AFM恒力模式下倾角和摩擦力对测量结果影响的研究
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摘要
纳米测量是纳米科技领域研究的一个重要的分支。原子力显微镜(Atomic Force Microscope,AFM)因具有以nm级分辨率获得样本表面的三维形貌的能力而被用作纳米测量的重要工具。半导体工业的迅速发展对AFM进行纳米尺度的半导体刻线形貌测量的需求尤为迫切。因此对AFM的工作模式及其测量误差的研究有着十分重要的理论和现实意义。恒力模式是AFM的主要工作模式之一,它具有分辨率高和测量速度快等优点,但其测量结果因受样本表面倾角和针尖-样本表面间摩擦力的影响而存在较大的测量误差。为克服上述缺点,本课题研究了摩擦力及倾角对测量结果的影响,并提出了消除该影响的一种新AFM工作模式。
     在综述了恒力模式下影响AFM测量结果的各种因素基础上,分析了摩擦力和倾角对测量结果的影响,证明这两个因素是测量误差的重要来源,研究了能够克服这两个因素影响的工作模式的可行性。
     研究了恒力模式下针尖和样本表面间的范德瓦尔斯力(van der Waals力,简称为vdW力)和摩擦力,并给出两种常用的悬臂梁——矩形梁和三角梁在法向力和切向力作用时悬臂梁末端的形变及偏转角,建立了恒力模式下针尖和样本表面间摩擦力和样本表面倾角与测量结果之间的数学模型。证明了摩擦力使测量结果产生明显误差,并且扫描方向改变导致的摩擦力方向的变化将使其测量结果产生明显差异。倾角除产生测量误差外,还可能导致样本表面上的一些点在恒力模式下无法得到正确的测量结果,即可能产生测量死点或测量死区。
     针对AFM在半导体刻线形貌测量中摩擦力和倾角影响测量结果的问题,提出一种消除倾角和摩擦力影响的AFM工作模式——EIIAF模式,在这种工作模式下,AFM针尖保持与样本表面接触,扫描方向垂直于悬臂梁的长轴方向。在测量过程中,AFM反馈控制器控制扫描器沿z轴移动样本,保持针尖-样本表面间的vdW力恒定。分析了摩擦力和倾角对针尖的受力的影响,研究了悬臂梁末端沿z轴方向偏转角和沿x轴方向扭转角与vdW力之间的关系,建立其数学模型,推导出了样本表面形貌高度的重建算法。提出两个基于EIIAF模式的扩展工作模式:横向恒高模式和补偿模式,并分析了它们的优缺点。在这两种工作模式中,放宽了对vdW力恒定的要求,但仍可得到较精确的测量结果,并使AFM反馈控制器简化。
     研究EIIAF模式及其两种扩展模式中摩擦力及倾角与测量结果和测量过程中vdW力之间的数学关系。证明在这三种工作模式下摩擦力和倾角不会对测量结果产生影响。但在两种扩展模式下这两个因素可能导致vdW力的误差,并由此导致在一些情况下出现不可测点或不可测区。能够通过改变扫描器运动方向消除这里的不可测点或不可测区,从而实现对表面任何形貌的测量。
     在理论和仿真研究基础上,利用测量梯形截面的Si刻线样本,实验验证了EIIAF模式的可行性,并与恒力模式下测量结果对比,验证新工作模式消除摩擦力和倾角对测量结果影响的效果。实验结果分析证明了由这两个因素导致的恒力模式下的测量误差能够被理论公式适当的描述,并且EIIAF模式能够消除这两个因素给测量带来的影响。
     说明校准悬臂梁弹性常数和针尖-样本表面间的摩擦系数对于在该模式下样本表面形貌和vdW力的精确测量是十分重要的。改造原AFM的模拟控制系统为数字控制系统,并在原有功能基础上增加了所提出的新AFM工作模式的测量功能。
Nanometer measurement is an important branch of nanotechnology. Atomic force microscopes (AFM), which obtain three dimensional images of sample surface with nanometer level resolution, are increasingly being used as tools for nanometer dimensional measurement. As the rapid development of semiconductor industry, there is an urgent need for semiconductor step topography measurement. Therefore the research on the operation mode and measurement error of AFM has important academic and practical meanings. The constant force mode is one of the AFM main operation modes, which has the advantage of high resolution and rapid measurement speed and so on. But it still has bigger measurement error due to the inclination angle of sample surface and friction between the tip and sample surface. To overcome the above limitations, the influence on measurement results of the friction and inclination angle is studied, and a novel AFM operation mode which can eliminating the above two factors is proposed in the paper.
     Based on the summary about the influence factors on AFM measurement results in the constant force mode, the effects on measurement results of the friction and the inclination angle is analyzed. It shows that these two factors are the important contributors of measurement error. Then the feasibility of overcoming the effects coming from these two factors is studied.
     We studied that the van der Waals (vdW) force and friction between the tip and sample surface in the constant force mode, and gave the deformation and deflection at the end of cantilever in the vertical and lateral force of two kinds of cantilevers including rectangular and triangular cantilever. Then the mathematic model of measurement result witch is a function of friction and inclination angle is founded. It shows that the friction leads to significant measurement errors, and the change of the friction direction originating from scanning direction alteration can make results different obviously. The inclination angle not only can bring measurement, but also make that some points on the sample surface not able to get correct measurement results in the constant force mode, which is referred to dead point and dead zone of the measurement.
     Aim at the problem of the friction and inclination angle have an influence on the measurement results, an AFM operation mode of eliminating influence of inclination angle and friction——EIIAF mode is presented. In this operation mode, AFM tip keep the contact with the sample surface, and the scanning direction is vertical with the long axis of cantilever. In the measurement process the AFM feedback controller make the scanner move the sample along z-axis and keep the vdW force between the tip and sample surface constant. The effect of friction and inclination angle on force on tip is analyzed, then the relationship of the deflection along z-axis and the torsion along x-axis of the cantilever with the vdW force is studied, and the corresponding mathematic model is also founded. Additionally the reconstructed algorithm of sample surface topography height is proposed. Two extended operation mode is presented based on the EIIAF mode are given, which are lateral constant height mode and the compensating mode. Then their advantages and limitations are analyzed respectively. In these two operation mode, the request of keeping the vdW force constant is not very strict. But the relatively precise measurement result can be obtained, which can simplify the AFM feedback controller.
     The mathematic relationship of measurement result and vdW force with the friction and inclination angle in the EIIAF mode and the two extended mode is presented. It proves that in these three operation mode the friction and inclination angle have no effect on the measurement results. But in two extended operation mode, these two factors can make the error of the vdW force, accordingly produce unmeasured point and unmeasured zone. By means of changing the movement direction of scanner the unmeasured point and unmeasured zone can be eliminated and realize the measurement of all surface topography.
     Based on the study of theory and simulation, the experiments verify the feasibility of the EIIAF mode by measuring the Si step sample with the trapeziform cross section. And the measurement results are compared with the constant force mode in order to show the effect of eliminating the friction and inclination angle on measurement results. The experimental results show that the measurement error coming from these two factors in the constant force mode can be properly described by the theoretical formula, and the EIIAF mode can eliminate the influence of these two factors.
     It shows that the calibration of the flexibility constant and the friction coefficient between the tip and sample surface are very important to the precise measurement of sample topography and vdW force. The AFM is improved from the primary analog control system to digital control system, and add up the measurement function of the proposed novel AFM operation mode in the base of intrinsic functions.
引文
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