TLM of Analysis for the Calculation of Contact Resistance in P3HT OFETs
Transfer Line Method (TLM)was first suggested by the Luan and Neudeck for the calculation of contact resistance in amorphous silicon thin-film transistors in year 1992 [1]. Transfer line method is the standard approach for the calculation of contact resistance in the field-effect transistors by fitting the total ON resistance of a device as the function of channel lengths. The article deals with detail contact resistance calculation by TLM in an OFET.
Introduction
The total resistance (R) in an OFET can be divided into two parts. The channel resistance (R_{ch}) (is directly related with the sheet resistance (R_{sh}) and the total contact resistance, which are in series in an OFET. Mathematically,
...........................................(1)
Where, L is the channel length and W is the channel width.
**Contact Resistance:** As the name suggests, contact resistance is originated directly at the contact regions in an OFET i.e. the region between the metal contact and the semiconductor. Physically, the potential difference between the Fermi energy level of the metal contact and the HOMO (highest occupied molecular orbital) of the organic semiconductor, which is a small energy gap for the carrier to get injected into the channel, is the linear contact resistance. In addition, the contact resistane is also directly influenced by the doping of the organic semiconductor around the contact region. The total contact resistance (R_{c}) is the sum of the contact resistance appearing at the source and drain contact.
**Sheet Resistance:** The sheet resistance in an OFET is the resistance arising between to the semiconductor and the insulator interface. Following equation (1), when channel length (L) is very large in the orders of several micrometres, the current limiting factor is only the channel resistance. Because, for longer channel OFETs the contact resistance is very-very low. Now, when the channel length drops sharply, then the channel resistance also drops similarly. Hence, for very small channel length OFETs there exists the influence of the contact resistance on the device total resistance, which is observed as the comparativerly lower charge carrier mobility. Thus, it is very important to calculate the contact resistance in an OFET, which one hand gives the values which could be compared with other OFETs to optimize the device performance, in the other hand it is also helpful to calculate the actual sheet resistance. Since, sheet resisivity is inversely proportional with the charge-carrier mobility (equation (2)) and similarly, the mobility is inversely related with the contact resistance.
.......................(2)
..................(3)
where, is the sheet resistivity, q is the unit Coloumb charge, N is the charge density (/m^{3}) and μ is the charge-carrier mobility.
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**TLM Method of Analysis**
The ON resistance or the total OFET resistance is the sum of channel resistance and the contact resistance, as shown in equation (1). For the TLM analysis, the transistor must operate in the linear regime, because in the linear regime the potential at the source and the drain terminal is similar. Compared with the saturation regime when potential at the drain terminal is very high, then contact resistance would be measured relatively higher than expected. Consider, the linear regime of operation of an OFET,
...............(4)
Where, I_{dlin} is the current in the linear regime of OFET operation, C_{i} is the insulator capacitance per uni area, V_{ds} is the drain potential which tends to zero, V_{gs} is gate potential and V_{th} is the threshold voltage. Further, after replacing the ratio of drain voltage to drain current to equation (1), we get the following equation:
............(5)
After normalizing the total resistance with the channel width, we get the the total resistance as the function of the channel length.
.........(6)
The above equation, is the linear relation between the total resistance and the channel resistance, where the intercept along the y-axis of the plot directly gives the contact resistance.
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**Experimentation**
For the experimentation, P3HT OFETs with different channel length is electrically characterized. The OFETs are measured for constant Vds (Vds = -1V) but at different Vgs. Now, the device total resistance is calculated by dividing the drain potential by the drain current measured at different Vgs. These values are plotted against the channel length, as shown in figure (1). The y-intercept of the normalized total resistance plot agains the channel length gives the normalized contact resistance. The calculated contact resistance are again plotted at different gate potentials, as shown in figure (2).
*Figure (1): TLM analyis by plotting normalized total resistance with channel length.*
*Figure (2): Calculated values of the contact resistances plotted at different gate-potential. *
The normalized contact resistances is found to decreasing from 2000 ohms measured at V_{gs} = -2 V to almost 500 ohms compared to measured at V_{gs} = -8 V. The change of contact resistance with gate potential my be due to source-drain contact overlap [1]. **In very small channel length OFET, as in L = 100 nm, the contact resistance completely dominates the total resistance. Henre, the contact resistance would have significant effect on the charge carrier moblity as compared to the OFET with L = 1000 nm.** It would be also interesting to observe the charge-carrier mobiliy behavior for OFETs with same length scales. In the next calculation, the charge carrier mobility is calculated.
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Mobility is calculated by fitting the linear regime of transistor opeartion or the transfer curve of all the OFETs with equation (4) (please follow the link for detail calculation). Moblity is now plotted against the channel length in OFETs with channel length between 100 nm and 1000nm, as shown in figure (3).
*Figure (3): Plot of charge-carrier mobility versus channel length*
Interestingly, charge carrier mobility drops significantly in L = 100 nm OFETs as compared with the L = 1000 nm OFETs. This is due to the growing effect of contact resistance in small channel OFETs. Hence, mobility decreases with decreasing channel length.
It is difficult to extract the charge carrier moblity and the threshold voltage from the slope of the fitted curves. In addition, this method doesn't separate the origin of the calculated contact resistance is either from the source contact or the drain contact. Hence, an alternative method like 4-point probe method must be applied to clearly extract the source and the drain contact resistances.
**(*Please follow the PHD Thesis by Kah Yoong Chang, Realization and Characterization of Microcrystalline Silicon Thin-Film Transistors, Jacobs University Bremen (2008)*, for the detail report describing the mathematical calculation necessary for the extraction of these hidden parameters.) **
References
[1] S. Luan and G. W. Neudeck, An experimental study of the source/drain prasitic resitance effects in amorphous silicon thin-film transistors, J. Appl. Phys. 72, 766 (1992)
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