A scribing etching method for controlling resistance and resistance distribution of a heating film using a mathematical equation

Abstract

The application relates to a scribing etching method for controlling the resistance and resistance distribution of a heating film by using a mathematical equation, which comprises the following steps: using an automatic laser etching device to perform laser scribing etching on a non-standard thickness heating film, so that the resistance of the remaining heating film body is the same as that of a standard thickness heating film, the resistance distribution of the remaining heating film body conforms to the line type of the etching line, and the laser scribing etching is controlled by a mathematical equation to control the line type of the etching line. The application has the beneficial effects that the laser scribing etching method replaces the traditional mask etching method, reduces the etching workload, and shortens the etching time; the laser scribing etching method is controlled by a mathematical equation and an automatic laser etching device, can simply and flexibly control the resistance and resistance distribution of the heating film, does not need to adjust a magnetron sputtering device, and does not need to re-produce an etching template, thereby saving production time and cost.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of atomizing core heating film preparation, and particularly relates to a scribing etching method for controlling the resistance and resistance distribution of a heating film using mathematical equations. BACKGROUND

[0002] As a new method for preparing atomizing core heating films, the magnetron sputtering technology can sequentially deposit target materials of different materials on the surface of an atomizing core substrate to prepare a heating film with a thickness of only several microns, which has the advantages of corrosion resistance, low heavy metal release, etc. The atomizing core heating film prepared using the magnetron sputtering technology is continuously deposited on the surface of the atomizing core substrate, and an etching process is used to form an atomizing core with a hollow part heating film pattern, so that a better atomizing taste and atomizing energy consumption can be obtained, which is beginning to be understood and accepted by more and more consumers.

[0003] The existing preparation of a heating film using the magnetron sputtering technology and etching of the heating film have the following disadvantages:

[0004] 1. Traditionally, to ensure the stability of the thickness of the heating film and the consistency of the resistance value, the stability of the parameters of the magnetron sputtering equipment is required to be high. In production practice, if the resistance value of a batch of heating films fluctuates greatly, the production needs to be stopped, and the magnetron sputtering equipment needs to be re-adjusted, which increases the equipment cost and operating cost;

[0005] 2. Traditionally, the etching of the heating film uses a mask etching method, which needs to etch away the excess part of the heating film completely. This process has a large etching workload and a long etching time, which will increase the etching cost;

[0006] 3. Traditionally, the etching pattern of the mask etching method is fixed and unchangeable, so when the thickness of the heating film is different, no matter how much it is etched, the same resistance value of the heating film cannot be obtained. The magnetron sputtering equipment needs to be re-adjusted or the mask etching template needs to be re-made;

[0007] 4. Traditionally, the resistance value distribution of the heating film is determined by the shape of the mask etching template. If the resistance value distribution of the heating film is to be changed, the template needs to be re-made, which takes a long time and increases the production cost. If the resistance value distribution is to be changed while the resistance value remains unchanged, the difficulty will be greater;

[0008] 5. Heating films are commonly used in the atomizing core, a core component of electronic atomizing devices. In practice, it has been found that the resistance of the heating film exhibits a unique atomization effect and user taste experience when the resistance is higher closer to the geometric center and lower further away from the geometric center. However, this requires that a heating film with a fixed thickness cannot adopt a standard rectangular shape, but rather a shape that is wide at both ends and narrow in the middle with a smooth transition. This itself increases the difficulty of resistance control. Moreover, different heating films have different thicknesses, and it is necessary to produce the same resistance value every time with different heating film thicknesses. This further increases the difficulty of process control, because it is difficult to control the resistance value of the heating film after cutting by simply drawing straight lines and cutting proportionally. Summary of the Invention

[0009] To overcome the problems existing in the background technology, the present invention proposes a scribing etching method for controlling the resistance and resistance distribution of a heating film using mathematical equations. The method includes: using mathematical equations to control an automated laser etching device to perform laser scribing etching on a heating film of non-standard thickness. The etching process generates etching lines that separate a portion of the heating film from the main body, so that the resistance value of the remaining heating film body is the same as that of a heating film of standard thickness. The mathematical equations control the line shape of the etching lines, and the line shape of the etching lines controls the resistance distribution of the remaining heating film body.

