Gauge factor of thick-film resistors: Outcomes of the variable-range-hopping model

Abstract

Despite a large amount of data and numerous theoretical proposals, the microscopic mechanism of transport in thick film resistors remains unclear. However, recent low temperature measurements point toward a possible variable range hopping mechanism of transport. Here we examine how such a mechanism affects the gauge factor of thick film resistors. We find that at sufficiently low temperatures T , for which the resistivity follows the Mott's law R(T ) ∼ exp(T0/T ) 1/4 , the gauge factor GF is proportional to (T0/T ) 1/4 . Moreover, the inclusion of Coulomb gap effects leads to GF ∼ (T ′ 0 /T ) 1/2 at lower temperatures. In addition, we study a simple model which generalizes the variable range hopping mechanism by taking into account the finite mean inter-grain spacing. Our results suggest a possible experimental verification of the validity of the variable range hopping in thick film resistors.

Variable range hopping and thermally activated transport in molybdenum-based MXenes

“…1. Most of our compositions share characteristic features already observed in systems where highly conductive entities are separated by thin disordered regions such as granular metals and cermets [41][42][43][44][45][46][47][48][49][50]. The latter are defined herein as composites with high volume fractions of metal particles separated from each other by thin insulating layers.…”

“…The rationale for assuming VRH and thermal activation is that both relationships are characteristic of transport in disordered conductive media [41][42][43][44][45][46][47][48][49][50]. In such systems, E F is positioned in a band of localized states, separated from delocalized ones, that appear at higher energies, by a threshold referred to as the mobility edge, E C [53].…”

“…These low T 0 values are in much better agreement with those found in granular metals and cermets. In such "inhomogeneous" materials, the T 0 's usually range from 1 to 10 4 K [41][42][43][44][45][46][47], and the hopping is controlled by tunneling across thin insulating layers separating the highly metallic islands/grains [42], or the thin amorphous insulating films in the case of cermets [41,49]. Since in our materials it is reasonable to assume that the interflake space is disordered and DFT calculations confirm a large D(E F ) [40], we follow the lead of such models.…”

Tunneling-percolation origin of nonuniversality: Theory and experiments

“…72 A qualitatively similar enhancement of ⌫ as the temperature drops is expected also in models based on variable-range hopping mechanism of transport. 73 It should be pointed out, however, that in these works the problem of connectivity is not included so that the tunneling current flows on a network without percolation characteristics. Nevertheless, the percolation picture ͑with its corresponding critical exponents͒ seems to survive well also in the low-temperature tunneling regime.…”

Electro-mechanical properties of triblock copolymer styrene–butadiene–styrene/carbon nanotube composites for large deformation sensor applications

“…Pre-stretching will cause both an increase of the apparent Young modulus and a reorientation of the fillers to a unstable configuration. In this situation, a further increase of the stretching will lead both to larger internal stresses [23] and to larger variations of the conductive network, leading to larger values of the GF. Theoretical previous that aligned CNT make composite sample more sensitive (increase GF value) that non-aligned CNT [20] and this can be important to increase GF for bigger deformations, if the CNT align with the applied deformation in electromechanical tests.…”