IEEE ELECTRON DEVICE LETTERS, VOL. 34, NO. 1, JANUARY 2013
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Contact-Length-Dependent Contact Resistance of Top-Gate Staggered Organic Thin-Film Transistors Hong Wang, Ling Li, Zhuoyu Ji, Congyan Lu, Jingwei Guo, Long Wang, and Ming Liu, Senior Member, IEEE
Abstract—In this letter, a contact-length-dependent contact resistance model for top-gate staggered organic thin-film transistors (OTFTs) is proposed. The presented model can well describe the contact resistance increase as the distance by which the gate electrode overlaps the source and drain contact (contact length) decrease. Based on the contact resistance model, the contactlength-dependent cutoff frequency of OTFTs is described, and an optimized contact length can be obtained for high-frequency OTFT applications. Index Terms—Contact length, contact resistance, cutoff frequency, organic thin-film transistor (OTFT).
Fig. 1. Schematic cross section of the top-contact staggered OTFTs. ΔL is the contact length.
I. I NTRODUCTION
I
N RECENT years, organic thin-film transistors (OTFTs) have attracted extensive attention due to their low cost and compatibility with large-area fabrication [1], [2]. OTFTs are of interest for sensor arrays, flexible active-matrix displays, and RF identification tag applications [3], [4], in which the cutoff frequency is an important parameter. The staggered OTFTs are often used to obtain high frequency because of their smaller contact resistance and higher mobility compared with coplanar OTFTs [5]. In traditional staggered OTFTs, the gate electrode always overlaps the entire source and drain contacts. The distance by which the gate electrode overlaps the source and drain contacts is defined as contact length. The overlap can create a parasitic capacitance; hence, minimizing the contact length may obtain high cutoff frequency for OTFTs. However, with decreasing the contact length, the contact resistance becomes an important parameter limiting the mobility of staggered OTFTs [5]. Therefore, understanding the contact length influence on the contact resistance is essential to optimize device architecture for realizing high cutoff frequency of OTFTs. In this letter, we developed a contact-length-dependent contact resistance model for staggered OTFTs. Our model can well describe the increasing contact resistance when decreasing the contact length. In addition, the contact-length-dependent cutoff frequency is formulated, and an optimized contact length can be obtained for high-frequency OTFTs.
Manuscript received September 10, 2012; revised October 7, 2012; accepted October 8, 2012. Date of publication November 29, 2012; date of current version December 19, 2012. This work was supported in part by the National 973 Program under Grant 2011CB808404 and Grant 2009CB939703 and in part by the National Science Foundation of China under Grant 60825403, Grant 61001043, and Grant 61102025. The review of this letter was arranged by Editor A. Nathan. The authors are with the Laboratory of Nano-Fabrication and Novel Devices Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China (e-mail:
[email protected]). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LED.2012.2224631
Fig. 2. Schematic circuit diagram at the source contact for an OTFT based on the transmission-line model. Io is the total drain-to-source current, rch is the average channel resistance per unit channel length, and rceff is the vertical bulk and contact resistance per unit length.
II. M ODEL T HEORY The schematic cross section of the top-contact staggered OTFTs is shown in Fig. 1. For contact length (ΔL) less than transfer length (d) (transfer length is defined as the characteristic length of the charge carrier exchange between the contacts and the semiconductor when the distance by which the gate electrode overlaps the source and drain contacts is long enough), the current in the source region can be split into two components: transfer part in the overlap region and spreading part in the source contact outside the overlap region [6], [7]. The contact resistance can be expressed as R = Rco + Rsp
(1)
where Rco is the overlap region contact resistance, and Rsp is the spreading part resistance. To obtain Rco , we adopted the transmission-line model in our analysis [8], [9]. Fig. 2 illustrates the simplified schematic circuit diagram at the source contact. Io is the total drain-tosource current, rch is the average channel resistance per unit channel length and can be expressed as (2), and rceff is the vertical bulk and contact resistance per unit length. Thus rch =
1 μch Ci W (VG − VT )
(2)
where μch is the field-effect mobility of OTFTs, Ci is the capacitance per unit area of the gate insulator, W is the channel
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IEEE ELECTRON DEVICE LETTERS, VOL. 34, NO. 1, JANUARY 2013
width, and VG is the voltage between the gate and the average channel voltage above the source contact. (When rch is made position dependent, no analytical solution for the contact resistance can be found. Hence, we define rch as the average channel resistance per unit channel length and give VG a correction definition.) VT is the threshold voltage. At the source electrode side, the change in the channel current above the source electrode can be expressed as Vch (x) dIch (x) = −W dx rceff
(3)
where Ich (x) is the horizontal current in the channel at the dielectric/semiconductor interface at position x, and Vch (x) is the electrical potential at position x. From (3), we can obtain d2 Ich (x) W dVch (x) . =− dx2 rceff dx
(5)
(6)
With rceff L2T = W rch
(7)
− Lx
T
.