[0010] Preferably, controlling the line shape of the etching line using mathematical equations includes the following steps:

[0011] Step 1: Perform mathematical modeling on the patterned area of ​​the heating film and the etching lines to obtain two etching line equations A1 and A2;

[0012] Step 2: Obtain the formula R for the resistance of the heating film between the etching lines based on the etching line equation;

[0013] Step 3: Determine a certain influencing factor based on the heating film resistance formula. This influencing factor can affect the resistance value of heating films with the same etched lines of the same shape but different thicknesses from the standard films.

[0014] Step 4: Use numerical simulation to calculate and fit equation A3, which shows the relationship between the influencing factor and the resistance value of the heating film.

[0015] Step 5: Determine the equations A4 and A5 for etching lines drawn when etching heating films with the same shape but different thicknesses than the standard film, based on A3;

[0016] Step 6: Using automated laser etching equipment, etch A4 and A5 shaped etching lines on the non-standard thickness heating film, so that the non-standard thickness heating film has the same resistance value as the standard thickness heating film.

[0017] Preferably, step 1 comprises: projecting the heating film pattern area and etching line on a plane, taking the heating film pattern area as the origin, and taking the direction of the conductive column as the X axis to establish a rectangular coordinate system, and the etching line is a parabola symmetric to the X axis in the coordinate system, wherein the parabola above the X axis passes through the three points (-L / 2, d), (L / 2, d), and (0, b), and the parabola equation y(x) = ax 2 +b is obtained as A1:

[0018]

[0019] Similarly, the parabola equation below the X axis is obtained as A2:

[0020]

[0021] In the above two formulas, L and d are two constants of the heating film etching area (for example, when the heating film is in a rectangular shape before etching, L is the length of the rectangle, and 2d is the width of the rectangle), and different parabolas can be formed by adjusting the parameter b, b is the intersection of the parabola and the Y axis, and b is 1 / 2 of the width of the heating film at the narrowest point.

[0022] Preferably, step 2 comprises:

[0023] The resistance calculation formula is:

[0024]

[0025] Wherein, S is the cross-sectional area of the rectangle presented by the heating film before etching; L is the length of the rectangle presented by the heating film before etching; t is the thickness of the heating film; h is the height of the rectangle presented by the heating film before etching; and A1 and A2 are brought into the resistance formula to obtain the resistance of the heating film between the two etching lines as:

[0026]

[0027] The conductivity and thickness of the electrode and conductive column material are greater than those of the heating film material, and the resistance of the area between the heating film etching lines is much greater than the resistance of the electrode and conductive column, so the resistance R(t, b) between the two conductive columns can be simplified as:

[0028]

[0029] Preferably, step 3 comprises:

[0030] Wherein, let R(b1, t) be the initial resistance of the heating film with thickness t, R(b n , t) be the resistance of the heating film etching line at different b n values, and b1 and b n be a series of b values from large to small. The ratio of the two is as follows:

[0031]

[0032] After processing:

[0033]

[0034] From equation (7), L, d, b1, R(b1) are constants, then Only related to b n , and the thickness of the heating film t is irrelevant, and the conductivity of the heating film p is irrelevant, that is, the variable b is the influencing factor.

[0035] Preferably, step 4 comprises:

[0036] Select a standard thickness t b of the heating film, measure a series of b1, b2, b3,... b n of the parabolic line pattern of the heating film resistance R(b n ), and fit to obtain the relationship of , that is, A3.

[0037] Preferably, step 5 comprises:

[0038] Step 5.1: For a heating film with an unknown thickness t, measure its initial resistance value R1, and let the target resistance value be R, and the intersection of the parabolic line pattern of the heating film with the Y-axis be b', and the ratio of the two be R / R1.

