CN115809576B - Silicon-based MEMS (micro electro mechanical System) process and multi-physical field coupling device performance evaluation method - Google Patents
Silicon-based MEMS (micro electro mechanical System) process and multi-physical field coupling device performance evaluation method Download PDFInfo
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Abstract
The invention discloses a silicon-based MEMS technology and multi-physical field coupling device performance evaluation method, 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; based on the three-dimensional model after topology reconstruction, a process and design coupling model are established, and a physical field during coupling is determined based on a coupling physical environment; performing multi-physical field numerical simulation calculation; and performing device performance evaluation based on the simulation calculation result. The invention solves the coupling problem of MEMS manufacturing process and geometric configuration, and the innovative numerical algorithm and structure coupling can optimize the structure and manufacturing process of MEMS devices, thereby greatly saving the research and development cost and period of MEMS devices.
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. microelectromechanical systems (Microelectro Mechanical Systems), are the leading-edge research area of multi-disciplinary intersection developed on the basis of microelectronics. Over forty years of development, it has become one of the major technological areas of worldwide attention. The method relates to various disciplines and technologies such as electronics, machinery, materials, physics, chemistry, biology, medicine and the like, and has wide application prospect. By 2010, about 600 units of MEMS have been developed and produced worldwide, and hundreds of products including miniature pressure sensors, acceleration sensors, micro-inkjet printheads, digital micromirror displays have been developed, with MEMS sensors accounting for a significant proportion. MEMS sensors are novel sensors fabricated 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 mass production, easy integration and realization of intelligence. At the same time, feature sizes on the order of microns allow it to perform functions not possible with some conventional mechanical sensors.
In multiple physical fields, the physical fields are overlapped and mutually influenced, and the research on the multiple physical fields is to research the relationship among the physical properties of multiple interactions. For example, natural convection heat transfer studies the relationship between pressure field, velocity field, temperature field, magnetohydrodynamics studies the relationship between magnetic field, electric field, fluid field. As a interdisciplinary field of research, multiple physical fields cover various disciplines including mathematics, physics, engineering, electromagnetism, and the like. When the multi-physical field model is built, a corresponding partial differential equation is built according to each physical field, and finally a multi-physical field equation set is formed by simultaneous equations.
The current silicon-based MEMS sensor is widely applied to various electronic products, and because of the complex preparation process and high cost, how to perform the design of the silicon-based MEMS and the optimization of the technological process before the preparation is important. At present, a method for accurately detecting the performance of a device coupled by a silicon-based MEMS process and a multi-physical field model is not available 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 specific structure of the process simulation cannot be simulated yet. At present, a device in a manufacturing process can be designed and optimized through a numerical algorithm such as a finite element, however, the influence of residual stress and the like on the device caused by process steps cannot be analyzed, and a device performance evaluation method of the silicon-based MEMS for comprehensively judging the simultaneous process simulation and the device structure 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 method for evaluating device performance of a silicon-based MEMS process and multi-physical field coupling, the method comprising:
step S1), performing 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) based on the three-dimensional model after topology reconstruction, establishing a process and design coupling model, and determining a physical field during coupling based on a coupling physical environment;
step S4), performing multi-physical field numerical simulation calculation;
step S5) performing device performance evaluation based on simulation calculation results.
As an improvement of the above method, the silicon-based MEMS substrate of step S1) includes: crystal face, doping concentration, surface resistance and silicon slice containing silicon oxide layer of common silicon slice.
As an improvement 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 carrying out manufacturing process simulation according to the process parameters and the device size to obtain a process simulation model and basic sizes corresponding to different process steps.
As an improvement of the above method, the step S2) includes:
performing three-dimensional topological structure design and modeling based on a three-dimensional model of the simulation device;
and calculating the topological structure, and further refining and modeling to obtain a topological reconstructed three-dimensional model.
As an improvement of the above method, the step S3) includes:
based on the three-dimensional model after topology reconstruction, a process and design coupling model is established, and a three-dimensional grid is established;
and designing coupling boundary conditions, and determining the physical field type and corresponding parameters during coupling.
As an improvement of the above method, the step S4) includes:
establishing a three-dimensional grid model based on physical parameters of the device during operation 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, a Newton difference value and a central difference numerical algorithm; wherein the control 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-th physical variable of the material, v i Is the ith field variable, is a vector or scalar, s is the sink or source of the field.
