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Charge Transport Simulations for Organic Semiconductors

Hiroyuki Ishii

University of Tsukuba, Division of Applied Physics, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

1.1 Introduction

1.1.1 Historical Approach to Organic Semiconductors

Organic semiconductors have the potential to be used in future electronic devices requiring structural flexibility and large-area coverage that can be fabricated by low-cost printing processes. Ordinary organic materials such as plastics (polyethylene) have primarily been regarded as typical electrical insulators. However, graphite exhibits the high electrical conductivity [1], which has been attributed to their molecular structures, which are made of network planes of the conjugated double bonds of carbon atoms with the -electrons. There exist some organic molecules that have similar molecular structures, for example, aromatic compounds. Around 1950, Eley [2], Akamatu and Inokuchi [3], and Vartanyan [4] have reported that the phthalocyanines, violanthrones, and cyanine dyes have semiconductive characters, respectively. These characters are attributed to the intermolecular overlapping of the electron clouds of -electrons in the condensed aromatic rings. These materials were named as organic semiconductors [5]. However, in general, these organic semiconductors were still recognized as the insulating materials because resistivity of these organic semiconductors is much higher than that of inorganic semiconductors such as silicon and gallium arsenide. The resistivity is given as

where , , and represent the carrier concentration, elementary charge of a carrier, and the electron (hole) mobility, respectively. The high resistivity of the organic materials originates from the low carrier concentration and the low mobility.

The carriers can be chemically doped by using the electron-donor-acceptor complexes. In 1954, Akamatu et al. found that the electron-donor-acceptor complex between perylene and bromine is relatively stable and has very good electrical conductance [6]. In 1973, Ferraris et al. have reported that the complex between the electron donor tetrathiafulvalene (TTF) and the electron acceptor tetracyano--quinodimethane (TCNQ) has the very high conductivity comparable with the conductivities of metals such as copper [7]. Shirakawa et al. also showed that the organic polymer, polyacetylene, has a remarkably high conductivity at room temperature by chemical doping with iodine in 1977 [8]. These complexes are called organic conductors. The high electrical conductivity accelerated interest in organic conductors, not only because of their huge electrical conductivity but also by the possibility of superconductivity [9].

The multicomponent systems as mentioned above have some disadvantageous properties such as air and thermal instability in general. Therefore, semiconducting single-component organic compounds are likely to be much more suitable for use as molecular devices. From a viewpoint of the electronic device applications, mobility is very important to evaluate the device performance because it characterizes how quickly an electron can move in a semiconductor when an external electric field is applied. In 1960, Kepler [10] and LeBlanc [11] measured the mobility of an organic semiconductor by the time-of-flight (TOF) technique, where the flight time of carriers in a given electric field is determined by observing an arrival time kink in the current that is caused by a pulse-generated unipolar "charge carrier sheet" moving across a plane-parallel slice of a sample. They reported that the anthracenes have the mobility of 0.1-2.0 cm V s at room temperature and their mobilities increase as the temperature decreases. Friedman theoretically investigated the electrical transport properties of organic crystals using the Boltzmann equation treatment of narrow-band limit in the case of small polaron band motion [12]. Sumi also discussed the change from the band-type mobility of large polarons to the hopping type of small polarons, using the Kubo formula with the adiabatic treatment of lattice vibrations in the single-site approximation [13]. However, the mobility obtained by TOF technique is different from the mobility of actual devices such as field-effect transistors(FETs) because the charge carriers are induced at the interface between the organic semiconductor and the dielectric film by an applied gate voltage. Kudo et al. reported the field-effect phenomena of merocyanine dye films and their field-effect mobilities of - cm V s estimated from the measurements in 1984 [14]. Then, Koezuka et al. fabricated the actual FET utilizing polythiophene as a semiconducting material and reported the mobility of cm V s [15].

A major industrial breakthrough occurred in the application to electroluminescent (EL) devices. Tang and VanSlyke reported the first organic EL device based on a -conjugated molecular material in 1987 [16]. After that, typical industrial applications spread to light-emitting diodes (LEDs) [17, 18] and solar cells [19-21]. Recently, organic semiconductors are expected as the future electronic device semiconducting materials requiring structural flexibility and large-area coverage that can be fabricated by low-cost printing processes [22, 23]. However, we have a massive task for the realization of the "printed electronics," for example, increasing the mobility, improvement of the solubility, and thermal durability, suppressing the variations of device characteristics, decreasing the threshold voltage, and so on.

Although -conjugated polymers with aromatic backbones have been widely investigated as soluble organic semiconductors, further improvement of mobility of polymer semiconductors has disadvantages owing to the statistical distribution of molecular size and structural defects caused by mislinkage of monomers, which act as carrier traps in the semiconducting channel. Therefore, small molecular materials, such as pentacene (see Figure 1.1a), have advantages in terms of their well-defined crystal structure and ease of purification. At first, the organic transistors were fabricated utilizing the organic polycrystals. For example, the field-effect mobility of polycrystal thin-film transistors (TFTs) increases in proportion to the grain size [63, 64]. The mobility in the polycrystals is mainly limited by the grain boundaries, and the typical highest value is generally below 1.0 cm V s at room temperature. The temperature dependence with a thermally activated behavior indicates that the incoherent hopping process of spatially localized carriers between trap sites is dominated in the polycrystals [26]. In such a low-mobility regime, the charge transport mechanism has been investigated theoretically using the Marcus theory [65, 66] based on the small polaron model [67].

Figure 1 Molecular structures of (a) pentacene, (b) rubrene, (c) DNTT, (d) C-BTBT, and (e) DNT-V. (f) Annual change of the highest hole mobilities of different organic single-crystal field-effect transistors in the literature, and (g) the distribution of the reported mobilities for naphthalene [24], DNT-V [25], pentacene [26-35], DNTT [36-41], C-BTBT [42-49], and rubrene [29, 31], [50-62].

1.1.2 Recent Progress and Requirements to Computational "Molecular Technology"

Recent rapid progress in technology enables us to fabricate the very pure rubrene single-crystal FETs (see Figure 1.1b) with the high carrier mobility up to 40 cm2 V-1 s-1 at room temperature [60], which exceeds the mobility of amorphous silicon [68]. The high mobility attributes the exclusion of trap sites such as grain boundary in organic semiconductors. The mobility monotonically decreases with increasing temperature, [54]. The power-law temperature dependence is a typical characteristic of coherent band transport by spatially extended carriers, which is scattered by the molecular vibrations (phonons). The rubrene single crystals obtained by the physical vapor deposition method show the excellent high mobilities at room temperature, but their poor solubility is a serious problem for the printed electronics. In 2006, Takimiya et al. reported solution-processable organic semiconductors based on [1]benzothieno[3,2-][1]benzothiophene (BTBT) core [69] and dinaphtho[2,3-:2,3-]thieno[3,2-]thiophene (DNTT) core [36] with high mobility and stability, as shown in Figure 1.1c,d. Moreover, Okamoto et al. reported a new candidate semiconducting material based on V-shaped dinaphtho[2,3-:2,3-]thiophene (DNT-V) core (Figure 1.1e), with high mobility, solubility, and thermal durability [25]. Figure 1.1f,g shows annual change of the highest hole mobilities of different organic single-crystal FETs in the literature, and the distribution of the reported mobilities for naphthalene [24], DNT-V [25], pentacene [26-35], DNTT [36-41], C-BTBT...