtering deposition of a Cr—N thin film (a method for deposition under conditions where the input power is appropriately low). FIG. 1 is an explanatory diagram relating to a method for reducing the heat treatment temperature in sputtering deposition of a Cr—N thin film (a method for depositing a film under conditions that reduce the nitrogen content). FIG. 10 is a graph showing the results of TCR measurements on samples heat-treated at temperatures of 200° C. or less using a heat treatment temperature reduction method. FIG. 10 is a graph showing the measurement results of the gauge factor for a sample heat-treated at a temperature of 200° C. or less using the heat treatment temperature reduction method. 1 is an explanatory diagram illustrating the configuration of a strain gauge according to the present invention. A diagram showing the pattern shape of an actually fabricated thin-film element. FIG. 1 is a diagram showing a thin-film element array pattern formed in one film formation. 1 is a graph showing the relationship between the thermal shrinkage rate and the wire breakage rate for the production examples in Table 2. FIG. 1 is a graph showing the relationship between thermal shrinkage and TCR nonuniformity for the production examples in Table 2. FIG. 1 is a graph showing the relationship between the thermal shrinkage rate and the Gf nonuniformity for the production examples in Table 2. FIG. 10 is a graph showing the relationship between the heat treatment temperature and the disconnection rate for the first substrate and the second substrate. FIG. 10 is a graph showing the relationship between the heat treatment temperature and the TCR nonuniformity for the first substrate and the second substrate. FIG. 10 is a graph showing the relationship between the heat treatment temperature and the Gf nonuniformity for the first substrate and the second substrate. FIG. 10 is a graph showing the relationship between rigidity ratio and breakage rate for samples heat-treated at 180° C. and 200° C. 15 is an enlarged view of the stiffness ratio range of 200 to 300 kPa·m in FIG. 14 . FIG. 10 is an explanatory diagram showing the relationship between the thermal expansion coefficient and the breakage rate of a sample heat-treated at 180° C. and a sample heat-treated at 200° C. FIG. 1 is an explanatory diagram of the relationship between stiffness ratio and TCR non-uniformity for samples heat-treated at 180° C. and 200° C. An enlarged view of the stiffness ratio range of 200 to 300 kPa·m in FIG. 17 . FIG. 1 is an explanatory diagram of the relationship between the thermal expansion coefficient and the TCR nonuniformity of a sample heat-treated at 180° C. and a sample heat-treated at 200° C. FIG. 1 is an explanatory diagram of the relationship between stiffness ratio and Gf nonuniformity for samples heat-treated at 180° C. and samples heat-treated at 200° C. FIG. 1 is a graph illustrating the relationship between the thermal expansion coefficient and Gf nonuniformity of a sample heat-treated at 180° C. and a sample heat-treated at 200° C. FIG. 2 is an explanatory diagram illustrating the characteristics of a substrate that constitutes a strain gauge. FIG. 1 is an explanatory diagram showing the relationship between the nitrogen content and the temperature coefficient of resistance (TCR) of a thin-film element formed on a synthetic resin film. FIG. 1 is an explanatory diagram showing the relationship between the nitrogen content and the gauge factor (Gf) of a thin-film element formed on a synthetic resin film.

The key to solving this problem is thought to be the low heat resistance of the resin material. Therefore, in this invention, we attempted to improve this from the following two perspectives. One was to reduce the heat treatment temperature of the strain sensor thin film, and the other was to search for a resin substrate that would not cause problems within this reduced heat treatment temperature range.

Heat treatment of Cr-N thin films used as strain sensors is carried out to adjust the TCR to 0, and traditionally, heat treatment temperatures of 200-300°C have been used for substrates such as glass, ceramics, and metals. However, test results shown later indicate that for resin-based materials, even those with heat resistance, the heat treatment temperature must be kept below 200°C.

When producing thin films using methods such as sputtering, there are two methods for reducing the heat treatment temperature:

(1) Film deposition under conditions of moderately low input power (see Figure 1) (Reference: Niwa et al., Proceedings of the 32nd Symposium on Sensors, Micromachines and Application Systems, 28pm1-A-1 (2015)).

(2) Creating a thin film with a low nitrogen content (see Figure 2) (Reference: Japanese Patent No. 6159613).

By using these methods, the TCR of the fabricated Cr-N thin film before heat treatment (as-deposited film) becomes a small negative value, and the heat treatment temperature required to achieve a TCR of zero can be lowered.

