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Spectral and electrical investigations of triplet excitons on pulsed electron excitation of molecular crystals
R&fiat. Phys. Chem. Vol. 15, pp. 613-616 Pergamon Press Ud.. 1980. Printed in Great Britain
SPECTRAL AND ELECTRICAL INVESTIGATIONS OF TRIPLET EXCITONS ON PULSED ELECTRON EXCITATION OF MOLECULAR CRYSTALS A. K. KOSTIN and A. V. VANNIKOV Institute of Electrochemistry of Academy of Sciences of USSR, 117071 Moscow, Leninskii prospect, 3 I, U.S.S.R. (Receioed I5 November 1978)
Abstract-Excitation
of molecular crystals by the pulse of fast electrons results in volume generation of triplet excitons. The spectrum of optical absorption in T+T, of triplet excitons has been recorded. The maximum cross section of interaction of a light quantum with a triplet exciton is 4.6 x lo-” cm*. Annihilation of triplet excitons T + T 3
p + e with a probability ‘P,,~= 5 X tom4
leads to the formation of free charges.
OPTICAL
EXCITATION
Of
mOkCUkU
CQ’StiS
S,t& T,tSo) causes the formation of Frenkel triplet excitons. The values of concentration of triplet excitons achieved permit studying photoelectric phenomena and the kinetics of luminescence of lower exciton states (S, +SO. T,+S,,). Investigations of optical absorption are associated with generation of. considerable ’ concentration of triplet excitons in the crystal. The optical density measured is a function of the concentration of triplet excitons nT (T,-
single crystals of anthracene and stilbene on excitation by a pulse of a linear electron accelerator (E, = 4 MeV, ~~~~~~40 x 10m9s,D L- 10” eV cm-? and into photoconductivity on excitation by a laser pulse (A = 337.1 nm, 7PU~se = 10 X 10m9s). The spectral measurements were carried out in the region of 2.6-0.87 x IO’ cm-’ by the method of fast absorption spectrospectroscopy with photoelectric detection of the signal in the pass band Af=7MHz (4)
(1)
D(t) = IWIT(
which determines sity
the half-life of the optical den-
W)
=
= In 11 - AJ/.J,(o,t)]
where AK(o,t) is the change in absorption coefficient; AJ is the variable component of the current signal; .I,, is the photomultiplier current; t is the time, and w is the light frequency. The electrical measurements were carried out in the pass band of 50 MHz, the current pulse j(t) = U(t)/R reflects the relaxation process in the crystal. The charge mobility was determined by measuring the time of drift of the photogenerated carriers through the crystal in the electric field, with the condition S = K-’ e d, where K is the absorption coefficient, and d is the crystal thickness. All the experiments were conducted at a temperature of = 300 K using the technique described in.“’ The excitation of a anthracene single crystal by a pulse of accelerated electrons causes, in the spectral region of 1.3 - 2.5 x lO’cm_‘, short-lived optical absorption, which is accompanied by luminescence in the fluorescence region of the crystal
and the optical density is equal to (3)
- AK(N)8
K&77n,2)-‘S
where Km and rr1/2 is the annihilation constant and the half-life of the triplet excitons, K is the extinction coefficient, and 8 is the thickness of the exciton generation layer. The conditions necessary for optical measurements, which are hard to ensure under photoexcitation, can be realized by volume generation of triplet excitons by a pulse of ionizing radiation.“” The present investigation is a study into the spectral and electrical characteristics of molecular 613
614
A. K. KOSTINand A. V. VANNIKOV
(Fig. 1) and by a pulse of relaxation current, which has a rapid (j,) and a slow (jJ) component (Fig. 2). The luminescence time Tag,,, obeys the relation c 4 TI”,,,e R, where G and c are the lifetimes of the singlet and triplet excitons. Excitation by a laser pulse in the exciton absorption band of the crystal causes a photocurrent pulse. The transit time of the holes T&P) depends linearly on the electric field E-‘, which means that
Kd
01
the holes reach the electrode ity, which is determined by (5)
pP = ~/TTR(P)E
has a value pP = 0.5 ? 0.1 cm’ V’s_ in anthracene and EL,,= 2.2? 0.2 cm’ V’s_’ in stilbene. The duration of the electron photocurrent pulse 7, depends but slightly on E. The value of CL.can be determined from the condition n, = n,, by
je= em&
(6)
where je is the current density of the electron pulse, and cc, is equal to 0.1 r0.01 and 0.2? 0.02 cm?-‘s-’ in anthracene and stilbene, respectively. The experimental value of the electron lifetime TV is much less than the time of electron drift through the crystal TTR(e), which corresponds to the value of pe, which means that the free electrons are trapped by the defects in the crystal volume, and T. corresponds to the time to trapping of the electrons. The obtained value of T. = 10;” are determined by the concentration of defects in the crystal. (7)
FIG. 1. Optical absorption pulses. 1, experiment; 2, calculation by equation (15), 3, experimental luminescence pulse; 4, kinetics of charge recombination n(t) calculated by equation (8); 5, kinetics of reduction in optical density (Kd)-’ (1); 6, kinetics of luminescence decay I-“(t).
