Leakage- and tunneling-current through the gate dielectric of organic thin film transistor using retarded Green's function, creation and annihilation operators

Abstract

Abstract: One of the main challenges of current metal-oxide-semiconductor field effect transistors (MOSFETs) is the exponential increase in the tunneling- (and leakage-) current through the gate dielectric material while shrinking the gate dielectric material thickness. Over the last two decades, many researchers have attempted to find an alternative material for the gate dielectric of transistors that has the advantages of the current silicon oxide gate dielectric of MOSFETs but without its disadvantages. In the search for an excellent gate dielectric, researchers have compared the key electrical parameters with those of current gate dielectric materials. They applied equations, approaches, and relationships for their evaluations and estimations, which may be incomplete relationships and most likely did not lead to the correct evaluation probability. Among the cases, the great importance is the relationship with the leakage-current from the gate dielectric layer in organic field-effect transistors (OFETs) or thin-film transistors (TFTs). In these discussions and evaluations based on the conventional leakage-current relationship, interactions related to particle exchange and pinch-up displacement in the charge carrier transport channel, particularly the overlap of the wave functions of electrons (or holes) in the channel and at the interface layers, have not been considered. The novelty and specific objectives of the present work are: modifying the Hamiltonian operators based on self-energy (Σ), the retarded Green's function (GR), creation (C+ )/annihilation (C) operators, and the overlapping wave functions of the charge carriers in the gate and substrate systems; obtaining a more complete leakage-current density (J) relationship than the existing relationships; and comparing the electrical characteristics measurement results of five small molecule polymers: PEIE (0.8 nA/cm2), Ps (1 nA/cm2), PFS (2 nA/cm2), ph (4 nA/cm2), PMMA (20 nA/cm2) with previously reported findings. The obtained results can be highly useful for optimizing organic thin-film transistor formulations for potential use in next-generation nanoelectronic devices with lower energy consumption.

1. Introduction

Field-effect transistors (FETs) are at the heart of almost all electronic, optoelectronic, imaging, and amplifier components, and chips. Therefore, to increase the efficiency and effectiveness of these chips and systems, it is necessary to address the challenges they face. One of the parameters that have caused problems for these transistors is the increase in the leakage-current of carriers such as electrons and holes for even organic field-effect transistors (OFETs) with polymers and organic gate dielectric materials from the thin gate dielectric layer of the transistors, which is becoming more apparent with the increasing demand for the manufacture of nano-scale transistors.

In recent years, many people [1−4] have been looking for a gate dielectric that could replace the current gate dielectric of metal oxide semiconductor field effect (OFETs) and organic thin-film transistors (OTFTs). To do this, they studied and evaluated metal oxides and nitrites, as well as materials, such as silicon nitrite. The problem with the first transistors using metal oxides and nitrites was the formation of an undesirable intermediate layer between the silicon substrate and gate dielectric material. Silicon nitrite also has a relatively low dielectric constant and is unable to withstand the leakage-current. Others have turned to organic materials, and today they still hope that they can replace the gate dielectric and MOSFET transistors in general. The problem in this regard is that despite having a high dielectric constant, which is necessary to reduce leakage current, these materials have low mobility of electrons or holes in them, and since the current density output from the transistor is directly related to the mobility of these carriers, they have not shown acceptable results. The most important problems of this group of organic and polymeric materials are the low Ion/Ioff, low carrier mobility (μ), high threshold voltage (Vth), high subthreshold swimming (SS), high processing temperature, high manufacturing cost, and the efficiency of such transistors [5−9].

Subsequently, some researchers have studied nanocomposites and hybrid materials [9−11] and found some advantages, such as lower leakage and tunneling currents (its value is currently in the range of 10−6 −10−9 A/cm2), lower threshold voltage (its value for organic materials is currently in the range of 0.3 −6.6 V), and low synthesis temperature proce...