Absolute determination of photoluminescence

Absolute determination of photoluminescence quantum efficiency using an integrating sphere setup S. Leyre, E. Coutino-Gonzalez, J. J. Joos, J. Ryckaert, Y. Meuret, D. Poelman, P. F. Smet, G. Durinck, J. Hofkens, G. Deconinck, and P. Hanselaer Citation: Review of Scientific Instruments 85, 123115 (2014); doi: 10.1063/1.4903852 View online: http://dx.doi.org/10.1063/1.4903852 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Determination of the absolute internal quantum efficiency of photoluminescence in GaN co-doped with Si and Zn J. Appl. Phys. 111, 073106 (2012); 10.1063/1.3699312 Extremely high absolute internal quantum efficiency of photoluminescence in co-doped GaN:Zn,Si Appl. Phys. Lett. 99, 171110 (2011); 10.1063/1.3655678 Determination of the photoluminescence quantum efficiency of silicon nanocrystals by laser-induced deflection Appl. Phys. Lett. 98, 083111 (2011); 10.1063/1.3559224 Absolute photoluminescence quantum efficiency measurement of light-emitting thin films Rev. Sci. Instrum. 78, 096101 (2007); 10.1063/1.2778614 Self-absorption correction for solid-state photoluminescence quantum yields obtained from integrating sphere measurements Rev. Sci. Instrum. 78, 086105 (2007); 10.1063/1.2768926

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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 123115 (2014)

Absolute determination of photoluminescence quantum efficiency using an integrating sphere setup S. Leyre,1,2,3,a) E. Coutino-Gonzalez,4 J. J. Joos,5,6 J. Ryckaert,1 Y. Meuret,1 D. Poelman,5,6 P. F. Smet,5,6 G. Durinck,1 J. Hofkens,4 G. Deconinck,2 and P. Hanselaer1 1

ESAT/Light and Lighting Laboratory, KU Leuven, Technology Campus Ghent, Ghent 9000, Belgium ESAT/ELECTA, KU Leuven, Leuven 3001, Belgium 3 SOPPOM program, Zwijnaarde 9052, Belgium 4 Department of Chemistry, KU Leuven, Leuven 3001, Belgium 5 LumiLab, Department of Solid State Sciences, Ghent University, Ghent 9000, Belgium 6 Center for Nano- and Biophotonics (NB Photonics), Ghent University, Ghent 9000, Belgium 2

(Received 25 September 2014; accepted 26 November 2014; published online 24 December 2014) An integrating sphere-based setup to obtain a quick and reliable determination of the internal quantum efficiency of strongly scattering luminescent materials is presented. In literature, two distinct but similar measurement procedures are frequently mentioned: a “two measurement” and a “three measurement” approach. Both methods are evaluated by applying the rigorous integrating sphere theory. It was found that both measurement procedures are valid. Additionally, the two methods are compared with respect to the uncertainty budget of the obtained values of the quantum efficiency. An inter-laboratory validation using the two distinct procedures was performed. The conclusions from the theoretical study were confirmed by the experimental data. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4903852] I. INTRODUCTION

Photoluminescent materials have been thoroughly investigated since the first description of fluorescence by sir George Stokes in 1852.1 Since then, luminescent materials have found practical use in a broad range of applications. In fluorescent tubes and compact fluorescent lamps, luminescent materials are used to convert the UV emission from gas discharge lamps into visible light.2–4 In most solid-state lighting units, the blue emission from a light-emitting diode is combined with the yellow and red emission from luminescent materials to obtain white light.5, 6 In photovoltaics, luminescent materials can be used in luminescent solar concentrators7, 8 or in planar down shifting layers on top of a solar cells to enhance the spectral response at short wavelengths.9 Photoluminescent materials are also frequently used as marker materials for diagnostic purposes in the biomedical field,10, 11 and as whitening agents in laundry detergents and paper sheets.12, 13 Photoluminescent materials are described by their excitation and emission spectra and quantum efficiency (QE). The (internal) QE of a photoluminescent material is defined as the ratio of the number of emitted photons to the number of photons absorbed. The QE is a very important parameter, since it has a large influence on the total efficiency of the system. Next to the internal QE, the external QE can be defined as the ratio of the number of emitted photons to the number of incident photons. Since this quantity is highly dependent on the excitation wavelength, the quantity, and morphology of material, it will not be discussed further in this paper. Several procedures have been developed to determine the QE of luminescent materials, such as photoacoustic a) Author to whom correspondence should be addressed. Electronic mail:

[email protected] 0034-6748/2014/85(12)/123115/9/$30.00

spectroscopy (PAS), thermal lensing (TL), and optical-based methods. In the PAS method, the sound generated by the material during a periodic temperature variation due to illumination of the material with modulated or pulsed radiation, is measured. The intensity of these sound waves is correlated to the absorbed energy that is not re-emitted due to fluorescence. By comparing the intensity of the sound waves of the fluorescence test sample to the waves generated by a non-fluorescent sample under identical conditions, the QE of the evaluated sample can be determined within an accuracy of ±10%.14, 15 The TL technique was first introduced by Brannon and Madge16 and is based on the temperature dependent refractive index of transparent samples. When irradiated with a Gaussian excitation beam, the absorption in the sample causes a refractive index gradient, which results in convergence or divergence of the beam, hence the name “thermal lens.” Most liquids produce a diverging lens since their refractive index has a negative temperature coefficient. The refractive index gradient can be used to determine the absorption losses in the material and thus the QE of the fluorescent sample. This technique allows for the determination of absorptivities as low as 10−8 mm−1 .17, 18 The determination of the QE of photoluminescent materials by optical measurements can be divided into relative and absolute techniques.19 The disadvantage of the relative measurement approach is that it requires a well-known fluorescent standard with similar excitation and emission properties as the sample under examination.19 Therefore, the relative procedure will not be adopted in this study. The absolute measurement approach does not require a reference sample and is commonly performed with an integrating sphere. The advantage of the integrating sphere is that it allows the collection of all the light emitted and scattered

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by the fluorescent sample. This type of setup has been used by many authors to determine the QE of solutions, films, and powders.20–31 In this contribution, an integrating sphere-based setup to obtain a quick and reliable determination of the QE of strongly scattering photoluminescent materials is discussed. When using an integrating sphere setup for the absolute determination of the QE values, two different measurement procedures are coexisting. The first procedure is based on three measurements,20–22 while the second approach only requires two measurements.23–25 In this report, both measurement procedures are investigated by applying the rigorous integrating sphere theory, to examine whether two measurements are indeed sufficient or the third measurement is essential. Experimental data from several luminescent samples are gathered to confirm the theoretical conclusions. II. EXPERIMENTAL SETUP

In this study, the main integrating sphere setup uses an Oriel 300 W Xenon discharge lamp as illumination source. A diaphragm is positioned in front of the lamp housing and a lens is used to create an image of the diaphragm in the center of the sphere. An interference filter is used to select the desired excitation wavelength band. The fluorescent sample is positioned at the center of the integrating sphere (see Fig. 1). The sphere has an inner diameter of 150 mm, two one inch diameter sphere ports and one 1/2 inch detector port. The sphere is coated with an ODM98 coating from GigahertzOptik (reflectance 0.98 ± 0.01 from 400 to 800 nm and >0.93 between 250 nm and 2.5 μm). A spectrometer is connected to the sphere via a quartz fiber. The fiber end connected to the sphere is provided with a diffuser in order to have a uniform hemispherical angular responsivity.32 The spectrometer used in this setup is an Oriel Instruments 74055 MS260i. The spectrometer is used in combination with an Andor iDus 420 silicon CCD. A schematic presentation of the setup is given in Fig. 1. The spectral irradiance incident on the detector head Ee,λ,det is correlated to the spectral radiant flux e,λ injected in the sphere and directly hitting the sphere wall according to Eq. (1). Ee,λ,det (λ) = f (λ)e,λ (λ)

(1)

with f(λ) the sphere factor. The sphere factor f1 (λ) for an ideal sphere is given by Eq. (2). f1 (λ) =

ρ(λ) 1 2 4π R 1 − ρ(λ)

(2)

with ρ(λ) the spectral reflectance of the diffuse reflective sphere coating and R the inner sphere radius. When an absorbing sample is present in the sphere, the sphere factor must be altered to Eq. (3). f2 (λ) =

ρ(λ) 1 , 4π R 2 1 − ρ(λ)(1 − aindir (λ))

(3)

with aindir (λ) the indirect absorption in the sample caused by diffuse illumination of the sample from the sphere wall. The raw signal S from the CCD connected to the spectrometer, expressed in counts/s nm, is correlated to the incident spectral irradiance (expressed in W/m2 nm) on the detector area and to the spectral radiant flux injected in the sphere according to Eq. (4). S(λ) = SR(λ)Ee,λ,det (λ) = SR(λ)fi (λ)e,λ (λ)

