Quantum efficiency

The term quantum efficiency (QE) may apply to incident photon to converted electron (IPCE) ratio, of a photosensitive device or it may refer to the TMR effect of a Magnetic Tunnel Junction.

This article deals with the term as a measurement of a device’s electrical sensitivity to light. In a charge-coupled device (CCD) it is the percentage of photons hitting the device’s photoreactive surface that produce charge carriers. It is measured in electrons per photon or amps per watt. Since the energy of a photon is inversely proportional to its wavelength, QE is often measured over a range of different wavelengths to characterize a device’s efficiency at each photon energy level. The QE for photons with energy below the band gap is zero. Photographic film typically has a QE of much less than 10%, while CCDs can have a QE of well over 90% at some wavelengths.

Of solar cells
A solar cell’s quantum efficiency value indicates the amount of current that the cell will produce when irradiated by photons of a particular wavelength. If the cell’s quantum efficiency is integrated over the whole solar electromagnetic spectrum, one can evaluate the amount of current that the cell will produce when exposed to sunlight. The ratio between this energy-production value and the highest possible energy-production value for the cell (i.e., if the QE were 100% over the whole spectrum) gives the cell’s overall energy conversion efficiency value. Note that in the event of multiple exciton generation (MEG), quantum efficiencies of greater than 100% may be achieved since the incident photons have more than twice the band gap energy and can create two or more electron-hole pairs per incident photon.

Types
Two types of quantum efficiency of a solar cell are often considered:

External Quantum Efficiency (EQE) is the ratio of the number of charge carriers collected by the solar cell to the number of photons of a given energy shining on the solar cell from outside (incident photons).
Internal Quantum Efficiency (IQE) is the ratio of the number of charge carriers collected by the solar cell to the number of photons of a given energy that shine on the solar cell from outside and are absorbed by the cell.
The IQE is always larger than the EQE. A low IQE indicates that the active layer of the solar cell is unable to make good use of the photons. To measure the IQE, one first measures the EQE of the solar device, then measures its transmission and reflection, and combines these data to infer the IQE.

{\text{EQE}}={\frac {\text{electrons/sec}}{\text{photons/sec}}}={\frac {{\text{(current)}}/{\text{(charge of one electron)}}}{({\text{total power of photons}})/({\text{energy of one photon}})}}

{\text{IQE}}={\frac {\text{electrons/sec}}{\text{absorbed photons/sec}}}={\frac {\text{EQE}}{\text{1-Reflection}}}

The external quantum efficiency therefore depends on both the absorption of light and the collection of charges. Once a photon has been absorbed and has generated an electron-hole pair, these charges must be separated and collected at the junction. A “good” material avoids charge recombination. Charge recombination causes a drop in the external quantum efficiency.

The ideal quantum efficiency graph has a square shape, where the QE value is fairly constant across the entire spectrum of wavelengths measured. However, the QE for most solar cells is reduced because of the effects of recombination, where charge carriers are not able to move into an external circuit. The same mechanisms that affect the collection probability also affect the QE. For example, modifying the front surface can affect carriers generated near the surface. And because high-energy (blue) light is absorbed very close to the surface, considerable recombination at the front surface will affect the “blue” portion of the QE. Similarly, lower energy (green) light is absorbed in the bulk of a solar cell, and a low diffusion length will affect the collection probability from the solar cell bulk, reducing the QE in the green portion of the spectrum. Generally, solar cells on the market today do not produce much electricity from ultraviolet and infrared light (<400 nm and >1100 nm wavelengths, respectively); these wavelengths of light are either filtered out or are absorbed by the cell, thus heating the cell. That heat is wasted energy, and could damage the cell.

Quantum efficiency of Image Sensors: Quantum efficiency (QE) is the fraction of photon flux that contributes to the photocurrent in a photodetector or a pixel. Quantum efficiency is one of the most important parameters used to evaluate the quality of a detector and is often called the spectral response to reflect its wavelength dependence. It is defined as the number of signal electrons created per incident photon. In some cases it can exceed 100% (i.e. when more than one electron is created per incident photon).

