Method for simulating generation of chemical cleaning corrosion surface of silicon wafer

Abstract

The invention relates to the technical field of silicon wafer surface treatment, and discloses a method for simulating and generating a chemical cleaning corrosion surface of a silicon wafer, which comprises the following steps of: regarding the chemical cleaning corrosion surface of the silicon wafer as a plurality of two-dimensional spatial frequency functions; setting activation energy to distinguish anisotropy of different crystal faces on the etched surface of the silicon wafer; on the basis that the surface of the silicon wafer in the corrosion process follows a Boltzmann distribution function microcosmically, the Boltzmann distribution function is evolved to obtain corrosion probability distribution functions of different crystal faces on the surface of the silicon wafer in combination with activation energy of the crystal faces; combining the initial amplitude value function with the corrosion probability distribution function to obtain an amplitude function of anisotropic corrosion of different crystal faces on the surface of the silicon wafer; according to the two-dimensional space frequency function and the amplitude function, a simulation expression representing the silicon wafer corrosion surface is obtained; and simulating to obtain a visual surface profile diagram of the etched silicon wafer according to the simulation expression. According to the method, the generated visual surface profile diagram is more visual, and the simulation accuracy and universality can be improved.

Description

Technical Field

[0001] The invention relates to the technical field of silicon wafer surface treatment, and in particular to a method for simulating and generating a silicon wafer chemical cleaning and corrosion surface. Background Art

[0002] Simulation is an indispensable part of studying photovoltaic devices. It can effectively reduce experimental costs and improve the purposefulness of research. Optimizing simulation algorithms is an important means to improve simulation accuracy.

[0003] Currently, there are simulation platforms for simulating the surface of photovoltaic materials, mainly websites and photovoltaic simulation software. However, these simulation platforms mostly simulate the surface of photovoltaic materials in two-dimensional models, which are simplified models, and their morphological distribution is basically uniform, which is quite different from the actual surface of photovoltaic materials.

[0004] In other technical fields, there are also simulation methods for the surface roughness of other materials. For example, publication number CN114577798A discloses a rock fracture roughness modeling method based on the spatial frequency domain, which inputs the spatial frequency resolution, amplitude and phase angle into a preset rock surface roughness characterization function to obtain an expression of the rock fracture roughness model to be generated; then executes a visualization contour generation algorithm based on the expression to obtain a visualization contour of the corresponding rock fracture roughness model; this method can obtain a surface with completely random roughness, and the generated rock fracture roughness model is closer to natural rock. However, this simulation method for rough surfaces is mainly reflected in random surface simulation, and its algorithm lacks targeted improvements to photovoltaic materials used in photovoltaic devices (such as lack of targeted improvements to the anisotropy of silicon material surfaces in chemical cleaning and corrosion), so it is difficult to accurately simulate the chemical cleaning and corrosion surface of silicon wafers. Summary of the invention

[0005] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a method for simulating and generating a silicon wafer chemical cleaning corrosion surface to improve the accuracy and universality of the simulation.

[0006] Based on this, the present invention discloses a method for simulating and generating a silicon wafer chemical cleaning corrosion surface, comprising the following steps:

[0007] Step S1, treating the surface of the silicon wafer after chemical cleaning and corrosion as composed of multiple two-dimensional spatial frequency functions;

[0008] Step S2, setting activation energy to distinguish the anisotropy of different crystal planes on the surface of the silicon wafer chemically cleaned and etched;

[0009] Step S3, based on the fact that the surface of the silicon wafer microscopically obeys the Boltzmann distribution function during the chemical cleaning and etching process, combined with the activation energy of the silicon wafer crystal plane, the Boltzmann distribution function is evolved to obtain the corrosion probability distribution function of different crystal planes on the silicon wafer surface; then the defined initial amplitude value function is combined with the corrosion probability distribution function of different crystal planes on the silicon wafer surface to obtain the amplitude function expressing the anisotropic corrosion of different crystal planes on the silicon wafer surface during chemical cleaning and etching;

[0010] Step S4, according to the two-dimensional spatial frequency function of step S1 and the amplitude function of the anisotropic etching of different crystal planes in step S3, a simulation expression representing the chemical cleaning and etching surface of the silicon wafer is obtained;

[0011] Step S5: According to the simulation expression of step S4, a visualization surface profile generation algorithm is executed to simulate and obtain a visualization surface profile of the chemically cleaned and corroded silicon wafer.

