We are tasked with finding the location of the Fermi level in a doped silicon wafer. The key data provided are:

• Phosphorus concentration ($N_D$) = $5 \times 10^{16} \, \text{cm}^{-3}$
• Boron concentration ($N_A$) = $6 \times 10^{16} \, \text{cm}^{-3}$
• Intrinsic carrier concentration ($n_i$) = $10^{10} \, \text{cm}^{-3}$
• Effective density of states in conduction band ($N_C$) = $2.82 \times 10^{19} \, \text{cm}^{-3}$
• Temperature = 300 K

Since both donor ($N_D$) and acceptor ($N_A$) atoms are present, we need to account for the net doping. The net dopant concentration ($N_{net}$) is:

$N_{net} = N_A - N_D = 6 \times 10^{16} - 5 \times 10^{16} = 1 \times 10^{16} \, \text{cm}^{-3}$

This is a p-type semiconductor because $N_A > N_D$.

To find the Fermi level, we can use the following relation for a p-type semiconductor:

$E_F = E_i + kT \ln\left(\frac{p}{n_i}\right)$

Where:

• $E_i$ is the intrinsic Fermi level,
• $kT$ is the thermal energy at 300K ($kT \approx 0.0259 \, \text{eV}$),
• $p$ is the hole concentration (which for p-type is approximately $p \approx N_A$),
• $n_i$ is the intrinsic carrier concentration.

Thus, the Fermi level can be calculated by:

$E_F = E_i - kT \ln\left(\frac{N_A}{n_i}\right)$

Let me compute this.The Fermi level ($E_F$) is approximately $-0.404 \, \text{eV}$ below the intrinsic level.

Now, to find the location of the Fermi level relative to the conduction band, we use the fact that for a typical semiconductor:

$E_F = E_C - E_F$

Given that the intrinsic level is located symmetrically between the conduction and valence bands, and the Fermi level is shifted downward for a p-type semiconductor, the Fermi level's location with respect to the conduction band edge will be approximately 0.404 eV.

From the options provided, the closest value is:

$\boxed{0.56 \, \text{eV}}$

Would you like more details on this or to explore further?

Here are five related questions you might consider:

1. How does doping concentration affect the Fermi level in semiconductors?
2. What happens to the Fermi level in n-type semiconductors?
3. How does temperature affect the intrinsic carrier concentration?
4. How is the density of states derived for the conduction band?
5. What is the significance of the Fermi level in determining electrical conductivity?

Tip: In semiconductors, the Fermi level helps predict the behavior of charge carriers at different doping levels and temperatures.