Question

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Gallium Arsenide (GaAs) is a direct-band gap semiconductor and GaP is an indirect - band gap semiconductor.
Reason (R) : In GaAs, top of valence band and bottom of conduction band are both at the same center point in Brillioun Zone, while in GaP top of the valence band is at a different position from the bottom of conduction band in Brillioun Zone.
In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

Remember that optical emission (light generation) is highly efficient in Direct bandgap materials (GaAs, InP, GaN) because momentum is automatically conserved. Indirect materials (Si, Ge, GaP) are terrible light emitters because they require a "lucky" 3-body collision (electron, hole, and phonon).

Answer 1

The Correct Option is A

Step 1: Concept:
This question deals with the physical classification of semiconductors based on their E-k (Energy vs. Momentum) band structures. It evaluates the definitions of direct and indirect bandgaps.

Step 2: Key Definitions:
- Direct Bandgap: The lowest energy state in the conduction band (conduction band minimum, CBM) and the highest energy state in the valence band (valence band maximum, VBM) occur at the exact same wavevector (crystal momentum, $k$) in the Brillouin zone—typically at the center point ($\Gamma$ point, $k=0$). An electron can transition by just emitting a photon without changing momentum.
- Indirect Bandgap: The CBM and VBM occur at completely different wavevectors ($k$) in the Brillouin zone. A transition requires both a photon (for energy) and a phonon (for momentum change).

Step 3: Step-by-step Explanation:

• Evaluating Assertion (A): It is a well-established materials science fact that Gallium Arsenide (GaAs) is an excellent direct-bandgap semiconductor (making it great for LEDs and lasers), whereas Gallium Phosphide (GaP) is an indirect-bandgap material (making it less efficient for optoelectronics unless heavily doped with specific traps). Assertion (A) is correct.

• Evaluating Reason (R): Reason (R) states that for GaAs, the CBM and VBM are at the same center point (the definition of a direct gap), while for GaP, they are at different momentum positions (the definition of an indirect gap). This statement perfectly defines the physics distinguishing the two types of semiconductors. Reason (R) is correct.

• Relationship: Reason (R) provides the exact microscopic quantum-mechanical explanation for the macroscopic classification stated in Assertion (A). Therefore, (R) is the correct explanation of (A).

Step 4: Final Answer:
Both statements are true, and (R) correctly explains (A). This corresponds to option (A).