基于分子量级的化学机械抛光材料去除机理的理论和试验研究
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摘要
化学机械抛光(Chemical Mechanical Polishing,简称CMP)技术是目前实现集成电路全局平坦化的唯一广泛应用技术。CMP系统由抛光垫、芯片和抛光液组成。含有磨粒和化学试剂的抛光液在旋转的芯片和抛光垫之间流动。尽管CMP技术在微电子信息产业有广泛的应用,但是CMP的许多过程还不是很清楚。澄清CMP材料去除机理,能够为控制和优化CMP工艺参数提供理论指导。此外,随着特征尺寸的减小和芯片集成度的增加,需要建立定量预测CMP材料去除速率的数学物理模型,以此来满足未来超大规模集成电路(Ultra Large Scale Integration,简称ULSI)对平坦化的苛刻要求。
首先提出了分子量级的CMP材料去除机理;通过抛光垫/磨粒大变形理论、粘着力对磨粒压入芯片的影响、考虑表面缺陷的传质扩散估算、材料去除速率的量级估算和原子力显微镜(Atomic Force Microscope,简称AFM)微观试验、原位纳米测试系统(Nano-mechanical Testing System Tribo-indenter,简称NTS)微观试验以及椭圆偏振光谱仪(Spectroscopic Ellipsometry,简称SE)试验的方法,证实了本文提出的材料单分子层去除机理的科学性。随后,基于微观接触理论、概率统计原理和材料单分子层去除机理,建立了考虑磨粒/抛光垫大变形的数学物理方程。结合机械去除能和化学结合能平衡的原理,进一步建立了考虑磨粒大小、浓度和氧化剂浓度以及机械化学协调效应的数学模型。此外,基于分子量级的材料去除机理,本文还建立了考虑新鲜分子去除的材料去除递推模型,模型预测结果与宏观试验相吻合。最后,初步建立了预测氧化剂、缓蚀剂和螯合剂浓度对铜CMP材料去除速率影响规律的数学模型。
分子量级的材料去除机理为:化学作用将芯片表面的新鲜分子部分氧化成为氧化分子;磨粒将键能弱化的氧化分子去除;流动的抛光液将去除的原子/分子带走,露出新鲜表面,继续循环去除。采用理论和试验两个方面证实了本论文提出的材料单分子层去除机理的科学性。理论方面:考虑磨粒/抛光垫大变形的情况下,计算了磨粒压入芯片的深度为分子量级或者更小。模型进一步考虑了磨粒/芯片粘着力的影响,发现粘着力对磨粒/芯片接触力的影响显著,磨粒压入芯片的深度比不考虑粘着力时大2到4倍,但是仍然为分子量级。基于材料单分子层去除机理,采用量级估算的方法得到SiO_2和W芯片更适于用材料单分子层去除机理所描述。考虑芯片表面缺陷的情况下,CMP过程生成表面氧化分子层厚度和扩散厚度的估算表明:芯片表面生成氧化膜的厚度为1.0×10~(-3)nm量级。因此,认为CMP材料去除机理为单分子层去除。
采用NTS试验和他人的试验结果,应用线性回归的方法,研究了CMP材料单分子层去除机理。根据线性回归分析知,磨粒在芯片表面的划痕深度为1.0×10~(-11)m量级。应用SE测定了铜CMP过程中芯片表面氧化薄膜随时间的变化规律。因为CMP过程中,两个连续磨粒扫过芯片表面一点的间隔时间为1.0×10~(-8)s量级,根据Nishizawa曲线,计算得到CMP中,生成新鲜氧化薄膜的厚度为1.0×10~(-13)m量级。采用NTS测定0-100μN下磨粒压入芯片的深度,通过回归分析,计算出70nN下,磨粒压入芯片的深度为1.0×10~(-11)m量级。上述3组试验数据表明CMP材料去除机理为单分子层去除。此外,现在Cabot公司提供的磨粒直径为10nm,而且高质量的抛光后,表面很少有划痕出现,表面粗糙度为0.1nm左右,因此材料去除机理应该为单分子去除。
目前,磨粒尺寸和浓度对CMP材料去除速率的影响规律,还没有统一的定论。基于分子量级的材料去除机理,率先建立了预测磨粒大小、浓度和表面氧化剂浓度对材料去除速率影响规律的数学模型。模型考虑了氧化分子和芯片表面分子的结合能,以便说明磨粒尺寸对材料去除速率的三种不同影响规律。由于机械能和去除结合能耦合于磨粒直径,因此,磨粒大小和材料去除速率之间体现出了不同的非线性规律。此外,本模型还预测出,材料去除速率和去除结合能之间为非线性关系。模型还可以解释CMP众多参数对材料去除速率的影响,如抛光压力、相对速度、芯片表面硬度和抛光垫材料特性等。进一步建立了考虑芯片表面新鲜分子对材料去除速率影响的概率递推模型。结果表明:无论单独增加化学作用还是机械作用,都不能一直增加材料去除速率。当化学作用和机械作用相协调时,获得极大值去除速率。模型预测结果和他人试验相吻合。
最后,铜CMP的研究在全世界范围内仍然属于攻关性的研究。本文基于化学反应和机械去除动态平衡原理以及考虑化学反应速率常数,首次建立了系统考虑氧化剂浓度、缓蚀剂浓度和螯合剂浓度对材料去除速率影响的数学模型。结果表明,螯合剂和氧化剂对材料去除速率的影响规律相似。模型预测结果和试验数据定性结果相吻合。本模型的建立为铜CMP理论的研究提供了初步的理论平台。
Chemical mechanical polishing(CMP) has emerged to be most promising because it can provide the planarity necessary to build multilevel interconnect schemes.In the CMP process, a rotating wafer is pressed against a rotating pad while slurry including abrasive particles and chemical additives flows between the wafer surface and polishing pad.It synergizes the abrasive particles and chemicals in slurry.Despite its crucial importance in the microelectronic industry,many aspects of the CMP process remain unclear and ambiguous. Understanding of the fundamental of CMP material removal mechanism may offer insights into the control and optimization of the polishing process.In addition,as device size is shrinking and integration level of IC chip is increasing,a detailed quantitative model for material removal rate in CMP,is required for meeting the strict planarization requirements in the manufacturing the future generation Ultra Large Scale Integration(ULSI) chips.
