Optimization method of non-uniform heating electrode and corresponding MEMS (Micro Electro Mechanical System) micro hot plate

Abstract

The invention discloses an optimization method of a non-uniform heating electrode and a corresponding MEMS (Micro Electro Mechanical System) micro-hot plate, which are used for optimizing parameters of the non-uniformly arranged heating electrode in the MEMS micro-hot plate, and comprises the following steps: parametrically modeling the MEMS micro-hot plate in finite element software, and outputting uniformity performance through a group of specific parameters; in the initial stage, sampling point data obtained through finite elements are processed in an optimization algorithm script; and selecting a point with the highest performance expectation as a next sampling point through function distribution of random Gaussian process agent performance parameters, returning the point to the finite element model, and continuously iterating to complete optimization. By means of the method, ultrahigh uniformity control over the temperature standard deviation can be achieved in the effective working area of the hot plate.

Description

Technical Field

[0001] The present invention belongs to the technical field of MEMS micro-hotplates, and in particular relates to an optimization method for a non-uniform heating electrode and a corresponding MEMS micro-hotplate. Background Art

[0002] As a core component of miniaturized thermal control, microelectromechanical system (MEMS) micro-hotplates are widely used in gas sensors, biochips, infrared radiation sources, and other fields. Their core principle is to achieve precise control of the local temperature field through electrode heating, and temperature uniformity directly determines the performance boundary of the device: for example, in a gas sensor, if the surface temperature of the hotplate is unevenly distributed, the response efficiency of the sensitive material will produce regional differences, resulting in decreased detection sensitivity or even misjudgment; in a lab-on-a-chip, temperature gradients will interfere with the biochemical reaction dynamics within the microfluidic channel. Therefore, achieving high spatial temperature uniformity (typically required to be within ±0.5°C) is a key technical bottleneck in improving the functional reliability of MEMS micro-hotplates.

[0003] Chinese patent publication number CN113998663A discloses a MEMS micro-hotplate with a vacuum insulation layer, comprising: a silicon substrate; a vacuum insulation layer formed on the surface of the silicon substrate by a SON process; an insulating layer formed on the silicon substrate and the vacuum insulation layer; a heating electrode and a test electrode formed on the insulating layer and located directly above the vacuum insulation layer; a heating platform with a cantilever beam support structure formed by sequentially etching the insulating layer and the silicon substrate along the periphery of the vacuum insulation layer; and an insulation groove formed in the area directly below the heating platform by etching or corroding the insulating layer.

[0004] Chinese patent publication number CN117886276A discloses a MEMS micro-hotplate with high-precision temperature sensing function, including a substrate; an insulating support layer arranged on the substrate; a heating resistor layer arranged on the insulating support layer; an insulating protective layer arranged on the heating resistor layer; the heating resistor layer includes an adhesive layer with oxidation protection function, a platinum metal layer, and an oxidation protection layer.

[0005] However, traditional micro-hotplates often use a uniform, symmetrical electrode layout. Due to the boundary effect of heat conduction, the edges of the hotplate, due to their contact with the anchor points and their larger surface area, dissipate heat faster than the center, creating a non-uniform temperature field characterized by "high center and low edge." Experimental data shows that when the center temperature of a hotplate with a radius of 50 μm reaches 320°C, the edge temperature can drop below 240°C, a temperature gradient exceeding 30%. Summary of the Invention

[0006] The present invention provides an optimization method for a non-uniform heating electrode and a corresponding MEMS micro-hotplate, which can achieve ultra-high uniformity control of the temperature standard deviation within the effective working area of the hotplate.

[0007] A method for optimizing a non-uniform heating electrode is used to optimize the parameters of the non-uniformly arranged heating electrodes in a MEMS micro-hotplate, comprising the following steps:

[0008] (1) The MEMS micro-hotplate was parametrically modeled using a finite element proxy model. The parameters included the number of heating electrode turns, the heating electrode width, and the heating electrode distribution spacing.

[0009] (2) Determine the parameter constraints and perform coordinate transformation on the parameter constraints so that the parameters are mapped into a hypercube space;

[0010] (3) The optimization problem of the heating electrode in the finite element proxy model is converted into a mathematical expression, and the performance function is set as the coefficient of variation of the temperature on the MEMS micro-hotplate;

[0011] (4) Using the Latin hypercube sampling method in the hypercube space to sample the initial sample points;

[0012] (5) The parameter value of each initial sample point is passed into the finite element proxy model for calculation, and each initial sample point corresponds to a performance value; a proxy function is established through the Gaussian process, and the posterior distribution is calculated using all the obtained performance values, and the proxy function is updated;

[0013] (6) Calculate the value of the expected improvement acquisition function by updating the mean and variance of the proxy function; and select the point with the largest improvement expectation as the next sampling point;

[0014] (7) Inputting the parameter values of the sampling points selected in step (6) into the finite element proxy model to calculate and obtain new performance values;

[0015] (8) Determine whether the performance value obtained in step (7) meets the design requirements. If so, the optimization is completed. If not, the sampling point is added to the initial sample points and steps (5) to (7) are repeated.

