Various exciton annihilation processes are known to impact the efficiency roll-off of organic light emitting diodes (OLEDs); however, isolating and quantifying their contribution in the presence of other factors such as changing charge balance continue to be a challenge for routine device characterization. Here, we analyze OLED electroluminescence resulting from a sinusoidal dither superimposed on the device bias and show that nonlinearity between recombination current and light output arising from annihilation mixes the quantum efficiency measured at different dither harmonics in a manner that depends uniquely on the type and magnitude of the annihilation process. We derive a series of analytical relations involving the DC and first harmonic external quantum efficiency that enable annihilation rates to be quantified through linear regression independent of changing charge balance and evaluate them for prototypical fluorescent and phosphorescent OLEDs based on the emitters 4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran and platinum octaethylporphyrin, respectively. We go on to show that, in most cases, it is sufficient to calculate the needed quantum efficiency harmonics directly from derivatives of the DC light versus current curve, thus enabling this analysis to be conducted solely from standard light-current-voltage measurement data.

Bimolecular annihilation reactions involving energy transfer from one exciton to another or to a charge carrier are an important factor for both efficiency roll-off1–4 and operational degradation of organic light emitting diodes (OLEDs).5–8 Annihilation loss in OLEDs is frequently quantified by modeling their external quantum efficiency (EQE) roll-off versus current density;1,2,4,9,10 however, it is notoriously difficult to identify which mode of annihilation is dominant (e.g., triplet-triplet vs. triplet-polaron) and subsequently to disentangle its magnitude from competing roll-off processes such as declining charge balance that manifest with a similar (often unknown) functional dependence.3,4,11 This uncertainty makes it difficult to determine the presence and impact of annihilation in the course of routine device testing and therefore stands as an important characterization need for continuing OLED development.

Here, we introduce a simple analytical method to directly identify and extract OLED annihilation rates from standard light-current-voltage (LIV) measurement data. The foundation of this approach lies in a frequency domain EQE analysis and is most easily understood in analogy to impedance spectroscopy, where in this case both the current and electroluminescence intensity are measured using a lock-in amplifier at different harmonics of the sinusoidal dither superimposed on the DC device bias [see Fig. 1(a)]. In the presence of annihilation, the relationship between recombination current and light output (proportional to exciton density) becomes nonlinear, thereby mixing the different EQE harmonics in a manner that depends uniquely on the type and magnitude of annihilation as illustrated schematically in Fig. 1(b).

FIG. 1.

(a) Frequency-domain electroluminescence measurement. An OLED is driven by a small AC dither superimposed onto a DC bias. Light and current are measured with a lock-in amplifier at harmonics of the modulation frequency using a photodiode and small sampling resistor (<100 Ω), respectively. (b) Graphic illustration of mixing between current and light harmonics that results from annihilation. Current at a given harmonic is normally linked to electroluminescence at the same harmonic (solid lines); however, when annihilation is significant, nonlinearity in the exciton density mixes signals from neighboring harmonics (dashed lines).

FIG. 1.

(a) Frequency-domain electroluminescence measurement. An OLED is driven by a small AC dither superimposed onto a DC bias. Light and current are measured with a lock-in amplifier at harmonics of the modulation frequency using a photodiode and small sampling resistor (<100 Ω), respectively. (b) Graphic illustration of mixing between current and light harmonics that results from annihilation. Current at a given harmonic is normally linked to electroluminescence at the same harmonic (solid lines); however, when annihilation is significant, nonlinearity in the exciton density mixes signals from neighboring harmonics (dashed lines).

