CN113779807A - Quantitative description method for Bi segregation degree at Sn-Bi solder interface based on addition of alloying element M - Google Patents
Quantitative description method for Bi segregation degree at Sn-Bi solder interface based on addition of alloying element M Download PDFInfo
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- 238000005204 segregation Methods 0.000 title claims abstract description 87
- 238000005275 alloying Methods 0.000 title claims abstract description 46
- 238000000034 method Methods 0.000 title claims abstract description 42
- 229910020830 Sn-Bi Inorganic materials 0.000 title claims abstract description 39
- 229910018728 Sn—Bi Inorganic materials 0.000 title claims abstract description 39
- 229910000679 solder Inorganic materials 0.000 title claims abstract description 29
- 238000009792 diffusion process Methods 0.000 claims abstract description 29
- 230000004913 activation Effects 0.000 claims abstract description 20
- 229910052797 bismuth Inorganic materials 0.000 claims abstract description 16
- 238000011160 research Methods 0.000 claims abstract description 7
- 229910020874 Sn-M Inorganic materials 0.000 claims abstract description 6
- 229910008890 Sn—M Inorganic materials 0.000 claims abstract description 6
- 229910052718 tin Inorganic materials 0.000 claims abstract description 6
- 238000007792 addition Methods 0.000 claims description 20
- 238000004364 calculation method Methods 0.000 claims description 8
- 230000015572 biosynthetic process Effects 0.000 claims description 7
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- 239000013078 crystal Substances 0.000 claims description 4
- 230000005764 inhibitory process Effects 0.000 claims description 4
- 229910020929 Sn-Sn Inorganic materials 0.000 claims description 3
- 229910008827 Sn—Sn Inorganic materials 0.000 claims description 3
- 230000004888 barrier function Effects 0.000 claims description 3
- 229910052802 copper Inorganic materials 0.000 claims description 3
- 229910052737 gold Inorganic materials 0.000 claims description 3
- 229910052738 indium Inorganic materials 0.000 claims description 3
- 230000005012 migration Effects 0.000 claims description 3
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- 229910052697 platinum Inorganic materials 0.000 claims description 3
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- 229910052787 antimony Inorganic materials 0.000 claims description 2
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- 229910045601 alloy Inorganic materials 0.000 abstract description 4
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- 229910016338 Bi—Sn Inorganic materials 0.000 description 1
- 229910000978 Pb alloy Inorganic materials 0.000 description 1
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- 229910020922 Sn-Pb Inorganic materials 0.000 description 1
- 229910008783 Sn—Pb Inorganic materials 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
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- LQBJWKCYZGMFEV-UHFFFAOYSA-N lead tin Chemical compound [Sn].[Pb] LQBJWKCYZGMFEV-UHFFFAOYSA-N 0.000 description 1
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- G—PHYSICS
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
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Abstract
The invention discloses a quantitative description method for Bi segregation degree at an Sn-Bi solder interface based on addition of an alloying element M, belonging to the technical field of microelectronic interconnection materials. By calculating two parameters of diffusion activation energy and segregation energy, the improvement effect of the added alloying elements on Bi segregation is theoretically and quantitatively evaluated. And finally, parameters such as the bond strength and the bond length among metal bonds of Sn-Bi and Sn-M, Bi-M, the charge transfer condition of M and surrounding Sn and Bi and the like are used as auxiliary verification parameters to evaluate the accuracy of the method. By the method, an important reference basis is provided for designing and preparing the Sn-Bi solder doped with a small amount of alloy elements to solve the Bi coarsening problem caused by Bi segregation at the interface in the future, the experimental workload is reduced, the research efficiency is improved, and the method has a high practical value.
Description
Technical Field
The invention belongs to the technical field of microelectronic interconnection materials, and particularly relates to a quantitative description method for Bi segregation degree at an Sn-Bi solder interface based on addition of an alloying element M.
Background
The microelectronic industry is an important industry promoting the technological progress and economic development all over the world, and with the continuous development of the microelectronic industry, microelectronic interconnection materials are used as materials for connecting electronic components and substrates and between the components and play a vital role in realizing the functions and reliably operating electronic products. Tin-lead (Sn-Pb) solder has been widely used as a microelectronic interconnect material in electronic packaging for reasons of low production cost, suitable operating temperature and good mechanical properties. But long-term use of toxic lead elements can harm human health and pollute the environment. Therefore, much research effort has been directed to achieving lead-free solder by manufacturing Sn-based binary alloys containing elements of Bi, Ag, In, Cu, Zn, and the like.
