A TEMPERATURE DEPENDENT STUDY ON CHARGE DYNAMICS IN ORGANIC MOLECULAR DEVICE: EFFECT OF SHALLOW TRAPS ON SPACE CHARGE LIMITED BEHAVIOR

April 29, 2014 8:49 WSPC/Guidelines-IJMPB S021797921450088X

International Journal of Modern Physics BVol. 28, No. 15 (2014) 1450088 (11 pages)c© World Scientific Publishing Company

DOI: 10.1142/S021797921450088X

A temperature dependent study on charge dynamics in

organic molecular device: Effect of shallow traps on

space charge limited behavior

A. K. Mukherjee∗ and A. K. Kavala†

Department of Physics, Indian Institute of Technology Patna,

Patliputra Colony, Patna – 800013, India∗[email protected]

†[email protected]

Received 11 December 2013Revised 14 January 2014Accepted 22 January 2014Published 11 April 2014

Shallow traps play a significant role in influencing charge dynamics through organicmolecular thin films, such as pentacene. Sandwich cells of pentacene capped by goldelectrodes are an excellent specimen to study the nature of underlying charge dynamics.In this paper, self-consistent numerical simulation of I–V characteristics is performedat various temperatures. The results have revealed negative value of Poole Frenkel co-efficient. The location of trap energy level is found to be located at 0.24 eV above thehighest occupied molecular orbit (HOMO) level of pentacene. Other physical parametersrelated to trap levels, such as density of states due to traps and effective carrier densitydue to traps, have also been estimated in this study.

Keywords: Mobility; shallow trap; Poole–Frenkel; pentacene.

PACS numbers: 73.40.Mr, 73.40.Sx

1. Introduction

Over these years, pentacene has proved to be a promising material for electronic

applications, despite a band gap of 2.2 eV.1 A good amount of effort has gone

in improving the morphology and overall quality of thin film of pentacene. This

has been reflected in the ever increasing values of mobility, as reported in various

communications in the past decade.2–4 Especially the organic nature, and ease

of processing, has made pentacene an exotic material of intense experimental and

theoretical research.5–8 Unfortunately, thin films of pentacene cannot be fabricated

as a single crystal, unlike silicon. On an average, the crystallite size of pentacene

are roughly 0.592 nm, 0.734 nm and 1.563 nm for a, b and c, respectively.9 Usually,

thin films of very high quality are composed of microcrystallites of pentacene. These

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A. K. Mukherjee & A. K. Kavala

microcrystallites are oriented in all possible orientations. Such films give best value

of mobility which is, somewhere around 5 cm2/Vs.2–4 Nevertheless, it is far below

the values of mobility offered by silicon and other inorganic counterparts. There are

various reasons for low values of mobility, such as, presence of interface trap states

and interface barrier, disorder arising due to random orientation of crystallites,

charge traps present in the bulk of the semiconductor. Typically, when a hole in

pentacene hops from one crystallite to the other, the hole has a possibility to drown

in a charge trap. In the case of amorphous film of pentacene, the situation is even

more griever, as the trap density is much higher, as compared to the polycrystalline

form.

An experimental investigation on the existence of such charge traps is provided

by Seggern et al.10 Charge traps play a significant role in bringing down the ef-

fective mobility of the carrier. Therefore, parameters, such as, density of states for

traps, effective carrier density of traps and location of trap energy level in the band

diagram, are crucial in determining mobility. The charge transport properties of

pentacene can be studied in two possible geometries, namely, the organic field ef-

fect transistor (FET) setup and a sandwich cell setup. In earlier studies, various

research groups have fabricated pentacene-based sandwich cells and obtained its

I–V characteristics. Numerical modeling was also performed to match the simu-

lated data with the experimental values of current. In this regard, work by Knapp

et al. and Diao et al. could be highlighted.11,12 In all these simulations, the location

of trap energy were neither taken into account nor determined. Besides, the value

for density of trap states and mobility was assumed, so as to match the simulated

current with the experimental value. In the present communication, no such as-

sumption is made. The I–V characteristics of pentacene have been simulated for

a range of temperature. The data is analyzed to obtain many significant electronic

parameters related to traps in pentacene, such as its density of states, carrier den-

sity from traps and location of trap energy level. Besides, parameters pertaining to

mobility, such as the value of field free mobility and Poole–Frenkel coefficient have

also been worked out.

