<formula formulatype="inline"><tex>$1/f$</tex></formula> Electrical Noise in Planar Resistors: The Joint Effect of a Backgating Noise and an Instrumental Disturbance

Abstract

Any planar resistor (channel) close to a conducting layer left floating (gate) forms a capacitor <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> whose thermal voltage noise ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">kT</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> noise) has a backgating effect on the sheet resistance of the channel that is a powerful source of 1/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> resistance noise in planar resistors and, hence, in planar devices. This 1/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> spectrum is created by the bias voltage <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DS</sub> applied to the resistor, which is a disturbance that takes it out of thermal equilibrium and changes the resistance noise that existed in the unbiased device. This theory, which gives the first electrical explanation for 1/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> electrical noise, not only gives a theoretical basis for the Hooge's formula but also allows the design of proper shields to reduce 1/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> noise.