A semiconductor ceramic heater and a design method thereof
By establishing the length and heat expression of the heating wire, combining the area and radiation heat dissipation model, the heating wire radius and heat of the semiconductor ceramic heater were calculated, which solved the complex problems of the existing design process and achieved the temperature uniformity optimization of the heater.
Patent Information
- Application Number
- CN202510000205.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-02
- Publication Date
- 2025-03-14
- Estimated Expiration
- 2045-01-02
AI Technical Summary
The design process of existing semiconductor ceramic heaters is complex, time-consuming and labor-intensive, and it is difficult to quickly improve temperature uniformity.
By establishing the length expression and heat expression of each turn of heating wire, combining the area and radiation heat dissipation model of each area, the radius of each turn of heating wire and the heat required to increase to the target temperature are calculated, simplifying the design process.
It realizes rapid and accurate calculation of the design size of the heating wire, optimizes the design process of the heater, and improves the temperature uniformity of the ceramic heater.
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Figure CN119378044B_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the field of semiconductor ceramic heaters, and in particular to a semiconductor ceramic heater and a design method thereof. Background Art
[0002] As the main device for heating semiconductor wafers, the temperature uniformity of circular ceramic heaters is crucial and directly affects the yield of wafers. With the gradual development of the semiconductor industry, the requirements for the temperature uniformity of wafer heaters are further improved. However, improving the temperature uniformity of heaters often requires simulation and experiments, which is time-consuming and labor-intensive. Therefore, it is crucial to propose a method that can simplify the design process of semiconductor ceramic heaters. Summary of the invention
[0003] The purpose of this application is to provide a semiconductor ceramic heater and a design method thereof, which can simplify the design process of the semiconductor ceramic heater and improve the temperature uniformity of the semiconductor ceramic heater.
[0004] To achieve the above objectives, this application provides the following solutions.
[0005] In a first aspect, the present application provides a semiconductor ceramic heater design method, including: establishing an expression for the length of each circle of heating wire of a semiconductor ceramic heater; the length expression is related to the radius of each circle of heating wire; based on the expression for the length of each circle of heating wire, determining an expression for the heat generated by each circle of heating wire; the heat expression is related to the radius of each circle of heating wire and the amount of heat required to increase the temperature to a target; establishing an area expression for each region where a ceramic disc is divided by the heating wire; the area expression is related to the radius of each circle of heating wire; based on the area expression of each region and the expression for the heat generated by each circle of heating wire, determining a heat model assigned to each region; based on the area expression of each region and the target temperature of each region, determining a radiation heat dissipation model for each region; combining the heat model assigned to each region and the radiation heat dissipation model for each region, solving the radius of each circle of heating wire and the amount of heat required to increase the temperature to a target.
[0006] Optionally, the length expression is as follows.
[0007] .
[0008] .
[0009] .
[0010] In the formula, is the length of the first coil heating wire, is the radius of the first heating wire, is the radius of the second heating wire; For the Coil heating wire length, For the Radius of coil heating wire, For the Radius of coil heating wire, For the Radius of coil heating wire, is the arc length of the heating wire gap; For the Coil heating wire length, For the Radius of coil heating wire, For the Radius of coil heating wire; , is the total number of heating wire turns. Starting from the center of the ceramic disk, the number of heating wire turns along the radius of the ceramic disk is defined as .
[0011] Optionally, according to the expression of the length of each heating wire coil, the expression of the heat generated by each heating wire coil is determined, specifically including: according to the expression of the length of each heating wire coil and the total number of heating wire coils, an expression of the total length of the heating wire is established; according to the expression of the total length of the heating wire, the heat density expression is determined as: ; In the formula, is the caloric density, The heat required to raise the target temperature is is the total length of the heating wire; combining the total length expression of the heating wire and the heat density expression, the heat expression generated by each circle of the heating wire is obtained as follows: ; In the formula, For the The heat generated by the coil heating wire, For the Coil heating wire length.
[0012] Optionally, the area expression is as follows.
