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Micro-four-point probe Hall effect measurement method
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10.1063/1.2949401
/content/aip/journal/jap/104/1/10.1063/1.2949401
http://aip.metastore.ingenta.com/content/aip/journal/jap/104/1/10.1063/1.2949401

Figures

Image of FIG. 1.
FIG. 1.

The four-point probe configurations B and . The four probe pins (Nos. 1–4) have position vectors , , , and , respectively. In configuration B probe pins Nos. 1 and 3 are used for current injection, while probe pins Nos. 2 and 4 are used for potential measurements. In configuration the role of the probe pins is reversed.

Image of FIG. 2.
FIG. 2.

The arrangement of current injection sources (×) and modified images (◯) in the case of an insulating boundary at .

Image of FIG. 3.
FIG. 3.

The difference between measured voltages in configurations B and , when the region of interest is the upper half-plane, as a function of normalized position , where is the distance from the boundary to the probe center. Calculations [Eqs. (15) and (17)] are shown for four different angles, , between the line of the probe pins and the insulating boundary; the line of the probe pins and the boundary are parallel at .

Image of FIG. 4.
FIG. 4.

Position dependence of the average of the measured voltages in configurations B and when the region of interest is the upper half-plane. Voltages calculated from Eq. (18) for three different values of the relative Hall sheet resistance , 0.1, and 0.3, respectively, are shown. In silicon or germanium at ordinary magnetic flux densities.

Image of FIG. 5.
FIG. 5.

Arrangement of sources (*), ordinary images (×), and modified images (◯) in the narrow stripe .

Image of FIG. 6.
FIG. 6.

Position dependence of the difference between measured voltages in configuration B and when the region of interest is the stripe [Eq. (22); full line]. The width of the region is assumed to be , where is the probe pitch. For comparison the result for the upper half-plane region [Eq. (17); dashed line] is also shown. Finally, the approximate result from using only the first two terms in the infinite sum of Eq. (22) is shown, but cannot be distinguished from the full solution.

Image of FIG. 7.
FIG. 7.

Position dependence of the average measured voltages in configuration B and when the region of interest is the stripe [Eq. (23); upper set of curves]. The width of the region is assumed to be , where is the probe pitch. For comparison results for the upper half-plane region are also shown [Eq. (18); lower set of curves]. Results for three different values of the relative Hall sheet resistance are shown.

Image of FIG. 8.
FIG. 8.

SEM image of a pitch M4PP. The thick polysilicon cantilevers are coated with a 200 nm Ni thin film on a 10 nm Ti adhesion layer. The inset shows a close up SEM image of the cantilevers.

Image of FIG. 9.
FIG. 9.

Microscale Hall effect measurements on a boron doped ultrashallow junction in silicon. The silicon sample has been cleaved to form a semi-infinite sheet and a measurement scan from this edge was performed. The measurement data (●) and a fit (full line) using Eq. (17) with the Hall resistance and the position of the sample edge as fitting parameters are shown. The estimated position of the edge is .

Image of FIG. 10.
FIG. 10.

Illustration of a M4PP Hall effect measurement on a narrow stripe of highly doped Ge.

Image of FIG. 11.
FIG. 11.

Microscale Hall effect measurements on a wide -type Ge stripe, doped using a shallow boron implant. A line scan has been performed with a pitch probe between the two barriers. The measurement data (●) and a fit (full line) using Eq. (22) with the Hall sheet resistance, , first barrier position, , and stripe width, , as fitting parameters are shown.

Image of FIG. 12.
FIG. 12.

Arrangement of sources (×), modified images (◯), and ordinary images (+) in the upper right quarter plane case.

Tables

Generic image for table
Table I.

Hall sheet resistance and standard deviation extracted from M4PP Hall effect measurements on an ultrashallow boron doped junction in silicon. The active Hall sheet carrier density and Hall mobility are calculated from M4PP Hall effect and sheet resistance measurements using Eqs. (25) and (24). Four different experimental conditions with variation of electrode material (Au or Ni), probe pitch, , and measurement frequency, , were used.

Generic image for table
Table II.

Summary of measurements on the shallow -type germanium junction. The sheet resistance, and the Hall sheet resistance, , were measured using a pitch M4PP, and Hall sheet carrier density, , and Hall mobility, , calculated using Eqs. (25) and (24).

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/content/aip/journal/jap/104/1/10.1063/1.2949401
2008-07-11
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Micro-four-point probe Hall effect measurement method
http://aip.metastore.ingenta.com/content/aip/journal/jap/104/1/10.1063/1.2949401
10.1063/1.2949401
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