Chapter 2 · Visualization 5 of 6 · Section 2.7
C-V Curve Lab
Change the oxide, the doping, the gate material and the interface charge and watch the capacitance-voltage curve move. Compare the low-frequency and high-frequency curves.
Gate-body capacitance per unit area versus gate voltage
What to look for C′gb = C′ox C′c / (C′ox + C′c ), C′c = −∂Q′C /∂ψS = C′b + C′i
The accumulation plateau gives C′ox and hence tox . The minimum gives the depletion width and hence NA . The curve is shifted along the voltage axis by VFB = ΦMS − Q′o /C′ox . A p⁺ gate shifts it to the right of an n⁺ gate by about 1.1 V. At low frequency inversion electrons follow the signal and C′gb returns to C′ox . At high frequency they cannot, and C′gb stays at C′min . Try this Increase Q′o /q to 5×10¹¹ cm⁻². How far does the curve move? Repeat for tox = 10 nm. Compare NA = 10¹⁶ and 10¹⁸ cm⁻³. Where does C′min sit relative to C′ox in each? Switch the gate from n⁺ to p⁺ polysilicon and read the new VFB and VT in the panel.
Model: exact one-dimensional Poisson solution for a p-type MOS capacitor with Boltzmann statistics, following Chapter 2 of Tsividis and McAndrew, Operation and Modeling of the MOS Transistor . ni = 1010 cm⁻³ at 300 K, εs = 11.7 ε0 , εox = 3.9 ε0 , Q′o /q = 10¹⁰ cm⁻² unless a slider changes it. Values are for teaching and are not a process simulation.