Analysis of three elements of LED: IQE, LEE and EQE

I. IQE, LEE and EQE definition

First, the definitions and expressions of the internal quantum efficiency (IQE: Internal Quantum Efficiency), the light extraction efficiency (LEE) and the external quantum efficiency (EQE) are given as follows:

IQE = number of photons emitted by the active layer per unit time / number of electrons injected into the active layer per unit time = (Pint / (hv)) / (I / e) (1.1)

LEE = number of photons emitted into space per unit time / number of photons emitted from the active layer per unit time = (P / (hv)) / = (Pint / (hv)) (1.2)

EQE = number of photons emitted into space per unit time / number of electrons injected into the active layer per unit time = (P / (hv)) / (I / e) = IQE * LEE (1.3)

Among them, Pint is the optical power emitted in the active region, I is the injection current, and P is the optical power emitted into the free space. The internal quantum efficiency characterizes the ability of the LED active region to convert the injected electrical energy into light energy; the light extraction efficiency characterizes the ability of the LED active region to emit light energy; the external quantum efficiency characterizes the LED's ability to convert electrical energy into the outside world. The ability of visible light energy, the higher the external quantum efficiency, the higher the luminous efficiency. For an ideal LED device, all three parameters are 1, which can completely convert the injected electrical energy into visible light energy.

2. Influence IQE, LEE and EQE factors

Defects in the epitaxial layer limit the IQE of the LED. From the working principle of LEDs, we know that LEDs are based on the combined radiation of electrons and holes. However, electrons and holes also have another compounding mechanism - non-radiative recombination, as shown in Figure 1. When electrons and holes are non-radiatively combined, excess energy is transferred to nearby atoms in the form of phonons, increasing the kinetic energy of the atoms. Macroscopically, the LED temperature is raised.

Non-radiative recombination is associated with defects in the epitaxial layer. When a defect exists in the epitaxial layer, a recombination center is formed at the defect, and non-radiative recombination is more likely to occur at the recombination center. The higher the defect density, the more such composite centers are, and more composite carriers will be non-radiatively compounded. Therefore, in the region where the defect is concentrated, the luminous intensity is weak. The LEE limiting factor for LEDs is the refractive index of the material.

figure 1

When light is incident from a high refractive index substance to a low refractive index substance, it is known from Snell's law that total reflection occurs if the incident angle is too large. When total reflection occurs, light cannot enter a material with a low refractive index, and only light having an incident angle smaller than the critical angle of total reflection can be emitted when a low refractive index material is emitted. Therefore, total reflection reduces the light extraction efficiency, and only a part of the light inside the LED chip can be emitted. (Note: The above quoted my buddy's paper, he cited heavy weight).

For sapphire-based GaN multiple quantum well structure LEDs, the refractive indices of sapphire, GaN, and air are 1.7, 2.5, and 1, respectively, resulting in an escape angle of photons from GaN material to air (unpackaged) of only 23°, LEE Only 5%.

Considering the losses caused by electrodes and packages, EQE also needs to multiply Equation 1.3 by a factor less than one.

III. Improvements to IQE, LEE and EQE

Based on the above, the method of improving the IQE is mainly focused on improving the quality of the GaN epitaxial layer.

The improvement of LEE is mainly concentrated on the design of the package structure.

Although it can be found from Snell's simple calculation that even if a material with a refractive index between GaN and air is inserted between air and GaN, the LEE is not improved, but the shape of the material can change the LEE.

The improvement of IQE and LEE can naturally improve EQE.

The most wanted here is to talk about the relationship between the three parameter improvement rates.

For an amount a, if its value changes to b, its rate of change

n(%)=(ba)/a*100

or

b=a(1+n%)

We may use the above formula to use the formula 1.3 to calculate the relationship between the improvement rate of EQE and the improvement rate of IQE and LEE.

Assume that IQE, LEE, and EQE increase nIQE%, nLEE%, and nEQE%, respectively, due to a measure.

(1+nEQE%)EQE=(1+nIQE%)*IQE*(1+nIEE%)*LEE (3.1)

In the above formula, IQE, LEE and EQE are the LED index values ​​before taking measures respectively.

Introducing EQE=IQE*LEE

nEQE%=nIQE%+nIEE%+nIQE%*nIEE% (3.2)

Please remember this formula, he said that as long as a certain measure improves the IQE and LEE indicators, it will definitely reflect the improvement of EQE, and the EQE improvement rate is greater than the sum of IQE and LEE.

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