Error Propagation in Contact Resistivity Extraction Using Cross-Bridge Kelvin Resistors

The cross-bridge Kelvin resistor is a commonly used method for measuring contact resistivity (ρ
c
). For low ρ
c
, the measurement has to be corrected for systematic error using measurements of contact resistance, semiconductor sheet resistance, and device dimensions. However, it is not straightforward to estimate the propagation of random measurement error in the measured quantities on the extracted ρ
c
. In this paper, a method is presented to quantify the effect of random measurement error on the accuracy of ρ
c
extraction. This is accomplished by generalized error propagation curves that show the error in ρ
c
caused by random measurement errors. Analysis shows that when the intrinsic resistance of the contact is smaller than the semiconductor sheet resistance, it becomes important to consider random error propagation. Comparison of literature data, where ρ
c
<; 5 ·10
^-8
Ω · cm
²
has been reported, shows that care should be taken since, even assuming precise electrical data, a 1% error in the measurement of device dimensions can lead to up to ~ 50% error in the estimation of ρ
c
.