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Nanoelectronics

M.R. Cavallari

G. Santos

F.J. Fonseca Department of Electronic Systems Engineering, Polytechnic School of the USP, São Paulo, Brazil

Abstract

This chapter reviews organic materials from the point of view of application in electronic devices. After presenting techniques for obtaining thin films and thick layers from small organic molecules and polymers to manufacture the devices, the charge transport processes in these organic materials are discussed. Thin film transistors and light-emitting diodes, the main applications presented in this chapter, are discussed regarding configuration, manufacturing, and electrical and optical characterization, as appropriate.

Keywords

nanoelectronics

organic thin film transistors

mobility

microcontact printing

organic light-emitting diodes

electroluminescent polymers

organic semiconductors

acenes

polythiophenes

electrooptical characterization

2.1. Organic Materials for Nanoelectronics: Insulators and Conductors

Organic materials that have potential application in electronic products are small molecules (e.g., oligomers) or polymers whose structure is composed predominantly of carbon. The element carbon has six electrons distributed in levels 1s² 2s² 2p²; that is, it has four electrons in the highest level and median electronegativity (a tendency to share electrons rather than transfer them, which would correspond to covalent bonding). The sp² hybridization is characteristic of organic semiconductors. This state is shown in Fig. 2.1A for an ethylene molecule (or ethene). In this molecule, each carbon atom is hybridized as follows: σ bonds are formed on the plane defined by the carbon and hydrogen atoms with electrons strongly located between the nuclei of the atoms; however, π bonds also exist off the plane that enables a highly delocalized character.

Figure 2.1 (A) Carbon sp² hybridization in the ethylene molecule. Organic materials can be divided into small molecules [(B) pentacene, (C) fullerene] and polymers [monomer of (D) trans-, (E) cis-polyacetylene].

The π-conjugated molecules are characterized by alternating single and double bonds, with some examples shown in Fig. 2.1B–E. The bonds formed by overlapping of the p_z atomic orbitals (i.e., off the plane) create molecular orbitals ligands (π) and antiligands (π*) [1]. Electrons of the orbital ligand have less energy, and therefore, the orbital is known as the highest occupied molecular orbital (HOMO). Given that π bonds are typically weaker, these electrons are easily excited to the upper level and are free to move along the molecule, benefiting from the overlap of the p_z orbitals with neighboring atoms (delocalization of π orbitals). This higher energy level is known as the lowest unoccupied molecular orbital (LUMO). When the energy difference between the HOMO and LUMO levels is much greater than the thermal energy (k_BT, where k_B is Boltzmann’s constant and T is temperature) a forbidden band (i.e., bandgap) arises. In such a case, one can compare the HOMO to the valence band (VB) and the LUMO to the conduction band (CB) in an inorganic semiconductor or insulator.

Conjugated polymers exhibit electrical conductivity that can be typical of both insulators and conductors, according to chemical or natural modifications and the degree of doping. The idea of using polymers for their conductive properties appeared as recently as 1977 with the discoveries of Shirakawa et al. [2], in which trans-polyacetylene (Fig. 2.1D) doped with iodine exhibited conductivity of 10³ S cm⁻¹. The explanation of this discovery enabled Heeger, McDiarmid, and Shirakawa to win the Nobel Prize in Chemistry in 2000. Since then, interest in synthesizing other organic materials that exhibit this property has increased, and other polymers with the π-electron structure, such as those shown in Fig. 2.2 [polyaniline (PAni), polypyrrole (PPy), polythiophene (PT), polyfuran (PFu), poly(p-phenylene) (PPP), and polycarbazole (PCz)], have been synthesized and tested in electronic devices [3,4].

Figure 2.2 Chemical structure of monomers from the principal semiconducting polymers.
(A) Polyaniline (PAni), (B) polypyrrole (PPy), (C) polythiophene (PT), (D) polyfuran (PFu), (E) poly(p-phenylene) (PPP), and (F) polycarbazole (PCz).

The transport of charge carriers may be limited by injection because of the height of the potential barrier at the interfaces between different materials. When the electric field is sufficiently elevated or the height of the barriers is not significant, transport is dominated by the special charge accumulated on the organic semiconductor due to transport limitations [5]. In this case, the limiting factor of the electric current is the effective mobility of charge carriers (μ), defined by the ratio between the velocity of the carriers and the applied electric field. Greater mobilities than those found in hydrogenated amorphous silicon have been obtained for pentacene [6] and fullerene [7] (μ ∼ 6 cm² V⁻¹ s⁻¹), and although these values are still lower than those of monocrystalline silicon (μ ∼ 10² cm² V⁻¹ s⁻¹) [8], they are sufficient for the manufacturing of electronic products.

One of the advantages of organic semiconductors in relation to inorganic semiconductors is the possibility of synthesizing materials by modulating the bandgap and energy levels. This modulation generally provides materials with different optical properties and the ability to absorb and emit photons with wavelengths both inside and outside the visible range. In their simplest form, these devices, based on thin organic films, are composed of stacked layers positioned between two electrodes with high potential for application in light-emitting diodes (LEDs) [9], and even photovoltaics—organic solar cells (OSCs) [10]. Organic materials with these properties are promising for applications in information displays, such as mobile devices and large-scale screens, including their use in ambient illumination and flexible and transparent screens. Passive devices, such as resistors [11], capacitors [12], and diodes [13] can also be constructed. In addition to these devices, organic thin film transistors (OTFTs) [14], key elements for the implementation of electronic circuits, can be highlighted. If employed as field effect transistors (FETs) they can be used for various purposes, such as logic gates, processors, and memory [15,16]. Application of OTFTs in radio frequency identification devices (RFIDs) promises to revolutionize the automatic identification systems both in commercial applications and in industry [17]. Polymeric electronic memories are being investigated as an interesting alternative because of their compatibility with electronic circuits containing polymeric devices and miniaturization toward the nanoscale [18].

Among the conductive materials, PAni [19] (Fig. 2.2A), poly(3,4-ethylenedioxythiophene) doped with poly(styrenesulfonic acid) (PEDOT:PSS) [20], graphene sheets [21], and single-walled carbon nanotubes can be highlighted (Fig. 2.3). Graphene enables current modulation by an electric field, a typical behavior of semiconductors, but has greater potential for use in chemical sensors and electrodes. In turn, as shown in Fig. 2.3C, nanotubes can be separated into three categories with respect to the angle at which the graphene sheet is rolled: armchair, zigzag, or chiral. The rolling angle defined by the vector c_h = na₁ + ma₂ (n,m), where n and m are integers, produces electrical behavior typical of conductors or semiconductors. All armchair structures exhibit metallic properties, whereas the other two structures may have semiconducting or metallic properties depending on the diameter of the nanotube [22,23]. Some specific electrical properties of these materials can be exploited in the construction of devices different from inorganic semiconductors, such as molecular memories [15], oscillator monolayers [24], smart windows [25], artificial muscles [26], and biosensors [27].

