Time-Resolved Photoluminescence (TRPL)

For a simple carrier-balance description, let n(t) denote the carrier density whose temporal evolution is being followed. G(t) is the carrier-generation rate, while R(n) represents the total recombination rate. Their balance is

TRPL does not observe the carrier population directly. The detector records emitted photons. Under fixed optical collection and detection conditions, the intrinsic PL intensity at a given time therefore follows how rapidly radiative recombination events occur in the sample.

Here I_PL(t) is the photoluminescence intensity and R_rad(t) is the radiative recombination rate. Equation (3) expresses the key link between the optical signal and the underlying recombination dynamics.

To connect this radiative rate to the carrier populations, consider direct band-to-band recombination. A radiative event requires an electron and a hole to be present simultaneously. In the simplest description, the probability of such an event therefore scales with the product of the electron and hole concentrations.

In Equation (4), B is the bimolecular radiative recombination coefficient, while n and p are the electron and hole concentrations, respectively. Because both populations can change after excitation, the PL intensity does not in general follow either carrier concentration alone.

This distinction is important. A measured PL decay is shaped by the evolution of both carrier populations and by the recombination processes that connect them. Depending on doping, injection level, traps, interfaces and transport, the PL intensity can therefore decay differently from the carrier density itself.

A useful phenomenological description separates recombination into terms with different dependences on excess-carrier density. For a simplified charge-balanced case with n ≈ p ≈ Δn, the total recombination rate can be written as

An instantaneous effective carrier lifetime can be defined from the rate at which the excess-carrier population changes. With Δn denoting the excess-carrier density,

Only when the relevant recombination rate is approximately proportional to carrier density over the observed range does the carrier population approach a simple exponential decay with a nearly constant lifetime:

Even in this simple case, the observed PL signal does not necessarily share the same exponential time constant. For example, when n ≈ p ≈ Δn, Equation (4) gives I_PL ∝ Δn². The measured luminescence therefore responds to the carrier statistics as well as to the carrier decay itself.

Interfaces, diffusion, trap filling and detrapping can further modify the transient. This is why comparing decay shapes under controlled excitation conditions is often more informative than assigning a single “lifetime” number to every TRPL curve.

Each excitation pulse defines a timing reference. If t_exc is the time of the excitation pulse and t_det is the arrival time of a detected photon, the measured delay is

One photon contributes one count to the corresponding time bin. Repeating the excitation many times builds a histogram H(Δt) of photon-arrival events. After sufficient statistics have accumulated, the histogram follows the measured time-dependent luminescence signal:

TCSPC therefore does not record the entire decay from a single laser pulse. The curve emerges from many repeated excitation–detection cycles. This statistical approach enables high sensitivity and precise timing, but the measured decay still includes the temporal response of the complete instrument. That response is treated explicitly in the next section through the instrument response function (IRF).

The IRF includes contributions from the excitation-pulse duration, detector timing jitter and timing electronics. As a result, an intrinsically instantaneous optical event would still appear as a peak with a finite width in the measured time trace.

The measured signal is therefore the convolution of the true sample response with the IRF. Let I_sample(t) denote the intrinsic temporal luminescence response of the sample and I_meas(t) the signal recorded by the instrument:

In Equation (10), the symbol * denotes convolution and t′ is the integration variable. If the sample dynamics are much slower than the IRF, the influence of the instrument becomes small after the earliest part of the decay. If the sample dynamics occur on a comparable timescale, however, the rising edge and the fastest decay components are broadened by the instrument and cannot be read directly from the measured curve.

For quantitative fitting of fast dynamics, the IRF is therefore included in the model rather than ignored. A candidate sample response is calculated, convolved with the measured IRF, and the resulting curve is compared directly with the experimental data. This procedure is commonly called reconvolution fitting.

The simplest description is a single exponential. It is appropriate when the observed signal can be represented by one approximately constant effective decay rate over the fitted time range:

In Equation (12), τ is the decay constant of the fitted PL signal. It should only be identified directly with a carrier lifetime when the physical conditions connecting the PL intensity to the carrier population justify that interpretation.

Real semiconductor transients are frequently not described by a single exponential. A common empirical extension is a sum of exponential components:

Equation (13) can describe a fast initial decay followed by a slower tail, but the individual fitted components do not automatically correspond one-to-one to distinct recombination mechanisms. The same non-exponential transient can arise from carrier-density-dependent recombination, trapping and detrapping, diffusion toward interfaces, spatial inhomogeneity or combinations of these effects.

This is why a fitted time constant should be interpreted together with the measurement conditions. Excitation density, spectral detection window, sample thickness, interfaces and temperature can all change the measured transient. Comparing how the complete decay evolves when one of these conditions is varied is often more physically informative than comparing a single fitted number.

The excitation pulse determines the initial non-equilibrium carrier population. If F_abs is the absorbed optical energy per unit area and hν is the excitation-photon energy, the number of absorbed photons per unit area is

Increasing the excitation fluence generally increases the initial carrier density, which can change the relative importance of the recombination terms introduced in Equation (5). Trap filling, bimolecular radiative recombination and higher-order recombination can therefore alter both the early-time and late-time decay. For example, filling available traps can suppress a fast trap-mediated loss channel, while at higher carrier density stronger bimolecular or Auger-type recombination can accelerate the decay.

This makes excitation-dependent TRPL especially useful. Instead of assigning one lifetime to a sample, a series of decays measured over a controlled excitation range reveals how the dynamics evolve with carrier density.

Spectrally resolved TRPL adds another dimension. If carriers relax between energetic states, migrate between domains, diffuse through a gradient, or emitted photons are reabsorbed and re-emitted, the transient measured on the blue side of the spectrum can differ from the transient near the emission maximum or on the red side.

For quantitative comparison, excitation fluence, repetition rate, excitation wavelength, detection window and sample geometry should therefore be reported together with the fitted decay parameters.

Because the transient reflects radiative emission from a non-equilibrium carrier population, TRPL can be highly sensitive to changes that alter recombination or carrier transport. A slower or faster decay, a changed early-time response, or the appearance of a long tail can therefore provide evidence that the underlying carrier dynamics have changed.

The distinction matters because several physical processes can generate similar transient shapes. TRPL therefore becomes much more informative when a controlled experimental variable is changed: excitation density, surface treatment, interface composition, temperature, electrical bias or detection wavelength. The trend across those measurements provides the physical constraint that a single decay curve does not.

For photoluminescence, the external photoluminescence quantum yield is the ratio between the emitted and absorbed photon numbers:

Absolute PL therefore addresses how much light is emitted and, together with the spectral information required for absolute luminescence analysis, provides access to quantities such as PLQY, QFLS and implied V_OC. TRPL addresses when that light is emitted and how the transient changes with carrier density and sample conditions.