[0039] Step 5.2: Substitute R / R1 into the relationship to obtain b' corresponding to R;

[0040] Then the etching line equation A4 above the X-axis is obtained:

[0041]

[0042] The etching line equation A5 below the X-axis is:

[0043]

[0044] Preferably, step 6 comprises: inputting the algorithm of steps 1-5 into an automatic laser etching device, after the operator inputs L, d, R, the automatic laser etching device will obtain b' corresponding to R, and on the heating film with an unknown thickness, etch out the parabolic etching line above the X-axis passing through the three points (-L / 2, d), (L / 2, d), (0, b'), and the parabolic etching line below the X-axis passing through the three points (-L / 2, d), (L / 2, d), (0, -b'), then the resistance value of the heating film with an unknown thickness will be the same as the target resistance value.

[0045] The beneficial effects of the present application are: the laser scribing etching method replaces the traditional mask etching method, greatly reduces the traditional etching workload, significantly shortens the etching time, and the laser scribing etching method only needs to connect the heating film within the etching line to the circuit, and the heating film outside the etching line will not heat naturally without the need to etch the heating film outside the etching line with an etchant, thereby saving process and cost; the laser scribing etching method uses a mathematical equation to control an automatic laser etching device, converts the problem of resistance value change caused by thickness fluctuation of the heating film caused by unstable magnetron sputtering equipment into a problem of the numerical value of an influencing factor of the etching line equation, controls the etching line equation by changing the numerical value of the influencing factor, and then controls the automatic laser etching device to re-etch the heating film, so that the same resistance value of the heating film as the standard heating film can be obtained simply and flexibly, without the need to stop production and re-adjust the magnetron sputtering equipment; by changing the type of the etching line equation, the heating film with different resistance value distributions can be obtained without changing the resistance value, thereby greatly reducing the difficulty of realizing the same resistance value and different distributions, completely without the need to re-produce an etching template, thereby saving production time and cost. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 It is a mathematical modeling diagram of the projection of the heating film pattern area and the etching line on a plane.

[0047] Figure 2 It is a three-dimensional schematic diagram of scribing and etching of a planar heating film in Example 1.

[0048] Figure 3 It is a curve graph of R(b n ) / R(b b ) with variable b under different thicknesses of the planar heating film in Example 1.

[0049] Figure 4 It is a three-dimensional schematic diagram of scribing and etching of a curved surface heating film in Example 2.

[0050] Figure 5 It is a curve graph of R(b n ) / R(b b ) with variable b under different thicknesses of the curved surface heating film in Example 2.

[0051] In the figure: 1-conductive pile, 2-electrode, 3-heating film, 4-etching line. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical scheme and beneficial effects of the present application clearer, the preferred embodiments of the present application will be described in detail below to facilitate the understanding of the skilled in the art.

[0053] Example 1:

[0054] FromFigures 1-3 As can be seen in this embodiment: a scribing etching method for controlling the resistance and resistance distribution of a heating film using mathematical equations includes:

[0055] Step 1:

[0056] This embodiment uses a planar heating film. The heating film graphic area and etching lines are projected onto a plane. A Cartesian coordinate system is established with the geometric symmetry center of the heating film graphic area as the origin and the direction of the conductive pillars as the X-axis. If the etching line type is a standard parabola, then the etching line forms two parabolic segments symmetrical about the X-axis in the coordinate system, such as... Figure 1 As shown. The parabola located above the X-axis is assumed to pass through the points (-L / 2, d), (L / 2, d), and (0, b). Substituting these values ​​into the parabola's equation y(x) = ax... 2 +b yields A1:

[0057]

[0058] Similarly, the equation of the parabola below the X-axis is A2:

[0059]

[0060] Step 2:

[0061] The formula for calculating resistance is:

[0062]

[0063] Where S is the cross-sectional area of ​​the rectangle before etching; L is the length of the rectangle before etching; t is the thickness of the heating film; h is the height of the rectangle before etching; and substituting A1 and A2 into the resistance formula, the resistance of the heating film between the two etched lines is:

[0064]

[0065] The conductivity and thickness of the electrode and conductive pillar materials are greater than those of the heating film material. The resistance of the region between the etched lines of the heating film is much greater than the resistance of the electrodes and conductive pillars. Therefore, the resistance R(t, b) between the two conductive pillars can be simplified as follows:

[0066]

[0067] Ten sets of calculations were performed using numerical simulation, where L, d, and ρ were constants, and L = 6 mm, d = 2 mm, and ρ = 8200 kg / m³. 3 The results of the heating film resistance R(b,t) when variables b and t take different values ​​are shown in Table 1.

