Quantum Yield Bias in Materials With Lower Absorptance

Photoluminescence (PL) quantum yield (QY), which is defined as the ratio of emitted to absorbed photons, is the central quantity that characterizes light-emitting materials. It is an important parameter to assess the light efficiency of new materials, as well as identify novel photophysical mechanisms. While QY measurements are performed as standard in research and industry, accurate measurements are challenging. Here, we show that, besides known inaccuracies, PL QY measurements exhibit a surprising systematic bias. QY values are underestimated by a factor of two or more for samples with lower absorption, which can even lead to misinterpretation of results. We combine PL QY measurements of diluted Rhodamine 6G and two different semiconductor quantum dot solutions, via the standard integrating sphere method, with analytical modeling and ray-tracing simulations and find that, independent of the setup and luminescence mechanism, all measurements suffer from the same systematic underestimation of the QY. Through statistical analysis of the measured emitted and absorbed photon numbers, we uncover the origin of this underestimation in the asymmetry of the ratio distribution for low absorption, together with setup-specific features, such as signal offsets and nonlinearities. We suggest a robust calibration procedure to correct for this bias for precise evaluation of the QY in materials used for bioimaging, biosensing, and optoelectronic or photovoltaic devices.

Figure 1

(a) Schematic of “setup 1” for PL QY measurements using the IS technique (top cross-section view): The sample in the center of the sphere is excited directly by a fraction, F, of the incoming excitation beam [direct excitation (F = 1) and indirect excitation (F = 0) are shown]. Baffles prevent direct detection of the excitation and emission photons; see also Fig. S4 [41]. For comparative measurements, a setup with different geometry is used (“setup 2”), as described in Sec. 2. (b) Examples of typical spectra for R6G in ethanol that are recorded with the reference (blue) and sample (red) inside the IS. (c) Three examples of spectra used for the evaluation of PL QY, which are obtained by subtracting sample and reference measurements for R6G in ethanol [such as those in panel (b)] at different excitation wavelengths.

Figure 2

The PL QY of R6G in ethanol for (a)–(c) varying excitation wavelength and concentration, (d)–(f) varying thickness of the cuvette (i.e., optical path length), and (g)–(i) direct and indirect excitation conditions measured in two different setups (setups 1 and 2, description in Sec. 2). Legends in the bottom panels are the same for other related panels. The single-pass absorptances are shown in (a),(d),(g), and PL QY as a function of excitation wavelength are shown in (b),(e),(h) and replotted as a function of single-pass absorptance in (c),(f),(i). All data are corrected for reabsorption using the procedure described by Ahn et al. [23]. For comparison with the literature, the QY values determined by Faulkner [25] for 100 µM (the higher QY value) and 1 µM (the lower QY value) solutions of R6G in ethanol are plotted in (b),(c) in green.

Figure 3

(a) Absorption coefficients (full lines) and PL spectra (dashed lines) for R6G in ethanol (black), $\mathrm{Si}$ QDs in toluene (red), and CdSe QDs in hexane (blue). (b) PL QY dependence on the excitation wavelengths of CdSe QDs and $\mathrm{Si}$ QDs (the QY of the $\mathrm{Si}$ QDs below 360 nm is omitted, since the solvent is nontransparent in this spectral region). The dashed lines serve as guides to the eye. (c) PL QY from (b) replotted versus single-pass absorptance. For comparison, we add data for R6G from Fig. 2 (black symbols). The dashed lines serve as guides to the eye to emphasize the observed general trend of the QY. The critical absorptance value, A_crit, is indicated by the vertical dashed line.

Figure 4

Comparison of the experimental dependence of the PL QY of R6G on the single-pass absorptance (gray symbols) with simulated values from the AM (black line) and RTS (red symbols) approaches. For comparison, a peak value of the QY probability distribution [29] is also shown in the presence of measurement uncertainty in number of photons of α = 0.3% (green line).

Figure 5

Histograms of measured QY values of Rhodamine 6G in ethanol with a maximum QY of approximately 75% for different values of the single-pass absorptance (a) 20%, (b) 0.6%, (c) 2%, and (d) 0.8% (inset shows an enlargement of the negative QY range) achieved by varying sample concentration and excitation wavelengths (see the legends). The black solid line shows the fit using the ratio distribution for an experimental uncertainty of approximately 0.3% and experimental absorptance offset of approximately 1.7%. Dashed lines represent the measured value of the QY of approximately 81% [from Fig. 2].

Figure 6

(a) Experimentally determined dependences of the absorbed (gray symbols, left axis) and emitted (green symbols, right axis) photon fractions on the single-pass absorptance of the sample. The black line indicates the simulated dependence using the AM approach. The dashed curved line fits the experimental data with an absorption offset of 1.7%. The vertical straight dashed line indicates the position of A_crit. The inset shows a comparison of the AM approach (black lines) with the RTS approach for the fraction of absorbed (red circles) and emitted (red triangles) photons. Both approaches are in excellent agreement. (b) Linear dependence of the number of emitted and absorbed photons in the integrating sphere. The black line is a linear fit, the slope of which equals the ideal PL QY value. The inset shows an enlargement of the lowest signal range, unraveling small offset and nonlinearity.

Figure 7

QY versus excitation wavelength before (a) and after (b) correction for the absorption dependence of the QY methodology using Eq. (3). Different symbols represent different sample concentrations, as in Figs. 2 and 3. After correction, the QY of the Si QDs is constant at approximately 45% and independent of the sample concentration. Part of the excitation and concentration dependences of the QY of the CdSe QDs persists after correction, potentially related to instability of the ligands [10, 38, 39, 40]. The correction function was obtained by taking a moving average of the QY versus single-pass absorption dependence of R6G in Fig. 2. For reference, the corrected QY for R6G is also shown.