Close modal

While OLED impedance spectra are generally difficult to interpret due to complicating factors such as space charge accumulation, unknown trap distributions, and injection/heterojunction barriers,12,13 the relationship between electroluminescence and current density is accurately described via a simple rate equation. Consider applying a voltage, V=V0+V1eiωt, to an OLED under the usual condition that the dither is much smaller than the DC bias (V1V0). Because the IV relationship is nonlinear (i.e., diode-like), the resulting current density will contain additional harmonics, J=J0+J1eiωt+J2e2iωt+, as will the emitted electroluminescence intensity, L=L0+L1eiωt+L2e2iωt+, which has units of photons emitted per unit area per second. Assuming for simplicity a uniform recombination zone of width, a0, in the OLED emissive layer (EML), the exciton density, X (e.g., triplets in a phosphorescent OLED), can be described by the rate equation1,2

dXdt=JJfqa0XτkXXX2kXPXP.
(1)

Here, Jf accounts for current that does not contribute to exciton formation (i.e., recombination at traps or charge imbalance leakage current), τ is the natural exciton lifetime, q is the electronic charge, P is the polaron density, and kXX and kXP are the exciton-exciton (XXA) and exciton-polaron annihilation (XPA) rate coefficients, respectively. The exact nature of the excitons and polarons (e.g., singlet/triplet, host/guest exciton, electrons, or holes) is left general at this stage.

Because the light emission is directly proportional to the exciton density through the photoluminescence quantum yield, ηPL, and out-coupling efficiency, ηOC, via L=a0ηPLηOCτ1XαX, Eq. (1) can be rewritten and expanded harmonically in terms of L and J. Focusing initially on the simplest case, where XXA is dominant and XPA is negligible (kXP0), the quadratic annihilation term leads to harmonic mixing and contributions of the form L02+L12/2+L22/2+ at DC and 2L0L1+L1L2+ at the first harmonic (1ω). Retaining only the lowest order term for each frequency and dividing by the respective current density yields

J0Jf0J0ϕB0=a0α[1τ+kXXαL0]EQE0,
(2)

at DC and

J1Jf1J1ϕB1=a0α[1τ+iω+2kXXαL0]EQE1,
(3)

at the first harmonic. Here, EQE0=qL0/J0 and EQE1=qL1/J1 are the EQEs defined at each respective frequency and the terms ϕB are the corresponding charge balance factors that represent the fraction of total current at each harmonic that recombines to form excitons.

If the modulation frequency is low compared to the natural exciton decay rate (ωτ1), then the iω phase term in Eq. (3) is negligible and the ratio of EQE0 to EQE1 becomes

EQE0EQE1=[1+2kXXτ2a0ηPLηocL01+kXXτ2a0ηPLηocL0]1γ10,
(4)

where γ10=ϕB1/ϕB0 is defined as the 1ω to DC charge balance ratio and is approximately unity when ϕB0 varies slowly with current density as discussed below. In this case, Eq. (4) predicts that the EQE ratio will be equal to one at low brightness and will asymptote to two at high brightness when annihilation becomes dominant, providing a simple qualitative measure of how significant annihilation is at a given brightness. Quantitative extraction of kXX is subsequently facilitated by rearranging Eq. (4) as

γ10EQE0EQE1=[kXXτ2a0ηPLηoc](2EQE1γ10EQE0)L0,
(5)

which predicts that plotting the difference EQE0EQE1 versus (2EQE1EQE0)L0 will result in a linear relationship with slope equal to kXXτ2/a0ηPLηoc when γ101.

If the modulation frequency is also slow compared with the electrical response of the device (in practice ≲kHz modulation frequencies relative to the ∼μs scale turn-on time of the OLED),14,15 then DC steady-state conditions are reached at every moment in the slowly varying modulation. In this quasi-static regime, and in the limit of small modulation amplitude, EQE1 is equivalently given by the derivative of the DC light vs. current curve, that is, EQE1=q[dL0/dJ0]dEQE. Thus, the harmonic analysis above can be performed using standard LIV measurement data provided the point spacing is sufficient to accurately resolve dEQE.

