To understand the basic electrical behavior of an OFET, a p-type OFET (organic semiconductor is p-doped) with sufficiently large channel length (orders of 10 micrometres) is depicted in the figure (1), with suitable electrical connections. Source is grounded, at the drain- bias potential is applied and at the gate- suitable control potential is applied. Output current is measured at the drain terminal. For the constant gate potential, Id vs. Vds curve is obtained, termed as the output characteristics. Similarly for the constant drain potential, Id vs. Vgs curve is obtained, termed as the transfer characteristics. The output curve and the transfer curve are two major electrical charactersitics which describe the complete electrical behavior of an OFET. In this section, output and transfer characteristics of a typical OFET (L >> tox) would be discussed. For the nanoOFETs with channel length similar to oxide layers are termed as short-channel OFET, which would be discussed in another section (study of the short-channel (L = 70nm) OFET).
Fig(1): OFET with electrical potentials
Current equations for transistor operating in linear regime is calculated by following gradual channel approximation model (S. M. Sze, Physics of Semiconductors, 2002). Mathematically, transistor operating in linear regime (for Vds << Vgs - Vth) is described by the the following equation (as observed in figure 2):
Similarly, transistor operating in saturation regime (Vds > or = Vgs - Vth) is described by the following equation, with quadratic relation between gate potential and the output-current (as observed in figure 3):
Where, µ is the charge carrier mobility (assumed to be constant in GCA model), Cox is the oxide layer capacitance per unit area, Vth is the threshold voltage (the gate voltage when OFET goes to ON state).
Figure (2): Output Characteristic of a very large channel length OFET. Measurements are inside the glovebox (N2 atmosphere).
Figure (3): Transfer Characteristic of a very large channel OFET. Measurements are inside the glovebox (N2 atmosphere).
For a p-type OFET, under suitable gate potential (-Vgs), a thin conducting channel (with holes) is formed within the P3HT- insulator interface. At low drain bias potential (-Vds), the OFET starts conducting, the measured output current (-Id) linearly increases with increasing Vds. Thus, the transistor is termed as operating in linear-regime. At higher Vds, the electrical field at drain-gate interface goes much higher compared with source-gate interface. Due to higher gate field at drain contact, the channel region around the drain is pinched-off (depletion of holes in P-type OFET). So, current no longer increases linearly with increasing Vds. Thus, output current sturates, and the OFET is termed to be operating in saturation regime.
Typical output curve is depicted in figure (2), with distinct OFET operation in linear and saturation regime. At, low Vgs, channel fails to appear switcing OFF the OFET. Switching behavior, is clearly observed in the transfer curve of an OFET (figure 3). At higher -Vgs, transistor goes to ON state with relatively high current (orders of microamperes) compared to at lower +Vgs, transistor goes to OFF state with very low OFF current (orders of picoamperes). Further, the charge transport parametre like charge-carrier mobiliy and threshold voltage could be calculated by fitting the tranfer curve in either linear or saturation regime of transistor operation.
Note: (a) Detail discussion on the charge transport in FETs.
(b) Charge transport in crystalline semiconductors
(c) PIN Junction FETs