Figure 2.3 Chemical structure of the principal organic conductors.
(A) PEDOT:PSS and (B) graphene. Carbon nanotubes are obtained by rolling the graphene sheets in the direction c_h = (n,m). The chiral structure is limited by the zigzag and armchair cases defined in turn by the vectors (n,0) and (n,n), respectively. According to this representation, the angle between the zigzag structure and c_h is negative. Adapted from T.W., Odom, et al. Atomic structure and electronic properties of single-walled carbon nanotubes. Nature 391 (1998) 62–64 [22].

Organic electronic systems offer the advantage of being lightweight and flexible, and also cover large areas at a reduced cost [28]. Manufacturing techniques are diverse, but there is a tendency to produce integrated circuits by direct printing of all system components, dispensing with expensive and complex techniques, such as thermal oxidation and photolithography [29]. Nanoelectronics permit the development of products whose mechanically flexible component provides solutions of lower weight and greater biocompatibility because they are near to the body, as is the case for portable electronics [28]. In this context, one of the possible applications is to reduce the cost of integrated circuits in the disposable sensor industry [30].

Furthermore, it appears that currently, there is a demand for components with applications in environmental [31] and food [32] monitoring, the application of drugs [33] the detection of chemical and biological weapons [34], and the fabrication of electronic tongues and noses [35]. In medical diagnostics in situ [36], diseases at an early stage can be detected through the recognition of specific biomolecules chains (deoxyribonucleic acid, DNA). Based on the compatibility of semiconductors with biomolecules and living cells, one can expect the integration of biomedicine and automation via advanced cybernetics [27].

2.1.1. Techniques for Making Organic Films

Electrochemical polymerization is the polymerization reaction performed directly on the electrodes. This was the first technique used to form a semiconductor layer employed in the fabrication of organic transistors [37,38]. This technique is usually associated with the formation of disordered films of low mobility; the first organic thin film transistor (TFT) was polythiophene and exhibited μ ≈ 10⁻⁵ cm² V⁻¹ s⁻¹ [37].

Spin coating, one of the deposition techniques of polymeric films, is widely used in this field because of its low cost, simplicity, and capability to produce homogeneous films with adequate thickness control [39]. Application of the solution is performed on the substrate, which undergoes rotation; the resulting thickness is a function of the frequency and rotation time. Alternatively, organic materials can be cast by the liquid phase deposition technique, which consists of applying the solution to the fixed substrate. Due to longer time required for drying the deposited layer, this technique provides the material more time to organize and thus achieve higher crystallinity. In contrast, it is more difficult to control the thickness of the formed layer, which is usually in the micron range [40].

Vacuum thermal evaporation is used to obtain films of small organic molecules that can be challenging to prepare in solution form. It provides high thickness control on the nanometer scale and high film purity, as well as a high degree of ordering depending on the growth rate [41]. Films obtained by this technique tend to be highly ordered such that microcrystalline devices incorporating pentacene [6] and fullerene [7] may provide greater performance than those of hydrogenated amorphous silicon. Alternatively, a monocrystal can be obtained from lamination or transfer of a mold to the substrate [42–44]. Crystals of high purity and molecular ordering can be obtained under vacuum by physical vapor transport in a horizontal tube.

An alternative technique for the formation of nanometric films of small molecules or conjugated polymers is self-assembly or electrostatic self-assembly, which uses two ionic species to form successive fine film bilayers [45]. This method is highlighted because it is low cost and simple, can be performed at ambient temperature and permits precise control of the structure and film thickness.

Currently, printing techniques have progressed to the industry stage for the manufacture of commercial devices. Notable techniques include inkjet, screen [46], roll-to-roll [47], and microcontact printing (μCP) [48,49]. These techniques are capable of providing resolution down to 2 μm. Microcontact printing consists of the transfer (stamping) of conductive material (e.g., nanoparticles and PEDOT:PSS) in the process of additive binding of the mold to the substrate. As shown in Fig. 2.4, the process can be divided into two stages: (1) inking, which involves the formation of a conductive ink layer on the surface of a mold, followed by (2) stamping or transfer of this conductive layer onto a substrate.

Figure 2.4 Schematic diagram of the microcontact printing process (μCP).
(A) inking of the mold with conductive ink; (B) stamping of the conductive ink of the mold onto the substrate; and (C) substrate with the pattern of electrodes transferred from the mold.

Microcontacts can be alternatively obtained by a subtractive process known as imprint lithography [50]. Developed by Stephen Chou et al. [51], hot embossing, shown in Fig. 2.5, uses a polymer that can be thermally modified to conform to the relief of the mold. Under compression, this polymer is heated above its glass transition temperature (T_g) to flow through the channels of the stamp and then cooled down to solidify the patterned structures.

Figure 2.5 Hot embossing lithography.
(A) spin coating of the photoresist on the substrate; (B) embossing or imprinting the pattern of the mold with heat; and (C) postbaking to cure the transferred structures.

2.2. Process of Charge Transport in Organic Devices

Organic materials have a structure characterized on the atomic scale by disorganization, in which the charge carriers are delocalized in their molecules (or along the conjugation length of the polymer chains), where the rate-limiting step in transport is intermolecular (or between-chain) hopping of these carriers [52]. This structure, in the absence of crystallinity, inherently leads to a high density of defects and therefore a mobility (μ) of 10⁻⁷–10⁻³ cm² V⁻¹ s⁻¹ depending on the electric field and temperature. In the literature, the two main models of charge carrier injection in organic semiconductors are Fowler–Nordheim [53] or Schottky thermionic emission [54]. In the latter, the electric current (I) can be described as a function of the applied electric potential (V) generically as:

$I (V) = A A^{* *} T^{2} (e^{\frac{- φ_{B}}{k_{B} T}}) (e^{\frac{q (V_{a} - I R_{s})}{η k_{B} T}}) (1 - e^{\frac{- q (V_{a} - I R_{s})}{k_{B} T}})$ $I (V) = A A^{* *} T^{2} (e^{\frac{- φ_{B}}{k_{B} T}}) (e^{\frac{q (V_{a} - I R_{s})}{η k_{B} T}}) (1 - e^{\frac{- q (V_{a} - I R_{s})}{k_{B} T}})$

(2.1)

where A is the geometric area of the electrical contact of the device, A^** is Richardson’s constant, T is the temperature, q is the electron charge, R_s is the series resistance, k_B is Boltzmann’s constant, φ_B is the height of the potential barrier, and η is the factor of ideality. Under ideal conditions, such that R_s is negligible and the ideality factor is equivalent to one, Eq. 2.1 is reduced to describe the behavior of the diffusion current due to thermionic emission at the interface between the metal and the semiconductor. Another factor to be taken into consideration is the Richardson–Schottky thermionic emission, which defines the reduction of the potential barrier at the interface between the metal and semiconductor with the applied electric field. Thus, the current density (J = I/A) associated with this model is [8]

$\begin{array}{l} J = A^{* *} T^{2} e^{\frac{- (φ_{B} - β \sqrt{F})}{k_{B} T}} \\ A^{* *} = \frac{4 π q m^{*} k^{2}}{h^{3}} \\ β = \sqrt{\frac{q^{3}}{4 π ɛ_{r} ɛ_{0}}} \end{array}$ $\begin{array}{l} J = A^{* *} T^{2} e^{\frac{- (φ_{B} - β \sqrt{F})}{k_{B} T}} \\ A^{* *} = \frac{4 π q m^{*} k^{2}}{h^{3}} \\ β = \sqrt{\frac{q^{3}}{4 π ɛ_{r} ɛ_{0}}} \end{array}$