Among these potential candidates, the Sn — Bi eutectic alloy has a melting point of only 138 ℃, and has advantages in wettability, tensile strength, cost, and the like, compared to the Sn — Pb alloy. These properties make Sn-Bi alloys have great potential in particularly low temperature packaging operations. However, the Bi phase segregation enrichment in the packaging process is a key problem influencing the connection reliability of the Sn-Bi solder, and further influencing the wide application of the Sn-Bi solder in the field of electronic packaging. For the Sn-58Bi alloy, segregation of Bi at the solder-substrate interface is observed, forming a Bi-rich layer that is brittle in nature, which will lead to a reduction in the mechanical properties of the solder.
Although experiments have observed the presence of an interfacial Bi-rich phase in Sn-Bi solders, the underlying mechanism of Bi segregation is still unclear and no effective method to improve the enrichment of Bi phase segregation can be explored. Therefore, a quantitative description method is needed to theoretically evaluate the segregation degree of the material and accurately describe the improvement effect of the added alloying elements on the segregation degree of Bi in the Sn-Bi system. Aiming at the requirements, a quantitative description method for relieving Bi segregation degree at an Sn-Bi solder interface based on an additive element is provided. The method can provide important reference basis for designing and preparing the Sn-Bi solder which is doped with a small amount of alloy elements to improve the Bi coarsening problem caused by Bi segregation at the interface in future, is favorable for solving the bottleneck problem in the research of the microelectronic equipment interconnection material, reveals key factors influencing the performance of the Sn-Bi solder, reduces the experimental workload, improves the research efficiency and has stronger practical value.
Disclosure of Invention
In order to solve the problems, the invention provides a quantitative description method for Bi segregation degree at an Sn-Bi solder interface based on addition of an alloying element M, which comprises the following steps:
1) constructing a stable Sn surface model: constructing Sn surface models in different directions by using Sn primitive cell parameters, and selecting the most stable surface Sn (100) as a research object by taking surface energy as a judgment standard;
2) the main descriptors for quantifying the degree of Bi segregation on the Sn surface are proposed: bi is introduced into the most stable surface model of Sn, and the insertion position of Bi atoms is 1 to (n)General assembly-3) any one of the layers, in place of the Sn lattice in a thermodynamically stable position, using a quantum mechanical first principle approach:
a. simulating the outward precipitation process of Bi from the aspect of dynamics, and calculating the diffusion activation energy E of Bi atoms diffused on the surfaces of Sn at different layersdif；EdifThe lower the value of (b) is, the more easily the Bi atom diffuses in Sn;
b. calculating the segregation energy of Bi segregated to the surface of Sn in different layers from the thermodynamic angle on the aspect of energy
A negative value of (b) indicates that the segregation of Bi on the Sn surface is energetically favorable;
3) quantitative description of the degree of inhibition of Bi segregation by the added alloying element M: on the basis of the step 2), adding alloying elements into the Sn-Bi system in a form of replacing Sn atom lattice positions; in this state, the diffusion activation energy E is calculated again by the same method as that of step 2)dif′And segregation energy
I. Comparing the energy of the step 2) and the step 3):
by 2nd-1stFor example, if the Bi atom is from 2ndTo 1stDiffusion activation energy E ofdif′Diffusion activation energy Edif(ii) a The alloying element M has the function of inhibiting Bi atoms from diffusing on the surface of Sn, and finally has the function of improving the interface Bi segregation; if not, the method is not available;
if energy of segregation
The alloying element M has the function of improving the interface Bi segregation; if not, the method is not available;
comparing the energy levels of the different alloying element M additions:
Edifthe lower the value of (b) is, the more easily the Bi atom diffuses in Sn;
Said step 2) diffusion activation energy EdifAnd segregation energy
The calculation method comprises the following steps:
wherein ,EbIs the migration barrier energy of Bi atoms from the occupied Sn crystal lattice atom position to the adjacent vacant position;
wherein ,
is the total energy of a single Bi atom on the n atomic layer on the surface of Sn (100); n is 1 to (n)General assemblyInteger of/2 + 1); n isGeneral assemblyThe number of atomic layers of structured surface Sn (100).
Further, the number n of atomic layers of Sn (100) on the surface to be structuredGeneral assemblyAt least 9 layers, and a vacuum layer at least as thick as
The doped alloying element In the step 3) is Pt, Pd, Au, In, Ag, Sb, Ni, Ga, Al or Cu.
