Abstract
Electrostatic interactions are important in non-contact atomic force microscopy (AFM) measurement. Previous reports had focused on the calculation of electrostatic interactions in AFM with metal and dielectric samples, and the present work extended the discussion to semiconductor samples based on Green’s function theory and Debye-Hückel theory, considering sample dielectric polarization and free carriers at the same time. In order to enhance the calculation efficiency, an equivalent charge method was implemented and developed with a linear algebra-based algorithm. The calculation results of two limiting cases, metal and dielectric limit with infinite and zero carrier concentrations respectively, were in good agreement with the boundary element method. For a finite carrier concentration, it is found that the electrostatic force on the tip cone is quickly saturated whereas that on the tip apex slowly increases as the carrier concentration increases. On the other hand, the interaction radius on the sample surface is found independent of the sample free carriers, but it linearly increases as the tip-sample distance. Our work can be useful for the carrier concentration detection of semiconductor samples using non-contact electrical AFM modes such as Kelvin probe force microscopy and electrostatic force microscopy.
Highlights
Atomic force microscopy (AFM) and its non-contact electrical modes such as Kelvin probe force microscopy (KPFM) and electrostatic force microscopy (EFM) have been extensively used to characterize the surface electrical properties of metal, dielectric and semiconductor materials and devices.1,2 The electrostatic interaction between the AFM tip and sample is a fundamental problem that determines the output signal and imaging quality in these electrical non-contact AFM measurement
The electrostatic interactions of AFM tip with semiconductor samples were discussed in the frame of DebyeHückel theory and Green’s function theory, in which the metal and dielectric samples could be treated as special cases with zero and infinite Debye lengths respectively
A simple method for calculating the electrostatic interactions in AFM with semiconductor samples was proposed here in the frame of Debye-Hückel theory and Green’s function theory, in which the metal and dielectric samples can be thought as special cases with zero and infinite Debye lengths respectively
Summary
Atomic force microscopy (AFM) and its non-contact electrical modes such as Kelvin probe force microscopy (KPFM) and electrostatic force microscopy (EFM) have been extensively used to characterize the surface electrical properties of metal, dielectric and semiconductor materials and devices. The electrostatic interaction between the AFM tip and sample is a fundamental problem that determines the output signal and imaging quality in these electrical non-contact AFM measurement. EFM measurements on intrinsic and doped semiconductor materials have been reported such as carbon nanotube, NiOx, ZnO19 and GaN20 in recent years Their discussions about the experiment results have focused on the movement of minimum EFM phase shift on undoped and doped semiconductor samples, but neglecting the change of tip-sample interaction or capacitance caused by doping. The electrostatic interactions of AFM tip with semiconductor samples were discussed in the frame of DebyeHückel theory and Green’s function theory, in which the metal and dielectric samples could be treated as special cases with zero and infinite Debye lengths respectively. The tip electrostatic forces with bulk or thin-film semiconductor samples of various carrier concentrations were calculated, and the electric field strength above the sample surface was discussed. (3) A constant bias is applied between the tip and back electrode of the sample without contact loss
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