A method for characterizing wafer bonding strength

Abstract

The present invention discloses a wafer bond strength characterization method, which relates to the field of wafer bond testing. The method comprises: building a three-dimensional test model of interface fracture mechanics, analyzing the total deflection and shear modulus generated by the loading point during the test, and generating a compliance simulation calculation model corresponding to the three-dimensional test model in combination with the crack length; optimizing the compliance simulation calculation model based on the actual model state of the wafer bonding to obtain a compliance calculation model, and constructing an energy release rate calculation model in combination with the relationship between compliance and crack length; loading the bonded sample using a tensile testing machine, analyzing the peak load of the bonded sample according to the loading result, and obtaining the bond strength of the bonded sample in combination with the compliance calculation model and the energy release rate calculation model. The present invention calculates the crack length using the sample compliance obtained through the experiment, and substitutes it into the compliance calculation model and the energy release rate calculation model to obtain the bond strength characterization result. The measurement method is simple and the measurement result is more accurate.

Description

Technical Field

[0001] The present invention relates to the field of wafer bonding testing, and in particular to a method for characterizing wafer bonding strength. Background Art

[0002] Wafer bonding is a key technology in semiconductor manufacturing, mainly used to permanently combine two or more wafers with high precision. This process is particularly important in the fields of three-dimensional integrated circuits (3D ICs), micro-electromechanical systems (MEMS), optoelectronic devices, etc.

[0003] Traditional wafer bonding strength testing methods such as Figure 9 As shown, it is also called the blade insertion method. This method uses a wedge-shaped blade to insert into the wafer bonding interface. The length of the crack after the blade is inserted is observed by a CCD camera to calculate the bond strength. After the blade is inserted, the crack extension is a dynamic process, but due to S i The specimen arm is relatively rigid, resulting in relatively small deflection during the insertion process, which makes it difficult to effectively measure the crack length. At the same time, the measurement of crack length is also relatively subjective, which can easily lead to large errors in the measurement results.

[0004] Currently, no effective solutions have been proposed for the problems in related technologies. Summary of the Invention

[0005] In response to the problems in the related art, the present invention proposes a wafer bonding strength characterization method to overcome the above technical problems existing in the existing related art.

[0006] To this end, the specific technical solutions adopted in the present invention are as follows:

[0007] A wafer bonding strength characterization method, the characterization method comprising:

[0008] Build a three-dimensional test model for interface fracture mechanics, analyze the total deflection and shear modulus generated at the loading point during the test, and generate a compliance simulation model corresponding to the three-dimensional test model based on the crack length;

[0009] Based on the actual model state of wafer bonding, the compliance simulation calculation model is optimized to obtain the compliance calculation model. In combination with the relationship between compliance and crack length, the energy release rate calculation model is constructed.

[0010] The bonded samples were loaded using a tensile testing machine. The peak load of the bonded samples was analyzed based on the loading results. The bond strength of the bonded samples was obtained by combining the compliance calculation model and the energy release rate calculation model.

[0011] Preferably, a three-dimensional test model of interface fracture mechanics is constructed, the total deflection and shear modulus generated at the loading point during the test are analyzed, and a compliance simulation calculation model corresponding to the three-dimensional test model is generated in combination with the crack length, including:

[0012] Based on the interface fracture resistance characterization technology, a three-dimensional test model was built to perform fracture mode testing. The distance from the end of the pull ring to the front end of the initial crack and the pull ring length in the three-dimensional test model were obtained to calculate the crack length.

[0013] The Euler-Bernoulli technique and Winkler theory are used to adjust the test state of the 3D test model, obtain the elastic modulus and section moment of inertia of the beam in the transverse direction, and determine the beam deflection function of the 3D test model based on the elastic modulus and section moment of inertia.

[0014] The deflections of any two groups of load points during the fracture mode test are calculated based on the beam deflection function and the elastic foundation beam model, and a total deflection calculation function is generated. The total deflection calculation function is then modified based on the additional effect of shear deformation and the shear modulus.

[0015] The foundation modulus of the beam is analyzed based on the interface expansion of the crack, and the foundation modulus of the adhesion layer is calculated according to the stress change of the adhesion layer. Combined with the total deflection calculation function, a compliance simulation calculation model corresponding to the three-dimensional test model is generated.