[0068]

[0069] Table 1 plane heat film simulation calculation resistance value

[0070] Step 3:

[0071] Let R(b1, t b ) be the initial resistance of the heat film of standard thickness, and R(b1, t b ) be a constant, (b n , t) be the resistance of the heat film etching line at different b n values, b1 and b n be a series of b values from large to small. The ratio of the two is as follows:

[0072] After processing:

[0073]

[0074] From formula (7), L, d, b1, R(b1) are all constants, then is only related to b n , and is independent of the thickness t of the heat film and the conductivity p of the heat film, that is, the variable b is the influencing factor.

[0075] At the same time, the change curve of the ratio of the heat film resistance value R(b n ) in Table 1 to the resistance value R(b1) of the heat film of standard thickness is shown in Figure 3 . From Figure 3 it can be seen that the three curves basically coincide. Taking t=1.0mnm as the benchmark, when the thickness of the heat film changes by ±50%, under the same parabolic shape (i.e. the same b n ), the difference of R(b n ) / R(b1) is within ±0.5%. Therefore, R(b n ) / R(b1) is basically independent of the thickness of the heat film, and mainly changes with b n .

[0076] When the standard thickness of the heat film is t=1.0mm, and L=6mm, d=2mm, the relationship between b and R(b n ) / R(b1) is fitted by a polynomial, and the highest term is 3. The fitting relationship when the highest term is 3 is:

[0077]

[0078] Therefore, the parabolic equation is:

[0079]

[0080] Step 4:

[0081] For a unknown thickness of the heating film, the initial resistance value is R1, the target heating film resistance value is R, and the ratio of the two is R / R1; bring R / R1 into the relationship (8) to get the target resistance value R corresponding to the parameter b';

[0082] Then the etching line equation above the X axis is obtained:

[0083]

[0084] The etching line equation below the X axis is:

[0085]

[0086] Step 5:

[0087] The algorithm of steps 1-4 is input into the automatic laser etching equipment. After the operator inputs L, d, and R, the automatic laser etching equipment will get b' corresponding to R, and etch out the parabolic etching line above the X axis passing through the three points (-L / 2, d), (L / 2, d), (0, b') and the parabolic etching line below the X axis passing through the three points (-L / 2, d), (L / 2, d), (0, -b') on the unknown thickness of the heating film. Then the resistance value of the unknown thickness of the heating film will be the same as the target resistance value, and the resistance value distribution of the heating film will conform to the linear type of parabola, i.e. the middle resistance is the largest, and continuously decreases towards both ends.

[0088] Example 2:

[0089] From Figure 1 , Figure 4 , Figure 5 It can be seen that in this embodiment: a scribing and etching method for controlling the resistance value and resistance value distribution of the heating film using mathematical equations, comprising:

[0090] Step 1:

[0091] In this embodiment, the heating film is a curved surface. The heating film pattern area and etching line are projected on a plane, and a rectangular coordinate system is established with the geometric center of the heating film pattern area as the origin and the direction of the conductive column as the X axis. The etching line is a standard parabola, which appears as two parabolas symmetric to the X axis in the coordinate system, as shown in Figure 1 . Among them, the parabola located above the X axis passes through the three points (-L / 2, d), (L / 2, d), (0, b), and the parabola equation y(x) = ax 2 +b is obtained A1:

[0092]

[0093] Similarly, the parabola equation below the X axis is A2:

[0094]

[0095] Step 2:

[0096] The resistance calculation formula is:

[0097]

[0098] Where S is the cross-sectional area of the rectangle presented by the heating film before etching; L is the length of the rectangle presented by the heating film before etching; t is the thickness of the heating film; and A1 and A2 are brought into the resistance formula to obtain the resistance of the heating film between the two etched lines as:

[0099]

[0100] The conductivity and thickness of the electrode and the conductive column are greater than those of the heating film material, and the resistance of the area between the etched lines of the heating film is much greater than the resistance of the electrode and the conductive column, so the resistance R(t, b) between the two conductive columns can be simplified as:

