微电子器件界面结构传热与力学行为多尺度研究
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摘要
目前,微电子元器件已被广泛地应用在航空航天、军事及民用电子产品中。随着微电子设计制造技术的发展,微电子器件不断地向高密度、微型化、功能化方向发展,器件内部的结构也越来越复杂,界面结构及非连续性结构也越来越多。大量的研究表明界面结构是影响器件乃至整个系统正常工作的关键结构之一,超过90%的破坏和缺陷都首先出现在界面处。因此,对界面结构的传热及力学特性进行研究将具有重要意义,但是随着制造工艺的发展,由界面结构的纳米级尺寸使得传统的建模及分析手段已经不再适应,如何兼顾不同尺度下不同分析方法的优势,构建一种多尺度分析方法对界面结构的微尺度传热及界面力学特性进行研究是解决此问题的有效途径之一。
本文针对微电子制造过程中的界面结构的微尺度传热及力学特性进行了多尺度研究。一方面,从不同尺度下的分析方法入手,构建了基于分子动力学(Molecular Dynamic, MD)-界面元(Interface Stress Element, ISE)-有限元(Finite Element, FE)的多尺度模型及分析方法,并对一维力学及传热进行数值分析；另一方面,利用实验手段对界面结构的传热及力学特性进行研究。首先,利用磁控溅射技术制备不同材料构成的界面结构,分析制备工艺参数及制备方法对薄膜生长速率的影响；然后,基于瞬态热反射法及纳米压痕技术分别对界面结构的热特性及力学特性进行系统的研究。
首先,设计不同尺度下的耦合握手区(Handshake, HS),将不同尺度下的分析方法进行耦合,构建界面结构的MD-ISE-FE多尺度分析模型,提出了一种基于MD-ISE-FE的微观-宏观多尺度分析方法。在原子与微观尺度,通过设计MD-ISE握手区,将该区域的原子与界面元耦合在一起；同时在微观与宏观尺度下,通过本构方程将界面元与有限元直接耦合在一起。基于该模型对不同材料界面结构进行了一维传热及力学特性的数值研究,研究结果表明：由相同材料或者热力学特性相近材料构成的界面结构具有更好的界面传热及力学特性。
其次,针对扩散界面结构,在不同温度下研究了其微尺度传热及力学特性。一方面,在微观尺度下,界面的扩散厚度随温度的增加而逐渐增加(温度为300K时,界面的扩散厚度占界面厚度的5.19%)。根据现有结论可知：随着温度的增加,界面热导率会由于声子散射加剧而降低；但是本文研究结果发现：随着温度的增加,界面声子散射越来越严重,界面声子匹配度及声子传热速率降低；而界面热导率却呈现出先增加后减小去趋势。分别利用MD及MD-TTM (Two-Temperature Model)模型从声子及电子的角度对界面热导率进行了研究。研究发现：随着温度的增加(≤界面材料的再结晶温度),界面电子传热提高了界面结构的热导率。研究证明了金属界面结构微尺度传热是由声子及电子共同耦合作用的结果,且发现界面电子传热相对于界面声子占主导地位。另一方面,对不同材料界面结构的力学特性进行研究,通过对材料界面结构微观拉伸实验,研究了其应力应变特性。研究结果发现：扩散界面的应力应变曲线比理想不同材料界面的更加平缓；由相同材料构成的界面结合力及结合特性高于由不同材料构成的界面；界面金属扩散对界面结合力有一定的削弱作用,主要由于不同材料界面中产生金属间化合物的脆性所致,这也是引起界面处裂纹萌生及扩散的主要原因之一。
最后,利用磁控溅射技术、瞬态热反射法及纳米压痕技术,从实验的角度对界面结构的制备、传热及力学特性进行了研究。一方面,研究了不同功率及不同制备方法下的直流溅射速率。研究发现：直流溅射时薄膜的生长速率为射频溅射薄膜生长速率的近10倍,界面热导率随着厚度的增加而增加。另一方面,利用3ω瞬态热反射法对薄膜界面的传热参数进行提取及表征；同时利纳米压痕技术对界面结构的力学特性进行实验表征。研究发现：随界面结构厚度的增加热导率增加；随着压入深度的增加,界面的弹性模量与硬度基本呈现出下降的趋势。这与样品在制备过程的生长机理有关,在磁控溅射生长薄膜时,是从无到有,从薄到厚,先进行随机堆积,然后再进行有序成核生长并形成晶体结构。最开始生长的薄膜中间晶核及晶体结构较少、材料缺陷率大以及密度低等原因,从而导致了界面热导率随厚度增加而增加；弹性模量及硬度随着压入深度的增加而降低的现象。
以上研究不仅对多尺度计算方法进行了系统的研究,同时,对界面结构的界面传热及力学特性进行了系统的数值及实验研究,为进一步弄清不同材料界面的传热机制提供了基础,同时为微／纳电子器件设计制造提供了理论基础和设计手段。
Nowadays, the electronic devices are widely used in the fields of aerospace, military, civil and other electronic products. Coincident with the advancement of micro/nano design and manufacturing technologies, the micro-devices become more and more high density, microminiaturization and functional systemic. The interfacial strutures consist of different materials and some discontinuous structures become more complex, which is widely used in IC/MEMS devices. A lot of experiments show that the reliability of interfacial structures is one of the most important strutures which affect the performance of the whole device or system. Almost all of the deformations and defects always appear in the interface. Hence, the investigation of the interfical heat transfer and mechanical properties of interface structure is very useful for the designing and manufacturing of microelectronic. The size of the interfacial structures is in the nanoscale due to the development of manufacturing process. The size effect of the interface becomes more and more obvious. At this moment, the traditional modeling and analysis methods are not suitable any more in this nanoscale situation. The investigation on the heat transfer mechanism in the interfacial structure has been a main difficulty for microelectronic densign and manufacturing. It is a potential method to analyze the interfacial problems that how to build a multiscle analysis method by considering the advantages of different methods under different scales.
