Fact-checked by Grok 2 weeks ago

Quantum efficiency

Quantum efficiency (QE) is a fundamental metric in physics and optoelectronics that quantifies the ratio of the number of useful output quanta—such as electrons or photons—to the number of input quanta, typically photons or electrons, in a conversion process.^[1] This parameter, expressed as a fraction between 0 and 1 (or percentage), reflects the probabilistic nature of quantum interactions and is essential for evaluating device performance across various applications.^[1] In photodetectors and photovoltaic devices, such as solar cells, QE measures the number of charge carriers (electrons or holes) generated and collected per incident photon of a specific wavelength, directly influencing energy conversion efficiency.^[2] For light-emitting devices like LEDs, QE instead denotes the number of photons emitted per injected electron, governing radiative recombination efficiency and overall luminous output.^[3] QE is inherently wavelength-dependent, as absorption and emission processes vary with photon energy, and it often exhibits spectral response curves that peak in regions matching the device's material bandgap.^[2] Two primary variants distinguish QE based on what is considered "input": external quantum efficiency (EQE) accounts for all incident quanta, incorporating losses due to reflection, transmission, or non-absorption, while internal quantum efficiency (IQE) focuses solely on absorbed quanta or injected carriers, isolating intrinsic material and recombination efficiencies.^[2] EQE is particularly valuable for overall device benchmarking, whereas IQE aids in material optimization by excluding optical losses.^[2] In practice, achieving high QE (>90%) remains challenging due to non-radiative recombination, Auger effects, and defect states, but advancements in materials like perovskites and quantum dots have pushed limits in solar cells (EQE up to 100% in narrow bands)^[4] and LEDs (IQE exceeding 90%).^[5] Beyond energy and display technologies, QE plays a critical role in scientific instruments, including photomultiplier tubes for particle detection (QE ~20-40% typically) and CCD/CMOS sensors for imaging (QE up to 95% in silicon).^[6] In telecommunications and quantum computing, high-QE single-photon detectors enable secure data transmission and qubit manipulation.^[7] Ongoing research emphasizes enhancing QE through nanostructuring and defect passivation to approach theoretical limits, underscoring its centrality in advancing efficient, sustainable optoelectronic systems.

Definition and Fundamentals

Basic Concept

Quantum efficiency (QE) is a fundamental performance metric in optoelectronic devices, defined as the ratio of the number of useful output quanta—such as electrons or photons—to the number of input quanta, typically photons or electrons, in a conversion process.^[1] In photodetectors and photovoltaic devices, this corresponds to the number of charge carriers—such as electrons or holes—generated and collected to the number of incident photons of a given energy.^[2] ^[1] In light-emitting devices such as LEDs, QE instead measures the number of photons emitted per injected electron or electron-hole pair.^[3] This parameter quantifies the effectiveness of quantum conversion processes in materials and structures responsive to light.^[8] As a dimensionless quantity, QE is typically expressed as a percentage, with values ranging from 0% (no conversion) to 100% (perfect conversion of each quanta).^[2] The concept emerged in the early 20th century alongside the development of photodetectors, building on the quantum nature of the photoelectric effect, and gained quantitative prominence with the advancement of photovoltaic devices in the mid-20th century.^[9] The general expression for QE is given by \eta = \frac{N_{\text{out}}}{N_{\text{in}}}, where N_{\text{out}} represents the number of output quanta and N_{\text{in}} the number of input quanta.^[2] By measuring how efficiently input quanta are transformed into usable output, QE serves as a critical indicator of device performance, influencing the design and optimization of components like photodiodes and LEDs where high values are essential for achieving theoretical efficiency limits.^[1] Variants such as internal and external QE account for differences in considering absorbed versus incident quanta or injected carriers.^[10]

Internal vs. External Quantum Efficiency

In photodetectors and solar cells, internal quantum efficiency (IQE) is defined as the ratio of the number of charge carriers collected at the electrodes to the number of photons absorbed by the active material.^[11] This metric specifically evaluates the efficiency of processes following photon absorption, such as carrier generation, separation, and collection, while ignoring optical losses that occur prior to absorption, including reflection and transmission at the device surfaces.^[12] Mathematically, it is expressed as

\eta_{\text{IQE}} = \frac{\text{number of collected carriers}}{\text{number of absorbed photons}}.

High IQE values, often approaching 100%, indicate excellent material quality and minimal recombination losses within the absorber layer.^[13] External quantum efficiency (EQE), in contrast, measures the ratio of collected charge carriers to the total number of incident photons on the device, encompassing all optical and electrical losses from the point of incidence.^[12] It provides a holistic assessment of device performance under realistic illumination conditions and is given by

\eta_{\text{EQE}} = \frac{\text{number of collected carriers}}{\text{number of incident photons}}.

EQE is typically wavelength-dependent and lower than IQE due to parasitic optical losses, with peak values for moderate-efficiency solar cells ranging from 60% to 90%.^[12] The relationship between IQE and EQE arises from the absorptance of the device, defined as the fraction of incident photons that are absorbed (A = 1 - R - T), where R is the reflection coefficient and T is the transmission coefficient. Thus,

\eta_{\text{EQE}} = \eta_{\text{IQE}} \times A.