[0101]

[0102] Ten groups of calculations were performed using numerical simulation, where L, d, and p were constants, and L = 6 mm, d = 2 mm, and p = 8200 kg / m 3 When the variables b and t take different values in turn, the resistance value R(b, t) of the heating film is shown in Table 2:

[0103]

[0104]

[0105] Table 2: Resistance value of simulated curved heating film

[0106] Step 3:

[0107] Let R(b1, t b ) be the initial resistance of the heating film with standard thickness, and R(b1, t b ) be a constant, (b n ,t) be the resistance of the heating film etched line at different b n values, and the ratio of the two is as follows:

[0108]

[0109] After processing, we get:

[0110]

[0111] From formula (18), L, d, b1, and R(b1) are constants, so Only b nIt is related to the thickness t of the heating film and the conductivity ρ of the heating film, meaning that variable b is an influencing factor.

[0112] Meanwhile, the heating film resistance value R(b) in Table 2 n The curve showing the change in the ratio of the resistance value R(b1) of the heating film of standard thickness to the constant is shown below. Figure 5 .from Figure 5 As can be seen, the three curves basically overlap. Taking t = 1.0 mm as the baseline, when the heating film thickness changes by ±50%, the same parabolic shape (i.e., the same b) is achieved. n ), R(b n The difference between R(b) and R(b1) is within ±1%. Therefore, R(b) / R(b1) is within ±1%. n The ratio ) / R(b1) is basically unrelated to the thickness of the heating film, and mainly depends on b. n change.

[0113] Assuming the standard thickness of the heating film is t = 1.0 mm, and L = 6 mm, d = 2 mm, then b n With R(b) n The relationship between ) / R(b1) and the change of the expression is fitted using a polynomial. The fitting expression when the highest term is 3rd is as follows:

[0114]

[0115] Therefore, the equation of the parabola is:

[0116]

[0117] Step 4:

[0118] For a heating film of unknown thickness, its initial resistance is measured to be R1, and the resistance of the target heating film is R. The ratio of the two is R / R1. Substituting R / R1 into the relation (8), we obtain the parameter b′ corresponding to the target resistance R.

[0119] The equation for the etching line above the X-axis is then obtained:

[0120]

[0121] Equation of the etching line below the X-axis:

[0122]

[0123] Step 5:

[0124] The algorithm of steps 1-4 is inputted into the automatic laser etching equipment. After the operator inputs L, d, R, the automatic laser etching equipment will get b' corresponding to R, and etch out the parabolic etching lines above the X axis through the three points (-L / 2, d), (L / 2, d), (0, b') and the parabolic etching lines below the X axis through the three points (-L / 2, d), (L / 2, d), (0, -b') on the heat-generating film of unknown thickness. Then the resistance of the heat-generating film of unknown thickness will be the same as the target resistance, and the resistance distribution of the heat-generating film conforms to the linear type of parabola, i.e. the middle resistance is the largest, and continuously decreases towards both ends.

[0125] Finally, the above embodiment is the case of standard parabola. In actual production, the linear type of the etching line is not limited to parabola, but can also be other types of curves. At the same time, the line width of the etching line is between 0.02 mm and 0.5 mm, and the etching line can be 2 or more than 2. The b n With the change relationship of R(b n ) / R(b1), the highest order can be 3 or more than 3.

[0126] Finally, it is pointed out that the above preferred embodiments are only used to illustrate the technical solutions of the present application and are not limited. Although the present application has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made in form and details without departing from the scope defined by the claims of the present application.

