# Why Does The Quantum Efficiency Of Light Have Limits

The photon efficiencies QE and MQE are expressed in units of μmol/J (micromoles/joules).

Photon quantum efficiency indicates the ability of electrical energy to be converted to a quantum number of photons.

It can be seen from the unit that 1 joule of electrical energy is converted to 1 micromole of photon, and the photon quantum efficiency is 1.

In fact, 1 Joule of electrical energy cannot be converted into photons, which is the cause of photon quantum efficiency.

What is the definition of radiation?

Radiation is the process of transferring energy in the form of electromagnetic waves or photons.

For artificial light sources, the method of generating radiation is produced by consuming electrical energy.

For lighting, we are concerned with optical power, which is the integral of the radiation produced by the visible wavelength range.

For plant lights, radiation is the radiation integral of the plant photosynthesis and light form response wavelength range.

For LED devices, radiation is produced by the recombination of electrons and holes in the active region of the device, and this recombination results in photon generation.

Since electrical energy cannot be completely converted into photons, there is a problem of radiation efficiency.

It can be explained by WPE, EQE, IQE, Ie, Ee, Fe. We explain it here in a better way.

Usually we use a percentage to represent the radiation efficiency, so the above formula needs to be multiplied by 100%.

From the law of conservation of energy:

The electric power consumed by the device that generates radiation P = radiated power Pr + heating power Pt

This relationship tells us that part of the energy lost by LED is converted into light energy, and the rest is converted into heat.

Note: Products that claim to produce high-light quantum efficiency illuminators can check the heating power Pt to verify that there is so much radiant power. This experiment and calculation is simpler than measuring radiant power.

Through mathematical methods, the radiation efficiency can be expressed by the following formula:

This relationship has the following conclusions:

1. The radiation efficiency depends on Pt/Pr, that is, the ratio of the heating power to the optical radiation power.

2, usually Pt > Pr, so the radiation efficiency <50%.

3. When Pt = Pr, the radiation efficiency = 50%.

4. When the measured radiation efficiency reaches 50% or more, various methods are required for test verification.

5. Radiation efficiency can be verified and evaluated by thermodynamic measurements.

6. When measuring the radiation efficiency by integrating sphere spectroscopy, there will be an error of 8-30%.

7. The higher the radiation efficiency, the lower the heat generation of the plant lamp, and the lower the heat dissipation cost of the lamp structure.

Furthermore, for LED devices, the radiation efficiency of a single bead is greater than the radiation efficiency of a source consisting of multiple beads due to the loss of refraction between the bead.

Our research shows that the most important factor affecting the efficiency of light quantum is the radiation efficiency of light-emitting devices.

Energy distribution of photons

The energy of a single photon E = h.c / λ

In the PAR wavelength range, the energy ratio of the energy at 700 nm to the wavelength at 400 nm:

E400/E700 =700/400 =1.75, which means that blue light is 1.75 times larger than red light energy.

The relationship between the energy of the photon and the wavelength is as follows:

The quantum efficiency of light is related to the photon energy. At a certain wavelength of radiation, the quantum efficiency of light is proportional to the efficiency of radiation.

We assume that the quantum efficiency of LED packages with different wavelengths reaches 100%, and Ie, Ee, and Fe also reach 100%, but the energy (junction voltage) required for the composite carrier due to the PN junction and the photons of LEDs of different wavelengths. The energy is different, the conversion of electric energy to radiant energy must have physical loss, so there is a limit value for the conversion efficiency of electric energy to radiant energy.

LEDs of any wavelength (including invisible light) have limits on the quantum efficiency of light.

For example, in an ideal state, the photon energy at 440 nm is about 2.82 eV, and the junction voltage at 440 nm is 3.3 V, with a loss of 14.6%.

The wavelength of the radiation is determined by the band gap of the active region, and a wider band gap results in a higher energy emission, that is, a radiation having a shorter wavelength.

It can be seen that the radiation efficiency of blue light is lower than that of red light.

The photon quantum efficiency function = f(η, E), where E is the photon energy.

It can be seen from the above formula that for a certain wavelength of radiation, the photon energy is constant, and the efficiency of the photon quantum depends on the radiation efficiency.

In an ideal state, there is a limit to the photon efficiency due to the existence of a limit value for the radiation efficiency of the device.

Computational error problem

Usually we use the following formula to calculate the quantum efficiency of light:

QE=PPF/W

MQE=MPF/W

The calculation error of these two formulas depends on the actual measured SPD error, which is composed of the absolute error of the device and the relative error of the measurement technique.

For the integrating sphere spectrometry system, the absolute error is between 3-8%, and the relative error (user error) is between 10-30%. If the measurement mechanism is not understood, the user error can reach more than 50%.

From the above two calculation formulas, the error is difficult to evaluate. In fact, QE and MQE are parameters that are not related to the measurement. This is because there are other methods for calculating this parameter.

We use the spectral level calculation method, and the SPD used is the reliable data evaluated by our research. Our calculation method has less than 0.1% error for monochromatic light and less than 1% for fluorescence excited spectrum.

Although the QE=PPF/W calculation has a certain error, this formula is also a simple calculation method. As long as the error evaluation of the spectral basic parameters is controlled, the error of this calculation result is acceptable. After all, the integral method is used to calculate the photon. Efficiency is also a highly specialized calculation that requires a laboratory with professional competence.

The object light is a parametric product. The biggest characteristic of the parameterized product is that the parameters are related to each other and can be verified by calculation. The fake or virtual standard parameters are meaningless on the plant light.