Iwamoto M., Kwon Y.-S., Lee T. (Eds.) Nanoscale Interface for Organic Electronics

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CHAPTER 2

ANALYSIS OF CONTACT RESISTANCE AND SPACE-CHARGE

EFFECTS IN ORGANIC FIELD-EFFECT TRANSISTORS

Martin Weis, Takaaki Manaka and Mitsumasa Iwamoto

Department of Physical Electronics, Tokyo Institute of Technology,

2-12-1 O-okayama, Maguro-ku, Tokyo 152-8552, Japan

E-mail: iwamoto@pe.titech.ac.jp

We present a brief review on the limitation of charge injection

to organic field-effect transistor due to interface metal-organic

phenomenon, the contact resistance. Experimental methods for

estimation of the contact resistance are summarized and their analysis

is discussed. Voltage dependence of the contact resistance is carefully

studied in respect to the definition of contact resistance and its time

dependence during the device charging is illustrated. The physical

background provides design of contact resistance.

1. Introduction

Semiconductor devices using organic materials,

such as thin film

transistors,

and light emitting diodes,

have attracted a lot of research

interests. With the development of organic materials with high

mobilities, recent trend in the research on the organic field-effect

transistor (OFET) has been concentrated on the applied research

mostly focused on increase of carrier mobility and many experimental

approaches have been exerted. Among them are development of

modified surface gate insulator, use of single crystal semiconductor

layer, etc.

4,5

Along with these researches, the importance of the basic

research such as injection, accumulation and transfer mechanisms is

being recognized to improve the OFET performance. Even though there

is significant study, the device physics of OFET is not yet clear in

M. Weis, T. Manaka and M. Iwamoto 10

comparison with that of inorganic FET structures. Various theoretical

studies have been carried out to clarify the device physics of OFETs,

6-8

but attention was focused on transport phenomenon only. However,

recently was research aimed on OFET devices where it has been shown

that carriers injected from a source electrode dominate OFET operation.

Therefore deep understanding of injection processes is crucial for further

application of OFET.

However, improvement of the carrier transport in the OFETs revealed

another one bottleneck of OFETs: the charge injection. This barrier is

expressed by the contact resistance (R

) and in OFETs it is a serious

problem for practical applications.

9,10

The contact resistance R

has many

origins, such as the non-uniformity of organic semiconductors, the

presence of dipole layers at the interface, electrode resistance, and the

interfacial energy states.

11-13

At least two requirements — low-voltage

operation and high-frequency performance — are responsible for reducing

the values of the contact resistance R

Therefore, to optimize the

device performance, advanced techniques for preparing OFETs must be

developed. To drive OFETs more efficiently, modeling of OFETs,

while accounting for R

, where both the effect of barrier height for carrier

injection

and charge accessing time from the electrode to organic

material plays a crucial role, must be carried out. Note that the device

contact effect influences the device contact operation conditions, such as

the potential energy distribution in the channel of OFET.

The carrier

mechanism is influenced by R

at the metal-organic material interface

when the energy difference between the Fermi level of metal electrode

and the highest occupied molecular orbital (HOMO) of organic

semiconductor dominates over the hole injection. In addition, here is a

force from the applications side. Commercial use of organic devices

requires decrease of the OFET channel length as much as possible,

since the cut-off frequency as a main parameter for high-frequency

response is proportional to 1/L

(L: channel length). Hence so-called

0.7 scale-down rule is continuously employed for the improvement of

device performance. However, for a sub-micrometer channels the contact

resistance it is expected to be a major contribution to the device

resistance.

Hence, we cannot simply employ the scale-down rule, and

contact resistance is an important parameter for design of nanoscale

Analysis of Contact Resistance and Space-Charge Effects in OFETs 11

devices based on organic semiconductors. This is the most crucial

problem in nanoscale devices.