[0012] Preferably, in step S1, the formula (1) of the two-dimensional spatial frequency function is:

[0013] h1(x,y)=cos(2π(mx+ny)+φ(m,n))(1);

[0014] In formula (1), x, y are spatial coordinates; m, n are spatial frequencies, and the cutoff values ​​of spatial frequencies m, n are defined as M, N respectively; φ(m, n) is the phase angle added by the simulated surface.

[0015] Further preferably, in step S1, φ(m,n) is a uniformly distributed phase angle function or a phase angle constant.

[0016] Preferably, in step S2, when the silicon wafer is a single crystal silicon wafer, the activation energy values ​​of different crystal planes thereof are as follows:

[0017] E (100) =0.55eV,E (110) =0.52eV,E (111) =0.63 eV; where E is the activation energy; the subscripts (100), (110), and (111) of E are the crystal plane indices of silicon crystals.

[0018] Further preferably, in step S3, according to the cutoff value of the spatial frequency in step S1, the initial amplitude value function formula (2) is defined as:

[0019]

[0020] In formula (2), x, y are spatial coordinates; M, N are the cutoff values ​​of spatial frequencies m, n.

[0021] Further preferably, in step S3, the Boltzmann distribution function is:

[0022]

[0023] According to the activation energy of the silicon wafer crystal surface, the Boltzmann distribution function is evolved to obtain the corrosion probability distribution function formula (3) of different crystal surfaces on the silicon wafer surface:

[0024]

[0025] In formula (3), E i is the initial activation energy of the crystal surface corrosion reaction, E f is the final activation energy of the crystal surface corrosion reaction, k is the Boltzmann constant, and T is the absolute temperature.

[0026] More preferably, in step S3, the amplitude function formula (4) of the anisotropic etching of different crystal planes is:

[0027]

[0028] In formula (4), x, y are spatial coordinates; M, N are the cutoff values ​​of spatial frequencies m, n; P if (E) is the corrosion probability distribution function of different crystal planes.

[0029] More preferably, in step S4, the simulation expression (5) representing the chemical cleaning corrosion surface of the silicon wafer is:

[0030]

[0031] In formula (5), x, y are spatial coordinates; m, n are spatial frequencies; M, N are the cutoff values ​​of spatial frequencies m, n; φ(m, n) is the phase angle; i represents the initial state of the corrosion reaction, f represents the end state of the corrosion reaction, and P if (E) is the corrosion probability distribution function of different crystal planes.

[0032] Further preferably, in the step S5, the visualized surface contour map of the chemically cleaned and etched silicon wafer obtained by simulation is a three-dimensional contour map.

[0033] More preferably, the step S5 specifically includes:

[0034] Step S51, using simulation software, first set the spatial frequency resolution M, N;

[0035] Step S52, selecting a function or constant required for the phase angle;

[0036] Step S53: input the initial activation energy value E of the crystal surface corrosion reaction according to the simulated silicon wafer material properties.i ;

[0037] Step S54: convert the spatial frequency resolution M, N of step S51, the phase angle of step S52, and the initial activation energy value E of the crystal surface corrosion reaction of step S53 into i , input into the simulation expression (5) of step S4, and simulate and generate a three-dimensional visual surface contour map with anisotropy of the chemically cleaned and corroded silicon wafer.

[0038] Compared with the prior art, the present invention has at least the following beneficial effects:

[0039] 1. The simulated visual surface contour map is transformed from two-dimensional to three-dimensional, which is more intuitive.

[0040] 2. Its simulation can define silicon materials and express their specific corrosion methods such as anisotropy. It can more accurately simulate the chemical cleaning and corrosion surface of silicon wafers, which helps to reduce the cost of related research.

[0041] 3. By adjusting the characteristic parameters in the simulation expression (such as spatial frequency resolution, activation energy, etc.), this method can simulate the surface structure of different photovoltaic device materials (semiconductor materials) and under different conditions (such as reaction time and reaction temperature of chemical cleaning corrosion), and has a certain universality. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 The figure is a schematic diagram of the execution flow of a simulation expression for simulating and generating a method for chemically cleaning and corroding the surface of a silicon wafer according to the present embodiment.

