CN115809576A - Device performance evaluation method for coupling silicon-based MEMS (micro-electromechanical systems) process and multiple physical fields - Google Patents
Device performance evaluation method for coupling silicon-based MEMS (micro-electromechanical systems) process and multiple physical fields Download PDFInfo
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Abstract
The invention discloses a device performance evaluation method for coupling a silicon-based MEMS process and a multi-physical field, which comprises the following steps: performing manufacturing process simulation on a device with a silicon-based MEMS substrate to obtain a process simulation model; carrying out structural design topology on the process simulation model to obtain a three-dimensional model after topology reconstruction; establishing a process and design coupling model based on the three-dimensional model after topological reconstruction, and determining a physical field during coupling based on a coupling physical environment; carrying out multi-physical-field numerical simulation calculation; and evaluating the performance of the device based on the simulation calculation result. The invention solves the coupling problem of MEMS manufacturing process and geometric configuration, innovatively adopts numerical algorithm and structural coupling, can optimize the structure and manufacturing process of the MEMS device, and greatly saves the research and development cost and period of the MEMS device.
Description
Technical Field
The invention belongs to a silicon-based MEMS performance evaluation method in the field of electronic information, and particularly relates to a silicon-based film process and a device performance calculation simulation method of a multi-physical-field model.
Background
MEMS sensors, i.e. Micro Electro Mechanical Systems (MEMS), are a leading-edge research field of multidisciplinary intersection developed on the basis of microelectronics. Over forty years of development, it has become one of the major scientific and technological fields of world attention. It relates to various subjects and technologies such as electronics, machinery, materials, physics, chemistry, biology, medicine and the like, and has wide application prospect. By 2010, more than about 600 units have worked on MEMS development and production, and hundreds of products including miniature pressure sensors, acceleration sensors, micro-inkjet printheads, digital micro-mirror displays have been developed, with MEMS sensors being a significant proportion. MEMS sensors are new types of sensors manufactured using microelectronics and micromachining techniques. Compared with the traditional sensor, the sensor has the characteristics of small volume, light weight, low cost, low power consumption, high reliability, suitability for batch production, easiness in integration and realization of intellectualization. At the same time, feature sizes on the order of microns make it possible to perform functions that some conventional mechanical sensors cannot achieve.
In a multi-physical field, physical fields are mutually superposed and mutually influenced, and the research on the multi-physical field is to research the relationship among a plurality of physical attributes of interaction. For example, natural convection heat transfer studies the relationship between pressure field, velocity field, temperature field, and magnetohydrodynamics studies the relationship between magnetic field, electric field, fluid field. As a research field across subjects, the multi-physics field covers various subjects including mathematics, physics, engineering, electromagnetism, and the like. When a multi-physical field model is established, a corresponding partial differential equation is established according to each physical field, and finally the equations are simultaneously established to form a multi-physical field equation set.
The existing silicon-based MEMS sensor is widely applied to various electronic products, and because the preparation process is complex and high in cost, how to design the silicon-based MEMS before preparation and optimize the process is very important. At present, no method for accurately detecting the performance of a device coupled by a silicon-based MEMS process and a multi-physical-field model exists internationally. The evaluation of the process performance of the device can be carried out through molecular simulation in the process, but the change of the process simulation specific structure cannot be simulated. At present, a device manufactured by a process can be designed and optimized through numerical algorithms such as finite elements, however, the influence of residual stress and the like on the device caused by process steps cannot be analyzed, and a silicon-based MEMS device performance evaluation method for simultaneous process simulation and device structure comprehensive judgment is lacked.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a device performance evaluation method for coupling a silicon-based MEMS process and a multi-physical-field model.
In order to achieve the above object, the present invention provides a device performance evaluation method for coupling a silicon-based MEMS process with multiple physical fields, the method comprising:
step S1) carrying out manufacturing process simulation on a device with a silicon-based MEMS substrate to obtain a process simulation model;
step S2) carrying out structural design topology on the process simulation model to obtain a three-dimensional model after topology reconstruction;
step S3) establishing a process and design coupling model based on the three-dimensional model after topological reconstruction, and determining a physical field during coupling based on a coupling physical environment;
step S4), carrying out multi-physical-field numerical simulation calculation;
and S5) evaluating the performance of the device based on the simulation calculation result.
