Light absorption by d-dimensional organic semiconductors under exciton transitions between broad bands
Within the framework of the dipole approximation the line-shape of light absorption for exciton transitions between broad bands in one-, two- and three-dimensional organic semiconductor structures are calculated. Exciton damping due to lattice imperfections is accounted for as a frequency independen...
Збережено в:
| Опубліковано в: : | Semiconductor Physics Quantum Electronics & Optoelectronics |
|---|---|
| Дата: | 1999 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
1999
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/117858 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Light absorption by d-dimensional organic semiconductors under exciton transitions between broad bands / N. I. Grigorchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 1. — С. 25-30. — Бібліогр.: 21 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-117858 |
|---|---|
| record_format |
dspace |
| spelling |
Grigorchuk, N. I. 2017-05-27T09:30:08Z 2017-05-27T09:30:08Z 1999 Light absorption by d-dimensional organic semiconductors under exciton transitions between broad bands / N. I. Grigorchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 1. — С. 25-30. — Бібліогр.: 21 назв. — англ. 1560-8034 PACS 71.35; 71.36; 78.20; S12 https://nasplib.isofts.kiev.ua/handle/123456789/117858 Within the framework of the dipole approximation the line-shape of light absorption for exciton transitions between broad bands in one-, two- and three-dimensional organic semiconductor structures are calculated. Exciton damping due to lattice imperfections is accounted for as a frequency independent parameter. The obtained analytical expressions allow analyses of the line-shape for different space dimensions of structure depending on bandwidth difference, damping parameter and temperature. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Light absorption by d-dimensional organic semiconductors under exciton transitions between broad bands Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Light absorption by d-dimensional organic semiconductors under exciton transitions between broad bands |
| spellingShingle |
Light absorption by d-dimensional organic semiconductors under exciton transitions between broad bands Grigorchuk, N. I. |
| title_short |
Light absorption by d-dimensional organic semiconductors under exciton transitions between broad bands |
| title_full |
Light absorption by d-dimensional organic semiconductors under exciton transitions between broad bands |
| title_fullStr |
Light absorption by d-dimensional organic semiconductors under exciton transitions between broad bands |
| title_full_unstemmed |
Light absorption by d-dimensional organic semiconductors under exciton transitions between broad bands |
| title_sort |
light absorption by d-dimensional organic semiconductors under exciton transitions between broad bands |
| author |
Grigorchuk, N. I. |
| author_facet |
Grigorchuk, N. I. |
| publishDate |
1999 |
| language |
English |
| container_title |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| format |
Article |
| description |
Within the framework of the dipole approximation the line-shape of light absorption for exciton transitions between broad bands in one-, two- and three-dimensional organic semiconductor structures are calculated. Exciton damping due to lattice imperfections is accounted for as a frequency independent parameter. The obtained analytical expressions allow analyses of the line-shape for different space dimensions of structure depending on bandwidth difference, damping parameter and temperature.
|
| issn |
1560-8034 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/117858 |
| citation_txt |
Light absorption by d-dimensional organic semiconductors under exciton transitions between broad bands / N. I. Grigorchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 1. — С. 25-30. — Бібліогр.: 21 назв. — англ. |
| work_keys_str_mv |
AT grigorchukni lightabsorptionbyddimensionalorganicsemiconductorsunderexcitontransitionsbetweenbroadbands |
| first_indexed |
2025-11-26T00:08:25Z |
| last_indexed |
2025-11-26T00:08:25Z |
| _version_ |
1850592162408824832 |
| fulltext |
25© 1999, Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Semiconductor Physics, Quantum Electronics & Optoelectronics. 1999. V. 2, N 1. P. 25-30.
PACS 71.35; 71.36; 78.20; S12
Light absorption by d-dimensional organic semiconductors
under exciton transitions between broad bands
N. I. Grigorchuk
Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Kyiv, 252028, Ukraine
Abstract. Within the framework of the dipole approximation the line-shape of light absorption for
exciton transitions between broad bands in one-, two- and three-dimensional organic semiconduc-
tor structures are calculated. Exciton damping due to lattice imperfections is accounted for as a
frequency independent parameter. The obtained analytical expressions allow analyses of the line-
shape for different space dimensions of structure depending on bandwidth difference, damping
parameter and temperature.
