In a pure, or intrinsic, semiconductor, valence band holes and conduction-band electrons are always presenta)such that number of holes is greater than the number of electronsb)in equal numbersc)such that number of electrons is greater than the number of holesd)none of theseCorrect answer is option 'B'. Can you explain this answer?

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Answer

Pure Semiconductor: Valence Band Holes and Conduction-Band Electrons

In a pure, or intrinsic, semiconductor, the valence band holes and conduction-band electrons are always present. However, the number of these charge carriers can vary.

Valence Band and Conduction Band:
Before understanding the number of valence band holes and conduction-band electrons in a pure semiconductor, let's briefly discuss the valence band and conduction band.

- The valence band is the highest energy band that is fully occupied by electrons at absolute zero temperature. The electrons in the valence band are tightly bound to the atoms and do not contribute to electrical conductivity.

- The conduction band is the energy band located above the valence band. It contains energy levels that are vacant or can be easily occupied by electrons when an external energy source is applied. Electrons in the conduction band can move freely and contribute to electrical conductivity.

Number of Valence Band Holes and Conduction-Band Electrons:
In a pure semiconductor, the number of valence band holes and conduction-band electrons depends on the energy gap between the valence band and the conduction band. The energy gap is the energy difference between the valence band and the conduction band.

- When the energy gap is small:
- Some valence band electrons can gain enough energy to jump into the conduction band, leaving behind empty spaces in the valence band called 'holes.'
- The number of valence band holes is approximately equal to the number of conduction-band electrons.

- When the energy gap is large:
- The number of valence band holes is significantly greater than the number of conduction-band electrons.
- The energy required for valence band electrons to jump into the conduction band is too high, resulting in a limited number of conduction-band electrons.

Answer: Option B (in equal numbers)
Based on the explanation above, the correct answer is option B - in equal numbers. In a pure semiconductor, when the energy gap between the valence band and conduction band is small, the number of valence band holes and conduction-band electrons is approximately equal.

Answer

An intrinsic semiconductor, also called an undoped semiconductor or i-type semiconductor, is a pure semiconductor without any significant dopant species present. The number of charge carriers is therefore determined by the properties of the material itself instead of the amount of impurities. In intrinsic semiconductors the number of excited electrons and the number of holes are equal: n = p.

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