(4)

with SR the spectral response of the detection unit and fi the sphere factor given by Eq. (2) (no sample or a non-absorbing sample present) or Eq. (3) (absorbing sample present). The knowledge of the (relative) spectral response of the detection unit is essential for the determination of the QE of a luminescent sample, since numbers of photons at different wavelengths must be compared to each other. A halogen irradiance standard for the long wavelength region (400 nm–3 μm) and a deuterium irradiance standard for the short wavelength region (200 nm–400 nm) are used as external reference sources. The deuterium irradiance standard for the short wavelength range is essential because the halogen standard has very limited output in the short wavelength region, thus even a very small amount of stray light in the spectrometer would cause larger errors. The calibration sources are positioned in front of the entrance port of the integrating sphere (without sample present) and a calibration measurement is performed. The detected signal Scal can be expressed as a function of the spectral radiant flux of the calibration standard entering the sphere e,λ,cal , Eq. (5). Scal (λ) = SR(λ)f1 (λ)e,λ,cal (λ).

(5)

e,λ,cal is obtained by multiplying the spectral irradiance from the irradiance standard with the area of the entrance port. Since no sample is present in the sphere when performing the calibration measurement, sphere factor f1 is used. The detected signal is corrected for the spectral response by multiplying S with the ratio e,λ,cal /Scal . By substituting Eq. (5) into Eq. (4), the spectral response can be eliminated and the spectral response corrected signal is given by Eq. (6).

FIG. 1. Schematic representation of the integrating sphere setup.

S(λ)

e,λ,cal (λ) f (λ) = i e,λ (λ). Scal (λ) f1 (λ)

(6)


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Finally, Eq. (6) can be transformed in terms of the spectral photon flux ph,λ , Eq. (7). S(λ)

e,λ,cal (λ) λ f (λ) = i ph,λ (λ). Scal (λ) hc f1 (λ)

(7)

Herein, h is Planck’s constant and c is the speed of light. The left hand side of the equation represents the measured raw signal corrected for spectral response, expressed as a function of the photon flux and can be determined directly from experimental data. III. MEASUREMENT PROCEDURES A. Three measurement approach

The three measurement approach was first proposed by de Mello et al.20 and requires a measurement without the fluorescent sample in the sphere (Fig. 2(a)), a measurement with the fluorescent sample in the sphere but out of the path of the incident beam (Fig. 2(b)), and a measurement with the fluorescent sample in the sphere with the sample in the path of the incident beam (Fig. 2(c)). Following the notation proposed by de Mello et al.,20 the spectral region is divided into two components: “L” is the wavelength region of the incident irradiation (and falls typically within the excitation wavelength region of the sample), “P” is the emission wavelength region of the sample. When a luminescent sample is present in the sphere, a signal will be detected in both wavelength regions. When no sample is present in the sphere, there should be no signal in wavelength region P. In the following derivations, only materials with no overlap between excitation and emission spectra are considered. Extensions to the measurement procedures for materials with such an overlap have been presented in Refs. 33 and 34.

The following quantities are defined: La is the number of photons in the excitation wavelength region detected in the first measurement, Lb is the number of photons in the incident wavelength region with the sample present in the sphere but out of the path of the incident beam, and Lc is the number of photons in the incident wavelength region with the sample present in the sphere, directly illuminated by the incident beam. Pb is the number of photons in the emission wavelength region with the sample present in the sphere, out of the path of the incident beam and Pc is the number of photons in the emission wavelength region with sample present in the sphere and in the path of the incident beam. A schematic overview of the various quantities is presented in Fig. 2(d). Using the three measurement approach, the QE value is determined using Eq. (8).20–22 QE =

Pc − (1 − Adir )Pb , La Adir

(8)

with Adir the direct absorption, given by Eq. (9). Adir = 1 −

Lc . Lb

(9)

B. Two measurement approach

In the two measurement approach, only the measurement with no sample in the sphere (Fig. 2(a)) and with the sample in the path of the incident beam are performed (Fig. 2(c)). The quantities used are La , Lc , and Pc as defined in Sec. III A. Using this approach, the QE value is determined using Eq. (10).23, 24 QE =

Pc . L a − Lc

(10)

Equation (8) takes two more parameters (Lb and Pb ) into account compared to Eq. (10). However, it should be noted that combining Eqs. (8) and (9) does not allow a straight forward simplification resulting in Eq. (10), suggesting that both methods are inherently different. In Sec. IV, it will be investigated whether a more rigorous calculation of the two measurement methods indeed results in the same QE values and under which conditions and assumptions. IV. SPHERE CALCULATIONS A. Measurement without sample present in the sphere

FIG. 2. Schematic representation of the three measurement approach: (a) without sample in the sphere, (b) with the sample present in the sphere out of the path of the incident beam, (c) with the sample present in the sphere and in the path of the incident beam, and (d) a typical example of results obtained from the three measurements.

