**2. Methods of polymorph control in organic semiconductors**

Though polymorphism is observed on many organic semiconductors, the fabrication of each polymorph with high purity is very difficult. For instance, even for the extensively studied organic semiconductors like pentacene and BTBT derivatives, only part of their polymorphs have been useful to establish the correlation between the material molecular packing and its charge transport properties [17]. The difficulties for the investigations on polymorphism include the fabrication of pure polymorphs and the determination of their crystal structures, where the polymorph control is fundamental. Some of the polymorph control methods most commonly applied to organic semiconductors are discussed below.

## **2.1 Solvent control**

*Integrated Circuits/Microchips*

**1.1 What is polymorphism?**

OFETs have been obtained by controlling the polymorphic structures of organic semiconductors, revealing that the crystal polymorph control has become an efficient

Polymorphism refers to the ability for the same compound to adopt multiple crystalline packing states. Organic molecules assemble into crystals by weak intermolecular interactions, typically via van der Waals and electrostatic interactions. Many thermodynamic and kinetics factors (such as temperature, solvent mixtures, speed of crystallization, seeding, and pH) can have significant impacts on crystal growth, leading to polymorphism prevalent among organic materials. For instance, a continuous investigation on polymorphism has indicated that approximately one-third of organic substances show polymorphism under normal pressure conditions [19, 20]. Different polymorphs often have distinct physical properties such as solubility, melting point, and electrical, optical, and mechanical properties [21]. The interest in polymorphism has increased significantly in recent years, particu-

The charge transport property of organic semiconductors is sensitive to the molecular packing, where a slight change in molecular packing may result in huge difference in charge carrier mobility [23]. The side-chain engineering, which is efficient in tailoring the molecular packing, has been extensively applied to develop high-performance organic semiconductors [24–27]. However, the introduction of side chains alters the molecular structure, which makes the investigation on rela-

Polymorphism offers an opportunity to tailor the molecular packing of a material, without affecting its chemical components. For example, rubrene can crystallize into three crystalline polymorphs, including an orthorhombic, a triclinic, and a monoclinic phase (**Figure 1a**) [28–30]. Taking advantage of polymorphism, it is possible to fabricate OFETs from the same organic semiconductor but with different polymorphs, hence, with different properties (**Figure 1b**). Importantly, by

*(a) Molecular structure and the crystal phases of rubrene. (b) Schematic diagram for the fabrication of the* 

tionship between molecular packing and charge transport very complex.

strategy for the manufacture of high-performance OFETs [4, 17].

larly in the pharmaceutical and material science fields [17, 22].

**1.2 The role of polymorphism in OFET**

**66**

**Figure 1.**

*OFETs from microcrystals of different polymorphs.*

Solution process is important for the fabrication of organic semiconductor devices, which has the advantages of low-cost and large-area fabrication. In solution processes, solvent-induced polymorphism has been frequently observed in organic semiconductors such as DB-TTF [49], DT-TTF [50], TIPS-pentacene [51], and so on. Consequently, the solvent of choice for solution-processed organic semiconductors has become a commonly practiced method for highthroughput polymorph screening. For example, the triethylsilylethynyl anthradithiophene (TES-ADT) films can crystallize into two polymorphs from different solvents [52–54]. The polymorph selectivity for solution processes mostly relates to the polarity of solvents, while the concentration can also induce polymorphism [47, 55]. For instance, the C6-DBTDT molecules can crystallize into the α-phase and β-phase crystals from high concentration and dilute chlorobenzene solutions, respectively [47]. At the molecular level, the specific interactions between semiconductor and solvent molecules in the solution can induce the nuclei formation in a particular polymorph and therefore result in polymorph selectivity as a function of the solvent or the concentration [56].

#### **2.2 Temperature control**

The thermodynamic polymorphic selection is usually observed from deposition of organic semiconductors by physical vapor transport (PVT) processes [57]. In a study by Stevens et al., TMS-DBC crystals were synthesized in a crystallization tube by PVT method, where two polymorphs grew at different temperature regions [58]. The red low-temperature (LT) polymorph was obtained in regions with tube temperature about 25–65°C, while the yellow high-temperature (HT) polymorph grew in regions with temperature around 130–170°C. The two polymorphs were found extremely stable, which did not interconvert to the other crystal structure with subsequent solvent or thermal treatments. Temperature-induced polymorphism was also observed from TiOPC crystals fabricated by PVT technology [48]. Sheetlike *α*-phase TiOPC crystals were obtained on the substrate at the temperature zone of about 210°C, while ribbonlike *β*-phase crystals were grown at the temperature zone of about 180°C. For many polymorphic materials, most of the polymorphs are temperature sensitive, where thermal-induced phase transition is allowed. Consequently, temperature-induced polymorph selectivity is becoming an important strategy to access and study different polymorphs.

#### **2.3 Crystallization through kinetics control**

Crystallization through kinetics control is a powerful method for accessing metastable polymorphs, especially in thin-film geometry where kinetic trapping and thin-film confinement work in synergy. In a study by Wedl et al. [59], thin films of dihexylterthiophene (DH3T) were fabricated by spin coating, dip coating, drop casting, and physical vapor deposition, i.e., with very different crystallization speed. Three polymorphs of DH3T were discovered from the experiment, which was noted as the α-phase, β-phase, and the metastable thin-film phase. The crystallization speed was found to be a key parameter to control the respective polymorphs present in the films. The metastable thin-film phase was obtained from deposition techniques with fast crystallization speeds, such as physical vapor deposition, spin coating, drop casting with fast solvent evaporation, and dip coating with high withdrawal velocity. In contrast, a mixture of two stable polymorphs was observed in films fabricated by both drop casting and dip coating with slow evaporation of solvent. Crystallization kinetics control was also applied in a study by Giri et al. [14], wherein the solution shearing method with a function of shearing speed was utilized to fabricate thin films of TIPS-pentacene. Through fast solvent evaporation and quick crystallization, metastable states were kinetically trapped, which were relaxed to more stable states with toluene vapor annealing.

