In an n-type semiconductor, the fermi level lies 0.3 eV below the conduction band at 300 K. If the temperature is increased to 330K, where does the new position of the Fermi level lie?

Options

A. 0.55 eV below the conduction band
B. 0.44 eV below the conduction band
C. 0.33 eV below the conduction band
D. 0.27 eV below the conduction band

Answer

To solve the problem of determining the new position of the Fermi level in an n-type semiconductor when the temperature is increased from 300 K to 330 K, we can follow these steps:

### Step 1: Understand the Initial Conditions
At 300 K, the Fermi level (E_F) is given to be 0.3 eV below the conduction band (E_C). This can be expressed as:
\[ E_F = E_C - 0.3 \, \text{eV} \]

### Step 2: Analyze the Effect of Temperature on the Fermi Level
As the temperature increases, the thermal energy allows more electrons to move from the valence band to the conduction band. This means that the Fermi level will shift closer to the conduction band because the probability of finding electrons in the conduction band increases.

### Step 3: Determine the New Position of the Fermi Level
While we do not have a specific formula to calculate the exact new position of the Fermi level at 330 K, we can qualitatively state that the Fermi level will move closer to the conduction band. Since the Fermi level was initially 0.3 eV below the conduction band at 300 K, it will now be at a position that is less than 0.3 eV below the conduction band.

### Step 4: Evaluate the Options
We need to find the option that indicates the new position of the Fermi level is less than 0.3 eV below the conduction band. The options provided are:
1. 0.55 eV below the conduction band
2. 0.44 eV below the conduction band
3. 0.33 eV below the conduction band
4. 0.27 eV below the conduction band

Since we established that the new Fermi level must be closer to the conduction band than 0.3 eV, we can eliminate options 1, 2, and 3. The only option that is less than 0.3 eV is:

**Option 4: 0.27 eV below the conduction band.**

### Conclusion
Thus, the new position of the Fermi level at 330 K in the n-type semiconductor is 0.27 eV below the conduction band.

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