[0013] .
[0014] .
[0015] .
[0016] In the formula, The area of the area enclosed by the first circle of heating wire that divides the ceramic disk. For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The area of the ceramic disc divided by the heating wire and the edge of the ceramic disc. is the radius of the first heating wire, For the Radius of coil heating wire, For the Radius of coil heating wire, For the Radius of coil heating wire, is the radius of the ceramic disk; , is the total number of heating wire turns. Starting from the center of the ceramic disk, the number of heating wire turns along the radius of the ceramic disk is defined as .
[0017] Optionally, the thermal model is as follows.
[0018] .
[0019] .
[0020] .
[0021] In the formula, The heat distributed to the enclosed area divided by the first circle of heating wire is For the The coil heating wire and the The heating wire distributes the heat to the area divided by the ceramic disc. For the The heating wire and the edge of the ceramic disc distribute the heat to the area divided by the ceramic disc. The heat generated by the first coil of heating wire. For the The heat generated by the coil heating wire, For the The heat generated by the coil heating wire, For the The heat generated by the coil heating wire, The area of the area enclosed by the first circle of heating wire that divides the ceramic disk. The area of the ceramic disc divided by the second circle of heating wires and the first circle of heating wires, For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The area of the region where the ceramic disc is divided by the coil heating wire and the edge of the ceramic disc; , is the total number of heating wire turns. Starting from the center of the ceramic disk, the number of heating wire turns along the radius of the ceramic disk is defined as .
[0022] Optionally, the radiation heat dissipation model is as follows.
[0023] .
[0024] .
[0025] In the formula, The radiation heat dissipation of the area surrounded by the first circle of heating wires dividing the ceramic disk. For the The radiation heat dissipation of the area divided by the heating wire and the edge of the ceramic disc, is the surface radiation emissivity, is the Boltzmann constant, For the The coil heating wire and the The target temperature of the area divided by the ceramic disc by the coil heating wire, For the The target temperature of the area where the ceramic disc is divided by the heating wire and the edge of the ceramic disc. For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The area of the region where the ceramic disc is divided by the coil heating wire and the edge of the ceramic disc; , is the total number of heating wire turns. Starting from the center of the ceramic disk, the number of heating wire turns along the radius of the ceramic disk is defined as .
[0026] Optionally, the heat model allocated to each area and the radiation heat dissipation model of each area are combined to obtain the radius of each circle of heating wire and the heat required to raise the temperature to the target temperature, specifically including: based on the principle that the heat allocated to each area is equal to the radiation heat dissipation of each area in thermal equilibrium, the heat model allocated to each area and the radiation heat dissipation model of each area are formed into a group of equations; solving the group of equations to obtain the radius of each circle of heating wire and the heat required to raise the temperature to the target temperature.
[0027] In a second aspect, the present application provides a semiconductor ceramic heater, which includes: a heating wire and a ceramic disc; the heating wire is coiled on the ceramic disc in the form of concentric arcs; the radius of each circle of the heating wire is determined using the above-mentioned semiconductor ceramic heater design method.
[0028] Optionally, the number of turns of the heating wire is defined as follows along the radius of the ceramic disk starting from the center of the ceramic disk: ;No. Coil heating wire to The shape of the coil heating wire is sawtooth; The shape of the coil heating wire is sawtooth, or The coil heating wire is a circular ring, and a plurality of circles are evenly spaced on the circular ring; .
[0029] Optionally, each circle of the heating wire is a circular ring, and a plurality of circles are evenly spaced on the circular ring, and the number of circles on the outer circular ring is greater than the number of circles on the adjacent inner circular ring.
[0030] According to the specific embodiments provided in this application, this application has the following technical effects.
