Modeling and measurement of contact resistances

Abstract

This paper presents a generalized model of ohmic contacts and a unified approach for the accurate extraction of specific contact resistivity (ρ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> ) for ohmic contacts from measured contact resistance using the cross bridge Kelvin resistor, the contact end resistor, and the tranmsission line tap resistor test structures. A general three-dimensional (3-D) model of the contacts has been developed from the first principles and has been reduced to 2-D, 1-D, and 0-D (one lump) models with the necessary approximations. It is shown that the conventional I-D models overestimate the value of ρ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> because of the parasitic resistance due to 2-D current flow around the periphery of the contact window. Using 2-D simulations, we have accurately modeled the current crowding effects and have extracted accurate values of ρ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> independent of contact size and the test structure type. A theory of scaling of contacts has been developed and is applied to commonly used structures. A universal set of curves has been derived for each particular contact resistance test structure and, given the geometry of the structure, these allow accurate determination of ρ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> , Without the actual use of the 2-D simulator. Experimental and theoretical accuracy of the three test structures has been compared. Accurate values of ρ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> for various contact materials to n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> and ρ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> Si have been determined. The data confirm that in the past researchers have overestimated ρ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> , and that ρ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> will not limit device performance even with submicrometer design rules.