As an improvement of the above method, the step S4) further includes: establishing a two-dimensional grid model based on physical parameters and a device design coupling model when the device works; the method specifically comprises the following steps:
carrying out orthoparallel 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 the simulation calculation of the multi-physical field coupling 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 for calculation.
As an improvement of the above method, the step S5) includes:
based on the simulation calculation result of the step S4), analyzing the stress and temperature distribution conditions of the device under different process steps, and simulating the working state and related physical parameters of the simulation device under different working conditions after the process steps are completed; and further evaluating the performance of the device with the silicon-based MEMS substrate, and performing structural and process optimization according to the related physical parameters.
Compared with the prior art, the invention has the advantages that:
1. according to the invention, through the state between the coupling process and the multiple physical fields, a device performance evaluation method of the silicon-based MEMS under the action of the multiple physical fields is provided, and the problem of mutual coupling of the process and the structure of the silicon-based MEMS under the action of the multiple physical fields is solved;
2. the invention solves the coupling problem of MEMS manufacturing process and geometric configuration, and the innovative numerical algorithm and structure coupling can optimize the structure and manufacturing process of MEMS devices, thereby greatly saving the research and development cost and period of MEMS devices.
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 diagram of a process and design coupling model of the present invention;
fig. 5 is a diagram showing the results of calculation of the simulation values of the multiple physical fields 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 process simulation model, and performing MEMS process numerical calculation; topology and modeling are carried out on the three-dimensional structure of the silicon-based MEMS, so that three-dimensional multi-physical field coupling simulation is carried out; combining process simulation and multi-physical coupling to establish a process-multi-physical coupling composite model with a geometric configuration; based on the reconstructed composite model, creating a three-dimensional grid, and setting initial conditions and boundary conditions of a process and physical simulation; carrying out numerical solution on the composite model through 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 stress distribution of the silicon-based MEMS, so as to evaluate the device performance of the silicon-based MEMS under the complex condition.
The technical scheme of the invention is 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 the device by coupling the silicon-based MEMS process and the multi-physical field model according to the present invention comprises the following steps:
1: selecting a silicon-based MEMS substrate: through analyzing the function of the device, a proper silicon-based MEMS substrate is selected, wherein the proper silicon-based MEMS substrate comprises a crystal face, doping concentration, surface resistance, a 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, corresponding silicon-based MEMS substrates are prepared according to different functions and physical principles, and basic parameters and sizes of some devices are obtained;
the substrate comprises silicon wafers with different crystal plane directions, silicon wafers with conductivity which are aligned for doping, silicon wafer SOI (silicon on insulator) on silicon dioxide and the like, wherein the multi-layer silicon wafers with the insulating layers need to define physical parameters of different layers.
2: the device manufacturing process simulation as shown in fig. 2: performing process simulation on the established silicon wafer MEMS substrate, performing process parameter design, generating device structures under different processes, and obtaining device manufacturing process simulation results, wherein the steps are as follows:
step 1, determining technological parameters, and designing the technological parameters according to performance requirements of different device designs;
step 2, simulating a device process according to different design parameters and device sizes;
and step 3, obtaining a process simulation model of the three-dimensional device, and obtaining the basic size of the device after process simulation in each step.
3: the device structure design topology as in fig. 3: carrying out structural topology on the obtained model subjected to process simulation, and carrying out further refined modeling on the structure subjected to local process simulation, wherein the method comprises the following specific steps of:
step 1, obtaining a model after process simulation, and carrying out three-dimensional topological structure design and modeling;
and 2, calculating the structure after the topology of the device is obtained, and further carrying out structure refinement modeling.
4: process and device design coupling model building as in fig. 4: based on the three-dimensional model of topology reconstruction, a process and a design coupling model are established, a three-dimensional grid is established, a coupling boundary condition is designed, and the physical field type and corresponding parameters during coupling are determined, wherein the specific steps are as follows:
step 1, a three-dimensional grid is created based on a process and device design coupling three-dimensional digital model;
and 2, designing coupling boundary conditions based on the coupling physical environment, and determining the physical field type and corresponding parameters during coupling.