Claims

1. A scribing etching method for controlling the resistance and resistance distribution of a heating film using mathematical equations, characterized in that: An automated laser etching machine, controlled by mathematical equations, performs laser scribing etching on heating films of non-standard thickness. The etching process creates etching lines that separate a portion of the heating film from the main body, ensuring that the resistance of the remaining heating film is the same as that of a standard thickness heating film. The mathematical equations control the shape of the etching lines, which in turn controls the resistance distribution of the remaining heating film. Controlling the shape of the etching lines using mathematical equations includes the following steps: Step 1: Perform mathematical modeling on the patterned area of ​​the heating film and the etching lines to obtain two etching line equations A1 and A2; Step 1 includes: projecting the heating film pattern area and the etching lines onto a plane, establishing a rectangular coordinate system with the heating film pattern area as the origin and the direction of the conductive pillars as the X-axis. The etching lines in the coordinate system are two parabolic segments symmetrical about the X-axis. The parabola located above the X-axis is set to pass through the three points (-L / 2, d), (L / 2, d), and (0, b). Substituting these points into the parabola equation y(x) = ax 2 +b yields A1: Similarly, the equation of the parabola below the X-axis is A2: In the above two equations, L and 2d are the length and width of the rectangle before the heating film is etched. By adjusting the parameter b... n Different parabolas can be formed, b n It is the intersection of the parabola and the Y-axis, and b is 1 / 2 of the width of the heating film at its narrowest point; Step 2: Obtain the formula R for the resistance of the heating film between the etching lines based on the etching line equation; The formula for calculating resistance is: Where S is the cross-sectional area of ​​the rectangle before etching; L is the length of the rectangle before etching; t is the thickness of the heating film; h is the height of the rectangle before etching; and substituting A1 and A2 into the resistance formula, the resistance of the heating film between the two etched lines is: The conductivity and thickness of the electrode and conductive pillar materials are greater than those of the heating film material. The resistance of the region between the etched lines of the heating film is much greater than the resistance of the electrodes and conductive pillars. Therefore, the resistance R(b,t) between the two conductive pillars can be simplified as follows: Step 3: Determine a certain influencing factor based on the heating film resistance formula. This influencing factor can affect the resistance value of heating films with the same etched lines of the same shape but different thicknesses from the standard films. Step 4: Use numerical simulation to calculate and fit equation A3, which shows the relationship between the influencing factor and the resistance value of the heating film. Step 5: Determine the equations A4 and A5 for etching lines drawn when etching heating films with the same shape but different thicknesses than the standard film, based on A3; Step 6: Using automated laser etching equipment, etch A4 and A5 shaped etching lines on the non-standard thickness heating film, so that the non-standard thickness heating film has the same resistance value as the standard thickness heating film.

2. The scribing etching method for controlling the resistance and resistance distribution of the heating film using mathematical equations according to claim 1, characterized in that: Step 3 include: Where R(b1, t) is the initial resistance of the heating film of standard thickness, R(b n ,t) represents the etching lines of the heating film at different b n When the value is a resistor, b1 and b n Let b be a series of values ​​from largest to smallest, and the ratio between the two is as follows: After processing, the following was obtained: From formula (7), we know that L, d, b1, and R(b1) are all constants. Only with b n It is related to the heating film thickness t and the heating film conductivity ρ, i.e., variable b. n It is the impact factor.

3. The scribing etching method for controlling the resistance and resistance distribution of the heating film using mathematical equations according to claim 2, characterized in that: Step 4 includes: Select a standard thickness t b The heating film was used to measure a series of values, b1, b2, b3, ... b. n The heating film resistor R(b) with a parabolic shape n ), and obtained by fitting The relation is A3.

4. The method for scribing lines using mathematical equations to control the resistance value of the heating film pattern according to claim 3, characterized in that: Step 5 includes: Step 5.1: For a heating film of unknown thickness t, measure its initial resistance value R1 and the resistance value of the target heating film R, and the ratio of the two is R / R1; Step 5.2: Substitute R / R1 into the relation. Obtain b' corresponding to the target heating film resistance R; This yields the equation A4 for the etching line above the X-axis: Etching line equation A5 below the X-axis:

5. The method for scribing lines using mathematical equations to control the resistance value of the heating film pattern according to claim 4, characterized in that: Step 6 includes: inputting the algorithm from steps 1-5 into an automated laser etching device. After the operator inputs L, d, and R, the automated laser etching device will obtain b′ corresponding to R and etch parabolic etching lines above the X-axis passing through the three points (-L / 2, d), (L / 2, d), and (0, b′) and below the X-axis passing through the three points (-L / 2, d), (L / 2, d), and (0, -b′) on the heating film of unknown thickness. Then the resistance value of the heating film of unknown thickness will be the same as the target resistance value.

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