EFFECT OF EXCITON DIFFUSION AND REABSORPTION ON DECAY CURVE OF EXCITON LUMINESCENCE

(1)

HAL Id: jpa-00224960

https://hal.archives-ouvertes.fr/jpa-00224960

Submitted on 1 Jan 1985

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

EFFECT OF EXCITON DIFFUSION AND

REABSORPTION ON DECAY CURVE OF EXCITON LUMINESCENCE

H. Nishimura

To cite this version:

H. Nishimura. EFFECT OF EXCITON DIFFUSION AND REABSORPTION ON DECAY CURVE OF EXCITON LUMINESCENCE. Journal de Physique Colloques, 1985, 46 (C7), pp.C7-55-C7-59.

�10.1051/jphyscol:1985711�. �jpa-00224960�

(2)

JOURNAL DE PHYSIQUE

Colloque C7, suppl6ment au nOIO, Tome 46, octobre 1985 page C7-55

E F F E C T OF E X C I T O N D I F F U S I O N AND REABSORPTION ON DECAY CURVE O F E X C I T O N LUMINESCENCE

H. Nishimura

Department of Applied Physics, Osaka City University, Swniyoshi-ku, Osaka 558, Japan

Abstract - Well-known wavelength-dependent decay time of exciton luminescence is interpreted in a model based on exciton diffusion and reabsorption of the short wavelength of the luminescence spectrum. The decay curves of the singlet-exciton luminescence in anthracene, depending on wavelength, experimental geometry and penetration depth of incident light, are simulated very well by the model.

I - INTRODUCTION

Wavelength-dependent decay time of free exciton luminescence emitted in the fundamental absorption edge region has been extensively studied in semiconductors /1,2/ and molecular crystals /3-9/. In the studies, it has been shown that the decay times at the short wavelengths of the luminescence spectrum are shorter than the decay times at the long wavelengths. This fact has been interpreted in two different concepts;

(1) reabsorption at the short wavelength of the exciton luminescence /3-7/ and (2) relaxation of exciton polariton distribution in momentum space /1,2,8,9/. In the

second interpretation, polariton distribution has been assumed to be uniform in real space. In the present study for anthracene at room temperature, several facts which are inconsistent with the interpretations and assumption are presented; (1) the wavelength dependent decay time occurs only when the luminescence is excited in the one- photon absorption process and observed at the front crystal surface on which the

exciting light is irradiated, (2) at the back surface, the decay time is independent of the wavelength, and time delays are observed in the decay curves at the short wavelengths of the spectrum and (3) when the excitons are generated uniformly in the crystal in the two-photon absorption process, the wavelength-dependent decay time does not occur even at the front surface. These facts suggest that the relaxation of exciton distribution in real space should be considered to interpret the wave-

length-dependent decay time. In the present study, the diffusion equation is assumed to describe the relaxation of the exciton distribution in real space, and a new model based on exciton diffusion and wavelength-dependent reabsorption of exciton luminescence is proposed.

I1 - EXPERIMENTAL

The fundamental wave (580 nm) and the second harmonic (290 nm) of rhodamine 6G dye laser light pumped with an excimer laser (Lambda Pkiysik EMGSOMSC, FL2002) were used as pulsed excitation sources. The time durations of the 580 nm light and 290 nm light are 6 and 5 ns, respectively. The intensity of the exciting laser beam was attenuated by neutral density filters to avoid crystal damage and high density gener-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985711

(3)

C7-56 JOURNAL DE PHYSIQUE

ation of excitons. Sample crystals of anthracene were freely suspended in air by an adhesive tape to allow measurements of luminescence emitted from the front and back surfaces of the sample. Sample thicknesses were estimated from the b-polarized opti- cal density in the absorption edge region and with a michrometer. The incident light beam was directed to be perpendicular to the ab crystal face, and the b crystal axis was arranged to the polarization direction of the incident light. Luminescence from samples was detected with a photomultiplier tube (Hamamatsu Photonics R-955) through a grating monochrcmator (Nikon P-250). Decay curves of luminescence were measured using a nano second time-resolved fluorescence spectrophotometer in the Instrument Center, Institute for Molecular Science, Okazaki.

