RAPID COMMUNICATION

Effects of contact resistance on the evaluation of charge carriermobilities and transport parameters in amorphous zinc tin oxidethin-film transistors

Leander Schulz • Eui-Jung Yun • Ananth Dodabalapur

Received: 4 March 2014 / Accepted: 7 April 2014 / Published online: 23 April 2014

� Springer-Verlag Berlin Heidelberg 2014

Abstract Accurate determination of the charge transport

characteristics of amorphous metal-oxide transistors

requires the mitigation of the effects of contact resistance.

The use of additional electrodes as voltage probes can

overcome contact resistance-related limitations and yields

accurate charge carrier mobility values, trap depths and

temperature and carrier density dependencies of mobility

as well as trap depths. We show that large differences in

measured charge carrier mobility values are obtained

when such contact resistances are not factored out. Upon

exclusion of the contact resistance, the true temperature

dependence of charge carrier mobility appears in the form

of two clearly distinct mobility regimes. Analyzing these

revealed mobility regions leads to a more accurate

determination of the underlying transport physics, which

shows that contact resistance-related artefacts yield

incorrect trends of trap depth with gate voltage, poten-

tially leading to a misconstruction of the charge transport

picture. Furthermore, a comparison of low- and high-

mobility samples indicates that the observed effects are

more general.

1 Introduction

Transparent amorphous oxide semiconductors are

actively investigated for a range of applications

including sensors [4], memristors [18], active matrix

displays [21] and flexible electronics [11, 19]. The

active semiconductor materials can be deposited by a

variety of methods such as sputtering [8], pulsed laser

deposition [3], ink-jet printing [13], and other types of

solution-processing [14]. Electrical characterization of

these materials usually involves the fabrication of thin-

film transistor (TFT) structures which are then tested for

their linear and saturation characteristics, from which

key parameters such as the field-effect mobility, sub-

threshold swing and their temperature dependencies can

be evaluated.

One of the most promising amorphous oxide semicon-

ductors is solution-processable [7, 14, 22] zinc tin oxide

(ZTO) whose charge carrier mobilities can exceed 25 cm2/

Vs [2, 15, 20].

In this letter we report on the detailed current-voltage

characteristics of ZTO-based thin-film transistors (TFT)

and on the importance of gated 4-terminal measurements

as they reveal otherwise hidden energy and transport

regimes. A comparison of 2-terminal and 4-terminal

measurements shows that factoring out the effects of

contact resistance from the electrical measurement can be

vitally important in identifying the various trap-release

energy regimes, especially when the involved energy

values are small.

L. Schulz (&) � E.-J. Yun � A. Dodabalapur

Microelectronics Research Center, The University of Texas at

Austin, Austin, TX 78758, USA

e-mail: leander.schulz@outlook.com

A. Dodabalapur

e-mail: ananth.dodabalapur@engr.utexas.edu

Present Address:

L. Schulz

School of Physical Science and Technology, Sichuan University,

Chengdu, Sichuan 610064, China

Present Address:

E.-J. Yun

College of IT Engineering and Department of System Control

Engineering, Hoseo University, Asan, Choongnam 336-795,

South Korea

123

Appl. Phys. A (2014) 115:1103–1107

DOI 10.1007/s00339-014-8422-3

2 Results and discussion

We characterized the devices at various temperatures in the

range 69–330 K and extracted trap release energies. We

employ the term trap release energy instead of activation

energy as it more accurately describes the physical pro-

cesses in this system. To analyze data from these mea-

surements, we apply a charge transport model that is

applicable to ZTO and related amorphous oxide materials.

We compare measurements of a field-effect transistor

(FET) with a conventional 2-terminal configuration and

one that includes additional electrodes to factor out the

effects of contact resistance (4-terminal). The additional

electrodes are necessary to accurately characterize trans-

port in the linear regime of device operation. This config-

uration also allows for the correct determination of the trap

energies values as more than one energy regime is

revealed.

A bottom gate, top contact device structure was

employed, consisting of a platinum (Pt) gate, zirconium

dioxide (ZrO2) gate insulator, ZTO semiconductor and

patterned aluminum electrodes, and is illustrated in Fig. 1a.

