Monocrystalline silicon wafer subsurface damage depth prediction method

Abstract

The invention provides a monocrystalline silicon wafer subsurface damage depth prediction method, which is characterized by comprising the following steps: S1, based on an indentation fracture mechanics theory, obtaining a theoretical relationship between a subsurface damage deformation area depth and a subsurface microcrack depth after processing of a monocrystalline silicon wafer; s2, processing the monocrystalline silicon ingot to obtain a monocrystalline silicon wafer; s3, performing a nanoindentation experiment on the monocrystalline silicon wafer to obtain a relation curve between an elastic recovery parameter and a maximum imprinting load; s4, solving the depth of a sub-surface damage deformation area of the processed monocrystalline silicon wafer through the inflection point of the curve; and S5, predicting the subsurface microcrack depth of the monocrystalline silicon wafer in combination with the obtained theoretical relationship. According to the method, the subsurface damage depth can be accurately predicted only by measuring the depth of the subsurface damage deformation area through the nanoindentation experiment, the damage to the workpiece is minimum, the operation is simple during detection, the influence of the experience of an operator is small, and the detection cost and difficulty are reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of subsurface damage depth prediction, and in particular to a method for predicting the subsurface damage depth of a single crystal silicon wafer. Background Art

[0002] Single crystal silicon wafers are widely used in the semiconductor field due to their excellent physical and chemical properties. When used, single crystal silicon wafers are generally processed using processing equipment first.

[0003] There are many types of processing equipment for single crystal silicon wafers, such as diamond wire saw cutting, which is one of the most important processing technologies for single crystal silicon wafers;

[0004] However, because single-crystal silicon wafers are typically brittle, they are prone to subsurface damage during processing. This damage significantly reduces the fracture strength of the wafer and increases the probability of breakage, thereby affecting the wafer's service performance and lifespan. Accurately assessing subsurface damage in single-crystal silicon wafers is crucial for improving processing quality and reducing costs.

[0005] Currently, subsurface damage detection methods are primarily categorized as destructive and non-destructive. Destructive methods, such as cross-sectional microscopy and angle polishing, can provide relatively accurate results but are time-consuming and significantly influenced by operator experience. Non-destructive methods, while fast and highly accurate, still have limitations in quantitatively detecting micron-scale cracks. Summary of the Invention

[0006] The main purpose of the present invention is to provide a method for predicting the depth of sub-surface damage of single-crystal silicon wafers, so as to solve the problem that sub-surface damage detection of single-crystal silicon wafers is time-consuming and has low detection accuracy.

[0007] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0008] A method for predicting subsurface damage depth of a single crystal silicon wafer comprises the following steps:

[0009] S1. Based on the theory of indentation fracture mechanics, the theoretical relationship between the depth b of the subsurface damage deformation zone and the depth c of the subsurface microcracks after single crystal silicon wafer processing is obtained;

[0010] S2. Processing the single crystal silicon ingot to obtain single crystal silicon wafers;

[0011] S3. Perform nanoindentation experiments on single-crystal silicon wafers to obtain the elastic recovery parameter μ and the maximum imprint load F. m The relationship curve of

[0012] S4. Calculate the depth b of the subsurface damage deformation zone of the processed single crystal silicon wafer through the inflection point of the curve;

[0013] S5. Based on the obtained theoretical relationship, predict the subsurface microcrack depth c of the single crystal silicon wafer.

[0014] In the preferred solution, the process of establishing the theoretical relationship in S1 is as follows:

[0015] Use the indenter to scratch the workpiece, and according to the indentation fracture mechanics theory, the depth b of the deformation zone formed under the indenter and the depth c of the subsurface microcracks are obtained:

[0016]

[0017] Among them, E, H and K c are the elastic modulus, hardness and static fracture toughness of the workpiece material; α is the sharpness angle of the indenter; F n and F t are normal and tangential loads respectively; θ is the tilt angle; κ is the correction factor considering the elastic stress field; α k is a dimensionless number;

[0018] According to θ, F n and F t The relationship is:

[0019]

[0020] Among them, A n and A t are the normal and tangential projected contact areas between the indenter and the workpiece, A s is the shear contact area between the indenter and the workpiece;

[0021] According to A n 、A t and A s The equation of is used to determine the subsurface microcrack depth (c) through the relationship between the deformation zone depth and the subsurface microcrack depth:

[0022] c=K i b 4 / 3 ;

[0023] Among them, K i It is a coefficient related to the material properties of the workpiece and the sharpness angle α of the indenter.