X First, film formation tests using borosilicate glass (0.2 mm thick, samples other than those with nitrogen contents of 2.09% and 4.20%) and zirconia substrates (0.1 mm thick, samples with nitrogen contents of 2.09% and 4.20%) confirmed that even when heat treatment was performed at temperatures below 200°C using the existing heat treatment temperature reduction method, the TCR was actually near zero (within ±400 ppm/°C) and the gauge factor remained at a sufficiently large, favorable value. The results are shown in Figures 3 and 4. The nitrogen content was analyzed using a wavelength dispersive X-ray analyzer (WDS) for unpatterned (plain film) Cr-N thin films prepared under the same conditions using borosilicate glass (0.2 mm thick) as a substrate. Next, to investigate resin substrate elements, thin films were fabricated on each substrate under the same conditions as the zirconia substrate elements in Figures 3 and 4, and heat-treated at temperatures of 180°C, 200°C, and 220°C to prepare samples. Film formation yield and uniformity of properties were evaluated to search for a resin substrate that would not cause any problems.

Considering the issues from the past, zirconia substrates, which are already in practical use, have the advantage of excellent heat resistance and shape stability, as they do not deform due to heat even when heat-treated at 300°C. The properties that contribute to this are thought to be the lack of thermal shrinkage, a relatively small thermal expansion coefficient, and a large Young's modulus. On the other hand, when using polyimide as a substrate, thermal deformation occurs at the heat treatment temperature, making film formation difficult as cracks occur in the thin film formed, and there is also significant variation in the characteristics of the sensor thin film. Therefore, when comparing this with zirconia substrates, it is thought that there are problems with heat resistance and shape stability. In fact, resins undergo thermal shrinkage, have a relatively large thermal expansion coefficient, and a small Young's modulus.

Therefore, samples were prepared using a resin substrate with a high heat resistance temperature and low thermal shrinkage, and the manufacturing yield and characteristic variations of thin-film elements were evaluated, focusing on the thermal expansion coefficient and Young's modulus of the resin substrate. Only a limited number of resin materials can be made into films with a heat resistance of 200°C or higher, and even among these, many have relatively large thermal shrinkage coefficients and linear expansion coefficients. Several types of polyimide (PI), which has the highest heat resistance among resin film materials, and polyamide (PA), which is said to have the second highest heat resistance, were investigated. The substrate materials used in the study of this invention and their properties are shown in Table 1. Of the properties listed in the table, nominal values were used for thickness, heat resistance temperature, thermal shrinkage coefficient, thermal expansion coefficient, and Young's modulus.

In addition, a larger thickness is thought to be advantageous in terms of shape stability. In fact, as will be seen in the examples described below, even with the same resin material, a thinner thickness produced poor results, while a thicker thickness produced good results. Therefore, we believe that not only Young's modulus but also thickness is important, and investigated the factor of "rigidity," which includes both.

Generally, the stiffness _kN of a plate during tensile deformation is given by the following formula:

k _N =N/δ _N =E・A/L=E・t・w/L.

Here, N is the force acting on the plate in the tensile direction, _δN is the deformation in the tensile direction that occurs in the plate, E is the tensile modulus of elasticity of the plate, A is the cross-sectional area perpendicular to the tensile direction (= t × w), L is the length of the plate in the tensile direction, t is the thickness of the plate, and w is the width of the plate (length perpendicular to the tensile direction). As will be described later, since the substrate shape, film formation area, and thin film pattern shape of the test samples were all identical, w and L were the same for all samples, and the difference in substrate rigidity was determined only by the term E·t (tensile modulus of elasticity × thickness). In this invention, the value expressed by this term is referred to as the rigidity ratio, and this rigidity ratio was evaluated together with the thermal expansion coefficient.

(Structure of strain gauge)
The strain gauge according to one embodiment of the present invention shown in Figure 5 comprises a thin plate-shaped substrate 1 and a thin film element 2 arranged in a specified manner on one of a pair of main surfaces 101, 102 of the substrate 1. The substrate 1 is made of a resin having a stiffness ratio in the range of 200 to 1000 x ¹⁰³ Pa m and a thermal expansion coefficient in the range of 0 ppm/°C to 30 ppm/°C. The thin film element 2 is made of a Cr-N thin film having a nitrogen (N) content in the range of 2 to 8 at%, a temperature coefficient of resistance (TCR) within 0±400 ppm/°C, and a gauge factor of 3 to 20.