[0016] Preferably, the foundation modulus of the beam is analyzed based on the interface expansion of the crack, and the foundation modulus of the adhesion layer is calculated according to the stress change of the adhesion layer. The compliance simulation calculation model corresponding to the three-dimensional test model is generated in combination with the total deflection calculation function, including:

[0017] Based on the interface extension of the crack, the foundation modulus of the beam and the adhesion layer in series is defined, the elastic model of the beam in the longitudinal direction is analyzed, and the foundation modulus of the beam is calculated;

[0018] The lateral stress of the adhesion layer is calculated based on the Poisson's ratio and width of the adhesion layer, the foundation modulus of the adhesion layer is analyzed, and the deflection calculation function of the upper and lower beams in the 3D test model is obtained in combination with the 3D test model structure;

[0019] The total deflection of the three-dimensional test model at any loading point is calculated based on the deflection calculation function of the upper and lower beams, and a compliance simulation calculation model corresponding to the three-dimensional test model is generated according to the total deflection.

[0020] Preferably, the deflection calculation function of the upper and lower beams is expressed as:

[0021] ;

[0022] ;

[0023]

[0024] Where, δ represents the deflection of the upper and lower beams, represents the deflection of the upper beam in the 3D test model, represents the deflection of the lower beam in the 3D test model, m and n Represent the upper beam and the lower beam respectively. b represents the width of the cantilever beam in the 3D test model, c represents the distance from the initial crack front to the end of the model in the three-dimensional test model, l Indicates the distance from the end of the pull ring to the front end of the initial crack, P represents the load applied to the beam, E x Indicates that the beam is x Elastic modulus in the axial direction, I i represents the section moment of inertia, λ i represents a function of foundation modulus, elastic modulus and section moment of inertia, a represents the crack length, d Indicates the length of half the pull ring in the three-dimensional test model, h represents the thickness of the single-sided cantilever beam in the three-dimensional test model, G xy represents the shear modulus of the cantilever beam in the 3D test model.

[0025] Preferably, optimizing the compliance simulation calculation model based on the actual model state of wafer bonding to obtain the compliance calculation model, and combining the relationship between compliance and crack length to construct the energy release rate calculation model includes:

[0026] Based on the actual model state of wafer bonding, the silicon wafer is used as the beam on both sides of the three-dimensional test model, silicon dioxide is used as the adhesion layer, and the Young's modulus and Poisson's ratio of the wafer bonding are combined to optimize the compliance simulation calculation model;

[0027] Based on the functional relationship between compliance and crack length, a calculation function for the released energy per unit area of ​​interface crack extension in a three-dimensional test model is defined. The released energy calculation function is optimized in combination with the bonding model of wafer bonding to obtain an energy release rate calculation model.

[0028] Preferably, the expression of the compliance calculation model is:

[0029] ;

[0030] Where, C represents compliance, E s represents the Young's modulus of silicon, I2 represents the area moment of inertia of the second part of the three-dimensional test model, λ o Functions representing foundation modulus, elastic modulus, and section moment of inertia, a represents the crack length, d Indicates the length of half the pull ring in the three-dimensional test model, b represents the width of the cantilever beam in the 3D test model, G s represents the shear modulus of silicon, h represents the thickness of the single-sided cantilever beam in the 3D test model.

[0031] Preferably, the expression of the energy release rate calculation model is:

[0032] ;

[0033] Where, G represents the energy release rate, P represents the load applied to the beam, E s represents the Young's modulus of silicon, I 2 represents the area moment of inertia of the second part of the three-dimensional test model, λ o Functions representing foundation modulus, elastic modulus, and section moment of inertia, b represents the width of the cantilever beam in the 3D test model, a represents the crack length, d Indicates the length of half the pull ring in the three-dimensional test model, G s represents the shear modulus of silicon, h represents the thickness of the single-sided cantilever beam in the 3D test model.

[0034] Preferably, the bonding sample is loaded using a tensile testing machine, the peak load of the bonding sample is analyzed according to the loading result, and the bonding strength of the bonding sample is obtained by combining the compliance calculation model and the energy release rate calculation model.

[0035] After placing the bonded sample in the tensile testing machine fixture, set the loading rate to perform the loading operation, observe the loading process until the load decreases, and then unload the bonded sample to return the bonded sample to its initial position;

[0036] Repeat the loading operation until the bonded sample is completely separated, then stop the loading operation, upload the loading process data to a data storage device, and generate a load-displacement curve based on the loading process data;

[0037] The load-displacement curve is analyzed to obtain the compliance of the bonded sample. The compliance calculation model and the energy release rate calculation model are combined to calculate the crack length of the test sample and obtain the corresponding bond strength.

[0038] .

