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Activation Energy for Photoconduction in Molecular Crystals

Naoki Nagayama, Takashi Yamamoto, and Toshio Naito*

* Graduate School of Science and Engineering, Ehime University, Matsuyama 790-8577, Japan.

Tel: 81-89-927-9604, E-mail: [email protected]

Received: 2015-10-02 || Accepted: 2015-11-18 || Available online: 2015-11-22

Abstract

The carrier dynamics of photoconduction (PC) are

complicated because the systems contain optically and

thermally excited carriers with different relaxation

mechanisms. In addition, molecular crystals generally

have highly anisotropic and correlated electronic

systems. Accordingly, the photoconduction mecha-

nism of molecular crystals is full of unanswered basic

problems such as how to distinguish PC from a

coexistent thermal carrier’s contribution originating

from heating effects involved with irradiation. In this

work, the activation energy (Ea) for PC of molecular

crystals was found to decrease monotonically with an

increase in the intensity (I) of light. The values of Ea

upon irradiation were not related to band gaps, unlike

those for dark conductions. Based on the observed

I-dependence of the photocurrent (Iph), the

I-dependence of the Ea is explained quantitatively.

This Ea analysis makes it possible to clearly

distinguish PC from the coexistent conduction

originating from thermal carriers.

Keywords: Organic charge-transfer salt; Carrier

dynamics; Heating effect; Metal-dithiolene complex;

-conductor.

1. Introduction

Photoconduction (PC) is a well-known phenomenon

observed in a variety of compounds [1-5]. In addition to

unique experimental tools for studying carrier dynamics

in unusual conductors [1-3], PC is applied in various

imaging and sensor devices such as copy machines,

charge-coupled devices (CCD), complementary

metal-oxide-semiconductors (CMOS), and photovoltaic

cells [4,5]. Since such devices play an indispensable role

in daily life, clarifying the mechanism of PC is important

in order to develop more efficient photoconductors. The

carrier dynamics of PC are complicated, because the

systems contain both thermally and optically activated

carriers at the same time. As a result, in addition to the

relaxation of electrical conduction, that of optical and

thermal excitations takes places simultaneously in

photocarrier systems. Recently organic photoconductors

have attracted more and more attention because of their

possibility of light, flexible, and inexpensive products

with low power consumption. PC in organic compounds

can simultaneously involve different but nearly

degenerate energy bands. They generally exhibit marked

anisotropy in electrical conduction. Additionally, they are

characterized by strong electron-electron and electron-

phonon interactions, which often produce various kinds

of relaxation processes and meta-stable states. All of

these characteristics make the PC behavior more

complicated than other groups of materials. Thus, there

remain a number of basic problems and open questions

about the PC mechanism of organic compounds, which

includes how to distinguish PC from a coexistent thermal

carrier’s contribution originating from inevitable heating

effects. In order to solve these unanswered problems,

study on PC in single crystals is more advantageous than

that in thin films, because the former samples are

structurally well-defined, serving as a simplest model.

Therefore understanding and findings on single

crystalline samples can provide an important clue for

general and basic understanding of PC mechanism in

organic materials. In this perspective, the samples

selected in this study exhibit unusually large

photoresponse, i.e. photocurrent Iph, and marked

dependence on light-intensity I. Such samples have been

recently found among [Ni(dmit)2] salts, where dmit =

1,3-dithiole-2-thione-4,5-dithiolate (Figure 1). The

[Ni(dmit)2] radical anion salts have been paid particular

attention for long time as building blocks for molecular

optical materials, magnets, metals and superconductors

[6-18]. NMQ[Ni(dmit)2] (1) (NMQ = N-methyl

quinolinium; Figure 1) is a highly insulating molecular

salt when in the dark, but exhibits unusually high PC. At

200 K, it demonstrates ~880 times higher conductivity

when exposed to UV radiation (375 nm, 15.7 mWcm-2

)

than when in the dark [19].


75


Figure 1. Molecular structures.

The salt is a band insulator [Figure 2(a)]

having a two-dimensional network of

Ni(dmit)2 moieties [Figure 2(b)] which is

used as the PC conduction pathway. In

addition, there exists a non-linear dependence

of Iph on I. In conventional photoconductors,

whether they are organic or not, Iph is

proportional to I. Because the detailed

I-dependence of Iph including linearity can be

controlled by irradiation conditions in salt 1, it

is the sample of choice for covering different

patterns of Iph(I) of different photoconductive

materials. Herein are reported the

I-dependence of effective Ea for PC of

molecular crystals, and a quantitative

interpretation of the Ea behavior based on the

observed I-dependence of Iph. In the discus-

sion below, only the total number of carriers

in the PC is considered; the photoexcited

states are not considered in detail. This is

advantageous for application of the analysis

presented below to as wide a variety of

photoconductive materials as possible.