(Strain gauge manufacturing method)
A method for manufacturing a strain gauge according to one embodiment of the present invention includes (1) a film forming step and (2) a heat treatment step.

The Cr-N thin film was fabricated on the substrate using reactive sputtering, which involves introducing a small amount of nitrogen gas along with Ar. A magnetron-type high-frequency sputtering system with a magnet for general metals (non-ferromagnetic, i.e., low magnetic force) was used. The amount of nitrogen added was controlled by adjusting the flow rate of the introduced nitrogen gas. A Cr disk (3-inch diameter) with a nominal purity of 99.9% was used as the target. The pre-deposition vacuum (background vacuum), target-substrate distance (TS distance), deposition gas pressure, input power, and nitrogen flow rate ratio were set to 2 x ^10-5 Pa, 43 mm, 5 mTorr, 10 W, and 0.02-0.12%, respectively.

The sensing area of the prototype Cr-N thin-film strain gauge element was a lattice-shaped element consisting of eight folds, with a line width of 40 μm, line spacing of 50 μm, and a length (sensing length) of 1 mm. The element pattern was formed using photolithography and corrosion shaping techniques using a Cr etching solution. The thin film was approximately 100 nm thick. The pattern shape of the thin-film element that was actually fabricated is shown in Figure 6.

Figure 7 shows the thin-film element array pattern. In one deposition run, a Cr-N thin film is formed within a 30 mm x 30 mm area in the center of a 50 mm x 50 mm substrate, from which a total of 40 patterned elements are obtained, arranged in eight rows (1 to 8) horizontally and five columns (A to E) vertically.

The heat treatment was carried out by holding the sample in air at a specified temperature for 30 minutes. A Ni (nickel) thin film was formed by lift-off at a specified position on the prepared thin film, and this served as an electrode for measuring resistance. Lead wires connected to a power supply and voltmeter were soldered to this electrode, but before that, elements were individually cut out from the array of 40. The Ni thin film used as the electrode film was formed by overlaying an electrode film with low resistivity to prevent strain detection information from being included in the electrode and lead portions. Therefore, it was formed by overlaying the Cr-N thin film on the electrode tab and lead portions other than the sensing portion. The methods, systems, shapes, materials, and conditions for thin film formation, pattern formation, heat treatment, etc., according to the present invention are not limited to those of the present embodiment.

(1. Film forming process)
In the film formation process, a Cr—N thin film arranged in a specified manner on one main surface 101 of the substrate 1 is formed directly on the main surface by sputtering using a Cr target. During sputtering, the nitrogen flow rate is adjusted to, for example, a range of 0.02 to 0.05%. The thin-film elements 2 are arranged in a specified manner on the main surface 101 of the substrate 1 by known techniques such as masking and/or etching.

(2. Heat Treatment Process)
In the heat treatment step, the Cr—N thin film formed on the main surface 101 of the substrate 1 is heat treated at a temperature in the range of 180 to 200° C. The heat treatment time is adjusted to, for example, a range of 0.5 to 4 hours so that the Cr—N thin film achieves the desired characteristics. As a result, the thin film element 2 is formed, which is made of a Cr—N thin film having a nitrogen content in the range of 2.09 to 4.20 at %, a temperature coefficient of resistance (TCR) in the range of 45.1 ppm/° C. to 370.1 ppm/° C., and a gauge factor in the range of 16.6 to 17.9.

Examples and Comparative Examples
A thin plate-shaped member made of polyamide (trade name: Mictron (model number: ML)) was prepared as the first substrate. A thin plate-shaped member made of polyimide (trade name: Utopirex (model number: 25S)) was prepared as the second substrate. A thin plate-shaped member made of polyimide (trade name: Kapton (model number: 300V)) was prepared as the third substrate. A thin plate-shaped member made of polyimide (trade name: Kapton (model number: 100V)) was prepared as the fourth substrate. A thin plate-shaped member made of polyimide (trade name: Apical (model number: NPI)) was prepared as the fifth substrate. A thin plate-shaped member made of polyimide (trade name: Apical (model number: AH)) was prepared as the sixth substrate. A thin plate-shaped member made of polyimide (trade name: Upirex (model number: 75S)) was prepared as the seventh substrate. A thin plate-shaped member made of zirconia (trade name: Ceraflex (model number: A)) was prepared as the reference substrate. Table 1 summarizes the thickness, heat resistance temperature, Young's modulus (tensile modulus of elasticity), rigidity ratio, thermal expansion coefficient, and thermal shrinkage rate of each of the first substrate, second substrate, third substrate, fourth substrate, fifth substrate, sixth substrate, seventh substrate, and reference substrate.

