JP6555663B2 - Analysis device - Google Patents

Description

  The present invention relates to an analysis apparatus for analyzing mechanical characteristics of a fixed structure used in an element such as a MEMS.

  In recent years, various MEMS sensors having a mechanically movable structure manufactured using MEMS (Micro Electro Mechanical Systems) technology have been actively researched and developed, and are widely used in portable devices such as automobile airbags and smartphones. It is installed. When an excessive force is applied to such a MEMS sensor, the movable structure may be destroyed. For this reason, a method for preventing destruction of the MEMS sensor by controlling (restricting) the movable range of the movable structure is known.

  For example, according to Patent Document 1, as shown in FIG. 9, in a MEMS acceleration sensor having a movable structure 502 whose one end is fixed by a support portion 501 formed by processing a semiconductor substrate, a fixed structure 503, a solid structure Structures 504 are arranged above and below the movable structure 502. The fixed structure 503 and the solid structure 504 are used as stoppers (stopping parts) for restricting the movable structure 502 so that the movable structure 502 is not displaced more than a certain value (limit the operation range) when excessive acceleration is applied. Works.

  Thereby, even if an excessive force generated by acceleration is applied to the acceleration sensor, the movable structure 502 is not displaced more than a certain amount by the fixed structure 503 and the solid structure 504 serving as a stopper, and the movable structure 502 and the like are destroyed. It becomes possible to prevent.

JP 07-159432 A

http://www.cybernet.co.jp/ansys/case/tips/15.html T. Konishi et al., "An arrayed accelerometer device of a wide range of detection for integrated CMOS-MEMS technology", Japanese Journal of Applied Physics, vol.53, no.2, 027202, 2014.

  By the way, when an excessive force is applied to the MEMS sensor having the fixed structure serving as the stopper as described above, the movable structure is fixed by receiving more force than when the movable structure is in contact with the fixed structure. It will be pressed against the structure. In such a situation, when a force exceeding the bonding strength between the fixed structure and the semiconductor substrate or the mechanical strength of the fixed structure itself is applied, the fixed structure is destroyed. Therefore, it is important to analyze how much force the fixed structure can withstand, assuming the state described above.

  However, there is no technique for easily analyzing the fracture resistance of the fixed structure as described above. For example, Non-Patent Document 1 discloses a technique for analyzing delamination using a structural analysis program using a finite element method running on a user's computer. According to this, it is possible to analyze model separation by generating a three-dimensional structure model on a structural analysis program and providing a specified material definition method.

  However, the technique of Non-Patent Document 1 has a problem that it takes time and effort to create a three-dimensional model of a movable structure or a fixed structure. In addition, when the movable structure or fixed structure has a complicated shape, the required performance is high, such as requiring a large amount of memory capacity in the computer used for the calculation of analysis, and more time is required for the analysis. Problem. Further, when the analysis is performed again by changing the shape of the movable structure or the fixed structure, it is necessary to recreate the three-dimensional model from the beginning, and it is difficult to easily execute the analysis.

  In contrast, there is a technique for analyzing mechanical or electrical characteristics of a MEMS acceleration sensor, which is a MEMS element, using an electronic circuit design application running on a computer (see Non-Patent Document 2). In this technique, when a force such as electrostatic attraction or acceleration is excessively applied to the MEMS acceleration sensor, it can be easily analyzed that the movable structure comes into contact with the fixed structure and stops.

  However, this technique does not show an analysis of how much force the fixed structure can withstand. Furthermore, in the technique of Non-Patent Document 2, there is a method for analyzing the structure of a fixed structure serving as a stopper for a MEMS element having a movable structure such as an angular velocity sensor, a pressure sensor, and a vibration power generation element other than the MEMS acceleration sensor. It has not been revealed. As described above, conventionally, there is a problem that there is no technique for easily analyzing the characteristics of the MEMS element including the fixed structure for limiting the operation range of the movable structure.

  The present invention has been made to solve the above-described problems, and makes it possible to more easily analyze the characteristics of a MEMS element including a fixed structure for limiting the operation range of a movable structure. For the purpose.