2. Theory

Numerical modeling for I–V characteristics of a sandwich device could be performed

by solving three basic equations self-consistently, namely, (a) continuity equation for

holes, (b) Poisson’s equation and (c) drift-diffusion equation. Besides, the solutions

of these three equations are also coupled with Poole–Frenkel model variation of

mobility with electric field and Langevin model for recombination.13–18 For self-

consistent solution, widely accepted methods by Newton as well as Scherfetter-

Gummel are followed in this paper.19,20 In the I–V characteristics of all organic

sandwich devices, there is a certain voltage, called knee voltage (Vo), below which

the device shows ohmic characteristics, while for values of voltage above Vo, the

current follows the traits of space-charge-limited conduction (SCLC). In this report,

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A temperature dependent study on charge dynamics

the I–V characteristics of a two-dimensional sandwich cell is simulated. So, it would

be better to use line current density K, instead of its three-dimensional equivalent

J . The line current density K shows dependence on temperature, as well. In the

ohmic region of operation, the thermally activated nature of K is given by the

following relation21

K(T ) = qNvsµE exp(−∆Ec/kBT ) . (1)

Here, Nvs is density of states at the highest occupied molecular orbital (HOMO)

level of semiconducting molecule, q is the magnitude of electron charge, E is the

electric field, ∆Ec is the hole activation energy, kB is the Boltzmann constant and

µ is the charge-carrier-mobility. Since this paper deals with charge transport in a

pentacene sandwich cell, in which, majority carriers are holes, only hole mobility is

taken into consideration. The mobility is not a constant parameter. In general, it

depends on various factors such as electric field, temperature, dopant concentration,

presence of undesired impurities, traps, surface states etc.22–24 Taking all these

parameters into consideration, makes the extraction of field free mobility (µo) a

daunting task. However, an estimation could be made if the dependence of mobility

on one of the parameters, electric field E, is taken into account. For organic devices,

(2) shows the functional relationship between mobility and electric field.25

µ = µ0 exp(0.89γ√E) . (2)

Here, γ is the Poole–Frenkel coefficient. This relationship could be utilized to ex-

tract µ0 from the transfer characteristics of the pentacene-based FET. Although,

by the study or simulation of I–V characteristics of organic FET (OFET) values

of mobility could be extracted. But, these values are field-dependent values of mo-

bility. Determination of field inside the channel of OFET is another complicated

issue, as the field is determined by two orthogonally applied potential differences,

namely drain-source voltage (VDS) and gate-source voltage (VGS). Nevertheless,

the polarization of dielectric molecules and interface states makes the local field,

exceptionally complicated to estimate. As an oversimplification, the field due to

VDS could be taken as the effective field. This is because the drift of charge carriers

through the channel takes place from drain to source. Here, the leakage through the

gate dielectric is neglected. Mobility is involved in various other relations, which

can be further used to determine a number of important physical parameters for

the device, as explained below.

As mentioned earlier, the I–V characteristics of a two-dimensional device shows

signs of SCLC above knee voltage. It is to be noted that, the SCLC behavior in

organic molecular thin film device is trap limited. Charge traps are of various kinds

and it can be categorized in a number of ways. Based on location in a sandwich cell,

it could be interfacial trap or bulk trap.26,27 Based on the location of energy level in

the energy band diagram, a trap could be deep or shallow. Although, a number of

research work could be found on the role of deep traps and shallow traps in organic

electronic material, none clearly classifies under what condition a trap could be

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Fig. 1. Classification of traps in energy band diagram.