(2.2)

with the constants, where h is the Plank constant, ɛ_r is the relative dielectric constant, ɛ₀ is the electric vacuum permittivity, and m^* is the effective electron mass. The Fowler–Nordheim mechanism, in turn, consists of a tunneling model through the triangular potential barrier, governed by [8,53]

$J = \frac{q^{3} F^{2}}{8 π h φ_{B}} e^{\frac{- 8 π \sqrt{2 m^{*}} φ^{3 / 2}}{3 q h F}}$ $J = \frac{q^{3} F^{2}}{8 π h φ_{B}} e^{\frac{- 8 π \sqrt{2 m^{*}} φ^{3 / 2}}{3 q h F}}$

(2.3)

Both models are suitable for inorganic semiconductors but limited for organic semiconductors, which have disordered structures and a high defect density. Electrical conduction in the volume of these semiconductors is represented by space charge limited current (SCLC) models, as proposed by Rose and Lampert [54]. This theory considers the effect of traps on the displacement of the charge carriers; that is, it is assumed that there is a current limitation due to charge carriers trapped [trapped charge limited (TCL)] by defects or impurities. Initially, taking into account a low electrical potential applied and disregarding any injection barriers, the expectation is that mobility is low and governed by an ohmic behavior of thermally generated free carriers (n₀). In this case, electrical potential and current density are linearly related according to:

$J = \frac{q μ n_{0} V}{d}$ $J = \frac{q μ n_{0} V}{d}$

(2.4)

where μ is the mobility and d is the thickness of the thin film used in the structure with the electron transport function. If n₀ is negligible in relation to the injected charge carriers, there is a predominance of the SCLC mechanism, as

$J = \frac{9}{8} \frac{μ ɛ_{r} ɛ_{0} V^{2}}{d^{3}}$ $J = \frac{9}{8} \frac{μ ɛ_{r} ɛ_{0} V^{2}}{d^{3}}$

(2.5)

When the trap density is high, the quadratic dependency is only maintained if trapping of charge carriers in discrete energy levels or shallow traps occurs. In this condition, μ in Eq. 2.5 is modified by μ_eff = θμ, where θ = n/(n + n_t) represents the ratio between the density of free carriers (n) and the total density including those trapped (n_t). If they have an energy distribution, the traps will gradually be filled with an increase of the electric field; that is, θ is dependent on the electric field, and the electric current will increase with dependence higher than quadratic until all traps are filled. This behavior characterizes the TCL current regime; the accompanying equation shown in Eq. 2.6 corresponds to an exponential distribution h(E) = (H/k_BT_c)exp(E/k_BT_c), especially for deep traps, where N_v (or N_c) is the effective density of states in the valence (or conduction) band [5,55]

$J = μ q N_{c} {(\frac{ɛ_{r} ɛ_{0} m}{q H (m + 1)})}^{m} {(\frac{2 m + 1}{m + 1})}^{m + 1} \frac{V^{m + 1}}{d^{2 m + 1}}$ $J = μ q N_{c} {(\frac{ɛ_{r} ɛ_{0} m}{q H (m + 1)})}^{m} {(\frac{2 m + 1}{m + 1})}^{m + 1} \frac{V^{m + 1}}{d^{2 m + 1}}$

(2.6)

Assuming that the mobility is dependent on the electric field, an analytical solution exists that takes into account an arbitrary dependence on this factor and disregards the presence of traps. An analytical approximation was obtained by Murgatroyd [56] and incorporates the dependence of Poole–Frenkel mobility according to

$μ (F) = μ_{0} \exp (β (\sqrt{F} - \sqrt{F_{0}}))$ $μ (F) = μ_{0} \exp (β (\sqrt{F} - \sqrt{F_{0}}))$

(2.7)

where μ₀ is the mobility when F = F₀, which depends on F, and β is related to the system disorder. This parameter is often observed in disordered molecular materials, doped polymers and in most π-conjugated polymers [57]. The current density in this case is part of the free SCLC model of charge carrier trapping multiplied by the Poole–Frenkel mobility according to

$J \approx \frac{9}{8} \frac{μ_{0} ɛ_{r} ɛ_{0} V^{2}}{d^{3}} \exp (0.89 β \sqrt{\frac{V}{d}})$ $J \approx \frac{9}{8} \frac{μ_{0} ɛ_{r} ɛ_{0} V^{2}}{d^{3}} \exp (0.89 β \sqrt{\frac{V}{d}})$

(2.8)

In summary the organic devices and their electrical response, it is necessary to define if the electrical current is limited by the injection of charge carriers or by a spatial charge. In the latter case, it should be noted that the distribution of traps is in discrete or exponential levels through the dependence of μ on the electric field (F) and temperature (T).

2.3. Organic Thin Film Transistors

2.3.1. Structure of the TFT

Electronics technology has evolved rapidly over the last decades, and the trend is that the devices used in modern life are increasingly faster and compact. Currently, almost all electronic devices are based on extrinsic monocrystalline semiconducting silicon, whose conventional incorporation into FETs uses silicon substrates covered by silicon dioxide (SiO₂) obtained by thermal growth. Designed and patented by Lilienfeld in 1930 [58] but first manufactured in 1960 in the Bell laboratories by D. Kahng and M. Atalla [59], the FET transistor is miniaturized and integrated with millions of other transistors to implement highly complex and sophisticated circuits. However, for greater integration and consequently smaller size as predicted by Moore’s law [60], there is the possibility of overheating and interference (cross-talk) between components, which affects the overall performance. A potential solution for overcoming such limitations is to develop new materials and manufacturing technologies to perform the same functions commonly performed by conventional semiconductors.

OTFTs are characterized as a type of FET constructed by the deposition of organic layers on low cost substrates, such as glass and plastics. This type of device involves a wide range of applications, such as flexible displays [28], radio frequency identification tags [61,62], memories [63], textile electronics [64], and chemical, biological, and pressure sensors [27,65,66]. The bottom-gate geometry (Fig. 2.6A–B) currently adopted in research laboratories uses a highly doped silicon substrate covered with high-quality thermal SiO₂, easily found on the market [67]. In this structure, the gate electrode is on the dielectric, and electrical contacts of the source and drain are formed between the insulating and semiconducting layers. The current trend in hybrid transistors with such a structure is to deposit a dielectric layer with a high dielectric constant (high-k) because this allows for defining the gate electrode and contact channels for the implementation of circuits, in addition to functioning at a reduced operating voltage compared to SiO₂ (ɛ_r = 3.9). Cavallari et al. demonstrated the potential of silicon oxynitride (ɛ_r = 4.5) formed by plasma enhanced chemical vapor deposition (PECVD) for TFTs of the semiconductor poly (2-methoxy-5-(3,7-dimethyloctyloxy)-1,4-phenylenevinylene) (MDMO-PPV) operating at ± 20 V on Si [68]. In turn, Zanchin et al. employed titanium oxynitride (ɛ_r = 30) obtained by RF magnetron sputtering to produce TFTs of poly(3-hexylthiophene) (P3HT) that operated at ±3 V on glass [69].