As a modification of the above method, the silicon-based MEMS substrate of step S1) includes: the crystal face, doping concentration and surface resistance of a common silicon wafer and the silicon wafer containing a silicon oxide layer.
As a modification of the above method, the step S1) includes:
determining process parameters according to the design performance requirements of a device with a silicon-based MEMS substrate;
and simulating the manufacturing process according to the process parameters and the device size to obtain a process simulation model and basic sizes corresponding to different process steps.
As a modification of the above method, the step S2) includes:
designing and modeling a three-dimensional topological structure based on a three-dimensional model of the simulation device;
and calculating the structure after topology, and further refining and modeling to obtain a three-dimensional model after topology reconstruction.
As a modification of the above method, the step S3) includes:
establishing a process and design coupling model based on the three-dimensional model after topological reconstruction, and creating a three-dimensional grid;
designing coupling boundary conditions, and determining the type of the physical field and corresponding parameters during coupling.
As a modification of the above method, the step S4) includes:
establishing a three-dimensional grid model based on physical parameters of the device during working and a device design coupling model;
setting initial conditions and boundary conditions of multi-physical-field coupling simulation calculation, solving a control equation of multi-physical-field coupling, and setting finite element, newton difference and central difference numerical algorithms during calculation; wherein the control equation of the multi-physical field coupling is as follows:
f(m j ；v i ,s)＝0
where f is a differential operator, m j Is the j physical property variable of the material, v i Is the ith field variable, either vector or scalar, and s is the sink or source of the field.
As a modification of the above method, the step S4) further includes: establishing a two-dimensional grid model based on physical parameters of the device during working and a device design coupling model; the method specifically comprises the following steps:
carrying out orthographic and parallel projection on the three-dimensional coordinate system point set to one coordinate plane to obtain a two-dimensional grid model;
simplifying the initial conditions and boundary conditions of the multi-physical-field coupling simulation calculation according to the two-dimensional grid model, solving a control equation of the multi-physical-field coupling, and setting a finite element, a Newton difference value and a central difference numerical algorithm during calculation.
As a modification of the above method, the step S5) includes:
analyzing the stress and temperature distribution conditions of the device in different process steps based on the simulation calculation result of the step S4), and simulating the working state and related physical parameters of the simulation device after the process steps are finished in different working conditions; and further evaluating the performance of the device with the silicon-based MEMS substrate, and carrying out structure and process optimization according to relevant physical parameters.
Compared with the prior art, the invention has the advantages that:
1. the invention provides a method for evaluating the performance of a silicon-based MEMS device under the action of multiple physical fields through the state between a coupling process and the multiple physical fields, and solves the problem that the process and the structure of the silicon-based MEMS are mutually coupled under the action of the multiple physical fields;
2. the invention solves the coupling problem of MEMS manufacturing process and geometric configuration, innovatively adopts numerical algorithm and structural coupling, can optimize the structure and manufacturing process of the MEMS device, and greatly saves the research and development cost and period of the MEMS device.
Drawings
FIG. 1 is a flow chart of a device performance evaluation method of a silicon-based MEMS multi-physical field model of the present invention;
FIG. 2 is a schematic diagram of a device process simulation of the present invention;
FIG. 3 is a schematic diagram of a structural design topology model of the present invention;
FIG. 4 is a schematic view of the process and design coupling model of the present invention;
FIG. 5 is a diagram illustrating the result of numerical calculation of the multi-physics coupling simulation of the present invention, wherein FIG. 5 (a) is a stress distribution diagram, FIG. 5 (b) is a voltage distribution diagram, FIG. 5 (c) is a displacement distribution diagram, and FIG. 5 (d) is a current distribution diagram.
Detailed Description
The invention discloses a silicon-based film process and a device performance calculation simulation method of a multi-physical-field model, which comprises the following steps: establishing a silicon-based MEMS (micro-electromechanical systems) process simulation model, and calculating the process numerical value of the MEMS; carrying out topology and modeling on the three-dimensional structure of the silicon-based MEMS so as to carry out three-dimensional multi-physical-field coupling simulation; combining process simulation and multi-physical coupling, and establishing a process-multi-physical coupling composite model with a geometric configuration; establishing a three-dimensional grid based on the reconstructed composite model, and setting initial conditions and boundary conditions of a process and physical simulation; performing numerical solution on the composite model by algorithms such as a finite element method, a Newton interpolation method and the like; and analyzing different coupling load conditions of different processes, and calculating the stress distribution of the silicon-based MEMS so as to evaluate the device performance of the silicon-based MEMS under complex conditions.