[0031] The present application provides a semiconductor ceramic heater and a design method thereof, wherein the radius of each heating wire circle and the amount of heat required to raise the temperature to a target temperature are unknown quantities. By combining a heat model allocated to each region and a radiation heat dissipation model for each region, the radius of each heating wire circle and the amount of heat required to raise the temperature to a target temperature can be obtained by calculation. No simulation or experiment is required, and the design dimensions of the heating wire can be quickly and accurately calculated, thereby optimizing the heater design process and allowing the ceramic heater to have better temperature uniformity. BRIEF DESCRIPTION OF THE DRAWINGS
[0032] In order to more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.
[0033] Figure 1A schematic flow chart of a semiconductor ceramic heater design method provided in one embodiment of the present application.
[0034] Figure 2 A schematic diagram of the distribution of heating wires of a semiconductor ceramic heater provided in one embodiment of the present application.
[0035] Figure 3 Schematic diagram of the distribution of heating wires of the semiconductor ceramic heater provided in Example 1 of the present application.
[0036] Figure 4 This is a schematic diagram of the temperature field distribution of the semiconductor ceramic heater provided in Example 1 of the present application.
[0037] Figure 5 This is a schematic diagram of the heating wire distribution of the semiconductor ceramic heater provided in Example 2 of the present application.
[0038] Figure 6 This is a schematic diagram of the temperature field distribution of the semiconductor ceramic heater provided in Example 2 of the present application.
[0039] Figure 7 This is a schematic diagram of the first special pattern distribution of heating wires of a semiconductor ceramic heater provided in Example 3 of the present application.
[0040] Figure 8 Schematic diagram of the second special pattern distribution of heating wires of the semiconductor ceramic heater provided in Example 3 of the present application.
[0041] Fig. 9 A schematic diagram of the third special pattern distribution of the heating wires of the semiconductor ceramic heater provided in Example 3 of the present application.
[0042] Fig.10 Schematic diagram of the temperature field distribution of the first special pattern provided in Example 3 of the present application.
[0043] Fig.11 Schematic diagram of the temperature field distribution of the second special pattern provided in Example 3 of the present application.
[0044] Fig.12 Schematic diagram of the temperature field distribution of the third special pattern provided in Example 3 of the present application. DETAILED DESCRIPTION
[0045] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.
[0046] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.
[0047] In an exemplary embodiment, Figure 1 As shown, a semiconductor ceramic heater design method is provided, including the following steps 101 to 106.
[0048] Step 101: Establish an expression for the length of each turn of the heating wire of the semiconductor ceramic heater; the length expression is related to the radius of each turn of the heating wire.
[0049] Step 102: Determine the heat expression generated by each turn of the heating wire based on the length expression of each turn of the heating wire; the heat expression is related to the radius of each turn of the heating wire and the heat required to increase the temperature to the target temperature.
[0050] Step 103: Establish an area expression for each region of the ceramic disk divided by the heating wire; the area expression is related to the radius of each circle of the heating wire.
[0051] Step 104: Determine the heat model assigned to each region based on the area expression of each region and the heat expression generated by each coil of heating wire.
[0052] Step 105: Determine the radiation heat dissipation model of each area according to the area expression of each area and the target temperature of each area.
[0053] Step 106: Combine the heat model allocated to each area and the radiation heat dissipation model of each area to solve the radius of each circle of heating wire and the heat required to increase the temperature to the target temperature.
[0054] By implementing the above steps 101 to 106, with the radius of each heating wire circle and the amount of heat required to raise the temperature to the target temperature as unknown quantities, the radius of each heating wire circle and the amount of heat required to raise the temperature to the target temperature can be obtained by combining the heat model allocated to each area and the radiation heat dissipation model of each area. No simulation and experiment are required, which reduces the experimental material and time costs, can quickly and accurately calculate the design size of the heating wire, optimize the heater design process, and make the ceramic heater have better temperature uniformity.
[0055] In another exemplary embodiment of the present application, the length expression is as follows.
[0056] .
[0057] .
[0058] .