2. Materials and Methods

The single crystals of salts 1 and 2

(MV[Ni(dmit)2]2, MV = methyl viologen,

Figure 1) were prepared according to

previous reports [19, 23]. Electrical resistivity

measurements were carried out on single

crystals via a two-probe method in air using a

homemade cryostat and a UV laser (375 nm,

max 20 mW) with adjustable focus and

intensity. Many samples were studied in order

to examine sample-dependence and

reproducibility, as well as durability to

irradiation in air. The electrical resistivity was

measured along the longitudinal direction of

the single crystal (//b-axis for both salts 1 and 2), which coincides

with most conductive directions. At a given temperature the

current-voltage curves were measured from -10 V to +10 V with an

interval of 2 V, and Iph was the observed current under an applied

voltage of 10 V. Gold wires (25 m in diameter) and gold paste

(No.8560, Tokuriki Chemical Research Co., Ltd.) were used as

electrical contacts. In order to change the value of d (mm), the

distance L between the two electrical leads were decreased stepwise

by adding the Au paste after each measurement (Figure 3). Full

experimental details are provided in the Supporting Information.

Figure 2. Properties of salt 1 under dark conditions [19]. (a)

temperature-dependence of surface resistivity Rsq (inset) and

magnetic susceptibility (main panel), (b) two-dimensional

(honeycomb) network of Ni(dmit)2 moieties in the bc-plane,

which serves as a conduction pathway for PC. Broken lines

indicate strong intermolecular interactions because of MO

overlap. In (b), yellow, brown, grey, and open spheres

designate sulfur, carbon, nitrogen/nickel, and hydrogen atoms,

respectively. All figures are slightly modified, with

permission.


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Figure 3. Changing (decreasing) distance (L) between

electrical leads on the single crystal of salt 1.

3. Results and Discussion

3.1 Dependence of photocurrent on light-intensity,

and on distance between electrical leads. In contrast

with dark conductivity, even under a constant applied

voltage, Iph generally depends on experimental conditions

such as radiation wavelength/power [Figure 4(a)]/etc.

and the net distance (d) between electrical leads [Figure

4(b)]. This is because the number and relaxation time ()

of photocarriers depend on light intensity, wavelength

and so on. For instance, the longer d becomes, the fewer

photocarriers arrive at the opposite lead before they

optically relax and disappear.

In Fig. 4(b) the best-fit curve uses the following

equation,

𝑰𝒑𝒉𝑰𝒅𝒂𝒓𝒌

⁄ = 𝒚𝟎 + 𝑨𝐞𝐱𝐩 (−𝒅

𝝉)

, where y0, A, and = 1.08, 3.65, 0.56 (mm), respectively.

With regard to the non-linear dependence of Iph on I,

Iph is well described by a polynomial of I for salt 1

[Figure 4(a)]

𝐼𝑝ℎ = ∑ 𝐾i𝐼i

𝑖=0 (1), where Ki (i = 0,1,2,…) are experimentally-determined

constants (fitting parameters dependent on temperature T)

and K0 is equal to the observed current under dark

conditions Idark.

𝐾0 = 𝐼dark (2)

Depending on the irradiation conditions, some of the

coefficients Ki can be zero.

3.2 Dependence of activation energy on

light-intensity. The activation energy Ea of salt 1

decreases under 375 nm UV light with increasing I

(Figure 5).

In order to discuss the Ea behavior of the salt when

irradiated, both optically- and thermally-excited carriers

should be assumed to serve equally. Therefore, the

effective Ea [Ea(I)] can be described by:

𝐸𝑎(𝐼) = 𝑁𝑡ℎ(𝐼)

𝑁𝑡ℎ(𝐼)+𝑁𝑝ℎ(𝐼)𝐸𝑎,0 (3)

where Nth(I), Nph(I) and Ea,0 indicate the number of

thermally activated carriers, the number of optically

excited carriers, and the activation energy under dark

Figure 4. (a) Iph/Idark vs. I curve at 298 K with

different distances between the electrical leads (gold

wires) for the same single crystal. Closed circles:

observed; curves: best-fit curves using polynomials

similar to Eq. (1) (see Eq. (S1) and Table S1 in

Supporting Information). In order to estimate the net

effect of differences in travel path length of the

photocarriers, d does not include the spot diameter

(2r = 0.1 mm) of the UV laser (375 ±5 nm; see

inset). (b) Iph/Idark vs. d curve at 298 K (375 ±5 nm, I

= 12.6 Wcm-2

) for the same sample with that of

Figure 4(a). Closed circles: observed, and curve:

best-fit curve using the equation discussed in this

section on the left.