EQE mapping: Conventional measurement of the EQE will give the efficiency of the overall device. However it is often useful to have a map of the EQE over large area of the device. This mapping provides an efficient way to visualize the homogeneity and/or the defects in the sample. It was realized by researchers from the Institute of Researcher and Development on Photovoltaic Energy (IRDEP) who calculated the EQE mapping from electroluminescence measurements taken with an hyperspectral imager.

Spectral responsivity
Spectral responsivity is a similar measurement, but it has different units: amperes per watt (A/W); (i.e. how much current comes out of the device per incoming photon of a given energy and wavelength). Both the quantum efficiency and the responsivity are functions of the photons’ wavelength (indicated by the subscript λ).

To convert from responsivity (Rλ, in A/W) to QEλ (on a scale 0 to 1):

$QE_\lambda=\frac{R_\lambda}{\lambda}\times\frac{h c}{e}\approx\frac{R_\lambda}{\lambda} {\times} (1240\;{\rm W}\cdot {\rm nm/A})$
where λ is the wavelength in nm, h is the Planck constant, c is the speed of light in a vacuum, and e is the elementary charge.

Determination
$QE_\lambda=\eta =\frac{N_e}{N_\nu}$

where $N_e$ = number of electrons produced, $N_\nu$ = number of photons absorbed.

$\frac{N_\nu}t = \Phi_o \frac{\lambda}{hc}$

Assuming each photon absorbed in the depletion layer produces a viable electron-hole pair, and all other photons do not,

$\frac{N_e}t = \Phi_{\xi}\frac{\lambda}{hc}$

where t is the measurement time (in seconds), $\Phi_o$ = incident optical power in watts, $\Phi_{\xi}$ = optical power absorbed in depletion layer, also in watts.

Spectral sensitivity

The same size, measured inter alia for photodiodes, solar cells or photocathodes in units of amperes per watt, is referred to as spectral response (SR):

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

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

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

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

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

Measuring Principle
For the measurement of the quantum efficiency the exact knowledge of the (absolute) irradiated light power / photon number is necessary. This is usually achieved by a measuring device having the known quantum efficiency of a (calibrated) comparison receiver, ${\ displaystyle QE _ {\ mathrm {cal}}}$ , is calibrated. It then applies:

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

in which ${\ displaystyle I _ {\ mathrm {mes}}}$ the current measured for the test cell and ${\ displaystyle I _ {\ mathrm {cal}}}$ are the current measured for the comparative cell.

Measurement setup
For the illumination, a light source (xenon and / or halogen lamp) and a monochromator for selecting wavelength intervals are necessary. Suitable monochromators are filter monochromators or lattice monochromators. The monochromatic light is passed as homogeneously as possible on the receiver surface to be tested.

The measurement of the signal is often done with lock-in amplifiers to improve the signal-to-noise ratio; For this purpose, 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:

the rate of photons that actually takes effect (the rest is absorbed in another way)
the proportion of the energy of the photon being transferred (apart from the multiphoton absorption, only one photon will ever be involved): the energy of the emitted photon will be lower by the Stokes shift than that of the incident photon.
Practical significance
Among other things, 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 efficiency of photocathodes can reach values of over 50%. Current peak values are:

Cs 2 Te at 213 nm: ~ 20%
GaAsP around the 460… 540 nm: ~ 50%
GaAs around 550… 720 nm: ~ 25%
InP – InGaAsP just over 1000 nm: ~ 1%
The quantum efficiency of single-crystal photodiodes can reach 90%; monocrystalline silicon photodiodes achieve a spectral sensitivity of about 0.5 A / W at the optimum reception wavelength around 900 nm; Solar cells usually do not reach this value – they are polycrystalline or amorphous, and their efficiency is optimized to the widest possible range in the visible spectral range (sunlight).

There are quantum yields of fluorescent dyes used for the analysis of 2 to 42%, which strongly depend 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 efficiency of phosphors used for illumination purposes (cold cathode fluorescent lamps (CCFL), fluorescent lamps, white LEDs) is close to 100% according to different 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).

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

Source from Wikipedia

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