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Singlet exciton-charge carrier interaction in anthracene
Volume 9, number 1
SINGLET
CHEMICAL PliYSICS LETTERS
EXCITON-CHARGE
Dicision
CARRIER
INTERACTION
L April 1971
IN
ANTHRACENE
N. WAKAYAMiS and D. F. WILLIAMS of Chemistry, Nctional Research Council of Canada, Otfarta. Cana& Receivad 23 November 1970
The singlet exciton-charge carrier annihilation rate constant KS has been measured CLSXi x 10-5cm3 set-1 for hoies and electrons. The mngnitude of Ks is discussed with respect to the magnitude of rhc electron-hole recombination rate constant.
Although
exciton-enciton
and carrier-carrier
interactions have been investigated extensively. little work has been reported concerning the kinetics of exciton annihilation by charge carriers_ IIelfrich [l] determined the triplet exciton-e:ectron annihilation rate constant, and Wotherspoon et al. [2] have noted a modulation of fluorescence by trapped holes. In this paper we report the results of experiments involving singlet and triplet exciton annihilation by both holes and electrons. The crystals were cleaved 11ab plane from high purity ingots, which always had tripiet exciton lifetimes in excess of 25 msec. Either holes or electrons were injected into these crystals by means of the rewective injecting contacts [1,3] together with a transparent non-injecting counter electrode. Solution electrodes were in fact used for several of these measurements. although no difference was found for solid electrodes. Since it has been observed that many electrodes normally blocking will inject carriers under high density space-charge-limited currents, great care was taken to ensure no electroluminescence developed in the contact combinations used. Specifically, concentrated sodium hydroxide was used as the electron injection counter electrode and aqueous sodium chloride as the hole injection counter electrode. Currents 01 up-to 10-5 A/cm2 could easily be obtained The crystal complete with electrodes was then placed in a fast phosphoroscope (excitation and observation periods of 0.2 msec, dead time 0.9 msec), such that either a laser shone through the transparent electrode and the delayed fluorescence emfttlng from the crystal side was monitored, or this geometry:was reversed. A cold 95588 photomultiplier together with the necessary voltage supply, amplifier, time constant and r&corder!
or time averaging computer served as the delayed fluorescence detector system. A high power Xe-Ne laser was used as the excitation source since this will produce a uniform density of either singlet or triplet excitons throughout the crystal. The laser intensity was monitored throughout the experiment. The change of fluorescence was then measured as a function of crystal current with both increasing and decreasing voltages. The concentration of triplet excitation in anthracene is governed by the well-known equation 1418 dnT -=c&-@zT-~?z;. dt
(1)
where 3 is the excitation intensity, no is the triplet exciton density. and @ and y are the mono and bimolecular decay constants, respectively. Under low illumination intensities. monomolecular triplet decay dominates. 139 >> ytz$. and the very weak delayed fluorescence decays exponentially. To show these kinetic conditions were applicable, it was always checked that the deiayed fluorescence was proportionaL to the square of the laser intensity. This delayed fluorescence results from the formation of singlei excitons by triplet-triplet annihilation, the yq term in eq. (1). Under these circumstsnces. the interaction of the triplet exciton with charge carriers was determined by monitoring (a) tte steady-state delayed fluorescence intensity, or (b) the deIayecJ fluorescence decay rate or (c) the steady-state phosphorescence intensity or (d) the phosphorescence decay rate all as a function of the free carrier density. High voltages applied in a reverse bias to the crystal did not affect either a. b. c or d showing these effects were
Volume 9, number 1
CHEMICAL PHYSICS LETTERS
1 April 1971
solely due to the injected carriers. These results will be discussed in a separate paper; however, the triplet exciton-hole (or electror) interaction rate constant was always found to be about lo-%m3sec-I. With high laser intensities. the linear ter,n in eq. (1) may be neglected, and the delayed fluorescence intensity I under steady-state conditions is then given by I = f$Qru,
(2,
where Q is the fluorescence quantum efficiency. o[ the absorption coefficient of the exciting light with intensity. and J a numerical factor (0 C/C 1). The delayed fhorescence is linearly proportional to the laser intensity under these kinetic conditions. and this was experimentally verified. Under these conditions the quenchire of fluorescence is not caused by the triplet-carrier interaction, since even under high currents p’nT+=yn + where @‘)-I is the reduced triplet lifetime. Thus the fluorescence quenching is due either to a change iny. which seems unlikely, or is due to a decrease in the fluorescence quantum efficiency Q presumably by a dipole-carrier interaction. With high currents. -10-6 A. 1~12, the fluorescence intensity could be reduced by =60’%. Since the crystal dimensions. electrode area and crystal currents are known. the total carrier density (_Nt)and free carrier density (Nf) of either
radiative decay constants of the unperturbed crystaL Thus (kl + kz)-l is actually the observed singlet exciton lifetime including reabsorption effects, and this has been shown lo be about 25 nsec [6]. It was experimentally found (fig. 1) that the fluorescence intensity decrease (Z. - Zj/l = K(hqt (RI+ k2) was proportional to the total carrier concentration, and to the laser intensity under the higii intensity condition, showing that the interaction was indeed bimolecular. Thus we can put K(N) = K,Nt. In fact a slight superlinearity in this dependence was often observed at high currents. The interaction rate constant is then
holes or electrons which cause the measured decrease in fluorescence can be calculated from
ezsily obtained versus carrier
the equations are present.
