We have designed silicon NMOS capacitor. The metal gate has a gate potential M=1eV, the p layer is doped with an acceptor concentration of N₁=1x10¹6cm²³. The oxide has a thickness of 1000 angstroms. Based on this design find the following: a) Calculate the oxide capacitance (Farads/cm2) Cox b) Calculate the equilibrium depletion thickness Xdo c) Calculate the flatband voltage VFB d) Calculate the threshold voltage Vth e) Calculate the maximum depletion thickness Xdmax f) Calculate the minimum Capacitance Cmin

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**Silicon NMOS Capacitor Design Analysis**

In this section, we delve into the specifics of a silicon NMOS capacitor design. The capacitor features a metal gate with a gate potential of \(\phi_M = 1\) eV. The p-layer is characterized by an acceptor concentration of \(N_A = 1 \times 10^{16}\) cm\(^{-3}\). Additionally, the oxide layer in this setup has a thickness of 1000 angstroms.

**Tasks:**

Based on the given design parameters, below are the tasks to perform:

a) **Calculate the Oxide Capacitance (\(C_{ox}\))**: Express the result in Farads per square centimeter (F/cm\(^2\)).

b) **Determine the Equilibrium Depletion Thickness (\(x_{d0}\))**: Evaluate the thickness of the depletion region at equilibrium.

c) **Compute the Flatband Voltage (\(V_{FB}\))**: Calculate the voltage at which the energy bands of the semiconductor are flat, indicating zero band bending.

d) **Find the Threshold Voltage (\(V_{th}\))**: Calculate the voltage required to accumulate a strong inversion layer at the semiconductor-oxide interface.

e) **Evaluate the Maximum Depletion Thickness (\(x_{dmax}\))**: Determine the maximum extent of the depletion region that can be achieved.

f) **Calculate the Minimum Capacitance (\(C_{min}\))**: Compute the minimum value of capacitance achievable given the designed parameters. 

These calculations are fundamental in understanding the electrical characteristics and performance of the NMOS capacitor in various applications.
Transcribed Image Text:**Silicon NMOS Capacitor Design Analysis** In this section, we delve into the specifics of a silicon NMOS capacitor design. The capacitor features a metal gate with a gate potential of \(\phi_M = 1\) eV. The p-layer is characterized by an acceptor concentration of \(N_A = 1 \times 10^{16}\) cm\(^{-3}\). Additionally, the oxide layer in this setup has a thickness of 1000 angstroms. **Tasks:** Based on the given design parameters, below are the tasks to perform: a) **Calculate the Oxide Capacitance (\(C_{ox}\))**: Express the result in Farads per square centimeter (F/cm\(^2\)). b) **Determine the Equilibrium Depletion Thickness (\(x_{d0}\))**: Evaluate the thickness of the depletion region at equilibrium. c) **Compute the Flatband Voltage (\(V_{FB}\))**: Calculate the voltage at which the energy bands of the semiconductor are flat, indicating zero band bending. d) **Find the Threshold Voltage (\(V_{th}\))**: Calculate the voltage required to accumulate a strong inversion layer at the semiconductor-oxide interface. e) **Evaluate the Maximum Depletion Thickness (\(x_{dmax}\))**: Determine the maximum extent of the depletion region that can be achieved. f) **Calculate the Minimum Capacitance (\(C_{min}\))**: Compute the minimum value of capacitance achievable given the designed parameters. These calculations are fundamental in understanding the electrical characteristics and performance of the NMOS capacitor in various applications.
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