CN112861278B - Method for calculating length of initial cleavage crack of semiconductor material - Google Patents

Method for calculating length of initial cleavage crack of semiconductor material Download PDF

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CN112861278B
CN112861278B CN202110051691.8A CN202110051691A CN112861278B CN 112861278 B CN112861278 B CN 112861278B CN 202110051691 A CN202110051691 A CN 202110051691A CN 112861278 B CN112861278 B CN 112861278B
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initial cleavage
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高睿
姜晨
黄鹏辉
蒋金鑫
郎小虎
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University of Shanghai for Science and Technology
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Abstract

The invention designs a method for calculating the length of an initial cleavage crack of a semiconductor material, which comprises the following steps: firstly, determining the optimal cleavage crystal orientation according to the unit cell structure of the semiconductor material, secondly, calculating the mechanical parameters (elastic modulus and Poisson's ratio) and fracture toughness of key materials of the crystal orientation, and finally, combining a stress intensity factor and a fracture toughness formula to obtain the initial cleavage crack length of the optimal cleavage crystal orientation.

Description

Method for calculating length of initial cleavage crack of semiconductor material
Technical Field
The invention relates to a method for calculating the length of an initial cleavage crack of a semiconductor material, and belongs to the technical field of semiconductor optoelectronic device processes.
Background
With the rapid development of semiconductor and photoelectric technologies, semiconductor lasers are widely used in the fields of data communication, laser medicine, laser processing and the like due to a series of advantages of high efficiency, small size, low cost, high reliability and the like. The semiconductor material has high electron mobility and is a direct band gap, and the resonant cavity surface which is taken as the substrate material is taken as a key component of the semiconductor laser, so that the performance and the reliability of the semiconductor laser are greatly influenced.
Meanwhile, the method has the advantages of mechanical cleavage, high efficiency and good universality, and is gradually one of important methods for preparing the resonant cavity surface of the laser at present. Cleavage is the splitting of a material along one or several parallel planes when the material is subjected to directed mechanical stresses, these split planes being referred to as cleavage planes. However, the existing cleavage processing process is often accompanied with technical defects such as cleavage surface damage and the like, which causes problems such as formation of corrugated cracks on the cavity surface after cleavage, too small effective cleavage size and the like, and limits the application range of the laser to a certain extent. In order to further master the cleavage processing mechanism of the resonant cavity surface, improve the cleavage processing quality, and promote the development of the ultra-precision cleavage processing technology, it is very important to calculate the cleavage crystal directions of different semiconductor materials and the initial cleavage crack lengths of the crystal directions.
Disclosure of Invention
The invention aims to provide a method for calculating the initial cleavage crack length of a semiconductor material, which accurately calculates the initial cleavage crack length of the optimal cleavage processing crystal orientation which meets the various requirements simultaneously by considering the influence of a variable-angle slicing knife in cleavage equipment on the initial cleavage crack length due to different unit cell structures of different semiconductor materials and obvious anisotropy of material mechanical parameters, and fills the gap of theoretical research of the cleavage processing.
In order to achieve the purpose, the technical scheme of the invention comprises the following steps:
step 1: and determining the cleavage crystal orientation. Combining the unit cell structure of the semiconductor material, calculating the plane spacing of each crystal plane of different materials to obtain the optimal cleavage crystal direction (i.e. the crystal direction corresponding to the crystal plane with the largest plane spacing), wherein the plane spacing d is expressed as:
Figure BSA0000230937860000021
in the formula: ρ is the bulk density (i.e., the number of atoms contained in a unit volume of the unit cell); n is the number of atoms contained in a unit cell area; a and B are the length and width of the unit cell, respectively.
Step 2: the initial cleavage crack length was calculated.
(1) Normal line load p (x). In the dicing process of the cleavage processing, since the dicing blade is in the shape of a quadrangular pyramid, the load between the blade and the workpiece is actually uniformly distributed in a triangular shape. Meanwhile, a two-dimensional rectangular coordinate system is established by taking the contact point of the tool bit tip and the workpiece as an original point O, and the obtained normal load P (x) is as follows:
Figure BSA0000230937860000022
in the formula: l is half of the diagonal length of the cutter head profile; theta is the vertex angle of the cutter head; and P is a preset normal load.
(2) Projected contact area A of tool bit and workpieces. Based on pyramid-shaped tool bit contactEmpirical formula of area, machining method in scribing process, tool bit corner and contact area AsExpressed as:
Figure BSA0000230937860000023
in the formula: n is a fitting coefficient; omega is the tool bit deflection angle.
(3) And calculating key mechanical parameters of the anisotropic material. Based on generalized hooke's law, the elastic modulus E and poisson's ratio μ of a material in a unit cell are calculated from equations (4) and (5), respectively.
Figure BSA0000230937860000024
Figure BSA0000230937860000025
In the formula: s11、S12、S44The coefficient is a flexibility coefficient and can be obtained by calculation of a stress-strain matrix; l is the vector in any direction in the unit cell, l1＝sinαcosβ、l2＝sinαsinβ、l3Sin α is the component of the vector on the X, Y, Z axis, l1+l2+l3＝1，l1、l2、l3∈[0，1](ii) a m is an arbitrary vector perpendicular to the l vector, m1＝cosαcosβcosγ-sinβsinγ、m2＝cosαsinβcosγ+cosβsinγ、m3The components of the vector on the X, Y, Z axis, m, are sin β cos γ, respectively1+m2+m3＝1，m1、m2、m3∈[0，1]. Composite modulus of elasticity ErThe mechanical properties of the material are more accurately reflected by comprehensively considering the elastic modulus and the Poisson ratio of the workpiece material and the tool bit material, the calculation method is shown in formula (6), and the hardness H is measured by normal line load P (x) and projection contact area AsCalculated as shown in equation (7).
Figure BSA0000230937860000031
H＝P(x)/As (7)
In the formula: ejAnd mujThe modulus of elasticity and the poisson's ratio of the cutter head are respectively.
(4) Fracture toughness KIC. The fracture toughness plays a key role in the cleavage processing, which directly influences the initial cleavage crack length and the subsequent cleavage surface morphology in the scribing process, and the fracture toughness KICCalculated by the formula (8).
Figure BSA0000230937860000032
In the formula: a is1、b1、c1And a2、b2、c2Are all fitting coefficients.
(5) Initial cleavage crack length c. According to the stress intensity factor K of the initial cleavage crack, when the stress intensity factor K is equal to the fracture toughness KICI.e. K ═ KICAn initial cleave crack length is obtained. In addition, since z is 0.5x + nP in the coordinate system, the stress intensity factor K is as shown in equation (10).
Figure BSA0000230937860000033
In the formula: c is the initial cleavage crack length. Then, the initial cleavage crack length c is calculated by combining the formulas (8) and (9) and is shown in the formula (10).
Figure BSA0000230937860000034
The invention has the advantages that: aiming at the problem that different semiconductor materials need a large number of process experiments to determine the optimal cleavage crystal orientation and the optimal process parameters, the method can quickly determine the initial cleavage crack length of the optimal cleavage crystal orientation of the semiconductor materials under different process parameters, provide reliable theoretical basis for the process parameters, and fill in the gap of theoretical research in cleavage processing.
Drawings
FIG. 1 is a schematic flow chart of a method for calculating the initial cleavage crack length of a semiconductor material according to the present invention;
FIG. 2 is a schematic view of an atomic arrangement of GaAs crystal faces in a calculation method for the initial cleavage crack length of a semiconductor material according to the present invention;