00 00 00 *o *o ro sogo o o o o o o tF 290 nrn EXCITATION r

l l

> lo 293 K *.*.* TB

W o 1.30 urn

Fig. 1

-

Luminescence spectra I and decay times r of an anthracene crystal 30 pm thick, and the b-polarized absorption spectrum K.

- -

g 2 - In z

W + f

% I - Z W U In W z

z ⁰

I11

-

^RESULTS

-

- O ~ ~ " ' ~ " ' ! ~ " " ~ ~ " ' ~ ~ '

(0.1) I

-

^3x105⁵

... _{- 1} U

g

...

"4.... 'c' . . I

Figure 1 shows the luminescence spectra and decay times of an anthracene crystal with the size of 10x10x0.03 mm3 observed under 290 nm excitation and at 293 K. The

luminescence is strongly polarized along the b crystal axis (P=0.7 at 405 m ) . The b-polarized absorption spectrum measured in a sample 7 um thick is shown in the

figure. The solid curve in the absorption spectrum is the one reported by Matsui and Ishii /lo/ who have obtained it from the Kramers-Kronig analysis of a reflectance spectrum. The lwninescence spectrum and decay time depend on the experimental geometry. In the backward-scattering geometry, the decay times TB show wavelength dependence. The decay times at the short wavelengths are smaller than the decay times at the long wavelengths. In the forward-scattering geometry, however, the decay times T~ are independent of the wavelength and are equal to the decay times T~ at the long wavelengths. The luminescence spectrum also depends on the experimental geometry.

The 0-0 and 0-1 intramolecular vibrational bands in the spectrum IF observed in the forward-scattering geometry have the peaks which are shifted to the longer wavelength than those in the spectrum IB in the backward-scattering geoxetry.

The luminescence spectrum and decay times excited in the two-photon absorption process (580 nm excitation), in which the excitons are generated uniformly in the crys-' tal, are shown in Fig. 2. In this case, the spectrum and decay time are independent of the experimental geometry, and the wavelength-dependent decay time does not occur.

The decay curves of the exciton luminescence in the one-photon absorption process (

290nmexcitation) are observed as a function of the luminescence wavelength. The typical decay curves observed in the backward- and forward-scattering geometries are shown in Figs. 3 and 4. When the decay curves are observed at the wavelength longer than 430 nm, where the crystal is almost transparent, they show a single exponential form with a decay time of 20 ns, and depend neither on the wavelength nor on the experimental geometry. However, when the decay curves are observed at the wavelengths shorter than 430 nm, where the crystal is less transparent, they depend on both the wavelength and experimental geometry; in the backward-scattering geometry, the decay curves show nonexponential form with shorter decay times than 20 ns, while in the

450 400 350 0

3 500 300 (nrn) -l

WAVELENGTH

(4)

.o .o .o .o .o mo .o 00. o m 0.0.0. TWO PHOTON EXCITATION ( 580 nrn 1 'C8

u 293 K

W

0 ^O 'CF

1.30 urn

- o ~ " " ~ " ' ! ~ ' ~ " ~ " ' * ~ ~ '

-

- ^Y

-

^3x10'^F

5 = -

z

W

W l - U

Y

WU V) W

300 (nrn) WAVELENGTH

Fig. 2 - Luminescence spectrum I and decay times r of an anthracene crystal 30 um thick, under the excitation in the two-photon absorption (580 nm) at 293 K.

Fig. 3 - Decay curves in the backward- Fig. 4 - Decay curves in the forward- scattering geometry. scattering geometry.

forward-scattering geometry the decay curves show single exponential forms with different time delays (%lo ns at A<405 nm). The decay time in this case is 20 ns. The decay curves in the two-photon absorption process (580 nm excitation), on the other hand, are observed to be independent of the experimental geometry and wavelength.

The decay curves show a single exponential form with the decay time of 20 ns. No time delay, other than the delay due to detection system, is observed in the decay curves.

IV - DISCUSSION

The present results at room temperature would show the significance to take account of the relaxation of the exciton distribution in real space, since the results, decay times and spectra, depend on the experimental geometry and on the penetration depth of the-incident light. To describe the relaxation of the exciton spatial distribution, the diffusion equation is assumable. The diffusion equation is a good expres- sion for an exciton energy propagation when radiative part in the energy propagation is insignificant. If the radiative part is significant, the diffusion of exciton spatial distribution deviates more or less from the form in the diffusion equation.

