CN115809576B - Silicon-based MEMS (micro electro mechanical System) process and multi-physical field coupling device performance evaluation method - Google Patents

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

Device performance evaluation method for silicon-based MEMS technology and multi-physics coupling

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 and simulation method of a multi-physics model.

Background technique

MEMS sensors, namely Microelectro Mechanical Systems, are a multidisciplinary cutting-edge research field developed on the basis of microelectronics technology. After more than 40 years of development, it has become one of the major scientific and technological fields that attract world attention. It involves electronics, machinery, materials, physics, chemistry, biology, medicine and other disciplines and technologies, and has broad application prospects. As of 2010, there are approximately 600 units around the world engaged in the development and production of MEMS, and have developed hundreds of products including micro pressure sensors, acceleration sensors, micro inkjet print heads, and digital micromirror displays. Among them, MEMS sensors account for a considerable proportion. MEMS sensors are new sensors manufactured using microelectronics and micromachining technology. Compared with traditional sensors, it has the characteristics of small size, light weight, low cost, low power consumption, high reliability, suitable for mass production, easy integration and intelligentization. At the same time, the feature size on the order of microns allows it to complete certain functions that cannot be achieved by traditional mechanical sensors.

In multiphysics, various physical fields superimpose and influence each other. Studying multiphysics is to study the relationship between multiple interacting physical attributes. For example, natural convection heat transfer studies the relationship between the pressure field, velocity field, and temperature field, and magnetohydrodynamics studies the relationship between the magnetic field, electric field, and fluid field. As an interdisciplinary research field, multiphysics covers various disciplines including mathematics, physics, engineering, electromagnetics, etc. When establishing a multi-physics model, the corresponding partial differential equations are first established based on each physical field, and finally the simultaneous equations form a multi-physics equation system.

Current silicon-based MEMS sensors have been widely used in various electronic products. Due to the complexity and high cost of their preparation process, it is crucial to design and optimize the process of silicon-based MEMS before preparation. Currently, there is no method in the world that accurately detects the performance of devices coupled with silicon-based MEMS processes and multi-physics models. In terms of technology, molecular simulation can be used to evaluate the process performance of the device, but the changes in the specific structure of the process simulation cannot be simulated. Currently, devices in the manufacturing process can be designed and optimized through numerical algorithms such as finite element. However, it cannot analyze the impact of residual stress caused by process steps on the device itself. There is a lack of silicon-based MEMS that combines process simulation and comprehensive evaluation of device structure. device performance evaluation method.

Contents of the invention

The purpose of the present invention is to overcome the shortcomings of the existing technology and propose a device performance evaluation method that couples a silicon-based MEMS process with a multi-physics model.

In order to achieve the above objectives, the present invention proposes a device performance evaluation method for coupling silicon-based MEMS technology and multi-physics fields. The method includes:

Step S1) Perform manufacturing process simulation on the device with a silicon-based MEMS substrate to obtain a process simulation model;

Step S2) Perform structural design topology on the process simulation model to obtain a three-dimensional model after topology reconstruction;

Step S3) Based on the topologically reconstructed three-dimensional model, establish a process and design coupling model, and determine the physical field during coupling based on the coupling physical environment;

Step S4) Perform multi-physics numerical simulation calculations;

Step S5) Perform device performance evaluation based on simulation calculation results.

As an improvement of the above method, the silicon-based MEMS substrate in step S1) includes: the crystal plane, doping concentration, surface resistance of an ordinary silicon wafer, and a silicon wafer containing a silicon oxide layer.

As an improvement of the above method, step S1) includes:

Determine process parameters based on the design performance requirements of devices with silicon-based MEMS substrates;

According to the process parameters and device size, the manufacturing process simulation is performed to obtain the process simulation model and the basic dimensions corresponding to different process steps.

As an improvement of the above method, the step S2) includes:

Three-dimensional topology design and modeling based on the three-dimensional model of the simulated device;

Calculate the structure after topology, further refine the modeling, and obtain the three-dimensional model after topology reconstruction.