As a first manufacturing condition for the strain gauge, the nitrogen flow ratio was adjusted to 0.02% during the film formation process, and the heat treatment temperature of the Cr—N thin film was adjusted to 180°C during the heat treatment process. As a second manufacturing condition for the strain gauge, the nitrogen flow ratio was adjusted to 0.02 to 0.12%, more preferably 0.02 to 0.05%, during the film formation process, and the heat treatment temperature of the Cr—N thin film was adjusted to 200°C during the heat treatment process. As a third manufacturing condition for the strain gauge, the nitrogen flow ratio was adjusted to 0.05% during the film formation process, and the heat treatment temperature of the Cr—N thin film was adjusted to 220°C during the heat treatment process. The nitrogen flow ratio refers to the ratio F1/(F1+F2) of the nitrogen gas flow rate F1 to the sum of the nitrogen gas flow rate F1 and the argon gas flow rate F2 in the sputtering chamber. In the film formation process, the pressure in the sputtering chamber was adjusted to 5 mTorr.

The strain gauge groups of Example 1, Example 3, Example 5, Comparative Example 4, and Reference Example 1 were fabricated using the first, second, third, fourth, and reference substrates, respectively, according to the first fabrication conditions. The strain gauge groups of Example 2, Example 4, Comparative Example 3, Example 6, Comparative Example 5, Example 7, and Reference Example 2 were fabricated using the first, second, third, fifth, sixth, seventh, and reference substrates, respectively, according to the second fabrication conditions. The strain gauge groups of Comparative Examples 1 and 2 were fabricated using the first and second substrates, respectively, according to the third fabrication conditions. The strain gauge groups consist of 40 strain gauges arranged in 8 rows and 5 columns.

Table 2 summarizes the fabrication conditions for the strain gauge groups of Examples 1 to 7, Comparative Examples 1 to 5, and Reference Examples 1 and 2 (hereinafter referred to as "each fabrication example") and the evaluation results described below.

(Strain gauge evaluation)
The resistance values of all 40 Cr-N thin film strain sensor elements (see Figure 7) formed simultaneously under the same conditions in one film formation were measured using a tester capable of measuring up to 20 MΩ. The percentage of the value obtained by dividing the number of elements that could not be measured due to cracks in the thin film by the total number of elements, 40, was taken as the "breakage rate," and was used as an index for evaluating the film formation yield.

The resistance for the temperature coefficient of resistance (TCR) measurement was measured using the DC four-terminal method with a digital multimeter, and the TCR value was calculated from the resistance values of the thin-film element measured at different temperatures in a temperature-controllable thermostatic chamber. Here, TCR refers to the value in the temperature range of 0 to 50°C.

The gauge factor (Gf) was determined by applying strain to a 50mm x 250mm x 1.6mm thick SUS304 plate bonded to the strain body using a continuous cantilever method, and measuring the change in resistance when strain was applied from positive to negative, approximately 600με (=0.06%). The strain required to calculate Gf was measured using a commercially available strain gauge (Kyowa Electronics, KFG-2-350-C1-11) bonded to the same SUS plate strain body at a position where the same amount of strain would be applied. A commercially available general-purpose instant adhesive was used for bonding.

Of the 40 elements fabricated, the TCR and Gf were measured for a total of 16 elements, essentially 1A, 2A, 1E, 2E, 3B, 4B, 3D, 4D, 5B, 6B, 5D, 6D, 7A, 8A, 7E, and 8E in the arrangement shown in Figure 7. If any of these elements were unmeasurable due to a broken wire, an adjacent element was measured instead, bringing the total number of measurements to 16. As an index for evaluating the variation in the TCR and Gf values, the "non-uniformity" was calculated using the maximum, minimum, and average values of the 16 measurement results, as given by the following formula: Here, |f(x)| represents the absolute value of f(x).

(Heterogeneity) = |{(Maximum value) - (Minimum value)}/(Average value)|.

