To determine the location of the Fermi level ($E_F$) with respect to the conduction band edge ($E_C$) for a doped intrinsic Si wafer at 300K, we can follow these steps:

Step 1: Find the net doping concentration

Given:

• Phosphorus atoms (donors) = $N_D = 5 \times 10^{16} \, \text{cm}^{-3}$
• Boron atoms (acceptors) = $N_A = 6 \times 10^{16} \, \text{cm}^{-3}$

The net doping concentration can be calculated as: $N_D - N_A = 5 \times 10^{16} - 6 \times 10^{16} = -1 \times 10^{16} \, \text{cm}^{-3}$ Since $N_A > N_D$, this is a p-type semiconductor with a net acceptor concentration of $10^{16} \, \text{cm}^{-3}$.

Step 2: Use the formula for the hole concentration

In a p-type semiconductor, the hole concentration ($p$) is approximately equal to the net acceptor concentration ($N_A - N_D$): $p \approx N_A - N_D = 10^{16} \, \text{cm}^{-3}$

Step 3: Calculate the electron concentration

The electron concentration $n$ in a p-type semiconductor can be found using the mass action law: $n \cdot p = n_i^2$ where $n_i = 10^{10} \, \text{cm}^{-3}$ is the intrinsic carrier concentration.

Thus, the electron concentration $n$ is: $n = \frac{n_i^2}{p} = \frac{(10^{10})^2}{10^{16}} = 10^4 \, \text{cm}^{-3}$

Step 4: Use the formula for the Fermi level

The Fermi level with respect to the conduction band edge ($E_F - E_C$) in a p-type semiconductor is given by: $E_F - E_C = kT \ln\left(\frac{n}{N_C}\right)$ where:

• $kT = 0.0259 \, \text{eV}$ at 300K
• $N_C = 2.82 \times 10^{19} \, \text{cm}^{-3}$
• $n = 10^4 \, \text{cm}^{-3}$

Substituting these values into the equation: $E_F - E_C = 0.0259 \ln\left(\frac{10^4}{2.82 \times 10^{19}}\right)$ $E_F - E_C = 0.0259 \ln(3.55 \times 10^{-16})$ $E_F - E_C = 0.0259 \times (-35.57)$ $E_F - E_C \approx -0.92 \, \text{eV}$

Step 5: Conclusion

Thus, the Fermi level is approximately 0.92 eV below the conduction band edge.

The correct answer is: d) 0.92 eV

Would you like more details on any step, or have any other questions?

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Here are 5 related questions to expand on this topic:

1. How does temperature affect the intrinsic carrier concentration in a semiconductor?
2. What happens to the Fermi level position when the doping level increases?
3. How does the effective density of states at the conduction band ($N_C$) change with temperature?
4. How would the Fermi level shift in an n-type semiconductor under similar conditions?
5. What are the key differences between intrinsic and extrinsic semiconductors?

Tip: Always ensure to check whether a semiconductor is n-type or p-type by comparing donor and acceptor concentrations before calculating the Fermi level.