[0039] Preferably, analyzing the load-displacement curve to obtain the compliance of the bonded sample, and combining the compliance calculation model with the energy release rate calculation model to calculate the crack length of the test sample, and obtaining the corresponding bond strength includes:

[0040] Analyze the linear state of the rising portion of the load-displacement curve, determine the slope of the load-displacement curve based on the linear state, and determine the compliance of the bonded sample based on the slope;

[0041] Obtain the peak load corresponding to the highest point of the load-displacement curve, and substitute the compliance into the compliance calculation model to obtain the crack length of the bonded sample;

[0042] The crack length and peak load are substituted into the energy release rate calculation model to calculate the critical energy release rate and obtain the bond strength of the bonded sample.

[0043] The beneficial effects of the present invention are:

[0044] The present invention constructs a compliance calculation model and an energy release rate calculation model by constructing a three-dimensional test model, eliminating the need to measure the crack length. The crack length is calculated by the sample compliance obtained from the experiment, and is substituted into the compliance calculation model and the energy release rate calculation model to obtain the bond strength characterization result. The measurement method is simple and the measurement result is more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0046] Figure 1 is a flow chart of a method for characterizing wafer bonding strength according to an embodiment of the present invention;

[0047] Figure 2 is a schematic diagram of a fracture mode in a method for characterizing wafer bonding strength according to an embodiment of the present invention;

[0048] Figure 3 is a schematic diagram of a test model in a method for characterizing wafer bonding strength according to an embodiment of the present invention;

[0049] Figure 4 2 is a schematic diagram of an elastic foundation beam model in a method for characterizing wafer bonding strength according to an embodiment of the present invention;

[0050] Figure 5 is a schematic diagram of a bonding model in a method for characterizing wafer bonding strength according to an embodiment of the present invention;

[0051] Figure 6 1 is a schematic diagram of a fixture in a method for characterizing wafer bonding strength according to an embodiment of the present invention;

[0052] Figure 7 2. It is a schematic diagram of a tensile test in a method for characterizing wafer bonding strength according to an embodiment of the present invention;

[0053] Figure 8 1 is a schematic diagram of a load-displacement curve in a method for characterizing wafer bonding strength according to an embodiment of the present invention;

[0054] Figure 9 Schematic diagram of a blade insertion method in a method for characterizing wafer bonding strength according to an embodiment of the present invention. DETAILED DESCRIPTION

[0055] To further illustrate each embodiment, the present invention provides drawings, which are part of the disclosure of the present invention. They are mainly used to illustrate the embodiments and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. By referring to these contents, ordinary technicians in this field should be able to understand other possible implementation methods and the advantages of the present invention.

[0056] According to an embodiment of the present invention, a method for characterizing wafer bonding strength is provided.

[0057] The present invention will now be further described with reference to the accompanying drawings and specific embodiments. Figure 1 As shown, according to the wafer bonding strength characterization method of an embodiment of the present invention, the characterization method includes:

[0058] Step S1: construct a three-dimensional test model for interface fracture mechanics, analyze the total deflection and shear modulus generated at the loading point during the test, and generate a compliance simulation calculation model corresponding to the three-dimensional test model in combination with the crack length;

[0059] Step S2, optimizing the compliance simulation calculation model based on the actual model state of wafer bonding to obtain a compliance calculation model, and constructing an energy release rate calculation model based on the relationship between compliance and crack length;

[0060] Step S3: Loading the bonded sample using a tensile testing machine, analyzing the peak load of the bonded sample based on the loading result, and obtaining the bond strength of the bonded sample by combining the compliance calculation model and the energy release rate calculation model.

[0061] In one embodiment, in the process of constructing a three-dimensional test model for interface fracture mechanics, analyzing the total deflection and shear modulus generated at the loading points during the test, and generating a compliance simulation calculation model corresponding to the three-dimensional test model in combination with the crack length, the three-dimensional test model can be constructed based on the interface fracture resistance characterization technology, a fracture mode test can be performed, and the distance from the end of the pull ring to the front end of the initial crack and the pull ring length in the three-dimensional test model can be obtained to calculate the crack length; the test state of the three-dimensional test model can be adjusted using the Euler Bernoulli technique and Winkler theory to obtain the elastic modulus and section moment of inertia of the beam in the transverse direction, and the beam deflection function of the three-dimensional test model can be determined based on the elastic modulus and section moment of inertia; the deflections of any two groups of load points during the fracture mode test can be calculated based on the beam deflection function and the elastic foundation beam model to generate a total deflection calculation function, and the total deflection calculation function can be corrected based on the additional effect of shear deformation and the shear modulus; the foundation modulus of the beam can be analyzed based on the interface crack extension, and the foundation modulus of the adhesion layer can be calculated based on the stress change of the adhesion layer, and the compliance simulation calculation model corresponding to the three-dimensional test model can be generated in combination with the total deflection calculation function.

