Question 1 of 9intermediate🔍 AnalyzeShort Answer2 marks

C, Si and Ge have same lattice structure. Why is C insulator while Si and Ge intrinsic semiconductors?

Correct Answer

C, Si, and Ge have the same lattice structure and four valence electrons, but their bonding electrons lie in different orbits. The 4 bonding electrons of C, Si, and Ge lie in the second, third, and fourth orbit, respectively.

Consequently, the energy required to take out an electron differs. The energy gap for C is very large (5.4 eV), whereas for Si and Ge, it is smaller (1.1 eV and 0.7 eV, respectively). Due to this large energy gap, the number of free electrons for conduction is negligibly small in C, making it an insulator. In contrast, Si and Ge have smaller gaps, allowing a significant number of free electrons for conduction, making them intrinsic semiconductors.

Exercise: Example 14.1 | Q: Example 14.1 | (Page Page 7)
For More Understanding

Explanation

The answer is derived directly from Example 14.1 and the surrounding text in the provided context. It highlights that while the lattice structure is identical, the difference arises from the orbital position of valence electrons (2nd for C, 3rd for Si, 4th for Ge). This leads to a significant difference in the energy gap (EgE_g). The context explicitly states the energy gaps (5.4 eV for C, 1.1 eV for Si, 0.7 eV for Ge) and concludes that C has negligibly small free electrons compared to Si and Ge.

Solution Steps

  1. Step 1: Identify the location of bonding electrons for each element (C: 2nd orbit, Si: 3rd orbit, Ge: 4th orbit).

  2. Step 2: Compare the energy gap values provided in the text (C: 5.4 eV, Si: 1.1 eV, Ge: 0.7 eV).

  3. Step 3: Conclude that a large energy gap results in negligible free electrons (Insulator), while smaller gaps allow significant conduction (Semiconductor).

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