Micro-four-point probe Hall effect measurement method

Abstract

We report a new microscale Hall effect measurement method for characterization of semiconductor thin films without need for conventional Hall effect geometries and metal contact pads. We derive the electrostatic potential resulting from current flow in a conductive filamentary sheet with insulating barriers and with a magnetic field applied normal to the plane of the sheet. Based on this potential, analytical expressions for the measured four-point resistance in presence of a magnetic field are derived for several simple sample geometries. We show how the sheet resistance and Hall effect contributions may be separated using dual configuration measurements. The method differs from conventional van der Pauw measurements since the probe pins are placed in the interior of the sample region, not just on the perimeter. We experimentally verify the method by micro-four-point probe measurements on ultrashallow junctions in silicon and germanium. On a cleaved silicon ultrashallow junction sample we determine carrier mobility, sheet carrier density, and sheet resistance from micro-four-point probe measurements under various experimental conditions, and show with these conditions reproducibility within less than 1.5%.

Undoped and in-situ B doped GeSn epitaxial growth on Ge by atmospheric pressure-chemical vapor deposition

“…This competition actually occurs on the substitutional sites of the GeSn matrix. Using GeSn:B mobility values measured by micro-Hall measurements, 15 reported in Fig. 3(b), and sheet resistances measured by the micro-four-point-probe (M4PP) technique, 16 the active concentration of B in GeSn was calculated and is reported as function of the B 2 H 6 partial pressure, also in Fig.…”

Mesoscopic current transport in two-dimensional materials with grain boundaries: Four-point probe resistance and Hall effect

“…The maximum possible magnitude of the Hall effect signals is maxðjDR i jÞ ¼ 2R H , i.e., it can take any value between À2R H and 2R H . 17 It follows that the presence of a Hall effect signal is therefore also an indication of a defective material.…”

“…At the center of the shaded square, four equally spaced white dots show the positions of the four probe pins. This symmetric position of the M4PP ensures that in the case of a perfect uniform film, dual configuration measurements yield the sheet conductance of the material, 22 i.e., G s ¼ G 0 and that the Hall signals vanish, 17 i.e., DR i ¼ 0.…”

“…The average resistance R i depends on the sheet resistance including geometrical magnetoresistance. 17 For a sample with a highly non-uniform conductance and samples that are not simply connected, it is furthermore convenient to redefine the configuration resistances such that RÃ maxðj R i jÞ ; RC minðj R i jÞ ; RB RÃ À RC :…”

“…14 M4PP metrology can be used to measure the sheet resistance (or sheet conductance), and in addition, the method allows for extraction and evaluation of geometry related parameters such as the resistance ratio 15,16 and the Hall effect signal caused by the Lorentz force. 17 In previous work, 18 we developed a finite element (FE) model to investigate how the M4PP signature differs for measurements on 2D and quasi-1D materials; these signatures had already been observed experimentally. 15,16 We successfully validated the FE approach by comparing calculations for a single line defect to the analytical result.…”