  The analysis apparatus according to the present invention is a description language for describing the electrical behavior of an electronic circuit by a mathematical expression, and is a first equivalent circuit that is generated as first equivalent circuit data describing a model of a MEMS element having a movable structure. Data generating means, second equivalent circuit data generating means for generating, as second equivalent circuit data described in the above description language, a model of a fixed structure serving as a stop unit that limits the operation range of the movable structure, and first equivalent Circuit analysis means for analyzing the characteristics of the MEMS element and the mechanical characteristics of the fixed structure based on the third equivalent circuit data obtained by connecting the circuit data and the second equivalent circuit data.

  In the above analysis apparatus, the first equivalent circuit data generating means is a model in which the operation of the movable structure partially supported by the support portion fixed to the substrate is connected between the support portion and the movable structure by a spring. Generated as first equivalent circuit data described in the above description language.

  In the analysis apparatus, the second equivalent circuit data generating means generates second equivalent circuit data using parameters including the adhesion strength and the contact area between the fixed structure attached to the substrate and the substrate.

  As described above, according to the present invention, it is possible to obtain an excellent effect that the characteristics of the MEMS element including the fixed structure for limiting the operation range of the movable structure can be analyzed more easily.

FIG. 1 is a configuration diagram showing a configuration of an analysis apparatus according to an embodiment of the present invention. FIG. 2 is a configuration diagram illustrating a model of the MEMS element including the fixed structure 211 to be analyzed. FIG. 3 is a configuration diagram illustrating a model of the MEMS element including the fixed structure 211 to be analyzed. FIG. 4 is a configuration diagram illustrating a model of the MEMS element including the fixed structure 211 to be analyzed. FIG. 5 is an explanatory diagram illustrating a state in which each part in the model of the MEMS element including the fixed structure in the embodiment is an equivalent circuit diagram in an electronic circuit design application using a hardware description language. FIG. 6 is a characteristic diagram showing the results of actual analysis using the circuit diagram described with reference to FIG. 5 and inputting the design parameters of the MEMS element and the design parameters of the fixed structure 211. FIG. 7 is a characteristic diagram showing a result of actual analysis performed by inputting the design parameters of the MEMS element and the design parameters of the fixed structure 211 using the circuit diagram described with reference to FIG. FIG. 8 is a perspective view showing a configuration of a fixed structure 400 including a base portion 401 and an elastic beam portion 402. FIG. 9 is a configuration diagram showing a partial configuration of the MEMS acceleration sensor.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a configuration diagram showing a configuration of an analysis apparatus according to an embodiment of the present invention. The analysis apparatus includes a first equivalent circuit data generation unit 101, a second equivalent circuit data generation unit 102, and a circuit analysis unit 103. In addition, the analysis apparatus includes a data input unit 111.

  The first equivalent circuit data generation unit 101 is a description language for describing the electrical behavior of an electronic circuit (electronic circuit element) as a mathematical expression in accordance with input data input by a user operating the data input unit 111. Generated as first equivalent circuit data describing a model of a MEMS element having a structure. As a description language, there is a hardware description language (HDL). For example, the first equivalent circuit data generation unit 101 uses a model in which the operation of the movable structure partially supported by the support unit fixed to the substrate is connected between the support unit and the movable structure by a spring. Generated as first equivalent circuit data described in a hardware description language.

  The second equivalent circuit data generation unit 102 describes in a description language a model of a fixed structure serving as a stop unit that restricts the operation range of the movable structure in accordance with input data input by a user's operation of the data input unit 111. Generated as second equivalent circuit data. For example, the second equivalent circuit data generation unit 102 generates second equivalent circuit data described in a hardware description language using parameters including adhesion strength and contact area between the fixed structure attached to the substrate and the substrate. .