In this study,the paper firstly proposes a material removal mechanism at molecular scale. And then this molecular scale removal mechanism has got wide support form many aspects such as large contact deformation of pad/particle,the effect of adhesion force on the indentation depth of particle into wafer surface,the order-of-magnitude calculation of material removal on the basis of chemical kinetics and transport phenomena under the wafer surface defect condition,and the nano-scale experiments carried out by atomic force microscope(AFM)、nano-mechanical testing system tribo-indenter(NTS) and spectroscopic ellipsometry(SE).Thirdly,with the consideration of the pad/particle large deformation,a new mathematical model is presented based on the molecular scale removal mechanism, probability statistics and micro contact mechanics.In order to interpret the influence of the abrasive particle size、concentration,oxidizer concentration and chemical mechanical synergy on material removal,another comprehensive model is proposed resting on the energy equilibrium knowledge in relation to the mechanical removal energy and chemical binding energy.Furthermore,the paper also reports another model being incorporation of the fresh wafer surface atoms removal.Finally,this dissertation also develops a novel mathematical model to systematically govern the combinational effects of oxidizer,complexing agent and inhibitor on polishing rate in CMP of copper.
A more likely scenario for the process of the molecular scale removal mechanism has three steps:(ⅰ) chemical actions covert strongly the fresh wafer surface atoms/molecules into reacted molecular species;(ⅱ) mechanical actions deliver the energy that removes the weakly bonded reacted molecular species;(ⅲ) the slurry fluid washes the wafer surface,and the fresh surface sites are exposed,which is subsequently etched and removed.This molecular scale removal mechanism is verified form experimental and theoretical study.On one extreme, a mathematical model with the consideration of particle/pad large deformation states that the indentation depth of particle into wafer surface is at molecular scale or less.The effect of the adhesion force is also addressed,which strongly shows that the adhesion force can significantly influence the load force of particle/wafer.This model also predicts that the indentation depth of a particle into wafer surface considering the adhesion force is 2 or 4 times than that of no adhesion force.However,the magnitude of the indentation depth is still on the order of molecular scale.In the following,order-of magnitude calculations are used to support this new mechanism.And a closed-form equation supported by published experimental data is derived of the material removal rate in terms of the molecular removal mechanism.The results show that the material removal mechanism of SiO_2 and W can be explained by the molecular scale removal mechanism.In another magnitude analysis,the growth rate and diffusion thickness of the oxide layer are quantitatively evaluated.The calculation reports that the diffusion depth for case of Si wafer is on the order of 1.0×10~(-3) nm, indicating the CMP material is removed at molecular scale.