This equation highlights that EQE is inherently limited by the device's ability to capture incident light, whereas IQE isolates the intrinsic efficiency of carrier utilization.^[11] Consequently, IQE is generally greater than EQE, as the former assesses the quality of the active material and internal charge transport mechanisms, while the latter evaluates the overall system performance, including optical engineering aspects like anti-reflection coatings.^[12] A representative example occurs in thin-film solid-state dye-sensitized solar cells, where IQE values reach 88–90%, demonstrating effective carrier collection from absorbed photons, but EQE peaks at or below 60% owing to insufficient light trapping and parasitic absorption in the thinner active layers (around 2 μm).^[14] In such devices, enhancing light management through texturing or nanostructures can narrow the gap between IQE and EQE without altering the material's internal properties.^[14]

Theoretical Basis

Key Equations

The quantum efficiency (QE) for a monochromatic light source at wavelength \lambda is defined as the ratio of the number of charge carriers collected to the number of incident photons, expressed mathematically as

\eta(\lambda) = \frac{J_{sc}/q}{P_{in} / (hc/\lambda)},

where J_{sc} is the short-circuit current density, q is the elementary charge, P_{in} is the incident optical power density, h is Planck's constant, and c is the speed of light.^[2] This formulation arises from equating the photocurrent to the collected electron flux and the incident photon flux, with the energy per photon given by hc/\lambda.^[12] For spectral cases, the external quantum efficiency (EQE) as a function of wavelength relates to the spectral responsivity R(\lambda), which is the ratio of photocurrent density to incident power density at \lambda, via

\text{EQE}(\lambda) = \frac{\lambda R(\lambda) q}{hc},

where the units ensure a dimensionless quantity (with R(\lambda) in A/W, \lambda in m, q in C, and hc in J·m).^[2] The integrated spectral EQE over a range of wavelengths contributes to the total short-circuit current density as J_{sc} = q \int \text{EQE}(\lambda) \Phi(\lambda) \, d\lambda, where \Phi(\lambda) is the incident photon flux spectral density.^[12] The derivation of EQE from internal quantum efficiency (IQE) incorporates optical losses step by step. First, the fraction of incident light reflected is R(\lambda), so the non-reflected fraction is $1 - R(\lambda). Of this, the absorbed fraction follows the Beer-Lambert law, where the transmittance T(\lambda) = e^{-\alpha(\lambda) d} for absorption coefficient \alpha(\lambda) and device thickness d, yielding absorption A(\lambda) = 1 - R(\lambda) - T(\lambda). Thus, EQE(\lambda) = IQE(\lambda) \times A(\lambda), assuming no scattering losses.^[2] For opaque devices where T(\lambda) \approx 0, this simplifies to EQE(\lambda) = IQE(\lambda) \times (1 - R(\lambda)).^[12] In photochemistry, quantum yield \Phi parallels QE but quantifies chemical events per absorbed photon, defined as \Phi(\lambda) = \frac{\text{number of events (e.g., molecules reacted)}}{\text{number of photons absorbed at } \lambda}, distinguishing it from electrical QE by focusing on reaction products rather than charge collection.^[15] Theoretically, the maximum QE is \eta = 1 (100%), corresponding to perfect photon-to-carrier conversion without losses; for broadband illumination, the Shockley-Queisser limit imposes a detailed-balance constraint, yielding a maximum efficiency of approximately 33% for a single-junction cell with a 1.1 eV bandgap under AM1.5 spectrum due to radiative recombination and spectrum mismatches.

Factors Affecting QE

Quantum efficiency (QE) in optoelectronic devices is significantly influenced by optical losses, which occur primarily due to reflection at interfaces governed by the Fresnel equations. These equations describe how light reflects and transmits at boundaries between materials with different refractive indices, leading to reduced photon absorption in the active layer; for instance, in semiconductor photodetectors, surface reflections can decrease the external quantum efficiency (EQE) by up to several percent without anti-reflection coatings.^[16]^[17] Additionally, transmission losses through non-absorbing layers, such as passivation or window coatings, allow photons to pass without generating electron-hole pairs, further lowering the fraction of incident light that contributes to photocurrent.^[16] Recombination losses represent another major factor degrading QE, encompassing both radiative and non-radiative processes that reduce the number of charge carriers collected. Radiative recombination, while desirable in light-emitting devices, competes with carrier extraction in photodetectors, but non-radiative pathways—particularly Shockley-Read-Hall (SRH) recombination via defect states in the bandgap—dominate losses by trapping electrons and holes without photon emission.^[18] SRH recombination rates increase with defect density. Surface recombination, a localized form of non-radiative loss at interfaces, further diminishes carrier collection by providing recombination sites near the device's edges, especially in thin-film structures where diffusion to electrodes is limited.^[18] Absorption-related factors also play a critical role, stemming from mismatches between photon energy and the material's bandgap. Photons with energies below the bandgap cannot excite electrons across the gap, resulting in zero QE at those wavelengths, while excess energy from higher-energy photons is lost as heat via thermalization.^[2] In indirect semiconductors, Urbach tail effects—exponential band tails due to disorder—extend sub-bandgap absorption but introduce inefficient carrier generation, broadening the absorption edge and reducing sharp QE onset. These tails, characterized by Urbach energy parameters typically 20-50 meV, are more pronounced in amorphous or polycrystalline materials, leading to parasitic losses in the near-bandgap region.^[19] Material-specific properties further modulate QE through inherent structural and electronic characteristics. In perovskites, high defect tolerance arises from their ionic lattice, enabling near-unity IQE (>95%) even with moderate defect densities, as shallow traps do not strongly localize carriers.^[4] Conversely, in silicon, EQE is highly sensitive to active layer thickness relative to minority carrier diffusion length (around 100-300 μm in high-quality wafers), where thicker layers enhance long-wavelength absorption but increase recombination if diffusion lengths are short.^[2] Temperature dependence adversely affects QE, primarily through enhanced non-radiative recombination as thermal energy activates defect-mediated processes. Rising temperatures increase SRH rates following Arrhenius behavior with activation energies of 10-100 meV; for example, in III-nitride quantum wells, non-radiative lifetimes shorten dramatically above 300 K.^[20]^[21] This thermal activation also broadens the bandgap slightly, shifting absorption edges and exacerbating losses at operational wavelengths. Wavelength dependence of QE reflects the interplay of absorption and loss mechanisms, with peak values typically occurring near the bandgap energy where photon absorption is efficient and thermalization losses are minimal. At longer wavelengths (lower energies), QE drops sharply below the bandgap due to insufficient photon energy for excitation, while at shorter wavelengths (higher energies), it declines from surface reflection, rapid thermalization, or UV-induced damage.^[2] This spectral profile, often sigmoid-shaped, underscores the need for bandgap engineering to match target illumination spectra.^[22]

