Fast micro Hall effect measurements on small pads

Frederik Westergaard Østerberg, Dirch Hjorth Petersen, Peter F. Nielsen, Erik Rosseel, Wilfried Vandervorst, Ole Hansen

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Sheet resistance, carrier mobility, and sheet carrier density are important parameters in semiconductor production, and it is therefore important to be able to rapidly and accurately measure these parameters even on small samples or pads. The interpretation of four-point probe measurements on small pads is non-trivial. In this paper we discuss how conformal mapping can be used to evaluate theoretically expected measurement values on small pads. Theoretical values calculated from analytical mappings of simple geometries are compared to the values found from the numerical conformal mapping of a square onto the infinite half-plane, where well-established solutions are known. Hall effect measurements are performed to show, experimentally, that it is possible to measure Hall mobility in less than one minute on squares as small as 7070 lm2 with a deviation of 66.5% on a 1r level from accurate reference measurements, when only small sheet resistance variations are present. For samples with a sheet resistance variation of more than 5%, a more time consuming method must be used. Here, the theoretically expected measurement values are computed based on the sheet resistance variation using a finite element method. This more accurate method has an experimental repeatability of 61.6% even on inhomogeneous samples.
Original languageEnglish
Article number033707
JournalJournal of Applied Physics
Issue number3
Publication statusPublished - 2011


  • Finite element analysis
  • Hall mobility
  • Carrier density
  • Conformal mapping
  • Geometry

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