[0062] In one embodiment, in the process of analyzing the foundation modulus of the beam based on the interface expansion of the crack, calculating the foundation modulus of the adhesion layer according to the stress change of the adhesion layer, and generating the compliance simulation calculation model corresponding to the three-dimensional test model in combination with the total deflection calculation function, the foundation modulus of the beam and the adhesion layer in series can be defined based on the interface expansion of the crack, the elastic model of the beam in the longitudinal direction can be analyzed, and the foundation modulus of the beam can be calculated; the lateral stress of the adhesion layer can be calculated according to the Poisson's ratio and width of the adhesion layer, the foundation modulus of the adhesion layer can be analyzed, and the deflection calculation function of the upper and lower beams in the three-dimensional test model can be obtained in combination with the three-dimensional test model structure; the total deflection generated by the three-dimensional test model at any loading point can be calculated based on the deflection calculation function of the upper and lower beams, and the compliance simulation calculation model corresponding to the three-dimensional test model can be generated according to the total deflection.

[0063] In one embodiment, in the process of optimizing the compliance simulation calculation model based on the actual model state of wafer bonding to obtain the compliance calculation model, and combining the relationship between compliance and crack length to construct an energy release rate calculation model, the silicon wafer can be used as the beams on both sides of the three-dimensional test model according to the actual model state of wafer bonding, silicon dioxide can be used as the adhesion layer, and the compliance simulation calculation model can be optimized in combination with the Young's modulus and Poisson's ratio of wafer bonding; based on the functional relationship between compliance and crack length, the release energy calculation function corresponding to the unit area of ​​interface crack extension in the three-dimensional test model is defined, and the release energy calculation function is optimized in combination with the bonding model of wafer bonding to obtain the energy release rate calculation model.

[0064] In one embodiment, when loading the bonded sample using a tensile testing machine, analyzing the peak load of the bonded sample based on the loading results, and combining the compliance calculation model and the energy release rate calculation model to obtain the bonding strength of the bonded sample, after placing the bonded sample on the tensile testing machine fixture, the loading rate can be set to perform the loading operation, and the loading process can be observed until the load drops and the bonded sample is unloaded to return the bonded sample to its initial position; the loading operation is repeated until the bonded sample is completely separated and the loading operation is stopped, and the loading process data is uploaded to a data storage device, and a load-displacement curve is generated based on the loading process data; the load-displacement curve is analyzed to obtain the compliance of the bonded sample, and the crack length of the test sample is calculated in combination with the compliance calculation model and the energy release rate calculation model to obtain the corresponding bonding strength.

[0065] In one embodiment, in the process of analyzing the load-displacement curve, obtaining the compliance of the bonded sample, and calculating the crack length of the test sample by combining the compliance calculation model and the energy release rate calculation model to obtain the corresponding bonding strength, the linear state of the rising part of the load-displacement curve can be analyzed, and the slope of the load-displacement curve can be judged according to the linear state, and the compliance of the bonded sample can be determined based on the slope; the peak load corresponding to the highest point of the load-displacement curve is obtained, and the compliance is substituted into the compliance calculation model to obtain the crack length of the bonded sample; the crack length and the peak load are substituted into the energy release rate calculation model, the critical energy release rate is calculated, and the bonding strength of the bonded sample is obtained.

[0066] It should be explained that interface fracture mechanics is an effective method to characterize the fracture resistance of material interfaces and predict interface reliability. There are three main fracture modes of material interfaces (such as Figure 2 As shown in the figure), Type I: opening type, the normal stress is perpendicular to the crack surface, and the expansion direction is perpendicular to the normal stress; Type II: sliding type, the shear stress is parallel to the crack surface, and the expansion direction is parallel to the shear stress; Type III: tearing type, the shear stress is parallel to the crack front, and the expansion direction is perpendicular to the shear stress. The DCB method essentially measures the interfacial fracture energy when the phase angle is close to 0°, so the DCB test process can be regarded as a pure Type I fracture mode.