According to the verification method of the quantitative description method, compared with Sn-Bi, Sn-Sn and Bi-Bi metal bonds formed by analyzing the addition of the alloying element M, if the bond strength of the metal bonds after addition is enhanced and the bond length is reduced, the fact that the alloying element M can form stronger metal bonds with Bi atoms is proved, Bi is restrained in the Sn body, the segregation of Bi to the outside or the surface is prevented, and the formation of a Bi-rich phase is inhibited.
The invention has the beneficial effects that:
1. the invention provides a quantitative description method for relieving Bi segregation degree at an Sn-Bi solder interface based on an added element by utilizing a calculation simulation means. According to the two descriptors of the segregation degree (diffusion activation energy and segregation energy) and the corresponding calculation formula provided in the method, the segregation degree of Bi at the Sn-Bi solder interface can be intuitively measured. The method accurately evaluates the improvement condition of the alloying elements on the Bi segregation degree, screens out the elements which can effectively improve the Bi segregation at the interface in theory, purposefully obtains the alloying elements which can effectively improve the Bi segregation, greatly reduces the large-batch repetitive work, and further provides theoretical guidance for improving the embrittlement failure problem caused by the Bi segregation at the interface.
2. The quantitative description method for relieving the Bi segregation degree at the Sn-Bi solder interface based on the added elements, which is designed by the invention, quantitatively represents the Bi segregation degree theoretically by means of a first principle calculation method, greatly simplifies the experimental work, provides necessary theoretical basis and theoretical guidance for the component design of a novel solder, is beneficial to solving the bottleneck problem in the research of microelectronic equipment interconnection materials, thereby seeking technical breakthrough and promoting research and development production, and has important strategic significance for the application of Sn-Bi solder in the microelectronic packaging technology.
Drawings
FIG. 1 is a scheme in 1stA side view of Sn (100) into which Bi atoms and an alloying element M are introduced;
FIG. 2 shows the segregation energy of Bi in the presence of M atoms in the second layer of Sn (100);
FIG. 3 is a schematic diagram showing the bonding of Bi atoms to Sn (100);
FIG. 4 is a diagram showing the bonding of Bi atoms to Sn (100) after the introduction of an alloying element M.
Detailed Description
The invention is described in further detail below with reference to the following figures and specific examples:
the invention provides a quantitative description method for relieving Bi segregation degree at an Sn-Bi solder interface based on an additive element, which comprises the following steps: firstly, a stable Sn surface model is constructed, and then the improvement effect of the added alloying elements on Bi segregation is theoretically and quantitatively evaluated by calculating two parameters of diffusion activation energy and segregation energy. And finally, parameters such as the bond strength and the bond length among metal bonds of Sn-Bi and Sn-M, Bi-M, the charge transfer condition of M and surrounding Sn and Bi and the like are used as auxiliary verification parameters to evaluate the accuracy of the method.
Example 1
The invention provides a quantitative description method for relieving Bi segregation degree at an Sn-Bi solder interface based on an additive element, which comprises the following specific steps:
1) constructing a stable Sn surface model: firstly, establishing Sn matrix primitive cells, and obtaining the lattice constant of Sn by a quantum mechanics first principle calculation method
On the basis, the most stable surface of Sn is Sn (100) by comparing the surface energies, so that the surface model constructed in the simulation is (2 multiplied by 3) Sn (100) surface, the atoms are 9 layers in total, and the vacuum layer is
The structure is shown in figure 1;
2) the main descriptors for quantifying the degree of Bi segregation on the Sn surface are proposed: adding Bi into a Sn (100) surface model, replacing a Sn lattice position at a thermodynamic stable position, and placing Bi on 1 part of the Sn surfacest-5thRespectively calculating two parameters of diffusion activation energy and segregation energy of Bi atoms to quantitatively measure the segregation degree of Bi;
a) first, the diffusion activation energy E of Bi atoms was calculateddifThe diffusion of Bi follows a vacancy mechanism, i.e., Bi will jump from a Sn lattice site to a vacancy on the adjacent outer surface, leaving a vacancy at the initial position. Introduction of diffusion activation energy EdifTo characterize the diffusion difficulty of Bi atoms at different positions on the Sn surface, the formula is as follows:
wherein ,EbIs the migration barrier energy of Bi atoms from the occupied Sn crystal lattice atom position to the adjacent vacant position;
Edifrepresenting the difficulty degree of Bi atom diffusion on the surface of Sn;
Edifthe lower the value of (b) is, the more easily the Bi atom diffuses into Sn. It was found by calculation that the diffusion activation energy decreases from 0.59eV to 0.32eV during the diffusion of Bi to the Sn (100) outer surface, which means that Bi easily migrates to the Sn outer surface, which explains the segregation of Bi from a kinetic point of view.
