# Quantum yield

The quantum yield (also quantum efficiency or quantum efficiency ; or in the special case fluorescence yield ) indicates the relationship between the light quanta involved in a resulting event (e.g. light absorption, fluorescence emission, a photochemical reaction of a molecule, a recombination of charge carrier pairs, etc.) and the triggering event (such as the Totality of the available photons). The quantum yield is common . ${\ displaystyle \ leqq 1}$

In fluorescence spectroscopy , the quantum yield of a fluorophore indicates the ratio between the number of emitted and absorbed photons. The difference is the competing Auger effect . The ratio of generated photons generated holes to be also referred to as fluorescence yield (engl. Fluorescence yield ). The fluorescence yield is usually assigned to a shell corresponding to the original ionization and is therefore always less than or equal to one. The total fluorescence yield (sum over all shells for cascade effects) can consequently also be greater than one.

In detectors for photons ( photomultiplier ; semiconductor detectors such as photodiodes and CCDs ), the quantum yield indicates the probability with which an electron is released by the photoelectric effect and thus the photon can be detected. In solar cells , the quantum yield is decisive for the energy yield.

The quantum yield is also a measure of the productivity of a photoreaction . In the case of chemical reactions induced by light, the quantum yield is the number of converted molecules per number of absorbed photons. The quantum yield is dependent on the energy of the photon and thus on the wavelength of the light (or the electromagnetic radiation ). In the case of chain reactions (e.g. photopolymerization reactions ) it can be greater than one secondarily.

## Quantum efficiency of photoreceivers, phosphors and semiconductor light sources

In photovoltaics , with photodiodes and other photo receivers , the quantum efficiency (QE) describes the ratio of electrons that contribute to the photocurrent to the number of irradiated photons at a certain light wavelength : ${\ displaystyle N_ {e}}$ ${\ displaystyle N _ {\ nu}}$

${\ displaystyle QE (\ lambda) = {\ frac {N_ {e}} {N _ {\ nu} (\ lambda)}} = {\ frac {I} {q \ cdot \ Phi _ {p} (\ lambda )}} = {\ frac {h \ cdot f \ cdot I} {q \ cdot \ Phi _ {L} (\ lambda)}}}$

Here is the elementary charge , the photocurrent , the number of photons per time and the radiation power . ${\ displaystyle q}$${\ displaystyle I}$${\ displaystyle \ Phi _ {p}}$${\ displaystyle \ Phi _ {L}}$

Correspondingly, in the case of light emitting diodes and laser diodes, the QE denotes the ratio of emitted photons to the number of recombining electron- hole pairs and, in the case of phosphors, the ratio between the number of emitted photons of the new wavelength and the absorbed photons of the excitation wavelength.

### Spectral sensitivity

The same quantity, measured among other things in photodiodes, solar cells or photocathodes in the unit amperes per watt, is called spectral sensitivity (SR - for spectral response ):

${\ displaystyle SR (\ lambda) = {\ frac {I} {P (\ lambda)}}}$

where the light output is at a particular wavelength. ${\ displaystyle P (\ lambda) = \ Phi _ {p} (\ lambda) h \ nu}$

The relationship with quantum efficiency is: ${\ displaystyle QE (\ lambda)}$

${\ displaystyle QE (\ lambda) = {\ frac {SR (\ lambda)} {\ lambda}} \ cdot {\ frac {hc} {q}}}$

The factor is for a spectral sensitivity in A / W and wavelength in m. ${\ displaystyle hc / q}$${\ displaystyle 1 {,} 239842 \ cdot 10 ^ {- 6}}$

### Measuring principle

Precise knowledge of the (absolute) irradiated light power / number of photons is necessary to measure the quantum efficiency. This is usually achieved by calibrating a measuring device using the known quantum efficiency of a (calibrated) comparison receiver,,. The following then applies: ${\ displaystyle QE _ {\ mathrm {cal}}}$

${\ displaystyle QE = QE _ {\ mathrm {cal}} \ cdot {\ frac {I _ {\ mathrm {mes}}} {I _ {\ mathrm {cal}}}}}$

where are the current measured for the test cell and the current measured for the comparison cell . ${\ displaystyle I _ {\ mathrm {mes}}}$${\ displaystyle I _ {\ mathrm {cal}}}$

### Measurement setup

A light source ( xenon and / or halogen lamp ) and a monochromator for the selection of wavelength intervals are required for the lighting . Filter monochromators or grating monochromators can be used as monochromators. The monochromatic light is directed as homogeneously as possible onto the receiver surface to be tested.

The signal is often measured using lock-in amplifiers to improve the signal-to-noise ratio ; for this, the light signal must be periodically modulated (pulsed) with an optical chopper .

## Quantum efficiency vs. Quantum yield

There are two factors that limit a quantum-induced process in its efficiency:

1. the rate of photons that actually takes effect (the rest is absorbed in a different way)
2. the proportion of the energy of the photon that is transmitted (apart from the multiphoton absorption only one photon will be involved): the energy of the emitted photon will be lower than that of the incident photon by the Stokes shift .

## Practical meaning

The quantum yield is important for the characterization of photodiodes , photocathodes of photocells , image intensifiers and photomultipliers , but also of phosphors , fiber lasers and other (light-pumped) solid-state lasers .

The quantum yield of photocathodes can reach values ​​of over 50%. Current peak values ​​are:

• Cs 2 Te at 213 nm: ~ 20%
• GaAsP around 460 ... 540 nm: ~ 50%
• GaAs around 550 ... 720 nm: ~ 25%
• InP - InGaAsP just over 1000 nm: ~ 1%

The quantum yield of single crystal photodiodes can reach 90%; Monocrystalline silicon photodiodes achieve a spectral sensitivity of about 0.5 A / W at the optimal reception wavelength of around 900 nm; Solar cells usually do not achieve this value - they are polycrystalline or amorphous, and their efficiency is optimized for the broadest possible range in the visible spectral range (sunlight).

The quantum yields of the fluorescent dyes used for the analysis are from 2 to 42%, which depend heavily on the solution used. The dye indocarbocyanine has a value of 28% at an excitation wavelength of 678 nm (red) and a fluorescence maximum at 703 nm.

The quantum yield of phosphors used for lighting purposes ( cold cathode fluorescent lamps (CCFL) , fluorescent lamps , white light-emitting diodes ) is close to 100% according to various sources. According to Henning Höppe, there are quantum yields of 70 to 90% at excitation wavelengths of 253.65 nm (mercury vapor gas discharge) and 450 nm (blue LED).

Quantum yield also plays a role in photosynthesis and the productivity of agricultural crops.