Quantum efficiency

A graph showing variation of quantum efficiency with wavelength of a CCD chip in the Hubble Space Telescope's Wide Field and Planetary Camera 2.

The quantum efficiency (QE), or incident photon to converted electron (IPCE) ratio,[1] of a photosensitive device or a charge-coupled device (CCD) 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.[2] QE is a measurement of a device's electrical sensitivity to light. 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%,[3] while CCDs can have a QE of well over 90% at some wavelengths.

Quantum efficiency of solar cells

A graph showing variation of internal quantum efficiency, external quantum efficiency, and reflectance with wavelength of a crystalline silicon solar cell.

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 of quantum efficiency

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.

$\text{EQE} = \frac{\text{electrons/sec}}{\text{photons/sec}}= \frac{\text{current}/\text{(charge of 1 electron)}}{(\text{total power of photons})/(\text{energy of one photon})}$

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 which 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); this light is either filtered out or absorbed by the cell, heating the cell. That heat is wasted energy, and could lead to damage to the cell.[4]

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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).[5] 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[6] (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 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.

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References

1. ^ Shaheen, Sean (2001). "2.5% efficient organic plastic solar cells". Applied Physics Letters 78 (6). Bibcode:2001ApPhL..78..841S. doi:10.1063/1.1345834. Retrieved 20 May 2012.
2. ^ Definition of quantum efficiency in Photonics Dictionary
3. ^ Träger, Frank (2012). Handbook of Lasers and Optics. Berlin Heidelberg: Springer. p. 603. ISBN 9783642194092.
4. ^ Silicon nanoparticle film can increase solar cell performance
5. ^ Definition of responsivity in Photonics Dictionary
6. ^ A. Rogalski, K. Adamiec and J. Rutkowski, Narrow-Gap Semiconductor Photodiodes, SPIE Press, 2000
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