e LT − 1 rceff . ΔL LT W 1 + (e LT − 1)(1 − e− LΔL T )
(16)
When the horizontal current in the channel flows arriving at position x = ΔL, the current will spread into the source contact [7], [8], as shown in Fig. 3. We proposed that the spreading region contact resistance Rsp is in parallel connection of intrinsic resistance Rint and current spreading generated resistance Rspr , as described in (17). Thus −1 1 1 + . (17) Rsp = Rint Rspr Based on Fig. 3 and the above discussion, the spreading region contact resistance Rsp is given by a−ΔL
Rsp =
we can solve (6) for Ich (x) approximately as Ich (x) = Io e
ΔL
(4)
Substituting (5) into (3) gives 1 d2 Ich (x) = 2 Ich (x). dx2 LT
According to (12)–(15), the overlap region contact resistance is now calculated as Rco =
The variation of Vch (x) along x can be expressed as dVch (x) = −Ich (x)rch . dx
Fig. 3. Schematic diagram of current spreading in the source contact outside the overlap region. b is the thickness of the semiconductor film, and a is the source contact length.
1 1 + Rint Rspr
dx .
(18)
0
(8)
Then, (18) is rewritten as Then, Vch (x) can be expressed as rceff − x I o e LT . Vch (x) = LT W
a−ΔL
(9)
Rsp = 0
At position x greater than transfer length (d), Ich (x) will become zero; hence, Io can be expressed as d Io =
Vch (x) W dx. rceff
(10)
From (10), we can calculate the transfer length as (11)
In the case of the contact length less than transfer length, Ich (x) and Vch (x) at positions x = 0 and x = ΔL can be written as (12)–(15), respectively. Thus Ich (0) = Io
(12) ΔL −L
Ich (ΔL) = Io e T rceff Vch (0) = Io LT W rceff − ΔL Vch (ΔL) = I o e LT . LT W
+
tan α·(a−ΔL−x )·W ρ(x )
dx .
(19)
Where λ is a modulation parameter, tan α reads as tan α =
0
d = LT In2.
1 1 λrceff
b . a − ΔL
(20)
Based on the concepts that with ΔL increase, the spreading current is decreased, and the resistance of this region contribution for total contact resistance is decreased as well. ρ(x ) can be given by the following empirical formula: ρ(x ) = ρo e−ΔL .
(21)
With the help of (1), (16), and (19), the contact-lengthdependent contact resistance for staggered OTFTs can be eventually obtained.
(13) (14) (15)
III. R ESULTS AND D ISCUSSION According to the model described above, the relation between contact resistance and contact length is simulated, as shown in Fig. 4. The input parameters are μch = 0.5 cm2 /
WANG et al.: CONTACT-LENGTH-DEPENDENT CONTACT RESISTANCE OF TOP-GATE STAGGERED OTFTS
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Fig. 4. Simulation of the relationship between total contact resistance and contact length with different VG for top-gate staggered OTFTs.
versus, Ci = 10 nF/cm2 , W = 100 μm, LT = 10 μm, λ = 0.5, b = 50 nm, a = 40 μm, and ρo = 2 × 103 . Fig. 4 indicates that the contact resistance is increasing with contact length decreasing. When the contact length is reduced to a certain extent, the contact resistance dramatically increased. The simulated results have good agreement with previous experiment results [10]. In addition, VG related contact resistance gets a good explanation in the model [5], [11]–[13]; this further illustrates that the proposed model is suitable. With increasing of contact resistance, effect mobility μeff will substantially drop and can be calculated as [10] 2 μch Ci W R(VG − VT ) . (22) μeff = μch 1 − L + μch Ci W R(VG − VT ) The cutoff frequency fT of a field-effect transistor is often calculated as fT =
μeff (VG − VT ) . 2πL(L + 2ΔL)
(23)
From (23), the contact-length-related cutoff frequency of OTFTs can be obtained. Fig. 5 shows the simulation results of the relationship between cutoff frequency and contact length for staggered OTFTs at VG = 20 V. The input parameters are the same as used in Fig. 4. With decreasing of ΔL, fT will increase and reach maximum at a critical point of ΔL; then, continued reduction in the contact length, fT will decrease with ΔL decreasing; hence, an optimized contact length can be obtained for high-frequency OTFTs. Therefore, the model has guiding significance for OTFT structure design. IV. C ONCLUSION In summary, a contact-length-dependent contact resistance model for top-gate staggered OTFTs is presented. The model can well explain the variation of contact resistance with the changes in the contact length. Furthermore, with the help of the contact resistance model, the contact-length-dependent cutoff frequency of OTFTs is described, and an optimized contact length can be obtained for high-frequency OTFTs.
Fig. 5. Simulation of the relationship between cutoff frequency and contact length with different channel length for top-gate staggered OTFTs.
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