An Introduction to Quantum Efficiency

Quantum efficiency refers to the fraction of input energy that is converted into useful output energy:

Quantum efficiency is different for different devices but is typically dependent on the photon to electron ratio (or other physical entity involved in an interaction). For light-emitting diodes (LEDs), the input energy is the number of electrons injected and the output energy is the number of photons emitted. For solar cells the input energy is the number of absorbed photons and the electrons generated as a result is the output energy.

Quantum Efficiency of Light-Emitting Diodes

Quantum efficiency for light-emitting diodes (LEDs) is defined as the ratio of number of photons emitted to the number of electrons injected. For photons to be emitted, excitons must be formed from electron hole recombination. Therefore, quantum efficiency determines radiative recombination of excitons as a fraction of the total recombination of excitons in an light-emitting system.

Not all exciton recombination is radiative and such non-radiative processes will negatively impact LED efficiency.

Internal Quantum Efficiency (IQE) of LEDs

The internal quantum efficiency of LEDs is used to determine the number of photons generated inside the active layer per per input of electrons. The total internal quantum efficiency of an LED is calculated by multiplying the current injection efficiency (η_inj) and the radiative recombination efficiency (η_rad):

Current injection efficiency is highly dependent on the balanced injection of holes and electrons to radiatively recombine. If the ratio of electrons and holes entering the active layer is unbalanced this can lead to non-radiative losses (such as Auger recombination) and therefore inefficiencies. Significant excess of a particular charge carrier can lead to leakage without contributing to recombination.

External Quantum Efficiency (EQE) of LEDs

The total external quantum efficiency, η_ex, of a light emitting diode is determined by the ratio of electrons inputted and the photons outputted.  In other words, the number of outcoupled photons per injected charge. The difference here from internal quantum efficiency is that the photons that leave the device are measured, not just those generated.

η_ex is calculated by multiplying the internal quantum efficiency (η_int) as mentioned above and the extraction efficiency (η_ext). As a result of the internal quantum efficiency equation, the EQE calculation is presented as:

Photon extraction efficiency is used interchangeably with outcoupling efficiency. Both refer to the fraction of internally generated photons that successfully escape from the device into the external environment.

As such, the equation to determine EQE is also sometimes written as:

Where η_OC is equivalent to η_ext, η_r is the same as η_rad and γ multiplied by PLQY is equivalent to η_inj.

How to experimentally determine EQE of an LED

When evaluating the number of photons produced per electron injected, we examine the photon flux and the injected current over a given period of time:

During an experiment to determine EQE a photodetector is used to measure the total optical power (P) emitted by the LED. Photon flux is the total optical power divided by photon energy. Therefore, at a given wavelength (λ), photon flux can be determined:

Reasons for LED Quantum Inefficiency

Whilst there has been a huge amount of progress in increasing the external quantum efficiency of LEDs over the years, inefficiency still remains an issue. Here are some of the factors that reduce external quantum efficiency in LEDs:

• Non-radiative processes that negatively influence the radiative recombination efficiency:
  • Auger recombination: Energy is transferred to another carrier rather than being emitted as a photon inside the active layer
  • Shockley-Read-Hall (SRH) recombination: Happens through defect states within the bandgap (inside the active layer) and also occurs at the interfaces (trap-assisted) and is called surface recombination
  • Charge carrier leakage: electrons can fly over the active region to recombine with holes outside of the active layer
• Production of photons that do not fall in the detected wavelength range
  
• Photoluminescence Quantum Yield (PLQY): has strong positive correlation with EQE, the combination of active materials impacts the efficiency of photon emission.
• Dipole orientation: The horizontal orientation of the emissive transition dipole moment can improve the light out-coupling efficiency by up to 50% relative to a random orientation.
• The energy barriers for electrons and holes are also considered to be important in determining the device efficiency. A larger electron injection barrier / hole blocking barrier and a smaller hole injection barrier favor a high EQE.