1. because
[5].
assuming
only shallow
traps
Ocnsify
Carrier
Fig. 1. Fluorescence intensity change (IO-o/I versus free carrier density i 0) and tot.4 carrier density (0). The slope gives K M =z Uz~Nt(&l-kp) = 1.43 r: lo- I 2NtQC.1 +k2) = 5.7 x 10-s+.
K
3
=
from the fluorescence intensity density dependence shown in fig.
au,- m @I LfNtt)
. +
k2) .
Typical values for KS are given in table 1 toNf=N@.
(4)
where c is the crystal die!ectric constant, L the crystal thickness and 0 the ratio of the measured current to that predicted by Child’s law (trap free). 0 varied from ~1.0 - 10-d depending upon crystal preparation *. Assuming that the intera,rion of 2 singlet exciton with a charge carrier affords an additional mechanism for nonradiative exciton decay, the change of quantum yield of fluorescence with carrier density may be written as ’
-_ - kl t
kl
where kl and kz represent l
$1
k2 + I-C(N)’
the radiative and non-
The 8 of the dry~tal depends on the process Of growing. The detailed description
will be publiehed.
Tab!e 1 Values Of ~~ and B for various crystals
electron-singlet
(5 (3 (1 (1
- 7 ) - 8 ) - 2.2) - 10 )
exciton interactian
x10-4 x 10-3 x 10-2 x 10-2
hole-singlet
3 3 7 7
X 10-5 x 10’5 x 10-5 x 10-5
exciton interaction
1.3 x 10-3 (1.5 (2 i4 (3 -
2.2 2.2 8.8 5.7
) x lO-2 jXl0’2 ) x10-2 ) x 10-2
1.9 x 10-5 3.6 6.0 1.8 4
~10’~ x 10-5 x10-s x 10-5
CHEMICAL PHYSICS LETTERS
Volume 9, number 1 gether
with the approximate
9 values.
The con-
sistency of Ks. in comparison to 6 justifies the use of Nt in this analysis, whereas in evaluating Ktriplet, the density of free carriers is the pertinent parameter. In view of the large value of Ks. especialIy when compared to the accepted value for the electron-hole interaction parameter [7] =lO-fkm3sec -1, these results for h’s require further examination. Let us denote the reaction cross section between a carrier and singlet exciton as u, and let their respective thermal velocities be given by u and 1’. Then since this interaction is considered to be bimolecular. we may express the reaction rateK(N) as
= zqjl
- l9)a + ONtO(“f 2
324,
u
17’
Theoretically both u and v have been predicted to be about 106 cm see-l [ 8.91. For almost trapfree conditions, 3 ==1, the first term in eq. (7) may be neglected and where 8 << 1, the second term may be neglected_ The majority of the experimental results reported fall into the latter case, but at higher current densities this assumption becomes less valid. From eq. (7) and fig. 1 (which contains the experimental results which showed the greatest superlinearity). fig. 2 may be obtained. the slope ;f “h_:“h gives o(u+u9. 3~) = 1.6 x 10-4 cm set _ Thus the carrier velocities u are found tc be a factor of abogt 2.5 larger than the exciton velocities. This is well within the error limits 01 the theoretical determination of thermal velocities, Assuming 1, z IO6 cm set- i andKs = (5k3)X lo-5 cm2 set -l. we find u = 5 x lo-l1 cm2. a very large cross section which is comparable to that predicted by a simple Langevin theory for electronhole recombination [7]. Since the singlet excitoncharge carrier interaction is presumably dominated by a dipole-charge carrier interaction it is considerably weaker and of shorter range than the coulomb interaction involved in electronhole recombination. Thus, the magnitudes of KS reported indicate that the carrier thermal ve-
F I =
L April 1971
I
i 0.2 % t
O!A
0
I
I
I
I
I 2 3 4 5 x D’o cm-’ Free Carrier Density
Fig. 2. Variation of the decrease in deIa>-sad fluorescence intensity (inctuding corrections for carrier trapping) with the free carrier densitr;. locity is greater than the exciton velocity. and that the electron-hole cross section may have been underestimated. Detailed studies of doped crystals and temperature eEEects at present under investigation
should cIarify
this situation.