Figure 2 explores these predictions numerically for a realistic OLED dominated by XXA in the presence of changing charge balance. A typical power law IV characteristic is assumed with recombination (JR0) and leakage current (Jf0) components divided according to the fictitious charge balance simulated in Fig. 2(a) (right-hand scale). The light output is calculated according to Eq. (1) at DC assuming ηPL=0.4, ηoc=0.2, a0=5 nm, τ=88μs, and kXX=4×1014 cm3 s−1, typical for a classic phosphorescent OLED based on platinum octaethylporphyrin (PtOEP).1,16,17 In Fig. 2(a), red lines indicating the 1ω EQE and charge balance quantities have been calculated both via direct numerical Fourier transform from Eq. (1) using a dithered bias voltage and as derivatives of the DC LIV (i.e., as dEQE), which were verified to be equivalent.

FIG. 2.

(a) DC (black lines) and first harmonic (1ω, red lines) EQEs and charge balance factors simulated for an OLED in the presence of XXA. Dashed lines show EQEs for the same device in the limit of perfect, unchanging charge balance, ϕB0=1. (b) Simulated EQE0/EQE1 ratios with and without charge imbalance. In the presence of XXA, this ratio asymptotes between 1 and 2 if charge balance remains constant; changes in charge balance can force the ratio outside of these bounds. (c) Linearized EQE differences plotted in the form of Eq. (5) to facilitate extraction of the annihilation coefficient, kXX. The dashed green line shows the exact linearity that results for a device with unchanging charge balance whereas the black line illustrates the result for changing charge balance, demonstrating that the same annihilation slope can still be identified.

FIG. 2.

(a) DC (black lines) and first harmonic (1ω, red lines) EQEs and charge balance factors simulated for an OLED in the presence of XXA. Dashed lines show EQEs for the same device in the limit of perfect, unchanging charge balance, ϕB0=1. (b) Simulated EQE0/EQE1 ratios with and without charge imbalance. In the presence of XXA, this ratio asymptotes between 1 and 2 if charge balance remains constant; changes in charge balance can force the ratio outside of these bounds. (c) Linearized EQE differences plotted in the form of Eq. (5) to facilitate extraction of the annihilation coefficient, kXX. The dashed green line shows the exact linearity that results for a device with unchanging charge balance whereas the black line illustrates the result for changing charge balance, demonstrating that the same annihilation slope can still be identified.

Close modal

Figure 2(b) displays the EQE0/EQE1 ratio for the simulated device together with the reference case of unchanging charge balance (dashed line). Extension of the EQE ratio outside of the annihilation-relevant y-axis range between one and two occurs when γ101, providing a clear visual indication that annihilation is not the dominant loss mechanism at these current densities. Despite the clear impact of changing charge balance, Fig. 2(c) shows that re-plotting the simulation data in the form of Eq. (5) still yields a clearly recognizable linear region from which it is possible to obtain an accurate extraction of kXX within 10% of the true value defined by the γ10=1 reference.

The robustness of this extraction method in the presence of changing charge balance can be understood more clearly from reference to the quasi-static derivative definition of γ10 via ϕB1=1dJf0/dJ0. From this, γ10=1 whenever dJf0/dJ0=Jf0/J0 (i.e., when Jf0 is linearly related to J0), which defines a region of locally unchanging charge balance (dϕB0/dJ=0). This condition is always met when the charge balance reaches a peak, and thus an approximately linear slope still manifests in this region to reveal the magnitude of annihilation in Fig. 2(c). Further inspection of Eq. (5) shows that, to first order, deviation of γ10 from unity translates to a y-intercept in the fit line, with γ10<1 resulting in a positive intercept that marks the onset of declining charge balance.