As an improvement of the above method, the step S3) includes:

Based on the topologically reconstructed 3D model, establish a process and design coupling model and create a 3D mesh;

Design coupling boundary conditions and determine the physical field type and corresponding parameters during coupling.

As an improvement of the above method, step S4) includes:

Establish a three-dimensional mesh model based on the coupling model of the physical parameters of the device during operation and the device design;

Set the initial conditions and boundary conditions for multi-physics coupling simulation calculations, solve the control equations of multi-physics coupling, and set the finite element, Newton difference and central difference numerical algorithms during calculation; the control equations of multi-physics coupling are:

f(m _j ; v _i ,s)=0

Among them, f is a differential operator, m _j is the j-th physical property variable of the material, _vi is the i-th field variable, which is a vector or scalar, and s is the sink or source of the field.

As an improvement of the above method, the step S4) also includes: establishing a two-dimensional grid model based on the physical parameters of the device during operation and the device design coupling model; specifically including:

Perform orthoparallel projection of the three-dimensional coordinate system point set onto one of the coordinate planes to obtain a two-dimensional grid model;

Based on the two-dimensional grid model, the initial conditions and boundary conditions of the multi-physics coupling simulation calculation are simplified, the control equations of the multi-physics coupling are solved, and the finite element, Newton difference and central difference numerical algorithms are set during calculation.

As an improvement of the above method, step S5) includes:

Based on the simulation calculation results of step S4), analyze the stress and temperature distribution of the device under different process steps, simulate the working status and related physical parameters of the simulated device after the completion of the process steps under different working conditions; and then evaluate the performance of the device with a silicon-based MEMS substrate Device performance, and structural and process optimization based on relevant physical parameters.

Compared with the existing technology, the advantages of the present invention are:

1. The present invention proposes a device performance evaluation method for silicon-based MEMS under the action of multi-physics fields by coupling the state between the process and multi-physics fields, and solves the mutual coupling between the technology and structure of silicon-based MEMS under the action of multi-physics fields. The problem;

2. The present invention solves the coupling problem of MEMS manufacturing process and geometric configuration. The innovative numerical algorithm and structural coupling can optimize the MEMS device structure and manufacturing process, greatly saving the cost and cycle of MEMS device R&D.

Description of the drawings

Figure 1 is a flow chart of the device performance evaluation method of the silicon-based MEMS multi-physics model of the present invention;

Figure 2 is a schematic diagram of the device process simulation of the present invention;

Figure 3 is a schematic diagram of the structural design topology model of the present invention;

Figure 4 is a schematic diagram of the process and design coupling model of the present invention;

Figure 5 is a schematic diagram of the numerical calculation results of multi-physics coupling simulation of the present invention, wherein Figure 5(a) is a stress distribution diagram, Figure 5(b) is a voltage distribution diagram, Figure 5(c) is a displacement distribution diagram, and Figure 5(d) ) is the current distribution diagram.

Detailed ways

The invention discloses a silicon-based film process and a device performance calculation and simulation method of a multi-physics model, which includes: establishing a silicon-based MEMS process simulation model, performing numerical calculations of the MEMS process; and performing topology and modeling of the three-dimensional structure of the silicon-based MEMS. , thereby performing three-dimensional multi-physics coupling simulation; combining process simulation and multi-physics coupling to establish a process-multi-physics coupling composite model with geometric configuration; based on the reconstructed composite model, create a three-dimensional grid, and set the process and Initial conditions and boundary conditions for physical simulation; numerically solve the composite model through finite element method, Newton interpolation method and other algorithms; analyze different coupling load conditions of different processes, calculate the stress distribution of silicon-based MEMS, and evaluate the performance of silicon-based MEMS under complex conditions. MEMS-based device performance.

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 Figure 1, the device performance evaluation method of coupling the silicon-based MEMS process and the multi-physics model of the present invention includes the following steps:

1: Select a silicon-based MEMS substrate: Select a suitable silicon-based MEMS substrate by analyzing the function of the device, including the crystal surface of ordinary silicon wafers, doping concentration, surface resistance, and silicon wafers containing silicon oxide layers (SOI).

