Failure of Ohm’s law and circuit design

Abstract

Ohm's law is at the heart of circuit theory both for digital and analogue applications. Ohm's law depicts the linear current response I to the applied voltage V across a length of resistor. The resistance, as inverse slope of current-voltage (I-V)graph, is constant and is extensively used in the published literature. However, the linear response transforms to a sublinear response with current eventually saturating to a constant value I,m. Nonohmic behaviour is distinctly visible when applied voltage V is larger than the critical voltage v:e =V,L / e= (V> v,), V, is the thermal voltage with value 0.0259 V at room temperature and t ow(typically 100 urn) is the mean free path (mfp) in a nanoscale (L < 1000nm) device. The breakdown of Ohm's law affects heavily the flow of transporting carrier in a nanoscale device. The surge in direct resistance R~V/I and incremental FdV/dI changes the time constants, power consumption, voltage and current division laws. The transient RC switching delay in micro/nano-scale circuit is strongly affected by the surge in the resistance arising out of sub-linear current-voltage (I-V) characteristics. The goal is to investigate the circuit laws when Ohm's law is not applicable. Factors affecting the critical voltage beyond which Ohm's law fails in scaled-down nanostructures have been studied in this project.The theory to ID silicon nanowire, 2D AlGaAs nano-layer and 3D bulk resistor have been applied. The mechanism of current saturation is studied here. Numerical codes using MATLAB simulation software are developed. Each resistor in addition to its ohmic value R; must also be described by either the critical voltage V, or saturation current 1,01' connected by the relation v:e =I,olRo whose default value is assumed to be infinite when Ohm's law is applicable. The research framework is based on Non equilibriumArora's Distribution Function (NEADF).