designated as deep trap or shallow trap.11,12 Figure 1 clearly outlines deep traps

and shallow traps in the energy level diagram of an organic electronic molecule. In

any case, traps play a significant role in slowing down the movement of charge from

anode to cathode or vice versa. This in turn affects the mobility and the overall

line current density. The equation for SCLC takes a different form when such traps

are present, as shown in Eq. (3) (Refs. 28) as given below

K(T ) = 0.57εµθs(T )V 2

d2, (3)

where V is the applied voltage and d is the thickness of active layer in the sandwich

cell. Here, it is to be noted that the prefactor of 0.57, instead of 9/8 arise due to

two dimensionality of the device.29 θs(T ) is a factor which signifies fraction of free

charges that are actually taking part in conduction process across the sandwich

cell. It is given by the following expression, for only the hole device.30

θs(T ) =Nvs(T )

Nts(T )exp

{

−

(

Et − Ev

kBT

)}

. (4)

The surface density of states in valence band/HOMO (Nvs) is related to its three-

dimensional equivalent (Nv), and Nv is given by a standard relation for semicon-

ductor.31

Nv(T ) = 2

(

2πkBTm∗

h

h2

)3

2

. (5)

Here, Nts in (4) is the surface density of trap, m∗

h in (5) is the effective mass of

hole, h is the Planck constant and (Et − Ev) is the location of energy level in

energy diagram of the organic semiconductor. Since, Nv in Eq. (5) is proportional

to T 3/2 and µ in Eq. (3) goes as T−1/2, it indicates that a linear relationship of

ln(K/T ) versus 1/T should exist. In that case, the slope gives the value of trap

depth (Et − Ev). Density of states of traps (Nts) and effective carrier density of

traps (no) at various temperatures could be obtained, if the values of θs(T ) are

known.

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Here, the knee voltage of the I–V characteristics of these sandwich cell comes

for rescue, as it is related to θs(T ) through the following relation.19,22

Vo(T ) =qnosd

0.57ǫ0ǫrθs(T ). (6)

Here, nos is the number density of charge contributed from charge traps. In the

next section, various physical parameters for a two dimensional sandwich cell of

pentacene, such as, Nvs, Nts, θs(T ) and nos are obtained.

3. Results and Discussion

A schematic diagram of the two dimensional sandwich cell with pentacene as an

active material is shown in Fig. 2. The thickness of pentacene layer is kept at

250 nm while for the gold electrodes at top and bottom of the active layer, is

60 nm. The I–V characteristics of Au (top)/pentacene/Au (bottom) sandwich cell

is numerically modeled for a range of temperatures lying between 150 K to 350 K,

as shown in Fig. 3. For all simulations, the voltage is allowed to vary in the range

of −1 V to 1 V, as this range is used by other researchers,12,32 who have made

their experimental study on similar sandwich cells based on pentacene. The series

of I–V characteristics at various temperature reveals an interesting behavior. All

data points show ohmic behavior initially for a certain voltage value, known as

knee voltage (Vo). For values of voltages above Vo, the I–V curve deviates from

linearity and curves up, showing SCLC nature. The knee voltage could be extracted

from these plots by extending the line corresponding to I–V data for low voltage

values, typically near 0 V, and drawing an asymptote to the I–V curve for high

voltage value, typically near 1 V. The low-voltage I–V line and the high-voltage-

asymptote intersect at a point. The voltage value corresponding to this point is

the knee voltage.33 Following this procedure, values of Vo is extracted for all I–

V data corresponding to various temperatures. Table 1 shows these values as a

function of temperature. For the extraction of activation energy (∆Ec), the value

of current corresponding to 0.3 V is extracted from these I–V characteristics of

all temperatures. The reason for choosing 0.3 V is that it is much below the knee

Fig. 2. A schematic of Au/pentacene/Au sandwich device.

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Fig. 3. I–V characteristics of Au (top)/pentacene/Au (bottom) sandwich cell at (a) 150 K(b) 250 K (c) 300 K and (d) 350 K. Note: change in order of magnitude in the current.

Table 1. Knee voltage and corresponding current as function oftemperature.

Temperature (K) Knee voltage (V0) (V ) Current (A)

150 0.62 0.20× 10−13

250 0.58 0.30× 10−10

300 0.50 0.50× 10−9

350 0.35 0.45× 10−8

voltages of all the temperature dependent I–V data. See Table 1 for more details.