b) Comparing the segregation energy of Bi on different layers to Sn surface in terms of energy from the thermodynamic angle
Thereby determining the segregation tendency of Bi to the surface of the Sn system, and the formula is as follows:
wherein ,
is the total energy of a single Bi atom positioned on the nth atomic layer on the surface of Sn (100), and n is a positive integer of 1-5;
3) Quantitative description of the degree of inhibition of Bi segregation by the added alloying elements: adding M into the Sn (100) surface model, wherein the thermodynamically stable position is the Sn lattice position (including the Sn lattice positions at the upper and lower adjacent layers of Bi atoms and the adjacent Sn lattice positions at the two sides of the same layer) for replacing the adjacent position of a Bi atom, and calculating the diffusion activation energy and the segregation energy of the Bi when the alloying elements doped into the system exist again by adopting the same calculation formula in the step 2). Taking Ag atom as an example, after adding Ag atom, Bi is 2ndTo 1stThe diffusion activation energy during diffusion increases from 0.32eV to 0.44eV, which indicates that the addition of Ag inhibits the diffusion of Bi atoms at the Sn surface, eventually improving interfacial Bi segregation. The segregation energy results are shown in FIG. 2. With Bi in 1stThe segregation energy was compared with-0.57 eV, and it was found that the segregation energy of Bi was larger than-0.57 eV in the presence of all the doped M atoms. This means that these alloying elements all have an effect of improving the interface Bi segregation to some extent. Wherein, compared with other additive elements, the Ni, Pd, Pt and Au have more obvious improvement effect on Bi segregation.
The fact that the segregation energy of Bi was 0.07eV and was increased by 0.64eV as compared with the segregation energy of-0.57 eV in the case where Ni atoms were added, indicates that the improvement effect of Bi segregation was excellent when some of the atoms represented by Ni atoms were added. The segregation energy after addition of the other alloying elements M this variable is shown in Table 1.
Table 1 shows the segregation energy of Bi in the presence of M atoms in the second layer of Sn (100)
Method verification
And analyzing the bond length and bond strength auxiliary parameters of the Sn-Bi, Sn-M and Bi-M metal bonds after the alloying element M is added, and verifying the accuracy of the method.
Table 2 shows the dissolution energy of the alloying elements themselves and the bond strengths and bond lengths of Sn-Bi and Sn-M, Bi-M after different alloying elements M are added. Wherein, as shown in FIGS. 3 and 4, BOBi-Sn2Is Bi and Sn2Strong bond between atoms, Sn2Atom represents Sn atom substituted after M is added; BOBi-Sn1Is Bi and Sn adjacent layer1Strong bond between atoms, BOBi-MSBO is a strong bond between Bi and MBi-SnIs the total bond strength between Bi and all adjacent Sn atoms.
Compared with Sn-Bi, Sn-Sn and Bi-Bi bonds, the addition of the alloying element M results in the enhancement of each metal bond and the reduction of the bond length, and then the element is proved to be capable of forming a stronger metal bond with Bi atoms, so that Bi is restrained in the Sn body, and the segregation of Bi to the outside or the surface is prevented, and the formation of a Bi-rich phase is inhibited. This result is consistent with the improved degree of quantitative description of Bi segregation using the diffusion activation energy and segregation energy as parameters, which demonstrates the accuracy of quantitative characterization of the degree of inhibition of Bi segregation by alloying elements in the Sn-Bi system based on the quantitative description method for alleviating the degree of Bi segregation at the Sn-Bi solder interface by adding elements.
Table 2 shows the solubility energy of the alloying element itself and the bond strengths and bond lengths of Sn-Bi and Sn-M, Bi-M before and after the addition of the alloying element M.