FIG. 3 is a schematic view of the calculation method of the initial cleavage crack length l and the m vector of the semiconductor material according to the present invention;
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings. For gallium arsenide (GaAs) semiconductor materials as an example, a rectangular pyramid diamond knife with a vertex angle of 140 degrees is selected as a scribing cutter head, and the length of the diagonal line of the profile is 20 micrometers. The calculation flow is shown in fig. 1.
Step 1: and determining the cleavage crystal orientation. The unit cell of GaAs semiconductor material is a face-centered cubic structure with bulk density rho of 4/b3(b is unit cubic unit cell side length). Through the formula (1), the interplanar distances d of the (100), (110) and (110) crystal planes (the atomic arrangement is shown in the figure (2)) are calculated to be b, 1.41b and 0.87b respectively, the interplanar distance value of the (110) crystal plane is maximum, and the (110) crystal plane is the best cleavage plane of the GaAs material and corresponds to the [110 ] crystal plane]The crystal orientation is the best cleavage crystal orientation.
Figure BSA0000230937860000041
In the formula: ρ is the bulk density (i.e., the number of atoms contained in a unit volume of the unit cell); n is the number of atoms contained in a unit cell area; a and B are the length and width of the unit cell, respectively.
Step 2: the initial cleavage crack length was calculated.
(1) Normal line load p (x). In the dicing process of the cleavage processing, since the dicing blade is in the shape of a quadrangular pyramid, the load between the blade and the workpiece is actually uniformly distributed in a triangular shape. Meanwhile, a two-dimensional rectangular coordinate system is established by taking the contact point of the tool bit tip and the workpiece as an original point O, and the obtained normal load P (x) is as follows:
Figure BSA0000230937860000042
in the formula: l is half of the diagonal length of the cutter head profile; theta is the vertex angle of the cutter head; and P is a preset normal load.
(2) Projected contact area A of tool bit and workpieces. Based on the empirical formula of the contact area of the pyramid-shaped tool bit, the processing method in the scribing process, the tool bit corner and the contact area A are combinedsExpressed as:
Figure BSA0000230937860000043
in the formula: n is a fitting coefficient; omega is the tool bit deflection angle.
(3) And calculating key mechanical parameters of the anisotropic material. Based on generalized Hooke's law, GaAs (100) crystal plane [110 ]]The elastic modulus E and poisson's ratio μ of the material on the cleaved crystal can be calculated from equations (4) and (5), respectively. Wherein the GaAs material has a flexibility coefficient S11、S12、S44Are respectively 11.7e-12Pa、3.7e-7Pa、16.8e-12Pa, and the vector diagrams of l and m in the unit cell are shown in FIG. 3.
Figure BSA0000230937860000051
Figure BSA0000230937860000052
Is calculated to obtain [110]The crystal-direction elastic modulus and the poisson ratio were 141.9Gpa and 0.19, respectively. Modulus of elasticity E of diamond segmentsjAnd poisson ratio muj1140GPa and 0.07 respectively, and the above values are substituted into the formula (6) to obtain the composite elastic modulus Er129.9GPa, and the hardness H of the material can be calculated by the formula (7)And (5) calculating to obtain.
Figure BSA0000230937860000053
H＝P(x)/As (7)
(4) Fracture toughness KIC. The fracture toughness plays a key role in the cleavage processing, which directly influences the initial cleavage crack length and the subsequent cleavage surface morphology in the scribing process, and the fracture toughness KICCalculated by the formula (8).
Figure BSA0000230937860000054
In the formula: a is1、b1、c1And a2、b2、c2Are all fitting coefficients.
(5) Initial cleavage crack length c. According to the stress intensity factor K of the initial cleavage crack, when the stress intensity factor K is equal to the fracture toughness KICI.e. K ═ KICAn initial cleave crack length is obtained. In addition, since z is 0.5x + nP in the coordinate system, the stress intensity factor K is as shown in equation (10).
Figure BSA0000230937860000055
In the formula: c is the initial cleavage crack length. Then, by combining equations (8) and (9), the initial cleavage crack length c is calculated as shown in equation (10) assuming that the tool tip completely cuts into the material, i.e., x is 0 and L is 10 μm.
Figure BSA0000230937860000056

