Quantitative Kelvin probe force microscopy
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Quantitative Kelvin probe force microscopy Christine Baumgart, Manfred Helm, and Heidemarie Schmidt Institute of Ion Beam Physics and Materials Research, Forschungszentrum Dresden-Rossendorf e.V., P.O. Box 510119, 01314 Dresden, Germany ABSTRACT In this paper we report on the investigation of electrostatic forces between a conductive probe and semiconducting materials by means of Kelvin probe force microscopy measurements. Due to the formation of an asymmetric electric dipole at the semiconductor surface, the measured KPFM bias is related with the energy difference between Fermi energy and respective band edge. Quantitative Kelvin probe force microscopy measurements on semiconductors, namely on a conventional dynamic random-access memory cell and on a cross-sectionally prepared Si epilayer structure, are presented. INTRODUCTION Failure analysis and optimization of nanoelectronic devices demand knowledge of their electrical properties. Especially, quantitative dopant profiling of semiconducting materials is of utmost importance for the semiconductor industry. The most straightforward nanometrology technique is the Kelvin probe force microscopy (KPFM) where electrostatic forces are detected at a lock-in frequency below the resonance frequency of the cantilever. The KPFM technique is derived from a method developed by Lord Kelvin in 1898 [1] and was primarily combined with the AFM technique to investigate electrostatic forces between probe and metals [2] and between probe and semiconductors [3]. KPFM has also been used to investigate the electrostatic forces between probe and insulators, e.g. caused by the Madelung surface potential [4]. We note that a mathematical description of the electrostatic forces between tip and sample is of strong contemporary interest, see for example Refs. [4,5], and strongly depends on the distance between the surface of the sample and the equilibrium rest position of the oscillating tipcantilever system. The true height has to be calibrated for quantitative electrostatic force measurements using KPFM. For quantitative dopant profiling in semiconductors the measured KPFM bias has to be evaluated with a correct physical model. Nonnenmacher et al. [2] interpreted the measured KPFM bias as the contact potential difference (CPD) between the conductive probe and the sample material. However, since its introduction the CPD model could not be used for quantitative dopant profiling. Observed differences between CPD simulations and KPFM measurements have been mainly ascribed to charges trapped in surface states [6-10]. Only recently we were able to show that the CPD model is not suitable to describe the KPFM signal above semiconducting materials [11]. Due to the asymmetric electric dipole which is naturally formed in the semiconductor surface region, the electrostatic force between probe and sample can only be minimized by applying [EC − EF(n)]/e and [EV − EF(p)]/p to n-type and p-type conducting regions, respectively. Quantitative KPFM measurements are successfully shown on a conventi
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