From the prototype testing described above, we investigated a resin substrate material with excellent heat resistance that exhibits the required characteristics and is suitable for producing strain gauges with minimal variation with a high yield. As shown in Figure 23, the required characteristics are a TCR of ±400 ppm/°C or less, a Gf of 3 to 20, a deposition yield of 90% or more (i.e., a wire breakage rate of 10% or less) within the nitrogen content range of 2 to 8 at% in the Cr-N thin film, and a wire breakage rate of 10% or less. It is also preferable that the non-uniformity of the Cr-N thin film characteristics be no more than twice the value of the reference example (an existing zirconia substrate element in practical use). Note that a wire breakage refers to a state in which cracks occur in the thin film element due to substrate deformation or other reasons, making it impossible to measure the resistance value.

For TCR and Gf measurements, samples with a large number of breaks were not included in the evaluation results because there were fewer than 16 non-break samples, which would result in a difference in the total number of non-uniformity tests, and because such samples with a large number of breaks may show extremely poor measurement results, making it impossible to assemble 16 valid samples.

Figure 8 shows the breakage rate versus heat shrinkage rate. Figure 9 shows the TCR non-uniformity. Figure 10 shows the Gf non-uniformity. In both cases, the worst results were observed at a heat shrinkage rate of 0.05%, and no consistent trend was observed. In particular, the TCR non-uniformity showed better values at the highest heat shrinkage rate of 0.5%. These results demonstrate that a heat shrinkage rate of at least 0.5% or less does not affect the breakage rate, TCR non-uniformity, or Gf non-uniformity.

Figure 11 shows the breakage rate versus heat treatment temperature for the first substrate (polyamide Mictron) and the second substrate (polyimide Upilex), both of which have a low thermal expansion coefficient and a high Young's modulus. In Figure 11, the upper limit of the preferred numerical range for the breakage rate is indicated by a dashed line. Figure 12 shows the TCR non-uniformity for the first and second substrates. In Figure 12, the upper limit of the preferred numerical range for the TCR non-uniformity is indicated by a dashed line. Figure 13 shows the Gf non-uniformity for the first and second substrates. In Figure 13, the upper limit of the preferred numerical range for the Gf non-uniformity is indicated by a dashed line.

As can be seen from Figure 13, there were no problems with Gf non-uniformity. On the other hand, as can be seen from Figure 11, the breakage rate for the first substrate increased sharply at 220°C, falling outside the preferred range. As can be seen from Figure 12, when the heat treatment temperature for the second substrate was 200°C or lower, the TCR non-uniformity was within the preferred range, but fell outside the preferred range at a heat treatment temperature of 220°C.

Figure 14 shows the wire breakage rate versus stiffness ratio for samples heat-treated at 180°C and samples heat-treated at 200°C. Figure 15 shows an enlarged view of the stiffness ratio range of 200 to 300 kPa·m in Figure 14. Figure 16 shows the wire breakage rate versus thermal expansion coefficient for samples heat-treated at 180°C and samples heat-treated at 200°C. As can be seen from Figures 14 to 16, the wire breakage rates for the fourth substrate sample heat-treated at 180°C and the third substrate sample heat-treated at 200°C exceeded the upper limit of the preferred numerical range. As can be seen from Figure 16, even though the fourth and third substrates heat-treated at 180°C have the same thermal expansion coefficient, the wire breakage rate for the former was 97.5%, while the wire breakage rate for the latter was 0%.

The breakage rate for the fourth substrate sample heat-treated at 180°C is not due to the influence of the thermal expansion coefficient, but rather, as can be seen in Figure 14, is thought to be due to the small rigidity ratio. Therefore, as can be seen in Figure 15, substrates with rigidity ratios below 200 kPa·m are undesirable. Furthermore, Figures 14 and 15 show that the breakage rate for the sample heat-treated at 200°C does not show a uniform change with the rigidity ratio, indicating that the rigidity ratio is not the cause of the undesirable high breakage rate. On the other hand, Figure 16 shows that the breakage rate for the sample heat-treated at 200°C increases with increasing thermal expansion coefficient, reaching a value that is large enough to exceed the upper limit of the preferable numerical range at 27 ppm/°C. Therefore, it was found that the breakage rate for the sample heat-treated at 200°C depends on the thermal expansion coefficient, and that it becomes large enough to exceed the upper limit of the preferable numerical range at values exceeding approximately 15 ppm/°C.