[0016] Furthermore, the MEMS micro-hotplate structure includes a heating substrate and a heating electrode arranged below the heating substrate;

[0017] The heating electrodes adopt a non-uniformly arranged coil structure, and the distribution spacing of the heating electrodes gradually increases from the outside to the inside; by increasing the density of the heating electrodes in the edge area, the additional heat dissipation caused by conduction of the thermal anchor point in this area is compensated; by reducing the density in the central area, the accumulation of heat in the center is avoided.

[0018] In step (1), the heating electrode distribution spacing in the parameters is expressed as a vector:

[0019] d=[d1,d2,d3...d k,d k+1 ];

[0020] Where, d k represents the distance between the kth circle of heating electrodes and the k-1th circle of heating electrodes, and k represents the number of turns of the heating electrodes.

[0021] In step (2), the parameter constraints are as follows:

[0022] d1+d2+...+d k =r;

[0023] d i >w+t min ,i=2,3...k;

[0024] d0,d k+1 >w / 2;

[0025] Where r is the radius of the heating substrate, w is the width of the heating electrode, and t min It is the minimum pitch of photolithography.

[0026] In step (2), the coordinate transformation is performed on the parameter constraints. The specific process is as follows:

[0027] First, normalize the constraints

[0028]

[0029] Thus, the constraints become

[0030] ||D||0=1;

[0031] D i >0,i=1,...k+1;

[0032] Where D represents the normalized spacing variable. Assuming that each component in D is a random variable with restricted uniform distribution in [0,1], their mathematical expectations are

[0033]

[0034] The mixed-layer binary tree decomposition method is used to decompose k into binary form, and then the parameters are weighted to satisfy ||D||0=1 and condition.

[0035] In step (3), the performance function is set as:

[0036] f(D)=[F1,F2,D3...,D k ],0 <D i <1;

[0037] Minf(D)

[0038] In step (4), based on the number of turns k of the heating electrode, the k-dimensional parameter cube space is divided into n intervals in each dimension to ensure that there is only one sample point in each interval. By independently and randomly permuting and combining each dimension, the samples are prevented from clustering when projected into any dimension, thereby ensuring the uniformity of the global spatial distribution.

[0039] In step (6), the formula of the expected improvement acquisition function is as follows:

[0040]

[0041] Where, f * is the current optimal point, μ(D) and σ(D) are the predicted expectation and variance of the candidate point, Φ(.) and φ(.) are the cumulative distribution function (CDF) and probability density function (PDF) of the standard normal distribution, respectively, and ξ ≥ 0 is a trade-off parameter that controls the preference between exploration and exploitation (when ξ = 0, it is the standard EI).

[0042] A MEMS micro-hotplate comprises a heating substrate and non-uniformly arranged heating electrodes arranged below the heating substrate, wherein the parameters of the heating electrodes are optimized using the above-mentioned optimization method.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] 1. The present invention adopts a non-uniformly distributed heating electrode network. By adjusting the electrode density and geometric topology, the heat generation power in the edge area of the hot plate can compensate for its additional heat dissipation, and the electrode density inside can be reduced to prevent heat accumulation, thereby achieving uniform temperature control with small standard deviation within the effective working area of the hot plate.

[0045] 2. The present invention uses finite element software to parametrically model the MEMS micro-hotplate, which can output uniform performance through a specific set of parameters. The sampling point data obtained initially through finite element analysis is processed in the optimization algorithm script. The function distribution of the performance parameters is represented by a random Gaussian process, and the point with the highest performance expectation is selected as the next sampling point. This point is returned to the finite element model and optimized through continuous iteration. The present invention combines the Bayesian algorithm to find the optimal electrode distribution. Bayesian optimization shows significant advantages in convergence time, and can more quickly find a solution close to the global optimum, greatly shortening the time required for optimization. It also has good interpretability and is robust to local optima. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Schematic diagram of the MEMS micro-hotplate structure in an embodiment of the present invention.

[0047] Figure 2Schematic diagram of non-uniformly arranged heating electrodes in an embodiment of the present invention.