[0024] In the preferred embodiment, θ, F n and F t The relationship is:

[0025]

[0026] In the preferred embodiment, A s The equation is:

[0027]

[0028] In the preferred embodiment, A t The equation is:

[0029]

[0030] In the preferred embodiment, A n The equation is:

[0031]

[0032] In a preferred embodiment, the subsurface damage depth is determined by the maximum subsurface microcrack depth.

[0033] In a preferred solution, in S3, the single crystal silicon wafer used for testing is cut from the center of the processed single crystal silicon wafer.

[0034] In a preferred solution, after S5, the following steps are further included:

[0035] S6. Use a scanning electron microscope to observe the subsurface morphology of the processed single-crystal silicon wafer and measure the subsurface microcrack depth, which is compared with the predicted value to verify the effectiveness of the subsurface damage depth prediction method.

[0036] The preferred solution includes the following data optimization steps:

[0037] S71. Collect 20-50 sets of nanoindentation experimental data of single crystal silicon wafers with different process parameters and different material properties, and the predicted values of the subsurface damage deformation zone depth, subsurface microcrack depth data, and the actual values of the subsurface damage depth;

[0038] S72. Construct a neural network model based on the predicted value and actual value of the data;

[0039] S73, after obtaining the predicted subsurface microcrack depth data of the single crystal silicon wafer in S5, inputting the data into the neural network model;

[0040] S74. The neural network model outputs the optimized predicted value of the subsurface microcrack depth.

[0041] The present invention provides a method for predicting the subsurface damage depth of a single-crystal silicon wafer. By adopting the above scheme, the following beneficial effects are achieved:

[0042] 1. Simply by measuring the depth of the subsurface damage deformation zone through nanoindentation experiments, the subsurface damage depth can be accurately predicted, minimizing damage to the workpiece.

[0043] 2. The detection operation is simple and is less affected by the operator's experience, which reduces the detection cost and difficulty.

[0044] 3. The prediction process is time-saving and more efficient.

[0045] 4. The test results are highly accurate and precise.

[0046] 5. Compared with the existing technology that only detects the damage depth of the plastic deformation zone, this application can predict the damage depth of the median crack, thereby predicting the sub-surface damage depth, which can meet more detection needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0048] Figure 1 Flowchart of the present invention;

[0049] Figure 2 In the figure, a is a schematic diagram of the conical indenter; b is a schematic diagram of the contact area between the conical indenter and the workpiece;

[0050] Figure 3 This is a schematic diagram of crack damage caused by a sharp indenter scratching a brittle material;

[0051] Figure 4 In the figure, a is a single crystal silicon wafer and a single crystal silicon wafer sample used for testing; b is the nanomechanical properties testing system used;

[0052] Figure 5 At different loads F m = Load-displacement curves at 10 mN, 50 mN, 100 mN, 200 mN, 300 mN, and 400 mN;

[0053] Figure 6 is the maximum imprint depth h m and residual depth h r Relationship diagram with maximum imprint load;

[0054] Figure 7 is the elastic recovery parameter μ and the maximum imprint load F m Relationship diagram;

[0055] Figure 8 This is the subsurface morphology of a single crystal silicon wafer sample. DETAILED DESCRIPTION

[0056] In the embodiment of the present application, the silicon ingot material properties are selected as follows: density ρ = 2.33 g / cm3, Young's modulus E = 129.5 GPa, Poisson's ratio ν = 0.24, hardness H = 9.5 GPa, fracture toughness

[0057] Single crystal silicon wafer size: length × width × height = 156 × 156 × 0.2 mm.