[0067] The test model proposed in this embodiment is as follows Figure 3 As shown in Figure 1, the total deflection acting at point A is equal to the superposition of part I (AB) and part II (BC), as shown in Equations 1 to 3 below:

[0068] ;

[0069] L = d +( l + c );

[0070] a = l + d ;

[0071] Where, δ A is the load point A The total deflection at It is the second part at point B The curl of a is the crack length; d It is half the length of the metal pull ring; l is the distance from the end of the metal pull ring to the front end of the initial crack; c is the distance from the initial crack front to the end of the sample; L is the distance from the loading point to the end of the sample, and Part I and Part II are respectively at point A 、 B Deflection at

[0072] Since the height to length ratio of part I is large, it cannot be calculated as a beam. After calculation, it was found that when the crack length is greater than 10mm If it is less than 1%, then the first part can be considered as rigid, i.e. ≈0, so the total deflection acting at the load point A becomes the following equation 4:

[0073] ;

[0074] According to the Euler-Bernoulli formula and Winkler theory, the sample arm on either side of the DCB model part II is regarded as a beam structure with a partial area free and the rest supported by the elastic foundation, as shown in Figure 4 As shown, the beam deflection α ( x ) can be established by the following equations 5 to 7:

[0075] ;

[0076] ;

[0077] ;

[0078] Where, E x It's Liang Zai x Elastic modulus in the axial direction, I x corresponds to x Section moment of inertia of the beam at position, k is the foundation modulus, It is a function of the foundation modulus, elastic modulus and section moment of inertia. The corresponding boundary conditions are as follows:

[0079] ;

[0080] Where, M l 、 S l are the bending moment and shear force at the left end of the beam, M r 、 S r are the bending moment and shear force at the right end of the beam, P is the load applied to the beam.

[0081] Then the deflection differential equation that satisfies the above boundary conditions is (- l ,0) and (0, c The solution within the range of ) is shown in Equation 9:

[0082] ;

[0083] The details are shown in the following equations 10 and 11:

[0084] ;

[0085] ;

[0086] It should be noted that A 、 B It is part of the solution to the above differential equation. It has no actual physical meaning. It just replaces the longer formula after the equation with a letter to simplify the form of the solution.

[0087] Combine Figure 4 The elastic foundation beam model shown in Equation 9 and the beam deflection equation can be obtained as well as The specific expressions are shown in Equations 12 and 13 below:

[0088] ;

[0089] ;

[0090] Combining Equation 3, Equation 4, Equation 12, and Equation 13, we can get δ A The specific expression of is shown in the following formula 14:

[0091] ;

[0092] Considering the additional influence of shear deformation in the cracked part of the sample, Equation 4-14 needs to be modified. According to the elasticity theory, a correction term caused by the shear effect is added to the right side of Equation 14. The rewritten expression is shown in Equation 15:

[0093] ;

[0094] Where, b is the width of the cantilever beam in the DCB model; h is the thickness of the single-sided cantilever beam in the DCB model; G xy is the shear modulus of the cantilever beam in the DCB model.

[0095] Observing Equation 15, we can find that the unknown variables include the foundation modulus k and crack length a ( l and c It can be transformed into a The crack length can be obtained by establishing a functional relationship with the compliance, and the compliance data can be measured by tensile tests. Therefore, the unknown variable in Equation 15 is essentially only the foundation modulus. k ,for Figure 3 In the DCB model, the beams on both sides are bonded together by an intermediate adhesive layer. The foundation modulus of the beam and the adhesive layer are defined as k 1 and k 2. Assume that the crack propagates along the interface between the upper beam and the adhesive layer, and consider the lower beam and the adhesive layer as a series spring system, as shown in Equations 16 and 17 below:

[0096] k t = k 1;

[0097] ;

[0098] Where, k t is the foundation modulus of the upper beam; k b is the foundation modulus of the series system of lower beam and adhesion layer.

[0099] In a typical beam-elastic foundation problem, the foundation modulus is completely independent of the beam parameters. However, in the DCB model, the elastic foundation compensates for the missing half of the beam, so the foundation modulus is not independent. Instead, its value is related to the half-height and width of the beam and is linked to the average transverse strain and transverse stress in the beam. The specific relationships are shown in Equations 18 to 20:

[0100] ;

[0101] ;

[0102] ;

[0103] Where, 、 are the transverse stress and transverse strain of the beam respectively; For Liang Zai y Elastic modulus in the direction.

[0104] According to Equation 18, Equation 19 and Equation 20, we can get k The expression of 1 is shown in Equation 21 below:

[0105] ;

[0106] By considering the stress-strain relationship of the adhesion layer, we can get k 2, assuming that the axial strain in the adhesion layer is suppressed, that is, =0, then according to Hooke's law under plane stress conditions and the foundation model established above, the following equations 22 to 24 can be obtained:

[0107] ;

[0108] ;

[0109] ;

[0110] In the above formula, 、 are the lateral stress and lateral strain of the adhesion layer, respectively; For the adhesion layer y Elastic modulus in the direction; 、 is the Poisson’s ratio of the adhesion layer; w is the width of the adhesion layer; t Half the thickness of the adhesion layer.