Measurement Techniques

Spectral Responsivity

Spectral responsivity, denoted as R(\lambda), quantifies the response of a photodetector or photovoltaic device to incident light as a function of wavelength \lambda. It is defined as the ratio of the output signal—typically the photocurrent or photovoltage—to the incident optical power, expressed in units of amperes per watt (A/W) for current responsivity or volts per watt (V/W) for voltage responsivity.^[23] This metric provides a direct measure of how effectively a device converts optical power into an electrical signal at specific wavelengths, serving as a fundamental parameter in optoelectronic device characterization.^[24] The relationship between spectral responsivity and external quantum efficiency (EQE) is given by the equation

R(\lambda) = \frac{q \lambda}{h c} \times \mathrm{EQE}(\lambda),

where q is the elementary charge ($1.602 \times 10^{-19} C), h is Planck's constant ($6.626 \times 10^{-34} J·s), c is the speed of light ($3 \times 10^8 m/s), and \lambda is the wavelength in meters. This formula links the dimensionless EQE, which represents the fraction of incident photons generating collectible charge carriers, to the practical engineering unit of responsivity by accounting for the energy of individual photons. Rearranging the equation allows conversion from responsivity to EQE:

\mathrm{EQE}(\lambda) = \frac{h c}{q \lambda} \times R(\lambda),

often expressed as a percentage for clarity, facilitating the translation between power-based and photon-based performance metrics.^[25] Spectral responsivity is typically evaluated across a broad range from ultraviolet (UV, ~200–400 nm) to infrared (IR, up to ~2000 nm or beyond), tailored to the absorption properties of the device's semiconductor material. The curve's shape reflects the wavelength-dependent absorption coefficient \alpha(\lambda), which dictates the depth and efficiency of photon absorption within the active layer; for instance, strong absorption in the visible range for silicon-based devices leads to peak responsivity around 600–900 nm, while edges drop off due to bandgap limitations or reduced absorption.^[26] This spectral dependence arises because shorter wavelengths (higher energy) are absorbed near the surface, potentially increasing recombination losses, whereas longer wavelengths penetrate deeper but may fall below the bandgap energy.^[27] The importance of spectral responsivity lies in its ability to enable wavelength-specific performance comparisons across devices and materials, essential for optimizing broadband applications. It forms the basis for standardized testing protocols, such as ASTM E1021, which outlines methods for measuring responsivity in photovoltaic devices under controlled monochromatic illumination to ensure reproducibility and certification.^[28] Through the EQE relation, it provides a standardized pathway to assess quantum efficiency without direct photon counting, bridging theoretical material properties with real-world electrical output.^[28]

Experimental Determination

The experimental determination of quantum efficiency (QE) in photovoltaic devices typically employs the monochromator method, which utilizes a tunable monochromatic light source to probe the device across a range of wavelengths. A broadband light source, such as a xenon arc lamp or quartz-tungsten-halogen (QTH) lamp, is coupled with a grating monochromator to produce narrowband illumination (typically 1-10 nm bandwidth) that is scanned from ultraviolet to near-infrared wavelengths, often 300-1100 nm for silicon-based cells. The photocurrent generated by the device under test is measured using a low-noise current amplifier, while the incident photon flux is quantified simultaneously with a calibrated reference detector, such as a silicon photodiode traceable to national standards, positioned in the optical path. This setup allows calculation of external quantum efficiency (EQE) as the ratio of collected charge carriers to incident photons at each wavelength, following the procedures outlined in IEC 60904-8.^[29]^[30] For solar cells, particularly those exhibiting nonlinear behavior like perovskites or organics, white bias light is integrated into the measurement to simulate operating conditions under the AM1.5 global spectrum and mitigate effects such as sub-bandgap absorption or trap filling that could distort QE values. The bias light, often from an adjustable-intensity QTH or LED array providing uniform illumination at 0.1-1 sun equivalent, ensures the device is forward-biased near maximum power point, improving measurement accuracy by up to 10-20% in low-response regions. Calibration of the incident flux relies on reference cells certified under IEC standards, which account for spectral mismatch and ensure traceability with uncertainties below 1% for the reference itself.^[31]^[32] Spatial mapping of EQE assesses uniformity across a device or module, employing a focused monochromatic beam (spot size 0.1-1 mm) scanned via motorized stages over the sample surface while measuring local photocurrents. This technique reveals variations due to material inhomogeneities or processing defects, with setups often incorporating automated positioning for resolutions down to micrometers. Common error sources include stray light from monochromator scattering, which can inflate QE by 1-5% in the tails of the spectrum and requires correction via background subtraction or baffle improvements, and angular dependence of responsivity, where off-normal incidence alters effective path length and necessitates measurements at multiple angles per IEC guidelines. Overall measurement uncertainty typically ranges from ±2-5%, dominated by flux calibration and noise, though rigorous protocols can reduce it to ±1-2% in controlled labs.^[33]^[34]^[35]^[36] Advances in measurement techniques have enhanced sensitivity and spatial resolution, including refined lock-in amplification for detecting sub-picoampere signals in low-EQE regimes, enabling reliable measurements down to $10^{-5} with noise rejection over 100 dB. Hyperspectral imaging has been applied for two-dimensional QE mapping, capturing full spectral cubes (e.g., 400-1000 nm at 5 nm resolution) across device areas to correlate local optoelectronic properties like recombination losses, achieving sub-millimeter mapping speeds suitable for large-area analysis in perovskites.^[30]^[37] These methods, often integrated with machine learning for data processing, support higher-throughput characterization while maintaining traceability to standards. Internal quantum efficiency (IQE) is derived from EQE by accounting for optical losses: \mathrm{IQE}(\lambda) = \frac{\mathrm{EQE}(\lambda)}{A(\lambda)}, where A(\lambda) is the absorptance at wavelength \lambda, calculated as A(\lambda) = 1 - R(\lambda) - T(\lambda) with reflection R(\lambda) and transmission T(\lambda) measured separately using integrating spheres or spectrophotometers. This isolates the intrinsic efficiency of carrier generation and collection from absorption inefficiencies.^[2]

Applications in Photovoltaics

QE in Solar Cells

Quantum efficiency (QE), particularly external quantum efficiency (EQE), is fundamental to the performance of photovoltaic (PV) devices as it directly influences the short-circuit current density J_{sc}, a primary determinant of power conversion efficiency (PCE) defined by \eta_{PV} = \frac{J_{sc} V_{oc} FF}{P_{in}}, where V_{oc} is the open-circuit voltage, FF is the fill factor, and P_{in} is the incident power density.^[38] The J_{sc} is given by J_{sc} = q \int_0^\infty EQE(\lambda) \Phi_{sun}(\lambda) \, d\lambda, where q is the elementary charge and \Phi_{sun}(\lambda) is the solar photon flux spectrum, highlighting how EQE quantifies the fraction of incident photons converted to collected charge carriers.^[39] Ultimately, QE sets an upper bound on PV efficiency, as idealized models like the Shockley-Queisser limit assume EQE = 1 for photons above the bandgap to achieve theoretical maxima around 33% for single-junction silicon cells under AM1.5 illumination.^[38] In practical silicon solar cells, peak EQE values typically range from 80% to 90% in the 600–900 nm wavelength region, reflecting effective carrier collection but limited by parasitic absorption and recombination.^[39] Multi-junction solar cells, designed to capture broader spectral ranges, achieve EQE exceeding 90% across sub-cell bands, with maximal values up to 96.7% reported at specific wavelengths like 810 nm, enabling PCEs over 40% in concentrated light.^[40] These values underscore QE's role in scaling current generation, though real-world deviations from ideal EQE=100% impose fundamental limits on single-junction efficiencies below 30%.^[39] Spectral mismatch losses occur when the incident solar spectrum does not optimally overlap with the EQE curve, reducing J_{sc} relative to an ideal uniform spectrum at peak EQE; this is quantified by the spectral mismatch factor M = \frac{\int EQE(\lambda) S(\lambda) \, d\lambda}{\left( \int S(\lambda) \, d\lambda \right) \times \max(EQE)}, where S(\lambda) is the solar irradiance spectrum, representing the ratio of actual to maximum achievable current.^[41] For standard AM1.5G conditions, M typically falls between 0.85 and 0.95 for silicon cells, indicating 5–15% potential current loss due to mismatched photon energies.^[42] In tandem solar cells, QE is evaluated across cascaded sub-cells, where photons not absorbed by upper junctions reach lower ones, necessitating balanced EQE integration for current matching in series-connected configurations to maximize overall J_{sc}.^[43] Current matching requires the photon-generated currents in each sub-cell—computed from their respective EQE and the filtered spectrum—to be equal, often achieved by tuning sub-cell bandgaps or thicknesses, as deviations can limit tandem PCE to the lowest sub-cell current.^[44] For example, III–V/Si tandems target EQE overlaps yielding matched currents around 14–15 mA/cm² under 1-sun illumination.^[43] Improvements in EQE are realized through anti-reflection coatings (ARCs), which minimize front-surface reflection losses (typically 30% bare silicon to <5% coated), boosting average EQE by 5–10% across the visible spectrum and enhancing J_{sc} by 1–2 mA/cm².^[45] Surface passivation layers, such as SiO₂ or Al₂O₃, reduce recombination at interfaces by lowering surface recombination velocity from >10⁴ cm/s to <10 cm/s, thereby improving internal QE and overall EQE, especially at wavelengths prone to surface losses. These strategies have enabled silicon heterojunction cells to approach 27% PCE with EQE peaks near 95%.^[46]

Types of QE Curves

Quantum efficiency (QE) curves, particularly external quantum efficiency (EQE) spectra, serve as diagnostic tools for understanding charge generation, transport, and collection in solar cells, revealing distinct shapes influenced by material properties, device architecture, and loss mechanisms. In single-junction solar cells, the EQE curve typically adopts a bell-shaped profile when plotted against wavelength or photon energy, featuring a broad peak within the absorption bandgap where photon-to-electron conversion is most efficient. The width of this peak is closely tied to the Urbach energy, a measure of the exponential tail in the absorption edge due to disorder or defects, which broadens the curve and reduces sharp cutoffs; lower Urbach energies (e.g., around 20-50 meV in high-quality crystalline materials) indicate reduced sub-bandgap absorption and improved performance.^[19]^[47] Deviations from the ideal rectangular response in these bell-shaped curves provide insights into recombination and transport limitations. A pronounced drop in EQE at short wavelengths (blue region, <500 nm) often stems from surface recombination, as high-energy photons are absorbed near the front surface, generating carriers vulnerable to rapid recombination at interfaces unless mitigated by passivation layers. Conversely, the gradual decline at long wavelengths (red region, >800 nm) reflects insufficient minority carrier diffusion lengths, where carriers excited deep in the absorber fail to reach the junction before recombining, particularly in materials with low mobilities like thin-film silicon or organics.^[2]^[48] In organic photovoltaic (PV) devices, poor charge transport and interfacial barriers can lead to an S-shaped EQE curve, characterized by a slow initial rise followed by a plateau and sharp falloff, signaling charge accumulation at heterointerfaces that impedes extraction under low fields. This shape is prevalent in bulk heterojunction organics due to imbalanced mobilities and energy level mismatches, reducing overall efficiency unless addressed through morphology optimization or interlayers.^[49]^[50] Multi-junction solar cells exhibit step-like EQE curves, where the response decreases in discrete steps corresponding to the bandgaps of stacked sub-cells, allowing spectral splitting for higher efficiency. For instance, in GaInP/GaAs tandem cells, the EQE remains high up to ~690 nm (1.8 eV, GaInP top cell), then steps down to the GaAs response until ~880 nm (1.4 eV), beyond which it approaches zero, enabling current matching analysis.^[51]^[52] EQE curves are conventionally plotted as a function of wavelength (in nm) for alignment with solar spectra or photon energy (in eV) for bandgap correlation, with linear scales for peak regions and logarithmic scales in low-QE tails (<1%) to resolve subtle recombination effects or sub-bandgap features.^[2]^[53]

Applications in Optoelectronics

QE in Image Sensors

In image sensors, quantum efficiency (QE) plays a pivotal role in determining the signal-to-noise ratio (SNR), as it quantifies the fraction of incident photons converted into charge carriers, thereby generating more electrons per photon to enhance signal strength relative to noise.^[54] Higher QE directly improves low-light performance by increasing the Poisson noise-limited SNR, where the signal electrons dominate over photon shot noise.^[55] The effective QE of a sensor is further modulated by the fill factor, which represents the active photosensitive area of each pixel; lower fill factors, common in designs with on-pixel circuitry, reduce the overall photon capture efficiency, necessitating microlens arrays to mitigate this loss.^[56] Charge-coupled device (CCD) and complementary metal-oxide-semiconductor (CMOS) image sensors differ in architecture and QE performance, with CCDs traditionally offering higher QE due to their dedicated charge transfer without integrated electronics blocking light paths.^[57] Modern CMOS sensors, however, have closed the gap through advancements in pixel design, achieving comparable or superior QE in many applications while providing lower power consumption and faster readout.^[58] Back-illuminated sensors, applicable to both types, significantly boost QE by exposing the photosensitive layer directly to light, avoiding obstruction from wiring; these designs routinely exceed 90% QE across the visible spectrum (400–700 nm), enabling superior sensitivity for scientific and consumer imaging.^[59] Silicon-based image sensors exhibit peak QE between 500 and 600 nm, aligning with green light where the bandgap allows efficient electron-hole pair generation, often reaching up to 95% in optimized devices.^[60] For infrared (IR) extension, quantum dot (QD) integration in hybrid sensors provides tunable QE by varying dot size to adjust absorption edges, enabling sensitivity up to 2000 nm or beyond while maintaining compatibility with silicon readout circuits.^[61] This tunability supports applications like night vision, where traditional silicon QE drops sharply above 1000 nm. Noise sources profoundly influence effective QE, particularly in low-light conditions where readout noise—arising from amplification and digitization—can dominate the signal, effectively reducing QE by masking weak photon-generated charges.^[62] At higher illuminations, the full well capacity, which limits the maximum charge per pixel (typically 10,000–100,000 electrons in modern sensors), caps the dynamic range, preventing saturation while QE remains constant; exceeding this capacity leads to nonlinear response and blooming.^[63] The historical evolution of QE in image sensors transitioned from front-side illuminated designs in the late 20th century, which suffered from ~30% QE due to light attenuation by overlying metal layers, to back-side illuminated architectures emerging in the 2000s that achieved ~80% QE by thinning the silicon and illuminating from the backside. This shift, driven by CMOS scaling and thinning techniques, revolutionized imaging fidelity in digital cameras and scientific instruments by the mid-2000s. As of 2025, further advancements in scientific CMOS (sCMOS) sensors have pushed QE toward 95–99% in the visible range through backside illumination and anti-reflective coatings, enhancing low-light performance in applications like astronomy and microscopy.^[64]

EQE Mapping

EQE mapping refers to spatially resolved measurements of external quantum efficiency (EQE) that provide detailed insights into the uniformity and performance variations across optoelectronic devices, such as pixel arrays in image sensors. These techniques enable the identification of local defects, non-uniformities, and structural influences on light conversion efficiency by scanning or array-based probing of the device surface.^[65] Common methods include laser beam scanning via light beam induced current (LBIC) systems, where a focused laser spot is raster-scanned across the sample while measuring the local photocurrent to compute EQE at specific wavelengths. Alternatively, micro-spectrometer arrays allow parallel spectral measurements over multiple points, facilitating high-throughput mapping of EQE(λ) distributions without mechanical scanning. These approaches build on overall sensor EQE principles by adding spatial dimensions to reveal pixel-to-pixel variations.^[65]^[66] Spatial resolution in EQE mapping can achieve sub-micron levels using advanced scanning probe techniques, such as near-field optical microscopy combined with photocurrent detection, which is essential for defect analysis like isolating dead pixels or material inhomogeneities in dense pixel arrays. In CMOS image sensors, such maps highlight effects from microlens misalignment, where variations in light focusing lead to reduced EQE in misaligned pixels due to oblique incidence losses.^[67]^[65] Data from EQE mapping is typically visualized as 2D heatmaps showing EQE values at a fixed wavelength (e.g., 850 nm) overlaid on the device topography, with color gradients indicating performance gradients. Complementary statistical analysis, including variance calculations and Gaussian-fitted histograms, quantifies overall uniformity and isolates anomalous regions for further investigation.^[65]

References

[1]
Quantum Efficiency - RP Photonics
A quantum efficiency is the percentage of input photons which contribute to a desired effect – for example, light detection in a photodetector.<|control11|><|separator|>
[2]
Quantum Efficiency | PVEducation
The quantum efficiency (QE) is the ratio of the number of carriers collected by the solar cell to the number of photons of a given energy incident on the solar ...Missing: applications physics
[3]
Internal Quantum Efficiency - an overview | ScienceDirect Topics
Internal quantum efficiency (η int) is defined as the ratio of the total number of photons generated by an LED to the number of electrons injected.<|control11|><|separator|>
[4]
[PDF] Lecture 19-20 - MIT OpenCourseWare
The internal quantum efficiency (IQE) of an LED is determined by the ration of the radiative recombination rate to the recombination rate due to all ...
[5]
[PDF] Chapter 8 Detectors - Physics 123/253
The quantum efficiency, QE, is a common measure of detector efficiency. It is usually defined as the fraction of photons incident on the detector that actually.
[6]
[PDF] Single-Photon Sources and Detectors Dictionary
Sep 7, 2023 · N.B. Quantum efficiency differs from internal efficiency in that the internal efficiency in- cludes both the gain and transduction mechanisms ...
[7]
Quantum Efficiency - an overview | ScienceDirect Topics
Quantum efficiency is defined as the ratio of number of photons emitted to the number of photons injected. For example if only one photon is emitted out of 100 ...<|control11|><|separator|>
[8]
First Practical Silicon Solar Cell | American Physical Society
Apr 1, 2009 · In April, 1954, researchers at Bell Laboratories demonstrated the first practical silicon solar cell. The story of solar cells goes back to an ...Missing: quantitative quantum<|control11|><|separator|>
[9]
An Introduction to Quantum Efficiency | External and Internal - Ossila
Quantum efficiency refers to the fraction of input energy that is converted into useful output energy. This varies for applications such as solar cells and ...Missing: physics | Show results with:physics
[10]
[PDF] Chapter 5 Photodetectors and Solar Cells - Cornell University
The quantum efficiency (also called the external quantum efficiency) of a photodiode is defined as, ... The internal quantum efficiency of a photodiode is defined ...
[11]
[PDF] Lecture 7 - Device Fundamentals - MIT OpenCourseWare
Sep 29, 2011 · Technical Terms: - Solar Conversion Efficiency. - External Quantum Efficiency. - Internal Quantum Efficiency. What does this really mean? 4.
[12]
[PDF] ME 432 Fundamentals of Modern Photovoltaics
Oct 30, 2023 · • “External quantum efficiency” is defined as the number of electrons out per ... • For this we use the internal quantum efficiency. Example ...
[13]
https://oasis.mechse.illinois.edu/wp-content/uploads/2023/10/ME432-Class28-Oct30.pdf
[14]
quantum yield (Q04991) - IUPAC Gold Book
The integral quantum yield is Φ ( λ ) = n u m b e r o f e v e n t s n u m b e r o f p h o t o n s a b s o r b e d For a photochemical reaction, ...
[15]
Parasitic Reflections – examples, effects, minimization - RP Photonics
The sensitivity and the quantum efficiency of photodiodes is reduced by reflections, e.g. on the semiconductor chip surface.
[16]
Reducing Optical Reflection Loss for Perovskite Solar Cells Via ...
Aug 8, 2022 · According to the Fresnel equation (Equation 1), the optical reflection loss at the interface between different mediums is inevitable due to ...
[17]
Types of Recombination - PVEducation
Recombination Through Defect Levels. Recombination through defects, previously known as Shockley-Read-Hall (SRH or RHS) recombination, occurs via a trap ...
[18]
Reducing Shockley–Read–Hall recombination losses in the ...
Oct 18, 2021 · In this work, we discuss the reduction of the integrated SRH recombination rate in the depletion region (U SRH dep) by changing the emitter material.
[19]
Unraveling Urbach Tail Effects in High-Performance Organic ...
May 16, 2022 · Two independent techniques, namely, photothermal deflection spectroscopy (PDS) and sensitive sub-bandgap external quantum efficiency (s-EQE), ...Abstract · Figure 1 · Figure 3
[20]
Below the Urbach Edge: Solar Cell Loss Analysis Based on Full ...
Jul 3, 2023 · We suggest a new solar cell loss analysis using the external quantum efficiency (EQE) measured with sufficiently high sensitivity to also account for defects.
[21]
Perovskite Solar Cells with Near 100% Internal Quantum Efficiency ...
The internal quantum efficiencies approach 100% in 3-mm-thick single-crystal perovskite solar cells under weak light.
[22]
Temperature dependent radiative and non-radiative recombination ...
Oct 30, 2024 · By combining the resulting PL IQE values with the ns-PL lifetimes, we further intensively redetermined the radiative and non-radiative ...
[23]
Temperature dependence of nonradiative recombination processes ...
Invited Article. Temperature dependence of nonradiative recombination processes in UV-B AlGaN quantum well revealed by below-gap excitation light.
[24]
Quantifying the Absorption Onset in the Quantum Efficiency of ...
Mar 6, 2021 · The external quantum efficiency (EQE), also known as incident-photon-to-collected-electron spectra are typically used to access the energy ...<|control11|><|separator|>