Claims (1)

1. A method for calculating the length of an initial cleavage crack of a semiconductor material is characterized by comprising the following steps:
step 1: determining cleavage crystallographic direction
Combining the unit cell structure of the semiconductor material, calculating the plane spacing of each crystal plane of different materials to obtain the optimal cleavage crystal direction (i.e. the crystal direction corresponding to the crystal plane with the largest plane spacing), wherein the plane spacing d is expressed as:
Figure FSB0000198252870000011
in the formula: ρ is the bulk density (i.e., the number of atoms contained in a unit volume of a unit cell), N is the number of atoms contained in a unit cell area, and a and B are the length and width of the unit cell, respectively;
step 2: calculating initial cleavage crack length
(1) Normal line load P (x)
In the scribing process of the cleavage processing, because the scribing cutter head is in a quadrangular pyramid shape, the load between the cutter head and the workpiece is actually uniformly distributed in a triangular shape, and meanwhile, a two-dimensional rectangular coordinate system is established by taking the contact point of the cutter head tip and the workpiece as an original point O, and the obtained normal line load P (x) is as follows:
Figure FSB0000198252870000012
in the formula: l is half of the length of a diagonal line of the tool bit profile, theta is a tool bit vertex angle, and P is a preset normal load;
(2) projected contact area A of tool bit and workpieces
Based on the empirical formula of the contact area of the pyramid-shaped tool bit, the processing method in the scribing process, the tool bit corner and the contact area A are combinedsExpressed as:
Figure FSB0000198252870000013
in the formula: n is a fitting coefficient, and omega is a tool bit deflection angle;
(3) calculating key mechanical parameters of anisotropic material
Based on generalized hooke's law, the elastic modulus E and poisson's ratio μ of a material in a unit cell are calculated by equations (4) and (5), respectively:
Figure FSB0000198252870000014
Figure FSB0000198252870000015
in the formula: s11、S12、S44The coefficient is a flexibility coefficient and can be obtained by calculation of a stress-strain matrix; l is the vector in any direction in the unit cell, l1＝sinαcosβ、l2＝sinαsinβ、l3Sin α is the component of the vector on the X, Y, Z axis, l1+l2+l3＝1，l1、l2、l3∈[0，1](ii) a m is an arbitrary vector perpendicular to the l vector, m1＝cosαcosβcosγ-sinβsinγ、m2＝cosαsinβcosγ+cosβsinγ、m3The components of the vector on the X, Y, Z axis, m, are sin β cos γ, respectively1+m2+m3＝1，m1、m2、m3∈[0，1](ii) a Composite modulus of elasticity ErThe mechanical properties of the material are more accurately reflected by comprehensively considering the elastic modulus and the Poisson ratio of the workpiece material and the tool bit material, the calculation method is shown in formula (6), and the hardness H is measured by normal line load P (x) and projection contact area AsCalculated as shown in equation (7):
Figure FSB0000198252870000021
H＝P(x)/As (7)
in the formula: ejAnd mujRespectively the elastic modulus and the Poisson ratio of the cutter head;
(4) fracture toughness KIC
Fracture toughness plays a key role in the cleavage processingSo that the initial cleavage crack length and the subsequent cleavage surface morphology in the scribing process, the fracture toughness KICCalculated by equation (8):
Figure FSB0000198252870000022
in the formula: a is1、b1、c1And a2、b2、c2Are all fitting coefficients;
(5) initial cleavage crack length c
According to the stress intensity factor K of the initial cleavage crack, when the stress intensity factor K is equal to the fracture toughness KICI.e. K ═ KICThe initial cleavage crack length is obtained, and in addition, z is 0.5x + nP in the coordinate system, so the stress intensity factor K is as shown in formula (9):
Figure FSB0000198252870000023
in the formula: c is the initial cleavage crack length, and then the initial cleavage crack length c is calculated by combining the formulas (8) and (9) and is shown as a formula (10):
Figure FSB0000198252870000031
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CN100402413C (en) * 2005-08-24 2008-07-16 中国科学院金属研究所 Prefabricated method for thin film microcrack and special apparatus for the same
US8993410B2 (en) * 2006-09-08 2015-03-31 Silicon Genesis Corporation Substrate cleaving under controlled stress conditions
US20150258769A1 (en) * 2014-02-05 2015-09-17 John Farah Rapid Thinning of GaN and SiC Substrates and Dry Epitaxial Lift-off
US9718215B2 (en) * 2015-04-15 2017-08-01 Halo Industries, Inc. Capacitive clamping process for cleaving work pieces using crack propagation

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US5240670A (en) * 1991-08-22 1993-08-31 Texas Instruments Incorporated Method of improving the mechanical properties of semiconductor materials

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