[0058] Saw wire parameters: saw wire diameter D = 86.9 μm, saw wire core diameter d = 74 μm, abrasive density N = 424 pieces / mm2, abrasive diameter dm = 12 μm.

[0059] Process parameters: saw wire feed speed v f =2.5mm / min, saw wire speed v s =1800m / min.

[0060] Figure 4 (a) shows a single crystal silicon wafer and a single crystal silicon wafer sample used for testing. Figure 4 (b) shows the nanomechanical properties testing system used.

[0061] like Figure 1-8 As shown, the steps of the method for predicting the subsurface damage depth of a single crystal silicon wafer in the present application are as follows:

[0062] S1. Based on the theory of indentation fracture mechanics, the theoretical relationship between the depth b of the subsurface damage deformation zone and the depth c of the subsurface microcracks after single crystal silicon wafer processing is obtained;

[0063] S2. Processing the single crystal silicon ingot to obtain single crystal silicon wafers;

[0064] S3. Perform nanoindentation experiments on single-crystal silicon wafers to obtain the elastic recovery parameter μ and the maximum imprint load F. m The relationship curve of

[0065] S4. Calculate the depth b of the subsurface damage deformation zone of the processed single crystal silicon wafer through the inflection point of the curve;

[0066] S5. Based on the obtained theoretical relationship, predict the subsurface microcrack depth c of the single crystal silicon wafer.

[0067] S6. Use a scanning electron microscope to observe the subsurface morphology of processed single crystal silicon wafers and measure the subsurface microcrack depth. Compare it with the predicted value to verify the effectiveness of the subsurface damage depth prediction method.

[0068] The technical solutions are further defined as follows:

[0069] In step S1, the theoretical relationship establishment process is as follows:

[0070] Based on the following assumptions: there is elastic-plastic contact between the indenter and the workpiece; the indenter is rigid; and the workpiece material is an isotropic brittle material. In this embodiment, a diamond wire saw is used to cut a single crystal silicon ingot. The diamond wire saw cutting process can be regarded as a series of scratching processes, and the scratching process can be regarded as a series of imprinting processes along the scratching direction. When a sharp indenter (for example, a conical indenter) is used to scratch the workpiece, a series of cracks will be generated. According to the indentation fracture mechanics theory, a plastic deformation zone with spherical symmetry will be formed under the indenter, and median and lateral cracks will initiate under the deformation zone. Due to the presence of normal and tangential loads on the indenter, the crack will have an inclination angle relative to the scratching direction. When the inclination is taken into account, the calculation formulas for the deformation zone depth b and the subsurface microcrack depth c can be expressed as:

[0071]

[0072] Among them, E, H and K c are the elastic modulus, hardness and static fracture toughness of the workpiece material; α is the sharpness angle of the indenter; F n and F t are normal and tangential loads, respectively; θ is the tilt angle; κ is the correction factor for considering the elastic stress field (κ = 2.23); α k is a dimensionless number (for a conical indenter, α k =0.032). θ、F n and F t The relationship can be expressed as:

[0073]

[0074] Among them, A n and A t are the normal and tangential projected contact areas between the indenter and the workpiece, respectively. s is the shear contact area between the indenter and the workpiece.

[0075] Substituting formula (3) and formula (4) into formula (1) and formula (2), we get:

[0076]

[0077] Formula (5) and Formula (6) show that the depth of the deformation zone (b) and the depth of the subsurface microcracks (c) can be calculated by the material properties (E, H, K c ), the sharpness angle of the indenter (α), and the contact area between the indenter and the workpiece (A n 、A t 、A s ) to confirm.

[0078] Then calculate the indenter sharpness angle (α), scratch depth (h c) and the material elastic recovery coefficient (μ) related to A n 、A t and A s The equation (subscript c represents the relevant parameters of the conical indenter).

[0079] The schematic diagram of a conical indenter scratching the workpiece surface is as follows: Figure 2 As shown, a Cartesian coordinate system Oxyz is established, where the origin is the intersection of the workpiece surface and the indenter rotation axis, the coordinate axis Ox is opposite to the scratching direction, and Oz is consistent with the indenter rotation axis. In the xy plane, and is the normal projected contact area between the indenter and the workpiece; in the yz plane, S ΔAC′B It is the tangential projected contact area between the indenter and the workpiece. and is the interface between the indenter and the workpiece. Then A n ,A t , and A s It can be expressed as:

[0080]

[0081] A t =S ΔAC′B (8);

[0082]

[0083] in, and It is the micro shear area between the indenter and the workpiece.