The authors wish to thank Yves Lupien for the crystals.
growing
RE FEREINCES ill W.HeLfrich. Phvs.Rev.Letuxs 16 (1966) 401. iZi N. Wotherspoon: M. Pope and J. Bu&os.~ Chem. Phvs. Letters 5 (1970) 453. [31 W.‘Helfrich and W.G.Schneider. Phya. Rev. Letters 14 (1965) 229. [al R. G.Kepler. J. C. Caris. I?. Avakian and E. Abrameon. Phys. Rev. Letters 10 (1963} 400. (5) N. F. Mott and R. W. Gurney. ELectronic processes in ionic cr_vstals (Clarendoo Press. Oxford. 1940). [S] S. Singh. W. J. Jones. W. Siebrand. B. P. Stoicheff and W.G.Schneider. J. Chem. Phys. 42 (L965) 330. [71 M.Silver and R.Sharma. J.Chen. Phys. -16(1967’) 692. [f3] R.Silbey. J. Jortner. S.X. Rice and EkT. Vala. J. Chem.Phys. 4.2 (1965) 733. (91 S.A. Rice and J. Jortner. Physics and chemistq- of organic solid state. Vol. 3 (Lntcrscience. New York. 1967) p. 359: M.Trltfaj. Czech.J.Phys. 6 (1956) 533: 8 11958) 510.
47
SINGLET
CHEMICAL PliYSICS LETTERS
EXCITON-CHARGE
Dicision
CARRIER
INTERACTION
L April 1971
IN
ANTHRACENE
N. WAKAYAMiS and D. F. WILLIAMS of Chemistry, Nctional Research Council of Canada, Otfarta. Cana& Receivad 23 November 1970
The singlet exciton-charge carrier annihilation rate constant KS has been measured CLSXi x 10-5cm3 set-1 for hoies and electrons. The mngnitude of Ks is discussed with respect to the magnitude of rhc electron-hole recombination rate constant.
Although
exciton-enciton
and carrier-carrier
interactions have been investigated extensively. little work has been reported concerning the kinetics of exciton annihilation by charge carriers_ IIelfrich [l] determined the triplet exciton-e:ectron annihilation rate constant, and Wotherspoon et al. [2] have noted a modulation of fluorescence by trapped holes. In this paper we report the results of experiments involving singlet and triplet exciton annihilation by both holes and electrons. The crystals were cleaved 11ab plane from high purity ingots, which always had tripiet exciton lifetimes in excess of 25 msec. Either holes or electrons were injected into these crystals by means of the rewective injecting contacts [1,3] together with a transparent non-injecting counter electrode. Solution electrodes were in fact used for several of these measurements. although no difference was found for solid electrodes. Since it has been observed that many electrodes normally blocking will inject carriers under high density space-charge-limited currents, great care was taken to ensure no electroluminescence developed in the contact combinations used. Specifically, concentrated sodium hydroxide was used as the electron injection counter electrode and aqueous sodium chloride as the hole injection counter electrode. Currents 01 up-to 10-5 A/cm2 could easily be obtained The crystal complete with electrodes was then placed in a fast phosphoroscope (excitation and observation periods of 0.2 msec, dead time 0.9 msec), such that either a laser shone through the transparent electrode and the delayed fluorescence emfttlng from the crystal side was monitored, or this geometry:was reversed. A cold 95588 photomultiplier together with the necessary voltage supply, amplifier, time constant and r&corder!