The interfacial heat transfer mechanism and mechanical properties of the interface sturctures in the mciro/nano electronic manufacturing are investigated based on the numerical and experimental methods in this paper. On the one hand, the multiscale model and analysis method is put forward based on the molecular dynamic, interface stress element and finite element methods in this paper. And it is used to analyze the mechanical and heat transfer of interfacial structure in one dimensional. On the other hand, the different interface samples are prepared by the magnetron sputtering method. And then, the thermal porperties and mechanical charateristics of the interface structure are investigated based on the experimental methods (3co transient heat reflection method and nanoindentation). The main research and results in this paper are included as follows,
Firstly, a multiscale method based on MD-ISE-FE is put forword to investigate the charateristics from the nanoscal to macroscale in this paper, which is built by the design of different handshake regions conneced the different methods in different scales. In the handshake regions of ISE and FE, the stiffness matrixs and load matrixs of ISE and FE are coupled dicretly; meanwhile, the mapping operator methods and interpolation algorithm are used to connect the atoms and the interfacial element in the MD and ISE handshake regio. The Hamiltonian is used to describe the engery of the handshake regions. The multiscale model is solved based on the sequence coupling method. The one dimensional heat transfer and tensile are calclulated based on the multiscale model and the sequence coupling method. Comparing with some references, the results prove that the MD-ISE-FE multiscale modeling and analysis method is feasible and useful for understanding the interfacial reliability. The mechanical and heat transfer of interfacial structure in one dimensional have been investigated based on MD-ISE-FE multiscale method, the results show that the charateristics of heat transfer and mechanical of interface structure consisting of the same materials or similar materials are better than that of interface structure consisting of dissimilar mateirals.
Secondly, the thermal performances of the interface structure are investigated under differernt temperatures. The interfacial diffusion thickness of interface structure increases with the temperature increasing in nanoscale (Especially, the percentage of the interfacial diffusion thickness in the whole interface thickness is about5.19%when the tempartue is300K.). It indicates that the phonon scattering becomes more and more serious with the temeperature increasing, which also reduces the phonon coincident degree in the interfacial heat transfer. All these fators of phonon would reduce the interfacial thermal conductivity. But the results in this paper show that the phonon coincident degree decreases with the temperature increasing, while, the change of the thermal conductivity increases firstly and then to decrease. The interfacial heat transfer mechanism of the interface is explained from the coupling of the phonon and electron. It is found that the effciency of eletron heat transfer is enhanced with the termperature increasing (lower than the recrystallization temperature). The results prove that the micro/nanocscale heat transfer mechanism of the interface structure is the coupling results of phonon and eletron. And it is found that the electron is the main fator in the interfacial heat transfer compared with Phonon.