#### **2.4 Templating via heterogeneous nucleation**

Organic molecules are assembled by weak intermolecular interactions into their crystalline form, which can be affected by the molecule-surface interaction and the molecule-molecule interaction from additives. In other words, substrates and additives can act as templates to alter the crystal structure of organic semiconductors.

The substrate can promote heterogeneous nucleation of a particular polymorph due to specific interface interactions. On the substrate-thin-film interface, substrate-induced polymorphs (SIPs) are usually observed in the first few molecular layers, whose molecular packing are different from that in the bulk of the film. For example, two SIPs were firstly observed in thin films of pentacene, including a thin-film phase with d-spacing of 15.4 Å and a single-layer phase with d-spacing of 16.1 Å [32, 60, 61]. In contrast, the single-crystal phase of pentacene

**69**

*Crystal Polymorph Control for High-Performance Organic Field-Effect Transistors*

exhibits the d-spacing of 14.1 Å [62–64]. SIPs were also observed in films of the 2,7-dioctyloxy-BTBT (C8O-BTBT-OC8) derivative [10]. The C8O-BTBT-OC8 molecules adopt a slipped π-π stacking in bulk crystal while exhibiting a herringbone packing motif in the thin-film phase. However, the SIP of C8O-BTBT-OC8 is a metastable form induced by the substrate, which is converted to the bulk form in 6 months or by chloroform vapor annealing. Although SIPs are commonly observed in thin films of organic semiconductors, studies on the formation of

Polymer additives have been demonstrated effective for polymorph control. In a study on polymorphism of TIPS-pentacene, conjugated polymer additives including poly(3-hexylthiophene) (P3HT) and region random TIPS-pentacenebithiophene polymer (PnBT-RRa) were used to template the formation of a polymorph [66]. Two new polymorphs of TIPS-pentacene were obtained, including the phase II and phase III that were synthesized form TIPS-pentacene/PnBT-RRa blend and TIPS-pentacene/P3HT blend, respectively. Compared to the phase I obtained from pure TIPS-pentacene, the phase II exhibits very small changes in crystal structure, which is attributed to the structural similarity between TIPS-pentacene and PnBT-RRa as well as their strong intermolecular interactions. In contrast, the crystal structure of phase III exhibits a large difference compared to the phase I, due to the lack of structural similarity between TIPS-pentacene and P3HT. These results demonstrate the possibility of using polymer additives as templates for

Postdeposition processing is a commonly used method to investigate phase transition, from which various polymorphs can be accessed. Solvent and thermal annealing is widely used for postdeposition treatments to increase crystallinity, to enlarge grain size, and in some cases to alter the molecular packing in films of organic semiconductors [67–69]. In a study by Hiszpanski et al. [70], three polymorphs of contorted hexabenzocoronene (c-HBC) have been obtained by the application of both thermal and solvent vapor annealing. The P21/c polymorph of c-HBC is obtained from the amorphous film by thermal annealing. In contrast, polymorph II is accessed from either the amorphous film or the P21/c polymorph by tetrahydrofuran vapor annealing. Subsequently, thermal annealing of polymorph II always yields polymorph II. From an investigation by Campione et al., α-tetrathiophene (α-4T)/LT single crystals were obtained by the floating-drop technique, and a crystal to crystal phase transition was observed at 191°C from α-4T/LT to α-4T/HT,

In addition to the major methods summarized above, a variety of novel approaches have been developed to control polymorphs. A direct strategy to change the crystal phase is to apply pressure on crystals. For instance, pressure-induced phase transition was observed from rubrene and fullerene derivatives [72–76]. Ito et al. and Segara et al. reported mechanically induced phase transitions [77, 78]. The nucleation of a polymorph is often affected by many processing parameters. For example, Lee et al. successfully fabricated a metastable polymorph of quaterrylene diimide by flow-assisted crystallization [79]. He et al. synthesized a new polymorph of Cl2-NDI by vapor sublimation in air [18]. Even light can have effects on polymorph formation. As investigated by Pithan et al., two polymorphs of sexithio-

phene were obtained in dark and illumination environments [33].

*DOI: http://dx.doi.org/10.5772/intechopen.91905*

accessing various polymorph phases.

obtaining large and thick α-4T/HT single crystals [71].

**2.5 Postdeposition control**

**2.6 Other methods**

SIPs are limited [65].

#### *Crystal Polymorph Control for High-Performance Organic Field-Effect Transistors DOI: http://dx.doi.org/10.5772/intechopen.91905*

exhibits the d-spacing of 14.1 Å [62–64]. SIPs were also observed in films of the 2,7-dioctyloxy-BTBT (C8O-BTBT-OC8) derivative [10]. The C8O-BTBT-OC8 molecules adopt a slipped π-π stacking in bulk crystal while exhibiting a herringbone packing motif in the thin-film phase. However, the SIP of C8O-BTBT-OC8 is a metastable form induced by the substrate, which is converted to the bulk form in 6 months or by chloroform vapor annealing. Although SIPs are commonly observed in thin films of organic semiconductors, studies on the formation of SIPs are limited [65].

Polymer additives have been demonstrated effective for polymorph control. In a study on polymorphism of TIPS-pentacene, conjugated polymer additives including poly(3-hexylthiophene) (P3HT) and region random TIPS-pentacenebithiophene polymer (PnBT-RRa) were used to template the formation of a polymorph [66]. Two new polymorphs of TIPS-pentacene were obtained, including the phase II and phase III that were synthesized form TIPS-pentacene/PnBT-RRa blend and TIPS-pentacene/P3HT blend, respectively. Compared to the phase I obtained from pure TIPS-pentacene, the phase II exhibits very small changes in crystal structure, which is attributed to the structural similarity between TIPS-pentacene and PnBT-RRa as well as their strong intermolecular interactions. In contrast, the crystal structure of phase III exhibits a large difference compared to the phase I, due to the lack of structural similarity between TIPS-pentacene and P3HT. These results demonstrate the possibility of using polymer additives as templates for accessing various polymorph phases.

