Anisotropic random resistor networks: a model for piezoresistive response of thick-film resistors

TL;DR

This paper models the piezoresistive response of thick-film resistors using anisotropic percolative resistor networks governed by tunneling, revealing universal behaviors near the metal-insulator transition.

Contribution

It introduces a minimal percolative resistor network model with tunneling to describe transport and piezoresistive properties of thick-film resistors, highlighting universal critical behaviors.

Findings

Piezoresistive response is model-dependent away from the percolation threshold.

Near the metal-insulator transition, the anisotropy exhibits power-law behavior.

A universal relation between conductance and anisotropy is identified.

Abstract

A number of evidences suggests that thick-film resistors are close to a metal-insulator transition and that tunneling processes between metallic grains are the main source of resistance. We consider as a minimal model for description of transport properties in thick-film resistors a percolative resistor network, with conducting elements governed by tunneling. For both oriented and randomly oriented networks, we show that the piezoresistive response to an applied strain is model dependent when the system is far away from the percolation thresold, while in the critical region it acquires universal properties. In particular close to the metal-insulator transition, the piezoresistive anisotropy show a power law behavior. Within this region, there exists a simple and universal relation between the conductance and the piezoresistive anisotropy, which could be experimentally tested by common cantilever bar measurements of thick-film resistors.