Figure 2.6 Possible structure of organic thin film transistors (OTFTs) according to the relative position of the gate (G), source (S) and drain electrodes (D): bottom gate (A) top contact (staggered) or (B) bottom contact (coplanar); top gate (C) bottom contact or (D) top contact. The width (W) and length (L) of the channel between the source and drain are shown in (A).

It was recently demonstrated that organic dielectrics are promising materials for the construction of OTFTs, as they (1) can be processed via solutions, (2) produce thin films on transparent glass and plastic substrates (with the possibility of being flexible), (3) are suitable for the construction of photosensitive OTFTs in the field of optoelectronics because of the optical transparency of these films, and (4) may possess a high dielectric constant up to 18 [70,71]. An immediate opportunity to use organic dielectric layers appears in top-gate OTFTs (Fig. 2.6C–D) if the process of the deposition of organic dielectrics does not damage or remove the lower layers. The main organic dielectrics addressed in the literature are shown in Fig. 2.7.

Figure 2.7 Organic insulators for modifying the dielectric semiconductor interface in OTFTs.
polymethylmethacrylate (PMMA), polyethylene (PE), divinyltetramethyldisiloxane-bis (benzocyclobutene) (BCB), polycarbonate (PC), polystyrene (PS), polyimide (PI), and poly(4-vinylphenol) (P4VP).

2.3.2. Modeling of the Characteristic Curves

Most OTFTs found in the literature have the structure of an FET, in which conduction occurs in the channel between the source and drain electrodes, and is modulated by the gate voltage (V_GS) [72,73]. The selection of the metal–insulator–semiconductor (MIS) structure is due to extensive use of metal–oxide–semiconductor FET (MOSFET) technology in the digital circuits market and because it is the structure most used in amorphous silicon TFTs [74]. The core structure of the device is the MIS capacitor of Fig. 2.8A, whose gate electrode controls the charge density (n_Q) in the transistor channel and therefore its conductance. The density of accumulated charges in the triode regime [75] can be described by:

$\begin{array}{l} n_{Q} = \frac{C_{i} (V_{G S} - V_{T})}{q} \\ C_{i} = \frac{ɛ_{r} ɛ_{0}}{x_{i}} \end{array}$ $\begin{array}{l} n_{Q} = \frac{C_{i} (V_{G S} - V_{T})}{q} \\ C_{i} = \frac{ɛ_{r} ɛ_{0}}{x_{i}} \end{array}$

(2.9)

is the capacity per area, ɛ_r where q is the elementary charge, V_T is the threshold voltage, C_i = x_i is the relative dielectric constant, ɛ₀ is the electrical permittivity of the vacuum, and x_i is the thickness of the dielectric film. Unlike the enrichment and depletion FETs whose conduction channel is formed by inversion, OTFTs function by the accumulation of charges in the channel. Furthermore, the semiconductor at the interface with the dielectric does not need to be doped for the formation of the channel because a channel is formed that permits the passage of current between the source and drain for a nonzero V_DS, even if V_GS = 0 (Fig. 2.8B). Thus, a positive threshold voltage (V_T) is defined that decreases the concentration of holes in the dielectric/semiconductor interface and eliminates current flow in the transistor (Fig. 2.8C).

Figure 2.8 Field effect devices.
(A) MOS capacitor; p-FET transistor in the regimes of (B) triode; (C) cut-off; and (D) saturation.

Given that the concentration of charges available for transport in the channel depends on the voltage difference between the terminals of the MIS capacitor, what would happen if the source voltage was maintained at zero as the drain voltage became increasingly negative (note that in a p-TFT, the operating voltages are negative)? In this case, a nonhomogeneous charge distribution in the channel is observed, and when V_GS − V_DS > V_T, the concentration of holes is minimal near the drain electrode, leading to competition between two phenomena that occur simultaneously:

1. an increasingly negative drain voltage would increase the current circulating between the source and drain electrodes;

2. choking of the channel around the drain due to the low concentration of holes would tend to limit the current in the channel (a phenomenon known as pinch-off). This situation leads to saturation of the current that would ideally remain constant (Fig. 2.8D).

Characteristic curves for I_D versus V_DS for a p-TFT of P3HT obtained experimentally are shown in Fig. 2.9A. When V_DS > V_GS − V_T, the OTFT operates in the triode region and the drain current is described by [74]

$I_{D} = μ C_{i} \frac{W}{L} V_{D S} [(V_{G S} - V_{T}) - \frac{V_{D S}}{2}]$ $I_{D} = μ C_{i} \frac{W}{L} V_{D S} [(V_{G S} - V_{T}) - \frac{V_{D S}}{2}]$

(2.10)

where μ is the carrier mobility, W is the channel width, and L is the channel length. It is observed that at low drain voltages, that is, |V_DS| << 2|V_GS − V_T|, the current exhibits a linear behavior (or ohmic) as a function of V_DS:

$I_{D} \approx μ C_{i} \frac{W}{L} V_{D S} (V_{G S} - V_{T})$ $I_{D} \approx μ C_{i} \frac{W}{L} V_{D S} (V_{G S} - V_{T})$

(2.11)

Figure 2.9 Characteristic curves of p-transistors with 50 nm of P3HT deposited from 4.3 mg mL⁻¹ chloroform by spin coating on a substrate of p⁺ − Si (190 nm) with W = 1.1 mm, and L = 10 μm.
(A) I_D versus V_DS, (B) I_D versus V_GS, and (C) hysteresis of I_D versus V_GS.

The parameters μ and V_T can be obtained from the transconductance of the channel in this regime [74]:

$g_{m} = {\frac{\partial I_{D}}{\partial V_{G S}}|}_{V_{DS} = constant} = μ C_{i} \frac{W}{L} V_{DS}$ $g_{m} = {\frac{\partial I_{D}}{\partial V_{G S}}|}_{V_{DS} = constant} = μ C_{i} \frac{W}{L} V_{DS}$

(2.12)

where the intersection of the approximate straight line with the x axis (V_GS0) is equal to

$V_{GS 0} = V_{T} + \frac{V_{D S}}{2}$ $V_{GS 0} = V_{T} + \frac{V_{D S}}{2}$

(2.13)

Considering that V_DS < V_GS − V_T, the transistor operates in the saturation region as described by Eq. 2.14:

$I_{D} = \frac{1}{2} μ C_{i} \frac{W}{L} {(V_{GS} - V_{T})}^{2}$ $I_{D} = \frac{1}{2} μ C_{i} \frac{W}{L} {(V_{GS} - V_{T})}^{2}$

(2.14)

Mobility can be extracted through the first derivative of

\sqrt{I_{D}}

$\sqrt{I_{D}}$

in relation to V_GS:

$\frac{\partial \sqrt{I_{D}}}{\partial V_{GS}} = \sqrt{\frac{1}{2} μ C_{i} \frac{W}{L}}$ $\frac{\partial \sqrt{I_{D}}}{\partial V_{GS}} = \sqrt{\frac{1}{2} μ C_{i} \frac{W}{L}}$

(2.15)

where the intersection of the approximate line with the x axis (V_GS1) is equivalent to V_T (Fig. 2.9).