[0043] Figure 2 It is a three-dimensional visualized surface contour diagram simulated and generated by a method for simulating and generating a silicon wafer chemical cleaning and corrosion surface in this embodiment.

[0044] Figure 3 This is another three-dimensional visualized surface contour diagram simulated and generated by a method for simulating and generating a silicon wafer chemical cleaning and corrosion surface in this embodiment. DETAILED DESCRIPTION

[0045] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below in conjunction with specific implementation methods.

[0046] Example

[0047] A method for simulating and generating a silicon wafer chemical cleaning and corrosion surface in this embodiment, see Figure 1 , including the following steps:

[0048] Step S1, spatial oscillation can be represented by a spatial frequency function: h(x)=cos(2πνx), where ν is the spatial frequency. Corresponding to this embodiment, the surface of the silicon wafer after chemical cleaning and etching can be regarded as composed of multiple two-dimensional spatial frequency functions, wherein the formula of a single two-dimensional spatial frequency function is shown in the following formula (1):

[0049] h1(x,y)=cos(2π(mx+ny)+φ(m,n))(1);

[0050] In formula (1), x, y are spatial coordinates; m, n are spatial frequencies, and the cutoff values ​​of spatial frequencies m, n are defined as M, N respectively; φ(m, n) is the phase angle added by the simulated surface.

[0051] In step S1, according to actual needs, φ(m,n) can be selected as a uniformly distributed function (such as a uniformly distributed random function in the interval from 0 to π), or can also be selected as a constant (such as π4).

[0052] Furthermore, for silicon wafers used in photovoltaic devices, different crystal planes of chemical cleaning and etching will show different reaction rates, which has the characteristics of anisotropic etching. In order to truly simulate the anisotropic etching of different crystal planes on the surface of silicon wafer chemical cleaning and etching, this embodiment also makes the following improvements in step S2 and step S3 in sequence.

[0053] Step S2: setting activation energy to distinguish the anisotropy of different crystal planes on the surface of the silicon wafer chemically cleaned and etched.

[0054] In step S2, taking a single crystal silicon wafer as an example, the activation energy values ​​of different crystal planes are as follows:

[0055] E (100) =0.55eV,E (110) =0.52eV,E (111) =0.63eV; E is the activation energy; the subscripts (100), (110), and (111) of E are the crystal plane indices of silicon crystals, which are parameters defined based on the spatial arrangement of atoms in the crystal; different crystal planes have different physical and chemical properties, so they can be distinguished by different activation energy values.

[0056] Step S3, combining the initial amplitude value function and the corrosion probability distribution function of different crystal planes on the silicon wafer surface, the amplitude function formula (4) for expressing the anisotropic corrosion of different crystal planes on the silicon wafer surface during chemical cleaning corrosion is obtained:

[0057]

[0058] In formula (4), x, y are spatial coordinates; M, N are the cutoff values ​​of spatial frequencies m, n; P if(E) is the corrosion probability distribution function of different crystal planes.

[0059] In step S3, according to the cutoff value of the spatial frequency in step S1, the initial amplitude value function formula (2) is defined:

[0060]

[0061] In formula (2), x, y are spatial coordinates; M, N are the cutoff values ​​of spatial frequencies m, n.

[0062] In step S3, during the chemical cleaning and etching process, the surface of the silicon wafer microscopically obeys the Boltzmann distribution function Therefore, by distinguishing the anisotropy of different crystal planes using the activation energy E of the crystal plane, the Boltzmann distribution function can be evolved, and then the corrosion probability distribution function formula (3) of different crystal planes on the silicon wafer surface can be obtained:

[0063]

[0064] In formula (3), E i is the initial activation energy of the crystal surface corrosion reaction, E f is the final activation energy of the crystal surface corrosion reaction, k is the Boltzmann constant, and T is the absolute temperature.