and the drift mobil-
nd, = (WT.)-’ = lOI cmm3
where u is the cross section of electron interaction with the defect, and Y is the electron velocity in the conduction band. The value p = pP + CL, makes it possible to determine the volume concentration of the charges, using the value of the relaxation current. In the case of recombination luminescence the decay must obey the charge relaxation kinetics. Since 7.4 Tjc1/2) + 7&p) and cupP pCLe,the determining process of relaxation of n(t) is the charge recombination
(8)
dn dt=
-epnZle60
where EELis the absolute dielectric constant of the crystal. It can be seen from Fig. 1 that the luminescence decay does not follow the kinetics of charge recombination. The knietics of luminescence decay is described by the equation (9) FIG. 2. Relaxation current pulses. 1, experiment: 2, calculation by equation (11); 3, j,(t), the difference between curves 1 and 2; 4, calculation by equation (12); 5, kinetics of slow component j;‘(t).
I(t) -
2 =- Km&&
where K,, and no, are the annihilation constantC5-” and the concentration of triplet excitons, which means that the luminescence corresponds to
615
Spectral and electrical investigations of triplet excitons
delayed excitons
fluorescence
in annihilation
of triplet
T+TKTT-SO+S~sO+hY a,
(10)
cps is the probability of formation of S on annihilation of triplet excitons. Extrapolation of P’(t) to t = 0 gives a value no, = lOI cmm3, which corresponds to the radiation yield per 1OOeV of absorbed energy G(T) = 6.9 f 1.7 in anthracene and 3.620.7 in stilbene. Calculation of the kinetics of charge relaxation, taking into account the shape of the exciting pulse, for instance for anthracene
where Gti,=) is the radiation yield of charge pairs per 100 eV:***) shows that the rapid compnent of the pulse current jr(t) corresponds to recombination of the charges generated within the time of action of the exciting pulse (Fig. 2). The kinetics of the slow component of the relaxation current coincides with the kinetics of fluorescence decay I-“‘(t) and the kinetics of decay of the optical density (K&‘(t) (Fig. 1). The lifetime of the singlet excitons is much shorter than the half-life of the current signal and of the intensity of the delayed fluorescence TVQ 7j=cl/2) = ~~(~1~). The relaxation current curve is described by the equation (Fig. 2)
the stationary volume concentration of the singlet excitons with an allowance for their formation by the mechanism of (10) and disappearance as a result of conversion and annihilation shows that the relaxation current J. (t) is not determined by the annihilation of singlet excitons. The formation of an ion pair may be the result of direct excitation of an electron into the conduction band of the crystal on annihilation of triplet excitons (2ET 5 E, for anthracene) or, which is more probable, is associated with the interaction of a singlet exciton with a crystal defect, whose concentration, according to the pulsed-photoconductivity measurements, is equal to n# = lOI cm-3.(2+ The kinetics of decay of the optical density is described by the equation (Fig. 1).
where K is the extinction coefficient, nT is the concentration of triplet excitons, determined by the decay kinetics of fluorescence and satisfying the equation of the relaxation current curve. The maximum cross section of the interaction of a light quantum with a triplet exciton is r)= 4.6 X lo-” cm. The integral JKdv of the experimental spectrum yields the value of the oscillator strength of the optical band f = 0.4. With respect to the So -level, the positions of the maxima in the optical absorption spectrum, e.g. of an anthracene crystal, correspond to Ei - 3.8, 3.9, 4.1 eV. The obtained value of the absorption coefficient Kymar (Fig. 3) shows that optical absorption is associated with T, + T, transitions of triplet excitons, as in a napthalene single crystal.“’ Kd
which corresponds to charge formation hilation of triplet excitons
on anni-
T+Tzp+e
(13)
where (pp.== 5 x lO+ IS ’ the probability of charge formation on annihilation of triplet excitons. The Vale Of (pp.= corresponds to the probability of charges escaping beyond the Coulomb radius R, of an ion pair with the initial Q&C = exp (-R/r), distance between the charges. (14)
e*
p=6%,,KT
In
01
. .
