Voltage and temperature dependence of capacitance of high-k HfO/sub 2/ MIM capacitors: a unified understanding and prediction

High-k MIM capacitors like HfO/sub 2/ are of great interest for Si analog and RF applications recently. This work is intended to explain the dependences of VCC on dielectric thickness and frequency as well as the temperature dependence of capacitance of HfO/sub 2/ MIM capacitors. Based on a free carrier injection model, a unified understanding is achieved for the first time: (1) the thickness (t) dependence of VCC (/spl alpha/), which exhibits a relation of /spl alpha//spl prop/t/sup -n/, is an intrinsic property due to E-field polarization; (2) the frequency dependence of VCC, the stress induced VCC, and temperature dependences of capacitance are all due to change of relaxation time with different carrier mobility in the insulator. This model is also applied to predict the VCC for future applications.