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) 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. QE is a measurement of a device's electrical sensitivity to light. Since the energy of a photon depends on (more precisely, 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. Photographic film typically has a QE of much less than 10%, while CCDs can have a QE of well over 90% at some wavelengths.

Quantum efficiency of solar cells

Main article: Quantum efficiency of a solar cell

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

The quantum efficiency of a solar cell is a very important measure for solar cells, as it gives information on the amount of current that a given 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 current and the highest possible current (if the QE was 100% over the whole spectrum) gives the electrical efficiency of the solar cell.

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 and therefore 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. In somewhat technical terms, the quantum efficiency can be viewed as the collection probability due to the generation profile of a single wavelength, integrated over the device thickness and normalized to the number of incident photons.

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 (R_λ, in A/W) to QE_λ (on a scale 0 to 1):

$QE_{\lambda }={\frac {R_{\lambda }}{\lambda }}\times {\frac {hc}{e}}\approx {\frac {R_{\lambda }}{\lambda }}{\times }(1240\;{\rm {W}}\cdot {\rm {nm/A}})$

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.

$N_{\nu }/t=\Phi _{o}{\frac {\lambda }{hc}}$

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

$N_{e}/t=\Phi _{\xi }{\frac {\lambda }{hc}}$

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.

See also

• Quantum efficiency of a solar cell
• Quantum yield
• DQE (imaging)