The substrates on which these devices were constructed

were p-type silicon wafers. The detailed device fabrication

process has already been reported [14, 16].

The channel length, L, and width, W, of the TFTs are 75

and 750 lm, respectively. The two voltage probes, V1 and

V2 reach 10 lm into the channel from the source/drain and

result in an effective channel length, Leff = 30 lm. These

two additional electrodes are symmetrically located in the

channel with respect to the source and drain electrodes.

Such a configuration is ideally suited to evaluate the linear

characteristics of the transistor. The carrier density varia-

tion between these additional electrodes is relatively small,

allowing us to make a very reasonable assumption that the

carrier density is approximately constant. This is especially

true for small, applied source-drain biases. Measurements

involving the use of these additional electrodes V1 and V2

are designated 4-terminal (4T) measurements, whereas

measurements that involve only the source and drain (apart

from the gate) are designated as two-terminal (2T) mea-

surements. All measurements were performed with a

Desert Cryogenics Cryoprobe station at a pressure of the

order of 10-4 mbar. Typical room temperature output

characteristics are shown in Fig. 1b.

b 1.0

0.8

0.6

0.4

0.2

0.07

I DS (

µA)

VG10 V

9.5 V . . . .0.0 V

VDS (V)

a

PtZrO2

ZTO

S D

Leff

L

V1 V2

6543210

Fig. 1 a Schematic structure of the sample: Pt = platinum (gate),

ZrO2 = zirconium dioxide (gate dielectric), ZTO = zinc tin oxide and

Al = aluminum. The probes V1 and V2 were used to measured the

potential difference within the channel and thereby avoiding the

contact resistance and other issues at the electrode-ZTO interface.

The effective channel length, L, reduces to Leff. b Typical output

characteristics of a ZTO TFT

0.020

0.015

0.010

0.005

0.0002T LIN

0.14

0.12

0.10

0.08

0.06

0.04

0.02

0.00

67 K 132 K 70 K 141 K 73 K 150 K 76 K 160 K 79 K 170 K 82 K 181 K 85 K 192 K 90 K 212 K 95 K 233 K 102 K 254 K 109 K 275 K 116 K 300 K 124 K 330 K

2T SATµ 4

T, L

IN (

cm2 /V

s)µ 2

T, L

IN (

cm2 /V

s)µ 2

T, S

AT (

cm2 /V

s)

0.30

0.25

0.20

0.15

0.10

0.05

0.00

7654321

4T LIN

VG - VON (V)

a

b

c

Fig. 2 Device mobilities at different temperatures calculated as

explained in the text for the low mobility sample. a The 2T saturation

mobility, b the 2T linear mobility, and c 4T linear mobility. The

temperature dependences are similar. Note that l4T�lin [l2T�sat [l2T�lin

1104 L. Schulz et al.

123

The transfer curves were measured in the linear region

employing the 2T and 4T configurations at VDS = 1 V

values. The saturation characteristics, which are less sen-

sitive to the potential drops at the source and drain elec-

trodes, were measured in the 2T configuration at

VDS = 7 V. From these transfer curves, the mobilities

under different conditions are determined.

In the case of the 2T measurements, the 2T linear

mobility, l2T�lin, where the difference of the gate voltage and

the onset voltage, VG-VON, is[VDS, is given by: [10, 23]

l2T�lin ¼oIDS

oVG

L

W

1

CZrO2

1

VDSð1Þ

IDS and CZrO2ð210 nF/cm2 [16]) are the current between drain

and source, and the capacitance per unit area of the ZrO2

dielectric. If VG � VON\VDS, then the device operates in the

saturation mode and the mobility is calculated from: [10]

l2T�sat ¼offiffiffiffiffiffiffi

IDS

p

oVG

� �

2L

W

1

CZrO2

ð2Þ

For the 4T measurements, only the voltage difference

within the effective channel is considered, thereby

excluding the contact resistance at the aluminum-ZTO

interfaces. This leads to a modification of the standard FET

linear regime mobility equation and can be expressed as:

l4T�lin ¼oIDS

oVG

Leff

W

1

CZrO2

1

ðV2 � V1Þð3Þ

The different device mobilities described above are shown

in Fig. 2 as a function of VG � VON for temperatures

ranging from 69 K to 330 K. The applied gate voltage, VG,

was corrected by the onset voltage, VON, at which the

mobile carriers start to accumulate in the channel, to ensure

that the temperature dependence of the mobilities is

accurately determined [10, 15, 23].

