K Absolute quantum yield of luminescent materials
K Absolute quantum yield of luminescent materials
The absolute quantum yield (efficiency) of luminescence η is a very important quantity, especially for evaluating application prospects of a particular phosphor. The only way to asses η is by experiment and this experiment is, as already stressed several times, difficult and delicate (like all absolute measurements of similar type). Specialized laboratories are mostly dedicated to this (p.516) purpose. The intensity of luminescence in current experimental basic research is measured in relative units only. Nevertheless, even then occasionally there is a need to evaluate η absolutely. It might thus be of importance to outline the principles of the measurement of luminescence efficiency.
There are basically three experimental techniques for evaluating η for photoluminescence: (1) absolute optical; (2) relative optical; and (3) photocalorimetric one. The first method basically evaluates the exact amount of both the absorbed light energy and the energy emitted by the sample. The second one, relative optical, can be realized more easily, because it relies upon a comparison of the measured sample with a luminescence standard. It may, however, be less accurate because of the uncertainty related to η of the applied standard. The photocalorimetric or photoacoustic method consists in the transformation of the absorbed excitation energy into heat and takes into account the processes of nonradiative recombination. Its implementation is difficult owing to the necessity to ensure good thermal isolation of the sample from its surroundings and to detect very small temperature variations (mK).
Also measurements of electro luminescence efficiency can be classified as absolute or relative, the latter relying on a known standard. In principle, the assessment of η in the case of electroluminescence is easier than that for photoluminescence because the supplied excitation energy can be evaluated quite smoothly through measurement of the excitation electric current.
We shall outline three particular experimental approaches: an absolute photoluminescence method, a relative photoluminescence method and an absolute electroluminescence method.
Absolute determination of photoluminescence η [1]
A schematic of one possible experimental setup is shown in Fig. K.1. The central component here happens to be an integration sphere, which is a hollow spherical solid with inner surface covered by a nonluminescent, strong diffusion reflecting film (MgO). The sphere has four ports, located in the equatorial plane: an excitation port for input of the excitation beam, a port destined to detect the excitation radiation (photodetector A), a port to detect the emitted luminescence radiation (photodetector B) and the sample port. A sample holder (quartz tube) can contain both a liquid sample and a solid one (powder). The excitation radiation is scattered by a diffuser upon entering the sphere. Suitable glass filters are located in front of the photodetectors in order to let through only the excitation (photodetector A) or photoluminescence (photodetector B)
The absorbed optical power P _{abs} is evaluated by comparing two sets of data from the photodetector A, recorded with and without the sample (a reflecting blind flange is fixed in the relevant port instead of the sample) inside the sphere.
The emitted radiation power P _{em} is determined by making use of similar data from the photodetector B (measurements with and without the sample). Knowledge of the spectral sensitivity of both detectors as well as of the spectral sensitivity of the sphere is indispensable. The photoluminescence power efficiency η _{P} = P _{em}/P _{abs} can then be assessed; hence, the quantum efficiency η will subsequently be determined with the aid of the relation $\eta =\left(\overline{{\lambda}_{\text{em}}}/{\lambda}_{\text{ex}}\right)\eta \text{p}$, where $\overline{{\lambda}_{\text{em}}}$ is the wavelength of an average energy luminescence photon. As for the details, the reader is referred to the original work [1]. The accuracy of fixing η in this manner may be relatively high (error 〈 1%).
Relative determination of photoluminescence η
This method is based on comparison of the emission intensity of the material under study (in relative units) with an analogous measurement performed on a luminescence standard whose photoluminescence quantum efficiency is known. An identical excitation wavelength λ _{ex} is applied in both cases, and similarities in the spectral position and width of both emission spectra appear advantageous for eliminating additional corrections. Of basic importance is then to ensure that the same amount of excitation energy is absorbed in both cases. This is feasible to arrange in liquid samples (solutions) of phosphors only, when the absorbed optical power can be written as
where R stands for the reflectivity of the cell filled with the investigated solution, l is the cell length, ε(hν_{ex}) is usually called the molar absorption or extinction coefficient and c denotes the substance concentration (number of moles per unit volume). By varying the concentration c we can thus easily tune the same value of P abs in both cases. Furthermore, there is no need to know the values of the molar coefficients ε, but we are able to achieve the desired result in a purely empirical way—through a suitable choice of both concentrations so that the excitation beam has the same intensity upon passing through the cells in both cases. It may appear that for semiconductors as solids the method is useless; nevertheless, it can be nicely applied to colloidal dispersions of semiconductor nanocrystals, as will be mentioned below.