Keywords: low-dimensional organic crystals, light absorption, exciton transitions.
Paper received 01.03.99; revised manuscript received 02.04.99; accepted for publication 19.04.99.
1. Introduction
Various organic semiconductors (OS) have been a sub-
ject of intensive studies for many years. Due to the num-
ber of physical effects and their potential applications in
electronic and optical devices in newly available materi-
als [1]-[3] there has been increasing interest in the inves-
tigation of organic structures of low dimensionality [4]-
[6].
It is well known [7] - [8] that in contrast to the atomic
spectra (or spectra of simple molecules) the spectra of
orqanic compounds contain the discrete lines along with
the broad bands(∼102-103 cm-1). The nature of these bands
attracts the attention of researchers during four last decades.
Using a method of selective laser excitation, Personov
has shown that at rather low temperatures the broad bands
are caused by a non-uniform broadening and in them the
huge number of narrow no-phonon lines is hidden. At the
same time it was observed [7] that some spectra of the or-
ganic compounds embedded in frozen matrices of n-paraf-
fins, remain a broadband even at sufficiently low tempera-
tures and are not split on numbers of fine lines as one might
expect from results of [9].
As a rule, the band broadening in the absence of an ex-
ternal action or dephasing processes is connected with the
scattering of excitons on phonons, impurities, dislocations
and other lattice imperfections reducing the lifetime of ex-
citon. For the perfect OS one of basic mechanisms of the
exciton energy losses usually comes from their interaction
with phonons. Especially, it seems, the multi-phonon pro-
cesses may play considerable role in the formation of broad
bands. However, phonons not always can give the appre-
ciable contribution to the formation of the broad bands in
organic structures [10]. At low temperatures the broad band
could be expected also due to inhomogeneous broadening
of close located no-phonon lines, but for absorption the
contribution of such mechanism can practically be neglect-
ed [11].
There arise a problem of interpretation of broad bands
in OS, which are not split on separate lines at low tempera-
tures and not broaden with temperature rising.
An attempt to examine this problem for 3D-crystals as
well as for the case of narrow exciton bands was under-
taken by us earlier in [12-13]. We treated the simple two-
band model, in which the distribution of excitons over sub-
levels of the lowest band was considered as established,
and their photo-excitation to a higher band was studied. This
looks like a two-photon problem [14-15], but differs only
by the fact, we consider the 1st exciton band as a band of
thermalized exciton states. This work represents an exten-
sion of techniques previously [12] applied to the bulk ma-
terials.
In this paper, we apply the above stated approach to
calculate the absorption in OS of low spatial dimensional-
N. I. Grigorchuk: Light absorption by d-dimensional organic ...
2 6 SQO, 2(1), 1999
ity for another marginal case of broad exciton bands. Using
the model mentioned above we have calculated here the
contour shape of light absorption for one-, two-, and three-
dimensional (1D, 2D and 3D) periodic OS. We also have
lead comparison the line shapes of light absorption in OS
of different dimensionality.
The rest of the paper is arranged as follows. In Sec. 2
we shortly describe our working model and the tasks
considered. In Sec. 3 we present the basic formulae for
calculation. Section 4 is devoted to the discussion of results
and Sec. 5 to the conclusions.
2. Model and main assumptions
We study a periodic OS with simple nondegenerate bands
whose extrema are located at the center of the Brillouin
zone. Every elementary cell contains only one molecule.
We assume that the exciton bands are sufficiently sepa-
rated and that the configuration mixing of exciton states
in each band is absent. The excitons are supposed to be
capable to perform a Bloch-wave-like coherent motion.
In the media with the large dielectric constant exciton
motion can be described by means of the effective mass
approximation [16]. According to this approach, the en-
ergy of an exciton in the lowest band may be written
down as follows
∑
=
=
−−=
D
j ij
ij
ijii i
m
k
Bk
1
22
,2,1,
2
)(
h
ε (1)
where {k
i1
, k
i2
, ..., k
iD
} are the components of the exciton
quasi-momentum vector k
i
in the D-dimensional space, B
ij
is the bandwidth of the i-th band in the j-th direction, and
m
ij
is the exciton mass. m
ij
is connected with the band pa-
rameter B
ij
by means of the relation: 22 / jijij amB h= , where
a
j
is the lattice constant. Using Eq. (1) for ε
i
(k
i
), the distri-
bution function of excitons over sublevels of the first exci-
ton band one may to express in the form
∏
=
−
=
D
j
m
k
Tk
ijjj
D
B
j
j
Be
manTk
kW
1
2
2/2
1
1
2
1
2
12
)(
h
hπ
, (2)
where n
j
is the number of knots in j-th direction and T is the
temperature. Hence, in case of broad bands for any dimen-
sionality of OS, the excitons in the 1st band can be consid-
ered as ordinary gas obeying usual Boltzmann statistics.
