Investigation of Sub-threshold slope in Nanoscale P3HT Organic FETs (OFETs)
This article deals with the comparative analysis of sub-threshold slope parametre in the nanometre sized bottom-gate bottom-contact OFETs. The nanoOFETs are fabricated on the 58nm thin silicon dioxide insulator on the n-doped silicon substrate. All the devices are fabricated by the e-beam lithography processes. For the measurement, 0.5 wt% of P3HT P200 (45 nm thin) semiconductor is spin-coated on the sample inside the glove-box (N2 and air is less than 0.5 ppm).
The study is very important in any OFET analysis because the sub-threshold property is directly related with the bulk transport characteristics of the device, since the bulk property in one hand reflects the OFF state of the device and in the other hand it gives the electrical measurement of the trapped charges within the devices. Hence, for the device sub-threshold characterization, firstly sub-threshold slope would be introduced, considering the physical significance and the importance of this parameter for the analysis of an OFET. Secondly, basic steps in calculating sub-threshold slope would be discussed concentrating on a bottom-gate bottom-contact OFETs with channel length of L = 100 nm and a L = 10 μm. Device basic transport parameter like mobility and threshold voltages would also be calculated additionally. The comparative analysis would also hint us the effect of decreasing channel length on the transport behavior. Further, the calculated sub-threshold slopt would be plotted for different channel length OFETs. Finally, comprehensive device analysis would be done from the plots.
Introduction and Theory:
Field-dependent onset of the transistor is characterizied by the parameter termed as sub-threshold slope. Mathematically, inverse of the logarithmic change of drain current with drain voltage (slope of the log Id vs Vgs plot) below the threshold voltage is the sub-threshold slope (S).
Smaller values of this slope is usually desirable, because smaller is the sub-threshold slope faster is the transistor siwtching from OFF to ON state. It must noted that, the current in the transitor in the sub-threshold zone is due to carrier concentraion withing the channel. In MOSFETs, the sub-threshold slope in room temperature is 70 mV/decade . However, in OFETs worst value of sub-threshold slope maybe obtained (would be calculated in the result section), is due to the fact that in MOSFETs the slope is directly measured at the Fermi edge and there is abrupt change in the density of states with very high mobility of carriers. But in OFETs gradual rise in the density of states is observed around the sub-thresold zone (which is under relatively lower gate potential) and the carriers are only in lower occupied state of the semiconductor where available states for occupation is already very low. So, observed sub-threshold slope is much worst in OFETs. Further, sub-threshold slope degrades with decreasing channel length. Which follows the fact that shorter channel length OFETs are difficult to switch OFF.
To calculate the sub-threshold slope of an OFET, the transfer characteristics is measured for two different OFETs. First, OFET with channel length (L) of 100 nm is electrically characterized (the transfer characteristics is shown in figure 1). Here, the device is measured for Vds = -1 V and Vgs changing between +10 V and -10 V. Second, OFET with channel length (L) of 10 μm is also electrically characterized (the transfer characteristics is shown in figure 2). The plots are plotted in logarithmic scale. In both the cases, square root of the drain current is also plotted to calculated saturation mobility (μsat). The slope of the square root change of drain current with drain potential gives the μsat and the gate potential where drain current increases sharply is the threshold voltage (Vth).
Figure (1): Transfer characteristic of a L = 100 nm OFET.
The current measured at Vgs = -10 V is unexpectedly larger is due to first measurement the measuring system which is not reliable.
Figure (2): Transfer characteristic of a L = 10 μm OFET.
Table 1: Calcualted device transport parametres
Moblity of OFET with L = 10 μm is much higher compared to the channel length of L = 100 nm. Because, the ON to OFF current ratio in L = 100 nm OFET is very small compared to L = 10 μm OFET. Thus, measured slope is one order smaller in short channel devices. Is might be due to increased effect of contact resistance in smaller channel device.
Further, to calculate the sub-threshold slope, the transfer plots from the figures (1) and (2) are re-plotted after taking logarthming value of the drain current at different gate voltages concentrating more on the sub-threshold regime (+Vgs region). The stipper rise in drain current in both forward and backward measurement is considered for the calculation of the slope for Vgs = +0 V to Vgs = +5 V. The fitted equation (y=mx+c) of the plot gives the value of slope (m) = 1/S, where S is the sub-threshold slope and m is the inverse sub-threshold slope. The equation is fitted in the Microsoft Excel 2007. Since, L = 100 nm OFET has higher hystersis in the sub-threshold regime the average sub-thresold value is calcualted to minimize the error in the calculation.
Figure (3): Calculation of sub-threshold slope in L = 100 nm OFET.
Figure (3): Calculation of sub-threshold slope in L = 10 mm OFET.
Table 2: Calculated device sub-threshold slope (S) parameters
Sub-threshold slope in forward measurement
|Sub-threshold slope in backward measurement
Mean Sub-threshold slope
|| S = 1/m (forward)
||S = 1/m (backward)
||S = volt/decade (average)
From table 2, it is observed that sub-threshold slope in smaller channel length is larger in the device compared with larger channel length. This measurement also follows the earlier result from the mobility of shorter channel length i.e. the smaller devices have lower mobility because they are difficult to switch OFF.
Figure (5): Variation of sub-threshold slope with increasing channel length in P3HT OFETs.
To better understand the behavior of sub-threshold slope parameter in smaller channel OFETs, sub-threshold slope is again calculated for nanoOFETs with channel lengths between 100 nm and 180 nm and plotted together as shown in figure (5). Interestingly, sub-threshold slope gets worst with decreasing channel length in nanoOFETs.
From the measurement of different bottom-contact bottom-gate p-type OFET, it is extracted that the transistor with shorter channel length has lower mobility because they are difficult to switch-off which is charctertized by very low sub-threshold slope and higher positive threshold voltage. Hence, the sub-threshold slope has also described the switching behavior of OFETs. However, it is still difficult to extract the charge trapping property with the similar analysis. Hence, it needs more extensive insight and also the different model to clearly describe the the behavior.
 W. Brüttings, 'Physics of Organic Semiconductors', Wiley VCH (2005)