When no sample is present in the sphere, the spectral photon flux in the sphere is equal to the incident flux from the excitation source: ph,λ,in . Since the photon flux in the sphere in the “P”-region is zero, only the photon flux in the incident wavelength region can be determined. Following the definitions by de Mello et al.,20 the quantities L and P have been calculated by multiplying the detected signal S(λ) with the wavelength and correcting for the spectral response. This corresponds to the quantity in the left hand side of Eq. (7). Referring to Eq. (7), and using fi (λ) = f1 (λ) and ph,λ = ph,λ,in , the photon flux incident in the sphere La can be expressed as Eq. (11), by integrating the incident


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photon flux over the incident wavelength range λinc . ph,λ,in (λ)dλ. La =

(11)

λinc

ph,λ = ph,λ,em,tot , and taking fi = f1 (assuming no absorption at the emission wavelength), and is given by Eq. (17). Pb = w(λ )QE λem

B. Measurement with sample in the sphere out of the beam

×

When the sample is present in the sphere, the detected signal in the incident wavelength range will decrease due to the indirect absorption by the sample. This indirect absorption is accounted for by the modified sphere factor f2 given in Eq. (3). In this case, the photon flux Lb is expressed by Eq. (12). f2 (λ) (λ)dλ. (12) Lb = f1 (λ) ph,λ,in λinc

The indirect absorption by the sample of the incident light will cause a subsequent emission in the emission wavelength region. Since the indirect absorption occurs in an iterative process, accounted for by the sphere factor, the emitted photon flux will also have several contributions. The first contribution at emission wavelength λ due the first indirect absorption in the sphere (ph,λ,em,1 (λ )) is given by Eq. (13). aindir (λ)ρ(λ)ph,λ,in (λ)dλ. ph,λ,em,1 (λ ) = w(λ )QE λinc

(13) Herein, w(λ ) is a weight derived from the emission spectrum of the luminescent material. It accounts for the weight of the emission wavelength λ in the emission spectrum. The weight factors are normalized according to Eq. (14). w(λ )dλ = 1. (14) λem

The contribution to the photon flux at the emission wavelength λ (ph,λ,em,2 (λ )), generated after the second indirect absorption of the incident beam is given by Eq. (15). ph,λ,em,2 (λ ) = w(λ )QE aindir (λ)ρ(λ)

λinc

C. Measurement with sample in the sphere directly illuminated by the beam

When the sample is present in the sphere and the incident beam directly hits the sample, a fraction of the incident light will be immediately absorbed, which is referred to as the direct absorption (Adir (λ)). The flux in the sphere is immediately decreased to a fraction 1 − Adir (λ). Subsequently, multiple reflections in the sphere cause indirect absorption, which is accounted for by using sphere factor f2 (λ). Substituting ph,λ by (1 − Adir (λ))ph,λ,in and fi = f2 in Eq. (7), results in Lc , given by Eq. (18). f2 (λ) (1 − Adir (λ))ph,λ,in (λ)dλ. (18) Lc = f1 (λ) λinc

In the emission wavelength region, both direct and indirect absorption contribute to the emitted flux. The contribution at emission wavelength λ due to the direct absorption (ph,λ,em,dir (λ )) is given by Eq. (19). ph,λ,em,dir (λ ) = w(λ )QE Adir (λ)ph,λ,in (λ)dλ. (19) λinc

The total contribution to the emission due to the indirect absorption is similar to the contribution for the measurement with the sample out of the beam, given in Eq. (16), but has to be reduced with a factor 1 − Adir (λ). The total emission due to both direct contribution and the contribution caused by the indirect absorption at emission wavelength λ (ph,λ,em,tot (λ )) is given by Eq. (20). Adir (λ) ph,λ,em,tot (λ ) = w(λ )QE λinc