  The circuit analysis unit 103 analyzes the mechanical characteristics of the MEMS element and the fixed structure based on the third equivalent circuit data obtained by connecting the first equivalent circuit data and the second equivalent circuit data. The circuit analysis unit 103 analyzes the mechanical characteristics of the MEMS element and the fixed structure by simulating the operation state of the MEMS element including the fixed structure based on the third equivalent circuit data. The first equivalent circuit data and the second equivalent circuit data described in the description language are languages that can be input to the circuit analysis unit 103.

  The circuit analysis unit 103 is a simulator used in a design device that designs an electronic circuit from equivalent circuit data described in the above description language. “SPICE” can be used as this simulator. The simulation results are output in units such as amperes and ohms. By replacing these units with units such as displacement and force, analysis results of the mechanical characteristics of the MEMS element and the fixed structure can be obtained.

  The analysis device is a computer device including a CPU (Central Processing Unit), a main storage device, an external storage device, a network connection device, and the like, and is used for designing a known electronic circuit developed in the main storage device. Each function mentioned above is implement | achieved because CPU operate | moves with an application. Each function may be distributed among a plurality of computer devices.

  FIG. 2 is a configuration diagram illustrating a model of the MEMS element including the fixed structure 211 to be analyzed. The model illustrated in FIG. 2 is a MEMS acceleration sensor. The MEMS element includes a lower electrode 202 formed on a semiconductor substrate 201 and a movable structure 203 that is spaced apart from the upper position of the lower electrode 202. The movable structure 203 is modeled on the assumption that it is connected to the anchor for anchor 204 via a spring 205 and a dash pod (attenuator) 206.

  In addition to the element configuration described above, fixed structures 211 are provided on both sides of the movable structure 203. The fixed structure 211 is attached to the formation surface of the lower electrode 202 of the semiconductor substrate 201. The distance between the contact portion of the fixed structure 211 and the contact portion of the movable structure 203 with which the movable structure 203 comes into contact is L. In this example, the following description will be given on the assumption that the fixed structure 211 acts as a stopper (stop portion) for limiting the displacement of the movable structure 203.

  According to the embodiment, the description language for describing the electrical behavior of the electronic circuit by a mathematical expression is an equivalent circuit describing each configuration of the MEMS element including the fixed structure that limits the operation range of the movable structure. By analyzing, the mechanical characteristics of the fixed structure can be analyzed more easily.

  Here, the destruction of the fixed structure 211 will be described. When acceleration is applied to the movable structure 203 in the MEMS element shown in FIG. 2 from the bottom surface of the semiconductor substrate 201 toward the upper surface of the movable structure 203, the movable structure 203 receives a force F generated by the applied acceleration. Then, the semiconductor substrate 201 moves from the bottom surface toward the top surface of the movable structure 203. At this time, the distance x that the movable structure 203 moves is obtained by “x = F / k (1)” where the spring constant of the spring 205 is k.

  Further, it is known that the capacitance value between the movable structure 203 and the lower electrode 202 is inversely proportional to the distance between the movable structure 203 and the lower electrode 202. Therefore, it is possible to know the acceleration value applied to the movable structure 203 by measuring the capacitance value between the movable structure 203 and the lower electrode 202.

  Here, when the value of the distance x that the movable structure 203 moves becomes equal to the distance L between the movable structure 203 and the fixed structure 211, the movable structure 203 is fixed to the fixed structure 211 as shown in FIG. The distance that the movable structure 203 moves toward the upper surface of the movable structure 203 is limited. Furthermore, when the force generated by the acceleration exceeds the bonding strength between the fixed structure 211 and the semiconductor substrate 201 or the mechanical strength of the fixed structure 211 itself, the fixed structure 211 is destroyed as shown in FIG. . Such mechanical characteristics of the fixed structure 211 can be analyzed by the third equivalent circuit data obtained by connecting the first equivalent circuit data indicating the model of the MEMS element and the second equivalent circuit data indicating the model of the fixed structure.

  FIG. 5 is an explanatory diagram illustrating a state in which individual portions in the model of the MEMS element including the fixed structure illustrated in FIG. 2 are circuit diagrams. As shown in FIG. 5, the MEMS element shown in FIG. 2 can be configured as an equivalent circuit including six modules, module 1 to module 6.