Once the bracketed annihilation term in Eq. (4) is known from the linear fit of Eq. (5), the “annihilation-only” component of the EQE ratio [the green dashed line in Fig. 2(b)] can be reconstructed, enabling γ10 to be determined as a function of current density by dividing it by the actual EQE ratio [i.e., by dividing the green dashed line by the black line in Fig. 2(b)]. Using the quasi-static derivative definition of γ10 subsequently leads to a first order differential equation

dJf0dJ0γ10Jf0dJ0+(γ101)=0
(6)

that can be used to solve for Jf0 by numerical integration of J0 and the (now known) function for γ10. This requires an initial condition value for Jf0 which, although not rigorously known, should be well-approximated in OLEDs with near-unity internal quantum efficiency18 as Jf0IC0 (i.e., perfect charge balance) when γ10 crosses/or is equal to unity.

The same methodology can be applied to the situation when XPA is the dominant annihilation process. In this case, it can be argued on general grounds (see Sec. S1 of the supplementary material19) that the relationship between exciton and charge carrier density in the recombination zone can be expressed in the form X=CPβ, where β1 and C is a constant. Proceeding in the same manner as above, it is straightforward to show for β=2, and subsequently to verify numerically for general β, that the EQE ratio is given by

EQE0EQE1=[1+(1+1β)CkXPτ(τL0a0ηPLηOC)1/β1+CkXPτ(τL0a0ηPLηOC)1/β]1γ10
(7)

and can be linearized for kXP extraction as

γ10EQE0EQE1=CkXPτ[(1+1β)EQE1γ10EQE0](τL0a0ηPLηOC)1β.
(8)

Equations (7) and (8) are the XPA analogs of Eqs. (4) and (5) for XXA and therefore XPA device analysis would proceed similar to that described above. In the case of space charge limited (SCL) transport20 assumed in previous XPA analyses,2,9β=2 as described in the supplementary material,19 and thus Eq. (7) predicts that the EQE ratio of an OLED dominated by XPA would asymptote toward a value of 3/2, in contrast with the value of 2 for XXA.

Initial testing of these predictions was carried out on classic double heterostructure fluorescent and phosphorescent OLEDs shown in the inset of Fig. 3(a) using emissive layers doped, respectively, with 2 wt. % DCM laser dye [4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H- pyran] or 8 wt. % PtOEP. Efficiency roll-off in these devices has been studied previously,1,3 where it was shown that the PtOEP device is strongly affected by triplet-triplet XXA, whereas annihilation is negligible for its DCM counterpart. Devices were fabricated via vacuum thermal evaporation on pre-patterned indium tin oxide anodes with LiF (0.7 nm)/Al (80 nm) cathodes (4 mm2 active device area) and were subsequently packaged in a N2 glove box using a thin layer of ultraviolet-curable adhesive (Norland, NOA 63) and a glass cover slip.

FIG. 3.

(a) DC external quantum efficiency, EQE0, measured for fluorescent DCM and phosphorescent PtOEP devices shown in the inset. The two OLEDs share a 40 nm thick N,N′-di(1-naphthyl)-N,N′-diphenyl-(1,1′-biphenyl)-4,4′-diamine (NPD) hole transport layer and have 10 nm thick EMLs consisting of either tris-(8-hydroxyquinoline) aluminum (Alq3) doped with 2 wt. % DCM or 4,4′-bis(N-carbazolyl)-1,1′-biphenyl (CBP) doped with 8 wt. % PtOEP. The 20 nm thick hole blocking layer in each case consists of either bis(8-hydroxy-2-methylquinoline)-(4-phenylphenoxy)aluminum (BAlq) or bathocuproine (BCP), and both devices have a LiF (0.7 nm)/Al (80 nm) cathode. (b) Derivative-based linear EQE difference plot for the PtOEP (maroon squares) and DCM (orange circles) devices. Solid squares indicate the PtOEP data range used for linear regression to extract kXX. Locations that correspond to current densities of 0.1 mA/cm2 and 1 mA/cm2 are indicated by arrows for reference.

FIG. 3.