[0111] According to Equation 22, Equation 23 and Equation 24, we can get k The expression of 2 is shown in Equation 25 below:

[0112] ;

[0113] but k t 、 k bIt can be obtained by combining Equations 16, 17, 21, and 25. Then, combined with Equation 15, the deflection expressions of the upper and lower beams in the DCB model can be obtained, as shown in Equations 26 and 27 below:

[0114] ;

[0115] ;

[0116] Where, 、 are the deflections of the upper beam and lower beam in the DCB model, respectively.

[0117] The above-derived expressions for the deflection of the loading point are based on Figure 4 The single cantilever beam solution of the elastic foundation beam model. Considering that the DCB model is a double cantilever beam structure, the total deflection δ generated at the loading point should be the superposition of the deflections of the upper and lower beams, as shown in Equation 28:

[0118] ;

[0119] The total compliance of the DCB model is C It can be calculated according to the following formula 29:

[0120] ;

[0121] Where, δ represents the deflection of the upper and lower beams, represents the deflection of the upper beam in the 3D test model, represents the deflection of the lower beam in the 3D test model, m and n Represent the upper beam and the lower beam respectively. b represents the width of the cantilever beam in the 3D test model, c represents the distance from the initial crack front to the end of the model in the three-dimensional test model, l Indicates the distance from the end of the pull ring to the front end of the initial crack, P represents the load applied to the beam, E x Indicates that the beam is x Elastic modulus in the axial direction, I i represents the section moment of inertia, λ i represents a function of foundation modulus, elastic modulus and section moment of inertia, a represents the crack length, d Indicates the length of half the pull ring in the three-dimensional test model, h represents the thickness of the single-sided cantilever beam in the three-dimensional test model, G xyrepresents the shear modulus of the cantilever beam in the 3D test model.

[0122] The actual model for wafer bonding is S i / S i O 2 / S i Sandwich structure, so it can be S i The chip is considered as a beam, and the surface S i O The 2nd layer is considered as the middle adhesive layer. S i 、 S i O 2 is considered as a homogeneous material with equal width, then the relevant variables in the above expression can be further simplified as shown in the following equation 30:

[0123] ;

[0124] Where, E s 、 E o They are S i and S i O 2 Young's modulus, G s yes S i The shear modulus, v s 、 v o They are S i and Poisson's ratio of SiO2; I 2 for S i O 2 Sectional moment of inertia of part II in the model.

[0125] As shown in Equations 31 to 33 below:

[0126] ;

[0127] ;

[0128] ;

[0129] Then Equation 29 can be rewritten as shown in Equation 34:

[0130] ;

[0131] According to the content of fracture mechanics, the energy released per unit area by the interface crack extension of the DCB model is a function of the derivative of the compliance with respect to the crack length, as shown in Equation 35:

[0132] ;

[0133] From the above formula, we can calculate the energy release rate G The value of the compliance C Derivative the crack length a, from Equation 34 we can know C In the expression It's all about a Therefore, the calculation of its derivative is more complicated and some approximate processing is needed to simplify the calculation process. hour, The values ​​of are approximately equal to 1. This approximation is valid before the crack extends to the end of the DCB model. C and G The final expressions are shown in Equations 36 and 37 below:

[0134] ;

[0135] ;

[0136] Wafer bonding mainly includes S i - S i Bonding and S i O 2- S i O 2. The actual calculation model difference between the two types of bonding is mainly reflected in the foundation modulus of the upper and lower beams. k There is a difference. S i - S i Bonding, due to bare S i The native oxide layer on the surface is thin, so Figure 3 In the DCB model, the middle adhesion layer is considered to be thinner, that is, , substituting into formula 25, we can know ,Will k Substituting 2 into formula 17, we can get k b = k 1, therefore, for S i - Si For the bonded model, the foundation modulus of the upper and lower beams is equal to S i The foundation modulus of the beam is given by Equation 38 below:

[0137] ;

[0138] According to formula 7, it is applicable to S i - S i Bonding Model As shown in Equation 39:

[0139] ;

[0140] and S i - S i Bonding Model C and G The actual expression of is shown in Equations 40 and 41 below:

[0141] ;

[0142] ;