The transition matrix element from the initial | f
1
k
1
> to
the more higher quantum state | f
2
k
2
> (f
i
describes some
other quantum numbers), in the dipole approximation look
similarly to that one derived in [12]. The dipole approxima-
tion is valid provided the exciton coherence length is much
less than the wavelength in organic structure of the absorbed
photon. We will neglect the photon momentum as an
infinitesimal value comparing with any other pulses in the
system. Then for transition frequency we get
[ ]∑
=
−−Ω≅
D
j
jjjff akB
1
22
1 2/1
12
δω , (3)
where Ω is the energy distance between the bottoms of the
first and second exciton bands.
Averaging the matrix element over an initial states,
which are populated with the statistical weight given by Eq.
(2), and summing over all final ones, one finds the prob-
ability of transition between examined states. This prob-
ability is directly proportional to the dimensionless fre-
quency function [12]
2/2
2
)(
D
B
D
Tk
F
Ω=
π
ω h
×
∫ ∏ ∫
∞
=
−
+−ℜ×
0
1
)2/(21D
j
BitAx
jj
it jjD edx
am
edt
π
π
δε
(4)
which in general form defines the line-shape of light ab-
sorption by excitons for such transitions. Here
∑
=
Γ+Ω−=−Ω=Ω
D
j
DDjD iB
1
2/, ωεδ ,
)2/( 2
1
2 TkamA Bjjj h= (5)
The boundaries of the 1st exciton band are accounted
by second integral of Eq.(4). The symbol ℜ means that the
real part of the expression should be taken. Beyond the ex-
ponent of Eq. (4) we have omitted the terms of the order of
magnitude of equal to, or even higher than the δB/Ω
D
. This
corresponds to the assumption that the energy distance be-
tween the first and second exciton bands should much more
exceed the difference of their width:
Ω >> 2D δB. (6)
The damping of the excitons due to phonons or lattice
imperfections is accounted for by a frequency-indepen-
dent parameter Ã. We also have assumed that
δB / Ã >> 1, (7)
i.e., we considered that the difference of two band width is
much more than any possible damping in OS. It is necessary
to keep in mind, that variable t is dimensional variable (in
contrast to another one, x) and is measured in seconds.
3. Basic formulae
Let us consider the temperatures for which A
j
>> 1. Then
the integration limits in second integral of the Eq. (4) may
be extended to infinity, and using the Poisson integral
∫
∞
∞−
− = απα /
2
dxe x
, equation (4) can be presented as
N. I. Grigorchuk: Light absorption by d-dimensional organic ...
27SQO, 2(1), 1999
×
Ω=
2/2
)(
D
B
D
Tk
F
hω
∏ ∫
=
∞
−
+ℜ×
D
j j
j
jjj
it
B
A
it
Bma
edt D
1
0
2/1
21
δδ
ε
(8)
It is easy to see, that the integral of complex conjugate
integrand is reduced to integral of Eq. (8) by changing
t ⇒ -t. Formally, it allows the integral of Eq. (8) to be
represented as a half of the integral in the limits from - ∞
up to ∞. Then the expression (8) may be considered as ex-
ponential Fourier transform. Determining the Fourier-im-
age for the cases D = 1, 2, 3, we receive then:
x
xxD
xxe
F
ε
παω
εα−
= ℜΩ=1|)( , (9)
×Ω== yxxyDF ααπω 2|)(
[ ])(0
)(
2
1
yxxyIe
xyyx ααε
εαα
−ℜ×
+−
(10)
×Ω= ⊥⊥= ||||3 2|)( ααπω DF
−−ℜ× ⊥⊥
− ⊥⊥
⊥ ||||11
|| )(;
2
3
;
2
1
||
||
εααε εα Fe , (11)
where
kk Âδ−Ω=Ω , lkkl ÂÂ δδ −−Ω=Ω ,
k
k
k
Â
A
δ
α 2
= ,
2/Γ+++Ω−= iÂÂ lkkl δδωε , ⊥= ||,;,,, zyxlk , (12)
I
0
(x) is the modified Bessel function of zeroth-order with
complex argument,
1
F
1
(a,b,z) is confluent gypergeometric
function, which, in particular, at a = 1/2, b = 3/2 takes the
form [17]:
xerf
x
xF
π
2
1
,
2
3
,
2
1
11 =
− , (13)
where erf x is the probability integral. The formulae (9)-
(11) describe the shape of absorption bands for a general
case of an anisotropic lattice: rectangular, as in the case of
2D-semiconductors, or with the allocated symmetry axis,
as for 3D-case, for which the cylindrical symmetry was
chosen for instance.
