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PROBLEM 2: Consider an MOS capacitor with a gate oxide 1.35 nm thick. The Si substrate doping is $N_A = 10^{15} cm^{-3}$. The gate voltage is selected so that the sheet density of electrons in the inversion layer is $n_s = 10^{15} cm^{-2}$. Assume room temperature and that $|Q_i| = qn_s = \sqrt{2\epsilon_s k_B T n_i^2/N_A} e^{\psi_s/2k_BT} Answer the following questions: a. What is the surface potential? Compare it with $2\phi_F$. b. How much does the surface potential need to increase to double the inversion\ layer density? c. How much does the gate voltage need to increase to double the inversion layer density? d. Explain in words why it is difficult to increase the surface potential for an MOS capacitor above threshold.

          PROBLEM 2:
Consider an MOS capacitor with a gate oxide 1.35 nm thick. The Si substrate doping is $N_A = 10^{15} cm^{-3}$. The gate voltage is selected so that the sheet density of electrons in the inversion layer is $n_s = 10^{15} cm^{-2}$. Assume room temperature and that
$|Q_i| = qn_s = \sqrt{2\epsilon_s k_B T n_i^2/N_A} e^{\psi_s/2k_BT}
Answer the following questions:
a. What is the surface potential? Compare it with $2\phi_F$.
b. How much does the surface potential need to increase to double the inversion\ layer density?
c. How much does the gate voltage need to increase to double the inversion layer density?
d. Explain in words why it is difficult to increase the surface potential for an MOS capacitor above threshold.

PROBLEM 2:
Consider an MOS capacitor with a gate oxide 1.35 nm thick. The Si substrate doping is NA = 10^15 cm^-3. The gate voltage is selected so that the sheet density of electrons in the inversion layer is ns = 10^15 cm^-2. Assume room temperature and that
|Qi| = qns = √(2 kB T ni^2/NA) e^/2kBT
Answer the following questions:
a. What is the surface potential? Compare it with2.
b. How much does the surface potential need to increase to double the inversion layer density?
c. How much does the gate voltage need to increase to double the inversion layer density?
d. Explain in words why it is difficult to increase the surface potential for an MOS capacitor above threshold.

Added by Joaquin N.

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