JAIST Repository: An investigation of correlation between transport characteristics and trap states in n-channel organic field-effect transistors

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Title

An investigation of correlation between transport

characteristics and trap states in n-channel

organic field-effect transistors

Author(s)

Kawasaki, Naoko; Ohta, Yohei; Kubozono,

Yoshihiro; Konishi, Atsushi; Fujiwara, Akihiko

Citation

Applied Physics Letters, 92(16):

163307-1-163307-3

Issue Date

2008-04-23

Type

Journal Article

Text version

publisher

URL

http://hdl.handle.net/10119/4408

Rights

Copyright 2008 American Institute of Physics.

This article may be downloaded for personal use

only. Any other use requires prior permission of

the author and the American Institute of Physics.

The following article appeared in Naoko Kawasaki,

Yohei Ohta, Yoshihiro Kubozono, Atsushi Konishi,

Akihiko Fujiwara, Applied Physics Letters,

92(16), 163307 (2008) and may be found at

http://link.aip.org/link/?APPLAB/92/163307/1

Description

An investigation of correlation between transport characteristics

and trap states in n-channel organic field-effect transistors

Naoko Kawasaki,1Yohei Ohta,1Yoshihiro Kubozono,1,a兲 Atsushi Konishi,2and Akihiko Fujiwara2

1

Research Laboratory for Surface Science, Okayama University, Okayama 700-8530, Japan

2

Japan Advance Institute of Science and Technology, Ishikawa 923-1292, Japan

共Received 4 March 2008; accepted 25 March 2008; published online 23 April 2008兲

Transport characteristics in n-channel organic field-effect transistors are discussed on the basis of density of states共DOS兲 for trap states determined with multiple trap and release model. First the trap-free intrinsic mobilities, the activation energies, and total effective DOS for conduction band are determined with the effective field-effect mobility versus temperature plots and total DOS of trap states. Second the general formula for subthreshold swing S applicable to organic field-effect transistors is derived and the surface potentials are determined from the S determined from the transfer curves and the DOS for the trap states according to the general formula. © 2008 American Institute of Physics. 关DOI:10.1063/1.2908886兴

Field-effect mobility␮ for thin film organic field-effect transistors 共OFETs兲 is at most ⬃1 cm2_V−1_s−1_{, which is}

lower by three to four orders of magnitude than those in metal-oxide-semiconductor共MOS兲 field-effect transistors.1–4 This low ␮ value in thin film OFETs originates from both facts that␲-conduction network is not sufficiently expanded in the whole channel region and that trap states are formed in the gap between highest occupied molecular orbital共HOMO兲 and lowest unoccupied molecular orbital共LUMO兲. The trap states are produced by existence of impurities, artificial dop-ing, defects, and other disturbance of lattice periodicity. The total shallow and deep trap states were recently estimated by photoinduced carrier transfer measurements.5,6

Density of states 共DOS兲 for the trap states Nt共␧兲 at the

interface between gate dielectric and active layers in OFETs can be determined with multiple trap and release 共MTR兲 model.7–9 Here ␧ is the energy measured from LUMO for electron共or HOMO for hole兲. The Nt共␧兲 in unit of cm−2eV−1

is given by the following equation:7

Nt共␧兲 = C₀ e

冉

d␧a dVG

冊

−1 , 共1兲

where C0, e, ␧a, and VG are gate capacitance per area,

el-emental charge, activation energy, and applied gate voltage, respectively. The␧awas determined from the temperature T

dependence of drain current ID;␧ais approximately equal to

␧. Lang et al. determined the Nt共␧兲 for pentacene crystal FET

and showed an exponential decay for the increased␧ above the top of HOMO band and a single peak due to bias-stressed defect.7

Recently, we have studied trap states for C60dendrimer

Langmuir–Blodgett共LB兲 film and C60 thin film FETs共Ref. 8兲 on the basis of MTR model. The Nt共␧兲 values for the FETs

showed a simple exponential decay with an increase in␧.8 The plots were fitted with the following equation:

Nt共␧兲 = Nt共0兲exp共−␤␧兲. 共2兲

The DOS, Nt共0兲, for the trap states at ␧=0 and the slope

␤ of exponential DOS tail for LB FET were 8.1

⫻1019_cm−3_eV−1 _共6.1⫻1013_cm−2_eV−1_{兲 and 6.4 eV}−1_,

re-spectively, while the Nt共0兲 and ␤ for C60 thin film FET

were 2.0⫻1019_cm−3_eV−1 _共1.5⫻1013_cm−2_eV−1_{兲 and}

5 eV−1_.8

The Nt共␧兲 for LB film FET are higher by a factor of

4 than that for C₆₀FET at␧=0.1–0.4 eV. In this estimation,8 the depth of trap states is assumed as 7.5 nm on the basis of the previous report.7,10

In this letter, we have discussed a correlation between DOS of trap states determined by our group for the LB and C₆₀ FETs 共Ref. 8兲 and their transfer characteristics. First,

intrinsic mobility ␮0, difference between trap state and

LUMO level ␧a

⬘

and total effective DOS for conduction

band Nc have been determined from effective field-effect

mobility ␮eff共T兲, as a function of T and Nt共␧兲 in the C60

dendrimer LB and C60 thin film FETs. Here, the ␧a

⬘

corre-sponds to the activation energy determined from ␮eff共T兲-T

plot, and it should be approximately equal to ␧a.

Further-more, the surface potentials␾s’s, have been determined for

these FETs by use of the new S formula applicable to OFETs developed in this study.

First, the correlation has been investigated between ␮eff共T兲 and Nt共␧兲. Here, ␮eff共T兲 in n-channel FET device is

given by11–14 ␮eff共T兲 =␮0

冒

再

1 + Nt Nc exp

冉

␧a

⬘

kBT

冊

冎

. 共3兲

The Nt and kB are the total DOS for the trap states and

the Boltzmann constant, respectively. The ␮0 corresponds

to the ␮eff共T兲 in trap-free FET device. The above formula

implies that the increase in Nc by the high crystallinity

of thin films or high␲-conduction network, and the decrease in Nt by the reduction of defects and impurities

play an important role to the realization of high ␮eff共T兲

value.

The ␮eff共T兲 was obtained from ID1/2-VG plot at VDS

= 100 V with the general formula for saturation drain

a兲_{Electronic mail: [email protected].}

APPLIED PHYSICS LETTERS 92, 163307共2008兲

0003-6951/2008/92共16兲/163307/3/$23.00 92, 163307-1 © 2008 American Institute of Physics

current.15,16 We can estimate the Nt by using the following expression:

冕

0 ⬁ Nt共␧兲d␧ =

冕

0 ⬁ Nt共0兲exp共−␤␧兲d␧ = Nt共0兲 ␤ = Nt. 共4兲

For the LB FET, the Nt has been estimated to be 1.3

⫻1019_cm−3 _共9.5⫻1012_cm−2_{兲 from the N}

t共0兲 of 8.1

⫻1019_cm−3_eV−1 _共6.1⫻1013_cm−2_eV−1_{兲 and the ␤ of}

6.4 eV−1 reported in Ref.8according to Eq.共4兲. The plot of ␮eff共T兲-1000/T for the LB FET is shown in Fig.1共a兲. The

plot can be well fitted by Eq.共3兲, and the␮₀,␧_a

⬘

and Ncfor

LB FET have been determined to be 0.02 cm2_V−1_s−1_,

100 meV, and 1.1⫻1020_cm−3 _共8.3⫻1013 _cm−2_兲,

respec-tively. The␮0of 0.02 cm2V−1s−1is the maximum value of

this LB FET expected in the case of trap free. This small␮₀ value implies the formation of incomplete␲-conduction net-work responsible for the n-channel transport because the value is directly associated with the mobility of free carriers in the conduction band. The␧a

⬘

is almost the same as that,

110 meV, for the pentacene thin film FET,11 which was es-timated with the same equation as Eq.共3兲; the grain size of pentacene thin films was 100– 200 nm.