In the case, when we deal with the isotropic organic
structure (the lattice has the square or cubic form) then in
the previous formulae it is necessary to put
BBB lk δδδ ≡= , ααδ ≡−Ω≡Ω jD BD , , (14)
where D describes, as well as above, the dimensionality of
the OS. Next, taking in the Eq. (1) into consideration that
π
2
lim
0
=
→ x
xerf
x , (15)
we obtain
2/
|)(
1
)2/(
11
1
Γ+Ω−
ℜΩ=
Γ+Ω−−
=
i
e
F
i
D ω
παω
ωα
, (16)
)2/(
22
2|)( Γ+Ω−−
= ℜΩ= i
D eF ωαπαω , (17)
×Ω==
2/3
33 2|)( απω DF
)2/(
3
32/ Γ+Ω−−Γ+Ω−ℜ× iei ωαω . (18)
Thus, the formulae (16)-(18) with accounting of damp-
ing describe the band shape, which arise by light absorption
in 1D-, 2D- and in 3D isotropic OS. This our result can be
reached by another way, when, for example, at evaluating
of the second integral in Eq. (4) the saddle-point integra-
tion is used. The most simple expressions for the band
shape can be obtained in the absence of the damping
(Ã → 0). They are easily appeared from Eqs. (16)-(18). In
the other limit case, when the width of both bands coincides,
i.e. δB = 0, the absorption curve takes the form of sym-
metric Lorentz with the half-width of Ã/2.
At last, extracting the real part from Eqs. (16)-(18) we
obtain the expressions enabling to calculate immediately the
line shape of absorption for various dimensionalities of OS:
×
+Γ
Ω=
−
= 2/12
1
||
1
11 )1(
cos2|)(
1
x
e
xF
x
D
γ
γπγ
×
−+−++ γtan11 1
2
11
2
1 xxxx , (19)
||2
22
2cos2|)( x
D exF γγπγ −
= Γ
Ω= , (20)
×
Γ
Ω= −
=
||3
33
3cos22|)( x
D exF γγγπγ
×
−++++ γtan11 3
2
33
2
3 xxxx . (21)
N. I. Grigorchuk: Light absorption by d-dimensional organic ...
2 8 SQO, 2(1), 1999
In these expressions
2/Γ= αγ , (22)
Γ+=
Γ
Ω−
= /2,
2/ 12
1
1 Bxxx δ
ω
, Γ+= /413 Âxx δ . (23)
The region of variable change for x
1
has restriction,
which follows from the condition
1
2
11
2
1
2 11tan xxxx −+++≤γ . (24)
For x
1
which do not obey the condition (24), the func-
tion F(x
1
) = 0. Analyzing expressions (19)-(21), it is pos-
sible to make a conclusion that with increase of the dimen-
sionality D of the OS the absorption band, as a whole, is
shifted to the short-wave range of a spectrum proportion-
ally to the value of 2DδB/Γ.
In order to compare the shape of the absorption band
for OS of different spatial dimensionalities, we bring in
coincidence the origin of the different frequency scales, by
setting
xxxx ≡== 321 , (25)
It means that we have chosen
Ω
1
≈ Ω
2
≈ Ω
3
≡ Ω. (26)
Such approximation unsignificantly will affect relative
intensity of lines, because in accordance with our previous
assumption (6), the energy distances between the first and
following exciton band much more exceeds width of the
1st band in any of the k-directions.