[0059] In the formula, is the length of the first coil heating wire, is the radius of the first heating wire, is the radius of the second heating wire; For the Coil heating wire length, For the Radius of coil heating wire, For the Radius of coil heating wire, For the Radius of coil heating wire, is the arc length of the heating wire gap; For the Coil heating wire length, For the Radius of coil heating wire, For the Radius of coil heating wire; , is the total number of heating wire turns. Starting from the center of the ceramic disk, the number of heating wire turns along the radius of the ceramic disk is defined as .
[0060] In another exemplary embodiment of the present application, the above step 102 can be replaced by the following steps 201 to 203.
[0061] Step 201: Establish an expression for the total length of the heating wire according to the expression for the length of each coil of the heating wire and the total number of coils of the heating wire.
[0062] Step 202: According to the total length expression of the heating wire, the heat density expression is determined as: In the formula, is the caloric density, The heat required to raise the target temperature is is the total length of the heating wire.
[0063] Step 203: Combining the total length expression of the heating wire and the heat density expression, the heat expression generated by each coil of the heating wire is obtained as follows: In the formula, For the The heat generated by the coil heating wire, For the Coil heating wire length.
[0064] In another exemplary embodiment of the present application, the area expression is as follows.
[0065] .
[0066] .
[0067] .
[0068] In the formula, The area of the area enclosed by the first circle of heating wire that divides the ceramic disk. For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The area of the ceramic disc divided by the heating wire and the edge of the ceramic disc. is the radius of the first heating wire, For the Radius of coil heating wire, For the Radius of coil heating wire, For the Radius of coil heating wire, is the radius of the ceramic disk; , is the total number of heating wire turns. Starting from the center of the ceramic disk, the number of heating wire turns along the radius of the ceramic disk is defined as .
[0069] In another exemplary embodiment of the present application, the thermal model is as follows.
[0070] .
[0071] .
[0072] .
[0073] In the formula, The heat distributed to the enclosed area divided by the first circle of heating wire is For the The coil heating wire and the The heating wire distributes the heat to the area divided by the ceramic disc. For the The heating wire and the edge of the ceramic disc distribute the heat to the area divided by the ceramic disc. The heat generated by the first coil of heating wire. For the The heat generated by the coil heating wire, For the The heat generated by the coil heating wire, For the The heat generated by the coil heating wire, The area of the area enclosed by the first circle of heating wire that divides the ceramic disk. The area of the ceramic disc divided by the second circle of heating wires and the first circle of heating wires, For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The area of the region where the ceramic disc is divided by the coil heating wire and the edge of the ceramic disc; , is the total number of heating wire turns. Starting from the center of the ceramic disk, the number of heating wire turns along the radius of the ceramic disk is defined as .
[0074] In another exemplary embodiment of the present application, the radiation heat dissipation model is as follows.
[0075] .
[0076] .
[0077] In the formula, The radiation heat dissipation of the area surrounded by the first circle of heating wires dividing the ceramic disk. For the The radiation heat dissipation of the area divided by the heating wire and the edge of the ceramic disc, is the surface radiation emissivity, is the Boltzmann constant, For the The coil heating wire and the The target temperature of the area divided by the ceramic disc by the coil heating wire, For the The target temperature of the area where the ceramic disc is divided by the heating wire and the edge of the ceramic disc. For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The coil heating wire and the The area of the ceramic disc divided by the coil heating wire; , is the total number of heating wire turns. Starting from the center of the ceramic disk, the number of heating wire turns along the radius of the ceramic disk is defined as .
[0078] In another exemplary embodiment of the present application, the above step 106 can be replaced by the following steps 301 to 302.
[0079] Step 301: Based on the principle that the heat allocated to each region is equal to the radiation heat dissipation of each region in thermal equilibrium, the heat model allocated to each region and the radiation heat dissipation model of each region are combined into an equation group.
[0080] Step 302: Solve the equation group to obtain the radius of each heating wire circle and the heat required to increase the temperature to the target temperature.
[0081] Below Figure 2 Taking the semiconductor ceramic heater in which the total number of heating wire turns is 7 as an example, the method of the present application is described in detail.