2. Contact Resistance Definition

The charge transport through the OFET device is usually discussed

by three processes: (i) carrier injection from the source electrode,

(ii) transport through the channel and (iii) extraction from the channel to

the drain electrode. This can be roughly described by three independent

resistors, as is illustrated in Fig. 1. The resistance associated with carrier

injection and accumulation bellow the electrode is denoted as a parasitic

resistance R

, while resistance depicting carrier transport across the

channel region is denoted as a channel resistance R

. Intuitively, the

channel resistance is proportional to the channel length

ds g gs th

d ( )

V L

I WC V V

= =

−

(1)

where the drain-source current I

is ruled by the drain-source and

gate-source voltages, V

and V

, and is proportional to the gate

insulator capacitance per unit of area C

, mobility

and channel width

and length W and L, respectively. This relation valid in the linear region

(i.e. V

– V

» V

) gives us possibility to separate parasitic resistance by

electrical measurements of transistors with various channel lengths.

Source

Drain

Gate insulator

Gate

Active layer

Fig. 1. A schematic view of the organic field-effect transistor (OFET) with channel

resistance R

and parasitic resistance R

M. Weis, T. Manaka and M. Iwamoto 12

The parasitic resistance describes carrier injection and transport

through the organic semiconductor film to the interface with the gate

insulator. For simplicity, we neglect ohmic wire resistance (lead

resistance). Hence, the parasitic resistance can be separated to the contact

resistance R

and semiconductor resistance R

expressing injection and

transport

= R

+ R

. (2)

Here the contact resistance is usually significantly higher than resistance

of organic semiconductor thin film. Thus the parasitic resistance is

usually unified with the contact resistance. Description by the equivalent

electric circuit can be useful and the Maxwell-Wagner model

is found

as a powerful tool for description of charging of transistor.

22,23

There, the

OFET is modeled as metal-insulator-semiconductor (MIS) structure with

a contact resistance (see Fig. 2).

Using this equivalent circuit the surface charge Q

accumulated on

the organic semiconductor–gate insulator interface is in steady state

approximately calculated as

s g gs ds

1 ' ,

Q LWC V V

 

= − −

 

 

(3)

Source

Gate

Fig. 2. The Maxwell-Wagner model of OFET as a double layer capacitor.

Analysis of Contact Resistance and Space-Charge Effects in OFETs 13

where

and

stand for the Maxwell relaxation times of semiconductor

and insulator, respectively. Here we must point out reduced gate voltage

through the potential drop on the resistor R

= R

/(R

+ R

This charge is conveyed along the OFET channel to the drain electrode

by the average electric field

' ' /

E V L

formed between the source

and drain electrodes, where

ds ds c ds

' – '

V V R I

. Note here idea of ohmic

contact for the contact resistance, i.e. potential drop across the resistance

c ds

V R I

∆ =

, which is valid only if the channel resistance is larger than

parasitic resistance. Hence, as a result through the OFET flows current

gs c ds

s s

' '

' ' .

V R I

Q Q

I E

L L L

µ µ

−

= =

(4)

In other words, potential drop across the R

resistor influences carrier

accumulation as well as carrier transport. By substitution of Eq. (3) to

Eq. (4) we can obtain

s ds

ds eff

Q V

L L

(5)

with effective mobility

eff

ch tr

µ µ

τ τ

 

 

 

, (6)

where transit time

reaches form

gs th ds

( ' )

V V V

− −

(7)

and time required for charging of organic semiconductor–gate insulator

below the source electrode time

is expressed as follows

ch c gs

R C

(8)

Here, the

= C

WL represents capacitance of source-gate electrode

system. In detail, the charging time directly corresponds to the contact

resistance and thus can be used for R

evaluation in the experiment.

