Formal Comparison of Correction Formulae for Spreading Resistance Measurements on Layered Structures

Abstract

The spreading resistance of a metal contact on a semiconductor sample is analysed for infinite geometry, with three different boundary conditions: a specified potential of the contact, a uniform contact current density and a current density dependent on contact resistance. The cases of a thin layer on a perfectly conducting substrate and on a non-conducting substrate are analysed each for the boundary conditions of uniform current density and of the current density distribution valid for the infinite geometry. With a perfectly conducting substrate the two boundary conditions yield about 10% difference. With a non-conducting substrate calculations based on both current density distributions produce in the thin layer approximation the same In r dependence required. The constant terms in both approaches are different by 5% and the constant current density result in addition agrees with the result obtained with a totally different transmission-line approach. The actual three-point-probe measurement situation is discussed. The danger of correcting the precise spreading resistance measurement results with an error of 1%, with formulae derived on the basis of a formal model which is sensitive to the choice of the boundary conditions by up to 10%, is stressed. The effects of undefined thickness, bevel edge and transition layer curving upwards are mentioned as further complications.