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conditions [~ (0.24 ± 0.02) eV], respectively. First,

it should be noted that dark- and photo-conductivity

(dark and ph, respectively) are proportional to the

dark- and photo-current (Idark and Iph, respectively)

under a constant applied voltage, and that the currents

are proportional to the respective number of carriers:

𝜎 ∝ 𝐼 (4a)

𝐼 ∝ 𝑁 (4b)

where , I, and N can designate dark and ph, Idark and Iph,

and Nth(I) and {Nth(I) + Nph(I)}, respectively.

Figure 5. I-dependence of Ea(I) for salt 1. Data observed

in air (for corresponding data for other samples, see

Figure S2 in Supporting Information). Best fit curves

generated using Eq. (10a) with fitting parameters in

Table S2 in the Supporting Information.

Under dark conditions, the sample is in a thermal

equilibrium, and thus the number of thermally excited

carriers Nth(0) follows a Boltzmann distribution [20].

Under radiation, the sample is no longer in a thermal

equilibrium, and some of the electrons are excited to

unoccupied states [21]. In such a state, the sample

temperature is not always equal to that of the

surroundings, because of the heat involved with radiation.

Thus, Nth is a function of I, which can be described by:

𝑁𝑡ℎ(𝐼) = 𝑎 + 𝑏𝐼 (5)

where 𝑎 and 𝑏 are constants. The first constant

corresponds to the number of carriers under dark

conditions, while the latter is primarily dependent upon

the heat capacity of the sample, including the electrical

contacts, under a given set of radiation conditions. Nth

can be described by Eq. (5) because the heat involved

with radiation is proportional to I under a given set of

experimental conditions.

Considering Eq. (4b),

{𝑁𝑡ℎ(𝐼) + 𝑁𝑝ℎ(𝐼)} ∝ 𝐼𝑝ℎ (6)

Then, as the observed Iph obeys Eq. (1),

𝑁𝑡ℎ(𝐼) + 𝑁𝑝ℎ(𝐼) = 𝐴 ∑ 𝐾i𝐼i

𝑖=0 (7)

where A is a proportionality constant, and

𝐴 =𝐿2

𝑉𝜇𝑒 (8)

where L, V, , e indicate distance between the two

electrical leads, applied voltage, mobility of the carriers,

and elementary charge, respectively, as shown in

Supporting Information.

Substitution of Eqs. (5) and (7) in Eq. (3) gives

𝐸𝑎(𝐼) = 𝑎+𝑏𝐼

𝐴 ∑ 𝐾i𝐼i 𝐸𝑎,0 (10a)

Eq. (10a) may be transformed into a linear relationship in

order to unambiguously fit the observed behavior as

follows:

𝐸𝑎(𝐼) ∑ 𝐾i𝐼i

𝑖=0 = 1

𝐴(𝑎 + 𝑏𝐼)𝐸𝑎,0 = 𝑎′ + 𝑏′𝐼 (10b)

where 𝑎′ =𝐸𝑎,0

𝐴𝑎, and 𝑏′ =

𝐸𝑎,0

𝐴𝑏.

3.3 Comparison of observed behavior with theory.

The validity of the discussion thus far can be evaluated

by comparing Eq. (10b) and the observed behavior. All of

the parameters Ki in Eq. (10b) can be determined directly

from the observation of Iph vs. I, i.e. the relationship in Eq.

(1), as shown in Figure 4. (The parameters obtained

from the curve-fitting (Ki, a’, and b’) are in Table S2 in

the Supporting Information.) Similarly, the I-dependence

of Ea can be directly observed, as shown in Figure 5.

Thus, using Eq. (10b) and the values of Ki, a curve-fitting

analysis was carried out on the I-dependence of

𝐸𝑎(𝐼) ∑ 𝐾i𝐼i (Figure 6). All of the relationships were

found to be linear, which means that Eq. (10b) is

consistent with the observed behavior.

3.4 Separation of thermally activated carriers from

optically activated carriers. Here if is known, this

analysis enables Nth(I) [Eq. (5)] and Nph(I) [Eq. (11)] to

be found unambiguously using the values of AKi, 𝑎′, 𝑏′,

and 𝐸𝑎,0 as shown below. Otherwise, it is always

difficult to distinguish unavoidable thermal effects from

purely optical effects in these kinds of experiments.