4. Discussion of results
Using the Eqs. (19)-(21), in Fig.1 (A, B) the curves of light
absorption for different dimensionality of OS are plotted.
All curves correspond to the same certain temperature which
enters into parameter γ. The upper panel (A) of the Fig. 1 is
consistent with δB/Γ = 8, whereas its lower panel (B)
corresponds to the value δB/Γ = 16. Both parts of the figure
clearly indicate that under band-to-band exciton transitions
with increase of the dimensionality of OS, first of all, the
long-wave wing of the absorption band is appreciably
changed: the intensity of light absorption is increased and
becomes the highest one (for any frequency of this wing)
for 2D-semiconductors. For them, the maximum of inten-
sity corresponds to the transition frequency ω = Ω − 4δB.
For both the 1D and 3D-OS there is an additional shift
of the maximum (besides that caused by the difference of
the width of two bands) in the direction of the violet spectra
range. For 3D-structure this shift somewhat exceeds one
obtained in 1D-structure. At given δB/Γ = 8, the relative
intensities of lines are the highest ones for 2D-structure and
become minimal for 3D-structure. If one chooses the value
δB/Γ twice large, then intensity of absorption gets highest
for one-dimensional structure, and for three-dimensional one
becomes even less (see lower panel of Fig. 1). Most simply
the relative intensity of lines could be estimated for one of
displayed frequencies. So, for example, at x = 0, with in-
crease of dimensionality of OS, it will be described by
ratio of:
)tan1(2:2:)tan1( γγπγγ +− , (27)
which are applicable both for arbitrary temperatures and
for any ratio δB/Γ satisfying the condition of Eq. (24). An
enhancement of the ratio δB/Γ at fixed temperature results,
as it is easy to see from Eqs. (19)-(21), to reduction of γ;
consequently, the line intensity is increased in one-dimen-
sional case, whereas in two- and three-dimensional cases it
decreases only. Moreover, in three-dimensional case this
reduction is the most essential. Such tendency maintains
also for frequencies close to the frequency of absorption
peak and varies only on wings of absorption (see Fig.1).
Comparing the absorption curves for the OS of different
dimensions (for the same values of the assumed parameters),
it should be noted that the line appreciably broadens for
transitions from 1D- to 2D-OS. The opposite situation, i.e.,
a narrowing the line occurs for the transition from the 2D to
the 3D case. However, the half-width of the absorption curve
Fig. 1. The contour shape of light absorption under exciton
transitions between broad bands for 1D-, 2D-, and 3D-dimen-
sional organic semiconductors, A = 4: δB = 8Ã (panel A); δB=
= 16Ã (panel B).
--
N. I. Grigorchuk: Light absorption by d-dimensional organic ...
29SQO, 2(1), 1999
in the 3D case remains somewhat larger than one in the 1D
case (see Fig. 1, A-, B-panels). The line broadening in the
2D case may be explained by the fact that for normal light
incidence the probability of the transfer of excitation be-
tween molecules in a plane increases compared to that in a
linear chain proportionally to both the number of
neighboring molecules and to the wave function overlap.
However, in the bulk, this probability is decreased, and the
absorption curve is narrowed almost to the width of the 1D
structure. This effect is caused by the decrease of the effec-
tive bandwidth difference, which may be due to the increase
of the effect of exciton dynamics. Influence of the exciton
motion on the line-shape of optical absorption was studied
in more detail, for example, in [18] and results as a rule in
line narrowing.
Generally, the line-shape is the product of two factors,
the probability for optical transitions between the first and
second bands and the Boltzmann distribution of the exci-
ton kinetic energies. From Eqs. (19)-(21) it follows that the
line-shape of absorption under exciton transitions between
broad bands depends in the same measure both on the tem-
perature and the width difference of two bands. Moreover,
both factors act in the same direction. For instance, the
decrease of the difference of δB gives the same result as
temperature lowering: the intensity of absorption falls. From
the physical point of view, this is due to an equal probabil-
ity for an exciton with the defined value of k
1
to scatter on
a phonon or an another exciton. The numerical evaluation
for 3D-OS exhibits that twofold enhancement of the δB or
temperature, results in the decreasing in the intensity of the
absorption as much.
