Question

Germanium crystal is doped at room temperature with a minute quantity of boron. The charge carriers in the doped semiconductor will be:

• A. electrons only
• B. holes only
• C. holes and few electrons
• D. electrons and few holes

Hint:

In a p-type semiconductor (e.g., germanium doped with boron), the majority carriers are holes due to acceptor impurities. At room temperature, thermal generation creates a small number of electrons as minority carriers.

Answer 1

The Correct Option is C

Step 1: Characterize the semiconductor material and doping agent.
Germanium (Ge) is a Group IV semiconductor possessing 4 valence electrons. Boron (B) is a Group III element with 3 valence electrons. When germanium is doped with boron, the boron functions as an acceptor impurity due to its deficiency of one valence electron compared to germanium.Step 2: Ascertain the resulting semiconductor type.
As boron contributes fewer valence electrons, it generates a vacancy, or hole, within the valence band for every boron atom integrated into the germanium lattice. This process yields a p-type semiconductor, where holes are the predominant charge carriers.Step 3: Examine charge carrier behavior at ambient temperatures.
- In a p-type semiconductor, holes, generated by acceptor impurities (boron), are the majority carriers.
- At room temperature, thermal energy can induce the excitation of some electrons from the valence band to the conduction band, consequently creating holes. This inherent process generates a limited quantity of electron-hole pairs intrinsically. Therefore, a small population of electrons will exist as minority carriers alongside the prevalent holes.Step 4: Correlate with provided choices.
The charge carriers within the doped germanium consist predominantly of holes (majority carriers) and a minor quantity of electrons (minority carriers resulting from thermal excitation). This configuration aligns with option (C).