Finally, the thermal properties (thermal resistance and thermal conductivity) and mechanical charateristcs (Elastic modulus and Hardness) of the interface structures are investigated based on the magnetron sputtering, transient heat reflection method and nanoindentation technology. On the one hand, the mechanical charateristics (Elastic modulus and Hardness) of the interface are studied in this paper. Some different interface structures (Cu/Cu and Cu/Al) are built for investigation. The stress-strain relationships of different interfaces are systemically investigated based on the tensile test simulation of the interface. It is found that the stress-strain curve of the diffusion interface is much smoother than that of the ideal interface structure consisting of different materials. The adhension force of the interface reduces in the metallic interface which maybe be caused by the brittleness of the intermetallic compound (IMC) generated in the diffusion interface. The IMC is also one of the most important reasons caused the crack in the interface. On the other hand, the sputtering rate is studied under different powers and different magnetron sputtering methods. The results show that the sputtering rate in the DC (Direct Current) magnetron sputtering is about ten times faster than that in the RF (Radio Frequecny) magnetron sputtering. The heat transfer parameters (thermal conductivity) of the interface samples are tested by using the3ω transient heat reflection method, the thermal conductivity increases with the thickness increasing. Meanwhile, the mechanical charateristics of the interface structure are tested based on the nanoindentation technology. It is foud that the elastic modulus and hardness of the interface reduce with the increase of the indentation depth. This phenomenon is caused by the growing mechanism in the sputtering process. In the films magnetron sputtering process, the film always start from scratch, and from thin to thick. In other words, the random accumulation is always in the begining, after that, the orderly nucleating growth and formation of crystal structure start in the next. There are lots of defects in the random accumulation step, which reduces the density in the beginning. It explains the phenomenon that the elastic modulus and hardness reduce with the increase of the indentation depth in the nanoindentation experiment.
The aboved investigations not only systemically studied on the multiscale numerical calculation, but also investigated the interfacial heat transfer and mechanical characteristic of the interface structure on numerical and experimental methods, which is useful for understanding the heat transfer mechanism in the dissimilar materials interface structure. And also implies a potential multiscale method for analyzing the interface performance and designing the interface in the micro/nano manufacturing.
