Experiment results of the gate-potential dependent Mobility observed in the P3HT OFETs
On application of an electric field (E), the charged carriers flow from the higher potential region to the lower potential region (electrons towards positive potential). Such collective flow of carriers is described by the parameter termed as the drift velocity (vd) of the carriers, which linearly increases with an applied electric field. Mathematically,
vd = μ E.........(1)
The constant quantity which scales the drift velocity on application of electric field is termed as the mobility of the carriers (μ) (either for the holes or for the electrons). Also, larger is the mobility higher is the drift velocity and higher is the current density (J). Mathematically,
J = vd (-e) n .............(2)
where, -e is single unit charge of an electron (-1.6E-19 Coloumbs) and n is the electron density (cm-3). Experimentally, it is observed that mobity of electron at 300 K in a crystalline Silicon solid is 1500 cm2/Vs for n = 5E22 cm-3 .
Calculation of the Charge Carrier Mobilty in P3HT OFETs : Transfer characteritics for a P3HT OFET has been depicted in figure (1). Transistor has been measured for different Id for changing Vgs, at Vds = -1 V. At +Vg, transistor gives very low OFF current remaining in OFF state of the transistor and for higher -Vgs, transistor switches to the ON state producing very high ON currents in the orders of 0.1 mA.
Mathematically, OFET operating in linear regime (Vds << Vgs - Vth), can be mathematically written as:
where, μ is the charge career mobility, W is the channel length, Cox is the oxide layer Capacitance per unit area, VGS is the applied gate potential, VT is the threshold voltage and Vds is the applied drain potential. Then from the above equation, charge carier mobility (linear) can be extracted by calculating slope of the Id vs. Vgs plot as shown in below figure (2):
Figure (1): Transfer curve of the OFET for W = 100 mm and L = 10 μm, fabricated on tox = 58 nm silicon dioxide layer. The transfer curve is measured at Vds = -1 V.
Then, calculated linear mobility is plotted against different gate source potentials in figure (2).
Figure (2): Gate-field dependent mobilty calculated at Vds =-1V and plotted for different Vgs .
In contrast to inorganic MOSFETs, it is clearly observed that in organic p-type P3HT OFETs, mobility is dependent on the applied gate electric field. For very low gate potential, mobility is zero (transistor is switched OFF), and for gate potential mobility exponentially rises (transistor is switchied ON). Futher, physically gate-field dependent dependent mobility has been described by Vissenberg and Matters Model .
 S. M. Sze, ''Physics of Semiconductor Devices'', 2nd edition, John Wiley and Sons (asia) (2005)]
 M. C. J. M. Vissenberg and M. Matters, "Theory of Field-Effect Mobility in Amorphous Organic Transistors," Phys. Rev. B., vol. 57, pp. 12964-12967, 1998.