[0143] for S i O 2- S i O 2 bonding, S i Surface thermal growth S i O 2The membrane has a certain thickness, so it cannot be ignored in the calculation process. In fact, S i O 2- S i O The 2-bond model is not like Figure 3 The asymmetric structure of the upper and lower beams shown has a real crack propagation interface. S i O The middle interface of the 2nd layer, such as Figure 5 Therefore, S i O 2- S i O 2 In the bonded model, both the upper and lower beams can be considered as S iLiang Yu S i O 2 adhesive layers in series with the spring system, then S i O 2- S i O The foundation modulus in the 2-bond model is given by Equations 42 and 44:

[0144] ;

[0145] ;

[0146] ;

[0147] Similarly, combined with formula 7, we can get the S i O 2- S i O 2 Bonding Model The specific expression of is shown in Equation 45 below:

[0148] ;

[0149] but S i O 2- S i O 2 Bonding Model C and G The actual expression of is shown in Equations 46 and 47 below:

[0150] ;

[0151] ;

[0152] The specific test process is as follows: Place the bonded sample on the fixture of the precision tensile testing machine, such as Figure 6 As shown, the loading operation is then performed at a loading rate of 5 μm / s, causing the displacement of the load point to increase at a constant rate until the crack begins to expand. When the load decreases, the sample is unloaded to return to its initial position. The loading and unloading operations are then repeated until the sample is completely separated. The schematic diagram of the tensile test is shown in Figure 7 ,This process is recorded by a computer connected to the tensile machine to obtain the load-displacement curve, such as Figure 8The rising portion of the curve is approximately linear, and the inverse of its slope is the compliance of the test specimen. The highest point of the curve corresponds to the peak load, and the decreasing load corresponds to the crack propagation process. Substituting the experimentally obtained compliance into Equation 40 or Equation 46 to obtain the corresponding crack length, and then substituting the peak load and crack length into Equation 41 or Equation 47 to calculate the critical energy release rate, the bond strength can be obtained.

[0153] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A wafer bonding strength characterization method, characterized in that: The characterization methods include: Build a three-dimensional test model for interface fracture mechanics, analyze the total deflection and shear modulus generated at the loading point during the test, and generate a compliance simulation model corresponding to the three-dimensional test model based on the crack length; Based on the actual model state of wafer bonding, the compliance simulation calculation model is optimized to obtain the compliance calculation model. In combination with the relationship between compliance and crack length, the energy release rate calculation model is constructed. The bonded sample is loaded using a tensile testing machine. The peak load of the bonded sample is analyzed based on the loading results. The bond strength of the bonded sample is obtained by combining the compliance calculation model and the energy release rate calculation model. The construction of a three-dimensional test model for interface fracture mechanics, analysis of the total deflection and shear modulus generated at the loading point during the test, and generation of a compliance simulation calculation model corresponding to the three-dimensional test model in combination with the crack length include: Based on the interface fracture resistance characterization technology, a three-dimensional test model was built to perform fracture mode testing. The distance from the end of the pull ring to the front end of the initial crack and the pull ring length in the three-dimensional test model were obtained to calculate the crack length. The Euler-Bernoulli technique and Winkler theory are used to adjust the test state of the 3D test model, obtain the elastic modulus and section moment of inertia of the beam in the transverse direction, and determine the beam deflection function of the 3D test model based on the elastic modulus and section moment of inertia. The deflections of any two groups of load points during the fracture mode test are calculated based on the beam deflection function and the elastic foundation beam model, and a total deflection calculation function is generated. The total deflection calculation function is then modified based on the additional effect of shear deformation and the shear modulus. The foundation modulus of the beam is analyzed based on the interface expansion of the crack, and the foundation modulus of the adhesion layer is calculated based on the stress change of the adhesion layer. Combined with the total deflection calculation function, a compliance simulation calculation model corresponding to the three-dimensional test model is generated; The analysis of the foundation modulus of the beam based on the interface expansion of the crack, the calculation of the foundation modulus of the adhesion layer based on the stress change of the adhesion layer, and the generation of the compliance simulation calculation model corresponding to the three-dimensional test model in combination with the total deflection calculation function include: Based on the interface extension of the crack, the foundation modulus of the beam and the adhesion layer in series is defined, the elastic model of the beam in the longitudinal direction is analyzed, and the foundation modulus of the beam is calculated; The lateral stress of the adhesion layer is calculated based on the Poisson's ratio and width of the adhesion layer, the foundation modulus of the adhesion layer is analyzed, and the deflection calculation function of the upper and lower beams in the 3D test model is obtained in combination with the 3D test model structure; The total deflection of the three-dimensional test model at any loading point is calculated based on the deflection calculation function of the upper and lower beams, and the compliance simulation calculation model corresponding to the three-dimensional test model is generated according to the total deflection; The method of optimizing the compliance simulation calculation model based on the actual model state of wafer bonding to obtain the compliance calculation model and constructing the energy release rate calculation model based on the relationship between compliance and crack length includes: Based on the actual model state of wafer bonding, the silicon wafer is used as the beam on both sides of the three-dimensional test model, silicon dioxide is used as the adhesion layer, and the Young's modulus and Poisson's ratio of the wafer bonding are combined to optimize the compliance simulation calculation model; Based on the functional relationship between compliance and crack length, a calculation function for the energy released per unit area of ​​interface crack extension in a three-dimensional test model is defined. This function is then optimized using the wafer bonding model to obtain an energy release rate calculation model. The method of loading the bonded sample using a tensile testing machine, analyzing the peak load of the bonded sample according to the loading result, and obtaining the bond strength of the bonded sample by combining the compliance calculation model and the energy release rate calculation model includes: After placing the bonded sample in the tensile testing machine fixture, set the loading rate to perform the loading operation, observe the loading process until the load decreases, and then unload the bonded sample to return the bonded sample to its initial position; Repeat the loading operation until the bonded sample is completely separated, then stop the loading operation, upload the loading process data to a data storage device, and generate a load-displacement curve based on the loading process data; The load-displacement curve is analyzed to obtain the compliance of the bonded sample. The compliance calculation model and the energy release rate calculation model are combined to calculate the crack length of the test sample and obtain the corresponding bond strength.