This our result essentially differs from one obtained
earlier [13] for the case of narrow exciton bands.
The well known mechanism of inhomogeneous broad-
ening due to static disorder in the quasiperfect crystal, seems
to play more important role for solutions [7]. An estima-
tion may be done by comparing the values of the energy
dispersion of one of the exciton levels with the band-width
difference δB. The first one is found to be much less for the
considered system.
The Eqs. (19)-(21) describe the line-shape in the case
when the effective masses of an exciton m
1
and m
2
in the
first and second bands have positive sings. When effective
masses of an exciton are negative then the transition fre-
quency, at k
2
= k
1
becomes
[ ]∑
=
−+Ω≅
D
j
jjjff akB
1
22
1 2/1
12
δω , (28)
hence, replacing in the Eq. (4) the integral over dx on the
integral
{ }∫−
++=
π
π
δ 2
1 )2/(exp yBitAdyi j , (29)
one gets the general expression for the line-shape of ab-
sorption with negative exciton masses. Further, it is easy to
see that at replacement of variable y → π-x, the integral i
1
of Eq. (29) passes in to the last integral of Eq. (4). If one
takes into account also that
{ } TkBTk BB e
Z
e /3/)( 111
1=− kTr ε
, (30)
(where Tr is the trace, and Z is the statistical sum) then it
becomes clear that the expression for the function F(ω) keeps
the former kind as in Eq. (4). This means that for negative
exciton masses the shape of absorption curves will be de-
fined by the same formulae (9)-(11). Such conclusion is clear
from physical reasons as well: under simultaneous changes
of the signs of the exciton effective masses in the first and
in the second bands, in the case of direct transitions, the
energy distances between bands is kept for each of wave
vectors of Brillouin zone.
For many organic compounds which in experiment dis-
play preferentially the properties of individual molecules,
our model is invalid. It seems it may hold for those OS which
exhibit generally the crystalline properties that are associ-
ated with the coherent motion and the band structure [19].
To the last category one may attribute, for example, the low
dimensional crystal structure of 1, 2, 4, 5-thetrachlorbenzene,
1,4-dibromnaphthalene, etc. For such OS there are both
numerous experiments (e.g., [20]) and numerical calculations
(e.g., [21]) studying the light absorption due to the exciton
transitions from the ground state to the singlet or triplet ex-
citon bands. But we are not aware of any data on the exciton
absorption caused by transitions between exciton bands in
these OS. Moreover, we are not aware of any experiments
on transformation of the absorption line-shape with changing
dimensionality of the same material.
5. Conclusions
Surmising, we can conclude that within the framework
of the two-band model the additional nonthermal broad-
ening mechanism arises owing to the difference between
the density of states of the bands under consideration.
In the case of broad exciton bands, the difference of their
widths and temperature of MC are two main comparable
factors responsible both for the contour shape and for the
intensity of absorption. The increase of band difference gives
the same result as an enhancement of the temperature of
OS: the intensity of light absorption decreases, and the ab-
sorption maximum shifts to the short-wave spectrum range.
The absorption contour essentially broadens at transi-
tions from 1D- to 2D-OS and is narrowed appreciably at
transition from 2 to 3D-dimensionality. Thus, there is an
additional shift to the violet spectra range due to the differ-
ence of widths of two bands. This shift is proportional to the
dimensionality of the structure.
Simultaneous changing of the signs of the effective
masses does not change the form of an absorption contour.
If the state of the lowest band are evenly filled by exci-
tons, one can study the states density of higher-lying bands.
Benchmark applications to nonlinear exciton-to-
biexciton absorption are anticipated.
N. I. Grigorchuk: Light absorption by d-dimensional organic ...
3 0 SQO, 2(1), 1999
References
1. T. Tokihiro, Y.Manabe, and E. Hanamura, Superradiance of
Frenkel Excitons in Linear Systems // Phys. Rev. B, 47(4), pp.2019-
2030 (1993).
2. Y. Shimoi and S. Abe, Theory of Triplet Exciton Polaron and
Photoinduced Absorption in Conjugated Polymers // Phys. Rev.
B, 49 (20), pp. 14113-14121 (1994).