The same model can be applied to n-OTFTs, taking into account that the operating voltages are positive. As in p-TFTs, the threshold voltage (V_T) is opposite to the working voltage (and hence is negative), and the increase in channel conductivity is given by the accumulation of negative charges (or electrons) at the semiconductor/dielectric interface.

Analyzing the curve of I_D versus V_GS in Fig. 2.9B, it is possible to observe two operating regimes: (1) the cut-off region in which V_GS > V_on (the characteristic voltage for a given p-transistor) and the current I_D = I_off ≈ 0, and (2) subthreshold, in which I_D depends exponentially on V_GS. In this regime, it is possible to define the subthreshold slope (S), which corresponds to the increase of |V_GS| needed to increase |I_D| by a factor of ten. It is expected that both S and V_T tend to zero to reduce the operating voltage of the electronic circuits, typically approximately 5 V. From the operating current (I_on) defined for an arbitrary pair of V_DS and V_GS, the current modulation can be calculated from the relationship between I_on and I_off. As in the case of amorphous silicon TFTs, nonidealities, such as hysteresis and current leakage by the dielectric (I_leakage) adversely affect the device performance [76,77]. Hysteresis is bistable operation of the transistor current and appears as a difference in I_D during ascending and descending scans of V_DS or V_GS. An illustration of these techniques is shown in Fig. 2.9.

In an organic transistor, the mobility of charge carriers is more properly assumed to depend on the overdrive voltage (i.e., the difference between V_GS and V_T) [78] according to

$μ = k {(V_{GS} - V_{T})}^{γ}$ $μ = k {(V_{GS} - V_{T})}^{γ}$

(2.16)

where k contains information on the morphology of the film, mainly related to the ease of hopping between sites, and γ is related to the width of an exponential distribution of states (DOS) by γ = 2(T_c/T−1). A possible explanation is given by the variable-range hopping model proposed by Vissenberg and Matters [79], in which carriers participate in the current flow only when they are excited to an energy level termed the transport energy. If the carrier concentration is high, the initial average energy is close to the transport energy, which reduces the required activation energy and thus increases mobility considerably. Alternatively, according to the multiple trapping and release and transport model [80], only one fraction of the charge induced by the gate contributes to current flow in the channel. The remaining part continues to be trapped in an exponential tail of localized states. Since the ratio between free carriers and traps is greater in high-injection conditions, the mobility increases with increasing gate voltage. In both cases, the drain current I_D in the triode regime becomes:

$I_{D} = C_{i} \frac{W}{L} k {(V_{G S} - V_{T})}^{γ + 1} V_{D S}$ $I_{D} = C_{i} \frac{W}{L} k {(V_{G S} - V_{T})}^{γ + 1} V_{D S}$

(2.17)

In the saturation regime, the current becomes:

$I_{D} = \frac{1}{γ + 2} C_{i} \frac{W}{L} k {(V_{G S} - V_{T})}^{γ + 2}$ $I_{D} = \frac{1}{γ + 2} C_{i} \frac{W}{L} k {(V_{G S} - V_{T})}^{γ + 2}$

(2.18)

The presence of disorder in the thin film semiconductor generally involves the occurrence of Poole–Frenkel phenomena, in which the dependence of the field effect mobility and the longitudinal electric field can be described by Eq. 2.7 [56]: the relationship between β and γ can be derived from Eqs. 2.3 and 2.11 [81].

Elevated contact resistances (R_s) decrease the effective voltage applied to the transistor and consequently the performance of devices. In high-mobility organic semiconductor TFTs, that is μ > 10⁻¹ cm² V⁻¹ s⁻¹, the value of R_s can be estimated from the resistance of the device in the triode regime (R_on) and the resistance of the channel in the triode regime (R_channel):

$R_{on} = \frac{V_{DS}}{I_{D}} = R_{channel} + R_{S} = \frac{L}{μ_{i} C_{i} W (V_{G S} - V_{T, i})} + R_{S}$ $R_{on} = \frac{V_{DS}}{I_{D}} = R_{channel} + R_{S} = \frac{L}{μ_{i} C_{i} W (V_{G S} - V_{T, i})} + R_{S}$

(2.19)

where μ_i and V_T,i are intrinsic parameters of the material [82].

2.3.2.1. Field Effect Mobility

Organic semiconductors present mobility dependent on morphology and thus on the electric field and temperature. For this reason, the evolution in performance of these devices is intrinsically related to the study of the influence of each layer and fabrication conditions for their operation. In fact, the first polythiophene FET obtained by electrochemical polymerization exhibited field effect mobilities of only 10⁻⁵ cm² V⁻¹ s⁻¹. The regularity in the arrangement of radicals in the molecule, as in poly(3-alkylthiophenes) (P3AT), can greatly affect the morphology and thus the charge transport in a film semiconductor [83]. These radicals can be incorporated into the polymer chain at three different regioregularities: head-to-head (HH), tail-to-tail (TT), and head-to-tail (HT), as shown in Fig. 2.10. A regiorandom polymer has both configurations in the same chain, and these are randomly distributed, whereas a regioregular polymer has only one of these regioregularities in their chains. The latter tend to have a lower bandgap energy, and higher order and crystallinity in the solid state, in addition to increased electroconductivity [84]. In 1996, Bao et al. reported remarkable results in regioregular P3HT FETs deposited by casting: μ ≈ 0.015–0.045 cm² V⁻¹ s⁻¹ [40].

Figure 2.10 Regioregularities in poly(3-hexylthiophene).

The final morphology of the film is related to the applied solvent. For example, Bao et al. observed that P3HT precipitated during evaporation of the solvent tetrahydrofuran (THF), resulting in a nonuniform and discontinuous film. Electron microscopy revealed the presence of lamellar micrometric and granular nanometric crystals. Using solvents, such as 1,1,2,2-tetrachloroethane and chloroform, the FET mobility increased from 6.2 × 10⁻⁴ to c. 5 × 10⁻² cm² V⁻¹ s⁻¹ [40]. Comparatively, films from derivatives of poly(para-phenylenevinylene) (PPV), important for application in OLEDs and OSCs, have mobilities on the order of 10⁻⁵–10⁻⁴ cm² V⁻¹ s⁻¹ [85,86]. The fact that these materials have an amorphous structure and that transport of charge carriers in films of these materials occurs by hopping limits the mobility [87].

Monocrystalline or highly ordered polycrystalline films deposited by vacuum sublimation exhibit field effect mobilities greater than 0.1 cm² V⁻¹ s⁻¹ [88]. This performance allows the manufacture of many flexible commercial devices, such as the first microprocessor on plastic presented in Table 2.1.

