Errors in Resistivities Calculated by Multilayer Analysis of Spreading Resistances

Abstract

The use of multilayer analysis schemes for calculating resistivity profiles from spreading resistance measurements in semiconductors is well established. All of the techniques make use of the approximation that the current density at a perfectly conducting probe can in all cases be represented by the current density which would exist in a medium of unitorm resistivity. We present improved approximate current density profiles for the case of a probe in contact with a single layer over an infinite substrate for a wide range of layer thickness to probe radius ratios and layer resistivity to substrate resistivity ratios. Using these we find the errors incurred using the standard approximation to be limited to 10% when the layer thicknesses become smaller than 10% of the probe radius and less for larger thicknesses. We find-there is a large class of current density profiles for which the situation is no worse, which may be desirable for reasons other than accuracy.

Defect Characterization in Monocrystalline Silicon Grown Over SiO2

“…Single crystal growth over amorphous substrates has received considerable attention recently (1)(2)(3)(4)(5)(6)(7)(8). Such structures are potentially useful in the area of solidstate device fabrication.…”

“…The most successful have been the scanning laser technique (5,6) and the strip heater method (7,8). If it is possible to preferentially melt the deposited silicon film in the vicinity of the single crystal seed, crystallization of the melt from the seed can occur via liquid phase epitaxy.…”

The Relation Between the Correction Factor and the Local Slope in Spreading Resistance

“…In particular, the three probe-current densities which were used were the Schumann and Gardner, the Choo uniform, and the ring delta function forms. These current densities and their extent of current constriction are discussed in detail elsewhere (3). These three forms of the current density gave rise to the curves denoted by A, B, and C, respectively.…”

“…The corresponding relation between the correction factor and the local slope of the spreading resistance is [5] where the local slope of the spreading resistance, M (x), is given by Eq. [3] and 2a In (S/a) K, _…”

“…2 J where S is the separation between the probes, J0(~a) and JI(~S) are the Bessel functions of zero and first order, respectively, A(x, ~) is the kernel of the integral and is related to the resistivity structure, Iv(Xa) is the Hankel transform of the generalized probecurrent density (3), and ~. is the integration variable.…”