% 14 X IO-* cm
I.5
2.0
(pp.= Y
where &, is the average value of the absolute high-frequency dielectric constant. Estimation of RPC Vol. 15, No. 5-C
Frc. 3.
Spectra
25
-
x ICi~cm-
of absorption of triplet exciton. 1, anthracene; 2, stilbene.
616
A. K. Kosn~ and A. V. VANNIKOV
As has been shown, under the conditions of the experiment carried out, the excitation of molecular crystals by a pulse of accelerated electrons leads to volume generation of triplet excitons. The formation of triplet excitons is evidently mainly determined by direct excitation by fast electrons of the optically forbidden TI + So transition and the electron-hole pair recombination. Annihilation of triplet excitons with a probability r~,,~= 5 X lo4 results in charge formation. REFERENCES 1. M. HIGLJCHI T. NAKAYAMA and N. ITOH.J. Phys. Sot. Japan 1976,40,250.
2. A. K. KO~IN, V. V. SAVEL’EVand A. V. VANNIKOV, Fiz. Tverd. Tela 1978,20,871. 3. A. K. Kosrr~, V. V. SAVEL’EVand A. V. VANNIKOV, Phys. Stat. Sol. (b) 1978,87, 255. 4. A. K. KOSI-INand A. V. VANNIKOV,Fur. Tverd. Tela 1978,20,3407. 5. P. AVAIUANand R. E. MERRIFIELD, Mol. Cryst. 1968,5, 37. 6. T. A. KING and R. VOLTZ.Proc. R. Sot. Series A, 1966,289,424. 7. R. G. KEPLER,Treatise on Solid State ChemistryCrystalline and Noncrystalline Solids (Edited by N. B. Hannay). Vol. 3, pp. 615678. Plenum Press, New York 1976. 8. P. MARKand W. HELFIUCH.J. Appl. Phys. 1%2, 33, 205.
SPECTRAL AND ELECTRICAL INVESTIGATIONS OF TRIPLET EXCITONS ON PULSED ELECTRON EXCITATION OF MOLECULAR CRYSTALS A. K. KOSTIN and A. V. VANNIKOV Institute of Electrochemistry of Academy of Sciences of USSR, 117071 Moscow, Leninskii prospect, 3 I, U.S.S.R. (Receioed I5 November 1978)
Abstract-Excitation
of molecular crystals by the pulse of fast electrons results in volume generation of triplet excitons. The spectrum of optical absorption in T+T, of triplet excitons has been recorded. The maximum cross section of interaction of a light quantum with a triplet exciton is 4.6 x lo-” cm*. Annihilation of triplet excitons T + T 3
p + e with a probability ‘P,,~= 5 X tom4
leads to the formation of free charges.