The linear and saturation mobility values increase with

temperature as shown in Fig. 2. The room temperature 2T

linear and saturation mobilities are approximately 0.02 and

0.14 cm2/Vs, respectively, and are considerably lower than

the 4T linear mobility of 0.25 cm2/Vs. The difference

between 2T linear and saturation mobilities can be

explained by the different average electric fields in the

channel in the linear and saturation regimes. Under satu-

ration, the higher drain-source voltages result in improved

charge carrier injection from the electrodes and a larger

measured mobility value, whereas in the linear regime,

contact resistance effects reduce the measured mobility

considerably. Use of the 4T configuration factors out the

influence of contact resistance on the measured mobility

and hence we get the highest mobility values at a given

temperature. It must also be noted that the average charge

carrier density in the channel in the linear regime is higher

than in the saturation regime for a given gate voltage,

which leads to higher measured mobilities when contact

resistance effects are absent. Similar observations have

been reported for InGaZnO FETs by Abe et al. and Jeong

et al. [1, 9].

In many small channel length TFTs, the linear mobility

values determined with the conventional 2T methods are

significantly underestimated because of the high contact

resistance at the metal-semiconductor interface. This leads

to a large disparity between the 2T linear and saturation

mobility. This is often the case in other TFTs where contact

resistance plays a key role, such as organic TFTs. After

correcting for contact resistance, the linear mobility

increases steadily with gate voltage before saturating or

decreasing slightly at the highest gate voltages. The latter

behavior is also observed in TFTs with other semicon-

ductor active layers and is attributed to the charge carriers

being drawn closer to the interface with the gate insulator.

Interfacial roughness and enhanced trapping at the inter-

face can lead to lower mobilities [6, 17]. The increasing

mobility with carrier density is one of the signatures of

multiple trap and release (MTR) type transport [12].

0.18

0.16

0.14

0.12

0.10

141210864

1000/T (1/K)

4T LIN

ETR = 6.9±0.2 meV

Regime 1 Regime 2

µ 4T

, LIN

(cm

2 /Vs)

µ 2T

, LIN

(cm

2 /Vs)

EC

E

N(E)

tail states

N2D

EF,2

EF,1

b

a0.015

0.014

0.013

0.012

2T LIN

ETR = 3.4±0.2 meV

Fig. 3 a The 2T linear and b 4T linear mobility as a function of

reciprocal temperature for VG - VON = 1 V. Once the contact

resistance has been factored out, two distinct regimes appear

Effects of contact resistance 1105

123

The MTR model describes the behavior of charge car-

riers close to the mobility edge, an energy threshold that

separates localized and extended states [12]. The inset of

Fig. 3a illustrates the schematic energy versus the density

of states, N(E), near the conduction band edge, EC, of a

semiconductor. A two-dimensional density of states is

assumed, since the channel electrons are confined to a few

nm thick layer. The band tail states represent the localized

states. For charge carriers that are excited from the local-

ized states into the extended states beyond EC, the tem-

perature-dependent mobilities are calculated using Fermi-

Dirac statistics:

leff /1

1þ eETR=kBTð4Þ

where ETR ¼ EC � ET is the energetic difference between

the mobility edge and the trap energy. It is very important

to employ Fermi-Dirac statistics in calculating trap depths,

when the trap depths are lower than kBT : Use of Boltzmann

statistics can lead to substantial errors.

In addition to the large difference between the values of

the linear 2T and 4T mobilities, the comparison of the

temperature-dependent mobility for a given voltage, VG -

VON, also demonstrates the importance of 4T measurements

in the determination of the energies involved in charge

transport. Fig. 3a shows the 2T linear mobility for VG -

VON = 5 V. The 2T linear mobility monotonically decrea-

ses as the temperature decreases. A typical approach [7, 15]

