The Micro-circuit Engineering in the Nonohmic Domain

Considering the breakdown of Ohm´s law in micro-circuits, the direct and differential (incremental) resistance is shown to rise dramatically in the regime where applied voltage V triggering the nonohmic behavior is larger than the critical voltage V_co = (V_t / lscr_o ) L, where V_t is the thermal voltage lscr_o, is the Ohmic mean free path, and L is the length of the conducting channel. This resistance blow-up becomes more pronounced for a smaller-length resistor in a circuit where two resistors of equal ohmic values are connected in a series or parallel configuration. The power consumed not only is reduced but also is a linear function of voltage as compared to quadratic behavior in the ohmic regime. These results are of immense value to circuit engineers and those doing device characterization to extract parasitic and contact transport parameters.