λinc

(1−Adir (λ))aindir (λ)ρ(λ) ph,λ,in (λ)dλ. + 1−ρ(λ)(1−aindir (λ))

×(1 − aindir (λ))ρ(λ)ph,λ,in (λ)dλ. (15) The total emitted flux at emission wavelength λ (ph,λ,em,tot (λ )) is obtained by adding all further contributions, given by Eq. (16). ph,λ,em,tot (λ )

= w(λ )QE λinc

aindir (λ)ρ(λ) (λ)dλ dλ . (17) 1−ρ(λ)(1−aindir (λ)) ph,λ,in

aindir (λ)ρ(λ) (λ)dλ. 1 − ρ(λ)(1 − aindir (λ)) ph,λ,in

(20) Again, the photon flux in the emission wavelength region “Pc ” is derived by applying Eq. (7), with ph,λ = ph,λ,em,tot and sphere factor fi = f1 , Eq. (21). Adir (λ) Pc = w(λ )QE

(16)

λem

Finally, the photon flux in the emission wavelength region Pb is derived by applying Eq. (7) with the injected flux

+

λinc

(1−Adir (λ))aindir (λ)ρ(λ) ph,λ,in (λ)dλ dλ . (21) 1−ρ(λ)(1−aindir (λ))


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According to de Mello et al., this expression should be equal to Adir .20 Indeed, Eq. (23) can be interpreted as a weighted average of Adir (λ) over the incident wavelength range. After substitution of the ratio f2 (λ)/f1 (λ) using Eqs. (2) and (3), this weighted average (Adir (λ)) is explicitly given by Eq. (24).

D. Three measurement method

Since the expressions for the photon flux values involved (La , Lb , Lc , Pb , and Pc ) have been established, it can be evaluated whether the formula for the quantum efficiency given by Eq. (8) indeed corresponds to the real QE value. First, the values of Lc and Lb are substituted in Eq. (9) to obtain the direct absorption Adir , Eq. (22). 1−

Lc =1− Lb

λinc

Adir (λ)

f2 (λ) (1 − Adir (λ))ph,λ,in (λ)dλ f1 (λ) λinc

Adir = .

f2 (λ) (λ)dλ f1 (λ) ph,λ,in

1−

λinc

.

For monochromatic irradiation, Eq. (24) indeed results in the direct absorption by the sample at the irradiation wavelength (which is the case in the work of de Mello et al., where the formula was first proposed and a laser was used as illumination source).20 Filling out the corresponding expressions for the number of photons in the formula to determine the QE value with the three measurement approach, given by Eq. (8), results in Eq. (25). Since the expression in Eq. (9) results in the weighted average value, Adir in Eq. (8) was replaced with Adir .

.

(23)

λinc

⎤ (1 − Adir (λ))aindir (λ)ρ(λ) (λ).dλ dλ ph,λ,in ⎢ ⎥ 1 − ρ(λ)(1 − aindir (λ)) ⎢ ⎥ λinc ⎢λem ⎥ ⎢ ⎥ aindir (λ)ρ(λ) ⎢ ⎥ −(1 − A ) w(λ )QE (λ)dλ dλ ⎣ ⎦ dir 1 − ρ(λ)(1 − aindir (λ)) ph,λ,in ⎡

Pc − (1 − Adir )Pb = La Adir

(1 − ρ(λ)) (λ)dλ 1 − ρ(λ)(1 − aindir (λ)) ph,λ,in

(24)

f2 (λ) A (λ)ph,λ,in (λ)dλ f1 (λ) dir

Lc λinc = f2 (λ) Lb (λ)dλ f1 (λ) ph,λ,in

(22)

Rearranging Eq. (22) by bringing the terms to the same denominator, results in Eq. (23).

λinc

(1 − ρ(λ)) (λ)dλ 1 − ρ(λ)(1 − aindir (λ)) ph,λ,in

w(λ )QE

Adir (λ) +

λem

λinc

.