[0084] In the contact area between the indenter and the workpiece, the indenter head profile equation can be expressed as:

[0085]

[0086] Let x=0, z=0 in formula (10), point A(x A ,y A ,z A )、B(x B ,y B ,z B ) can be expressed as:

[0087] x A =0,y A =-h c tanα,z A =0(11);

[0088] x B =0,y B =h ctanα,z B =0(12);

[0089] The elastic recovery of the material will cause the difference between the scratch groove and the residual groove. Assume that the contour of the residual groove bottom in the yz plane is a part of a triangle.

[0090] The residual groove depth is h rc Let y=0、z=h in formula (10) rc , point C(x C ,y C ,z C )、C'(x C′ ,y C′ ,z C′ ) can be expressed as:

[0091] x C =(h rc -h c )tanα,y C =0,z C =h rc (13);

[0092] x C′ =0,y C′ =0,z C′ =h rc (14);

[0093] Then the surface ACC′ can be expressed as:

[0094] h rc yh c tanαz+h rc h c tanα=0(15);

[0095] Eliminating z from equations (10) and (15) gives the arc in the xy plane: The expression:

[0096]

[0097] arc It is the intersection of the workpiece surface and the indenter head, and its equation can be expressed as:

[0098]

[0099] Combining formulas (16) and (17), we can get A n :

[0100]

[0101] Combining formulas (11) and (14), we can get At :

[0102] A t =h c h rc tanα(19);

[0103] Micro shear area between the indenter and the workpiece It can be expressed as:

[0104]

[0105] Furthermore, the shear area A s It can be expressed as:

[0106]

[0107] Formulas (7)-(21) show that the contact area of the conical indenter (A n ,A t ,A s ) and the sharpness angle (α) of the indenter, the scratch depth (h c ) and residual groove depth (h rc )related.

[0108] The elastic recovery parameter of the workpiece is defined as μ = h rc / h c , formulas (18) and (19) can be simplified as:

[0109]

[0110]

[0111] Formulas (7)-(23) show that the contact area of the sharp indenter (A n ,A t ,A s ) and the sharp angle of the indenter (α), the scratch depth (h c ) and the elastic recovery parameter μ.

[0112] According to the above relationship, A n 、A t and A s Substituting the equation into equations (5) and (6), we obtain the equations for the deformation zone and subsurface microcrack depth caused by the conical indenter:

[0113]

[0114] Where μ = sinλ.

[0115] These equations show that the depth of the deformation zone (b) and the depth of the subsurface microcracks (c) can be determined by the workpiece material properties (E, H, Kc , μ), indenter sharpness angle (α) and scratch depth (h c ). Based on the relationship between the deformation zone depth and the subsurface microcrack depth, the subsurface microcrack depth (c) can be determined as:

[0116] c=K i b 4 / 3 (26);

[0117] Among them, K i Is a coefficient that is related to the workpiece material properties (elastic modulus E, hardness H, static fracture toughness K c , elastic recovery parameter μ) and the indenter sharpness angle α, and is calculated according to formulas (24) and (25):

[0118]

[0119] In step S3, the single crystal silicon wafer sample used for testing is cut from the center of the single crystal silicon wafer cut by diamond wire saw, such as Figure 4 As shown in (a), the nanoindentation experiment was conducted to measure the depth of the subsurface damage deformation zone. The nanomechanical properties testing system was used to perform an indentation experiment on a single crystal silicon wafer sample with a load of 10mN to 400mN. Figure 4 As shown in (b), an indentation experiment was performed using a Berkovich diamond indenter at room temperature, where the loading, holding, and unloading times were 20 seconds.