OPTICAL
EXCITATION
Of
mOkCUkU
CQ’StiS
S,t& T,tSo) causes the formation of Frenkel triplet excitons. The values of concentration of triplet excitons achieved permit studying photoelectric phenomena and the kinetics of luminescence of lower exciton states (S, +SO. T,+S,,). Investigations of optical absorption are associated with generation of. considerable ’ concentration of triplet excitons in the crystal. The optical density measured is a function of the concentration of triplet excitons nT (T,-
single crystals of anthracene and stilbene on excitation by a pulse of a linear electron accelerator (E, = 4 MeV, ~~~~~~40 x 10m9s,D L- 10” eV cm-? and into photoconductivity on excitation by a laser pulse (A = 337.1 nm, 7PU~se = 10 X 10m9s). The spectral measurements were carried out in the region of 2.6-0.87 x IO’ cm-’ by the method of fast absorption spectrospectroscopy with photoelectric detection of the signal in the pass band Af=7MHz (4)
(1)
D(t) = IWIT(
which determines sity
the half-life of the optical den-
W)
=
= In 11 - AJ/.J,(o,t)]
where AK(o,t) is the change in absorption coefficient; AJ is the variable component of the current signal; .I,, is the photomultiplier current; t is the time, and w is the light frequency. The electrical measurements were carried out in the pass band of 50 MHz, the current pulse j(t) = U(t)/R reflects the relaxation process in the crystal. The charge mobility was determined by measuring the time of drift of the photogenerated carriers through the crystal in the electric field, with the condition S = K-’ e d, where K is the absorption coefficient, and d is the crystal thickness. All the experiments were conducted at a temperature of = 300 K using the technique described in.“’ The excitation of a anthracene single crystal by a pulse of accelerated electrons causes, in the spectral region of 1.3 - 2.5 x lO’cm_‘, short-lived optical absorption, which is accompanied by luminescence in the fluorescence region of the crystal
and the optical density is equal to (3)
- AK(N)8
K&77n,2)-‘S
where Km and rr1/2 is the annihilation constant and the half-life of the triplet excitons, K is the extinction coefficient, and 8 is the thickness of the exciton generation layer. The conditions necessary for optical measurements, which are hard to ensure under photoexcitation, can be realized by volume generation of triplet excitons by a pulse of ionizing radiation.“” The present investigation is a study into the spectral and electrical characteristics of molecular 613
614
A. K. KOSTINand A. V. VANNIKOV
(Fig. 1) and by a pulse of relaxation current, which has a rapid (j,) and a slow (jJ) component (Fig. 2). The luminescence time Tag,,, obeys the relation c 4 TI”,,,e R, where G and c are the lifetimes of the singlet and triplet excitons. Excitation by a laser pulse in the exciton absorption band of the crystal causes a photocurrent pulse. The transit time of the holes T&P) depends linearly on the electric field E-‘, which means that
Kd
01
the holes reach the electrode ity, which is determined by (5)
pP = ~/TTR(P)E
has a value pP = 0.5 ? 0.1 cm’ V’s_ in anthracene and EL,,= 2.2? 0.2 cm’ V’s_’ in stilbene. The duration of the electron photocurrent pulse 7, depends but slightly on E. The value of CL.can be determined from the condition n, = n,, by
je= em&
(6)
where je is the current density of the electron pulse, and cc, is equal to 0.1 r0.01 and 0.2? 0.02 cm?-‘s-’ in anthracene and stilbene, respectively. The experimental value of the electron lifetime TV is much less than the time of electron drift through the crystal TTR(e), which corresponds to the value of pe, which means that the free electrons are trapped by the defects in the crystal volume, and T. corresponds to the time to trapping of the electrons. The obtained value of T. = 10;” are determined by the concentration of defects in the crystal. (7)
FIG. 1. Optical absorption pulses. 1, experiment; 2, calculation by equation (15), 3, experimental luminescence pulse; 4, kinetics of charge recombination n(t) calculated by equation (8); 5, kinetics of reduction in optical density (Kd)-’ (1); 6, kinetics of luminescence decay I-“(t).
and the drift mobil-
nd, = (WT.)-’ = lOI cmm3
where u is the cross section of electron interaction with the defect, and Y is the electron velocity in the conduction band. The value p = pP + CL, makes it possible to determine the volume concentration of the charges, using the value of the relaxation current. In the case of recombination luminescence the decay must obey the charge relaxation kinetics. Since 7.4 Tjc1/2) + 7&p) and cupP pCLe,the determining process of relaxation of n(t) is the charge recombination
(8)
dn dt=
-epnZle60
where EELis the absolute dielectric constant of the crystal. It can be seen from Fig. 1 that the luminescence decay does not follow the kinetics of charge recombination. The knietics of luminescence decay is described by the equation (9) FIG. 2. Relaxation current pulses. 1, experiment: 2, calculation by equation (11); 3, j,(t), the difference between curves 1 and 2; 4, calculation by equation (12); 5, kinetics of slow component j;‘(t).