  Here, the module A301 is a module that calculates the electrostatic attractive force acting on the movable structure 203, and the module B302 is a motion equation module that calculates the acceleration of the movable structure 203 from the force acting on the MEMS element as the acceleration sensor. The module C303 is a module for calculating a restoring force by the spring 205.

  The module D304 is a module for terminating the spring 205 by the fixing anchor 204, the module E305 is a module for calculating acceleration applied to the MEMS element, and the module F306 is for calculating mechanical characteristics of the fixed structure 211. It is configured as a module.

  Module A301, module B302, module C303, module D304, and module E305 constitute a MEMS element model, and module F306 constitutes a fixed structure 211 model.

  Each module is described in, for example, a hardware description language, and the operation of each equivalent circuit is shown. As the hardware description language, “Verilo-a” can be used. By using such a description language, you can freely describe the physical and electrical characteristics of each module corresponding to the model of each part of the MEMS element by setting conditional branches, initial conditions, and expressions using mathematical functions. can do.

  As described above, the analysis of the fixed structure 211 using the equivalent circuit constituted by the modules corresponding to the respective parts will be described.

  First, in the module F306, as the design parameters of the fixed structure 211, the adhesion strength P of the fixed structure 211 to the semiconductor substrate 201 and the contact area A between the fixed structure 211 and the semiconductor substrate are set. The module F306 is connected to the module B302 for calculating the equation of motion, and the force F applied to the MEMS element and the acceleration of the movable structure 203 of the MEMS element calculated using the module B302 are input to the module F306. Configure as follows.

  In the analysis, the adhesion strength P of the fixed structure 211 to the semiconductor substrate 201, a value P × A obtained by multiplying the contact area A between the fixed structure 211 and the semiconductor substrate, and the force F applied to the MEMS element are compared. . If the force F applied to the MEMS element is smaller than P × A, it is determined that the movable structure is stopped by the fixed structure 211 as shown in FIG. 3, and the speed of the movable structure 203 is set to zero. The displacement of the movable structure 203 is made equal to the position of the fixed structure 211.

  On the other hand, if the force F applied to the MEMS element is larger than P × A, it is determined that the fixed structure 211 is broken as shown in FIG. Calculate velocity and displacement.

  By performing each calculation described above using a simulator used in a design apparatus for designing an electronic circuit, the mechanical characteristics of the MEMS element and the fixed structure 211 can be analyzed.

FIG. 6 is a result of actual analysis performed by inputting the design parameters of the MEMS element and the design parameters of the fixed structure 211 using the circuit diagram described with reference to FIG. In this analysis, as the acceleration to be applied, an acceleration that changes with a sine wave with an amplitude of 2G (G = 9.8 m / s ² ) and a period of 49 Hz is applied from 0 msec to 40 msec, and then changes with a sine wave with an amplitude of 25000 G and a period of 49 Hz. The change in capacitance value between the lower electrode 202 and the movable structure 203 when the acceleration to be applied was applied after 40 msec was calculated. Regarding the sign of the applied acceleration, the direction (upward) from the lower electrode 202 of the MEMS element toward the movable structure 203 was positive.

  As shown in FIG. 6, it can be seen that the capacitance value changes as a sine wave according to the applied acceleration until the analysis time of 40 msec. On the other hand, after 40 msec, the capacitance value changes according to the applied acceleration, and when the acceleration reaches 3G, the fixed structure 211 is contacted and the movable structure 203 stops.

  Thereafter, when the applied acceleration is 11000 G, the force generated by the applied acceleration exceeds the value obtained by multiplying the adhesion strength P of the fixed structure 211 and the contact area A between the fixed structure 211 and the semiconductor substrate 201. It is determined that the fixed structure 211 is destroyed. In this analysis, it is assumed that the movable structure 203 moves away from the lower electrode 202 upward at infinity after the fixed structure 211 is destroyed. As a result, the mechanical characteristics of the fixed structure 211 can be analyzed.