[0120] In steps S3-S4, corresponding data results are obtained through nanoindentation experiments and analyzed. Figure 5 is the load-displacement curve under 5 kinds of loads, where h m is the maximum imprint depth, h r is the residual depth. Figure 6 is the relationship between the imprint depth and the imprint load. Figure 7 The elastic recovery parameter μ and the maximum imprint load F are shown. m The relationship curve of F m As the value of μ increases, it decreases first (F m ≤200mN), then increase (F m ≥200mN), indicating that there is a turning point. Take F m The value is 100~200mN, corresponding to the maximum imprint depth h m The value is 4.1 to 7.4 μm, which can be regarded as the deformation zone depth b.

[0121] Furthermore, the subsurface microcrack depth is predicted by combining the theoretical relationship between the depth of the subsurface damage deformation zone and the depth of the subsurface microcrack in step S1. The relationship between the depth of the deformation zone (b) and the depth of the subsurface microcrack (c), i.e., Ki The value of the material properties (elastic modulus E, hardness H, static fracture toughness K c , elastic recovery parameter μ) and the indenter sharpness angle (α), and are calculated using the above formula.

[0122] Depend on Figure 7 As shown, the value of μ is approximately 0.35. Based on the 3D morphology of the abrasive particles, the sharpness angle α is preferably normally distributed between 46° and 82°, and is close to 66°. Based on this, the subsurface microcrack depth is predicted to be 5.8 to 11.3 μm. Because the subsurface damage depth is determined by the maximum subsurface microcrack depth, the predicted subsurface damage depth is 11.3 μm.

[0123] In step S6, in order to verify the effectiveness of the subsurface damage depth prediction method, a scanning electron microscope is used to observe the subsurface morphology of the processed single crystal silicon wafer. Figure 8 The subsurface morphology of a single-crystal silicon wafer sample is shown. The measured deformation zone depth ranges from 5.1 to 5.3 μm, which is within the 4.1 to 7.4 μm range measured in steps S3-S4. The median crack depth ranges from 7.7 to 11.0 μm, with a maximum value of 11.0 μm, which is very close to the subsurface damage depth of 11.3 μm in step (3), demonstrating the effectiveness of the proposed prediction method.

[0124] In a further embodiment, the following data optimization steps are included:

[0125] S71. Collect 20-50 sets of nanoindentation experimental data of single crystal silicon wafers under different process parameters (such as saw wire feed speed, saw wire speed, abrasive density, etc.) and different material properties (elastic modulus, hardness, fracture toughness, etc.), the predicted values of the subsurface damage deformation zone depth, the subsurface microcrack depth data and the actual value of the subsurface damage depth; the actual value can be the value measured in S6.

[0126] S72. Construct a neural network model based on the predicted value and the actual value of the data, preferably a multi-layer perceptron (MLP);

[0127] Among them, the predicted value, process parameters, and material properties are the input layer, and the actual value is the output layer;

[0128] S73, after obtaining the predicted subsurface microcrack depth data of the single crystal silicon wafer in S5, inputting the data into the neural network model;

[0129] The input data include nanoindentation experimental data, predicted values of subsurface damage deformation zone depth and subsurface microcrack depth data;

[0130] S74. The neural network model outputs the optimized predicted value of the subsurface microcrack depth.

[0131] By training the neural network model, the relationship between the subsurface damage deformation zone depth, the subsurface microcrack depth data prediction value and the actual subsurface damage depth under different process parameters and material properties is obtained, so as to optimize the prediction value and increase the accuracy of the detection results.

[0132] The prediction method of this application is mainly used to predict the sub-surface damage depth of single-crystal silicon wafers. The fine diamond wire saw cutting method used is only one of the processing methods. Based on the above method, the present invention can also be extended to predict the sub-surface damage depth of other brittle materials and adapt to other processing methods.