Furthermore, the␮₀,␧a

⬘

, and Ncvalues for C60thin film

FET have been determined to be 0.37 cm2_V−1_s−1_{, 120 meV,}

and 2.6⫻1020_cm−3_共2.0⫻1014 _cm−2_{兲, respectively, from the}

fitted line 关Fig. 1共a兲兴. The ␮0 for C60 FET is higher by a

factor of 20 than that of the LB FET, but the␧a

⬘

is almost the

same as that for the LB FET. The small␮0reflects the small

mobility of free carriers, which is produced by a large pho-non scattering and scattering by the defects共disorder of lat-tice periodicity兲.16

Therefore, it can be concluded that the lattice disorder of LB films is larger than that of C₆₀ thin films formed by thermal deposition. On the other hand, the same␧a

⬘

suggests the same width in the distribution of trap

states. Therefore, the similar slope found in the Nt共␧兲-␧ plots

for LB and C60thin film FETs共shown in Ref.8兲 is consistent

with almost the same␧a

⬘

found in these devices. The ␧a

⬘

of

⬃100 meV shows a broad distribution of trap states in both FETs.

The Nc values for LB and C60 are 8.3⫻1013 and 2.0

⫻1014_cm−2_{, respectively. The N}

c for C60 is slightly higher

than that for LB FET, showing that the crystallinity of C₆₀ thin films is higher than that of LB films. We tried to estimate the DOS for conduction band for the ideal close-packed layer of C₆₀. Here, it should be noticed that the depth of the chan-nel for C60 thin films is the monolayer scale, 1 nm,17 rather

than the trap depth, 7.5 nm.7,10The number of C60molecules

for 1 nm is 1.4⫻1014_cm−2_{, and the number of levels can be}

calculated to be 8.4⫻1014_cm−2 _{by a consideration of both}

threefold degenerated LUMO levels and two spin states.18 The Ncfor real C60FET device共2.0⫻1014cm−2兲 is less than

a quarter of the expected value for ideal close-packed layer 共8.4⫻1014_cm−2_{兲, showing that the real C}

60 thin films are

disordered. Thus, the total effective DOS for conduction band could be obtained from the Nt共␧兲 value and the

␮eff共T兲-T plot.

The S is defined by the following equation:16

S = dVG d log共ID兲 = ln 10

冒

冉

冋

e kBT −

再

d d␾s

冉

−d␾s dx

冊

冒

冉

− d␾s dx

冊

冎

册

d␾s dVG

冊

, 共5兲 where x is the depth of C60 thin films; the position at x = 0

refers to the interface between SiO2 gate dielectric and C60

thin films. Equation共5兲is available for ID-VGplot in any VDS

region. In general analysis for MOS FET which operates in an inversion regime, the second term in the parentheses of denominator of the right side of Eq. 共5兲 can be neglected because this term is replaced by 1/共2␾S兲=1/关2␾共0兲兴, where

␾共0兲 is the potential␾共x兲 at x=0 in the depletion regime, and 1/共2␾s兲 is very small compared to e/kBT in the weak

inver-sion regime. When the second term is neglected and d␾s

dVG

=

冋

1 +eNt共␧兲 + CD

C0

册

−1

is introduced into Eq. 共5兲, the S is given by well known formula16 S =

冉

kBT e

冊

共ln 10兲

冋

1 + eNt共␧兲 + CD C0

册

, 共6兲

where CD is the depletion region capacitance. Here, it

should be noted that the CDis strictly vanishing in the

accu-mulation regime because the depletion layer is not formed. However, as previously reported,8 the theoretical S values, 2.2 V/decade for LB FET and 1.8 V/decade for C₆₀ FET, calculated with Eq.共6兲at CD= 0 were smaller by a factor of

5 than the experimental S determined from ID-VG plots in

VDS= 100 V at 300 K 共10.2 V/decade for the LB FET and

7.9 V/decade for the C60FET兲 关Figs.1共b兲and1共c兲兴.

Highly purified C₆₀should be an intrinsic semiconductor with band gap EG of 2.6 eV,19 but the thin films of C60

formed by thermal deposition of normal grade of C60

共purity⬎99.5%兲 show n-type semiconductorlike electronic structures.20Therefore, the channel region is concluded to be formed by major carriers共or electrons兲 in the real n-channel C60 thin film FET, showing that Eq.共6兲must be

fundamen-tally changed to the formula which is applicable to the OFETs, i.e., accumulation region. In the accumulation re-gime, the second term cannot be neglected because it is not represented by 1/共2␾s兲 and actually 1/共2␾s兲 is not small in

