Magnetic field-modulated exciton generation in organic semiconductors: an intermolecular quantum correlation effect

Abstract

Magnetoelectroluminescence (MEL) of organic semiconductor has been experimentally tuned by adopting blended emitting layer consisting of both hole and electron transporting materials. A theoretical model considering intermolecular quantum correlation is proposed to demonstrate two fundamental issues: (1) two mechanisms, spin scattering and spin mixing, dominate the two different steps respectively in the process of the magnetic field modulated generation of exciton; (2) the hopping rate of carriers determines the intensity of MEL. Calculation successfully predicts the increase of singlet excitons in low field with little change of triplet exciton population. Comment: 16 pages, 4 figures

Full text

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Magnetic field-modulated exciton generation in organic
semiconductors: an intermolecular quantum correlation effect

B. F. Ding*, Y. Yao*, X. Y. Sun, Z. Y. Sun, X. D. Gao, Z. T. Xie, Z. J. Wang, X. M.
Ding, Y. Z. Wu, X. F. Jin, C. Q. Wu†, and X. Y. Hou††

Surface Physics Laboratory, Department of Physics, Fudan University,
Shanghai 200433, People’s Republic of China

Magnetoelectroluminescence （MEL） of organic semiconductor has been experimentally tuned
by adopting blended emitting layer consisting of both hole and electron transporting materials. A
theoretical model considering intermolecular quantum correlation is proposed to demonstrate two
fundamental issues: (1) two mechanisms, spin scattering and spin mixing, dominate the two
different steps respectively in the process of the magnetic field modulated generation of exciton;
(2) the hopping rate of carriers determines the intensity of MEL. Calculation successfully predicts
the increase of singlet excitons in low field with little change of triplet exciton population.