By analyzing and defining the functions of the device, according to different functions and physical principles, the corresponding silicon-based MEMS substrate is prepared to obtain some basic parameters and dimensions of the device;

The substrate includes silicon wafers with different crystal plane directions, silicon wafers with conductivity that are aligned and doped, and silicon wafers SOI on the silicon dioxide insulating layer. Among them, multi-layer silicon wafers with insulating layers require different layers. Define physical parameters.

2: Device manufacturing process simulation as shown in Figure 2: Perform process simulation on the established silicon wafer MEMS substrate, design process parameters, generate device structures under different processes, and obtain device manufacturing process simulation results. The steps are as follows:

Step 1, determine the process parameters, and design the process parameters according to the performance requirements of different device designs;

Step 2: Simulate the device process based on different design parameters and device dimensions;

Step 3: The obtained process simulation model of the three-dimensional device can obtain the basic dimensions of the device after process simulation in each step.

3: Device structure design topology as shown in Figure 3: Carry out structural topology on the model after process simulation, and further refine the modeling of the structure after local process simulation. The specific steps are as follows:

Step 1: Obtain the model after process simulation and carry out three-dimensional topological structure design and modeling;

Step 2: Calculate the structure after obtaining the device topology, and further perform structural refinement modeling.

4: Establishment of process and device design coupling model as shown in Figure 4: Based on the three-dimensional model of topology reconstruction, establish process and design coupling model, create three-dimensional grid, design coupling boundary conditions, determine the physical field type and corresponding parameters during coupling, specifically Proceed as follows:

Step 1: Create a three-dimensional grid based on the coupled three-dimensional digital model of the process and device design;

Step 2: Based on the coupling physical environment, design the coupling boundary conditions and determine the physical field type and corresponding parameters during coupling.

5: Multi-physics coupling simulation calculation of device process and structure as shown in Figure 5, where Figure 5(a) is the stress distribution diagram, Figure 5(b) is the voltage distribution diagram, Figure 5(c) is the displacement distribution diagram, Figure 5(d) is the current distribution diagram. The specific steps are: based on the three-dimensional mesh model generated by the steps of establishing the coupling model of physical parameters and device design when the device is working, setting the initial conditions and boundary conditions for calculation, solving the basic formula of multi-physics coupling, and setting the finite element and Newton difference during calculation. Numerical algorithms such as value and central difference. The governing equations of multiple physics 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 _j is the physical property variable of the material, which can be one or more; _vi is a field variable, which can be a vector or scalar, and can have one or more; s is the sink or source of the field, in general 1 below.

The specific steps for device multi-physics coupling simulation calculation are as follows:

Step 1. The three-dimensional mesh model is generated based on the coupling model establishment step of physical parameters and device design when the device is operating;

Step 2: Set the initial conditions and boundary conditions for calculation, solve the basic formulas for multi-physics coupling, and set numerical algorithms such as finite element, Newton difference and central difference during calculation.

For device simulation calculations, the following two-dimensional model related methods should also be included:

For the two-dimensional grid model, the two-dimensional grid model is generated based on the steps of establishing a coupled model of physical parameters and device design when the device is operating;

The two-dimensional model needs to simplify the boundary conditions and initial conditions, and needs to use different unit types. The calculation method refers to the calculation formula in the three-dimensional model for projection on the two-dimensional plane.

6: MEMS device performance evaluation under complex conditions: Analyze the distribution of multi-physical parameters of the device under different multi-physics conditions based on simulation operation results, and evaluate complex conditions based on device usage conditions and process steps, performance constraints and physical limitations of the material body. Understand the physical properties of MEMS devices and achieve process and design optimization. The specific steps are as follows:

Step 1. Based on the basic analysis results, analyze the stress and temperature distribution of the device under different process steps, and simulate the working status and related physical parameters of the device after the completion of the process steps under different working conditions;

Step 2: Based on the multi-physics coupling simulation of the process and device working conditions under the above different situations, the performance of the MEMS device can be evaluated, and the structure and process can be optimized based on the relevant physical parameters.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the embodiments, those of ordinary skill in the art will understand that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and they shall all be covered by the scope of the present invention. within the scope of the 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.