### **2.5 Postdeposition control**

*Integrated Circuits/Microchips*

**2.2 Temperature control**

The thermodynamic polymorphic selection is usually observed from deposition of organic semiconductors by physical vapor transport (PVT) processes [57]. In a study by Stevens et al., TMS-DBC crystals were synthesized in a crystallization tube by PVT method, where two polymorphs grew at different temperature regions [58]. The red low-temperature (LT) polymorph was obtained in regions with tube temperature about 25–65°C, while the yellow high-temperature (HT) polymorph grew in regions with temperature around 130–170°C. The two polymorphs were found extremely stable, which did not interconvert to the other crystal structure with subsequent solvent or thermal treatments. Temperature-induced polymorphism was also observed from TiOPC crystals fabricated by PVT technology [48]. Sheetlike *α*-phase TiOPC crystals were obtained on the substrate at the temperature zone of about 210°C, while ribbonlike *β*-phase crystals were grown at the temperature zone of about 180°C. For many polymorphic materials, most of the polymorphs are temperature sensitive, where thermal-induced phase transition is allowed. Consequently, temperature-induced polymorph selectivity is becoming an

important strategy to access and study different polymorphs.

relaxed to more stable states with toluene vapor annealing.

**2.4 Templating via heterogeneous nucleation**

Crystallization through kinetics control is a powerful method for accessing metastable polymorphs, especially in thin-film geometry where kinetic trapping and thin-film confinement work in synergy. In a study by Wedl et al. [59], thin films of dihexylterthiophene (DH3T) were fabricated by spin coating, dip coating, drop casting, and physical vapor deposition, i.e., with very different crystallization speed. Three polymorphs of DH3T were discovered from the experiment, which was noted as the α-phase, β-phase, and the metastable thin-film phase. The crystallization speed was found to be a key parameter to control the respective polymorphs present in the films. The metastable thin-film phase was obtained from deposition techniques with fast crystallization speeds, such as physical vapor deposition, spin coating, drop casting with fast solvent evaporation, and dip coating with high withdrawal velocity. In contrast, a mixture of two stable polymorphs was observed in films fabricated by both drop casting and dip coating with slow evaporation of solvent. Crystallization kinetics control was also applied in a study by Giri et al. [14], wherein the solution shearing method with a function of shearing speed was utilized to fabricate thin films of TIPS-pentacene. Through fast solvent evaporation and quick crystallization, metastable states were kinetically trapped, which were

Organic molecules are assembled by weak intermolecular interactions into their crystalline form, which can be affected by the molecule-surface interaction and the molecule-molecule interaction from additives. In other words, substrates and additives can act as templates to alter the crystal structure of organic semiconductors. The substrate can promote heterogeneous nucleation of a particular polymorph due to specific interface interactions. On the substrate-thin-film interface,

substrate-induced polymorphs (SIPs) are usually observed in the first few molecular layers, whose molecular packing are different from that in the bulk of the film. For example, two SIPs were firstly observed in thin films of pentacene, including a thin-film phase with d-spacing of 15.4 Å and a single-layer phase with d-spacing of 16.1 Å [32, 60, 61]. In contrast, the single-crystal phase of pentacene

**2.3 Crystallization through kinetics control**

**68**

Postdeposition processing is a commonly used method to investigate phase transition, from which various polymorphs can be accessed. Solvent and thermal annealing is widely used for postdeposition treatments to increase crystallinity, to enlarge grain size, and in some cases to alter the molecular packing in films of organic semiconductors [67–69]. In a study by Hiszpanski et al. [70], three polymorphs of contorted hexabenzocoronene (c-HBC) have been obtained by the application of both thermal and solvent vapor annealing. The P21/c polymorph of c-HBC is obtained from the amorphous film by thermal annealing. In contrast, polymorph II is accessed from either the amorphous film or the P21/c polymorph by tetrahydrofuran vapor annealing. Subsequently, thermal annealing of polymorph II always yields polymorph II. From an investigation by Campione et al., α-tetrathiophene (α-4T)/LT single crystals were obtained by the floating-drop technique, and a crystal to crystal phase transition was observed at 191°C from α-4T/LT to α-4T/HT, obtaining large and thick α-4T/HT single crystals [71].

#### **2.6 Other methods**

In addition to the major methods summarized above, a variety of novel approaches have been developed to control polymorphs. A direct strategy to change the crystal phase is to apply pressure on crystals. For instance, pressure-induced phase transition was observed from rubrene and fullerene derivatives [72–76]. Ito et al. and Segara et al. reported mechanically induced phase transitions [77, 78]. The nucleation of a polymorph is often affected by many processing parameters. For example, Lee et al. successfully fabricated a metastable polymorph of quaterrylene diimide by flow-assisted crystallization [79]. He et al. synthesized a new polymorph of Cl2-NDI by vapor sublimation in air [18]. Even light can have effects on polymorph formation. As investigated by Pithan et al., two polymorphs of sexithiophene were obtained in dark and illumination environments [33].

### **3. Charge transport in OFETs with different polymorphs**

Polymorphism is an important platform to study the charge transport mechanism in organic semiconductors because in polymorphs the crystal structure is the only variable, while the chemical structure remains identical [80]. By studying a polymorphic organic semiconductor, changes in charge transport can be directly associated with the differences in molecular packing. Many studies have attempted without success to reveal the relationship between charge transport and molecular packing, including experimental studies and quantum chemical calculations on different polymorphs.

#### **3.1 Theoretical studies**

Charge transport in inorganic semiconductors is well described by the bandlike charge transport model. In contrast, to describe charge transport in organic semiconductors is much complex, where both electron–electron and electron–phonon interactions must be taken into account [81, 82]. A phonon is described as a particle-like quantized mode of vibrational energy, which arises from oscillating atoms within a crystal. In organic crystals, the molecule packing can be significantly disrupted by thermal functions due to the weak intermolecular interactions. Therefore, the charge transport behavior of organic semiconductors is temperature dependent [83]. It turns out that a charge-hopping model is commonly observed at near and above room temperatures [84], while a band-like transport model is typically observed in single crystals at lower temperatures [85].

