Question

The energy gap is much more in silicon than in germanium because

• A. It has less number of electrons
• B. It has high atomic mass number
• C. Its crystal has much stronger bonds called ionic bonds
• D. Its valence electrons are more tightly bound to their parent nuclei
• E. Its valence electrons are more loosely bound to their parent nuclei

Hint:

Smaller atoms generally have larger band gaps. As you move down a group in the periodic table, the atomic size increases and the energy gap decreases because valence electrons are further from the nucleus.

Answer 1

The Correct Option is D

Concept: The forbidden energy gap in a semiconductor is the energy required to break a covalent bond and move an electron from the valence band to the conduction band. This gap size depends on the strength of the atomic attraction.

Step 1: {Analyze the atomic radii of Si and Ge.}
Silicon ($Z=14$) is smaller than Germanium ($Z=32$). In Silicon, the valence electrons are in the $n=3$ shell, which is closer to the nucleus than the $n=4$ shell of Germanium.

Step 2: {Relate atomic size to nuclear attraction.}
Because Silicon's valence electrons are closer to the nucleus, they experience a stronger electrostatic pull from the parent nuclei compared to the more shielded electrons in Germanium.

Step 3: {Link nuclear attraction to the energy gap.}
Tighter electron binding means more external energy is required to excite an electron into the conduction band. Consequently, Silicon has a wider band gap ($\approx 1.1$ eV) than Germanium ($\approx 0.7$ eV).