Figure 17 shows the TCR non-uniformity versus stiffness ratio for samples heat-treated at 180°C and 200°C. Figure 18 shows an expanded view of the stiffness ratio range of 200 to 300 kPa·m in Figure 17. Figure 19 shows the TCR non-uniformity versus thermal expansion coefficient for samples heat-treated at 180°C and 200°C. Figures 17 to 19 show similar results to those shown in Figures 14 to 16 for the samples heat-treated at 200°C. Furthermore, as can be seen from Figures 20 and 21, there were no problems with Gf non-uniformity within these ranges for either stiffness ratio or thermal expansion coefficient for either the samples heat-treated at 180°C or 200°C.

From the above results, it was found that the conditions for the substrate characteristics for strain gauges, under which the breakage rate is 10% or less and the non-uniformity of the thin film characteristics is less than twice that of the reference example (an existing zirconia substrate element in practical use), are a thermal expansion coefficient of 0 to 30 ppm/°C and a rigidity ratio in the range of 200 to 1000 x ¹⁰³ Pa·m when heat treated in the temperature range of 180 to 200°C. The characteristics of each substrate and the boundaries of the ranges are shown in Figure 22.

In Figure 22, plots representing combinations of stiffness ratio and thermal expansion coefficient for each of the first, second, third, fourth, fifth, sixth, seventh, and reference substrates are indicated by circled numbers from 1 to 7 and open circles. The first specified range S1 for stiffness ratio-thermal expansion coefficient shown in Figure 22 means that the stiffness ratio falls within the range of 200 to 1000 x ¹⁰³ Pa-m and the thermal expansion coefficient falls within the range of 0 ppm/°C to 30 ppm/°C. The second specified range S2 for stiffness ratio-thermal expansion coefficient shown in Figure 22 means that the stiffness ratio falls within the range of 227.5 to 682.5 x ¹⁰³ Pa-m and the thermal expansion coefficient falls within the range of 3 to 27 ppm/°C. 22 shows that the plots representing the combinations of stiffness ratios and thermal expansion coefficients of the first, second, third, fifth, and seventh substrates are included in the first and second specified ranges S1 and S2, while the plots representing the combinations of stiffness ratios and thermal expansion coefficients of the fourth, sixth, and reference substrates are outside the first and second specified ranges S1 and S2.

By using a resin substrate that meets the above conditions, the problem of easily broken substrates in existing zirconia-substrate Cr-N thin-film strain gauge elements is resolved. Furthermore, as can be seen from Table 3, the first and second substrates allow for the deposition of Cr-N thin films with good yield and without breakage, almost as readily as the reference substrate (zirconia substrate), and the non-uniformity (variation) of TCR and Gf is improved to an equal or greater extent. From a practical standpoint, the present invention offers significant improvements, making it possible to provide highly sensitive, temperature-stable strain gauges that are easier to handle than conventional ones and have fewer problems with characteristic variation and drift.

A heat treatment temperature exceeding 200°C is undesirable because it increases the wire breakage rate, reduces the film formation yield, and increases the TCR non-uniformity, resulting in instability of the characteristics. The lower limit of the heat treatment temperature is not particularly limited because the effect of temperature is reduced, but 160°C, at which the characteristics do not change significantly, is also preferable, and 180°C is even more preferable. Furthermore, a thermal expansion coefficient exceeding 30 ppm/°C is undesirable because it increases the wire breakage rate, reduces the film formation yield, and increases the TCR non-uniformity, resulting in instability of the characteristics. Furthermore, a rigidity ratio below 200 × 10 ³ Pa·m is undesirable because it abruptly increases the wire breakage rate and significantly reduces the film formation yield. On the other hand, even if the rigidity ratio is too high, there are no problems with the wire breakage rate or the uniformity of the characteristics, but in the case of a resin film substrate with a small Young's modulus, the thickness increases, making it impossible to accurately measure the gauge factor. In the present invention, it is considered undesirable for the Young's modulus to exceed approximately 1000×10 ³ Pa·m from the maximum Young's modulus of 13 GPa and the maximum film thickness of 75 μm among the resin films tested.

The values of the temperature coefficient of resistance and gauge factor as a function of nitrogen content as thin-film properties of the resin substrate are shown in Figures 23 and 24, respectively. As with the zirconia substrate (reference example) and glass substrate shown in Figures 3 and 4, the temperature coefficient of resistance for the resin substrate exhibited values near zero across all nitrogen contents investigated, and the gauge factor tended to decrease as the nitrogen content increased. When the heat treatment temperature reduction technique discussed in this invention was followed, Cr—N thin films exhibited a temperature coefficient of resistance (TCR) within ±400 ppm/°C and a gauge factor (Gf) of 3 to 20 at a nitrogen content of 2 to 8 at%. By using this technique, conditions, and a substrate with the above-mentioned properties, it is possible to provide the desired strain gauge.