[0048] Figure 3 This is a flow chart of a method for optimizing a high temperature uniformity MEMS micro-hotplate structure based on Bayesian optimization according to an embodiment of the present invention.

[0049] Figure 4 To optimize the heat distribution on the front hot plate;

[0050] Figure 5 To optimize the heat distribution on the hot plate;

[0051] Figure 6 To optimize the heat distribution cut on the hot plate diameter;

[0052] Figure 7 This is the convergence curve of the Bayesian optimization in the embodiment of the present invention. DETAILED DESCRIPTION

[0053] The present invention will be described in further detail below with reference to the accompanying drawings and examples. It should be noted that the following examples are intended to facilitate understanding of the present invention and do not have any limiting effect on the present invention.

[0054] The present invention proposes a MEMS micro-hotplate structure that uses non-uniformly arranged heating electrodes for heating.

[0055] like Figure 1 As shown, the MEMS micro-hotplate includes non-uniformly distributed heating electrodes 1, a heating substrate 2, mechanical anchor points 5, a back cavity 3 and a base 4.

[0056] The heating substrate 2 is a circular thin film structure, and the material is a low thermal conductivity medium. The central area is covered with an insulating layer to achieve balanced heat diffusion, and a process margin is reserved in the edge area to be compatible with the micro-machining process.

[0057] The mechanical anchor points 5 are symmetrically distributed at the edge of the heating substrate 2. The width and length of the mechanical anchor points 5 are optimized based on the thermal resistance control requirements. The width of the mechanical anchor points 5 is optimized to provide mechanical support while limiting the heat conduction rate.

[0058] The back cavity 3 is located directly below the heating substrate 2 and is formed by using a depth-to-width ratio optimization process. The wall uses air to isolate the thermal coupling path between the cavity and the base 4.

[0059] The substrate 4 is made of silicon-based material, with an oxide insulating layer provided on the surface. A metal PAD 41 is integrated in the edge area and connected to the heating electrode 1 .

[0060] like Figure 2As shown, the heating electrode 1 is designed based on the principle of gradient thermal compensation and adopts a non-uniform distribution mode in the effective heating area; multiple spiral electrodes are set in the outer ring area, the winding density gradually decreases from the outside to the inside, the adjacent wire spacing is synchronously gradient expanded, and the electrode line width is dynamically adjusted. By increasing the Joule heat power density in the edge area, the additional heat dissipation caused by conduction of the thermal anchor point in this area is compensated; sparsely distributed electrodes are used in the central area to avoid heat accumulation in the center.

[0061] When current passes through the coil of the heating electrode, a heat source is generated, and the heat source density is proportional to the square of the current density and the resistivity.

[0062] According to Fourier heat transfer theory, the thermal field in a steady state satisfies the Poisson equation. Here, k is the heat transfer coefficient, T(r) is the temperature at a point r from the center of the circle, and Q(r) is the size of the heat source at that point r from the center, determined in the previous step.

[0063]

[0064] The plate is axisymmetric, and Poisson's equation is expressed as

[0065]

[0066] The solution for the heat distribution is

[0067]

[0068] Among them, T center is the temperature at the center of the hot plate.

[0069] When the heat source is evenly distributed, the temperature decreases parabolically as the radius r increases. 2 During decay, the temperature of the hot plate is uniformly distributed, and T does not change with r. This illustrates the advantage of a non-uniformly distributed heat source.

[0070] like Figure 3 As shown, a method for optimizing a non-uniformly heated electrode comprises the following steps:

[0071] Step 1: Model the hot plate with non-uniform electrode distribution. Build a finite element proxy model of the MEMS micro-hot plate and parameterize its structure, such as the spacing between wires and the wire width. Express the parameters as vectors:

[0072] d=[d1,d2,d3...d k ,d k+1 ];

[0073] Among them, d krepresents the distance between the center of the kth coil and the k-1th coil, where k represents the number of turns. There are some constraints on these parameters, such as the total spacing cannot exceed the disk radius and the spacing cannot be smaller than the line width. Furthermore, due to photolithography accuracy, the spacing cannot be less than the line width plus the minimum photolithography accuracy. These constraints can be expressed as:

[0074] d1+d2+...+d k =r;

[0075] d i >w+t mib ,i=2,3...k;

[0076] d0,d k+1 >w / 2;

[0077] Where r represents the radius of the heated substrate, w is the line width, and t min It is the minimum pitch of photolithography.