𝑁𝑝ℎ(𝐼) = {𝑁𝑡ℎ(𝐼) + 𝑁𝑝ℎ(𝐼)} − 𝑁𝑡ℎ(𝐼)

= 𝐴(𝐾0 + 𝐾1𝐼 + 𝐾2𝐼2 + 𝐾3𝐼3 + ⋯ ) − (𝑎 + 𝑏𝐼)

= (𝐴𝐾1 − 𝑏)𝐼 + 𝐴𝐾2𝐼2 + 𝐴𝐾3𝐼3 + ⋯ (∵ 𝐴𝐾0 −

𝑎 = 0) (11)

If Eq. (1) is replaced with other types of equations, the

discussion thus far remains essentially unaltered, except


78


for the details of Eqs. (7), (10a), and (10b). In fact, salt 1

gave different I-dependences of Iph [Eq. (1)] under

different measurement conditions. However, the analysis

here still can be applied to give similarly consistent

results (See Figures S2 and S3 in Supporting

Information).

Figure 6. I-dependence of Ea(I)(Ki I i

) for the same

sample with that in Figure 5. Data observed in air (for

corresponding data for other samples, see Figure S3 in

Supporting Information). Best fit lines generated using

Eq. (10b). Fitting parameters are in Table S2 in the

Supporting Information.

3.5 Similar analysis of a different salt. In order to

examine the validity of the discussion thus far, the same

analysis is applied to salt 2, which belongs to

“photomagnetic conductors” [22,23]. Salt 2 is a non-

magnetic insulator under dark conditions, yet it produces

paramagnetic metallic state under UV (375 nm) irradia-

tion. There is an interaction between the localized spins

on the MV cations and the carriers on the [Ni(dmit)2]

anions, which is corroborated by ESR and temperature-

dependent electrical resistivity measurements (for the

crystal structure and the physical properties, see Figures

S4-S6 in Supporting Information). Thus the carrier

dynamics in PC in salt 2 is different from those in salt 1,

as experimental results for such an interaction or

localized spins in PC have not been observed in salt 1.

The results corresponding to Figures 4-6 are shown in

Figures 7(a)-7(d), respectively. Irrespective of d, Ea(I) is

also well described by Eq. (10a) [Figure 7(c)], and Ea(I)

× Iph(I) is linearly dependent on I [Figure 7(d)]. For the

obtained fitting parameters, see Tables S4 and S5 in

Supporting Information. These results mean that the

analysis of Ea and separation of thermal and

photocarriers’ contributions can be valid in different PC

mechanism as long as Iph(I) is known like Eq. (1). How

this analysis can be generalized is now under study by

examination of further different kinds of PCs.

Figure 7. (a) Iph/Idark vs. I curve at 298 K with different

distances between the electrical leads (gold wires) for the

same single crystal of salt 2. Circles and squares:

observed; curves: best-fit curves using Eq. (S1) (for

details, see Table S4 in Supporting Information). (b) Iph

vs. I curve for salt 2. The same data as in Figure 7(a).

Circles and squares: observed; curves: best-fit curves


79


using Eq. (1) (for details, see Table S5 in Supporting

Information). (c) Ea(I) vs. I curve for salt 2. Data

observed in air. Best fit curves generated using Eq. (10a)

with fitting parameters in Table S5 in the Supporting

Information. (d) I-dependence of Ea(I)(Ki I i

) for the

same sample with that in Figures 7(a) - 7(c). Data

observed in air. Best fit lines generated using Eq. (10b).

(Fitting parameters are in Table S5 in the Supporting

Information.)

4. Conclusion

In the temperature-dependence of PC of some molecular

crystals, finite values of Ea were observed to be

dependent on I and could be explained on the assumption

that thermally activated and optically activated carriers

equally serve as carriers. Examination of the

I-dependences of Ea and Iph makes it possible to

experimentally distinguish PC from the coexistent

conduction originating from thermal carriers. This

analysis considered to be applied to other

photoconductive materials as long as the I-dependences

of Iph and values of are known.

Acknowledgement

The authors gratefully acknowledge financial support

from Grant-in-Aid for Research Promotion, Ehime

University, and also technical support from the Integrated

Center for Sciences, Ehime University.

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[20] If the possibility that there are different bands for

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constant at a given temperature and I. Thus, this


80


correction does not alter the succeeding discussion.

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Activation Energy for Photoconduction in Molecular Crystalsccaasmag.org/chem_2012/vol2/Naito-photoconduction.pdf · Activation Energy for Photoconduction in Molecular Crystals Naoki