In anthracene, this deviation seems to be negligible for the follou-ing reasons, (1)

(5)

C7-58 JOURNAL DE PHYSIQUE

the overlap between the luminescence and absorption spectra is not significant (see Fig. l), (2) the radiative propagation length must be very small (<1 pm) compared with the excito diffusion length ($14 urn) because of the large absorption coefficient (>lo4 an-') for the luminescent photons in the short wavelength region in which the overlap is considerable, and (3) the exciton lifetime (20 ns) is longer than the diffusion time (%lo ns) of the excitons through the crystal. (The estimations of the exciton-diffusion length and time will be shown later). Accordingly, it can be imag- ed that the excitons diffusing in the crystal are transformed into photons as an in- ternal conversion of an exciton into a photon and part of the photons at the short wavelengths of the luminescence spectrum are reabsorbed before they reach crystal surface. In detail, when the excitons are generated in the vicinity of the crystal surface by a pulsed light excitation and diffuse in the crystal, it is expected that the short wavelengths of the luminescence spectrum become unobservable at the front surface as the excitons leave from the front surface, because of reabsorption, so that the decay time TB observed at the front surface is shorter than the exciton lifetime TO. Contrary, at the back surface, the short wavelengths, unobservable at first, become observable as the excitons approach to the back surface, so that time delays appear in the decay curves with the decay time TO. On the other hand, the

long wavelengths of the luminescence spectrum are observable at both the front and back surfaces without being restricted, because of the crystal transparency in the wavelength region. In this case, the decay times rB and rF are coincident with the exciton lifetime TO. Furthermore, when the excitons are generated uniformly in the crystal in the two-photon excitation (580 nm), the decay curves of the exciton luminescence is expected to show a single exponential form with TO, irrespective of the luminescence wavelength and experimental geometry, because the initial uniform distribution of the excitons does not diffuse with time progression. These expectations are consistent with the experimental results.

Decay curves, therefore,are expected to be simulated using the one dimensional diffusion equation,

and using time dependent intensities of the exciton luminescence emitted from the front IB(t) and back IF(t) surfaces,

a a

IB(t) = (Otn(x,t)/~O)e-KIX dx, IF(t) = ~o{n(x,t)/~O)e - K ~ (9.-x) d x , (2) where, the decrease of the luminescence intensity due to readsorption, dependent on wavelength, is considered. In eq. (11, x is chosen to be perpendicular to the ab crystal face. D and TO are diffusion coefficient and lifetime of excitons. n(x,t) describes the distribution of excitons along the x direction at time t. In eq. (2), 8 is the crystal thickness' and K1 is the absorption coefficient for the luminescent photons. The boundary condition at the crystal surfaces at x=O and x=ll, and the initial spatial distribution of the excitons along the x direction at t=O are given, respectively, by

-K2X

an(x,t)/ax = 0, and n(x,O) = noe , (3)

where, K~ is the absorption coefficient for the exciting light. The solution of the diffusion equation for the boundarz and initial conditions is

n(x, t) = e-t/TO ? Cke-D(kn/a) tcos (kvx/a) ,

k=O

k - K t .

where, Ck = (2nO/K2R) {1-(-1) e }/[l+(kn/K2R) '1, and CO = Ck/21k,0. ( 4 ) BY substituting n(x, t) into eq. (2) , wavelength-dependent decay curves, IB(t) and IF(t) , are obtained as

-K R

1 (t) = (no/K1~2R~o) (1-e 1 (1-e-K2a)e-t/T~

B

+,z1

^(Ck/K1~O)^111-(-1)ke-K1a~/{l+(k~/~l~) 2 ~ 1 e- ~ C D (kr/R) 2 + l / ~ o ~ , ₍_{5 )}

k -K a

+k?'l(ck/~l~o) L { (-1) -e 1 }/{l+(kn,~~~) 21, e-t'D(kn")2+1'7~'. (6)

Using nqs. (5) and (61, the decay curves measured are simulated very well as shown by the solid curves in Figs. 3 and 4. In the simulations, the values for K2, TO and R

(6)

were assumed to be 6 x 1 0 ~ cm-l, 20 ns and 30 vm, respectively. From the best fit, the only one unknown parameter D, the diffusion coefficient perpendicular to the ab crystal face, is determined to be 100 cm2s-l. From the values of D and TO, the exciton diffusion length

L=G

is estimated to be 14 Um. The value of D obtained here at 293 K is very much larger than the value, (1052) cm2s-l, along the a crystal axis which has been obtained at 1.8 K in a picosecond transient grating method by Rose et al./ll/. The larger value of D at higher temperature would show that the motion of the exciton at high temperature is diffusive and is assisted by phonons as is the case in an activated situation rather than hindered by them.