The OFET devices mostly work at near and above room temperatures and follow a hopping transport mechanism. The hopping mobility can be deduced from the Marcus theory through Eq. (1) [17, 86]: \_*π*

$$\begin{array}{l} \text{(1)} \quad \text{[17, 86]:}\\ \text{Eq. (1)} \text{ [17, 86]:} \end{array}$$

$$\mu\_{\text{hop}} = \frac{e\alpha^2 t^2}{k\_B T \hbar} \left[ \frac{\pi}{2E\_{\text{pol}} k\_B T} \right]^{\frac{1}{2}} \exp\left(-\frac{E\_{\text{pol}}}{2K\_B T}\right) \tag{1}$$

where *e* is electron charge, *a* is the spacing between molecules, *t* is the charge transfer integral, *kB* is the Boltzmann constant, *T* is temperature, *ℏ* is Planck constant, and *E*pol is the polaron binding energy. The polaron binding energy is related to the reorganization energy (λreorg) via *E*pol = λreorg/2. The reorganization energy (λreorg) depicts both the intramolecular and intermolecular contributions to the change in the geometry of the molecules during charge transfer [87]. In organic crystals, two major parameters affect the charge carrier mobility, which are the transfer integral (*t*) and the reorganization energy (λreorg). The transfer integral and the reorganization energy can be quantitatively determined by quantum chemical calculations, and therefore, the hopping mobility can be estimated. In general, organic semiconductors with higher transfer integral and lower reorganization energy have higher charge carrier mobility.

Taking advantages of the quantum chemical calculations, the relationship between molecular packing and charge transport can be examined. For instance, Bredas et al. simulated the sexithiophene dimers to understand the effect of the molecular overlap on the transfer integral between adjacent molecules [88]. First, the HOMO and LUMO energy splittings were examined with a variation in the intermolecular distance between the conjugated planes. Next, by keeping the bottom molecule and the intermolecular distance between the sexithiophene (6T) dimers (4 Å) fixed, the effects of lateral molecular displacement along the conjugated plane on the energy splittings were examined by moving the top 6T molecule. The energy splitting is directly proportional to the charge transfer integral (*t*). The electronic splittings of HOMO and LUMO exhibit an exponential decay

**71**

**Figure 2.**

*Crystal Polymorph Control for High-Performance Organic Field-Effect Transistors*

provides an opportunity to improve the performance of OFETs.

**3.2 Thin-film transistors with different polymorphs**

as the intermolecular distance is increased. In contrast, the HOMO/LUMO energy splittings show large oscillations and tend to abate as the lateral displacement along the conjugated plane is increased. These results indicate that charge transport in organic semiconductors is sensitive to molecular packing. Consequently, altering the molecular packing, i.e., tuning the polymorph structure of organic semiconductors,

Organic thin-film transistors are easy to fabricate in large area by solution processing and therefore have been widely used in various electronic devices like electronic paper [89] and medical sensors [90, 91]. However, the semiconductor processing method and conditions can greatly affect the molecular packing motif and consequently can dramatically affect the device performance (see Section 2). To date, the knowledge on how the charge transport in semiconductor films depends on molecular packing motif is still very limited. In this section, the relationship between molecular packing and charge transport will be discussed, giving some

Pentacene is a benchmark organic semiconductor synthesized in 1912 [92], which exhibits excellent charge transport performance in thin-film transistor [93]. To date, there are five different polymorphs known for pentacene [9, 31, 32, 94]. As shown in **Figure 2**, the five polymorphs of pentacene are classified by their molecular layer thickness (d-spacing), where four thin-film forms exhibit d-spacing of 14.1, 14.4, 15.0, and 15.4 Å [31], and a monolayer form shows d-spacing of 16.1 Å [60]. However, among the five polymorphs, complete structural data have only been determined for the 14.1 and 14.4 Å polymorphs, where the 14.1 Å polymorph shares a similar packing as the single crystals. The single crystal of pentacene was

> V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

*(a) Schematic drawing of the crystal structures of the pentacene polymorphs [31]. Copyright 2003, American Chemical Society. (b) Normal views of the ab planes of the bulk and the monolayer structures of pentacene* 

[43, 95]. A recent study by Ji et al.

*DOI: http://dx.doi.org/10.5772/intechopen.91905*

recent investigations as examples.

reported with mobility around 5–40 cm2

*[60]. Copyright 2004, American Chemical Society.*

*3.2.1 Pentacene*

as the intermolecular distance is increased. In contrast, the HOMO/LUMO energy splittings show large oscillations and tend to abate as the lateral displacement along the conjugated plane is increased. These results indicate that charge transport in organic semiconductors is sensitive to molecular packing. Consequently, altering the molecular packing, i.e., tuning the polymorph structure of organic semiconductors, provides an opportunity to improve the performance of OFETs.

#### **3.2 Thin-film transistors with different polymorphs**

Organic thin-film transistors are easy to fabricate in large area by solution processing and therefore have been widely used in various electronic devices like electronic paper [89] and medical sensors [90, 91]. However, the semiconductor processing method and conditions can greatly affect the molecular packing motif and consequently can dramatically affect the device performance (see Section 2). To date, the knowledge on how the charge transport in semiconductor films depends on molecular packing motif is still very limited. In this section, the relationship between molecular packing and charge transport will be discussed, giving some recent investigations as examples.

#### *3.2.1 Pentacene*

*Integrated Circuits/Microchips*

different polymorphs.

**3.1 Theoretical studies**

**3. Charge transport in OFETs with different polymorphs**

typically observed in single crystals at lower temperatures [85].

*μ*hop = *ea*<sup>2</sup> *t* \_ 2 *kBTℏ* [

Marcus theory through Eq. (1) [17, 86]:

energy have higher charge carrier mobility.