[0082] Figure 2 The shape parameters in are: is the radius of the ceramic disk; For the Radius of coil heating wire, , ; The 7 coils of heating wire divide the ceramic disc into 8 areas, which are defined as area 1, area 2, area 3, area 4, area 5, area 6, area 7 and area 8 in sequence along the radius direction of the ceramic disc starting from the center of the ceramic disc. is the arc length of the heating wire gap, which is approximately equal to the width of the heating wire gap; The lead wire is connected to both ends of the first coil of heating wire.
[0083] Setting ceramic disk parameters: surface radiation emissivity , the Boltzmann constant ; The target temperature is equal to the target temperature of each area divided by the heating wire. ; The amount of heat required to raise the target temperature.
[0084] Among the above physical quantities, the known quantities are , , and , needs to be entered manually. The unknown quantity is and .
[0085] Total length of heating wire: .
[0086] Caloric density: .
[0087] The length of each coil of heating wire is as follows.
[0088] Lap 1: .
[0089] Lap 2: .
[0090] ...n-1th round: .
[0091] The nth circle: .
[0092] The heat generated by each coil of the heating wire is as follows.
[0093] Lap 1: .
[0094] Lap 2: .
[0095] ...n-1th round: .
[0096] The nth circle: .
[0097] The n coils of heating wire divide the ceramic disk into n+1 areas. , the area of each region is as follows.
[0098] Region 1: .
[0099] Region 2: .
[0100] ...Region n-1: .
[0101] Region n: .
[0102] Region n+1: .
[0103] The heat generated by each coil of heating wire is distributed between two adjacent areas, assuming that the heat is evenly distributed according to the area ratio as follows.
[0104] Heat distribution to zone 1: .
[0105] Heat distribution to zone 2: .
[0106] ...The amount of heat allocated to area n-1 is: .
[0107] The amount of heat allocated to zone n is: .
[0108] The amount of heat allocated to area n+1 is: .
[0109] The temperatures in different areas are: , , …, , and , assuming that the temperature is the same at all locations in each zone.
[0110] The radiant heat dissipation in different areas is as follows.
[0111] Region 1: .
[0112] Region 2: .
[0113] ...Region n-1: .
[0114] Region n: .
[0115] Region n+1: .
[0116] The following set of equations must be satisfied for thermal equilibrium.
[0117] Region 1: .
[0118] Region 2: .
[0119] ...Region n-1: .
[0120] Region n: .
[0121] Region n+1: .
[0122] So far, we have obtained n+1 systems of equations, which contain n+1 unknown quantities ( , ), MATLAB can be used to solve the radius of each heating wire and the heat required to raise the temperature to the target temperature.
[0123] The present application can be applied to semiconductor processing, solid heat transfer and other related fields. The present application can quickly and accurately calculate the design size of the heating wire, optimize the heater design process, and make the ceramic heater have better temperature uniformity, providing convenience for practical engineering applications.
[0124] Based on the same inventive concept, the embodiment of the present application also provides a semiconductor ceramic heater using the semiconductor ceramic heater design method mentioned above. The implementation solution provided by the semiconductor ceramic heater to solve the problem is similar to the implementation solution recorded in the above method, so the specific limitations in one or more semiconductor ceramic heater embodiments provided below can refer to the limitations of the semiconductor ceramic heater design method above, and will not be repeated here.
[0125] In an exemplary embodiment, a semiconductor ceramic heater is provided, comprising: a heating wire and a ceramic disc; the heating wire is coiled on the ceramic disc in the form of concentric arcs; the radius of each circle of the heating wire is determined by the above-mentioned semiconductor ceramic heater design method.
[0126] Each coil of heating wire can be designed in a variety of shapes. The following three shapes are taken as examples: the first is an arc, the second is: starting from the center of the ceramic disc and along the radius of the ceramic disc, the number of coils of the heating wire is defined as ;No. Coil heating wire to The shape of the coil heating wire is sawtooth; The shape of the coil heating wire is sawtooth, or The coil heating wire is a circular ring, and a plurality of circles are evenly spaced on the circular ring; The third type: each coil of the heating wire is a circular ring, and a plurality of circles are evenly spaced on the circular ring, and the number of circles on the outer circular ring is greater than the number of circles on the adjacent inner circular ring.