2. The wafer bonding strength characterization method according to claim 1, wherein: The deflection calculation function of the upper and lower beams is expressed as follows: ； ； Where, δ represents the deflection of the upper and lower beams, represents the deflection of the upper beam in the 3D test model, represents the deflection of the lower beam in the 3D test model, m and n Represent the upper beam and the lower beam respectively. b represents the width of the cantilever beam in the 3D test model, c represents the distance from the initial crack front to the end of the model in the three-dimensional test model, l Indicates the distance from the end of the pull ring to the front end of the initial crack, P represents the load applied to the beam, E x Indicates that the beam is x Elastic modulus in the axial direction, I i represents the section moment of inertia, λ i represents a function of foundation modulus, elastic modulus and section moment of inertia, a represents the crack length, d Indicates the length of half the pull ring in the three-dimensional test model, h represents the thickness of the single-sided cantilever beam in the three-dimensional test model, G xy represents the shear modulus of the cantilever beam in the 3D test model.

3. The wafer bonding strength characterization method according to claim 2, wherein: The expression of the compliance calculation model is: ； Where, C represents compliance, E s represents the Young's modulus of silicon, I 2 represents the area moment of inertia of the second part of the three-dimensional test model, λ o Functions representing foundation modulus, elastic modulus, and section moment of inertia, a represents the crack length, d Indicates the length of half the pull ring in the three-dimensional test model, b represents the width of the cantilever beam in the 3D test model, G s represents the shear modulus of silicon, h represents the thickness of the single-sided cantilever beam in the 3D test model.

4. The wafer bonding strength characterization method according to claim 3, wherein: The expression of the energy release rate calculation model is: ； Where, G represents the energy release rate, P represents the load applied to the beam, E s represents the Young's modulus of silicon, I 2 represents the area moment of inertia of the second part of the three-dimensional test model, λ o Functions representing foundation modulus, elastic modulus, and section moment of inertia, b represents the width of the cantilever beam in the 3D test model, a represents the crack length, d Indicates the length of half the pull ring in the three-dimensional test model, G s represents the shear modulus of silicon, h represents the thickness of the single-sided cantilever beam in the 3D test model.

5. The wafer bonding strength characterization method according to claim 1, wherein: The loading rate is 5 μm / s.

6. The wafer bonding strength characterization method according to claim 1, wherein: The analysis of the load-displacement curve to obtain the compliance of the bonded sample, and combining the compliance calculation model with the energy release rate calculation model to calculate the crack length of the test sample to obtain the corresponding bond strength includes: Analyze the linear state of the rising portion of the load-displacement curve, determine the slope of the load-displacement curve based on the linear state, and determine the compliance of the bonded sample based on the slope; Obtain the peak load corresponding to the highest point of the load-displacement curve, and substitute the compliance into the compliance calculation model to obtain the crack length of the bonded sample; The crack length and peak load are substituted into the energy release rate calculation model to calculate the critical energy release rate and obtain the bond strength of the bonded sample.

Images