Polymorphism is an important platform to study the charge transport mechanism in organic semiconductors because in polymorphs the crystal structure is the only variable, while the chemical structure remains identical [80]. By studying a polymorphic organic semiconductor, changes in charge transport can be directly associated with the differences in molecular packing. Many studies have attempted without success to reveal the relationship between charge transport and molecular packing, including experimental studies and quantum chemical calculations on

Charge transport in inorganic semiconductors is well described by the bandlike charge transport model. In contrast, to describe charge transport in organic semiconductors is much complex, where both electron–electron and electron–phonon interactions must be taken into account [81, 82]. A phonon is described as a particle-like quantized mode of vibrational energy, which arises from oscillating atoms within a crystal. In organic crystals, the molecule packing can be significantly disrupted by thermal functions due to the weak intermolecular interactions. Therefore, the charge transport behavior of organic semiconductors is temperature dependent [83]. It turns out that a charge-hopping model is commonly observed at near and above room temperatures [84], while a band-like transport model is

The OFET devices mostly work at near and above room temperatures and follow a hopping transport mechanism. The hopping mobility can be deduced from the

> \_1 2 exp (−

\_ *E*pol

<sup>2</sup>*K*B*T*) (1)

\_*π*

2 *E*pol *kBT*]

Taking advantages of the quantum chemical calculations, the relationship between molecular packing and charge transport can be examined. For instance, Bredas et al. simulated the sexithiophene dimers to understand the effect of the molecular overlap on the transfer integral between adjacent molecules [88]. First, the HOMO and LUMO energy splittings were examined with a variation in the intermolecular distance between the conjugated planes. Next, by keeping the bottom molecule and the intermolecular distance between the sexithiophene (6T) dimers (4 Å) fixed, the effects of lateral molecular displacement along the conjugated plane on the energy splittings were examined by moving the top 6T molecule. The energy splitting is directly proportional to the charge transfer integral (*t*). The electronic splittings of HOMO and LUMO exhibit an exponential decay

where *e* is electron charge, *a* is the spacing between molecules, *t* is the charge transfer integral, *kB* is the Boltzmann constant, *T* is temperature, *ℏ* is Planck constant, and *E*pol is the polaron binding energy. The polaron binding energy is related to the reorganization energy (λreorg) via *E*pol = λreorg/2. The reorganization energy (λreorg) depicts both the intramolecular and intermolecular contributions to the change in the geometry of the molecules during charge transfer [87]. In organic crystals, two major parameters affect the charge carrier mobility, which are the transfer integral (*t*) and the reorganization energy (λreorg). The transfer integral and the reorganization energy can be quantitatively determined by quantum chemical calculations, and therefore, the hopping mobility can be estimated. In general, organic semiconductors with higher transfer integral and lower reorganization

**70**

Pentacene is a benchmark organic semiconductor synthesized in 1912 [92], which exhibits excellent charge transport performance in thin-film transistor [93]. To date, there are five different polymorphs known for pentacene [9, 31, 32, 94]. As shown in **Figure 2**, the five polymorphs of pentacene are classified by their molecular layer thickness (d-spacing), where four thin-film forms exhibit d-spacing of 14.1, 14.4, 15.0, and 15.4 Å [31], and a monolayer form shows d-spacing of 16.1 Å [60]. However, among the five polymorphs, complete structural data have only been determined for the 14.1 and 14.4 Å polymorphs, where the 14.1 Å polymorph shares a similar packing as the single crystals. The single crystal of pentacene was reported with mobility around 5–40 cm2 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> [43, 95]. A recent study by Ji et al.

#### **Figure 2.**

*(a) Schematic drawing of the crystal structures of the pentacene polymorphs [31]. Copyright 2003, American Chemical Society. (b) Normal views of the ab planes of the bulk and the monolayer structures of pentacene [60]. Copyright 2004, American Chemical Society.*

reported that the polymorph with d-spacing of 16.2 Å has a mobility of up to 30.6 cm2 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> [93]. As for the other polymorphs, to stabilize and isolate a pure polymorph for transistor fabrication has been challenging. Thus, more investigation on the relationship between molecular packing and charge transport for pentacene remains a serious topic of research.

#### *3.2.2 6,13-Bis(triisopropylsilylethynyl)-pentacene*

In 2001, Anthony et al. introduced triisopropylsilylethynyl (TIPS) group to the pentacene core, obtaining a very soluble pentacene derivative, i.e. TIPSpentacene [46]. Different from the herringbone-stacked pentacene molecules, the TIPS-pentacene molecules adopt a brick-wall stacking in solid state. Several recent investigations have revealed that TIPS-pentacene exhibits polymorphism. For instance, Diao et al. fabricated five different polymorphs of TIPS-pentacene by using the solution shearing technology [15]. The five polymorphs have been categorized into three families: I and Ib, II and IIb, and III. Within each family, there is only a slight change in one or two unit cell parameters between the polymorphs. Among different family (polymorphs I, II, and III), the main structural differences are changes in the π-π stacking distance and the extent of overlap between adjacent molecules (**Figure 3**). Form I has larger π-π stacking distance than that of forms II and III, where pair I in form III exhibits a record low-stacking distance of less than 3 Å. As a result, form I exhibits ambipolar charge transport property, with hole and electron mobility of 3.8 and 6.81 cm2 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> , respectively. Form II shows the highest mobility up to 11 cm2 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> . In sharp contrast, form III possesses the lowest mobility around 0.09 cm2 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> . The quantum chemical calculations indicate a much smaller hole transfer integral for form III compared to form I and form II. Form II with moderate π-π stacking distance has the largest hole transfer integral

#### **Figure 3.**

*Comparison of the three major polymorphs of TIPS-pentacene in their π-π stacking (A) and molecular offset along the conjugated backbone (B, C) as obtained from the crystallographic refinement calculations [15]. Copyright 2014, American Chemical Society.*

**73**

*3.3.1 Rubrene*

up to 20 cm2

 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

*Crystal Polymorph Control for High-Performance Organic Field-Effect Transistors*

distance does not always help to improve charge transport properties.

attribute the mobility drop entirely to crystal structure change.

α-phase film exhibited the highest hole mobility of 0.4 cm<sup>2</sup>

 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

crystallinity, orientation, grain size, grain boundaries, and so on.