3. L.Rossi, G. Lanzani, and F. Garnier, Charged Photoexcitations
in Thiophene-based Molecular Semiconductors // Phys. Rev. B,
58(11), pp. 6684-6687 (1998).
4. A. Tomioka, and K. Miyano, Numerical Study of Excitons in a
Two-Dimensional Organic Dye Aggregate // Phys. Rev. B, 54(5),
pp. 2963-2967 (1996).
5. N.T. Harrison, G.R. Hayes, R.T. Philips, and R.H. Friend, Sin-
glet Interaction Exciton Generation and Decay in Poly (p-Phe-
nylenevinylene) // Phys. Rev. Lett., 77(9), pp. 1881-1884 (1996).
6. S. Abe, M. Schreiber, W.P. Su, and Y. Yu, Excitons and Nonlin-
ear Optical Spectra in Conjugated Polymers // Phys. Rev. B, 45(16)
pp. 9432-9435 (1992).
7. Spectroscopy and Excitation Dynamics of Condensed Molecu-
lar Systems, ed. by V.M. Agranovich and Hochstrasser, North-
Holland, Amsterdam (1983).
8. V.L. Broude, E.I. Rashba, and E.F. Sheka, Spectroscopy of mo-
lecular excitons, Energoizdat, Moskow (1981).
9. R.I.Personov, Selective spectroscopy of a complex molecules in
solutions and its application, Preprint of Institute of Spectrosco-
py (USSR), No.14, Troitsk (1981).
10. M. Higuchi, T. Nakayama, and N. Iton, Studies of Higher Trip-
let Exciton Bands through T-T Absorption in Naphthalene Sin-
gle Crystal // J. Phys. Soc. Jpn. 40(6), pp. 250-257 (1976).
11. O.N. Karataev, T.M. Naumova, V.P. Karpov and M. Ju. Kali-
tievskii, Bandwidth and Shape of Bands under T-T Absorption,
in «Modern Problems of Spectroscopy of crystals», Naukova
Dumka, Kyiv (1976), pp. 188-195.
12. N. I. Grigorchuk, L. G. Grechko, Lineshape of Light Absorption
by Thermalized Frenkel Excitons under Band-to-Band Transi-
tions // Phys.Stat.Sol.(b), 153(2), pp. 633-640 (1989).
13. N. Grigorchuk, Line-Shape of Light Absorption by Excitons in
One-, Two- and Three-Dimensional Molecular Structures // Sol-
id State Commun.,100(12), pp. 861-864(1996).
14. F. X. Bronold and A. R. Bishop, Nonlinear Optics of Conjugat-
ed Polymers: A coupled Exciton-Phonon Gas Approach // Phys.
Rev. B, 53(20), pp. 13456-13476(1996).
15. A. Shimizu, T. Ogawa, and H. Sakahi, Two-Photon Absorption
Spectra of Quasi-Low-Dimensional Exciton Systems // Phys. Rev.
B, 45(19), pp. 11338-11341 (1992).
16. D. P. Craig, and S. H. Walmsley, Excitons in Molecular Crystals.
Theory and Applications. Benjamin, New York, Amsterdam,
(1968).
17. M. Abramovitz and I. Stegun, Handbook of Mathematical Func-
tions, Dover, New York (1972).
18. B. N. J. Person, F. M. Hoffman, and R. Ryberg, Influence of
Exciton Motion on the Shape of Optical Absorption Lines: Ap-
plications to Vibrations at Surfaces // Phys. Rev. B, 34(4),
pp.2266-2283(1986).
19. H.Haken, and P. Reineker, The Coupled Coherent and Incoher-
ent Motion of Excitons and its Influence on the Line Shape of
Optical Absorption // Zeitschrift Phys. 249(1), pp. 253-268(1972).
20. D.M. Burland, U. Kunzelmann, and R.M. MacFarlane, Exci-
ton Scattering Processes in (1,4)-Dibromnaphthalene // J. Chem.
Phys. 67(5), pp. 1926-1934 (1977).
21. M.Schreiber, and Y. Toyazawa, Numerical Experiments on the
Absorption Lineshape of the Exciton under Lattice Vibrations. I.
The Overall Lineshape // J. Phys. Soc. Jpn. 51(5), pp. 1528-1536
(1982).
|