[25]
Responsivity – photodetectors, photodiodes, sensitivity - RP Photonics
The responsivity of a photodetector is the photocurrent per incident unit optical power. It should not be confused with the sensitivity.
[26]
Spectral Responsivity - an overview | ScienceDirect Topics
Spectral responsivity is the output signal (current or voltage) response to monochromatic radiation incident on the detector, modulated at a frequency f.
[27]
External Quantum Efficiency - an overview | ScienceDirect Topics
The EQE (λ) formula calculates the ratio of charge carriers collected to absorbed photons [29,30]. (3) E Q E = h c R λ e λ. where, h, c, Rλ, and q are ...
[28]
Spectral Response | PVEducation
The spectral response is the ratio of the current generated by the solar cell to the power incident on the solar cell.
[29]
[PDF] Photovoltaic Spectral Responsivity Measurements - NREL
ASTM Standard E1021 estimates a 0.3% re- peatability and 1.7% reproducibility limit in the spectral mis- match parameter calculated using the spectral response ...
[30]
E1021 Standard Test Method for Spectral Responsivity ... - ASTM
Apr 16, 2025 · This test method measures the differential spectral responsivity of a photovoltaic device. The procedure requires the use of white-light bias.
[31]
[PDF] Improved Grating Monochromator Set-Up for EQE Measurements of ...
Grating monochromator set-ups are widely in use for the measurement of the external quantum efficiency (EQE) of solar cells.
[32]
https://www.renewableenergyworld.com/solar/instrumentation-for-quantum-efficiency-measurement-of-solar-cells-part-2/
[33]
The effect of bias light on the spectral responsivity of organic solar ...
We propose a new, simple, experimental method to more accurately determine S and EQE under bias illumination.
[34]
Instrumentation for Quantum Efficiency Measurement of Solar Cells
Oct 12, 2010 · A typical bias light source is a QTH (white light) source of adjustable output intensity that enables uniform illumination of the sample cell.
[35]
Mapping the performance of solar cells with nanoscale resolution
Sep 16, 2015 · Map of effective external quantum efficiency (EQE) overlaid on the topography of a CdTe solar cell. These measurements were acquired using ...
[36]
Analysis and mitigation of errors in external quantum efficiency ...
Jul 1, 2023 · IEC 60904-8, 2014 edition [7] describes a non-destructive technique to measure the spectral response(SR) of a cell embedded inside the ...
[37]
Angular‐dependent spectral responsivity—Traceable ...
Nov 27, 2017 · This paper is targeting at the characterization of AOI effects in PV devices causing optical losses in their performance.
[38]
Establishment and evaluation of photovoltaic quantum efficiency ...
The uncertainty for the quantum efficiency measurements has been calculated as the square root of the quadrature summation of each source of uncertainty ...
[39]
The Next Generation of Solar Cells - Utilizing Spectral Imaging - AZoM
Feb 16, 2024 · Hyperspectral imaging is a non-invasive spectroscopy technique that produces extensive three-dimensional datasets (or data cube), where each pixel contains a ...
[40]
Rapid Optimization of External Quantum Efficiency of Thin Film Solar ...
May 25, 2018 · The performance of a solar cell is often quantified by internal (IQE) and external (EQE) quantum efficiencies. IQE is the ratio of electrons ...
[41]
Enhanced conversion efficiency in Si solar cells employing ... - Nature
Oct 26, 2017 · As shown in Fig. 3b and Table 1, the calculated Jsc from EQE spectra are 32 mA/cm2 (the measured Jsc: 32.5 ± 0.6 mA/cm2) for solar cell without ...
[42]
Performance evaluation of multi-junction solar cells by spatially ...
The average EQE of cells C and D is about 80% and 90%, respectively. A maximal value of 96.7% was obtained in cell D at 810 nm. The slightly low EQE ...Missing: typical | Show results with:typical
[43]
Comprehensive Analysis of Spectral Mismatch Factor for Solar Cells ...
Aug 25, 2023 · The spectral mismatch factor for solar cells quantifies their relative performance in converting solar irradiance between the incident and ...Introduction · Data · Results · Conclusions
[44]
Spectral Mismatch Corrections Video Text Version - NREL
May 1, 2025 · Corrections can be made using the spectral mismatch factor M. This captures the difference in intensity between the AM 1.5G solar spectrum and the lamp ...
[45]
Current-Matched III–V/Si Epitaxial Tandem Solar Cells with 25.0 ...
Sep 23, 2020 · III–V/Si epitaxial tandems with a 1.7-eV GaAsP top cell promise stable power conversion efficiencies above the fundamental limit of Si single-junction cells.
[46]
Performance comparison of III–V//Si and III–V//InGaAs multi-junction ...
Mar 13, 2019 · EQE values exceeding 50% can be obtained for In0.51Ga0.49As from the GaInP/GaAs//In0.51Ga0.49As bottom cell in the wavelength region of 900–1600 ...Missing: typical | Show results with:typical
[47]
Effect of anti-reflection coating on the performance of silicon solar ...
May 3, 2021 · This experiment explores the effect of lithium fluoride (LiF) antireflection coating (ARC) on the performance of commercial silicon solar cellsIi. Experiment · A. External Quantum... · B. Electrical...
[48]
Silicon heterojunction solar cells with up to 26.81% efficiency ...