*These authors contributed equally to this work.
† Electronic mail: cqw@fudan.edu.cn
†† Electronic mail: xyhou@fudan.edu.cn
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In the field of organic spintronics [1-13], magnetoelectroluminescence (MEL), i.e., magnetic
field-modulated electroluminescence of organic semiconductor devices with nonmagnetic
electrodes has been widely studied [5-13], because it provides a promising way to understand the
spin dynamics in organic systems, such as organic semiconductors and biological systems [14].
Generally, MEL appears to enhance rapidly with magnetic field in the low field region (typically
<15mT) but to saturate or even weaken in the high field region（>30mT）[5,6,10,12].
Unanswered questions in this area include the reason why smaller electric field leads to larger
MEL[5,6,8,10,12,15], why insertion of an insulating layer LiF enhances MEL [10] and why
minority carriers dominate the magnetic field effect in organic semiconductors [6,15-17]. These
questions can be reduced to one basic issue, namely what determines the intensity of MEL in a
given magnetic field. Theories of inter-system crossing (ISC)[9,10,16] or triplet-triplet
annihilation (TTA) [12,13] have been proposed by some groups to qualitatively explain MEL.
Both ISC and TTA could be included in a so-called spin mixing (SM) mechanism which occurs
only in spin sub-levels through spin redistribution [6, 14, 18]. According to ISC or TTA, the
increase of singlet excitons should occur at the expense of triplet excitons. But Reufer et al found
that no change of singlet–triplet balance occurs, especially in low magnetic field [7]. Since MEL
correlates directly with magnetic field-modulated exciton generation, it is critical to consider how
magnetic field influences the process of exciton generation. Generally, exciton generation consists
of three steps[19]: I. carrier injection from electrodes and transport; II. formation of a
hole-electron pair at two adjacent molecules; III. formation of an exciton at one molecule by
hopping. Identifying in which step SM is active and which mechanism dominates beyond this step
is the essential question that must be addressed [6,18] .To this end a quantitative explanation of
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MEL is indispensable.
In this letter, we describe a model formulated by considering the intermolecular correlated
effect. Based on the model, the process of magnetic field-modulated step II and step III of exciton
generation is quantitatively studied both experimentally and theoretically. It is found that SM only
dominates magnetic field-modulated step III in high magnetic field, while spin scattering (SS), in
which the redistribution of both spins and charges is involved, controls the modulation of step Ⅱ
in low magnetic field. By studying the MEL of the organic light emitting diode (OLED) with a
blended emitting layer, it is found that hopping rate of carriers influences both SS and SM. This
proves that intermolecular quantum correlated effect plays an essential role in organic MEL and
suggests that the magnetic field effect in other relevant systems[3,14,16] should be reconsidered.
In present work, a special structure of OLED was designed to reveal the effect of
intermolecular correlation on exciton generation. The OLED was fabricated with a blended layer
of tris-(8-hydroxyquinoline) aluminum (Alq3) and N,N’-bis(l-naphthyl)-N,N’-diphenyl-1,l’-
biphentl-4,4’-diamine (NPB), acting as the fluorescent emitting layer, as shown in Fig. 1(a). The
device area is approximately 4×4 mm2. Besides, 40nm NPB and 50nm Alq3 form the
hole-transporting and electron-transporting layers respectively. Because of its wide band gap[20],
BCP (bathocuproine) is used as an exciton-blocking layer to prevent exciton diffusion from the
blended layer to the 50nm-thick Alq3 layer. The anode and composite cathode are ITO and LiF/Al
respectively.
Figure 1(b) shows the MEL of six representative devices with different blending volume ratios
of NPB to Alq3 as function of external magnetic field under constant driving current of 150µA.
The MEL is expressed by
) 0 (/ )] 0 ()( [(/ ELELB EL ELEL
−=∆
, where and
)(BEL
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) 0 (EL
are the electroluminescence with and without external magnetic field B respectively.
Similar to the reported results[6], each curve is characterized by fast enhancement in the low field
region followed by saturation in the high field region. The intensity of MEL under a given field
depends strongly on the blending ratio. To confirm the relation between MEL and blending ratio,
Fig. 1(c) shows
at 50mT under three different driving conditions—constant driving
current of 500µA, constant driving voltage of 7V, and constant initial brightness of 20cd/m
EL EL/
∆
2. With
the ratio increasing from 0% to 30%, under the condition of constant initial brightness of 20cd/m2,
increases from 3% to 7%. However, further increase of the ratio from 30% to 80%
causes
to decrease from 7% to 2%. MEL under the other two driving conditions shows
similar behavior. Experiments reveal an intrinsic relation between MEL and blending ratio. Liu et
al reported previously that electrical conductivity, which is determined by carrier mobility, reaches
a minimum around the blending ratio of 30% in a blended layer of NPB and Alq
ELEL/
∆
ELEL/
∆
3[21]. The ratio of
30% agrees well with the ratio in the present experiments in which MEL reaches its maximum.
Quantum mechanically, mobility of carriers is dominated by their hopping rate. The hopping rate
is one of the key factors that affect the interaction among intermolecular carriers, and is
intrinsically a result of correlated effect. All of the above experimental results demonstrate that a
correlated effect is likely to determine the intensity of MEL.
Based on the results shown in Fig. 1, it is proposed that the Hubbard model, a typical model
for correlated systems, can be used to describe such a correlated effect [22]. The Hamiltonian,
including both the intermolecular transportation of electrons/holes and the interaction between
electrons/holes and nuclear spins, reads
21
HHH
+=
, (1)
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The first part of (1) includes hopping and Coulomb interaction of carriers.
VnnnnUc.hcctddtH
e
j
e
j
h
i
ji
h
i
jj
e
jji
ji
i
h
i' ,i
+++++−=
↓↑↓↑
∑
,
∑
,
)(.)(
, '
†
,', , '
,
†
,1
σσσ
σ
σ
, (2)
where
†
,σ
id
(
σ , id
) and
†
,σ
j c
(
σ , j c
) create (annihilate) a hole and an electron with spin σ up (↑)
or down (↓) in the i- and j-th molecule, i′ and j′denote the neighbors of the i- and j-th
molecule,
h
' , and
i it
e
jjt
', are the hopping rates (in unit of µeV by the uncertainty principle
∆E∆t≈ħ/2) of hole and electron. U is the Coulomb repulsive energy between two holes or two
electrons with different spins at the same molecule,
h
inσ , (≡
†
,σ
id
σ , id
) and
e
j n
σ , (≡
†
,σ
j c
σ , j c
)
the corresponding hole and electron number operators, and V the attractive interaction between
hole and electron at the same molecule.
The second part of (1) shows the effect of an external magnetic field and hyperfine
interactions,
⎥
⎦
⎤
⎢
⎣
⎡
⋅++⋅+=
→
S
→
B
→
B
→
S
→
B
→
B
∑
i
,
e
j
j hypext
h
i
ihypext
j
B
gH)()(
,,
2
µ
, (3)
where g=2.0 for organic materials[7], µB is Bohr magneton, is the external magnetic field
chosen along the z-direction, and
is the effective nuclear magnetic field of i-th (j-th)
molecule that will be treated classically. For example, for holes,
ext
B
→
)(,ji hyp
B
→
)( sin)( cos
,
†
,i,
†
,i
,
,
†
,
i
,
†
,
i
,
,
↓↓↑↑↓↓↑↑
→
S
→
B
++−=⋅
ii
h
i
h
hypi
ii
h
i
h
hypi
h
i
h
ihyp
ddddBddddB
θθ
, (4)
where
h
iθ
is the angle between and hole spin.
i hyp
B
,
→
In this work, we focus on the intrinsic features of the organic semiconductor. The model is a
two-step one including only step II and step III of exciton generation mentioned above. Because
step II and step III are different, they are treated separately. Generally, hopping rates
h
' ,and
i it
e
jjt
',
vary from molecule to molecule due to the disorder of organic materials.
ht and
et are estimated
to be between 1µeV and 100µeV[23], depending on the blending ratio. U is taken as 0.1eV[24],
which is large enough to prevent double occupancy of the same polarity of carriers at one
molecule, yet spin exchange between two molecules still operates when many excitons interacting
5