or time averaging computer served as the delayed fluorescence detector system. A high power Xe-Ne laser was used as the excitation source since this will produce a uniform density of either singlet or triplet excitons throughout the crystal. The laser intensity was monitored throughout the experiment. The change of fluorescence was then measured as a function of crystal current with both increasing and decreasing voltages. The concentration of triplet excitation in anthracene is governed by the well-known equation 1418 dnT -=c&-@zT-~?z;. dt
(1)
where 3 is the excitation intensity, no is the triplet exciton density. and @ and y are the mono and bimolecular decay constants, respectively. Under low illumination intensities. monomolecular triplet decay dominates. 139 >> ytz$. and the very weak delayed fluorescence decays exponentially. To show these kinetic conditions were applicable, it was always checked that the deiayed fluorescence was proportionaL to the square of the laser intensity. This delayed fluorescence results from the formation of singlei excitons by triplet-triplet annihilation, the yq term in eq. (1). Under these circumstsnces. the interaction of the triplet exciton with charge carriers was determined by monitoring (a) tte steady-state delayed fluorescence intensity, or (b) the deIayecJ fluorescence decay rate or (c) the steady-state phosphorescence intensity or (d) the phosphorescence decay rate all as a function of the free carrier density. High voltages applied in a reverse bias to the crystal did not affect either a. b. c or d showing these effects were
Volume 9, number 1
CHEMICAL PHYSICS LETTERS
1 April 1971
solely due to the injected carriers. These results will be discussed in a separate paper; however, the triplet exciton-hole (or electror) interaction rate constant was always found to be about lo-%m3sec-I. With high laser intensities. the linear ter,n in eq. (1) may be neglected, and the delayed fluorescence intensity I under steady-state conditions is then given by I = f$Qru,
(2,
where Q is the fluorescence quantum efficiency. o[ the absorption coefficient of the exciting light with intensity. and J a numerical factor (0 C/C 1). The delayed fhorescence is linearly proportional to the laser intensity under these kinetic conditions. and this was experimentally verified. Under these conditions the quenchire of fluorescence is not caused by the triplet-carrier interaction, since even under high currents p’nT+=yn + where @‘)-I is the reduced triplet lifetime. Thus the fluorescence quenching is due either to a change iny. which seems unlikely, or is due to a decrease in the fluorescence quantum efficiency Q presumably by a dipole-carrier interaction. With high currents. -10-6 A. 1~12, the fluorescence intensity could be reduced by =60’%. Since the crystal dimensions. electrode area and crystal currents are known. the total carrier density (_Nt)and free carrier density (Nf) of either
radiative decay constants of the unperturbed crystaL Thus (kl + kz)-l is actually the observed singlet exciton lifetime including reabsorption effects, and this has been shown lo be about 25 nsec [6]. It was experimentally found (fig. 1) that the fluorescence intensity decrease (Z. - Zj/l = K(hqt (RI+ k2) was proportional to the total carrier concentration, and to the laser intensity under the higii intensity condition, showing that the interaction was indeed bimolecular. Thus we can put K(N) = K,Nt. In fact a slight superlinearity in this dependence was often observed at high currents. The interaction rate constant is then
holes or electrons which cause the measured decrease in fluorescence can be calculated from
ezsily obtained versus carrier
the equations are present.
1. because
[5].
assuming
only shallow
traps
Ocnsify
Carrier
Fig. 1. Fluorescence intensity change (IO-o/I versus free carrier density i 0) and tot.4 carrier density (0). The slope gives K M =z Uz~Nt(&l-kp) = 1.43 r: lo- I 2NtQC.1 +k2) = 5.7 x 10-s+.
K
3
=
from the fluorescence intensity density dependence shown in fig.
au,- m @I LfNtt)
. +
k2) .
Typical values for KS are given in table 1 toNf=N@.
(4)
where c is the crystal die!ectric constant, L the crystal thickness and 0 the ratio of the measured current to that predicted by Child’s law (trap free). 0 varied from ~1.0 - 10-d depending upon crystal preparation *. Assuming that the intera,rion of 2 singlet exciton with a charge carrier affords an additional mechanism for nonradiative exciton decay, the change of quantum yield of fluorescence with carrier density may be written as ’
-_ - kl t
kl
where kl and kz represent l
$1
k2 + I-C(N)’
the radiative and non-
The 8 of the dry~tal depends on the process Of growing. The detailed description
will be publiehed.