[0127] The first shape of the heating wire is shown in the following Examples 1 and 2, and the second and third shapes of the heating wire are shown in the following Example 3.
[0128] Embodiment 1: When , unit is mm. The unit is J. , , , , and The values are: 62.0670950596565, 87.8012106018174, 107.556810062063, 124.221154174734, 138.896972932923 and 2662. Design the heating wire according to the radius, such as Figure 3 The temperature field distribution is shown in Figure 4 As shown, when the temperature rises to 500°C, the temperature difference is 4%.
[0129] Embodiment 2: When , unit is mm, The unit is J. , , , , , , and The values are: 52.9962267370447, 75.2168669021401, 92.3946141330819, 106.957708470854, 119.804364658660, 131.496627487765, 142.170856540175 and 2650. Design the heating wire according to the radius, such as Figure 5 The temperature field distribution is shown in Figure 6 As shown, when the temperature rises to 500°C, the temperature difference is 3.6%.
[0130] Embodiment 3: Considering that the shape and size of the heating wire will have a certain influence on the temperature uniformity of the ceramic heater, the heating wire design is carried out based on some special patterns to provide a reference for the design of the ceramic heater. The first special pattern of the heating wire distribution is as follows: Figure 7 As shown, the second special pattern is as Figure 8 As shown, the third special pattern is as Fig. 9 The temperature field distribution of the first special pattern is shown as Fig.10 As shown in Figure 2, when the temperature rises to 500°C, the temperature difference is 3.2%. The temperature field distribution of the second special pattern is shown in Figure 2. Fig.11 As shown in Figure 2, when the temperature rises to 500°C, the temperature difference is 0.6%. The temperature field distribution of the third special pattern is shown in Figure 2. Fig.12 As shown, when the temperature rises to 500°C, the temperature difference is 0.4%.
[0131] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0132] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.
Claims
1. A method for designing a semiconductor ceramic heater, characterized in that: include: Establish the expression of the length of each coil of heating wire of semiconductor ceramic heater; The length expression is related to the radius of each heating wire circle; Determine the heat expression generated by each coil of heating wire according to the length expression of each coil of heating wire; the heat expression is related to the radius of each coil of heating wire and the heat required to increase the temperature to the target temperature; Establish an area expression for each region of the ceramic disk divided by the heating wire; the area expression is related to the radius of each circle of the heating wire; According to the area expression of each region and the heat expression generated by each coil of heating wire, the heat model assigned to each region is determined; Determine the radiation heat dissipation model of each area according to the area expression of each area and the target temperature of each area; Combining the heat model allocated to each area and the radiation heat dissipation model of each area, the radius of each heating wire and the heat required to increase to the target temperature are solved, including: According to the principle that the heat allocated to each area is equal to the radiation heat dissipation of each area in thermal equilibrium, the heat model allocated to each area and the radiation heat dissipation model of each area are used to form an equation group; The equation group is solved to obtain the radius of each heating wire and the heat required to increase the temperature to the target temperature.
2. The semiconductor ceramic heater design method according to claim 1, characterized in that: The length expression is: ； ； ； In the formula, is the length of the first coil heating wire, is the radius of the first heating wire, is the radius of the second heating wire; For the Coil heating wire length, For the Radius of coil heating wire, For the Radius of coil heating wire, For the Radius of coil heating wire, is the arc length of the heating wire gap; For the Coil heating wire length, For the Radius of coil heating wire, For the Radius of coil heating wire; , is the total number of heating wire turns. Starting from the center of the ceramic disk, the number of heating wire turns along the radius of the ceramic disk is defined as .
