A Closed-Form Quantum “Dark Space” Model for Predicting the Electrostatic Integrity of Germanium MOSFETs With High-$k$ Gate Dielectric

This paper provides a closed-form model of the “dark space (DS)” for Ge MOSFETs with high-
k
gate dielectrics. This model shows accurate dependences on barrier height, surface electric field, and quantization effective mass of the channel and gate dielectric. Our model predicts that the surface DS due to quantum confinement decreases with reverse substrate bias and increasing channel doping. Our model can be also used for devices with a steep retrograde doping profile. This physically accurate model will be crucial to the prediction of the subthreshold swing and electrostatic integrity of advanced Ge devices.