Tab!e 1 Values Of ~~ and B for various crystals
electron-singlet
(5 (3 (1 (1
- 7 ) - 8 ) - 2.2) - 10 )
exciton interactian
x10-4 x 10-3 x 10-2 x 10-2
hole-singlet
3 3 7 7
X 10-5 x 10’5 x 10-5 x 10-5
exciton interaction
1.3 x 10-3 (1.5 (2 i4 (3 -
2.2 2.2 8.8 5.7
) x lO-2 jXl0’2 ) x10-2 ) x 10-2
1.9 x 10-5 3.6 6.0 1.8 4
~10’~ x 10-5 x10-s x 10-5
CHEMICAL PHYSICS LETTERS
Volume 9, number 1 gether
with the approximate
9 values.
The con-
sistency of Ks. in comparison to 6 justifies the use of Nt in this analysis, whereas in evaluating Ktriplet, the density of free carriers is the pertinent parameter. In view of the large value of Ks. especialIy when compared to the accepted value for the electron-hole interaction parameter [7] =lO-fkm3sec -1, these results for h’s require further examination. Let us denote the reaction cross section between a carrier and singlet exciton as u, and let their respective thermal velocities be given by u and 1’. Then since this interaction is considered to be bimolecular. we may express the reaction rateK(N) as
= zqjl
- l9)a + ONtO(“f 2
324,
u
17’
Theoretically both u and v have been predicted to be about 106 cm see-l [ 8.91. For almost trapfree conditions, 3 ==1, the first term in eq. (7) may be neglected and where 8 << 1, the second term may be neglected_ The majority of the experimental results reported fall into the latter case, but at higher current densities this assumption becomes less valid. From eq. (7) and fig. 1 (which contains the experimental results which showed the greatest superlinearity). fig. 2 may be obtained. the slope ;f “h_:“h gives o(u+u9. 3~) = 1.6 x 10-4 cm set _ Thus the carrier velocities u are found tc be a factor of abogt 2.5 larger than the exciton velocities. This is well within the error limits 01 the theoretical determination of thermal velocities, Assuming 1, z IO6 cm set- i andKs = (5k3)X lo-5 cm2 set -l. we find u = 5 x lo-l1 cm2. a very large cross section which is comparable to that predicted by a simple Langevin theory for electronhole recombination [7]. Since the singlet excitoncharge carrier interaction is presumably dominated by a dipole-charge carrier interaction it is considerably weaker and of shorter range than the coulomb interaction involved in electronhole recombination. Thus, the magnitudes of KS reported indicate that the carrier thermal ve-
F I =
L April 1971
I
i 0.2 % t
O!A
0
I
I
I
I
I 2 3 4 5 x D’o cm-’ Free Carrier Density
Fig. 2. Variation of the decrease in deIa>-sad fluorescence intensity (inctuding corrections for carrier trapping) with the free carrier densitr;. locity is greater than the exciton velocity. and that the electron-hole cross section may have been underestimated. Detailed studies of doped crystals and temperature eEEects at present under investigation
should cIarify
this situation.
The authors wish to thank Yves Lupien for the crystals.
growing
RE FEREINCES ill W.HeLfrich. Phvs.Rev.Letuxs 16 (1966) 401. iZi N. Wotherspoon: M. Pope and J. Bu&os.~ Chem. Phvs. Letters 5 (1970) 453. [31 W.‘Helfrich and W.G.Schneider. Phya. Rev. Letters 14 (1965) 229. [al R. G.Kepler. J. C. Caris. I?. Avakian and E. Abrameon. Phys. Rev. Letters 10 (1963} 400. (5) N. F. Mott and R. W. Gurney. ELectronic processes in ionic cr_vstals (Clarendoo Press. Oxford. 1940). [S] S. Singh. W. J. Jones. W. Siebrand. B. P. Stoicheff and W.G.Schneider. J. Chem. Phys. 42 (L965) 330. [71 M.Silver and R.Sharma. J.Chen. Phys. -16(1967’) 692. [f3] R.Silbey. J. Jortner. S.X. Rice and EkT. Vala. J. Chem.Phys. 4.2 (1965) 733. (91 S.A. Rice and J. Jortner. Physics and chemistq- of organic solid state. Vol. 3 (Lntcrscience. New York. 1967) p. 359: M.Trltfaj. Czech.J.Phys. 6 (1956) 533: 8 11958) 510.
47