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In the context of semiconductors, band theory is an essential framework used to understand how electricity is conducted. Unlike metals, semiconductors have distinct energy bands: the valence band and the conduction band.

• The valence band is the highest range of electron energies where electrons are typically present at absolute zero temperature.
• The conduction band is above the valence band and is typically empty at absolute zero.
• The energy gap, or band gap, is the energy difference between these two bands.

To turn a semiconductor into a conductor, electrons must gain enough energy to jump from the valence band to the conduction band, making them free to move and thus conduct electricity.
In diamond, which is an insulator under normal conditions, light can provide the necessary energy to boost electrons across this energy gap, particularly if the light's photon energy matches or exceeds the band gap.

Photons are fundamental particles of light that carry energy, which depends on their frequency. The relationship between the energy of a photon and its frequency is given by Planck's equation: \[E = h \times u\]

• The symbol \(E\) represents the photon energy.
• The symbol \(h\) stands for Planck's constant, valued at approximately \(6.626 \times 10^{-34} \text{Js}\).
• The symbol \(u\) is the frequency of the photon.

By using this equation, you can determine the energy carried by photons of specific light. For diamond, light with shorter wavelengths such as 226 nm has photons with just enough energy. When these photons strike the diamond, they can excite electrons across the gap, leading to conduction.
Therefore, knowing the energy of photons helps us understand and calculate the minimum threshold energy needed to excite electrons in materials like diamond.

The conversion of wavelength to frequency is a crucial step in evaluating the energy of photons impacting a material. Light's speed is always constant in a vacuum and is given by \[c = \lambda \times u\]

• \(c\) is the speed of light \((3 \times 10^8 \text{m/s})\).
• \(\lambda\) represents the wavelength.
• \(u\) represents the frequency.

By rearranging the formula, you can express frequency as\[u = \frac{c}{\lambda}\]This equation is used to convert the wavelength of the light into its frequency. For example, with a wavelength of 226 nm, the frequency can be calculated to find out how much energy the light carries. This conversion forms the basis for calculating photon energy, as detailed in previous sections. Understanding these conversions enables us to precisely determine whether a material will absorb or conduct the energy provided by incoming photons.