The value of ∆Ec could be found in Table 2. (1) inconjuction with (2) can also be

utilized to obtain the Poole–Frenkel coefficient γ for pentacene by considering data

points for two voltage values at two different temperatures.

Table 2. Activation energy, Poole–Frenkel coefficient, traps levels, free field mobilityand mobility at 0.8 V.

Name Parameter Value Units

Activation energy ∆Ec 0.29 (eV)Poole–Frenkel coefficient γ −16.89× 10−3 ((V/cm)−1)Free field mobility µ 5× 106 (cm2/(Vs))Location of shallow trap Et −Ev 0.24 (eV)Charge-carrier mobility (at 0.8 VDS) µ 690 × 103 (cm2/(Vs))

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VGS(V)

Fig. 4. Transfer characteristics for pentacene-based OFET. The solid line show fit to the Eq. (8),the inset shows the schematic of pentacene FET used for the simulation.

The value of γ comes out to be −16.89×10−3 V/cm. The negative sign indicates

that mobility decreases with increment in electric field. Such phenomenon is not

new in the field of organic semiconductors.34 This could be due to freeing of trapped

charges from various trap sites present in the bulk of pentacene, as well as at the

interface. These excess charges cause an increase in the events of collision, thereby

decreasing the mobility of charge carriers in organic devices.

The field free mobility (µo) is a significant physical parameter that characterizes

an organic semiconductor. It appears in (1) in conjunction with (2). There are

two unknown physical parameter in (1), namely, Nvs and µo. The available data

is insufficient to extract both the parameters. Hence, to determine µo, mobility

values are extracted from numerically modeled transfer characteristics of pentacene-

based FET at various values of drain voltage to source voltage VDS . The transfer

characteristics of FET device is shown in Fig. 4. The inset shows a schematic

diagram used in this study. The straight line fitted to the data in Fig. 4 is the

equation

ID =

(

Z

LµCiVD

)

VG −

(

Z

LµCiVtVD

)

, (7)

where L is the channel length (30 µm), Z is the channel width (500 µm), Ci

(230 µF/m2) is the capacitance per unit area, Vt is the threshold voltage and VG

is the gate voltage. The mobility values thus extracted correspond to the electric

field E = VDS/L. Such extraction of µ from the slope of the straight line fit is

performed for five different values of VDS at unequal intervals but close to 0 V.

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Extrapolation was performed to obtain the field free value of µo. It is found to be

5 × 10−6 cm2/(Vs). It is quite low with respect to the mobility values obtained

from pentacene-based OFETs, where values as large as 5 cm2/(Vs) have been re-

ported.2–4 The reason for such a mismatch are quite a few, but significant. First, for

a quantum confined lower dimensional structure, it can be shown that the phonon

limited mobility of charge carriers is significantly lower than its higher dimensional

equivalent.35 Finally, the presence of traps lowers down the mobility by a significant

margin, as it is estimated in this analysis.

Charge conduction in amorphous or polycrystalline semiconductors, especially

of organic variety, exhibits space-charge limited (SCL) behavior. This nature of

charge flow could be treated as trap free SCLC or trap limited SCLC. It is highly

likely that such a material contains charge traps within its bulk. These charge traps

can function in bidirectional manner, i.e., it could trap charge which causes current

to get limited, or it can release the trapped charge at high electric fields which

causes mobility to decrease. The decrease of mobility has already been confirmed

by the negative value of Poole–Frenkel coefficient.

For the determination of Et − Ev, the data points for ln (K/T ) and (1/T )

are extracted for a voltage value of 0.8 V. This corresponds to the SCL regime

of I–V characteristics. A plot of these data points is shown in Fig. 5. It is fitted

with natural logarithm of (3) in conjunction with (4). The slope of the fit provides a

value of 0.24 eV for this parameter. The inset of Fig. 5 shows a representative energy

diagram of the sandwich cell. The determination of Nts is not straightforward. For

its evaluation, the value of density of state (Nvs) at HOMO level/valence band

edge is required. As mentioned in the previous section, it could be estimated in (5).

The effective mass of hole (m∗

h) could be taken as 8.92 times of mass of free hole.

