To calculate the body-effect coefficient $\gamma$ for a MOS device, we use the following formula:

$\gamma = \frac{\sqrt{2 q \varepsilon_s N_A}}{C_{ox}}$

Where:

• $q$ is the electron charge ($1.6 \times 10^{-19} \, C$),
• $\varepsilon_s$ is the permittivity of silicon ($\approx 11.7 \times 8.854 \times 10^{-14} \, F/cm$),
• $N_A$ is the acceptor doping concentration ($10^{16} \, /cm^3$),
• $C_{ox}$ is the oxide capacitance per unit area, given by: $C_{ox} = \frac{\varepsilon_{ox}}{t_{ox}}$ where $\varepsilon_{ox}$ is the permittivity of silicon dioxide ($3.9 \times 8.854 \times 10^{-14} \, F/cm$), and $t_{ox}$ is the oxide thickness (in cm).

Step 1: Calculate $C_{ox}$

Given:

• $t_{ox} = 20 \, nm = 20 \times 10^{-7} \, cm$,
• $\varepsilon_{ox} = 3.9 \times 8.854 \times 10^{-14} \, F/cm$,

$C_{ox} = \frac{3.9 \times 8.854 \times 10^{-14}}{20 \times 10^{-7}} \, F/cm^2$

Step 2: Calculate $\gamma$

Now, substituting the values of $q$, $\varepsilon_s$, and $N_A$, we calculate $\gamma$.

Let me calculate these values for you.The body-effect coefficient $\gamma$ for the MOS device is approximately $0.333 \, V^{0.5}$.

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. What is the significance of the body-effect coefficient in MOS devices?
2. How does the oxide thickness influence the body-effect coefficient?
3. How does the doping concentration affect the threshold voltage?
4. What role does the permittivity of materials play in MOS devices?
5. How can we reduce the body effect in MOS transistors?

Tip: Increasing the oxide thickness decreases the oxide capacitance, which in turn increases the body-effect coefficient $\gamma$.