(a) DC external quantum efficiency, EQE0, measured for fluorescent DCM and phosphorescent PtOEP devices shown in the inset. The two OLEDs share a 40 nm thick N,N′-di(1-naphthyl)-N,N′-diphenyl-(1,1′-biphenyl)-4,4′-diamine (NPD) hole transport layer and have 10 nm thick EMLs consisting of either tris-(8-hydroxyquinoline) aluminum (Alq3) doped with 2 wt. % DCM or 4,4′-bis(N-carbazolyl)-1,1′-biphenyl (CBP) doped with 8 wt. % PtOEP. The 20 nm thick hole blocking layer in each case consists of either bis(8-hydroxy-2-methylquinoline)-(4-phenylphenoxy)aluminum (BAlq) or bathocuproine (BCP), and both devices have a LiF (0.7 nm)/Al (80 nm) cathode. (b) Derivative-based linear EQE difference plot for the PtOEP (maroon squares) and DCM (orange circles) devices. Solid squares indicate the PtOEP data range used for linear regression to extract kXX. Locations that correspond to current densities of 0.1 mA/cm2 and 1 mA/cm2 are indicated by arrows for reference.

Close modal

Figure 3(a) shows the external quantum efficiency (EQE0) for each OLED and Fig. 3(b) plots their respective EQE0 and dEQE in the form of Eq. (5). The PtOEP device exhibits a linear region similar to that predicted in Fig. 2(c) for current densities ranging approximately 0.1–4 mA/cm2. At higher currents, the data display a characteristic bend back toward the ordinate axis, indicating that another roll-off mechanism becomes dominant. By contrast, the DCM data are never quite linear and display a continuous downward curvature. Attempting an approximate linear fit in spite of the curvature leads to an unphysical singlet-singlet XXA rate coefficient that is several orders of magnitude too large, indicating that XXA is not significant for these DCM devices over the measured current density range.3 In addition to DC characterization, the same analysis was performed using the dithered AC EQE lock-in amplifier experimental configuration shown in Fig. 1(a) and reasonable agreement between the two methods was confirmed; the comparison is detailed in Sec. S2 of the supplementary material.19 

Assuming ηOC0.2, the slope of the fitted PtOEP linear region in Fig. 3(b) together with its phosphorescent lifetime τ=88μs [Ref. 16] and quantum yield ηPL=0.4 [Ref. 17] results in kXX/a0=(1.6±0.2)×108 cm2 s−1, which is a figure of merit indicative of the annihilation intensity in the device. If the recombination zone is subsequently taken to be the emissive layer width (a0=10 nm), then this result yields kTTA=2kXX=(3.2±0.4)×1014 cm3 s−1, in agreement with the triplet-triplet annihilation (TTA) coefficient found previously for this device (the factor of 2 is inserted for consistency with the notation of previous work).1 

Figure 4(a) shows the EQE ratio for the PtOEP device together with the annihilation-only contribution [dashed green line cf. Fig. 2(b)] derived from the linear fit of kXX/a0. It is evident from extension of the measured EQE ratio above two that, while XXA is significant in this device, declining charge balance also becomes a factor at high current densities of >10 mA/cm2, which is confirmed by the rising shoulder of N,N′-di(1-naphthyl)-N,N′-diphenyl-(1,1′-biphenyl)-4,4′-diamine (NPD) emission shown in Fig. 4(b).3 Determining γ10 from the quotient of the measured EQE ratio and the extracted XXA contribution, and assuming an initial condition Jf0IC=0 when γ10 crosses unity, numerical integration of Eq. (6) results in the normalized charge balance of the device (ϕB0) plotted on the right hand scale.

FIG. 4.

Ratio of EQE0/dEQE (maroon squares, left-hand axis) for the PtOEP device as a function of current density. The dashed green line indicates the XXA contribution to the ratio derived from the linear fit in Fig. 3(b). The difference between the measured ratio and the XXA contribution is ascribed to changing charge balance, which is plotted on the right-hand axis. (b) Normalized electroluminescence spectra for the PtOEP device at varying current densities. Increasing NPD emission at λ430 nm for J>10 mA/cm2 indicates electron leakage into the hole transport layer, consistent with the decline in charge balance calculated in (a).