[0078] Step 2: Coordinate transformation to process constraints. In order to ensure that all points in the optimization search space are reasonable, we need to perform variable transformation so that the parameters are mapped to a hypercube space for optimization. First, normalize the constraints.

[0079]

[0080] Thus, the constraints become

[0081] ||D||0=1;

[0082] D i >0,i=1,...k+1;

[0083] Assuming that each component in D is a random variable with restricted uniform distribution in [0,1], their mathematical expectations are

[0084]

[0085] The mixed-layer binary tree decomposition method is used. Decompose k into binary form, and then weight the parameters, while satisfying ||D||0=1 and Condition. For example, when k = 12, the decomposition is 10 = 4 + 8. Decomposition into a two-layer binary tree and a three-layer binary tree.

[0086] D1=(1-p)b4b2b1

[0087] D2=(1-p)b4b2(1-b1) ....

[0089] D8=(1-p)(1-b4)(1-b6)(1-b7)

[0090] D9=pa2a1

[0091] D 10 =pa2(1-a1)

[0092] D 11 =p(1-a2)a3

[0093] D 12 =p(1-a2)(1-a3)

[0094] Among them, a i and b i Both are random variables uniformly distributed in [0,1], and p is a random variable with a mean of 1 / 3 in [0,1].

[0095]

[0096] This still ensures the desired homogeneity of the variables.

[0097] Step 3: Transform the optimization problem into a mathematical expression. Here, let the performance function be f(b), which is assumed to be the coefficient of variation of the temperature on the hot plate.

[0098] f(D)=[D1,D2,D3...,D k ],0 <D i <1;

[0099] Minf(D).

[0100] Step 4: Initial sample points are sampled in the hypercube space using Latin Hypercube Sampling (LHS). For the k-dimensional parameter cube space, each dimension is divided into n intervals, ensuring that each interval has only one sample point. By performing independent random permutations of each dimension, we avoid clustering of samples when projected onto any dimension, thus ensuring uniform global spatial distribution.

[0101] Step 5: Pass the sample parameter values into the COMSOL proxy model for calculation to obtain the performance value f(D) corresponding to each sample point. Establish the proxy function through the Gaussian process, and assume that the function obeys the distribution:

[0102] f(D)~GP(m(D),k(D,D′))

[0103] Where m(D) is the mean function and k(D,D′) is a kernel function such as an RBF kernel. After COMSOL calculations, the posterior distribution is calculated to update the surrogate function.

[0104] Step 6: Calculate the expected lift acquisition function using the mean and variance of the proxy function calculated in step 5.

[0105]

[0106] Where, f * is the current optimal point, μ(D) and σ(D) are the predicted expectation and variance of the candidate point, Φ(.) and φ(.) are the cumulative distribution function (CDF) and probability density function (PDF) of the standard normal distribution, respectively, and ξ ≥ 0 is a trade-off parameter that controls the preference between exploration and exploitation (when ξ = 0, it is the standard EI).

[0107] And select the point with the largest improvement expectation as the next collection point.

[0108] Step 7: Input the acquisition point coordinate information obtained in step 6 into the COMSOL proxy model for calculation to obtain the new performance value.

[0109] Step 8: Determine whether it meets the design requirements. If so, the optimization is completed. If not, add the collection points obtained in step 6 to the initial sample points and repeat steps 5-7.

[0110] like Figure 4 As shown, it is the heat distribution on the hot plate before optimization. The temperature standard deviation within the diameter of 50um is 4.3 degrees, the maximum temperature difference is 10 degrees, and the temperature distribution curve is parabolic. Figure 5 As shown in FIG, the heat distribution of the hot plate after optimization by the method of the present invention is shown, with a standard deviation of 0.3 degrees Celsius in the effective area and a maximum temperature difference of only 1 degree Celsius. Figure 6 As shown, the heat distribution intercepted on the diameter of the optimized hot plate is displayed. It can be seen that the color uniformity in the effective area of the hot plate is good.

[0111] like Figure 7 As shown in Figure 1, it is the convergence curve of Bayesian optimization. It can be seen that the optimization convergence effect is good and the design index can be achieved after 30 iterations.