Quantum Efficiency of Solar Cells

In solar cells, the quantum efficiency is the ratio of the number of charge carriers (electron-hole pair) collected to the number of incident photons. This is the opposite to light-emitting diodes.

The quantum efficiency of solar cells may be given as a function of wavelength or of energy. If all photons of a certain wavelength are absorbed and the resulting charge carriers are collected at their corresponding electrodes, then the solar cell is 100% efficient at that wavelength. The quantum efficiency for photons with energy below the band gap is zero as they do not possess enough energy to initiate exciton formation.

External Quantum Efficiency (EQE) of Solar Cells

The external quantum efficiency equation for solar cells is shown where the number of electrons flowing through the external circuit is divided by the number of incident photons:

This equation is the opposite to the light-emitting diode EQE equation. The focus here is maximizing photon absorption and charge generation. Nevertheless both devices face some similar issues of undesirable recombination.

For solar cells, an EQE is used to resolve the spectral mismatch of short-circuit current density, J_sc. The mismatch occurs as the spectral photon flux of a solar simulator is never exactly equal to that of the sun. J_sc is related to the EQE of the cell and the AM 1.5 spectral photon flux.

An example EQE curve of a solar cell typically extends from 300 nm to 1200 nm. The space above the EQE curve (blue shaded area) represents the fraction of photons that do not lead to current generation. Photons may be lost via reflection and this loss is also represented on the graph. Additionally, excitons generated after photon absorption may also recombine rather than separating and reaching their respective electrodes. This also contributes to the space above the EQE curve.

Internal Quantum Efficiency (IQE) of Solar Cells

By examining the fraction of photons absorbed by the cell (compared to those reflected), the internal quantum efficiency (IQE) can be determined. The IQE provides insight into which wavelengths of light are lost due to parasitic absorption or where charge-carrier collection is inefficient. This detailed analysis helps identify performance bottlenecks in the solar cell, such as inefficient charge separation or recombination losses within the material.

Reasons for Solar Cell Quantum Inefficiency

Solar cells experience inefficiency factors similar to other organic electronic devices, such as LEDs, including:

• Unwanted recombination of excitons: loss of charge carrier species before they reach an electrode
• Auger recombination: energy of a photoexcited carrier (electron or hole) is transferred to another carrier rather than being utilised for current generation. This energy transfer typically results in the excitation of the second carrier, which then relaxes back to its ground state by emitting energy as heat, rather than generating an electrical current. Auger recombination becomes more significant at high carrier concentrations, such as under intense illumination or in highly doped regions of the solar cell.
• Shockley-Read-Hall (SRH) recombination: occurs when defect states within the bandgap act as recombination centres. These defect states can trap charge carriers, allowing them to recombine with carriers of the opposite type (electrons with holes). SRH recombination is particularly prevalent at material defects, impurities, or at interfaces between different layers, where trap-assisted surface recombination can occur. It is a significant source of inefficiency, especially in materials or devices with poor quality control or high defect densities.
• Charge carrier leakage: This occurs when electrons and holes are not confined within the active region of the solar cell, causing electrons to "leak" over the barrier and recombine with holes outside the active layer. This type of loss is often related to poor design of the solar cell's energy band structure or insufficient barrier heights at the interfaces, which fail to adequately confine charge carriers within the desired region.
• The energy barriers for electrons and holes are also considered to be important in determining the device quantum efficiency.

Other issues that are unique to solar cell quantum inefficiency include:

• Photon reflection: occurs incoming photons are not absorbed by the solar cell but are instead reflected off its surface. This reflection is caused by differences in the refractive indices of the materials at the surface (e.g., the air and the solar cell). As a result, the reflected photons are lost and cannot contribute to the generation of charge carriers.
• Photon absorption efficiency: the band gap of the active materials dictates which photons can be absorbed.
• Device design: the thickness of the layers and their architecture can greatly influence EQE

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