I(t) -
2 =- Km&&
where K,, and no, are the annihilation constantC5-” and the concentration of triplet excitons, which means that the luminescence corresponds to
615
Spectral and electrical investigations of triplet excitons
delayed excitons
fluorescence
in annihilation
of triplet
T+TKTT-SO+S~sO+hY a,
(10)
cps is the probability of formation of S on annihilation of triplet excitons. Extrapolation of P’(t) to t = 0 gives a value no, = lOI cmm3, which corresponds to the radiation yield per 1OOeV of absorbed energy G(T) = 6.9 f 1.7 in anthracene and 3.620.7 in stilbene. Calculation of the kinetics of charge relaxation, taking into account the shape of the exciting pulse, for instance for anthracene
where Gti,=) is the radiation yield of charge pairs per 100 eV:***) shows that the rapid compnent of the pulse current jr(t) corresponds to recombination of the charges generated within the time of action of the exciting pulse (Fig. 2). The kinetics of the slow component of the relaxation current coincides with the kinetics of fluorescence decay I-“‘(t) and the kinetics of decay of the optical density (K&‘(t) (Fig. 1). The lifetime of the singlet excitons is much shorter than the half-life of the current signal and of the intensity of the delayed fluorescence TVQ 7j=cl/2) = ~~(~1~). The relaxation current curve is described by the equation (Fig. 2)
the stationary volume concentration of the singlet excitons with an allowance for their formation by the mechanism of (10) and disappearance as a result of conversion and annihilation shows that the relaxation current J. (t) is not determined by the annihilation of singlet excitons. The formation of an ion pair may be the result of direct excitation of an electron into the conduction band of the crystal on annihilation of triplet excitons (2ET 5 E, for anthracene) or, which is more probable, is associated with the interaction of a singlet exciton with a crystal defect, whose concentration, according to the pulsed-photoconductivity measurements, is equal to n# = lOI cm-3.(2+ The kinetics of decay of the optical density is described by the equation (Fig. 1).
where K is the extinction coefficient, nT is the concentration of triplet excitons, determined by the decay kinetics of fluorescence and satisfying the equation of the relaxation current curve. The maximum cross section of the interaction of a light quantum with a triplet exciton is r)= 4.6 X lo-” cm. The integral JKdv of the experimental spectrum yields the value of the oscillator strength of the optical band f = 0.4. With respect to the So -level, the positions of the maxima in the optical absorption spectrum, e.g. of an anthracene crystal, correspond to Ei - 3.8, 3.9, 4.1 eV. The obtained value of the absorption coefficient Kymar (Fig. 3) shows that optical absorption is associated with T, + T, transitions of triplet excitons, as in a napthalene single crystal.“’ Kd
which corresponds to charge formation hilation of triplet excitons
on anni-
T+Tzp+e
(13)
where (pp.== 5 x lO+ IS ’ the probability of charge formation on annihilation of triplet excitons. The Vale Of (pp.= corresponds to the probability of charges escaping beyond the Coulomb radius R, of an ion pair with the initial Q&C = exp (-R/r), distance between the charges. (14)
e*
p=6%,,KT
In
01
. .
% 14 X IO-* cm
I.5
2.0
(pp.= Y
where &, is the average value of the absolute high-frequency dielectric constant. Estimation of RPC Vol. 15, No. 5-C
Frc. 3.
Spectra
25
-
x ICi~cm-
of absorption of triplet exciton. 1, anthracene; 2, stilbene.
616
A. K. Kosn~ and A. V. VANNIKOV
As has been shown, under the conditions of the experiment carried out, the excitation of molecular crystals by a pulse of accelerated electrons leads to volume generation of triplet excitons. The formation of triplet excitons is evidently mainly determined by direct excitation by fast electrons of the optically forbidden TI + So transition and the electron-hole pair recombination. Annihilation of triplet excitons with a probability r~,,~= 5 X lo4 results in charge formation. REFERENCES 1. M. HIGLJCHI T. NAKAYAMA and N. ITOH.J. Phys. Sot. Japan 1976,40,250.
2. A. K. KO~IN, V. V. SAVEL’EVand A. V. VANNIKOV, Fiz. Tverd. Tela 1978,20,871. 3. A. K. Kosrr~, V. V. SAVEL’EVand A. V. VANNIKOV, Phys. Stat. Sol. (b) 1978,87, 255. 4. A. K. KOSI-INand A. V. VANNIKOV,Fur. Tverd. Tela 1978,20,3407. 5. P. AVAIUANand R. E. MERRIFIELD, Mol. Cryst. 1968,5, 37. 6. T. A. KING and R. VOLTZ.Proc. R. Sot. Series A, 1966,289,424. 7. R. G. KEPLER,Treatise on Solid State ChemistryCrystalline and Noncrystalline Solids (Edited by N. B. Hannay). Vol. 3, pp. 615678. Plenum Press, New York 1976. 8. P. MARKand W. HELFIUCH.J. Appl. Phys. 1%2, 33, 205.