1/T(K–1)

In(K/T

)

Fig. 5. Arrhenius plots for the SCLC conduction. Solid line shows the fit of logarithm of Eq. (4)in conjunction with Eq. (5) the inset shows energy band diagram of sandwich cell.

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This value has already been determined by Coropceanu in his work.36 Since the

sandwich device in this simulation study is a two-dimensional device, the density

of states in two dimensions (Nvs) are considered. Nv and Nvs are related with each

other by the relation

Nvs = (Nv)2/3 . (8)

Mathematically, similar relation exists between Nt and Nts. The value of θs (T )

corresponding to various temperature can be obtained using (3) and at a value of

0.8 V. A range of values is shown in Table 3. A plot of θs versus T in Fig. 6 reveal

that the fraction of charge participating in the conduction, within the sandwich

cell increase by five orders of magnitude with the strength of electric field across

the sandwich cell. This result is precisely in-phase with the prediction made earlier

in this section while analyzing for the negative value of Poole–Frenkel coefficient.

Table 3 also shows extracted values of Nvs, Nts and nos. The trap density of states

comes out to be of the order of 1028 cm−3, while the charge-carrier density due to

traps hovers around 1019 to 1025 cm−3. Simulation work has also been carried out in

the work of Diao et al. There, the assumed value of deep trap concentration is of the

order of 1015 cm−3.11 This value was used to model numerically the experimental

J–V characteristics of a pentacene sandwich cell. However, no reference to the

Table 3. Carrier concentrations trap carrier concentrations and effective carrier concentrationsas a function of temperature.

Temperature Line current Nvs Nts Effective carrier density(K) density (A/cm) (cm−2) (cm−2) of traps no (cm−2)

150 5.055 × 10−8 3.82× 1021 9.32× 1018 1.05× 1013

250 6.388 × 10−5 6.37× 1021 2.06× 1019 1.30× 1016

300 8.556 × 10−4 7.64× 1021 1.24× 1019 1.51× 1017

350 5.138 × 10−3 8.91× 1021 8.29× 1018 6.35× 1017

Fig. 6. Variation of θs as a function of temperature.

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role of shallow traps was made in that investigation. Besides, the location of trap

energy level was also not pointed out in that work. In the present communication,

we have obtained the location of energy level to be 0.24 eV above the HOMO level

of pentacene. And, as per the criteria described in theory section of this report, the

trap level energy so obtained belongs to the class of shallow trap.

4. Conclusion

Temperature dependent I–V characteristics of two-dimensional Au/pentacene/Au

sandwich cell has been simulated. The device shows both ohmic and SCL nature

below and above knee voltage, respectively. The temperature dependent data be-

longing to ohmic region has been analyzed to obtain a value of 0.29 eV for activa-

tion energy. Field free mobility and Poole–Frenkel coefficient (γ) are two important

physical parameters for electrical conduction through organic semiconductors. From

the numerically modeled output characteristics of pentacene-based FET, these two

parameters are extracted out and the values are 5 × 10−6 cm2/(Vs) for field free

mobility and −16.89× 10−3 cm/V for γ. The negative sign suggests that mobility

decreases with electric field which might be due to release of trapped charge from

the trap sites with increment in field value. Various other parameters such as den-

sity of states for traps, effective carrier density due to traps and location of trap

energy level are also determined from the temperature-dependent SCL I–V data

of the sandwich cell. The trap energy level is found to be located 0.24 eV above

the HOMO level of pentacene. It is also observed that the fraction of charge par-

ticipating in the process of conduction increases by five orders of magnitude with

temperature. Such increase in charge concentration could lead to increase in colli-

sion event, thereby decreasing the mobility. In this paper, the mobility depends on

electric field only, but it leaves a scope for an improved application of an adequately

complete model for mobility that would comprise both field and temperature de-

pendence. Analysis in this direction is already in progress.

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A TEMPERATURE DEPENDENT STUDY ON CHARGE DYNAMICS IN ORGANIC MOLECULAR DEVICE: EFFECT OF SHALLOW TRAPS ON SPACE CHARGE LIMITED BEHAVIOR