FIG. 4.

Ratio of EQE0/dEQE (maroon squares, left-hand axis) for the PtOEP device as a function of current density. The dashed green line indicates the XXA contribution to the ratio derived from the linear fit in Fig. 3(b). The difference between the measured ratio and the XXA contribution is ascribed to changing charge balance, which is plotted on the right-hand axis. (b) Normalized electroluminescence spectra for the PtOEP device at varying current densities. Increasing NPD emission at λ430 nm for J>10 mA/cm2 indicates electron leakage into the hole transport layer, consistent with the decline in charge balance calculated in (a).

Close modal

Joule heating or field-induced exciton dissociation21 could also play a role in the efficiency roll-off. However, because field-induced dissociation mainly affects the exciton formation process (i.e., before a Coulombically correlated carrier pair has recombined to form a tightly bound exciton), its distinction from charge imbalance is ultimately superficial since one cannot distinguish between a carrier pair that forms and is dissociated versus one that never forms at all. The effect of field-induced dissociation is thus implicitly included in ϕB0. Alternatively, Joule heating effects could be identified from pulsed LIV measurements.

Although the expressions derived above assume a uniform recombination zone, accounting for a spatially varying recombination zone does not materially change the analysis. Its primary effect is to change the slope of the linearized EQE plot (reflective of an average annihilation intensity) and to soften the transition between the asymptotes in the EQE ratio plot (their values remain unchanged). A recombination zone that changes significantly with current density would lead to curvature in the linearized EQE plot, making extraction of the annihilation intensity difficult. However, it still would not violate the asymptotes of the annihilation-limited EQE ratio, making this type of plot a robust identifier of devices in which annihilation is not the dominant cause of roll-off.

It is important to note that the harmonic EQE analysis developed here does not produce any “new” information not already contained in a standard LIV measurement. Rather, it simply repackages the data in a form that is more sensitive and conducive to identifying the effects of annihilation. Mixing among higher EQE harmonics (e.g., relationships involving EQE2, γ20, and so on) should provide additional constraints on the type and magnitude of annihilation and can, in principle, be determined from higher order LIV derivatives, dnL/dJn. However, in practice, measurement noise and finite point spacing of the DC LIV amplify fluctuations in the higher derivatives, preventing them from being recovered accurately. The value in direct frequency domain EQE harmonic analysis [i.e., as in Fig. 1(a)] is thus that the lock-in amplifier more effectively averages and recovers higher harmonics from the noise. The disadvantage is that the measurement takes longer to perform.

Looking forward, the added information contained in higher EQE harmonics may be sufficient to reliably deconvolve the magnitudes of two different annihilation processes such as, e.g., triplet-triplet and triplet-polaron annihilation when both are significant in a device. This goal is particularly important for understanding roll-off in state-of-the-art phosphorescent OLEDs known to be affected by both processes2,9 and is currently the subject of ongoing work. Similarly, increasing the modulation frequency beyond the quasi-static regime to obtain additional phase information in the form of frequency-dependent complex EQE spectra could help to characterize dynamic processes in the emissive layer such as charge trapping and exciton formation on emissive dopants. Finally, the analysis here should find straightforward extension to inorganic LEDs, where it may help to resolve ongoing questions about the role of Auger recombination in InGaN/GaN LED efficiency droop.22,23

This work was supported in part by the Dow Chemical Company and by the Air Force Office of Scientific Research Young Investigator Program.