**3.3 Single-crystal transistors with different polymorphs**

examples of single-crystal OFETs are introduced.

*3.2.4 5,11-Bis(triethylsilylethynyl)anthradithiophene*

*3.2.3 2,7-Dioctyl[1]benzothieno[3,2-b][1]benzothiophene*

and therefore exhibits the highest mobility. This result shows that small π-π stacking

2,7-Dioctyl[1]benzothieno[3,2-b][1]benzothiophene (C8-BTBT) is an extensive studied air-stable organic semiconductor, which often shows very high hole mobility in OFET devices [4, 96, 97]. In a recent study by Yuan et al., ultra-high mobility

polymorph of C8-BTBT film [4]. The metastable polymorph was fabricated by introducing polystyrene additive and using an off-center spin-coating method. After thermal annealing, the metastable polymorph was relaxed to the equilibrium polymorph, along with a sharp decrease of carrier mobility. However, the correlation between molecular packing and charge transport for the C8-BTBT films is difficult to establish. The authors stated that the beam damage during grazing incidence X-ray diffraction (GIXD) measurements made it impossible to obtain the precise crystal packing structure for the metastable polymorph. Moreover, the crystal alignment was also disrupted after thermal annealing, making it difficult to

5,11-Bis(triethylsilylethynyl)anthradithiophene (TES-ADT) is a high-performance organic semiconductor with good solubility [53]. In a study by Yu and colleagues, four polymorphs of TES-ADT was obtained in thin films, including three thin-film forms (*α*, *β*, and *γ* polymorphs) and one amorphous form [98]. The

two orders of magnitude higher than that of the *β* and *γ* polymorphs. However, in a study by Chen et al., the *β*-phase film fabricated from toluene by drop casting had a

that to directly correlate mobility to molecular packing from thin-film transistor with different polymorphs is challenging. It is known that many factors can affect the charge transport in thin-film transistors, including film morphology, degree of

Single-crystal transistors are preferred for fundamental studies on structurecharge transport relationships owning to their high molecular ordering and no grain boundaries. However, structure-property investigations have been successfully performed for only a small number of organic semiconductors by means of single-crystal transistors. Compared to thin-film transistors, the manufacture of single-crystal OFETs is more complicated, which generally requires the use of highprecision deposition or micromanipulation techniques. Moreover, the preparation of single crystals with different polymorphs is very difficult. In this section, some

Rubrene is an excellent organic semiconductor with single-crystal mobility

a triclinic, and two orthorhombic forms, have been known for a long time [30],

[99]. Four polymorphs of rubrene, including a monoclinic,

was obtained from thin-film transistors based on a metastable

 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

) than that of α-phase film from tetrahydrofuran

) [52]. The opposite results from these two investigations reveal

, which was about

*DOI: http://dx.doi.org/10.5772/intechopen.91905*

up to 43 cm<sup>2</sup>

 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

higher mobility (0.22 cm2

 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

(0.06 cm2

*Crystal Polymorph Control for High-Performance Organic Field-Effect Transistors DOI: http://dx.doi.org/10.5772/intechopen.91905*

and therefore exhibits the highest mobility. This result shows that small π-π stacking distance does not always help to improve charge transport properties.

#### *3.2.3 2,7-Dioctyl[1]benzothieno[3,2-b][1]benzothiophene*

*Integrated Circuits/Microchips*

 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

remains a serious topic of research.

*3.2.2 6,13-Bis(triisopropylsilylethynyl)-pentacene*

and electron mobility of 3.8 and 6.81 cm2

 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

highest mobility up to 11 cm2

est mobility around 0.09 cm2

30.6 cm2

reported that the polymorph with d-spacing of 16.2 Å has a mobility of up to

polymorph for transistor fabrication has been challenging. Thus, more investigation on the relationship between molecular packing and charge transport for pentacene

In 2001, Anthony et al. introduced triisopropylsilylethynyl (TIPS) group to the pentacene core, obtaining a very soluble pentacene derivative, i.e. TIPSpentacene [46]. Different from the herringbone-stacked pentacene molecules, the TIPS-pentacene molecules adopt a brick-wall stacking in solid state. Several recent investigations have revealed that TIPS-pentacene exhibits polymorphism. For instance, Diao et al. fabricated five different polymorphs of TIPS-pentacene by using the solution shearing technology [15]. The five polymorphs have been categorized into three families: I and Ib, II and IIb, and III. Within each family, there is only a slight change in one or two unit cell parameters between the polymorphs. Among different family (polymorphs I, II, and III), the main structural differences are changes in the π-π stacking distance and the extent of overlap between adjacent molecules (**Figure 3**). Form I has larger π-π stacking distance than that of forms II and III, where pair I in form III exhibits a record low-stacking distance of less than 3 Å. As a result, form I exhibits ambipolar charge transport property, with hole

> V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

a much smaller hole transfer integral for form III compared to form I and form II. Form II with moderate π-π stacking distance has the largest hole transfer integral

*Comparison of the three major polymorphs of TIPS-pentacene in their π-π stacking (A) and molecular offset along the conjugated backbone (B, C) as obtained from the crystallographic refinement calculations [15].* 

, respectively. Form II shows the

. In sharp contrast, form III possesses the low-

. The quantum chemical calculations indicate

[93]. As for the other polymorphs, to stabilize and isolate a pure

**72**

**Figure 3.**

*Copyright 2014, American Chemical Society.*

2,7-Dioctyl[1]benzothieno[3,2-b][1]benzothiophene (C8-BTBT) is an extensive studied air-stable organic semiconductor, which often shows very high hole mobility in OFET devices [4, 96, 97]. In a recent study by Yuan et al., ultra-high mobility up to 43 cm<sup>2</sup> V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> was obtained from thin-film transistors based on a metastable polymorph of C8-BTBT film [4]. The metastable polymorph was fabricated by introducing polystyrene additive and using an off-center spin-coating method. After thermal annealing, the metastable polymorph was relaxed to the equilibrium polymorph, along with a sharp decrease of carrier mobility. However, the correlation between molecular packing and charge transport for the C8-BTBT films is difficult to establish. The authors stated that the beam damage during grazing incidence X-ray diffraction (GIXD) measurements made it impossible to obtain the precise crystal packing structure for the metastable polymorph. Moreover, the crystal alignment was also disrupted after thermal annealing, making it difficult to attribute the mobility drop entirely to crystal structure change.