(25)

φph,λ,in (λ)dλAdir λinc

Since it was assumed that the fluorescent sample exhibits no overlap between excitation and emission spectrum, the variables dependent on the incident wavelength range (denoted with λ) are independent of emission wavelengths λ and vice versa. This simplifies Eq. (25) to Eq. (26). ⎡

⎛

⎤ (1 − Adir (λ))aindir (λ)ρ(λ) ⎞ ⎢ ⎜ ⎥ 1 − ρ(λ)(1 − aindir (λ)) ⎟ ⎢ ⎜ ⎟ ⎥ ⎣ ⎝ ⎠ ph,λ,in (λ)dλ⎦ aindir (λ)ρ(λ) −(1 − Adir ) λinc Pc − (1 − Adir )Pb 1 − ρ(λ)(1 − aindir (λ)) . = w(λ )QEdλ La Adir ph,λ,in (λ)dλAdir λem Adir (λ) +

(26)

λinc

Rearranging Eq. (26) by bringing the terms under the integral over the incident wavelength range on the same denominator, the numerator of this term can be simplified. Finally, Eq. (27) is obtained. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 157.193.57.7 On: Mon, 05 Jan 2015 09:30:25

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Pc − (1 − Adir )Pb = La Adir

Adir w(λ )QEdλ

ph,λ,in (λ)dλ

λinc

ph,λ,in (λ)dλAdir

λem

= QE.

(27)

λinc

Indeed, the three measurement procedure can be used to determine the QE value of a fluorescent material.

E. Two measurement method

For the two measurement approach, the QE value can be found using Eq. (10). Substituting La , Lc , and Pc as a function of the incident spectral flux, results in Eq. (28). (1 − Adir (λ))aindir (λ).ρ(λ) Adir (λ) + ph,λ,in (λ)dλ dλ w(λ )QE 1 − ρ(λ)(1 − aindir (λ)) λ λem Pc inc = . (28) f2 (λ) L a − Lc (1 − Adir (λ))ph,λ,in (λ)dλ φph,λ,in (λ)dλ − f1 (λ) λinc

λinc

Taking into account that quantities in the incident wavelength region are independent of the emission wavelength and vice versa, and filling out the ratio f2 (λ)/f1 (λ), Eq. (28) is transformed into Eq. (29). (1 − Adir (λ))aindir (λ)ρ(λ) Adir (λ)+ ph,λ,in (λ)dλ 1 − ρ(λ)(1 − aindir (λ)) λinc Pc . (29) = w(λ )QEdλ (1 − Adir (λ))(1 − ρ(λ)) La −Lc 1− ph,λ,in (λ)dλ λem 1 − ρ(λ)(1 − aindir (λ)) λinc

Reorganizing the numerator and denominator of the fraction leads to the elimination of the fraction and results in Eq. (30). Pc = w(λ )QEdλ La −Lc λem

λ

inc ×

=

λinc

Adir (λ) − Adir (λ)ρ(λ) + aindir (λ)ρ(λ) ph,λ,in (λ)dλ 1 − ρ(λ)(1 − aindir (λ)) ρ(λ)aindir (λ) + Adir (λ) − Adir (λ)ρ(λ) ph,λ,in (λ)dλ 1 − ρ(λ)(1 − aindir (λ))

w(λ )QEdλ = QE.

(30)

λem

It can be seen from Eq. (30) that the value determined by the two measurement approach yields the QE value of the fluorescent material as the three measurement procedure. It should be noted that the two measurement approach imposes no other assumptions or restrictions compared to the three measurement method.

F. Uncertainty analysis

Since both the two and three measurement approaches lead to the same theoretical QE value, it is interesting to perform an uncertainty analysis for both methods to determine which method is most accurate. For the two measurement procedure, the uncertainty analysis has already been performed by Johnson et al.23 and the uncertainty on the QE value (UQE ) is given

in Eq. (31). UQE =

UP2 c

+

La U (La − Lc ) La

2

+

Lc U (La − Lc ) Lc

2 . (31)

Herein UPc , ULc , and ULa are the uncertainty on the determination of Pc , Lc , and La , respectively. It is obvious from


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Eq. (31) that a small difference between La and Lc (or a small absorption by the sample) will result in a larger uncertainty on the QE value. For the two measurement approach, samples with low absorption therefore have QE values with a lower accuracy.

UQE =

Pc U Pc − (1 − Adir )PB P c

2

+

For the three measurement procedure, the uncertainty analysis is performed by following the law of propagating uncertainty. The uncertainty on the QE value (UQE ) is given by Eq. (32).