On the other extreme,a series of experiments was conducted to investigate the mechanism of CMP material removal in this research.Wear behavior between a single slurry particle and the wafer surface using AFM was proposed.The scratch depth under real CMP conduction is of an order of 1.0×10~(-11)m determined on the basis of the linear regression mechanism.The SE tool was used to study the relationship between the thickness of oxidized layer and chemical action time.Since real CMP chemical action time is of an order of 1.0×10~(-8)s,the thickness of the oxidized layer is of an order of 1.0×10~(-13)m evaluated by theoretical model based on the experiment data.In addition,the indentation depth of a single particle into the wafer surface was investigated using NTS with 70 nN force.The indentation depth is of an order of 1.0×10~(-11) m on the basis of the linear regression mechanism.Nowadays,the abrasive particle size provided by Cabot Company is around 10nm.In addition,few abrasive grooves are found in high-quality-finished polishing wafer surface.The combined calculations and experimental results indicate that the CMP material is removed at molecular scale.
No conclusive results have been proposed for the influence of the abrasive particle size on material removal during the CMP process.In this study,a mathematical model as a function of abrasive size and surface oxidizer concentration is presented for CMP.The influence in relation to the binding energy of the reacted molecules to the substrate is incorporated into the analysis so as to clarify the disputes on the variable experimental trends on particle size.It is shown that the mechanical energy and removal cohesive energy couple with the particle size, and being a cause of the non-linear size-removal rate relation.Furthermore,it also shows a nonlinear dependence of removal rate on removal cohesive energy.The model predictions are presented in graphical form and show good agreement with the published experimental data. Finally,variations of material removal rate with pressure,pad/wafer relative velocity,and wafer surface hardness,as well as pad characteristics are addressed.The present study also proposes a non-continuum statistic model for CMP material removal rate by a slurry particle, which considers the direct removal rate of the un-reacted surface sites.It is shown that higher chemical effects would not lead to a proportional increase of the removal rate.As chemical-mechanical synergetic effects are optimal,the removal rate is extremum.The predicted material removal rates follow trends similar to those shown by the experimental observations published previously.
At last,the copper CMP is still a challenging subject for developing ICs.The paper presents a novel mathematical model that systematically describes the role of oxidizer,complexing agent and inhibitor on the material removal in CMP of copper.The physical basis of the model is the steady-state oxidation reaction and etched removal in additional to mechanical removal.It is shown that the complexing agent concentration-removal relation follows a trend similar to that observed from the effects of oxidizer on Cu-removal in CMP.The model prediction trends show qualitatively good agreement with the published experimental data. The governing equation of copper removal provides an important starting point for delineating the copper CMP process in addition to its underlying theoretical foundation.
首先提出了分子量级的CMP材料去除机理;通过抛光垫/磨粒大变形理论、粘着力对磨粒压入芯片的影响、考虑表面缺陷的传质扩散估算、材料去除速率的量级估算和原子力显微镜(Atomic Force Microscope,简称AFM)微观试验、原位纳米测试系统(Nano-mechanical Testing System Tribo-indenter,简称NTS)微观试验以及椭圆偏振光谱仪(Spectroscopic Ellipsometry,简称SE)试验的方法,证实了本文提出的材料单分子层去除机理的科学性。随后,基于微观接触理论、概率统计原理和材料单分子层去除机理,建立了考虑磨粒/抛光垫大变形的数学物理方程。结合机械去除能和化学结合能平衡的原理,进一步建立了考虑磨粒大小、浓度和氧化剂浓度以及机械化学协调效应的数学模型。此外,基于分子量级的材料去除机理,本文还建立了考虑新鲜分子去除的材料去除递推模型,模型预测结果与宏观试验相吻合。最后,初步建立了预测氧化剂、缓蚀剂和螯合剂浓度对铜CMP材料去除速率影响规律的数学模型。