5: the device process and structure multi-physical field coupling simulation calculations are shown 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: based on the three-dimensional grid model generated in the step of building the physical parameters and the device design coupling model during the operation of the device, setting the initial conditions and boundary conditions of calculation, solving the basic formula of multi-physical field coupling, and setting numerical algorithms such as finite elements, newton difference values, center difference values and the like during the calculation. Wherein the control equation of the multiple physical fields can be uniformly expressed as:
f(m j ；v i ,s)＝0(i,j＝1,2,…n) (1)
where f is a differential operator; m is m j Is a physical variable of the material, and one or more of the physical variables can be used; v i Is a field variable, which may be a vector or a scalar, which may have oneOne or more of; s are the sink or source of the fields, typically 1.
The device multi-physical field coupling simulation calculation comprises the following specific steps:
step 1, establishing a three-dimensional grid model generated in the step based on physical parameters and a device design coupling model during the operation of a device;
and 2, setting initial conditions and boundary conditions of calculation, solving basic formulas of multi-physical field coupling, and setting numerical algorithms such as finite element, newton difference value, center difference value and the like during calculation.
For the simulation calculation of the device, the following two-dimensional model correlation method should be included:
for the two-dimensional grid model, the two-dimensional grid model generated in the step of building the coupling model based on the physical parameters of the device during operation and the device design;
the two-dimensional model needs to simplify boundary conditions and initial conditions, different unit types are needed, and the calculation method refers to a calculation formula in the three-dimensional model to carry out projection on a two-dimensional plane.
6: MEMS device performance evaluation under complex conditions: based on simulation operation results, the multi-physical parameter distribution condition of the device under different multi-physical field working conditions is analyzed, and according to the use condition and the process steps of the device, the performance constraint condition and the physical limitation of a material body, the physical performance of the MEMS device under the complex condition is evaluated, and the process and the design optimization are realized, wherein the specific steps are as follows:
step 1, analyzing stress and temperature distribution conditions of devices in different process steps based on basic analysis results, and simulating working states and related physical parameters of the simulation devices after the process steps are completed in different working conditions;
and 2, according to the multi-physical field coupling simulation under different conditions of the process and the working state of the device, evaluating the performance of the MEMS device, and carrying out structure and process optimization according to related physical parameters.
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present invention and are not limiting. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the appended claims.
Claims (3)
1. A method of device performance evaluation for silicon-based MEMS processing and multiple physical field coupling, the method comprising:
step S1), performing 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) based on the three-dimensional model after topology reconstruction, establishing a process and design coupling model, and determining a physical field during coupling based on a coupling physical environment;
step S4), performing multi-physical field numerical simulation calculation;
step S5), performing device performance evaluation based on simulation calculation results;
the step S2) includes:
performing three-dimensional topological structure design and modeling based on a three-dimensional model of the simulation device;
calculating a topological structure, and further refining and modeling to obtain a topological reconstructed three-dimensional model;
the step S3) includes:
based on the three-dimensional model after topology reconstruction, a process and design coupling model is established, and a three-dimensional grid is established;
designing a coupling boundary condition, and determining a physical field type and corresponding parameters during coupling;
the step S4) includes:
establishing a three-dimensional grid model based on physical parameters of the device during operation 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, a Newton difference value and a central difference numerical algorithm; wherein the control 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-th physical variable of the material, v i Is the ith field variable, which is a vector or scalar, s is the sink or source of the field;
establishing a two-dimensional grid model based on physical parameters and a device design coupling model when the device works; the method specifically comprises the following steps:
carrying out orthoparallel 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 the simulation calculation of the multi-physical field coupling according to a 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 for calculation;
the step S5) includes:
based on the simulation calculation result of the step S4), analyzing the stress and temperature distribution conditions of the device under different process steps, and simulating the working state and related physical parameters of the simulation device under different working conditions after the process steps are completed; and further evaluating the performance of the device with the silicon-based MEMS substrate, and performing structural and process optimization according to the related physical parameters.
2. The method for evaluating device performance of a silicon-based MEMS process and multiple physical field coupling as recited in claim 1, wherein the silicon-based MEMS substrate of step S1) comprises: crystal face, doping concentration, surface resistance and silicon slice containing silicon oxide layer of common silicon slice.
3. The method for evaluating device performance of a silicon-based MEMS process and multiple physical field coupling as recited in 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 carrying out manufacturing process simulation according to the process parameters and the device size to obtain a process simulation model and basic sizes corresponding to different process steps.
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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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