PB (1 − Adir ) U Pc − (1 − Adir )PB P b

with UPb and ULb the uncertainties on the determination of Pb and Lb , respectively. UAdir is the uncertainty in the determination of the direct absorption and is given by Eq. (33). 2 2 1 Lc ULb . (33) ULc + UAdir = L b − Lc Lb .(Lb − Lc ) The uncertainty in the determination of the direct absorption is largely dependent on the difference between Lb and Lc (or the absorption by the sample). Since the uncertainty on the direct absorption determination directly influences the uncertainty on the QE value, it can be concluded that for the three measurement approach, similar as with the two measurement method, samples with low absorption result in a less accurate QE value. From Eqs. (31) and (32), it is not obvious which approach yields the smallest uncertainty. In Fig. 3, the uncertainty on the result obtained with both methods is numerically compared for a fixed uncertainty of 1% on all measured quantities in the incident wavelength range and 2% on the quantities in

2

+

PB Adir U Pc − (1 − Adir )PB Adir

2 + ULa 2 + UAdir 2 , (32)

the emission wavelength range (since the latter usually generates a smaller signal). The parameters are the direct absorption Adir , the indirect absorption aindir , and the reflection coefficient on the wall ρ. The indirect absorption is correlated to the direct absorption and the size of the sample. To allow for straightforward calculations, spherical samples have been assumed, using the diameter as size parameter. The indirect absorption for nonspherical samples will be correlated to the size and indirect absorption in a similar way. The numerical comparison showed that the reflection coefficient of the sphere wall only has negligible influence on the uncertainty of the QE value, so the effect of this parameter on the QE uncertainty is not shown in Fig. 3. From Fig. 3, it can be observed that the direct absorption has indeed the largest influence on the uncertainty of the QE value. For samples exhibiting low absorption, a large uncertainty can be expected with both approaches. The uncertainty on the QE value obtained with the three measurement approach is independent of the sample size and is in most cases slightly smaller than the uncertainty obtained with the two measurement approach. The uncertainty on the QE value obtained with the two measurement approach depends on the samples size, but this dependence vanishes for samples exhibiting significant absorption. This uncertainty analysis shows that the two measurement method only results in a very limited decrease in accuracy compared to the three measurement approach.

V. EXPERIMENTAL RESULTS

FIG. 3. Uncertainty on the QE value obtained with the two measurement method (2 M) and three measurement method (3 M) as function of the direct absorption for a spherical sample with diameter 0.25 cm (squares, ), 1 cm (triangles, ), and 2 cm (circles, ◦) in a sphere with diameter 7.5 cm. The curves for the three measurement method obtained for different sample sizes coincide.

The two and three measurement approaches were adopted to determine the QE value of several commercial phosphors used in lighting applications and a selection of luminescent silver exchanged zeolites. The study was performed using the main setup discussed in Sec. II of this paper and two additional setups at two different laboratories. The main setup (hereafter referred to as setup a) is located at the Light and Lighting Laboratory, KU Leuven, Technology Campus Ghent, Belgium. Both the two and three measurement approaches can be adopted in this setup. The first additional setup (setup b) is at the Department of Chemistry, KU Leuven, Belgium and consists of an integrating sphere (100 mm diameter, coated with Spectralon),


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TABLE I. Comparison of the QE of luminescent (powder) samples obtained with the three QE setups: Setup (a) at the Light and Lighting Laboratory, Ghent, Setup (b) at the Department of Chemistry, Leuven, Setup (c) at the Department of Solid State Sciences, Ghent, and (d) the value provided by the manufacturer. 2 M and 3 M indicate whether the two or three measurement approach was used. The standard deviation was calculated over nine measurement values. Sample BaMgAl10 O19 :Eu2+ BaMgAl10 O19 :Eu2+ ,Mn2+ Y3 Al5 O12 :Ce3+ Sr2 Si5 N8 :Eu2+ LTA-K6 Ag6 FAUX-Na4.7 Ag5.7 FAUY-Na3.5 Ag3

λinc (nm)

QE (a) 2M

QE (a) 3M

QE (b) 2M

QE (b) 3M

QE (c) 2M

QE (d)

380 380 450 450 360 340 360 340 360

0.98 ± 0.03 0.83 ± 0.03 0.91 ± 0.02 0.74 ± 0.03 0.04 ± 0.01 0.32 ± 0.02 0.15 ± 0.02 0.43 ± 0.02 0.11 ± 0.01

0.98 ± 0.03 0.87 ± 0.03 0.92 ± 0.02 0.78 ± 0.03 ... ... ... ... ...

0.91 ± 0.03 0.88 ± 0.02 ... ... ... 0.30 ± 0.02 ... 0.43 ± 0.02 ...

