In a p-n junction, the width of the depletion layer changes depending on whether it is forward biased or reverse biased:

(i) Forward Biased:

• When a p-n junction is forward biased, the width of the depletion layer decreases.
• In forward bias, the positive terminal of the voltage source is connected to the p-type region, and the negative terminal is connected to the n-type region. This causes the majority carriers (holes in the p-type region and electrons in the n-type region) to move towards the junction.
• As the majority carriers move towards the junction, they neutralize some of the immobile ions in the depletion region, reducing the width of the depletion layer.
• The reduced width of the depletion layer allows for easier flow of current through the junction.

(ii) Reverse Biased:

• When a p-n junction is reverse biased, the width of the depletion layer increases.
• In reverse bias, the positive terminal of the voltage source is connected to the n-type region, and the negative terminal is connected to the p-type region. This creates an electric field that repels majority carriers away from the junction.
• As majority carriers are pushed away from the junction, the immobile ions in the depletion region create a larger electric field, widening the depletion layer.
• The widened depletion layer restricts the flow of current through the junction, resulting in very little current flow under reverse bias conditions.

In summary, forward biasing reduces the width of the depletion layer, facilitating current flow, while reverse biasing increases the width of the depletion layer, limiting current flow.

The relationship between the frequency νν of radiation emitted by an LED (Light Emitting Diode) and the band gap energy EE of the semiconductor material used to fabricate it is described by the Planck-Einstein equation and the semiconductor band theory.

The Planck-Einstein equation states:

E=h⋅νE=h⋅ν

Where:

• EE is the energy of the emitted photon,
• hh is Planck's constant (approximately 6.626×10−346.626×10−34 J·s),
• νν is the frequency of the emitted radiation.

For semiconductors, the band gap energy EE is the energy difference between the valence band and the conduction band. When an electron in the conduction band recombines with a hole in the valence band, it releases energy in the form of a photon. The energy of this photon is directly proportional to the band gap energy of the semiconductor material.

Therefore, for LEDs, the frequency νν of the emitted radiation is directly related to the band gap energy EE of the semiconductor material by the Planck-Einstein equation. As the band gap energy increases, the frequency of the emitted radiation also increases, resulting in a shift towards higher energy (shorter wavelength) light emission.

Gallium arsenide (GaAs) is commonly used in making solar cells for several reasons:

1. Efficiency: GaAs solar cells offer higher conversion efficiencies compared to traditional silicon solar cells. This is because GaAs has a narrower bandgap, allowing it to absorb a broader spectrum of light, including infrared wavelengths, which are not efficiently absorbed by silicon.

2. High Absorption Coefficient: GaAs has a high absorption coefficient, meaning it can absorb more photons within a shorter distance compared to silicon. This allows for the fabrication of thinner solar cells, reducing material usage and cost.

3. Temperature Stability: GaAs solar cells perform better at high temperatures compared to silicon solar cells. They have a lower temperature coefficient, meaning their efficiency decreases less with increasing temperature, making them suitable for applications in hot climates or environments.

4. Durability: GaAs is more resistant to radiation damage, making GaAs solar cells more suitable for use in space applications where they are exposed to high levels of radiation.

5. Flexibility: GaAs solar cells can be grown using various techniques, including epitaxial growth, which allows for the fabrication of thin, lightweight, and flexible solar cells. This flexibility is advantageous for applications such as space exploration missions and portable electronic devices.

Overall, the unique properties of GaAs make it an  material for solar cell applications, particularly in situations where high efficiency, durability, and temperature stability are crucial.

Intrinsic semiconductors are materials like pure silicon or germanium, which have a balance of electrons and holes due to thermal excitation. At absolute zero temperature (0 Kelvin), these materials would behave like perfect insulators because there wouldn't be any thermally generated charge carriers (electrons and holes) available for conduction.

However, as you increase the temperature, thermal energy provides electrons with enough energy to jump from the valence band to the conduction band, creating electron-hole pairs. This increases the conductivity of the semiconductor. The temperature at which the intrinsic semiconductor behaves like a perfect insulator depends on the energy gap between the valence band and the conduction band. This energy gap is known as the bandgap (Eg).

The relationship between the conductivity (σ) and temperature (T) in intrinsic semiconductors is given by the exponential equation known as the intrinsic carrier concentration equation:

ni=AT3/2e−Eg2kTni=AT3/2e−2kTEg

Where:

• nini is the intrinsic carrier concentration.
• AA is a constant.
• TT is the temperature in Kelvin.
• EgEg is the bandgap energy.
• kk is Boltzmann's constant.

As the temperature increases, the exponential term in the equation decreases. Therefore, at higher temperatures, the intrinsic carrier concentration increases, and the material becomes more conductive. Conversely, at lower temperatures, the intrinsic carrier concentration decreases, and the material behaves more like an insulator.

However, it's important to note that "perfect insulator" is a theoretical concept. In practical terms, even at low temperatures, there can still be some level of conductivity due to impurities or defects in the material.