The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and examples.
Example 1
As shown in fig. 1, the method for evaluating the performance of a device coupled by a silicon-based MEMS process and a multi-physical-field model according to the present invention comprises the following steps:
1: selecting a silicon-based MEMS substrate: by analyzing the functions of the devices, a proper silicon-based MEMS substrate is selected, including the crystal face, the doping concentration, the surface resistance, the silicon wafer (SOI) containing a silicon oxide layer and the like of a common silicon wafer.
The functions of the devices are defined through analysis, and corresponding silicon-based MEMS substrates are prepared according to different functions and physical principles, so that basic parameters and sizes of some devices are obtained;
the substrate comprises silicon wafers with different crystal face directions, silicon wafers with conductivity aligned for doping, silicon wafers SOI on a silicon dioxide insulating layer and the like, wherein the multilayer silicon wafers with the insulating layers need to define physical parameters for different layers.
2: device fabrication process simulation as shown in fig. 2: carrying out process simulation on the established silicon wafer MEMS substrate, carrying out process parameter design, generating device structures under different processes, and obtaining device manufacturing process simulation results, wherein the steps are as follows:
step 2, simulating the device process according to different design parameters and device sizes;
and 3, obtaining the process simulation model of the three-dimensional device, wherein the basic size of the device after process simulation in each step can be obtained.
3: the device structure design topology as shown in fig. 3: carrying out structural topology on the model after the process simulation is obtained, and further carrying out detailed modeling on the structure after the local process simulation, wherein the specific steps are as follows:
and 2, calculating the structure after the device topology is obtained, and further carrying out structure refinement modeling.
4: as shown in fig. 4, the process and device design coupling model is established: establishing a process and designing a coupling model based on a three-dimensional model of topological reconstruction, creating a three-dimensional grid, designing a coupling boundary condition, and determining a physical field type and corresponding parameters during coupling, wherein the specific steps are as follows:
and 2, designing a coupling boundary condition based on the coupling physical environment, and determining the type of the physical field and corresponding parameters during coupling.
5: the device process and structure multiphysics coupling simulation calculation is illustrated in fig. 5, where fig. 5 (a) is a stress profile, fig. 5 (b) is a voltage profile, fig. 5 (c) is a displacement profile, and fig. 5 (d) is a current profile. The method comprises the following specific steps: establishing a three-dimensional grid model generated in the step based on physical parameters of the device during working and a device design coupling model, setting initial conditions and boundary conditions of calculation, solving a basic formula of multi-physical-field coupling, and setting numerical algorithms such as finite elements, newton difference values, central differences and the like during calculation. Wherein the governing equation of the multiple physical fields can be uniformly expressed as:
f(m j ；v i ,s)＝0(i,j＝1,2,…n) (1)
wherein f is a differential operator; m is a unit of j Is a physical variable of the material, and can be one or more; v. of i Is a field variable, can be a vector or a scalar, and can have one or more; s is the sink or source of the field, typically 1.
The specific steps of the device multi-physical field coupling simulation calculation are as follows:
and 2, setting initial conditions and boundary conditions of calculation, solving a basic formula of multi-physical-field coupling, and setting numerical algorithms such as finite elements, newton difference values, central difference values and the like during calculation.
For the simulation calculation of the device, the following related methods of two-dimensional models are also included:
for the two-dimensional grid model, establishing the two-dimensional grid model generated in the step based on the physical parameters of the device during working and the device design coupling model;
the two-dimensional model needs to simplify boundary conditions and initial conditions, needs to use different unit types, and the calculation method refers to a calculation formula in the three-dimensional model to perform projection on a two-dimensional plane.