0.94 ± 0.02 0.84 ± 0.02 ... ... 0.03 ± 0.01 0.33 ± 0.03 0.16 ± 0.02 0.41 ± 0.01 0.10 ± 0.01

0.95 ± 0.03 0.90 ± 0.03 0.93 ± 0.03 0.79 ± 0.03 ... ... ... ... ...

0.96 ± 0.02 0.83 ± 0.02 ... ... ... ... ... ... ...

coupled to a commercial spectrofluorimeter (Horiba Jobin Yvon fluorolog FL3-22). The illumination section consists of a xenon light source in combination with a single monochromator, the detection section consists of a double monochromator in combination with a photon multiplier tube (PMT). The sample is positioned at the center of the sphere and a baffle is present in the sphere to prevent direct illumination of the detector from the sample. Both two and three measurement procedures can be used to obtain the QE of luminescent samples with this setup.35 The second additional setup (setup c) is at the Department of Solid State Sciences (LumiLab), Ghent University, Belgium and consists of an integrating sphere (152 mm diameter), coated with Spectralon. The powder sample is put in a bottom mounted cup and is illuminated with the light of blue or UVA LEDs, coupled in the sphere with an optical fiber and focused on the sample via a lens. The outgoing light is collected with another optical fiber, connected through a diffuser and analyzed by a monochromator (Princeton Instruments Acton SP2358) in combination with an EMCCD (Princeton Instruments ProEM 16002 ). A baffle is mounted between the sample and the optical fiber connecting sphere and detector. Due to the fixed sample position and illumination configuration, only the two measurement approach can be adopted in this setup. In Table I, the experimental data obtained with the three setups are presented for 7 different samples. The first four samples are commercial phosphors used in lighting applications, having blue, green, yellow, and red emission. When available, the QE values provided by the manufacturer of these commercial phosphors are given as well. The last three samples are silver loaded zeolite samples produced by the Department of Chemistry, KU Leuven.35 The excitation and emission spectra of the set of samples are presented in Fig. 4. The measurements in the different setups were performed on different powder samples obtained from the same batch, limiting the variation over the samples. From Table I, an acceptable agreement between the QE values obtained from the three setups can be observed for all samples, regardless of the employed measurement procedure (two or three measurements). This correspondence is valid for a broad range of materials with distinctive excitation and emission properties, and QE values. This confirms the theoretical conclusions derived by applying the rigorous integrat-

ing sphere theory. These results indicate that the determination of the QE is independent of the exact configuration of the integrating sphere setup and the measurement procedures evaluated in this report allow for reproducible results over various setups.

FIG. 4. Excitation (a) and emission (b) spectra of the luminescent samples used in this study.


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It should be noted that a correct determination of the spectral response of the system is critical for both measurement procedures. An error in the spectral response will introduce much larger deviations, compared to the deviations introduced due to the choice of the measurement procedure. VI. CONCLUSION

To determine the absolute quantum efficiency (QE) of photoluminescent materials, typically an integrating sphere setup is used to capture all scattered and emitted light. Such setup was developed to obtain a quick and reliable determination of the QE of all kinds of photoluminescent materials and particularly those of highly scattering materials. Nowadays, for this type of setup, two measurement procedures are coexisting: a two measurement and a three measurement approach. In the two measurement approach, both an empty sphere measurement and a measurement with the sample in the sphere with the excitation beam incident on the sample are performed. In the three measurement approach, an additional measurement with the sample in the sphere, but out of the excitation beam, is performed. Both approaches were thoroughly discussed starting from the rigorous integrating sphere theory. It was found that both methods theoretically lead to identical QE values. Experimental data were gathered among three different setups, adopting both measurement approaches. The experimental data showed an acceptable agreement of the QE values for all samples, regardless of the chosen measurement procedure and excitation and emission spectra, and QE values. It can be concluded that two measurements are sufficient to determine to QE of photoluminescent samples. The uncertainty analysis revealed that low absorption leads to inaccurate results for both methods. ACKNOWLEDGMENTS

The authors would like to thank the SIM (Flemish Strategic Initiative for Materials) and IWT (Flemish agency for Innovation by Science and Technology) for their financial support through the SIM-IWT ICON project “Solcap” (IWT 100733), and IWT for financial support through the SBOproject LumiCoR (IWT 130030). 1 G. 2 T.

G. Stokes, Philos. Trans. R. Soc. London 142, 463 (1852). Welker, J. Lumin. 48–49, 49 (1991).

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