[0112] The embodiments described above provide a detailed description of the technical solutions and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, supplements and equivalent substitutions made within the scope of the principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for optimizing a non-uniform heating electrode, characterized in that: The method is used to optimize the parameters of the non-uniformly arranged heating electrodes in the MEMS micro-hotplate, including the following steps: (1) The MEMS micro-hotplate was parametrically modeled using a finite element proxy model. The parameters included the number of heating electrode turns, the heating electrode width, and the heating electrode distribution spacing. (2) Determine the parameter constraints and perform coordinate transformation on the parameter constraints so that the parameters are mapped into a hypercube space; (3) The optimization problem of the heating electrode in the finite element proxy model is converted into a mathematical expression, and the performance function is set as the coefficient of variation of the temperature on the MEMS micro-hotplate; (4) Using the Latin hypercube sampling method in the hypercube space to sample the initial sample points; (5) The parameter value of each initial sample point is passed into the finite element proxy model for calculation, and each initial sample point corresponds to a performance value; a proxy function is established through the Gaussian process, and the posterior distribution is calculated using all the obtained performance values, and the proxy function is updated; (6) Calculate the value of the expected improvement acquisition function by updating the mean and variance of the proxy function; and select the point with the largest improvement expectation as the next sampling point; (7) Inputting the parameter values of the sampling points selected in step (6) into the finite element proxy model to calculate and obtain new performance values; (8) Determine whether the performance value obtained in step (7) meets the design requirements. If so, the optimization is completed. If not, the sampling point is added to the initial sample points and steps (5) to (7) are repeated.

2. The optimization method of the non-uniform heating electrode according to claim 1, characterized in that: The MEMS micro-hotplate structure includes a heating substrate and a heating electrode arranged below the heating substrate; The heating electrodes adopt a non-uniformly arranged coil structure, and the distribution spacing of the heating electrodes gradually increases from the outside to the inside; by increasing the density of the heating electrodes in the edge area, the additional heat dissipation caused by conduction of the thermal anchor point in this area is compensated; by reducing the density in the central area, the accumulation of heat in the center is avoided.

3. The optimization method of the non-uniform heating electrode according to claim 1, characterized in that: In step (1), the heating electrode distribution spacing in the parameters is expressed as a vector: <h2 style=";text-align:left;direction:ltr">d = [d1,d2,d3...d<h2 style=";text-align:left;direction:ltr"> k <h2 style=";text-align:left;direction:ltr"> ,d<h2 style=";text-align:left;direction:ltr"> k+1 <h2 style=";text-align:left;direction:ltr"> ]; Where, d k represents the distance between the kth circle of heating electrodes and the k-1th circle of heating electrodes, and k represents the number of turns of the heating electrodes.

4. The optimization method of the non-uniform heating electrode according to claim 3, characterized in that: In step (2), the parameter constraints are as follows: d1+d2+...+d k =r; d i >w+t min ,i=2,3...k; d0,d k+1 >w / 2; Where r is the radius of the heating substrate, w is the width of the heating electrode, and t min It is the minimum pitch of photolithography.

5. The optimization method of the non-uniform heating electrode according to claim 4, characterized in that: In step (2), the coordinate transformation is performed on the parameter constraints. The specific process is as follows: First, normalize the constraints Thus, the constraint condition becomes ||D||0=1; D i >0,i=1,...k+1; Where D represents the normalized spacing variable. Assuming that each component in D is a random variable with restricted uniform distribution in [0,1], their mathematical expectations are The mixed-layer binary tree decomposition method is used to decompose k into binary form, and then the parameters are weighted to satisfy ||F||0=1 and condition.

6. The optimization method of the non-uniform heating electrode according to claim 1, characterized in that: In step (3), the performance function is set as: <h2 style=";text-align:left;direction:ltr">f(F) = [F1,F2,F3...,F<h2 style=";text-align:left;direction:ltr"> k <h2 style=";text-align:left;direction:ltr"> ],0 <F <h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> <1; Minf(D).

7. The optimization method of the non-uniform heating electrode according to claim 1, characterized in that: In step (4), based on the number of turns k of the heating electrode, the k-dimensional parameter cube space is divided into n intervals in each dimension to ensure that there is only one sample point in each interval. By independently and randomly permuting and combining each dimension, the samples are prevented from clustering when projected into any dimension, thereby ensuring the uniformity of the global spatial distribution.

8. The optimization method for a non-uniform heating electrode according to claim 1, characterized in that: In step (6), the formula of the expected improvement acquisition function is as follows: Where, f * is the current optimal point, μ(D) and σ(D) are the predicted expectation and variance of the candidate point, Φ(.) and φ(.) are the cumulative distribution function and probability density function of the standard normal distribution, respectively, and ξ ≥ 0 is a trade-off parameter that controls the preference between exploration and exploitation.

9. A MEMS micro-hotplate, characterized in that: The invention comprises a heating substrate and non-uniformly arranged heating electrodes arranged below the heating substrate, wherein the parameters of the heating electrodes are obtained by optimizing the optimization method according to any one of claims 1 to 8.

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