comparison with e/kBT.16 In the accumulation regime of

n-type semiconductor, the␾共x兲 thin films can be represented as ␾共x兲 =kBT e

冤

ln 1 cos2

冉

C +

_冑

x 2LD

冊

冥

and LD is the Debye length, and C is cos−1关exp

共−e␾s/2kBT兲兴. By considering the relation d␾s/dx

=关d␾共x兲/dx兴x=0 and by substituting the above relation for

␾共x兲 into Eq.共5兲, the S is newly given by21 S =

冉

kBT e 共ln 10兲

冋

1 + eNt共␧兲 C0

册

冊

冒

冉

1 −1 2

冋

再

1 − exp

冉

− e␾s kBT

冊

冎

−1

册

冊

. 共7兲

163307-2 Kawasaki et al. Appl. Phys. Lett. 92, 163307共2008兲

In the accumulation regime, 兩␾s兩 is known to be only a

few kBT/e=25.9 mV at 300 K. Equation共7兲 refers to the S

formula for the electron accumulation of n-type semiconduc-tor. As␾sⰆ0 for the weak inversion region, i.e., hole layer

in n-type semiconductor, Eq. 共7兲 becomes Eq. 共6兲 where CD⫽0. Thus, Eq. 共7兲 can give the S value in all regime of

channel conduction in FET devices with n-type semiconduc-tor. It should be noticed that in the weak inversion regime, the S can be given by Eq.共6兲 for both p- and n-type semi-conductors but Eq. 共7兲 can be associated with only n-type semiconductor.

We can estimate the␾sfor LB and C60 FETs by

substi-tuting the experimental S estimated from ID– VG plot关Figs. 1共b兲 and 1共c兲兴 and the Nt共␧兲 at the corresponding VG

共⬍Vth兲 into the new S formula, Eq.共7兲. The␾svalue for C60

dendrimer LB FET has been estimated to be 26 mV from Nt共␧兲=2.5⫻1018cm−3eV−1 共1.9⫻1012cm−2eV−1兲 and the

experimental S of 10.2 V/decade, while that for C60thin film

FET was 27 mV from Nt共␧兲=2.1⫻1018 cm−3eV−1 共1.6

⫻1012_cm−2_eV−1_{兲 and the experimental S of 7.9 V/decade.}

These positive and small ␾s values indicate weak electron

accumulation at VGlower than Vthin both LB and C60FETs.

Thus a clear correlation between␮eff共T兲 and Nthas been

found and the Nc could be well estimated for OFETs.

Fur-thermore, the reliable␾scould be obtained from the

experi-mental S and the DOS of trap states on the basis of the universal S formula applicable to OFETs developed in this study. The␾s values confirmed a formation of electron

ac-cumulation layers in C₆₀ dendrimer LB and C₆₀ thin film FETs.

This work was partly supported by a Grant-in-Aid 共18340104兲 from MEXT, Japan.

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21_{The following equations:}

冋

e kBT −

再

d d␾s

冉

−d␾s dx

冊

冎

冒

冉

− d␾s dx

冊

册

d␾s dVG = e kBT

冋

1 − 1 2 sin2_C

册冋

1 + eNt共␧兲 C₀

册

−1 and 1 sin2_C=

冋

1 − exp

冉

− e␾s kBT

冊

册

−1 ,

are used in this derivation, and CD= 0 in the accumulation regime. FIG. 1. 共Color online兲 共a兲␮eff共T兲–1000/T plots for the C60dendrimer LB

FET and C₆₀thin film FETs are shown together with the fitting line with Eq.

共3兲. The large deviation of␮eff共T兲 from the fitted line, which is found in the

low 1000/T region 共T⬎300 K兲 of the LB FET, is due to the transition caused by a thermal fluctuation of C60dendrimer共Ref. 8兲. Therefore, the

␮eff共T兲 above 300 K in the LB FET was not used for the curve fitting.

ID– VGplots for共b兲 C60dendrimer LB and共c兲 C60thin film FETs. In共b兲 and

共c兲, the fitted lines are drawn in order to estimate S=关d log共ID兲/dVG兴−1.

163307-3 Kawasaki et al. Appl. Phys. Lett. 92, 163307共2008兲