M. Weis, T. Manaka and M. Iwamoto 14

However, the question what means the contact resistance still

remains. Although the contact resistance is common used term to reach

deep understanding of this phenomenon we need go to the physical

background. The contact resistance is the element of the equivalent

electric circuit only and stands for a potential drop due to metal/organic

interface. Note that this potential drop does not require to be just

on the metal/organic interface only, but it is distributed through the

organic semiconductor in film thickness direction. In detail, after

application of the gate-source voltage V

it is established potential drop

∆V

= V

/(C

+ C

) across the organic semiconductor film. This creates

an electric field E

= ∆V/d

: thickness of semiconductor film) as a

motive force for carrier injection. If there is present no injection barrier

the charge is successfully accumulated on the semiconductor–gate

insulator interface and its space-charge field fully compensates applied

electric field. As a result, no potential drop across the semiconductor

film is observed. However, if the transport of the charge is comparable

with charge injection and accumulation (i.e.

≈

), there is not enough

charge accumulated on the insulator surface and potential drop still

remain also in the steady state. Although the slow injection originates

from the carrier injection barrier ∆Φ (for hole (electron) injection it is

difference between the Fermi energy of metal and HOMO (or LUMO)

level of organic semiconductor), there can be distinguished various

microscopic mechanisms

: (a) thermionic (Schottky) injection, (b) field

emission (Fowler-Nordheim tunneling) or (c) defect-assisted injection.

This leads to the voltage dependence of contact resistance, that is,

contact resistance is defined nothing but by carrier injection mechanism.

3. Effect of Electric Field on Contact Resistance

Let us discuss here the thermionic injection, which is common observed

in metal/organic interface. Hence, the current density j on the interface is

described

by relation

exp ,

j AT

k T

 

∆Φ −

= −

 

 

(9)

Analysis of Contact Resistance and Space-Charge Effects in OFETs 15

where k

and A are the Boltzmann and Richardson constants, and

Schottky parameter (=

πε ε

, where e is elementary charge, and

is dielectric constant of organic semiconductor). Hence, the resistivity

as a reciprocal value of conductivity

is in linear approximation defined as

1 2

exp ,

exp( )

k T x

E x AT k T

σ β

−

 

∂ ∆Φ

 

= = =

 

 

 ∂

(10)

with

x E k T

= as an electric field parameter. The fraction x/exp(x)

depicts the local electric field dependence of the contact resistance; it is

denoted as a space-charge field factor F and its electric field dependence

is shown in Fig. 3(a). This electric field represents local field which

consists of applied (external) field as well as space-charge (internal)

field. Also note that in Eq. (10) the interface conductivity is independent

on mobility. This is in contradict with standard approach used for bulk

conductivity (

= en

, where n is carrier density).

For derivation of contact resistance is organic semiconductor treated

as a dielectric material with low intrinsic carrier density and an excess

injected charge accumulated on semiconductor–gate insulator interface

only. Since the electric field is assumed uniformly distributed across the

0 10 20 30

0.0

0.1

0.2

0.3

0.4

Space-charge field factor F (a.u.)

Electric field intensity (×10

V/cm)

(a)

0 -1 -2 -3 -4 -5

-2

-4

-6

0.6 0.8 1.0

-0.1

0.0

0.1

Slope: 0.499

Log (Log (Current))

Log (Voltage)

Drain-source current (µA)

Gate-source voltage (V)

(b)

Fig. 3. (a) The space-charge field factor F as a function of local electric field intensity

and (b) illustration of field effect on carrier injection for output characteristics of

pentacene OFET for various gate-source voltages (from -10 to -40 V) in low electric field

region. Inset depicts log

-log

scale for illustration of the Schottky injection.

M. Weis, T. Manaka and M. Iwamoto 16

organic semiconductor film from electrode to accumulated charge layer,

the contact resistance is evaluated as follows

= (11)

where S is effective injection area and d is potential drop length

representing distance on which potential drop appears (in our case

identical with semiconductor thickness d

In addition we must mention impact of contact resistance on carrier

injection in low electric field region. In ideal case the drain-source current

is only a linear function of drain-source voltage for V

– V

» V

. However,

in the experiment it can be observed deviation from ohmic contact as

is illustrated in Fig. 3(b). Detail analysis reveals thermionic injection

mechanism represented by the I ∝ exp(V

) relation with power exponent

α ≈ 0.5 (i.e. square root) of voltage, which is in accordance to Eq. (9).

