The term high-κ dielectric refers to a material with a high dielectric constant (κ, kappa), as compared to silicon dioxide. High-κ dielectrics are used in semiconductor manufacturing processes where they are usually used to replace a silicon dioxide gate dielectric or another dielectric layer of a device. The implementation of high-κ gate dielectrics is one of several strategies developed to allow further miniaturization of microelectronic components, colloquially referred to as extending Moore's Law. Sometimes these materials are called "high-k" (pronounced "high kay"), instead of "high-κ" (high kappa). Need for high-κ materials Silicon dioxide () has been used as a gate oxide material for decades. As metal–oxide–semiconductor field-effect transistors (MOSFETs) have decreased in size, the thickness of the silicon dioxide gate dielectric has steadily decreased to increase the gate capacitance (per unit area) and thereby drive current (per device width), raising device performance. As the thickness scales below 2 nm, leakage currents due to tunneling increase drastically, leading to high power consumption and reduced device reliability. Replacing the silicon dioxide gate dielectric with a high-κ material allows increased gate capacitance without the associated leakage effects. First principles The gate oxide in a MOSFET can be modeled as a parallel plate capacitor. Ignoring quantum mechanical and depletion effects from the Si substrate and gate, the capacitance of this parallel plate capacitor is given by where is the capacitor area is the relative dielectric constant of the material (3.9 for silicon dioxide) is the permittivity of free space is the thickness of the capacitor oxide insulator Since leakage limitation constrains further reduction of , an alternative method to increase gate capacitance is alter κ by replacing silicon dioxide with a high-κ material. In such a scenario, a thicker gate oxide layer might be used which can reduce the leakage current flowing through the structure as well as improving the gate dielectric reliability. Gate capacitance impact on drive current The drain current for a MOSFET can be written (using the gradual channel approximation) as where is the width of the transistor channel is the channel length is the channel carrier mobility (assumed constant here) is the capacitance density associated with the gate dielectric when the underlying channel is in the inverted state is the voltage applied to the transistor gate is the threshold voltage The term is limited in range due to reliability and room temperature operation constraints, since a too large would create