Table 2.1

A Comparative Table Between the First Flexible Microprocessor From An Organic Semiconductor and the Intel 4004 on Rigid Silicon

Microprocessor	Plastic	Intel 4004
Year of production	2011	1971
Number of transistors	3381	2,300
Area	1.96 × 1.72 cm²	3 × 4 mm²
Wafer diameter	6 in.	2 in.
Substrate	Flexible	Rigid
Number of pins	30	16
Voltage source	10 V	15 V
Power consumption	92 μW	1 W
Operational speed	40 operations s⁻¹	92,000 operations s⁻¹
P-type semiconductor	Pentacene	Silicon
Mobility	∼0.15 cm² V⁻¹ s⁻¹	∼450 cm² V⁻¹ s⁻¹
Operation	Accumulation	Inversion
Technology	5 μm	10 μm
Bus width	8 bit	4 bit

The silicon Intel 4004 microprocessor, whose performance is similar to that of pentacene, was produced in 1971, approximately 2 years after the arrival of humans on the moon on July 20, 1969 [15]. These small molecules, of great interest to the scientific community because of the high mobility of charge carriers, have been modified to allow for processing in the liquid phase. Such is the case of pentacene (0.1–0.5 cm² V⁻¹ s⁻¹) [89] and polythienylenevinylene (0.22 cm² V⁻¹ s⁻¹) [90], for which precursor materials were synthesized for their conversion into polymers during film treatment postdeposition. However, it should be noted that grain boundaries in polycrystalline films can play a key role in transistor performance, as they act as traps to charge carriers [91].

Finally, it should be noted that the interface between the gate dielectric and the semiconductor also plays an important role in charge transport, possibly representing up to three orders of magnitude depending on the dielectric used [92]. The SiOH groups present on the surface of SiO₂ act as electron traps. The passivation of these groups may occur by the deposition of self-assembled monolayers prior to the deposition of the semiconductor (Fig. 2.11A–B). In 2005, Chua et al. [93] verified a significant increase in the current in an n-type TFT of F8BT (Fig. 2.11C) when treating SiO₂ with monolayers of octadecyltrichlorosilane (OTS), hexamethyldisilazane (HMDS), or decyltrichlorosilane (DTS). According to Ohnuki et al. [94], these self-assembled films chemically react with SiOH groups, passivating surface defects and reducing the concentration of traps. A similar effect can be produced when using an organic insulator. Chua et al. in work dating from 2005, used polyethylene and divinyltetramethyldisiloxane-bis(benzocyclobutene) (BCB) together with calcium electrodes and demonstrated that it is possible to manufacture n-OTFTs and that the mobility of the electrons can be greater than that of the holes (until then, the opposite was believed). In 2008, Benson et al. [95] demonstrated complementary metal oxide semiconductor (CMOS) technology with organic transistors using pentacene TFTs obtained by replacing the dielectric with polymethylmethacrylate (PMMA), polycarbonate (PC), (polystyrene) PS, (polyimide) PI, or poly(4-vinylphenol) (P4VP).

Figure 2.11 Self-assembled monolayers for treating the surface of SiO₂: (A) OTS; (B) HMDS; (C) drain current (I_D) as a function of the gate voltage (V_GS) in an F8BT n-TFT for different treatments with self-assembled siloxanes or a polyethylene passivating film (buffer). Adapted from H. Ohnuki, et al. Effects of interfacial modification on the performance of an organic transistor based on TCNQ LB films. Thin Solid Films 516 (2008) 2747–2752 [93].

In summary, when seeking to overcome the threshold μ ≤ 10⁻¹ cm² V⁻¹ s⁻¹ in polymers, in the first decade of the 21st century, high mobility polymer, such as those shown in Fig. 2.12, were synthesized. The obtained p-semiconductors are mostly derivatives of polythiophene, such as poly[5,5-bis(3-dodecyl-2-thienyl)-2,2-bithiophene] (PQT-12) [96,97] and poly(2,5-bis(3-hexadecylthiophen-2-yl)thieno[3,2-b]thiophene (pBTTT) [98–100]. Among the n-types are poly(benzobisi midazobenzophenanthroline) (BBL) [101] and [N,N-9-bis(2-octyldodecyl)naphthalene-1,4,5,8-bis(dicarboximide)-2,6-diyl]-alt-5,59-(2,29-bithiophene) (P(NDI2OD-T2)) [102–104]. Finally, also pursued was the synthesis of ambipolar semiconductors, such as diketopyrrolopyrrole–benzothiadiazole copolymer (PDPP-TBT), studied by Ha et al. [105].

Figure 2.12 Chemical structure of high mobility polymers.
PQT-12, pBTTT, BBL, P(NDI2OD-T2), and PDPP-TBT.

In parallel, the effort for the development of small high mobility molecules, shown in Fig. 2.13, including those that can be processed in liquid medium, should be highlighted. In this case, the main p-semiconductor are acenes, such as tetracene [106] n-heteropentacenes (HP) [107] and rubrene [44,106,108,109] as well as the already mentioned thiophenes, such as trans-1,2-di[thieno[3,2-b][1]benzothiophenic-2-]ethylene (DTBTE) [110] dinaphtho-[2,3-b:2′,3′-f]thieno[3,2-b]-thiophene (DNTT) [43,111,112], and 2,7-dioctyl[1] benzothieno[3,2-b][1]benzothiophene (C₈-BTBT) [113]. Small acene molecules can be processed in solution by adding branches or radicals, which make them soluble and cause them to react with the adjacent molecule of the same semiconductor, resulting in the formation of a monocrystal. This is the case for 6,13-bis[triisopropylsilylethynyl] (TIPS) pentacene, crystallized from solution by heat treatment at 120°C under a 100 sccm flow of forming gas for 4 h [106]. The main n-type molecules are tetracyanoquinodimethane (TCNQ) [44,114] and N,N″-bis(n-alkyl)-(1,7 and 1,6)-dicyanoperylene-3,4:9,10-bis(dicarboximide) (PDIR-CN₂) [115,116]. In the class of ambipolar semiconductors, reduced graphene oxide (RGO) is highlighted [31,117]. Developments in the performance of organic semiconductors applied in FETs are presented in Table 2.2 via a comparative table.

Figure 2.13 Chemical structure of small high mobility organic molecules.
TIPS-pentacene, rubrene, DTBTE, C₁₀-DNTT, C₈-BTBT, TCNQ, and PDIF-CN₂ [118].