分子量级的材料去除机理为:化学作用将芯片表面的新鲜分子部分氧化成为氧化分子;磨粒将键能弱化的氧化分子去除;流动的抛光液将去除的原子/分子带走,露出新鲜表面,继续循环去除。采用理论和试验两个方面证实了本论文提出的材料单分子层去除机理的科学性。理论方面:考虑磨粒/抛光垫大变形的情况下,计算了磨粒压入芯片的深度为分子量级或者更小。模型进一步考虑了磨粒/芯片粘着力的影响,发现粘着力对磨粒/芯片接触力的影响显著,磨粒压入芯片的深度比不考虑粘着力时大2到4倍,但是仍然为分子量级。基于材料单分子层去除机理,采用量级估算的方法得到SiO_2和W芯片更适于用材料单分子层去除机理所描述。考虑芯片表面缺陷的情况下,CMP过程生成表面氧化分子层厚度和扩散厚度的估算表明:芯片表面生成氧化膜的厚度为1.0×10~(-3)nm量级。因此,认为CMP材料去除机理为单分子层去除。
采用NTS试验和他人的试验结果,应用线性回归的方法,研究了CMP材料单分子层去除机理。根据线性回归分析知,磨粒在芯片表面的划痕深度为1.0×10~(-11)m量级。应用SE测定了铜CMP过程中芯片表面氧化薄膜随时间的变化规律。因为CMP过程中,两个连续磨粒扫过芯片表面一点的间隔时间为1.0×10~(-8)s量级,根据Nishizawa曲线,计算得到CMP中,生成新鲜氧化薄膜的厚度为1.0×10~(-13)m量级。采用NTS测定0-100μN下磨粒压入芯片的深度,通过回归分析,计算出70nN下,磨粒压入芯片的深度为1.0×10~(-11)m量级。上述3组试验数据表明CMP材料去除机理为单分子层去除。此外,现在Cabot公司提供的磨粒直径为10nm,而且高质量的抛光后,表面很少有划痕出现,表面粗糙度为0.1nm左右,因此材料去除机理应该为单分子去除。
目前,磨粒尺寸和浓度对CMP材料去除速率的影响规律,还没有统一的定论。基于分子量级的材料去除机理,率先建立了预测磨粒大小、浓度和表面氧化剂浓度对材料去除速率影响规律的数学模型。模型考虑了氧化分子和芯片表面分子的结合能,以便说明磨粒尺寸对材料去除速率的三种不同影响规律。由于机械能和去除结合能耦合于磨粒直径,因此,磨粒大小和材料去除速率之间体现出了不同的非线性规律。此外,本模型还预测出,材料去除速率和去除结合能之间为非线性关系。模型还可以解释CMP众多参数对材料去除速率的影响,如抛光压力、相对速度、芯片表面硬度和抛光垫材料特性等。进一步建立了考虑芯片表面新鲜分子对材料去除速率影响的概率递推模型。结果表明:无论单独增加化学作用还是机械作用,都不能一直增加材料去除速率。当化学作用和机械作用相协调时,获得极大值去除速率。模型预测结果和他人试验相吻合。
最后,铜CMP的研究在全世界范围内仍然属于攻关性的研究。本文基于化学反应和机械去除动态平衡原理以及考虑化学反应速率常数,首次建立了系统考虑氧化剂浓度、缓蚀剂浓度和螯合剂浓度对材料去除速率影响的数学模型。结果表明,螯合剂和氧化剂对材料去除速率的影响规律相似。模型预测结果和试验数据定性结果相吻合。本模型的建立为铜CMP理论的研究提供了初步的理论平台。
Chemical mechanical polishing(CMP) has emerged to be most promising because it can provide the planarity necessary to build multilevel interconnect schemes.In the CMP process, a rotating wafer is pressed against a rotating pad while slurry including abrasive particles and chemical additives flows between the wafer surface and polishing pad.It synergizes the abrasive particles and chemicals in slurry.Despite its crucial importance in the microelectronic industry,many aspects of the CMP process remain unclear and ambiguous. Understanding of the fundamental of CMP material removal mechanism may offer insights into the control and optimization of the polishing process.In addition,as device size is shrinking and integration level of IC chip is increasing,a detailed quantitative model for material removal rate in CMP,is required for meeting the strict planarization requirements in the manufacturing the future generation Ultra Large Scale Integration(ULSI) chips.
In this study,the paper firstly proposes a material removal mechanism at molecular scale. And then this molecular scale removal mechanism has got wide support form many aspects such as large contact deformation of pad/particle,the effect of adhesion force on the indentation depth of particle into wafer surface,the order-of-magnitude calculation of material removal on the basis of chemical kinetics and transport phenomena under the wafer surface defect condition,and the nano-scale experiments carried out by atomic force microscope(AFM)、nano-mechanical testing system tribo-indenter(NTS) and spectroscopic ellipsometry(SE).Thirdly,with the consideration of the pad/particle large deformation,a new mathematical model is presented based on the molecular scale removal mechanism, probability statistics and micro contact mechanics.In order to interpret the influence of the abrasive particle size、concentration,oxidizer concentration and chemical mechanical synergy on material removal,another comprehensive model is proposed resting on the energy equilibrium knowledge in relation to the mechanical removal energy and chemical binding energy.Furthermore,the paper also reports another model being incorporation of the fresh wafer surface atoms removal.Finally,this dissertation also develops a novel mathematical model to systematically govern the combinational effects of oxidizer,complexing agent and inhibitor on polishing rate in CMP of copper.