6: evaluating the performance of the MEMS device under complex conditions: analyzing the distribution condition of multiple physical parameters of the device under different multi-physical-field working conditions based on simulation operation results, and evaluating the physical performance of the MEMS device under complex conditions according to the use condition of the device, process steps, performance constraint conditions and physical limitations of a material body, and realizing process and design optimization, wherein the method comprises the following specific steps:
and 2, evaluating the performance of the MEMS device according to the multi-physical-field coupling simulation under the process and device working states under different conditions, and performing structure and process optimization according to related physical parameters.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and are not limited. Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (8)
1. A method for evaluating device performance of a silicon-based MEMS process coupled with multiple physical fields, the method comprising:
step S1) carrying out manufacturing process simulation on a device with a silicon-based MEMS substrate to obtain a process simulation model;
step S2) carrying out structural design topology on the process simulation model to obtain a three-dimensional model after topology reconstruction;
step S3) establishing a process and design coupling model based on the three-dimensional model after topological reconstruction, and determining a physical field during coupling based on a coupling physical environment;
step S4), carrying out multi-physical-field numerical simulation calculation;
and S5) evaluating the performance of the device based on the simulation calculation result.
2. The method for evaluating the performance of a silicon-based MEMS process coupled with a multi-physical field model as claimed in claim 1, wherein the silicon-based MEMS substrate of step S1) comprises: the crystal face, doping concentration and surface resistance of a common silicon wafer and the silicon wafer containing a silicon oxide layer.
3. The method for evaluating the performance of a silicon-based MEMS process coupled with a multi-physical-field model device according to claim 1, wherein the step S1) comprises:
determining process parameters according to the design performance requirements of a device with a silicon-based MEMS substrate;
and simulating the manufacturing process according to the process parameters and the device size to obtain a process simulation model and basic sizes corresponding to different process steps.
4. The method for evaluating the performance of a silicon-based MEMS process coupled with a multi-physical-field model device according to claim 1, wherein the step S2) comprises:
designing and modeling a three-dimensional topological structure based on a three-dimensional model of the simulation device;
and calculating the structure after the topology, and further refining and modeling to obtain a three-dimensional model after the topology reconstruction.
5. The method for evaluating the performance of a silicon-based MEMS process coupled with a multi-physical-field model device according to claim 1, wherein the step S3) comprises:
establishing a process and design coupling model based on the three-dimensional model after the topology reconstruction, and creating a three-dimensional grid;
designing coupling boundary conditions, and determining the type of the physical field and corresponding parameters during coupling.
6. The method as claimed in claim 1, wherein the step S4) comprises:
establishing a three-dimensional grid model based on physical parameters of the device during working and a device design coupling model;
setting initial conditions and boundary conditions of multi-physical-field coupling simulation calculation, solving a control equation of multi-physical-field coupling, and setting a finite element, newton difference and central difference numerical algorithm during calculation; wherein the governing equation of the multi-physical field coupling is:
f(m j ；v i ,s)＝0
where f is a differential operator, m j Is the j physical property variable of the material, v i Is the ith field variable, either vector or scalar, and s is the sink or source of the field.
7. The method for evaluating the performance of a silicon-based MEMS process coupled with a multi-physical-field model as recited in claim 6, wherein the step S4) further comprises: establishing a two-dimensional grid model based on physical parameters of the device during working and a device design coupling model; the method specifically comprises the following steps:
carrying out orthographic and parallel projection on the three-dimensional coordinate system point set to one coordinate plane to obtain a two-dimensional grid model;
simplifying initial conditions and boundary conditions of multi-physical-field coupling simulation calculation according to a two-dimensional grid model, solving a control equation of multi-physical-field coupling, and setting a finite element, a Newton difference value and a central difference numerical algorithm during calculation.
8. The method for evaluating the performance of a silicon-based MEMS process coupled with a multi-physical-field model device according to claim 1, wherein the step S5) comprises:
analyzing the stress and temperature distribution conditions of the device in different process steps based on the simulation calculation result of the step S4), and simulating the working state and related physical parameters of the simulation device after the process steps are finished in different working conditions; and further evaluating the performance of the device with the silicon-based MEMS substrate, and carrying out structure and process optimization according to relevant physical parameters.
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| CN1448870A (en) * | 2003-05-14 | 2003-10-15 | 西安交通大学 | Computer-aided technique planning method for silicon micro-component |
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