4. Measurements of Contact Resistance

4.1. Transmission Line Method (TLM)

As is discussed above the total device resistance is the sum of the contact

resistance and the channel resistance, which is linearly dependent on the

channel length L. Hence, one of the simplest ways to evaluate contact

resistance is based on extrapolation of total resistance to the zero channel

length.

18,25,26

In detail, by measurement of the electrode system with

various channel lengths for the same semiconductor film it is possible to

construct total resistance versus channel length plot. There, the contact

resistance is estimated as the intercept for zero channel length, see Fig. 4.

Even though simplicity if this measurement is a great advantage, it

has few important drawbacks. First, we are forced to fabricate several

devices with identical properties in order to obtain total resistance versus

channel length plot. Second, contact resistance is affected by the charge

accumulated in the channel region, the TLM experiment should be done

with constant drain-source field, i.e. for precise measurements it is

necessary to scale drain-source voltage to channel length. Furthermore, this

method cannot distinguish contribution of the source and drain electrodes.

Analysis of Contact Resistance and Space-Charge Effects in OFETs 17

4.2. Other Electrical Measurements

Beside common used TLM setup also alternative electrical

measurements of the contact resistance were proposed: the gated four-

probe measurement

27-29

and the time-of-flight method.

The gated

four-probe measurement introduces two additional narrow electrodes

into the OFET channel, which are connected to high input impedance

electrometer to avoid drain-source current loss through these electrodes.

Extracted two additional potentials V

and V

from the channel region

give us in approximation of linear voltage dependence across the channel

possibility to estimate potential drops on the source and drain electrodes

as is illustrated in Fig. 5(a). Although this method has advantage of using

single device only, complicated electrode system can be used only for

longer channel lengths. In addition, for correct estimation of potential

drops on the source and drain electrodes it requires linear potential

profile across the channel, which is in steady state not always satisfied.

On the other hand, the time-of-flight method is a technique focused

on estimation of the time required for charge transport from the source to

drain electrode. As was discussed earlier the total transport time consists

of time required for carrier injection and accumulation bellow the source

electrode and carrier transport across the channel. In accordance to

0 20 40 60 80 100

Contact resistance

Gate-source voltage:

-40 V

-60 V

-80

-100 V

Total resistance (M

Ω

)

Channel length (µm)

Fig. 4. Transmission line method of top contact pentacene film with silver electrodes for

different gate-source voltages. Solid lines represent linear fit.

M. Weis, T. Manaka and M. Iwamoto 18

Eq. (7) the transit time is proportional to square of the channel length L

Therefore, the linear extrapolation of the transport time to the zero

channel length (see Fig. 5(b)) results to the charging time, which is

related to the contact resistance as is described by Eq. (8). In addition, it

is interesting to point out that the transient signal (voltage pulse) for

estimation of the contact resistance is used in experiment. In the transient

state the channel is not fully charged and still no space-charge field is

created. As a result, without space-charge field only ohmic transport is

established and the potential drop across the channel follows Eq. (1), i.e.

the linear potential across the channel is well satisfied. This is proved by

time-resolved experiment and simulation results

and can be understand

as a charging of semi-infinite interface.

4.3. Kelvin Probe Force Microscopy (KFM)

In contrast to previous methods based on linear approximation of the

potential across the channel region, the KFM gives chance to directly

measure surface potential profile. In this technique the atomic force

microscopy (AFM) with conductive tip is used for scanning of surface

morphology as well as surface potential.

17,32

Since the potential drop on

the electrode edge is measured directly, KFM is a strong tool for

0.0 0.5 1.0

Potential drop on drain

Potential (V)

Normalized channel length (µm)

Potential drop on source

(a)

(b)

Charging time

100

Transport time (µs)

Square of channel length (µm

)

Transit time

Fig. 5. Example of the result for (a) the gated four-probe measurement (for V

= 10 V)

and (b) the time-of-flight method, where the charging time corresponds to the contact

resistance.