A Threshold Voltage Definition Based on a Standardized Charge Versus Voltage Relationship

Threshold voltage defined by a band bending of twice the substrate intrinsic-to-Fermi level difference has been widely accepted. However, there are shortcomings with this analytical definition. Since the inversion condition is governed by the substrate Fermi level (i.e., majority carrier density per volume), inversion carrier density per area at threshold inadequately depends on substrate doping and temperature. Another problem is that the definition is not applicable to fully depleted thin body devices, such as FinFETs and silicon-on-insulator FETs, widely used today. To solve these problems, a new definition of threshold voltage is proposed, which is based on a standardized charge versus voltage relationship of ideal metal-oxide-semiconductor capacitors. Threshold voltage is specified by a threshold inversion carrier density per area, which is a simple function of gate oxide capacitance and thermal voltage. Dependence of the proposed threshold voltage on substrate doping, body thickness, and temperature for both bulk and double-gate FETs is discussed using semi-classical analytical equations.