Table 2.2

Comparative Table of Organic Semiconductors Applied in TFTs

	Deposition Technique^a			μ (cm² V⁻¹ s⁻¹)
Semiconductor	Deposition Technique^a	Substrate	Dielectric^b	μ_h	μ_e	V_T (V)	I_on/off	Year	References
PQT-12	S	Si	SiO₂/OTS-8	0.18	—	−5	10⁷	2005	[97]
pBTTT	S	Si	SiO₂/OTS	0.12	—	−4	—	2007	[98]
P3HT:TCNQ	S	Si	SiO₂/OTS	0.01	—	2,6	10⁴	2008	[114]
P3HT:RGO	S	Si	SiO₂	8 × 10⁻³	—	−5	10⁴	2011	[21]
BBL	S	Si	SiO₂	—	10⁻³	15	10⁵	2011	[101]
P(NDI2OD-T2)	S	Glass or PEN	PMMA	—	0.2–0.3	8	10^4–6	2011	[102]
PDPP-TBT	S	Si/SiO₂/OTS	D139	0.53	0.58	—	—	2012	[105]
Tetracene	E	—	Parylene-N	1	—	0	—	2010	[106]
TIPS-PEN	S	—	Parylene-N	0.05	—	0	—	2010	[106]
Rubrene	L	—	PE	4.7	—	0	10⁶	2011	[44]
RGO	S	Si	SiO₂	1	0.2	0	10²	2008	[117]
DTBTE	E	Si	SiO₂/OTS	0.5	—	−25	10⁶	2011	[110]
DNTT	L	Si	SiO₂/CYTOP	8.3	—	0	10⁸	2009	[43]
C₁₀-DNTT	S	Si	SiO₂	11	—	10	10⁷	2011	[111]
C₈-BTBT	S	Si/SiO₂	Parylene-C	31.3	—	−10	10⁷	2011	[113]
TCNQ	S	Si	SiO₂/HMDS	—	4.4	−3	10²	2008	[94]
PDIF-CN₂	L	Si	SiO₂/PMMA	—	6	−5–5	10⁴	2009	[115]

TFTs, Thin film transistors.

^a S, Processed in solution (e.g., spincoatinge casting); EV, thermal evaporation; L, lamination of monocrystals.

^b CYTOP, Commercial amorphous fluoropolymer [119].

2.3.2.2. Organic TFT-Based Sensors

The susceptibility of organic semiconductors to operating conditions and impurities is a limiting factor in the efficiency of photovoltaic and electroluminescent devices [organic light-emitting diodes (OLEDs)] but has found direct application in chemical sensors. Materials, such as acenes [120,121], oligothiophenes [122], polythiophenes [123], and poly(phenylenevinylene) [124] are semiconductors successfully used in this field. In the specific case of OTFT-based sensors, inorganic oxides (e.g., SiO₂, a high-dielectric constant hafnium oxide) [125] and cross-linked polymers [e.g., poly(4-vinylphenol)] [126,127] are primarily employed as insulators in academic laboratories. Conductive polymers, such as PAni [19] and PEDOT:PSS [20], have recently been used as electrodes, although gold remains the most widely used source and drain metal. Rigid silicon or flexible polymer substrates covered with a thin film conductor [127,128] are generally used as the gate electrode and substrate.

OTFT-based sensors rely on the interaction between chemical or biological analytes and the semiconductor active layer. These analytes may be specific to chemical modification and the incorporation of recognition sites into the transistor structure. However, alteration of the deposition conditions of each layer, a consequence of this modification, affects the device response signal because it is intrinsically related to the quality of interfaces in the device (i.e., insulator/semiconductor and electrode/semiconductor) [129] and the nanomorphology of the layers [130,131]. Direct interactions between the analyte and the active layer may occur via charge transfer or doping, resulting in a change in conductivity. Furthermore, analytes can be adsorbed and then diffuse through the grain boundaries, introducing new energy states located in the film (i.e., charge transport traps), thus increasing the resistance to charge transport. This effect is observed in the alteration of the mobility of charge carriers (μ) in a semiconductor film. The accumulation of analytes at the interface with the insulator, in turn, can change the local electric field distribution at this interface and thus the conductivity of the channel. In this case, the main parameter monitored is the threshold voltage (V_T). In both cases, the impact is in the variation of the current circulating in the channel (∆I_DS) [132].

One of the principal means of analyte interaction with organic materials is in the vapor phase. Pentacene is sensitive to environmental conditions, such as relative humidity [133], oxygen [134], and ozone (O₃) [135]. An 80% decrease of the saturation current for TFTs of pentacene can be observed as a result of an increase from 0% to 30% humidity [133]. In turn, Crone et al. mapped the detection of volatile organic species by a set of organic TFT-based sensors [136]. A total of 16 analytes in the vapor phase were studied by monitoring the ∆I_DS in 11 organic semiconductors. The sensitivity of the devices was extrapolated to approximately 1 ppm via electrical circuit-based analysis techniques [137]. These studies demonstrated that the analyte interacts with the semiconductor via van der Waals, permanent dipole–dipole or hydrogen bond electrostatic interactions. Chang et al. demonstrated the applicability of polythiophene derivatives deposited by printing in the detection of organic solvents, such as alcohols, acids, aldehydes, and amines [138]. The material of the active layer is principally altered by the insertion of functional groups along the polymer chain or at its ends. The use of polythiophene P3HT in electronic noses enables the detection of ammonia [139], a biomarker of diseases, such as infection in the gastrointestinal tract by the bacteria Helicobacter pylori, uremia, or renal insufficiency and hepatic cirrhosis [140]. Jeong et al. observed the dependence of μ, V_T, I_on/off, and S of devices, as shown in Fig. 2.14A, on the ammonia concentration in parts per million (ppm). The response of I_D over time as a function of the concentration in ppm is shown in Fig. 2.14B for four different values of W/L (identified by S1 to S4 in the legend).

Figure 2.14 (A) Schematic diagram of the OTFT-based gas sensor: gold on a thermal oxide forms the source and drain electrodes; the active layer is obtained by spin coating. (B) Response array of sensors I_D to the insertion of 10–100 ppm of gaseous ammonia into the chamber. Adapted from K.-H. Kim, S.A. Jahan, E. Kabir, A review of breath analysis for diagnosis of human health. TrAC 33 (2012) 1–8 [139].

Analyte detection in liquid medium can be accomplished using the ion-sensitive field effect transistor (ISFET), invented in 1970 by Bergveld [141]. OTFTs are generally considered incompatible with water because of uncertainty regarding their stability at high operating voltages and the possibility of physical delamination. In 2000, however, the ability of OTFTs to respond to ions in solution was demonstrated by Bartic et al. [142]. A pH meter was fabricated on a silicon wafer using an active layer of regioregular P3HT and a silicon nitride (Si₃N₄) dielectric. Since then, efforts have been made to commercialize these sensors. In 2003, Gao et al. integrated a reference electrode [143]. Two years later, Loi et al. fabricated an ISFET on the flexible film Mylar [30]. In 2008, Roberts et al. manufactured ISFETs of 5,5-bis-(7-dodecyl-9H-fluoren-2-yl)-2,2-bithiophene (DDFTTF) operating at 1 V [126]. These TFTs without encapsulation exceeded 10⁴ cycles of operation (V_GS of 0.3 at −1 V and V_DS = −0.6 V) without significant changes in their electrical parameters. Applicability was demonstrated in sensors of glucose, trinitrobenzene, cysteine, and methylphosphonic acid for concentrations on the order of parts per billion (ppb). An example of microfluidic integration with organic electronics for pH detection is shown in Fig. 2.15. In this case, stability of the polytriarylamine transistor (PTAA) processed by Spijkman et al. in 2010 is guaranteed by the presence of a bottom gate of SiO₂ and a top gate of Teflon and polyisobutylmethacrylate (PIBMA) [144].

Figure 2.15 OTFT-based chemical sensor stable in aqueous medium.
(A) Schematic diagram of the sensor in the aqueous flow cell, and (B) the current I_DS depends on the pH of the solution. Adapted from N.T. Kalyani, S.J. Dhoble, Organic light emitting diodes: energy saving lighting technology—a review. Renow. Sust. En. Rev. 16 (2012) 2696–2723 [144].

