Resistance blow-up effect in micro-circuit engineering

The nonlinearity in the I–V characteristics of a scaled-down micro/nano-scale resistive channel is shown to elevate the DC and signal resistance as current approaches its saturation value. The deviation from traditional circuit engineering takes place when the applied voltage is increased beyond the critical voltage Vc = (Vt/ℓ)L, where Vt is the thermal voltage, ℓ is the ohmic mean free path, and L is the length of the conducting channel. This resistance blow-up is more pronounced for a smaller-length resistor in a micro-circuit of two resistors with same ohmic value. The power consumed P = VI not only is lower but also is a linear function of voltage V as compared to the quadratic rise with V in the ohmic regime. The resistance blow-up effect also gives enhanced RC time constant for transients when a digital signal switches from low to high or vice versa. These results are of immense value to circuit designers and those doing device characterization to extract parasitic and transport parameters.