[0065] Step S4: Based on the two-dimensional spatial frequency function formula (1) of step S1 and the amplitude function formula (4) of the anisotropic etching of different crystal planes of step S3, the following simulation expression (5) for chemical cleaning and etching of the silicon wafer surface is obtained:

[0066]

[0067] In formula (5), x, y are spatial coordinates; m, n are spatial frequencies; M, N are the cutoff values ​​of spatial frequencies m, n; φ(m, n) is the phase angle; i represents the initial state of the corrosion reaction, f represents the end state of the corrosion reaction, and P if (E) is the corrosion probability distribution function of different crystal planes.

[0068] Step S5, according to the simulation expression (5) of the chemically cleaned and corroded silicon wafer surface in step S4, the existing physical model simulation software is used to execute the visualized surface profile generation algorithm to simulate and obtain the visualized surface profile of the chemically cleaned and corroded silicon wafer.

[0069] Step S5 specifically includes:

[0070] Step S51: Use existing physical model simulation software to first set the spatial frequency resolution M, N (for example, Figure 2 The M and N values ​​are 20; for example, Figure 3The value of M, N is 10).

[0071] Step S52: Select a function or constant used for the phase angle (for example, Figure 2 The phase angle is a constant π4; for example, Figure 3 The phase angle is a uniform distribution function in the range of 0 to π).

[0072] Step S53: input the initial activation energy value E of the crystal surface corrosion reaction according to the simulated silicon wafer material properties. i (Different activation energy values ​​can be input according to different crystal plane directions of the silicon wafer).

[0073] Step S54: The spatial frequency resolution of step S51, the phase angle of step S52 and the initial activation energy value E of the crystal surface corrosion reaction of step S53 are converted into i , input into the simulation expression (5) of step S4, simulate and generate a three-dimensional visual surface contour map with anisotropy of chemical cleaning and etching of silicon wafer (specifically, Figure 2 , 3 As shown), the three-dimensional visualized surface profile can be more intuitive and more accurately match the characteristics of the chemically cleaned and corroded surface of the silicon wafer.

[0074] In summary, the simulation method of this embodiment, with the help of physical model simulation software, adopts a new random method to simulate the surface morphology of the silicon wafer after chemical cleaning and corrosion. The simulation expression of this embodiment, through the coupling of the two-dimensional spatial frequency function, the defined initial amplitude value function and the corrosion probability distribution function of different crystal planes on the surface of the silicon wafer, simulates the visualized surface contour map of the surface structure (such as the pyramid velvet structure) after chemical cleaning and corrosion of the silicon wafer; by adjusting the characteristic parameters (such as spatial frequency resolution, activation energy, etc.) in the simulation expression, the surface structure of different photovoltaic device materials (semiconductor materials) and different conditions (such as the reaction time and reaction temperature of chemical cleaning and corrosion) can be simulated; using the anisotropic characteristics of the silicon material surface in chemical cleaning and corrosion, the simulation expression is improved for the anisotropic characteristics of the surface corrosion of the specific material, and the improved simulation expression of the above step S4 is obtained, so that the simulated morphology is more consistent with the morphology of the actual silicon wafer chemical cleaning and corrosion surface, thereby improving the accuracy and universality of the simulation.

[0075] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the embodiments of the present invention.

[0076] The technical solution provided by the present invention is introduced in detail above. Specific examples are used in this article to illustrate the principle and implementation mode of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation mode and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for simulating and generating a silicon wafer chemical cleaning and corrosion surface, characterized in that: The steps include: Step S1, treating the surface of the silicon wafer after chemical cleaning and corrosion as composed of multiple two-dimensional spatial frequency functions; Step S2, setting activation energy to distinguish the anisotropy of different crystal planes on the surface of the silicon wafer chemically cleaned and etched; Step S3, based on the fact that the surface of the silicon wafer microscopically obeys the Boltzmann distribution function during the chemical cleaning and etching process, combined with the activation energy of the silicon wafer crystal plane, the Boltzmann distribution function is evolved to obtain the corrosion probability distribution function of different crystal planes on the silicon wafer surface; then the defined initial amplitude value function is combined with the corrosion probability distribution function of different crystal planes on the silicon wafer surface to obtain the amplitude function expressing the anisotropic corrosion of different crystal planes on the silicon wafer surface during chemical cleaning and etching; Step S4, according to the two-dimensional spatial frequency function of step S1 and the amplitude function of the anisotropic etching of different crystal planes in step S3, a simulation expression representing the chemical cleaning and etching surface of the silicon wafer is obtained; Step S5: According to the simulation expression of step S4, a visualization surface profile generation algorithm is executed to simulate and obtain a visualization surface profile of the chemically cleaned and corroded silicon wafer.

