Electrical modelling of Kelvin structures for the derivation of low specific contact resistivity

Abstract

The characterisation of semiconductor processing steps requires the use of various test structures and devices. In developing low resistance ohmic contacts, test structures such as the Cross Bridge Kelvin Resistor which allow the extraction of the specific contact resistance, ρ c are commonly used. This paper describes the results of modelling undertaken on a Kelvin Resistor. The results suggest that the use of multiple structures allows the determination of very low values of ρ c. Introduction Continuing developments in semiconductor process technology have resulted in significant reductions in the specific contact resistance, ρc(Ω.cm2) of ohmic contacts. As device dimensions decrease, then so also must ρc in order not to compromise scaled device performance. Thus the derivation of ρc is an important part of device technology. The four terminal Cross Bridge Kelvin Resistor(CBKR) of fig.1 is commonly used to measure the contact interfacial resistance and so obtain an extracted value of specific contact resistance ρ’c. Error correction curves are then used to compensate for the semiconductor parasitic resistance and thus yield the true value of specific contact resistance ρc. However these correction curves, which are based on two dimensional models[1,2], become increasingly inaccurate due to the high correction factors occurring when low ρc values ( 1 for d/w=1. The difference between the two models is due to the 3-D model taking the vertical voltage drop in the semiconductor layer into account. Figures 4(a) and (b) give a good indication of of the improvement in accuracy in modelling the Kelvin structure in 3-D rather than 2-D. Fig. 4(a). Comparison of 2-D and 3-D models for the derivation of extracted ρ’c vs d/w for circular contacts. Fig. 4(b). Normalised values of ρ’c vs d/w for 2-D and 3-D models using square contacts. The variation of ρ’c/ρc with RSH=50Ω/o, is given in fig.5 where data for four RSH values at ρc=10-8 Ω.cm2 is plotted for circular contacts. A slight degradation in the linearity is observed as RSH increases to 200Ω/o, while an improvement occurs at lesser values. However, the linearity is more sensitive to the width of the test structure arms w, as illustrated by the data of fig. 6. Fig. 5. Normalised ρ’c values versus d/w (w=1μ m) for four RSH (Ω/o) values (circular contacts, ρc=10-8 Ω.cm2). Fig. 6. Normalised ρ’c values versus d/w for three test structure arm widths w, (circular contacts, ρ c=10-8 Ω.cm2). For example, extrapolation of the w=2μm curve in the 0.2<d/w<0.4 range yields a ρ’c/ρc value of ~0.65. Thus the ρc value obtained would be 6.5x10-9Ω.cm2, significantly less than the true value of 10-8 Ω.cm2. Note that this technique relies on the averaging of data from several test structures for the determination of ρc, whereas in conventional application of the CBKR test structure, one test structure followed by the application of a correction factor will yield a result. The data presented in this paper is derived from L-type CBKR models. A second type of Kelvin structure, the D-type structure, reduces the parasitic resistance contribution to the total resistance measured by further reducing the test structure arm widths. When the D-type structure is modelled, the data shows a greater non-linearity in ρ’c/ρc versus d/w despite a reduction in the magnitude of ρ’c/ρc compared with the equivalent L-type structure.