Claims (7)
1. A quantitative description method for Bi segregation degree at Sn-Bi solder interface based on addition of alloying element M is characterized by comprising the following steps:
1) constructing a stable Sn surface model: constructing Sn surface models in different directions by using Sn primitive cell parameters, and selecting the most stable surface Sn (100) as a research object by taking surface energy as a judgment standard;
2) the main descriptors for quantifying the degree of Bi segregation on the Sn surface are proposed: introducing Bi into the most stable surface model of Sn, replacing the position of Sn crystal lattice at the thermodynamic stable position, and utilizing a first principle method of quantum mechanics:
a. simulating the outward precipitation process of Bi from the aspect of dynamics, and calculating the diffusion activation energy E of Bi atoms diffused on the surfaces of Sn at different layersdif；EdifThe lower the value of (b) is, the more easily the Bi atom diffuses in Sn;
b. calculating the segregation energy of Bi segregated to the surface of Sn in different layers from the thermodynamic angle on the aspect of energy
A negative value of (b) indicates that the segregation of Bi on the Sn surface is energetically favorable;
3) quantitative description of the degree of inhibition of Bi segregation by the added alloying element M: on the basis of the step 2), adding alloying elements into the Sn-Bi system in a form of replacing Sn atom lattice positions of Bi atom adjacent positions; in this state, the diffusion activation energy E is calculated again by the same method as that of step 2)dif′And segregation energy
I. Comparing the energy of the step 2) and the step 3):
if diffusion activation energy Edif′Diffusion activation energy Edif(ii) a The alloying element M has the function of inhibiting Bi atoms from diffusing on the surface of Sn, and finally has the function of improving the interface Bi segregation; if not, the method is not available;
if it is
The alloying element M has the function of improving the interface Bi segregation; if not, the method is not available;
comparing the energy levels of the different alloying element M additions:
Edifthe lower the value of (a) is,the more easily Bi atoms are diffused in Sn;
2. The method for quantitatively describing the Bi segregation degree at the Sn-Bi solder interface based on the addition of the alloying element M as claimed in claim 1, wherein the step 2) is that the diffusion activation energy E isdifAnd segregation energy
The calculation method comprises the following steps:
wherein ,EbIs the migration barrier energy of Bi atoms from the occupied Sn crystal lattice atom position to the adjacent vacant position;
wherein ,
is the total energy of a single Bi atom on the n atomic layer on the surface of Sn (100);
3. The method for quantitatively describing the degree of Bi segregation at Sn-Bi solder interface based on the addition of alloying element M as claimed in claim 2, wherein n is 1 to (n)General assemblyInteger of/2 + 1); n isGeneral assemblyThe number of atomic layers of structured surface Sn (100).
4. The method of claim 3, wherein the method for quantitatively describing the degree of Bi segregation at the Sn-Bi solder interface based on the addition of the alloying element M,
is the (n) th phase regionGeneral assembly-1) total energy of Bi dissolved Sn (100) surface at atomic layer.
5. The method for quantitative description of Bi segregation degree at Sn-Bi solder interface based on addition of alloying element M as claimed in claim 3, wherein the atomic layer number n of the surface Sn (100) is constructedGeneral assemblyAt least 9 layers, and a vacuum layer at least as thick as
6. The method for quantitatively describing the Bi segregation degree at the Sn-Bi solder interface based on the addition of the alloying element M In claim 1, wherein the doped alloying element In the step 3) is Pt, Pd, Au, In, Ag, Sb, Ni, Ga, Al or Cu.
7. The method of validating the quantitative description method as claimed in any one of claims 1 to 6, wherein, by analyzing the Sn-Bi, Sn-M and Bi-M metallic bonds formed by the addition of the alloying element M as compared with the Sn-Bi, Sn-Sn and Bi-Bi metallic bonds formed by the non-addition of the alloying element M, if the metallic bonds are strongly strengthened and the bond length is reduced after the addition, it is proved that the alloying element M can form a stronger metallic bond with the Bi atom, which facilitates the binding of Bi in the Sn body, prevents the segregation thereof to the outside or the surface, and suppresses the formation of the Bi-rich phase.
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| WO2013137857A2 (en) * | 2012-03-12 | 2013-09-19 | The Massachusetts Institute Of Technology | Stable binary nanocrystalline alloys and methods of identifying same |
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| WO2013137857A2 (en) * | 2012-03-12 | 2013-09-19 | The Massachusetts Institute Of Technology | Stable binary nanocrystalline alloys and methods of identifying same |
| US20170283927A1 (en) * | 2016-03-31 | 2017-10-05 | Universitat De Barcelona | METHOD FOR THE DETERMINATION OF THE REPRESENTATIVE HOMOTOP OF A BINARY METALLIC NANOPARTICLE (AxB1-x)N AND METHOD FOR MANUFACTURING THE CORRESPONDING NANOPARTICLE |
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| CN113042931A (en) * | 2019-12-26 | 2021-06-29 | 有研工程技术研究院有限公司 | Theoretical design method for inhibiting Bi phase segregation in lead-free Sn-Bi solder |
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