Question

Indicate whether each statement is true or false: (a) The band gap of a semiconductor decreases as the particle size decreases in the \(1-10-\mathrm{nm}\) range. (b) The light that is emitted from a semiconductor, upon external stimulation, becomes longer in wavelength as the particle size of the semiconductor decreases.

Short answer

Both statements are False. (a) The band gap of a semiconductor increases, not decreases, as the particle size decreases in the \(1-10-\mathrm{nm}\) range due to quantum confinement. (b) The emitted light wavelength becomes shorter, not longer, as the particle size of the semiconductor decreases because of the increased energy gap between valence and conduction bands.

Step-by-step solution

Statement (a): The band gap of a semiconductor decreases as the particle size decreases in the \(1-10-\mathrm{nm}\) range.

In nano-sized semiconductors, as the particle size decreases, the confinement of the electrons and holes within the material increases. This phenomenon is called quantum confinement. When quantum confinement comes into the picture, the bandgap between the valence and conduction bands become wider than that of bulk semiconductors. As a result, the band gap of a semiconductor increases as the particle size decreases in the \(1-10-\mathrm{nm}\) range. Therefore, the statement is False.

Statement (b): The light that is emitted from a semiconductor, upon external stimulation, becomes longer in wavelength as the particle size of the semiconductor decreases.

When external stimulation, such as electric energy or light, is applied to a semiconductor, it can emit light. The emitted light wavelength is influenced by the energy gap between the conduction and valence bands. From statement (a), we know that the band gap increases with a decrease in particle size, meaning that the energy difference between the valence and conduction bands becomes bigger. The relationship between energy and wavelength is given by \(E=\dfrac{hc}{\lambda}\), where \(E\) is the energy, \(h\) is the Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength. As energy increases, the wavelength decreases. Therefore, as the particle size of the semiconductor decreases, the energy gap becomes larger and the emitted light wavelength becomes shorter, not longer. Thus, the statement is False.

Key concepts

Band Gap

In the world of semiconductors, understanding the band gap is crucial. The band gap is the energy difference between the valence band (where electrons are normally present) and the conduction band (where electrons move freely to conduct electricity). When enough energy is applied, electrons can "jump" from the valence to the conduction band, allowing current to flow.

For nano-sized particles, as the particle size decreases, an interesting effect known as quantum confinement occurs. This effect results in an increase in the band gap. Essentially, when the particle becomes very small, the physical constraints limit the motion of electrons and create larger gaps between energy levels. This causes the band gap to widen, which is contrary to the behavior seen in larger, bulk materials.

The increase in band gap with decreasing particle size is a key principle when studying the properties of nano-sized semiconductors, and it plays a significant role in how these materials interact with light.

Semiconductors

Semiconductors are materials that have a conductivity level between conductors (like metals) and insulators (like glass). They are key components in electronic devices as they can conduct electricity under certain conditions. This conductivity is largely controlled by the band gap.

In semiconductors, the electrons need enough energy to cross the band gap from the valence to the conduction band. This gap can be manipulated by changing the material's structure, such as through the quantum confinement effect seen in nano-sized semiconductors.

When a semiconductor particle is reduced to the nanoscale, its electronic properties can change dramatically. These changes can be utilized in various applications, from creating more efficient solar cells to designing novel optoelectronic devices. Got a semiconductor in your phone? You can thank their ability to switch between conducting and non-conducting states for powering countless gadgets!

Nano-sized Particles

Nano-sized particles, often within the range of 1 to 10 nanometers, showcase unique physical and chemical properties distinct from their bulk counterparts. When it comes to semiconductors in this size range, the phenomenon of quantum confinement cannot be ignored.

This confinement alters the behavior of electrons, which significantly impacts the material's optical and electronic properties. For instance, as the size of semiconductor particles decreases, the band gap widens. This increased band gap causes the material to absorb and emit light at shorter wavelengths.

These properties are harnessed in a variety of cutting-edge applications, including in the development of quantum dots. Quantum dots are tiny semiconductor particles that have unique luminescent properties and are used in displays, imaging, and even in medical diagnostics. Their colors can be precisely controlled by tailoring the size of the particles, making them an exciting area of research and application in nanotechnology.