Question

Silicon is doped with a pentavalent element. The energy required to set the additional electron free is about:

• A. 0.01 eV
• B. 0.05 eV
• C. 0.72 eV
• D. 1.1 eV

Hint:

When considering the energy levels in doped semiconductors, it's essential to remember that the extra electrons or holes introduced by the dopant have much lower ionization energies compared to the intrinsic semiconductor.

Answer 1

The Correct Option is B

Step 1: Understanding the concept of doping.
When silicon (Si) is doped with a pentavalent element (such as phosphorus or arsenic), an additional electron is introduced in the conduction band. This electron is loosely bound to the donor atom and requires a small amount of energy to be freed.
Step 2: Energy required to free the electron.
The donor energy level lies just below the conduction band, and the energy required to free the electron is typically very small. This energy is required to excite the electron from the donor level to the conduction band.
Step 3: Estimation of the energy.
In practice, the donor energy level in silicon is around \( 0.05 \, eV} \), which is much smaller than the band gap energy of silicon (\( \approx 1.1 \, eV} \)).
\[ Energy required} \approx 0.05 \, eV} \] Step 4: Numerical Calculation.
The energy required to release the electron is given by the difference between the donor energy level and the conduction band. This energy is typically measured experimentally, and for silicon doped with a pentavalent element, this value is approximately:
\[ E_{donor}} \approx 0.05 \, eV} \] Thus, the energy required to set the electron free is \( \boxed{0.05 \, eV}} \).