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Hall Effect Measurement System

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Physics


Principles

The determination of the electrical properties (resistivity, carrier concentration and mobility) of various materials and layers employs the van der Pauw and Hall methods.

Using a square shaped sample with small contacts at the corners, the resistivity is given by

images/f_rho_is.gif

Starting from

images/f_vh_is.gif

the Hall coefficient RH is defined by

images/f_rh_is.gif

with F  :  correction factor
  D  :  thickness
  RI / U  :  four point resistance of the sample
  RI / UB  :  Hall resistance at magnetic field B
  1, 2, 3, 4  :  clockwise counted sample contacts

Carrier concentration, mobility and the carrier type are now obtained using

images/f_rho_rh.gif

Assuming images/f_nggp.gif leads to

images/f_result.gif

with n, p  :  carrier concentration
  µn, p  :  carrier mobility
  b  :  = µn / µp

For images/f_pggn.gif similar expressions with positive sign result.


References

 [1]  R.N. Hall, Phys. Rev., 87, 387 (1952)
 [2]  L.J. van der Pauw, Philips Res. Rep., 13, 1 (1958)
 [3]  L. Cohausz, Ph.D. Thesis, Kassel 1987


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