Table 2 shows the evaluation results of the breakage rate of the strain gauge group of each fabrication example. The electrical resistance values of multiple thin-film elements (those of 40 that were not broken) that made up the strain gauge group were measured using a tester, and the breakage rate was evaluated as the ratio of the number of thin-film elements whose electrical resistance value was unmeasurable to the total number of thin-film elements. Table 2 shows that the breakage rate of each of the strain gauge groups of Examples 1 to 5 was significantly lower than that of each of the strain gauge groups of Comparative Examples 1 to 4, and was at the same level as or lower than that of each of the strain gauge groups of Reference Example 1 and Reference Example 2.

Table 2 shows the temperature coefficient of resistance (TCR) (average value) and the evaluation results of its non-uniformity for the strain gauge groups of each fabrication example. Table 2 shows that the TCR of each of the strain gauge groups of Examples 1 to 5 falls within the range of -186.1 to 370.1 ppm/°C, which is common to the strain gauge groups of Comparative Example 2, Comparative Example 3, Reference Example 1, and Reference Example 2. On the other hand, the TCR non-uniformity of each of the strain gauge groups of Examples 1 to 5 falls within the range of 0.263 to 1.916, similar to the strain gauge groups of Reference Example 1 and Reference Example 2, and is lower than the strain gauge groups of Comparative Examples 2 and 3.

Table 2 shows the gauge factor Gf (average value) and the evaluation results of its non-uniformity for the strain gauge groups of each fabrication example. Table 2 shows that the Gf of each of the strain gauge groups of Examples 1 to 5 falls within the range of 16.6 to 19.0, which is comparable to that of each of the strain gauge groups of Comparative Examples 2 and 3. It also shows that the non-uniformity of Gf for each of the strain gauge groups of Examples 1 to 5 falls within the range of 0.076 to 0.121, which is lower than that of each of the strain gauge groups of Comparative Examples 2 and 3, and is also lower than that of each of the strain gauge groups of Reference Examples 1 and 2.

Figure 23 shows the relationship between the nitrogen content and temperature coefficient of resistance (TCR) of thin-film element 2 formed on a synthetic resin film (first substrate) as substrate 1. Figure 23 shows that the temperature coefficient of resistance of thin-film element 2 exhibits a value close to zero when the nitrogen content is in the range of 2 to 10.5%.

Figure 24 shows the relationship between the nitrogen content and gauge factor (Gf) of thin-film element 2 formed on a synthetic resin film (first substrate) as substrate 1. Figure 24 shows that, in the nitrogen content range of 2 to 10.5%, the gauge factor of thin-film element 2 tends to decrease as the nitrogen content increases.

1: Substrate, 2: Thin-film element, 101: Upper surface (main surface) of substrate, 102: Lower surface (main surface) of substrate.

Claims (2)

a substrate made of a resin having a stiffness ratio in the range of 227.5×10 ³ Pa·m to 682.5×10 ³ Pa·m and a thermal expansion coefficient in the range of 3 ppm/°C to 27 ppm/°C;
a thin film element formed on the substrate;
A strain gauge comprising:
The thin film element is made of a Cr-N thin film having a nitrogen (N) content in the range of 2.09 at% to 4.20 at% , a temperature coefficient of resistance (TCR) of -186.1 ppm/°C to 370.1 ppm/°C , and a gauge factor of 16.6 to 19.0 . forming a thin-film element made of a Cr—N thin film disposed in a specified manner on a main surface of a substrate made of a resin having a stiffness ratio in the range of 227.5×10 ³ Pa·m to 682.5×10 ³ Pa·m and a thermal expansion coefficient in the range of 3 ppm/°C to 27 ppm/°C;
heat-treating the thin-film element at a temperature in the range of 180 to 200°C to adjust the nitrogen (N) content of the Cr-N thin film to a range of 2.09 at% to 4.20 at%, the temperature coefficient of resistance (TCR) of the Cr-N thin film to a range of -186.1 ppm/°C to 370.1 ppm/°C, and the gauge factor of the Cr-N thin film to a range of 16.6 to 19.0 ;
2. The method of claim 1, further comprising: