Photoluminescence (PL)¶

Scientific Introduction¶

Photoluminescence (PL) is a non-contact optical characterization technique used to probe the radiative recombination processes in semiconducting materials and photovoltaic devices. When a material absorbs photons with energy greater than its bandgap, electron-hole pairs are generated. The subsequent recombination of these charge carriers may result in the emission of photons, which is detected as photoluminescence.

PL measurements provide insight into:

Bandgap energy
Defect states and trap-assisted recombination
Carrier lifetimes
Radiative efficiency
Quasi-Fermi level splitting (QFLS)

Because PL is directly linked to recombination mechanisms, it is a powerful diagnostic tool for evaluating material quality and device performance.

Fundamental Principle¶

Upon excitation with photons of energy $h\nu_{exc} > E_g$, electrons are promoted from the valence band to the conduction band, leaving behind holes. The system relaxes toward equilibrium via several recombination pathways:

Radiative recombination
Shockley-Read-Hall (SRH) recombination
Auger recombination

Radiative recombination results in photon emission with energy approximately equal to the bandgap, thus the peak position indicates the effective bandgap: $$ h\nu_{em} \approx E_g $$ The measured PL intensity $I_{PL}$ is proportional to the radiative recombination rate: $$ I_{PL} \propto B n p $$ where:

$B$ is the radiative recombination coefficient
$n$ and $p$ are the electron and hole concentrations

Quasi-Fermi Level Splitting¶

Under steady-state illumination, separate quasi-Fermi levels for electrons ($E_{F,n}$) and holes ($E_{F,p}$) are established. The splitting between these levels determines the maximum achievable open-circuit voltage: $$ \Delta E_F = E_{F,n} - E_{F,p} $$ The emitted PL intensity is exponentially related to the quasi-Fermi level splitting: $$ I_{PL} \propto \exp\left(\frac{\Delta E_F}{k_B T}\right) $$ Thus, absolute PL measurements can be used to determine the implied open-circuit voltage ($V_{oc}^{implied}$): $$ q V_{oc}^{implied} = \Delta E_F $$

Photoluminescence Quantum Yield (PLQY)¶

Photoluminescence Quantum Yield (PLQY) quantifies the fraction of absorbed photons that are re-emitted radiatively. It is a direct measure of the radiative efficiency of a material and provides critical insight into non-radiative recombination losses.

PLQY is defined as: $$ \text{PLQY} = \frac{\text{Number of emitted photons}}{\text{Number of absorbed photons}} $$

In terms of recombination rates, PLQY can be expressed as: $$ \text{PLQY} = \frac{R_{rad}}{R_{rad} + R_{nonrad}} $$ where:

$R_{rad}$ is the radiative recombination rate
$R_{nonrad}$ is the non-radiative recombination rate

A PLQY of 1 (or 100%) indicates purely radiative recombination, whereas lower values indicate increasing dominance of non-radiative processes such as defect-assisted (Shockley–Read–Hall) recombination or Auger recombination.

Relation to Carrier Lifetime¶

PLQY can also be related to carrier lifetimes: $$ \text{PLQY} = \frac{\tau_{nonrad}}{\tau_{rad} + \tau_{nonrad}} = \frac{\tau_{eff}}{\tau_{rad}} $$ where:

$\tau_{rad}$ is the radiative lifetime
$\tau_{nonrad}$ is the non-radiative lifetime
$\tau_{eff}$ is the effective lifetime

High PLQY corresponds to long non-radiative lifetimes and low defect densities.

Absolute PLQY Measurement¶

Absolute PLQY measurements are typically performed using an integrating sphere. The integrating sphere allows simultaneous measurement of:

Total emitted photon flux
Total absorbed photon flux

The absorbed photon flux is determined from the difference between incident excitation light and transmitted/reflected excitation light.

By accounting for reflection and scattering losses, the absolute PLQY can be determined without requiring knowledge of detector collection efficiency.

Relevance for Photovoltaic Devices¶

In photovoltaic materials, PLQY is directly related to voltage losses. The quasi-Fermi level splitting under illumination is linked to radiative efficiency through: $$ \Delta E_F = \Delta E_{F,rad} - k_B T \ln\left(\frac{1}{\text{PLQY}}\right) $$ Low PLQY indicates strong non-radiative recombination and therefore increased voltage losses relative to the radiative limit.