  FIG. 7 is another example of a result obtained by actually inputting a design parameter of the MEMS element and a design parameter of the fixed structure 211 using the circuit diagram described with reference to FIG. In this analysis, the change in the capacitance value between the lower electrode 202 of the MEMS element and the movable structure 203 when an acceleration that linearly changes from 0 G to 100000 G was input as the applied acceleration was calculated. Moreover, three types of values S1, S2, and S3 were set for the area A of the fixed structure 211.

  As shown in FIG. 7, when the absolute value of the applied acceleration reaches 3G, the movable structure 203 comes into contact with the fixed structure 211, and the capacitance value becomes a constant value. It can be seen that when the acceleration is further applied thereafter, the fixed structure 211 is destroyed. It can also be seen that the acceleration values at which the fixed structure 211 is broken differ according to the three types of set areas S1, S2, and S3. From this result, it is possible to easily analyze the mechanical characteristics of the MEMS element and the fixed structure 211 by changing the design parameters of the fixed structure 211.

  As described above, according to the present invention, the MEMS element model is described as the first equivalent circuit data in the description language for describing the electrical behavior of the electronic circuit by the mathematical formula, and the model of the fixed structure is obtained. Since it is described as the second equivalent circuit data and the characteristics of the MEMS element and the mechanical characteristics of the fixed structure are analyzed based on the connected third equivalent circuit data, the fixed equivalent for limiting the operation range of the movable structure The characteristics of the MEMS element including the structure can be analyzed more easily.

  It should be noted that the present invention is not limited to the embodiment described above, and that many modifications can be implemented by those having ordinary knowledge in the art within the technical idea of the present invention. It is obvious.

  For example, in the above description, the fixed structure is a rigid body, but the fixed structure may be an elastic body. For example, as shown in FIG. 8, a fixed structure 400 including a base portion 401 and a beam portion 402 formed integrally with the base portion 401 and having elasticity of a cantilever structure may be used. In this fixed structure 400, in addition to the length l, width w, and thickness t of the beam portion 402, a module is created using the Young's modulus and spring constant of the beam portion 402 as parameters, and an equivalent circuit is constructed to make the movable structure movable. The state of displacement of the movable structure and the state of deformation of the fixed structure 400 (beam 402) in a state where the structure is in contact with the beam 402 may be analyzed. In this case, when a force exceeding the elastic limit of the fixed structure 400 is applied, the deformation of the fixed structure 400 does not return to the original state, and the fixed structure 0400 is described so as to indicate mechanical failure of the fixed structure 400. The contents of the module corresponding to can be described.

  In the above description, the case of an acceleration sensor is exemplified as the MEMS element. However, the present invention is not limited to this, and the MEMS element can be applied to various MEMS elements having a movable structure such as an angular velocity sensor, a pressure sensor, and a vibration power generation element. Needless to say, it can be applied.

  DESCRIPTION OF SYMBOLS 101 ... 1st equivalent circuit data generation part, 102 ... 2nd equivalent circuit data generation part, 103 ... Circuit analysis part, 111 ... Data input part.

Claims (3)

A first equivalent circuit data generating means for generating, as a first equivalent circuit data describing a model of a MEMS element having a movable structure, in a description language for describing an electrical behavior of an electronic circuit by a mathematical expression;
Second equivalent circuit data generating means for generating a model of a fixed structure serving as a stop unit that limits the operation range of the movable structure as second equivalent circuit data described in the description language;
An analysis apparatus comprising: circuit analysis means for analyzing mechanical characteristics of the MEMS element and the fixed structure based on third equivalent circuit data obtained by connecting the first equivalent circuit data and the second equivalent circuit data. . The analysis device according to claim 1,
The first equivalent circuit data generation means includes a model in which an operation of the movable structure partially supported by a support portion fixed to a substrate is connected between the support portion and the movable structure by a spring. An analysis apparatus that generates the first equivalent circuit data described in a description language. The analysis device according to claim 2 ,
The second equivalent circuit data generation means generates the second equivalent circuit data using parameters including an adhesion strength and a contact area between the fixed structure attached to the substrate and the substrate. Analysis device.

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