[0133] The above embodiments are merely preferred technical solutions of the present invention and should not be construed as limiting the present invention. The scope of protection of the present invention shall be the technical solutions set forth in the claims, including equivalent alternatives to the technical features of the technical solutions set forth in the claims. In other words, equivalent alternatives and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for predicting subsurface damage depth of a single crystal silicon wafer, characterized by: The steps include: S1. Based on the theory of indentation fracture mechanics, the theoretical relationship between the depth b of the subsurface damage deformation zone and the depth c of the subsurface microcracks after single crystal silicon wafer processing is obtained; S2. Processing the single crystal silicon ingot to obtain single crystal silicon wafers; S3. Perform nanoindentation experiments on single-crystal silicon wafers to obtain the elastic recovery parameter μ and the maximum imprint load F. m The relationship curve of S4. Calculate the depth b of the subsurface damage deformation zone of the processed single crystal silicon wafer through the inflection point of the curve; S5. Based on the obtained theoretical relationship, predict the subsurface microcrack depth c of the single crystal silicon wafer.

2. The method for predicting subsurface damage depth of a single crystal silicon wafer according to claim 1, wherein: The process of establishing the theoretical relationship in S1 is as follows: Use the indenter to scratch the workpiece, and according to the indentation fracture mechanics theory, the depth b of the deformation zone formed under the indenter and the depth c of the subsurface microcracks are obtained: Among them, E, H and K c are the elastic modulus, hardness and static fracture toughness of the workpiece material; α is the sharpness angle of the indenter; F n and F t are normal and tangential loads respectively; θ is the tilt angle; κ is the correction factor considering the elastic stress field; α k is a dimensionless number; According to θ, F n and F t The relationship is: Among them, A n and A t are the normal and tangential projected contact areas between the indenter and the workpiece, A s is the shear contact area between the indenter and the workpiece; Establish a Cartesian coordinate system Oxyz, where the origin is the intersection of the workpiece surface and the indenter rotation axis, the coordinate axis Ox is opposite to the scratching direction, and the direction of Oz is consistent with the indenter rotation axis. Mark point A (x A ,y A ,z A ) and point B(x B ,y B ,z B ), get A n 、A t and A s equation; According to A n 、A t and A s The equation of is used to determine the subsurface microcrack depth c through the relationship between the deformation zone depth and the subsurface microcrack depth: c=K i b 4 / 3 ; Among them, K i is a coefficient related to the workpiece material properties and the indenter sharpness angle α: Among them, λ is an intermediate variable, its value is λ=arcsinμ, and μ is the elastic recovery coefficient of the material.

3. The method for predicting subsurface damage depth of a single crystal silicon wafer according to claim 2, wherein: θ、F n and F t The relationship is:

4. The method for predicting subsurface damage depth of a single crystal silicon wafer according to claim 2, wherein: A s The equation is: Among them, h c is the scratch depth.

5. The method for predicting subsurface damage depth of a single crystal silicon wafer according to claim 2, wherein: A t The equation is:

6. The method for predicting subsurface damage depth of a single crystal silicon wafer according to claim 2, wherein: A n The equation is:

7. The method for predicting subsurface damage depth of a single crystal silicon wafer according to claim 1, wherein: In S3 , a single crystal silicon wafer for inspection is cut from the center of the processed single crystal silicon wafer.

8. The method for predicting subsurface damage depth of a single crystal silicon wafer according to claim 1, wherein: The subsurface damage depth is the maximum subsurface microcrack depth.

9. The method for predicting subsurface damage depth of a single crystal silicon wafer according to claim 1, wherein: After S5, it also includes: S6. Use a scanning electron microscope to observe the subsurface morphology of the processed single-crystal silicon wafer and measure the subsurface microcrack depth, which is compared with the predicted value to verify the effectiveness of the subsurface damage depth prediction method.

10. The method for predicting subsurface damage depth of a single crystal silicon wafer according to claim 1, wherein: The data optimization steps include the following: S71. Collect 20-50 sets of nanoindentation experimental data of single crystal silicon wafers with different process parameters and different material properties, and the predicted values of the subsurface damage deformation zone depth, subsurface microcrack depth data, and the actual values of the subsurface damage depth; S72. Construct a neural network model based on the predicted value and actual value of the data; S73, after obtaining the predicted subsurface microcrack depth data of the single crystal silicon wafer in S5, inputting the data into the neural network model; S74. The neural network model outputs the optimized predicted value of the subsurface microcrack depth.

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