Wide band-gap semiconductors have a band gap between 2 and 7 electron volts (eV), where 1 eV = 96.485 kJ/mol. The wide band-gap semiconductor GaN, used to construct the laser in Blu-ray DVD players, has a band gap of 3.44 eV. The material in the laser, Ga_xIn_1-xN, has some indium substituted for gallium. (b) If the light from the device is blue, does partial substitution of indium for gallium increase or decrease the band gap of Ga_xIn_1-xN compared to GaN?

Verified step by step guidance

1. Understand the relationship between band gap and light color: The color of the light emitted by a semiconductor is determined by its band gap. The energy of the emitted light corresponds to the energy difference between the conduction band and the valence band, which is the band gap.
2. Recall the band gap of GaN: GaN, a wide band-gap semiconductor, has a band gap of 3.44 eV, which is capable of emitting blue light in Blu-ray devices.
3. Consider the effect of substituting indium for gallium: Substituting indium for gallium in GaN to form Ga_xIn_1-xN alters the band structure and thus the band gap of the material.
4. Analyze the impact on band gap due to substitution: Generally, substituting a different element in the semiconductor lattice changes the electronic properties, including the band gap. The specific effect (increase or decrease) depends on the relative electronegativities and atomic sizes of the elements involved.
5. Determine the direction of band gap change: Since the emitted light is blue, similar to the emission from GaN, and knowing that blue light corresponds to a certain range of band gap energies, infer whether the substitution of indium increases or decreases the band gap relative to pure GaN.

Key Concepts

Band Gap Energy

The band gap energy is the energy difference between the valence band and the conduction band in a semiconductor. It determines the electrical conductivity and optical properties of the material. A larger band gap typically means the material can operate at higher voltages and temperatures, while a smaller band gap allows for easier electron excitation, affecting the color of emitted light.

Effect of Alloying on Band Gap

Alloying in semiconductors, such as substituting indium for gallium in GaN, can alter the band gap energy. The introduction of indium, which has a smaller band gap than gallium, generally leads to a decrease in the overall band gap of the alloy. This phenomenon is crucial in designing materials for specific optical applications, as it allows for tuning the emitted light's wavelength.

Wavelength and Color of Light

The color of light emitted by a semiconductor laser is directly related to its band gap energy. According to the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength, a smaller band gap corresponds to longer wavelengths (redder light), while a larger band gap corresponds to shorter wavelengths (bluer light). Thus, changes in the band gap due to material composition affect the color of the emitted light.