本文针对微电子制造过程中的界面结构的微尺度传热及力学特性进行了多尺度研究。一方面,从不同尺度下的分析方法入手,构建了基于分子动力学(Molecular Dynamic, MD)-界面元(Interface Stress Element, ISE)-有限元(Finite Element, FE)的多尺度模型及分析方法,并对一维力学及传热进行数值分析；另一方面,利用实验手段对界面结构的传热及力学特性进行研究。首先,利用磁控溅射技术制备不同材料构成的界面结构,分析制备工艺参数及制备方法对薄膜生长速率的影响；然后,基于瞬态热反射法及纳米压痕技术分别对界面结构的热特性及力学特性进行系统的研究。
首先,设计不同尺度下的耦合握手区(Handshake, HS),将不同尺度下的分析方法进行耦合,构建界面结构的MD-ISE-FE多尺度分析模型,提出了一种基于MD-ISE-FE的微观-宏观多尺度分析方法。在原子与微观尺度,通过设计MD-ISE握手区,将该区域的原子与界面元耦合在一起；同时在微观与宏观尺度下,通过本构方程将界面元与有限元直接耦合在一起。基于该模型对不同材料界面结构进行了一维传热及力学特性的数值研究,研究结果表明：由相同材料或者热力学特性相近材料构成的界面结构具有更好的界面传热及力学特性。
其次,针对扩散界面结构,在不同温度下研究了其微尺度传热及力学特性。一方面,在微观尺度下,界面的扩散厚度随温度的增加而逐渐增加(温度为300K时,界面的扩散厚度占界面厚度的5.19%)。根据现有结论可知：随着温度的增加,界面热导率会由于声子散射加剧而降低；但是本文研究结果发现：随着温度的增加,界面声子散射越来越严重,界面声子匹配度及声子传热速率降低；而界面热导率却呈现出先增加后减小去趋势。分别利用MD及MD-TTM (Two-Temperature Model)模型从声子及电子的角度对界面热导率进行了研究。研究发现：随着温度的增加(≤界面材料的再结晶温度),界面电子传热提高了界面结构的热导率。研究证明了金属界面结构微尺度传热是由声子及电子共同耦合作用的结果,且发现界面电子传热相对于界面声子占主导地位。另一方面,对不同材料界面结构的力学特性进行研究,通过对材料界面结构微观拉伸实验,研究了其应力应变特性。研究结果发现：扩散界面的应力应变曲线比理想不同材料界面的更加平缓；由相同材料构成的界面结合力及结合特性高于由不同材料构成的界面；界面金属扩散对界面结合力有一定的削弱作用,主要由于不同材料界面中产生金属间化合物的脆性所致,这也是引起界面处裂纹萌生及扩散的主要原因之一。
最后,利用磁控溅射技术、瞬态热反射法及纳米压痕技术,从实验的角度对界面结构的制备、传热及力学特性进行了研究。一方面,研究了不同功率及不同制备方法下的直流溅射速率。研究发现：直流溅射时薄膜的生长速率为射频溅射薄膜生长速率的近10倍,界面热导率随着厚度的增加而增加。另一方面,利用3ω瞬态热反射法对薄膜界面的传热参数进行提取及表征；同时利纳米压痕技术对界面结构的力学特性进行实验表征。研究发现：随界面结构厚度的增加热导率增加；随着压入深度的增加,界面的弹性模量与硬度基本呈现出下降的趋势。这与样品在制备过程的生长机理有关,在磁控溅射生长薄膜时,是从无到有,从薄到厚,先进行随机堆积,然后再进行有序成核生长并形成晶体结构。最开始生长的薄膜中间晶核及晶体结构较少、材料缺陷率大以及密度低等原因,从而导致了界面热导率随厚度增加而增加；弹性模量及硬度随着压入深度的增加而降低的现象。
以上研究不仅对多尺度计算方法进行了系统的研究,同时,对界面结构的界面传热及力学特性进行了系统的数值及实验研究,为进一步弄清不同材料界面的传热机制提供了基础,同时为微／纳电子器件设计制造提供了理论基础和设计手段。
Nowadays, the electronic devices are widely used in the fields of aerospace, military, civil and other electronic products. Coincident with the advancement of micro/nano design and manufacturing technologies, the micro-devices become more and more high density, microminiaturization and functional systemic. The interfacial strutures consist of different materials and some discontinuous structures become more complex, which is widely used in IC/MEMS devices. A lot of experiments show that the reliability of interfacial structures is one of the most important strutures which affect the performance of the whole device or system. Almost all of the deformations and defects always appear in the interface. Hence, the investigation of the interfical heat transfer and mechanical properties of interface structure is very useful for the designing and manufacturing of microelectronic. The size of the interfacial structures is in the nanoscale due to the development of manufacturing process. The size effect of the interface becomes more and more obvious. At this moment, the traditional modeling and analysis methods are not suitable any more in this nanoscale situation. The investigation on the heat transfer mechanism in the interfacial structure has been a main difficulty for microelectronic densign and manufacturing. It is a potential method to analyze the interfacial problems that how to build a multiscle analysis method by considering the advantages of different methods under different scales.
