Supplementary Information:
Extraction of the sub-bandgap density-of-states in polymer thin-film
transistors with the multi-frequency capacitance-voltage spectroscopy
Jaeman Jang, Jaehyeong Kim, Minkyung Bae, Jaewook Lee, Dong Myong Kim,
and Dae Hwan Kima)
School of Electrical Engineering, Kookmin University, Jeongneung-dong, Seongbuk-gu, Seoul
136-702, Korea
Jiyoul Leeb), Bang-Lin Lee, Bonwon Koo, and Yong Wan Jin
Display Device Laboratory, Samsung Advanced Institute of Technology, Yongin-si, 446-712,
Korea
PACS Numbers: 72.80.Le, 73.61.Ph, 85.30.Tv
a) Author to whom correspondence should be addressed. Electronic mail: drlife@kookmin.ac.kr
b) Author to whom correspondence should be addressed. Electronic mail: jiyoul.lee@samsung.com
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For the calculation of the I-V characteristics of organic TFTs, the basic semiconductor equations,
such as Poisson’s equation, carrier continuity equations, the drift-diffusion transport equation, the energy
balance transport equation and the displacement current equation, which are basically implemented in
Atlas-2D organic TFT module (Silvaco)1, were used. In order to fully take the physics of the transport in
polymer thin-films into accounts, the carrier hopping mobility model,2 Poole-Frenkel mobility model,3
Langevin recombination model,4 and Schottky contact model were included. The carrier hopping mobility
(p0) and Poole-Frenkel mobility (p,PF) models are as follows:
 p0
Etrp
Etrp
2
1

 
 
q 
3 13
3



  g ( E )dE ]  exp 2 ( )  [  g ( E ) dE ] 3 
kT  
4





(10)
 |E|
,
 E0 
 p , PF ( E )   p 0 exp 
(11)
with q=the elementay charge, =the attempt-to-jump frequency for holes (=11011 [Hz]), kT=the
thermal energy, Etrp=the transport energy level of holes, =the percolation constant (=1.5), = 1/carrier
localization radius (=5107 [cm-1]), E=the electric field, and E0=Poole-Frenkel factor (=1956 V/cm),
respectively. While the hopping model is dominated by the g(E)-dependent electric field, the PooleFrenkel mobility model describes the charge transport through the sub-bandgap DOS. Meanwhile, the
Langevin model is a well-known recombination model in organic TFTs.
In detail, the used mobility models are as follows:
- Hopping mobility model
 p0
Etrp
Etrp
2
1


qHOPP.V 0
3HOPP.BETA 13

[  g ( E )dE ] 3 exp[ 2(
) HOPP.GAMMA[  g ( E ) dE ] 3 ]
kT
4


2
HOPP.V0: attempt-to-jump frequency for holes (=11011 [Hz])
HOPP.BETA: percolation constant (=1.5)
HOPP.GAMMA: 1/carrier localization radius (=5107 [cm-1])
- Poole-Frenkel mobility model
 p PF ( E )   p 0 exp(
DELTAEP.PFMOB
|E|

)
kTPeff
E 0 P.PFMOB
DELTAEP.PFMOB: activation energy at zero field for holes (Default=0)
E0P.PFMOB: Poole-Frenkel factor (Default =1956 V/cm)
- Langevin recombination model
rL ( x, y, t )  A.LANGEVIN
q[ n ( E )   P ( E )]
 r 0
A.LANGEVIN: Langevin recombination constant (Default=1)
As shown in above equations, the extracted g(E) was directly used in the hopping mobility model,
and indirectly related with Poole-Frenkel mobility and Langevin recombination models.
Compared with the previous works,5, 6 our methodology clearly shows the improved accuracy. For
examples, the error rates (defined by the difference between the measured subthreshold swing and the
calculated one) of [5] and [6] are estimated to be 26.5 % and 19.5 %, respectively, while the maximum
error rate in our case is observed to be 3.1 % as shown in Fig. 4. Most probably, the error is attributed to
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the S/D contact model. As well known, in the Schottky contact model, the bias-dependence of S/D
resistance is complicated and can be accurately reproduced by the empirical or experimentally extracted
parameters rather than by the theoretical parameters. Therefore, in order to improve the accuracy of the
proposed model, the Schottky model parameters should be characterized more in detail and incorporated
into the I-V simulation.
References
1
ATLAS Device Simulation Software User’s Manual (Silvaco, Santa Clara, CA, 2005).
2
R. Coehoorn, W. F. Pasveer, P. A. Bobbert, and M. A. J. Michels, Phys. Rev. B 72, 155206 (2005).
3
L. Pautmeier, R. Richert, and H. Bassler, Synth. Mat. 37, 271 (1990).
4
P. W. M, Blom, M. J. M. De Jong, and S. Breedijk, Appl. Phys. Lett. 71, 930 (1997).
5
C. Krellner, S. Haas, C. Goldmann, K. P. Pernstich, D. J. Gundlach, and B. Batlogg, Phys. Rev. B 75,
245115 (2007).
6
E. J. Meijer, M. Matters, P. T. Herwig, D. M. de Leeuw, and T. M. Klapwijk, Appl. Phys. Lett. 76, 3433
(2000).
4