would be to apply an exponential function or Fermi-Dirac

statistics (Eq. 4) to fit the data and extract the trap release

energies as indicated by the dashed line. However, the

contact resistance can hide the true temperature dependence

of the mobility. Equivalent to Fig. 3a, Fig. 3b shows the 4T

linear mobility as a function of the inverse temperature for

VG - VON = 5 V. It is clear that two distinct mobility

regimes appear; a nearly constant regime and a thermally

activated regime, denoted as regime 1 and regime 2. The

slope of the thermally activated regime (regime 2) represents

again the trap release energy. In semiconductors such as

ZTO, however, the trap energies are very small, and con-

sequently ETR are calculated using Fermi-Dirac statistics

(Eq. 4) instead of the Boltzmann approximation. Since the

trap release energy, ETR, of 6.9 ± 0.2 meV is relatively low,

most charge carriers spend a considerable fraction of time in

the conduction band. Similar trap energies near 10 meV

below EC have been reported for ZTO by using a modulated

photocurrent measurement technique [5]. The nearly con-

stant mobility regime is likely due to a very large density of

electronic states close to the conduction band edge. The

corresponding energy value is too small to be determined

but is less than 1 meV.

Figure 4 shows the trap depths as a function of

VG - VON for both the 2 and 4-terminal configurations.

8

6

4

2

76543

4-Terminal 2-Terminal

Fermi-Dirac statistics

VG - VON (V)

E T

R (

meV

)

Fig. 4 Trap-release energies, ETR, determined using the Fermi-Dirac

distribution function for the 2T and 4T configurations

7

6

5

4

3

2

µ 4T

,Lin (

cm2 /V

s)

1210864

1000/T (1/K)

VDS = 5.5 V: ETR = 10.1±0.7 meVVDS = 4.5 V: ETR = 15±1 meV

1.4

1.2

1.0

0.8

0.6

0.4

µ 2T

,Lin (

cm2 /V

s)

VDS = 1.5 VVG - VON

4.5 V 5.0 V5.5 V 6.0 V6.5 V 7.0 V

a

b

Fig. 5 The 2T and 4T linear mobility for a sample with higher

mobility than the sample described in Fig. 3

1106 L. Schulz et al.

123

The trap depth is approximately constant for the 4T con-

figuration, possessing a value of 6–7 meV. The trap depths

evaluated from the 2T configuration monotonically

decreases, with increasing gate voltage, from 7 meV to

below 2 meV. This misleading trend has its origin in an

artefact arising from the contact resistance. With increasing

gate voltage, the contact resistance decreases leading to

enhanced drain currents. This effect is stronger at lower

temperatures, and is responsible for the apparent decrease

in trap depth with increasing gate voltage. It would be very

easy to conclude from the 2T characteristics that the trap

depth decreases because the Fermi level is moving signif-

icantly closer to the conduction band edge. This would

result in erroneous interpretation of the transport charac-

teristics. This example underlines the importance of mak-

ing artefact-free measurements when evaluating charge

transport phenomena in these amorphous oxide TFTs.

To substantiate and generalize our findings, similar

data for a sample with a higher mobility has been ana-

lyzed. Fig. 5 shows the 2T and 4T linear mobilities for

corrected gate voltages of 4.5–7 V. In the case of the 4T

linear mobility data, there is evidence that the trap ener-

gies decrease with increasing gate voltage, as is expected

in systems exhibiting MTR transport. However, because

of the low trap depths in this material system, the

mobility tends to saturate are higher temperatures.

Observing the temperature dependence in both the low

and high mobility samples we can conclude that ZTO

TFTs exhibit the signatures of MTR transport in the limit

of low trap depths.

3 Summary

In summary, we have shown that factoring out contact

resistance by employing four terminal (4T) structures is

essential for accurate electrical characterization of amor-

phous zinc tin oxide-based thin-film transistors. It was

found that the linear mobility measured with the 4T device

was considerably higher than the 2-terminal (2T) mobili-

ties, demonstrating the value of the 4T configuration in

accurately measuring linear mobilities. More importantly,

4T measurements in contrast to 2T measurements reveal

two distinct mobility regimes and strikingly different

variations of trap energies with gate voltage.

Acknowledgments Financial support of the Schweizerischer Na-

tionalfonds (SNF) with the grant numbers PBFRP2-138632 and

PBFRP2-142820 and of the Office of Naval Research with the grant

number A002181202 is gratefully acknowledged.

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