### *3.2.4 5,11-Bis(triethylsilylethynyl)anthradithiophene*

5,11-Bis(triethylsilylethynyl)anthradithiophene (TES-ADT) is a high-performance organic semiconductor with good solubility [53]. In a study by Yu and colleagues, four polymorphs of TES-ADT was obtained in thin films, including three thin-film forms (*α*, *β*, and *γ* polymorphs) and one amorphous form [98]. The α-phase film exhibited the highest hole mobility of 0.4 cm<sup>2</sup> V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> , which was about two orders of magnitude higher than that of the *β* and *γ* polymorphs. However, in a study by Chen et al., the *β*-phase film fabricated from toluene by drop casting had a higher mobility (0.22 cm2 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> ) than that of α-phase film from tetrahydrofuran (0.06 cm2 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> ) [52]. The opposite results from these two investigations reveal that to directly correlate mobility to molecular packing from thin-film transistor with different polymorphs is challenging. It is known that many factors can affect the charge transport in thin-film transistors, including film morphology, degree of crystallinity, orientation, grain size, grain boundaries, and so on.

#### **3.3 Single-crystal transistors with different polymorphs**

Single-crystal transistors are preferred for fundamental studies on structurecharge transport relationships owning to their high molecular ordering and no grain boundaries. However, structure-property investigations have been successfully performed for only a small number of organic semiconductors by means of single-crystal transistors. Compared to thin-film transistors, the manufacture of single-crystal OFETs is more complicated, which generally requires the use of highprecision deposition or micromanipulation techniques. Moreover, the preparation of single crystals with different polymorphs is very difficult. In this section, some examples of single-crystal OFETs are introduced.

#### *3.3.1 Rubrene*

Rubrene is an excellent organic semiconductor with single-crystal mobility up to 20 cm2 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> [99]. Four polymorphs of rubrene, including a monoclinic, a triclinic, and two orthorhombic forms, have been known for a long time [30], but the structure-charge transport relationship has only been discussed recently. In an investigation by Matsukawa et al., an orthorhombic single crystal exhibited high carrier mobility up to 1.6 cm2 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> , while that of the triclinic form was only 0.1 cm2 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> [29, 100].

The two polymorphs share similar π-π stacking distances, while the density of the π-stacking column in the (001) plane of orthorhombic crystal structure (**Figure 4a**) is much higher than that of the (0−11) plane of the triclinic crystal structure (**Figure 4b**). In other words, the π-π overlap along the carrier conduction direction in orthorhombic crystal is significantly larger than that in the triclinic crystal. Consequently, the orthorhombic crystal exhibits higher carrier mobility than the triclinic crystal.

#### *3.3.2 Tetrathiafulvalene*

Two polymorphs of tetrathiafulvalene (TTF), including a monoclinic orange crystal and a triclinic yellow crystals, were found many years ago [101]. The single-crystal transistors of the two polymorphs were fabricated by Jiang and colleagues recently [102]. Based on single-crystal transistors, the charge transport performance associated with molecular packing was discussed. The monoclinic *α*-form yielded a higher mobility of approximately 1.2 cm2 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> , while that of the triclinic *β*-form was around 0.23 cm<sup>2</sup> V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> . Compared to the *β*-form, the *α*-form shows strong π-π stacking along the short b axis and short contacts between S atoms (**Figure 5**), which may be the main factor contributing to the higher mobility.

#### *3.3.3 Dibenzotetrathiafulvalene*

Brillante et al. investigated the polymorphism of dibenzotetrathiafulvalene (DB-TTF), and four polymorphs were found [49]. The pure *α*-phase crystals were obtained from chlorobenzene or dimethylformamide solution [103]. In contrast, the *β*-phase crystals were synthesized from hot saturated toluene solution and were usually accompanied with the α-phase crystals. Moreover, *γ*-phase thin films were fabricated by ultra-high vacuum (UHV) vapor deposition on SiOx substrates at temperatures of 50–70°C and drop casting of colloidal composite solutions of polystyrene (PS) and DB-TTF. The fourth polymorph, the *δ*-phase, was obtained physically pure by crystallization from a mixture solution of isopropanol and nitromethane, as well as by vapor deposition under vacuum. However, among the four polymorphs, only the full-unit-cell parameters of the *α*- and *β*-phase crystals have been obtained (**Figure 6**).

In the *α*-phase crystal, the molecules adopt a face-to-face herringbone structure, possessing a good π-π overlap. Though the *β*-phase crystal also shows a herringbone

#### **Figure 4.**

*Crystallographic structures of (a) the orthorhombic crystal (CCDC, 1025043) as viewed as the (001) plane and (b) the triclinic crystal (CCDC, 991020) as viewed as the (0−11) plane.*

**75**

and 0.16 cm2

 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

*Crystal Polymorph Control for High-Performance Organic Field-Effect Transistors*

motif, the edge-to-face molecular packing neither results in π-π overlap between consecutive molecules in the stacks along b axis nor short contacts between adjacent columns. The solution-prepared single-crystal transistors based on *α*-phase crystal

*The molecular packing of (a) the α-phase (CCDC, 1111519) and (b) the β-phase (CCDC, 696271) crystals of* 

*Crystal packing of (a) α-TTF and (b) β-TTF with S*⋯*S interaction [102]. Copyright 2007, American Institute* 

Dithiophene-tetrathiafulvalene (DT-TTF) is a promising high-performance organic semiconductor, whose single-crystal OFETs were reported with high hole

prepared from a variety of solutions [104–106], which were named as the *α*-phase. In a study by Pfattner and colleagues, a new *β*-phase polymorph of DT-TTF was obtained as hexagonal-shaped platelet-like crystals [50]. The *β*-phase crystals were grown on some substrates from a solution of toluene or dichlorobenzene, mixed with crystals of the *α*-phase by ultrasonication of the solution before drop casting. The relative ratio of *β*-DT-TTF increased, whereas the *α*-phase was mostly obtained in the presence of small seed crystals. This indicates that the crystallization of *α*-phase probably starts in the solution, while the *β*-phase crystallizes directly on the substrate. The single-crystal OFETs of the two polymorphs were fabricated, and the device performances were measured, giving the hole mobilities of 1.18

the precise crystal structure of the *β*-phase crystal was not obtained, the analysis

 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

[103].