A more likely scenario for the process of the molecular scale removal mechanism has three steps:(ⅰ) chemical actions covert strongly the fresh wafer surface atoms/molecules into reacted molecular species;(ⅱ) mechanical actions deliver the energy that removes the weakly bonded reacted molecular species;(ⅲ) the slurry fluid washes the wafer surface,and the fresh surface sites are exposed,which is subsequently etched and removed.This molecular scale removal mechanism is verified form experimental and theoretical study.On one extreme, a mathematical model with the consideration of particle/pad large deformation states that the indentation depth of particle into wafer surface is at molecular scale or less.The effect of the adhesion force is also addressed,which strongly shows that the adhesion force can significantly influence the load force of particle/wafer.This model also predicts that the indentation depth of a particle into wafer surface considering the adhesion force is 2 or 4 times than that of no adhesion force.However,the magnitude of the indentation depth is still on the order of molecular scale.In the following,order-of magnitude calculations are used to support this new mechanism.And a closed-form equation supported by published experimental data is derived of the material removal rate in terms of the molecular removal mechanism.The results show that the material removal mechanism of SiO_2 and W can be explained by the molecular scale removal mechanism.In another magnitude analysis,the growth rate and diffusion thickness of the oxide layer are quantitatively evaluated.The calculation reports that the diffusion depth for case of Si wafer is on the order of 1.0×10~(-3) nm, indicating the CMP material is removed at molecular scale.
On the other extreme,a series of experiments was conducted to investigate the mechanism of CMP material removal in this research.Wear behavior between a single slurry particle and the wafer surface using AFM was proposed.The scratch depth under real CMP conduction is of an order of 1.0×10~(-11)m determined on the basis of the linear regression mechanism.The SE tool was used to study the relationship between the thickness of oxidized layer and chemical action time.Since real CMP chemical action time is of an order of 1.0×10~(-8)s,the thickness of the oxidized layer is of an order of 1.0×10~(-13)m evaluated by theoretical model based on the experiment data.In addition,the indentation depth of a single particle into the wafer surface was investigated using NTS with 70 nN force.The indentation depth is of an order of 1.0×10~(-11) m on the basis of the linear regression mechanism.Nowadays,the abrasive particle size provided by Cabot Company is around 10nm.In addition,few abrasive grooves are found in high-quality-finished polishing wafer surface.The combined calculations and experimental results indicate that the CMP material is removed at molecular scale.
No conclusive results have been proposed for the influence of the abrasive particle size on material removal during the CMP process.In this study,a mathematical model as a function of abrasive size and surface oxidizer concentration is presented for CMP.The influence in relation to the binding energy of the reacted molecules to the substrate is incorporated into the analysis so as to clarify the disputes on the variable experimental trends on particle size.It is shown that the mechanical energy and removal cohesive energy couple with the particle size, and being a cause of the non-linear size-removal rate relation.Furthermore,it also shows a nonlinear dependence of removal rate on removal cohesive energy.The model predictions are presented in graphical form and show good agreement with the published experimental data. Finally,variations of material removal rate with pressure,pad/wafer relative velocity,and wafer surface hardness,as well as pad characteristics are addressed.The present study also proposes a non-continuum statistic model for CMP material removal rate by a slurry particle, which considers the direct removal rate of the un-reacted surface sites.It is shown that higher chemical effects would not lead to a proportional increase of the removal rate.As chemical-mechanical synergetic effects are optimal,the removal rate is extremum.The predicted material removal rates follow trends similar to those shown by the experimental observations published previously.
At last,the copper CMP is still a challenging subject for developing ICs.The paper presents a novel mathematical model that systematically describes the role of oxidizer,complexing agent and inhibitor on the material removal in CMP of copper.The physical basis of the model is the steady-state oxidation reaction and etched removal in additional to mechanical removal.It is shown that the complexing agent concentration-removal relation follows a trend similar to that observed from the effects of oxidizer on Cu-removal in CMP.The model prediction trends show qualitatively good agreement with the published experimental data. The governing equation of copper removal provides an important starting point for delineating the copper CMP process in addition to its underlying theoretical foundation.
引文
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