1 Definition and concept

Internal quantum yield is a measure of how effectively a material converts absorbed excitation into a specified internal outcome. That outcome may be emission of light, generation of charge carriers, or another desired photophysical or photochemical event. The quantity is used to compare how well different substances, devices, or processes perform once energy has already entered the system.

1.1 Basic meaning

In its simplest sense, internal quantum yield asks: for each excitation absorbed by a material, how many useful events follow? If one absorbed photon leads to one emitted photon or one separated charge pair, the internal quantum yield is high. If much of the absorbed energy is lost through heat or other nonproductive pathways, the yield is lower.

1.2 Relation to absorbed excitations

The key feature of internal quantum yield is that the denominator is the number of absorbed excitations, not the number of incident photons or particles. This makes it a measure of internal conversion efficiency. It is therefore especially useful when a system absorbs only part of the incoming radiation, since the metric focuses on the fate of what was actually absorbed.

1.3 Difference from external quantum yield

External quantum yield includes the entire input-output chain, from incident excitation to the observed output. Internal quantum yield excludes losses that occur before absorption, such as reflection or transmission, and also excludes output losses such as imperfect light extraction. As a result, the internal value is typically equal to or greater than the external value for the same system.

1.4 Common notation and symbols

Notation varies by field. Internal quantum yield is often written as IQY or IQE, though IQE more commonly refers to internal quantum efficiency in device contexts. Some authors use the Greek letter eta, written as η, with subscripts indicating the process of interest, such as emission or charge collection. The exact symbol depends on the discipline and the measured outcome.

2 Mathematical formulation

2.1 General ratio expression

A general expression for internal quantum yield is the ratio of the number of desired internal events to the number of absorbed excitations. In symbolic form, it can be written as:

η_int = N_useful / N_absorbed

where N_useful is the number of successful events and N_absorbed is the number of absorbed quanta or excitations. This definition is adaptable to many systems, provided the numerator is clearly specified.

2.2 Quantum yield for emission processes

For emission processes, internal quantum yield describes the fraction of excitations that result in photon emission within the material. This applies to fluorescence, phosphorescence, and related luminescent mechanisms. The quantity is often governed by a competition between light-emitting and loss-producing pathways.

2.2.1 Radiative and nonradiative pathways

After absorption, an excited state may decay radiatively by emitting a photon or nonradiatively by transferring energy to vibrations, defects, or surrounding molecules. Internal quantum yield for emission is high when radiative decay dominates. In many materials, nonradiative relaxation is the principal cause of reduced yield.

2.2.2 Competing decay channels

The emission yield is shaped by several competing channels, including intersystem crossing, internal conversion, quenching by impurities, and exciton annihilation at high excitation densities. A common rate-based description expresses the yield as the radiative decay rate divided by the total decay rate. This framing highlights that yield depends on relative probabilities rather than on emission strength alone.

2.3 Quantum yield for charge-generation processes

In devices that convert absorbed energy into electrical carriers, internal quantum yield measures how many absorbed excitations produce free or collectable charges. This is relevant in photovoltaics, photoconductors, and photodetectors. The process may involve exciton separation, carrier transport, and charge extraction.

2.3.1 Carrier collection efficiency

When a photon is absorbed, the resulting excitation must often be separated into charge carriers and moved to contacts or active regions. Internal quantum yield in this context reflects the fraction of absorbed photons that lead to successful carrier collection. Efficient separation and transport increase the value, while trapping and recombination reduce it.

2.3.2 Recombination losses

Not all generated charges survive long enough to be collected. They may recombine geminately, recombine after separation, or become trapped in defect states. These recombination channels lower the internal quantum yield by removing carriers from the useful output pathway.

3 Measurement and determination

3.1 Experimental approaches

Internal quantum yield is usually determined indirectly by measuring absorbed excitation and the resulting output under controlled conditions. The appropriate method depends on whether the target process is light emission, charge generation, or another internal event. Experimental design must isolate the internal process from losses external to the material.

3.1.1 Photoluminescence methods

In luminescent materials, photoluminescence measurements are widely used. The sample is excited with known optical input, and the emitted light is collected and analyzed. When absorption is independently measured, the internal quantum yield can be derived from the emission relative to absorbed photons.

3.1.2 Time-resolved spectroscopy

Time-resolved techniques track how excited states decay over time. By measuring lifetimes and decay components, researchers can estimate radiative and nonradiative rates. These data help determine internal quantum yield and distinguish among competing relaxation processes.

3.1.3 Photocurrent-based measurements

For charge-generating systems, internal quantum yield may be inferred from photocurrent experiments. The sample is illuminated while the resulting electrical response is measured. After correcting for absorption and device geometry, the fraction of absorbed photons converted into collected current can be estimated.

3.2 Calibration and reference standards

Accurate determination requires calibration of detectors, excitation sources, and optical geometry. Reference standards with known emission or absorption properties are often used to validate the setup. Good calibration minimizes systematic bias and allows comparison between laboratories.

3.3 Error sources and uncertainty

Common error sources include incomplete absorption measurements, reabsorption of emitted light, background signals, detector drift, and uncertainty in sample thickness or concentration. In scattering or strongly absorbing media, distinguishing absorbed from transmitted or reflected excitation can be difficult. Careful correction procedures are essential for reliable results.

4 Factors affecting internal quantum yield

4.1 Material composition

The chemical composition of a material strongly influences its internal quantum yield. Dopants, ligands, host matrices, and alloying elements can alter excited-state behavior, either improving the desired pathway or introducing competing losses. Small compositional changes may produce large changes in performance.

4.2 Defects and impurities

Defects, vacancies, grain boundaries, and trace impurities often create trap states that promote nonradiative decay or carrier recombination. In luminescent systems, such sites can quench emission. In electronic materials, they may hinder charge separation and transport. High material purity generally supports higher yields.

4.3 Temperature effects

Temperature affects molecular motion, phonon interactions, and carrier trapping. At elevated temperatures, nonradiative relaxation is often enhanced, which can reduce internal quantum yield. In some systems, cooling suppresses loss channels and improves emission or charge survival.

4.4 Excitation intensity and concentration quenching

At high excitation intensity, excited states may interact with one another. This can lead to annihilation, saturation, or other density-dependent losses. In doped materials, excessive emitter concentration can also cause concentration quenching, where energy migrates to non-emissive sites. Under such conditions, internal quantum yield may decrease even if low-intensity performance remains strong.

4.5 Morphology and crystal quality

Structural order has a major effect on internal efficiency. Well-formed crystals, smooth films, and controlled nanostructures often reduce defect-related losses and improve transport. By contrast, disordered morphology can introduce traps, scattering, and inhomogeneous local environments that lower yield.

5 Applications

5.1 Light-emitting materials

Internal quantum yield is central to the evaluation of fluorescent dyes, phosphors, organic emitters, and semiconductor light sources. High internal emission yield is desirable because it indicates that absorbed energy is being efficiently converted into photons inside the material. The metric is useful in displays, lighting, and sensors.

5.2 Laser gain media

In laser materials, internal quantum yield affects how efficiently pump energy is converted into population inversion and stimulated emission. A high yield reduces wasted energy and can lower threshold requirements. It is therefore an important parameter in solid-state, liquid, and organic gain media.

5.3 Solar cells and photodetectors

For photovoltaic and photodetector devices, internal quantum yield describes the fraction of absorbed photons that produce usable electrical output. High values indicate effective exciton dissociation, charge transport, and collection. This makes the metric valuable for evaluating absorber materials and device architectures.

5.4 Fluorescent probes and bioimaging

In bioimaging, dyes and probes are often selected for their internal emission efficiency after excitation. A strong internal quantum yield can improve signal brightness and reduce the amount of probe needed. The metric is particularly important when comparing fluorophores under similar absorption conditions.

6.1 External quantum yield

External quantum yield measures the fraction of incident excitation that becomes the observed output. It includes optical losses before absorption and, in emission systems, losses in extracting light from the material or device. Internal quantum yield is a more intrinsic measure because it begins after absorption has occurred.

6.2 Quantum efficiency

Quantum efficiency is a broad term used in multiple scientific fields to describe the conversion of input quanta into output events. Depending on context, it may refer to internal or external behavior. Because usage is not fully standardized, the precise definition should always be checked.

6.3 Internal conversion and nonradiative relaxation

Internal conversion is a nonradiative process in which excited-state energy is converted into vibrational energy. More generally, nonradiative relaxation includes many pathways that dissipate excitation without producing the desired signal. These processes are major contributors to reduced internal quantum yield.

6.4 Photoluminescence quantum yield

Photoluminescence quantum yield is the fraction of absorbed photons that are re-emitted as photons under optical excitation. It is a specific form of internal quantum yield focused on luminescence. In many materials studies, the two terms are closely related, though the broader term can also apply to non-emissive outcomes.

7 Practical interpretation

7.1 Ideal and non-ideal limits

An internal quantum yield of 1, or 100 percent, means that every absorbed excitation produces the desired internal event. Real materials rarely achieve this limit under all conditions, because some loss channels are usually present. Values near unity indicate highly efficient internal conversion for the process being measured.

7.2 Comparison across materials

Comparisons are most meaningful when the same excitation conditions, sample environment, and definition of success are used. A value that is impressive in one class of materials may be ordinary in another. Interpreting the number requires attention to the mechanism, wavelength, temperature, and measurement method.

7.3 Reporting conventions

Published reports should specify the process being quantified, the excitation conditions, the method used to determine absorption, and any corrections applied to the data. Ambiguous terminology can lead to confusion, especially when internal and external measures are both discussed. Clear reporting helps ensure that values can be reproduced and compared across studies.