## Energy wavelength frequency of the photon and the solar spectrum

1.1 Photons: energy, wavelength and frequency

Light has wave-particle duality, and light will show volatility or particle nature according to different experimental conditions. In the interference experiment, the light exhibits volatility, while in the photoelectric experiment, the light exhibits the particle property. A beam of light is like a stream of particles.

When light and electromagnetic radiation exhibit the characteristics of particle flow, these particles are called photons, and waves are usually characterized by their wavelength, frequency and amplitude. Every photon of monochromatic radiation has an energy related to wavelength or radiation frequency (color). The photon energy is defined by the Planck equation:

E=hv=hc/λ

In the formula, h is a general constant, called Planck constant, h=6.625×10-34JS-1; v is the frequency, λ is the wavelength; c is the propagation speed of light in vacuum, which is a general constant ,c=3×108m/s.

Therefore, the above equation represents the conversion between the conduction band energy and frequency and wavelength of electromagnetic wave photons. When the radiation color (wavelength or radiation frequency) of the photon is known, the energy of the photon can be calculated using the Planck equation. Planck’s equation also shows the interaction of light and semiconductors. We can know the color of the corresponding light needed to excite electrons from the valence band to the conduction band through the band gap (see Figure 1.1).

Figure 1.1 Energy band diagram of a semiconductor

The intensity of a beam is determined by the number of photons it contains. Therefore, for a certain wavelength of photons, increasing the intensity is not by increasing the energy of a single photon, but only by increasing the number of photons.

The related expressions of photon energy hv (eV) and wavelength λ (um) are as follows:

λ=1.24/hv

1.2 Solar spectrum

The electric power produced by the solar cell is proportional to its area. The solar irradiance at the equator is about 1kW/m2 at 90°, which means that a solar cell with a size of 1cm2 receives 100mW. The radiant power of different wavelengths in the solar spectrum is also different (see Figure 1.3). The maximum intensity of the solar spectrum radiation is at the wavelength λ=0.5μm, and the intensity at λ=1um is reduced by half.

Figure 1.2 Solar spectrum under different atmospheric quality

The spectrum absorbed by a semiconductor is determined by its band gap. When the energy band gap is higher than the incident photon energy, electrons cannot be excited from the valence band to the conduction band. When the photon energy is higher than the energy band gap, electrons can be excited from the valence band to the conduction band, and the excess energy is released as thermal energy.

The atmosphere weakens the solar radiation reaching the surface of the earth, mainly because water vapor absorbs part of the infrared light, and the ozone layer absorbs part of the ultraviolet light. Air mass is defined as the degree of influence of the atmosphere on the solar radiation received on the earth’s surface. The lower the air quality, the smaller the atmospheric influence.