The interfacial heat transfer mechanism and mechanical properties of the interface sturctures in the mciro/nano electronic manufacturing are investigated based on the numerical and experimental methods in this paper. On the one hand, the multiscale model and analysis method is put forward based on the molecular dynamic, interface stress element and finite element methods in this paper. And it is used to analyze the mechanical and heat transfer of interfacial structure in one dimensional. On the other hand, the different interface samples are prepared by the magnetron sputtering method. And then, the thermal porperties and mechanical charateristics of the interface structure are investigated based on the experimental methods (3co transient heat reflection method and nanoindentation). The main research and results in this paper are included as follows,
Firstly, a multiscale method based on MD-ISE-FE is put forword to investigate the charateristics from the nanoscal to macroscale in this paper, which is built by the design of different handshake regions conneced the different methods in different scales. In the handshake regions of ISE and FE, the stiffness matrixs and load matrixs of ISE and FE are coupled dicretly; meanwhile, the mapping operator methods and interpolation algorithm are used to connect the atoms and the interfacial element in the MD and ISE handshake regio. The Hamiltonian is used to describe the engery of the handshake regions. The multiscale model is solved based on the sequence coupling method. The one dimensional heat transfer and tensile are calclulated based on the multiscale model and the sequence coupling method. Comparing with some references, the results prove that the MD-ISE-FE multiscale modeling and analysis method is feasible and useful for understanding the interfacial reliability. The mechanical and heat transfer of interfacial structure in one dimensional have been investigated based on MD-ISE-FE multiscale method, the results show that the charateristics of heat transfer and mechanical of interface structure consisting of the same materials or similar materials are better than that of interface structure consisting of dissimilar mateirals.
Secondly, the thermal performances of the interface structure are investigated under differernt temperatures. The interfacial diffusion thickness of interface structure increases with the temperature increasing in nanoscale (Especially, the percentage of the interfacial diffusion thickness in the whole interface thickness is about5.19%when the tempartue is300K.). It indicates that the phonon scattering becomes more and more serious with the temeperature increasing, which also reduces the phonon coincident degree in the interfacial heat transfer. All these fators of phonon would reduce the interfacial thermal conductivity. But the results in this paper show that the phonon coincident degree decreases with the temperature increasing, while, the change of the thermal conductivity increases firstly and then to decrease. The interfacial heat transfer mechanism of the interface is explained from the coupling of the phonon and electron. It is found that the effciency of eletron heat transfer is enhanced with the termperature increasing (lower than the recrystallization temperature). The results prove that the micro/nanocscale heat transfer mechanism of the interface structure is the coupling results of phonon and eletron. And it is found that the electron is the main fator in the interfacial heat transfer compared with Phonon.
Finally, the thermal properties (thermal resistance and thermal conductivity) and mechanical charateristcs (Elastic modulus and Hardness) of the interface structures are investigated based on the magnetron sputtering, transient heat reflection method and nanoindentation technology. On the one hand, the mechanical charateristics (Elastic modulus and Hardness) of the interface are studied in this paper. Some different interface structures (Cu/Cu and Cu/Al) are built for investigation. The stress-strain relationships of different interfaces are systemically investigated based on the tensile test simulation of the interface. It is found that the stress-strain curve of the diffusion interface is much smoother than that of the ideal interface structure consisting of different materials. The adhension force of the interface reduces in the metallic interface which maybe be caused by the brittleness of the intermetallic compound (IMC) generated in the diffusion interface. The IMC is also one of the most important reasons caused the crack in the interface. On the other hand, the sputtering rate is studied under different powers and different magnetron sputtering methods. The results show that the sputtering rate in the DC (Direct Current) magnetron sputtering is about ten times faster than that in the RF (Radio Frequecny) magnetron sputtering. The heat transfer parameters (thermal conductivity) of the interface samples are tested by using the3ω transient heat reflection method, the thermal conductivity increases with the thickness increasing. Meanwhile, the mechanical charateristics of the interface structure are tested based on the nanoindentation technology. It is foud that the elastic modulus and hardness of the interface reduce with the increase of the indentation depth. This phenomenon is caused by the growing mechanism in the sputtering process. In the films magnetron sputtering process, the film always start from scratch, and from thin to thick. In other words, the random accumulation is always in the begining, after that, the orderly nucleating growth and formation of crystal structure start in the next. There are lots of defects in the random accumulation step, which reduces the density in the beginning. It explains the phenomenon that the elastic modulus and hardness reduce with the increase of the indentation depth in the nanoindentation experiment.
The aboved investigations not only systemically studied on the multiscale numerical calculation, but also investigated the interfacial heat transfer and mechanical characteristic of the interface structure on numerical and experimental methods, which is useful for understanding the heat transfer mechanism in the dissimilar materials interface structure. And also implies a potential multiscale method for analyzing the interface performance and designing the interface in the micro/nano manufacturing.
引文
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