3. The semiconductor ceramic heater design method according to claim 1, characterized in that: According to the expression of the length of each coil of heating wire, the expression of the heat generated by each coil of heating wire is determined, which specifically includes: According to the length expression of each coil of the heating wire and the total number of coils of the heating wire, an expression for the total length of the heating wire is established; According to the total length expression of the heating wire, the heat density expression is determined as: ; In the formula, is the caloric density, The heat required to raise the target temperature is is the total length of the heating wire; Combining the total length expression of the heating wire and the heat density expression, the heat expression generated by each circle of the heating wire is obtained as follows: ; In the formula, For the The heat generated by the coil heating wire, For the Coil heating wire length.
4. The semiconductor ceramic heater design method according to claim 1, characterized in that: The area expression is: ； ； ； In the formula, The area of the area enclosed by the first circle of heating wire that divides the ceramic disk. For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The area of the ceramic disc divided by the heating wire and the edge of the ceramic disc. is the radius of the first heating wire, For the Radius of coil heating wire, For the Radius of coil heating wire, For the Radius of coil heating wire, is the radius of the ceramic disk; , is the total number of heating wire turns. Starting from the center of the ceramic disk, the number of heating wire turns along the radius of the ceramic disk is defined as .
5. The semiconductor ceramic heater design method according to claim 1, characterized in that: The thermal model is: ； ； ； In the formula, The heat distributed to the enclosed area divided by the first circle of heating wire is For the The coil heating wire and the The heating wire distributes the heat to the area divided by the ceramic disc. For the The heating wire and the edge of the ceramic disc distribute the heat to the area divided by the ceramic disc. The heat generated by the first coil of heating wire. For the The heat generated by the coil heating wire, For the The heat generated by the coil heating wire, For the The heat generated by the coil heating wire, The area of the area enclosed by the first circle of heating wire that divides the ceramic disk. The area of the ceramic disc divided by the second circle of heating wires and the first circle of heating wires, For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The area of the region where the ceramic disc is divided by the coil heating wire and the edge of the ceramic disc; , is the total number of heating wire turns. Starting from the center of the ceramic disk, the number of heating wire turns along the radius of the ceramic disk is defined as .
6. The semiconductor ceramic heater design method according to claim 1, characterized in that: The radiative heat dissipation model is: ； ； In the formula, For the The coil heating wire and the The radiation heat dissipation of the area surrounded by the ceramic disc divided by the heating wire ring, For the The radiation heat dissipation of the area divided by the heating wire and the edge of the ceramic disc, is the surface radiation emissivity, is the Boltzmann constant, For the The coil heating wire and the The target temperature of the area divided by the ceramic disc by the coil heating wire, For the The target temperature of the area where the ceramic disc is divided by the heating wire and the edge of the ceramic disc. For the The coil heating wire and the The area of the ceramic disc divided by the heating wire. For the The area of the region where the ceramic disc is divided by the coil heating wire and the edge of the ceramic disc; , is the total number of heating wire turns. Starting from the center of the ceramic disk, the number of heating wire turns along the radius of the ceramic disk is defined as .
7. A semiconductor ceramic heater, characterized in that: The semiconductor ceramic heater comprises: a heating wire and a ceramic disc; The heating wire is coiled around the ceramic disc in the form of concentric arcs; The radius of each circle of heating wire is determined by the semiconductor ceramic heater design method described in any one of claims 1-6.
8. The semiconductor ceramic heater according to claim 7, characterized in that: Starting from the center of the ceramic disk, the number of turns of the heating wire is defined in the radial direction of the ceramic disk as ; No. Coil heating wire to The shape of the coil heating wire is sawtooth; The shape of the coil heating wire is sawtooth, or The coil heating wire is a circular ring, and a plurality of circles are evenly spaced on the circular ring; .
9. The semiconductor ceramic heater according to claim 7, characterized in that: Each circle of the heating wire is a circular ring, and a plurality of circles are evenly spaced on the circular ring, and the number of circles on the outer circular ring is greater than the number of circles on the adjacent inner circular ring.
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