Current crowding and spreading resistance of electrical contacts with irregular contact edges

Abstract

Abstract Practical electrical contact edges are irregular either macroscopically due to fabrication errors or microscopically due to the nature of edge or surface roughness. However, electrical contact models typically assume ideal and regular contact geometries, where geometrical effects of the irregular electrode edges are not well characterized. This paper studies current crowding and spreading resistance of electrical contacts with irregular contact edges. Using finite element method based numerical simulations, we investigate the scaling of total resistance, spreading resistance, potential drop and current distribution for electrical contacts of tilted contact edges, with various electrode lengths <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>a</mml:mi> </mml:math> and edge angles <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>θ</mml:mi> </mml:math> . It is found that as the contact edge angle <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>θ</mml:mi> </mml:math> increases, the spreading resistance and therefore the total resistance decreases. This is attributed to the increased current crowding towards the corner of the longer electrode side edge when the edge tilt increases, leading to shorter current conduction paths. For a given edge tilt angle <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>θ</mml:mi> </mml:math> , the scaling of spreading resistance with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>a</mml:mi> </mml:math> follows closely that of zero edge angle <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>θ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:math> : the spreading resistance decreases with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>a</mml:mi> </mml:math> when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>a</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>h</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>1</mml:mn> </mml:math> and then converges to a constant when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>a</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>h</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>h</mml:mi> </mml:math> is the thickness of the conductor. The current density distribution near the electrical contacts are shown for different edge angles <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>θ</mml:mi> </mml:math> .