Is This MOS Capacitor Capacitance vs. Surface Potential Graph (Under Varying Temperatures) Physically Accurate?

Question

I’m analyzing the attached graph (which I wrote in Matlab), which shows the capacitance of an MOS capacitor as a function of the surface potential: $$\psi_s$$ for different temperatures. The graph displays distinct differences between the curves at various temperatures, and I want to confirm if these trends are consistent with theoretical expectations.

Questions:

1. Does the shape and behavior of the capacitance vs. surface potential curves align with physical results for an MOS capacitor under varying temperatures?
2. If the graph is correct, could someone explain the observed differences in capacitance as temperature changes (e.g., in terms of depletion width, carrier distribution, or other factors)?

System Parameters:

Here are the key parameters used for the analysis:
-Charge of an electron: $$q = 1.6 \times 10^{-19} \, \text{C}$$
-Boltzmann constant: $$k_B = 1.38 \times 10^{-23} \, \text{J/K}$$
-Vacuum permittivity: $$\varepsilon_0 = 8.85 \times 10^{-14} \, \text{F/cm}$$
-Relative permittivity of silicon: $$\varepsilon_{\text{Si}} = 11.8$$
-Relative permittivity of silicon dioxide: $$\varepsilon_{\text{ox}} = 3.9$$
-Doping concentration: $$N_A = 10^{15} \, \text{cm}^{-3}$$ -Oxide thickness: $$t_{\text{ox}} = 20*10^{-6} \, \text{cm}$$

Answer 1

20 micrometers is far larger than ever used in practice.

Na is typical. For a very large oxide thickness I expect the minimum capacitance to be not much smaller than Cox. I think something is wrong.

Also: phis(inv) is larger at low temperatures not smaller.