Understanding Semiconductor Bandgaps

This question asks us to arrange four common semiconductor materials based on the size of their bandgap energy at a temperature of 300K. The bandgap is a fundamental property of a semiconductor that determines its electrical and optical characteristics.

The bandgap ($\text{E}_g$) is the energy difference between the top of the valence band and the bottom of the conduction band in a semiconductor. Electrons need at least this amount of energy to move from the valence band to the conduction band, becoming free to conduct electricity. A larger bandgap generally means the material is more insulating and requires more energy to start conduction or emit/absorb higher-energy photons.

Bandgap Values at 300K

Let's look at the approximate bandgap values for the given materials at 300K:

• Si (Silicon): Approximately $\text{E}_g \approx 1.11 \, \text{eV}$ (Indirect bandgap)
• GaAs (Gallium Arsenide): Approximately $\text{E}_g \approx 1.42 \, \text{eV}$ (Direct bandgap)
• GaP (Gallium Phosphide): Approximately $\text{E}_g \approx 2.26 \, \text{eV}$ (Indirect bandgap)
• GaN (Gallium Nitride): Approximately $\text{E}_g \approx 3.4 \, \text{eV}$ (Direct bandgap)

Note that these values can vary slightly depending on the source and specific measurement conditions, but these are widely accepted approximate values at room temperature (300K).

Arranging by Ascending Bandgap

Ascending order means arranging from the smallest value to the largest value. Comparing the bandgap values:

$\text{E}_g(\text{Si}) = 1.11 \, \text{eV}$

$\text{E}_g(\text{GaAs}) = 1.42 \, \text{eV}$

$\text{E}_g(\text{GaP}) = 2.26 \, \text{eV}$

$\text{E}_g(\text{GaN}) = 3.4 \, \text{eV}$

Arranging these from smallest to largest bandgap:

$1.11 \, \text{eV}$ ($\text{Si}$) < $1.42 \, \text{eV}$ ($\text{GaAs}$) < $2.26 \, \text{eV}$ ($\text{GaP}$) < $3.4 \, \text{eV}$ ($\text{GaN}$)

Mapping these back to the letters used in the question (A=GaN, B=GaP, C=GaAs, D=Si):

Si (D) < GaAs (C) < GaP (B) < GaN (A)

Therefore, the ascending order of bandgap is D, C, B, A.

Final Order of Bandgap

Based on the analysis of the bandgap values at 300K, the materials arranged in ascending order of their bandgap are:

1. Si (D) - Smallest bandgap
2. GaAs (C)
3. GaP (B)
4. GaN (A) - Largest bandgap

The correct arrangement is D, C, B, A.

Revision Table: Semiconductor Bandgaps

Additional Information: Bandgap Types and Significance

Semiconductors can have either a direct or an indirect bandgap. This property is crucial for optical applications like LEDs and solar cells.

• Direct Bandgap: In direct bandgap semiconductors (like GaAs and GaN), the minimum energy of the conduction band aligns with the maximum energy of the valence band in terms of momentum. This allows electrons and holes to recombine directly, releasing energy efficiently as light (photons). This is why GaAs and GaN are used in LEDs and lasers.
• Indirect Bandgap: In indirect bandgap semiconductors (like Si and GaP), the minimum conduction band energy and maximum valence band energy do not align in momentum. Recombination requires interaction with a phonon (lattice vibration) to conserve momentum. This process is less efficient for light emission, making Si less suitable for LEDs compared to direct bandgap materials.

The bandgap also affects the operating temperature range and power handling capability of devices made from these materials. Materials with larger bandgaps, like GaN, can typically operate at higher temperatures and handle higher power levels, making them important for high-frequency and high-power electronics.