The decay curves measured in the two-photon absorption process (K2<0.1 cm-l) show a single exponential form with TO, irrespective of the wavelength and experimental geometry. This result is also simulated very well by eqs. (5) and (6) for K2=0.1 cm-l, namely, the simulated decay curve is a single exponential form with TO and independent of the values of K1, D and ..9

In the one-photon absorption process, the decay curves IF(t) measured at the wavelengths shorter than 405 nm show a time delay of about 10 ns for a sample 30 vm thick

(see Fig. 4). This time delay corresponds to the diffusion time of the exciton through the crystal along the x-axis, since the time delay in the simulations by eq.

(6) is larger for smaller value of D and for larger value of L.

Thus, the present model based on exciton diffusion and reabsorption of the short wavelength photons of the luminescence, is quite consistent with the experimental results. This consistency confirms the assumption in the model, that reabsorption of the short wavelength photons does not give rise to deviation of the exciton spatial distribution from the diffusion form. In the simulations, nonradiative decay of the exciton has not been considered, since the quantum yield of the exciton luminescence is nearly unity. In such a case, the decay time of the exciton luminescence repre- sents the radiative decay time, namely, intrinsic lifetime TO of the exciton.

For anthracene crystal, there is a trend to use thin crystals and powders instead of using thick crystals to measure the intrinsic lifetime of the exciton. usually, thin crystals and powders show a fairly short decay time of the exciton luminescence, while thick crystals show long decay time. The short decay time has been commonly considered to be intrinsic and the long one to be due to reabsorption effect, for the reason that thick crystals show strong reabsorption effect in the luminescence spectrum and thin crystals show less reabsorption effect. However, the luminescence spectrum of thick crystals is substantially the same as those of thin crystals and powders, when the luminescence is observed in the backward-scattering geometry and under the excitation by the light with small penetration depth /12/. Therefore, the dependence of decay time on sample size seems to be not attributed to reabsorption.

The short decay time in thin crystals and powders is rather likely to be attributed to the effect of crystal surface on decay time, since the probability of the excitons to be found at the crystal surface where the exciton lifetime is probably shorter than that in bulk, is larger in thinner crystals. Accordingly, it is concluded that the intrinsic lifetime of the singlet exciton in anthracene at room temperature is 20 ns in thick crystals rather than the small velue in thin crystals.

REFERENCES

/1/ Wiesner, P and Heim, U., Phys. Rev. (1975) 3071.

/2/ Askary, F and Yu, P. Y., Phys. Rev. B28 (1983) 6165.

/3/ Kobayashi, T. and Nagakura, S., Mol. Cryst. Liq. Cryst. 26 (1974) 33.

/4/ Gammill, L. S. and Powell, R. C., Mol. Cryst. Liq. Cryst. 25 (1974) 123.

/5/ Bateman, R. J., Chance, R. R. and Hornig, J. F., Chem. Phys. 4 (1974) 402- /6/ Galanin, M. D., Khan-Magometova, Sh. D., Chizhikova, Z. A . , ~ G c h u k , M. I. and Chernyavskii, A. F., J. Luminescence 9 (1975) 459.

/7/ Bale, A. G., Bridge, N. J. and Smith, D. B., Chem. Phys. Lett. 42 (1976) 166.

/8/ Galanin, M. D. and Khan-Magometova, Sh. D., J. Luminescence 18/19 (1979) 37.

/9/ ~alanin, M. D., Khan-Magometova, Sh. D. and Myashikov, E. N., Mol. Cryst. Liq.

Cryst. 51 (1980) 119.

/lO/Matsui, A. and Ishii, Y., J. Phys. Soc. Jpn. 3 (1967) 581.

/11/Rose, T. S., ~ighini, R. and Fayer, M. D,, Chem. Phys. Lett. 106 (1984) 13.

/l2/Nishimura, H., Yamaoka, T., Hattori, K., Matsui, A. and Mizuno, K., unpublished.