Modeling and Parameter Extraction on Pentacene TFTs
D. Oberhoff, K. P. Pernstich, D. J. Gundlach, and B. Batlogg Laboratory for Solid State Physics, ETH Zurich, Switzerland E-mail:
[email protected]
ABSTRACT
We report on an empirically based physical model developed for small-molecule organic thin film transistors (OTFTs). The model is an extension of an adapted MOSFET model for hydrogenated amorphous silicon TFTs accounting for an arbitrary energy distribution of mobile and trap states and allows the extraction of the parameters from the measured device characteristics. Ideally all parameters can be derived from the material properties of the organic semiconductor, but often those are masked by extrinsic effects. To provide model input and validation data sets we fabricated top contact pentacene TFTs on heavily doped and thermally oxidized wafers. The device structure allows the systematic study of the influence of the source and drain contacts and the properties of the semiconductor/metal interface on the device characteristics by varying the contact metal, deposition parameters, or the silane coupling agent used to treat the gate dielectric prior to deposition. From this a functional dependence of the contact and interface effects is incorporated into the model. The subthreshold regime is mainly used to test the charge trapping and charge-configuration model because charge-configuration related effects are usually more exposed in this regime. Currently the model routinely exhibits > 90% accuracy for most devices. Further insight into the actual physical mechanisms is expected from comparing the extracted trap state distributions with those extracted with other methods.
Keywords: Organic Semiconductors, Modeling, Pentacene, Parameter Extraction, Organic Thin Film Transistor
1. INTRODUCTION To date, parameter extraction and modeling of organic thin film transistors (OTFTs) have mainly relied on relationships developed to describe the drain current in above threshold operation for single crystal silicon metal-oxidesemiconductor field-effect transistors (MOSFETs). Adapted MOSFET models for hydrogenated amorphous silicon (a-Si:H) TFTs have been shown to reproduce more accurately the electrical characteristics of OTFTs, accounting for deviations from ideal MOSFET behavior such as gate bias dependent field-effect mobility. More recently, numerical models have been developed and applied by [1-3] to simulate small-molecule or polymer TFT characteristics. We report here on an ab initio model we developed to accurately simulate OTFT characteristics and improve the understanding of the device operation. Our model avoids the use of any parameters or functional dependencies to which physical meaning can not be attributed. We have sacrificed the analytic closed form in favor of a more flexible numeric model allowing for easy implementation of an arbitrarily complex DOS (Density of States).
Organic Field-Effect Transistors III, edited by Ananth Dodabalapur, Proceedings of SPIE Vol. 5522 (SPIE, Bellingham, WA, 2004) 0277-786X/04/$15 · doi: 10.1117/12.559789
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Top contact pentacene (Pc) TFTs were fabricated and characterized to provide model input data. The device structure is shown schematically in Fig. 1. The TFTs were fabricated on heavily doped and thermally oxidized silicon wafers. The heavily doped silicon serves as the gate electrode with contact made to the wafer backside and the silicon dioxide provides a high quality gate insulator. The use of silane coupling agents (SCAs) that form self assembled monolayers (SAMs) has been shown to advantageously modify the gate insulator surface properties and improve device performance [4-6]. We find that device behavior is strongly infIuenced by the choice of molecule used to form the SAM and a range of “good” and “bad” device performance can be obtained [7]. In this study we employ different SCA’s to provide distinctly dissimilar OTFT characteristics for characterization and modeling. Pc films (~ 40 nm thick) were deposited on the treated wafers by thermal evaporation from Pc twice purified by temperature gradient vacuum sublimation and patterned by shadow mask. Gold source (S) and drain (D) contacts (~ 50 nm thick) were deposited by thermal evaporation and patterned by shadow mask yielding devices with a constant channel width (W) of 600 µm and channel lengths (L) of 30, 50, 75, 100, 125, and 150 µm. Measurements were performed under an inert gas atmosphere avoiding the influence of oxidation and other contaminations and under filtered ambient light. The channel lengths exceed the thickness of the devices (active layer and gate insulator) by several orders of magnitude thus excluding short channel effects. y
Gate Electrode n++ Si
x Interface Layer
300nm 40nm
SiO2 Pc D
Metal Electrodes
VGS
S
VDS
Figure 1: Device schematic with external voltage sources shown to indicate biasing.
2. DERIVATION OF THE MODEL 1. Analytic Above-Threshold Models The most widely used analytic above threshold FET model for extracting device parameters of OTFTs is the Shockley Model. The derivation is straightforward and will not be given here. From Gauss’ Law the sheet density of charge at any point along the device channel is given by:
qind = −ε ox Eox = −ε ox
Vox ≡ −C ox (VGS − V ( x) − VT ) (1) t ox
where the threshold voltage (VT) absorbs the flat-band voltage which in turn includes the work-function difference between the gate electrode and the semiconductor and any built-in surface potential as well as any bias necessary to overcome depletion and similar effects. VGS is the gate-source voltage and Cox is the capacitance per unit area of the gate insulator. Assuming ohmic charge transport and integrating from source to drain yields the widely used expression for drain current (ID):
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ID =
V2 W µC ox (VGS − VT )VDS − DS (2) L 2
which for small drain-source bias (VDS) becomes linear:
I D ,lin =
W µC ox (VGS − VT )VDS (3) L
and has a maximum corresponding to device saturation:
(V − VT ) W = µC ox GS (4). L 2 2
I D , sat
This model is very simple as it involves only two parameters (field-effect mobility (µ) and VT) and three geometrical constants (L, W, and Cox). Eq. 4 fits many device’s characteristics relatively well and it allows for an easy extraction of its parameters µ and VT from the slope and the intercept of √ID vs. VGS in saturation, which are thus widely used to compare device performance. The mobility extracted using the above method is usually VGS dependent for strongly disordered systems such as a-Si:H and organic semiconductors. In [8] a power law has been proposed for this dependence which has been given physical backing (and the parameters physical meaning) in [9] where it is used to model a-Si:H TFTs using only the presence of exponential tail states and well defined mobility edges. The argumentation in [9] is as follows: An intrinsic mobility in the transport band(s) (beyond the mobility edge) is assumed to be constant. Exponential distributions of localized trap states tailing the bands are further assumed. The free and trapped charge density can be approximated, as long as the Fermi level is more than a few thermal voltages away from the mobility edge. In the case of hole transport this gives ψ 0 −ψ
qtrapped = eN t e
eVt
(5)
ψ 0 −ψ
q free = eN v e
k B Tt
where Ψ is the Fermi energy level relative to the mobility edge, Ψ0 its value at charge neutrality, Vt the characteristic slope of the tail states and NV and Nt the effective density of states for the valence band and the tail states. Using qfree
