Study On The Influence Of Inclination Angle And Friction For Imaging Results In AFM Constant Force Mode

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.