May 4, 2023 · Silicon heterojunction solar cells with up to 26.81% efficiency achieved by electrically optimized nanocrystalline-silicon hole contact layers.
[49]
Impact of Urbach energy on open-circuit voltage deficit of thin-film ...
Jun 15, 2020 · Urbach energy (EU) is estimated from external quantum efficiency. · Relation between VOC,def and EU is investigated among thin-film solar cells.
[50]
External quantum efficiency measurements used to study the ...
Jun 17, 2020 · In this work, we use the external quantum efficiency (EQE) technique to study the photoinduced degradation of two types of solar cells having CH 3 NH 3 PbI 3 ...
[51]
Charge accumulation induced S-shape J–V curves in bilayer ...
We study the origin of the S-shape effect in the current–voltage curve of bilayer heterojunction organic solar cell induced by the exciton blocking layer (EBL).
[52]
Investigation of the S-Shaped Current–Voltage Curve in High Open ...
We report our investigation on the S-shaped current–voltage characteristics in a hot-casting–processed (BA)2 (MA)3Pb4I13 Ruddlesden–Popper (RP) perovskite ...Abstract · Introduction · Results and Discussion · Experimental Methods
[53]
An efficient and stable photoelectrochemical system with 9% solar-to ...
Nov 21, 2019 · ... InGaP/GaAs double junction, consisting of the top (InGaP, Eg = 1.8–1.85 eV) and bottom cells (GaAs, Eg = 1.4 eV) under one sun illumination (Fig ...
[54]
Improved GaInP/GaAs/GaInAs inverted metamorphic triple-junction ...
Solar cell characterization includes external quantum efficiency (EQE) and reflectance (R), carried out using a custom-made system based on a Xe lamp and ...
[55]
What is External Quantum Efficiency (EQE) in Solar Cells? - EnliTech
Nov 13, 2024 · This article introduces External Quantum Efficiency (EQE) and explains the experimental procedure for EQE spectral measurements.Missing: hc) * | Show results with:hc) *
[56]
Quantum Efficiency in Scientific Cameras: A Beginner's Guide |
Aug 25, 2015 · A higher QE improves SNR by generating more signal (electrons) per photon. But excessive noise, due to poor electronics or inadequate cooling, ...
[57]
Quantum Efficiency and Signal-to-Noise Ratio in CCD Image Sensors
May 25, 2020 · Quantum efficiency of 100% would indicate that every photon is converted into a usable electron. Back-illuminated CCDs can achieve QE greater ...
[58]
Image Sensors - RP Photonics
What do quantum efficiency and fill factor mean for an image sensor? Quantum efficiency is the percentage of photons hitting the sensor that are converted ...
[59]
CCD vs CMOS Image Sensors: A Comprehensive Guide for ...
Aug 21, 2024 · Low-Light Performance: CCD sensors excel with higher quantum efficiency. Speed: CMOS sensors dominate with faster readout speeds. Noise ...How A Ccd Camera Works... · How A Cmos Sensor Works... · Ccd Vs Cmos: Breaking Down...
[60]
[PDF] CCD or CMOS - Key differences between both sensor technologies
Mar 1, 2024 · CCD and CMOS sensors belong to quantum detectors. ... By reducing the dark and fixed pattern noise as well as raising the quantum efficiency, ...<|separator|>
[61]
CMOS Image Sensor for Broad Spectral Range with >90% Quantum ...
Jul 26, 2023 · This article presents an approach for broadening the spectral range of complementary metal–oxide–semiconductor (CMOS) image sensors.
[62]
Quantum Efficiency - Teledyne Vision Solutions
Deep-depleted silicon sensors can provide a QE of >90% between 700 - 850 nm in comparison to >60% with traditional silicon sensors, as shown in Figure 2. B-BR- ...
[63]
Quantum Dots Short-Wave Infrared Image Sensor with Enhanced ...
Apr 23, 2025 · Quantum dots (QDs)-based photodetectors are promising alternatives to construct short-wave infrared (SWIR) image sensors at a low cost.Introduction · Results and Discussion · Supporting Information · References
[64]
[Readout Noise] – What is Readout Noise ? | - Tucsen
May 13, 2022 · The Quantum Efficiency (QE) of a sensor refers to the likelihood of photons hitting the sensor being detected in %. High QE leads to a more ...
[65]
Bit Depth, Full Well, and Dynamic Range | Teledyne Vision Solutions
This article describes another factor of scientific cameras that affects both the full well capacity and the dynamic range, namely the camera sensor bit depth.Missing: effective | Show results with:effective
[66]
Enhanced near infrared light trapping in Si solar cells with metal ...
EQE mapping. EQE maps were obtained using spatially-resolved light-beam induced current (SR-LBIC) measurements using the commercially available LOANA solar cell ...
[67]
Spectral response mapping of co-sensitized dye-sensitized solar ...
First EQE mapping of dye desorption in dye-sensitized solar cells. •. Ability to map spectral response at different wavelengths. •. Identifying different dye ...
[68]
Hybrid image sensor of small molecule organic photodiode on CMOS
May 5, 2020 · The device shows an EQE of ~30% and ~25% measured at 500 nm and 525 nm wavelengths of light respectively at short circuit condition. Furthermore ...
[69]
[PDF] Machine learning for advanced characterisation of silicon solar cells
Apr 15, 2023 · The method is then extended for automated efficiency-loss analysis, where a new deep learning framework identifies the defective regions in the ...<|control11|><|separator|>