2. The method for simulating and generating chemical cleaning and corrosion surface of silicon wafer according to claim 1, characterized in that: In step S1, the formula (1) of the two-dimensional spatial frequency function is: h1(x,y)=cos(2π(mx+ny)+φ(m,n))(1); In formula (1), x, y are spatial coordinates; m, n are spatial frequencies, and the cutoff values ​​of spatial frequencies m, n are defined as M, N respectively; φ(m, n) is the phase angle added by the simulated surface.

3. The method for simulating and generating chemical cleaning and corrosion surface of silicon wafer according to claim 2, characterized in that: In step S1, φ(m,n) is a uniformly distributed phase angle function or a phase angle constant.

4. The method for simulating and generating chemical cleaning and corrosion surface of silicon wafer according to claim 1, characterized in that: In step S2, when the silicon wafer is a single crystal silicon wafer, the activation energy values ​​of different crystal planes are as follows: E (100) =0.55eV,E (110) =0.52eV,E (111) =0.63 eV; where E is the activation energy; the subscripts (100), (110), and (111) of E are the crystal plane indices of silicon crystals.

5. The method for simulating and generating chemical cleaning and corrosion surface of silicon wafer according to claim 2, characterized in that: In step S3, according to the cutoff value of the spatial frequency in step S1, the initial amplitude value function formula (2) is defined as: In formula (2), x, y are spatial coordinates; M, N are the cutoff values ​​of spatial frequencies m, n.

6. A method for simulating and generating chemical cleaning and corrosion surface of a silicon wafer according to claim 1 or 5, characterized in that: In step S3, the Boltzmann distribution function is: According to the activation energy of the silicon wafer crystal surface, the Boltzmann distribution function is evolved to obtain the corrosion probability distribution function formula (3) of different crystal surfaces on the silicon wafer surface: In formula (3), E i is the initial activation energy of the crystal surface corrosion reaction, E f is the final activation energy of the crystal surface corrosion reaction, k is the Boltzmann constant, and T is the absolute temperature.

7. The method for simulating and generating chemical cleaning and corrosion surface of silicon wafer according to claim 6, characterized in that: In step S3, the amplitude function formula (4) of anisotropic etching of different crystal planes is: In formula (4), x, y are spatial coordinates; M, N are the cutoff values ​​of spatial frequencies m, n; P if (E) is the corrosion probability distribution function of different crystal planes.

8. The method for simulating and generating chemical cleaning and corrosion surface of silicon wafer according to claim 7, characterized in that: In step S4, the simulation expression (5) representing the chemical cleaning and corrosion of the silicon wafer surface is: In formula (5), x, y are spatial coordinates; m, n are spatial frequencies; M, N are the cutoff values ​​of spatial frequencies m, n; φ(m, n) is the phase angle; i represents the initial state of the corrosion reaction, f represents the end state of the corrosion reaction, and P if (E) is the corrosion probability distribution function of different crystal planes.

9. A method for simulating and generating a silicon wafer chemical cleaning and corrosion surface according to claim 1 or 8, characterized in that: In the step S5, the visualized surface contour map of the chemically cleaned and corroded silicon wafer obtained by simulation is a three-dimensional contour map.

10. The method for simulating and generating chemical cleaning and corrosion surface of silicon wafer according to claim 9, characterized in that: The step S5 specifically includes: Step S51, using simulation software, first set the spatial frequency resolution M, N; Step S52, selecting a function or constant required for the phase angle; Step S53: input the initial activation energy value E of the crystal surface corrosion reaction according to the simulated silicon wafer material properties. i ; Step S54: convert the spatial frequency resolution M, N of step S51, the phase angle of step S52, and the initial activation energy value E of the crystal surface corrosion reaction of step S53 into i , input into the simulation expression (5) of step S4, and simulate and generate a three-dimensional visual surface contour map with anisotropy of the chemically cleaned and corroded silicon wafer.

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