1.
M. A.
Baldo
,
C.
Adachi
, and
S. R.
Forrest
,
Phys. Rev. B
62
,
10967
(
2000
).
2.
S.
Reineke
,
K.
Walzer
, and
K.
Leo
,
Phys. Rev. B
75
,
125328
(
2007
).
3.
N. C.
Giebink
and
S. R.
Forrest
,
Phys. Rev. B
77
,
235215
(
2008
).
4.
C.
Murawski
,
K.
Leo
, and
M. C.
Gather
,
Adv. Mater.
25
,
6801
(
2013
).
5.
N. C.
Giebink
,
B. W.
D'Andrade
,
M. S.
Weaver
,
P. B.
MacKenzie
,
J. J.
Brown
,
M. E.
Thompson
, and
S. R.
Forrest
,
J. Appl. Phys.
103
,
044509
(
2008
).
6.
N. C.
Giebink
,
B. W.
D'Andrade
,
M. S.
Weaver
,
J. J.
Brown
, and
S. R.
Forrest
,
J. Appl. Phys.
105
,
124514
(
2009
).
7.
Y.
Zhang
,
J.
Lee
, and
S. R.
Forrest
,
Nat. Commun.
5
,
5008
(
2014
).
8.
Q.
Wang
,
B.
Sun
, and
H.
Aziz
,
Adv. Funct. Mater.
24
,
2975
(
2014
).
9.
N. C.
Erickson
and
R. J.
Holmes
,
Adv. Funct. Mater.
24
,
6074
(
2014
).
10.
S.
Wehrmeister
,
L.
Jäger
,
T.
Wehlus
,
A. F.
Rausch
,
T. C. G.
Reusch
,
T. D.
Schmidt
, and
W.
Brütting
,
Phys. Rev. Appl.
3
,
024008
(
2015
).
11.
J.
Scott
,
S.
Karg
, and
S.
Carter
,
J. Appl. Phys.
82
,
1454
(
1997
).
12.
M.
Schmeits
and
N. D.
Nguyen
,
Phys. Status Solidi A
202
,
2764
(
2005
).
13.
N. D.
Nguyen
and
M.
Schmeits
,
Phys. Status Solidi A
203
,
1901
(
2006
).
14.
S.
Barth
,
P.
Müller
,
H.
Riel
,
P. F.
Seidler
,
W.
Rieß
,
H.
Vestweber
, and
H.
Bässler
,
J. Appl. Phys.
89
,
3711
(
2001
).
15.
B.
Ruhstaller
,
T.
Beierlein
,
H.
Riel
,
S.
Karg
,
J. C.
Scott
, and
W.
Riess
,
IEEE J. Sel. Top. Quantum Electron.
9
,
723
(
2003
).
16.
Y.
Zhang
and
S. R.
Forrest
,
Chem. Phys. Lett.
590
,
106
(
2013
).
17.
A. K.
Bansal
,
W.
Holzer
,
A.
Penzkofer
, and
T.
Tsuboi
,
Chem. Phys.
330
,
118
(
2006
).
18.
C.
Adachi
,
M. A.
Baldo
,
M. E.
Thompson
, and
S. R.
Forrest
,
J. Appl. Phys.
90
,
5048
(
2001
).
19.
See supplementary material at http://dx.doi.org/10.1063/1.4923471 for the derivation of exciton-polaron EQE harmonic relations and comparison of AC direct and DC derivative-based harmonic analyses.
20.
M. A.
Lampert
,
Rep. Prog. Phys.
27
,
329
(
1964
).
21.
J.
Kalinowski
,
W.
Stampor
,
J.
Mȩżyk
,
M.
Cocchi
,
D.
Virgili
,
V.
Fattori
, and
P.
Di Marco
,
Phys. Rev. B
66
,
235321
(
2002
).
22.
J.
Cho
,
E. F.
Schubert
, and
J. K.
Kim
,
Laser Photonics Rev.
7
,
408
(
2013
).
23.
F.
Römer
and
B.
Witzigmann
,
Opt. Express
22
,
A1440
(
2014
).

Supplementary Material