The experimental arrangement of both the excitation and the detection paths may then be rather arbitrary, provided that in the course of measurement all experimental parameters remain fixed, apart from exchanging the cell with the measured solution for that containing the luminescence standard. An identical (p.518) geometrical localization in the cell of the luminescent spot as well as an identical spatial radiation pattern can be reasonably supposed in both cases.^{6}
A solution of quinine sulphate dihydrate in 1N sulphuric acid can serve as an example of a widely used international luminescence standard. It is a longterm stable, nonoxidizing liquid standard with emission maximum at λ _{em} = 450–460 nm and photoluminescence quantum yield η = 52% (under excitation wavelength λ _{ex} ranging from 224 to 390 nm and at a concentration of c = 10^{−2} M) [1]. However, for practical applications various organic dyes as luminescence standards appear to be more easily applied; they are available in powder form from several manufacturers (e.g. Exciton, Inc.) and are soluble in common solvents like ethanol and methanol. By way of example Rhodamine 6G in ethanol (η ≈ 94%, λ _{em} = 560–580 nm, concentration c = 10^{−7} − 10^{−2} M, room temperature) can be quoted. For the details the reader is referred to the literature [1–3]. It should be pointed out that the values of η for organic dyes, cited in the literature, fluctuate somewhat [4, 5] (η depends on purity of the dye, the solutions are not fully photostable in the long term, measurement temperature varies, etc.), which makes this method less reliable by comparison with the foregoing case.
What may constitute a difficulty with this method is residual light scattering in the sample. For instance, in a colloidal dispersion of luminescent Si nanocrystals (of size of a few nanometres) gathering of the nanocrystals into large agglomerates of about 100 nm in diameter occurs, which leads to Mie scattering of the excitation radiation. Given these circumstances, even if we prepare the standard and the colloidal solutions so that the transmitted excitation intensity coincides in both cases, eqn (K.1) does not straightforwardly give the absorbed power, because the exciting beam is attenuated in the colloid— in addition to useful absorption—also by light scattering. The problem can be solved by introducing artificial scattering into the standard solution, for instance by means of polystyrene beads of diameter similar to that of the nanocrystalline aggregates [6]. Figure K.2(a) presents an emission spectrum of a colloidal dispersion of Si nanocrystals (black curve) that comprises also a narrow line at 480 nm owing to elastic scattering of the excitation beam. The figure also contains an emission spectrum of a luminescence standard solution (Rhodamine 6G in ethanol, R6G grey curve), to which polystyrene beads with a diameter of 68 nm were added; a pure R6G ‘genuine’ solution does not exhibit any light scattering, see the grey shading. The number of beads was chosen so that the scattering line at 480 nm exhibited an amplitude equal to that observed in the Si colloidal dispersion; this compensated for the effect of light scattering.
By comparing the areas below the curves it become obvious that the quantum yield of the Sinanocrystal dispersion is smaller in comparison with η of R6G. Quantitative evaluation of the areas at varying excitation intensities then (p.519)
Absolute determination of electroluminescence η
We shall deal with the total (external) efficiency of injection electroluminescence η _{tot}, which was defined in Subsection 11.2.1 as η _{tot} = (number of photons emitted from sample surface/number of injected electron–holes pairs). The number of injected e–h pairs can be established from the excitation current density j = I/S, where I is the electric current flowing through the pn junction, therefore a quantity easily measurable, and S denotes the junction crosssection. This can be commonly evaluated on the basis of the sample geometry; for instance in a sample in the form of a thin film deposited on a nontransparent conductive substrate, S means the area of a semitransparent electrode from which the electroluminescence radiation emerges. The number of injected e–h pairs per second is then
where e is the electron charge.
We continue to suppose we have a planar sample with vertical radiation through the semitransparent electrode. Let us suppose further that our light detection system consists of a photomultiplier tube in connection with a photon counter, which provides data on the number of detected photons per second, n _{p}. We are then faced with a task defined basically by the experimental geometry: how to deduce the total number of photons emitted from the sample surface, n _{p0}, knowing the number of detected photons, n _{p}.
An example of a particular experimental setup is shown in Fig. K.3 [7]. The sample is fixed in a lightproof chamber and excited with current pulses from a pulsed generator. The luminescence radiation is collected closely above the sample by a ‘light pipe’ (a glass rod with polished ends). The rod faces a compartment of neutral glass filters (aimed at avoiding saturation of the photodetector) on which a photomultiplier is mounted. Obviously, n _{p} and n _{p0} are linked through the proportion n _{p} = ξn _{p0}, where the coefficient ξ 〈 1 comprises the effect of five factors:

1. Only part of the emitted radiation is coupled to the glass rod (factor c _{1}).

2. The rod itself causes a certain attenuation (factor c _{2}).
(p.520)

3. Only part of the radiation leaving the rod enters the filter compartment (factor c _{3}).

4. Only part of the luminescence beam impinges on the photodetector, owing to the finite dimensions of the photocathode and the beam divergence (factor c _{4}).

5. The quantum efficiency of the photocathode photoeffect η _{p} is less than unity, because not every photon gives rise to a pulse detected by the counter (factor η _{p}).
We can thus write
Taking into account eqn (K.2), the electroluminescence efficiency can then be transformed into a form suitable for numerical evaluation:
The photocathode quantum efficiency η _{p} along with the photocathode spectral sensitivity are listed in manufactures’ data sheets. The coefficients c_{i} ≤ 1 can be found by combining effortless experiments with easy computations.Thus, the part c _{1} from the total luminous flux emitted from a circular electric contact of diameter d and coupled to a light guide of diameter D at a height L above the sample (Fig. K.3) can be calculated by anticipating the cosine character of the radiation; the result reads [7]
The transmission coefficient of the light guide(c _{2}) can be found experimentally if a flat circular light source is installed instead of the sample. The circular source (e.g. a flat LED diode) should have its emission spectrum and spatial radiation pattern similar to those of the investigated sample. A photodiode fixed closely behind the opposite light guide end then measures the amount of transmitted light. The c _{3} coefficient can be determined again from experiment, namely, by measurement of the angular distribution of light—emitted by the above mentioned LED—at height d′ above the light guide exit. This intensity distribution is subsequently compared with the limiting dimensions of the neutral filter compartment. Finally, the c _{4} coefficient is to be calculated starting from the measured spatial radiation distribution at height d′ (which can be approximated by a Gaussian curve with dispersion w ^{2}/2), if we take into consideration the lateral dimensions of the PMT photocathode, its location at height L′ and the divergence of the luminescence beam. The result for a rectangular photocathode 2a × 2b reads
(p.521) where a′ = a (d′ /(d′ + L′)), b′ = b(d′ /(d′ + L′)) and erf$\left(x\right)=\left(2/\sqrt{\pi}\right){\displaystyle {\int}_{0}^{x}\mathrm{exp}\left({t}^{2}\right)\text{d}t}$ is the socalled error function. For the details, the reader is referred to [7].
In view of the approximations involved and of possible experimental errors the accuracy of this method cannot be overvalued; the relative error makes up to ~ 30%. However, even this value is helpful when assessing novel phosphors. Of course, if a reference standard light source (e.g. a LED diode calibrated in absolute units by the manufacturer) is available, the precision of the method may be increased considerably.
References
1. Rohwer, L. S. and Martin, J. E. (2005). J. Luminescence, 115, 77. 2. Kubin, R. F. and Fletcher, A. N. (1982). J. Luminescence, 27, 455. 3. Fischer, M. and Georges, J. (1996). Chem. Phys. Lett., 260, 115. 4. Abrams, B. L. and Wilcoxon, J. P. (2009). J. Luminescence, 129, 329. 5. Rohwer, L. S. and Martin, J. E. (2009). J. Luminescence, 129, 331. 6. Kůsová, K., Cibulka, O., Dohnalová, K., Pelant, I., Matějka, P., Žídek, K., Valenta, J., and Trojánek, F. (2009). Mater. Res. Soc. Symp. Proc., 1145, 1145MM0413. 7. Luterová, K. (1996). Transport and photoelectric properties of luminescent forms of silicon (in Czech). Diploma thesis, Charles University in Prague, Faculty of Mathematics and Physics, Prague.
Notes:
(^{6}) It might not be like this if the concentrations of the solutions differ substantially. Complications arising due to possible reabsorption of luminescence radiation may be avoided by choosing as low solution concentrations as possible (but still compatible with an acceptable value of the signaltonoise ratio).