[104]. Long plated crystals of DT-TTF can be easily

from the *α*-phase and *β*-phase crystals, respectively. Though

showed best hole mobility of up to 1.0 cm2

 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

*3.3.4 Dithiophene-tetrathiafulvalene*

mobility up to 3.6 cm2

**Figure 5.**

*of Physics.*

**Figure 6.**

*DB-TTF.*

*DOI: http://dx.doi.org/10.5772/intechopen.91905*

*Crystal Polymorph Control for High-Performance Organic Field-Effect Transistors DOI: http://dx.doi.org/10.5772/intechopen.91905*

#### **Figure 5.**

*Integrated Circuits/Microchips*

0.1 cm2

 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

than the triclinic crystal.

*3.3.2 Tetrathiafulvalene*

high carrier mobility up to 1.6 cm2

[29, 100].

triclinic *β*-form was around 0.23 cm<sup>2</sup>

*3.3.3 Dibenzotetrathiafulvalene*

but the structure-charge transport relationship has only been discussed recently. In an investigation by Matsukawa et al., an orthorhombic single crystal exhibited

The two polymorphs share similar π-π stacking distances, while the density of the π-stacking column in the (001) plane of orthorhombic crystal structure (**Figure 4a**) is much higher than that of the (0−11) plane of the triclinic crystal structure (**Figure 4b**). In other words, the π-π overlap along the carrier conduction direction in orthorhombic crystal is significantly larger than that in the triclinic crystal. Consequently, the orthorhombic crystal exhibits higher carrier mobility

Two polymorphs of tetrathiafulvalene (TTF), including a monoclinic orange

crystal and a triclinic yellow crystals, were found many years ago [101]. The single-crystal transistors of the two polymorphs were fabricated by Jiang and colleagues recently [102]. Based on single-crystal transistors, the charge transport performance associated with molecular packing was discussed. The monoclinic

> V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

Brillante et al. investigated the polymorphism of dibenzotetrathiafulvalene (DB-TTF), and four polymorphs were found [49]. The pure *α*-phase crystals were obtained from chlorobenzene or dimethylformamide solution [103]. In contrast, the *β*-phase crystals were synthesized from hot saturated toluene solution and were usually accompanied with the α-phase crystals. Moreover, *γ*-phase thin films were fabricated by ultra-high vacuum (UHV) vapor deposition on SiOx substrates at temperatures of 50–70°C and drop casting of colloidal composite solutions of polystyrene (PS) and DB-TTF. The fourth polymorph, the *δ*-phase, was obtained physically pure by crystallization from a mixture solution of isopropanol and nitromethane, as well as by vapor deposition under vacuum. However, among the four polymorphs, only the full-unit-cell parameters of the *α*- and *β*-phase crystals have been obtained (**Figure 6**). In the *α*-phase crystal, the molecules adopt a face-to-face herringbone structure, possessing a good π-π overlap. Though the *β*-phase crystal also shows a herringbone

*Crystallographic structures of (a) the orthorhombic crystal (CCDC, 1025043) as viewed as the (001) plane and* 

*(b) the triclinic crystal (CCDC, 991020) as viewed as the (0−11) plane.*

shows strong π-π stacking along the short b axis and short contacts between S atoms (**Figure 5**), which may be the main factor contributing to the higher mobility.

*α*-form yielded a higher mobility of approximately 1.2 cm2

, while that of the triclinic form was only

 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

. Compared to the *β*-form, the *α*-form

, while that of the

 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

**74**

**Figure 4.**

*Crystal packing of (a) α-TTF and (b) β-TTF with S*⋯*S interaction [102]. Copyright 2007, American Institute of Physics.*

#### **Figure 6.**

*The molecular packing of (a) the α-phase (CCDC, 1111519) and (b) the β-phase (CCDC, 696271) crystals of DB-TTF.*

motif, the edge-to-face molecular packing neither results in π-π overlap between consecutive molecules in the stacks along b axis nor short contacts between adjacent columns. The solution-prepared single-crystal transistors based on *α*-phase crystal showed best hole mobility of up to 1.0 cm2 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> [103].

#### *3.3.4 Dithiophene-tetrathiafulvalene*

Dithiophene-tetrathiafulvalene (DT-TTF) is a promising high-performance organic semiconductor, whose single-crystal OFETs were reported with high hole mobility up to 3.6 cm2 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> [104]. Long plated crystals of DT-TTF can be easily prepared from a variety of solutions [104–106], which were named as the *α*-phase. In a study by Pfattner and colleagues, a new *β*-phase polymorph of DT-TTF was obtained as hexagonal-shaped platelet-like crystals [50]. The *β*-phase crystals were grown on some substrates from a solution of toluene or dichlorobenzene, mixed with crystals of the *α*-phase by ultrasonication of the solution before drop casting. The relative ratio of *β*-DT-TTF increased, whereas the *α*-phase was mostly obtained in the presence of small seed crystals. This indicates that the crystallization of *α*-phase probably starts in the solution, while the *β*-phase crystallizes directly on the substrate. The single-crystal OFETs of the two polymorphs were fabricated, and the device performances were measured, giving the hole mobilities of 1.18 and 0.16 cm2 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> from the *α*-phase and *β*-phase crystals, respectively. Though the precise crystal structure of the *β*-phase crystal was not obtained, the analysis

of crystal structures for the two polymorphs revealed smaller distances between neighboring molecules in the *α*-phase crystal which may facilitate charge transport.
