Sketch the small-signal model for a MOS capacitor.
This can easily be accomplished with an understanding of the causes of capacitance within a MOSFET. Obviously, there is the oxide capacitance but there are also two other capacitances caused by the depletion layer, and by the inversion layer, . This equivalent circuit, therefore, is shown below.
Given a MOS Capacitor, sketch the capacitance vs. voltage curve at both low frequency (<1Hz) and high frequency (>100kHz).
I love MOSFETs and capacitance-based questions are great as they’re some of the first things you’re exposed to in an advanced FET class (since they’re just a two-terminal device). A plot of this capacitance is shown below. The capacitance at low values of VGB are approximately equal to the oxide-capacitance (although, recalling the previous question, cannot be exactly equal since the parallel combination of the inversion and depletion capacitors are in series with the oxide capacitor). At low frequencies, the inversion charge is able to change at the same rate as VGB and, thus, the inversion layer capacitance is larger at increasing values of VGB (remember, Q=VC). However, since the concentration of electrons can only be changed by thermal generation and recombination, the inversion charge struggles to keep up with a rapidly changing VGB. This results in a smaller amount of inversion charge which decreases the overall MOS capacitance.
(As a note: my absolute favorite textbook is called “Operation and Modeling of the MOS Transistor” by Yannis Tsividis and Colin McAndrew. Anybody with an interest in MOSFETs should absolutely BUY THIS BOOK as it explains everything you’d ever want to know about MOSFETs in a really great and understandable way.)