2.4. Organic Light–Emitting Diodes

2.4.1. Structure of Thin Films in OLEDs and Typical Materials Used

OLEDs [145] are fabricated in the form of a simple thin film structure by two electrodes and a conjugated polymer, with suitable energy levels for the emission of wavelengths in the visible region [146–148]. Among the conjugated polymers best known and currently studied are those derived from PPV [149], polyfluorene (PF), and polyvinylcarbazole (PVK) [150]. These materials emit wavelengths associated with the primary colors reddish-orange, greenish-yellow and blue, respectively. The emission spectrum of these materials is directly related to the bandgap that separates the HOMO from the LUMO, a characteristic equivalent to that of the inorganic semiconductor whose nomenclature is defined as the VB and CB, respectively [151]. Due to this separation, charge carriers can receive external power via high-energy photons or even by applying a potential difference to form a species denominated exciton. This exciton represents an electron–hole pair in an excited energy state whose radioactive decay is in a wavelength band characteristic of each material.

Joining of the materials used with functions of emission and conduction, when in thermal equilibrium, can produce energy barriers to the transport of charge carriers; as a result, recombination occurs outside the appropriate location for light emission, and loss may occur by nonradiative decay or lattice vibration [152]. Thus, auxiliary materials are usually employed to facilitate the reduction of such energy barriers. In a thin film structure, two classes of materials studied and applied for this purpose are termed hole transport layers (HTL) [153] and electron transport layers (ETL) [154]. Materials, such as PEDOT:PSS, MTDATA, and TPD are exploited for the hole transporting function; in contrast, materials, such as hydroxyquinoline aluminum (Alq3) and 2-(4-biphenylyl)-5-(4-tert-butylphenyl)1,3,4-oxadiazol (butyl-PBD) are used for the electron transport function. This classification arises from study of the energy levels of these materials, which provide appropriate and preferential transport of a specific type of charge carrier. Materials with HTL and ETL functions minimize the barrier heights both between the work function of the transparent electrode and the HOMO level of the polymer (∆h₁), and between the LUMO level and the working function of the metal (∆h₂), shown in Fig. 2.16.

Figure 2.16 Diagram of the energy levels considering a transparent electrode, a luminescent polymer, and a stacked metal in which ∆h₁ refers to the existing barrier height between the working function of the transparent electrode and the highest occupied molecular orbital (HOMO) level of the polymer and ∆h₂ to the barrier height between the lowest unoccupied molecular orbital (LUMO) level and the working function of the metal.

2.4.2. Electrooptic Characterization of OLEDs

The main parameters that characterize the performance of an OLED or LEC are power efficiency (η_WW), power luminous efficiency (η_P), luminous efficiency (h_L), and external quantum efficiency (h_EQE). Calculation of the power efficiency (η_WW) [155], also known in the literature as the wall plug efficiency [156], requires the optical power [P_opt (W)], which is determined as follows:

$P_{opt} = \int_{0}^{\infty} P_{OLED} (λ) d λ$ $P_{opt} = \int_{0}^{\infty} P_{OLED} (λ) d λ$

(2.20)

The electric power P_opt = VI. Thus, we obtain the dimensionless power or wall plug efficiency:

$η_{W W} = \frac{P_{opt}}{P_{ele}} = \frac{\int_{\infty}^{0} P_{OLED} (λ) d λ}{V I}$ $η_{W W} = \frac{P_{opt}}{P_{ele}} = \frac{\int_{\infty}^{0} P_{OLED} (λ) d λ}{V I}$

(2.21)

Applications of these devices as information displays or ambient lighting must take into account the perception of light based on the sensitivity of the human eye. Thus, for the total luminous flux [Φ_tot (lm)], we have:

$Φ_{tot} = \int_{0}^{\infty} K (λ) P_{OLED} (λ) d λ$ $Φ_{tot} = \int_{0}^{\infty} K (λ) P_{OLED} (λ) d λ$

(2.22)

where K(λ) = 683V(λ) (lm W⁻¹) and V(λ) is the photopic dimensionless response function. Fig. 2.17 shows the standard of the Commission Internationale de l’Eclairage (CIE) [157] of 1924 for V(λ), whose maximum point [V(λ) = 1] occurs for the yellowish-green wavelength at 555.17 nm.

Figure 2.17 Photopic response function V(l) according to the CIE 1924 with a standard accuracy of 1 nm. Adapted from Luminous efficiency graphic, http://www.cvrl.org/cie.htm [158].

Therefore, the power luminous efficiency [η_P (lm W⁻¹)] is defined by the relationship between the luminous flux and electrical power according to [152]:

$η_{P} = \frac{Φ_{tot}}{P_{ele}} = \frac{\int_{\infty}^{0} K (λ) P_{OLED} (λ) d λ}{V I}$ $η_{P} = \frac{Φ_{tot}}{P_{ele}} = \frac{\int_{\infty}^{0} K (λ) P_{OLED} (λ) d λ}{V I}$

(2.23)

In turn, calculation of the current luminous efficiency (η_L) requires the concepts of luminous intensity (i) and luminance (L_OLED). From a circular flux of light with a radius (r) of an infinitesimal area dA generated by a light source, as shown in Fig. 2.18, it is possible to assume for a distance (x), such that x >> r, the point light source hypothesis [152].

Figure 2.18 Circular scattering representative of light scattering.

The detection of this signal (stereo-radian photon flux) is defined as the luminous intensity (i), where its scale is a function of the polar (θ) and azimuth angles (φ) such that dΩ is the infinitesimal variation of the emission angle. Thus, the total luminous flux emitted is defined according to:

$Φ_{tot} = \int_{0}^{2 π} \int_{0}^{θ / 2} i (θ, ϕ) sen θ d ϕ d θ$ $Φ_{tot} = \int_{0}^{2 π} \int_{0}^{θ / 2} i (θ, ϕ) sen θ d ϕ d θ$

(2.24)

For simplification purposes, the photon flux is usually considered only as a function of θ, whose reference is 90 degree in relation to the surface. In this case, the approximation of a Lambertian surface [159] is used, corresponding to an intensity of i(θ) = i₀cos(θ). Thus, the total luminous flux is defined as

$Φ_{tot} = 2 π \int_{0}^{π / 2} i_{0} \cos θ sen θ d θ$ $Φ_{tot} = 2 π \int_{0}^{π / 2} i_{0} \cos θ sen θ d θ$

(2.25)

Eq. 2.25 for a Lambertian surface has a solution of πi₀; that is., i₀ = 1 candela (cd) in the normal direction, which is equivalent to Φ_tot = π lumen (lm). In practice, optical characterization begins by measuring the luminance [L_OLED (cd m⁻²)] defined by

$L_{OLED} = \frac{i (θ = 0 °)}{A}$ $L_{OLED} = \frac{i (θ = 0 °)}{A}$

(2.26)

Thus, the luminous efficiency [η_L (cd A⁻¹)] [157] can be defined as the ratio between L and the current density (J = I/A) according to

$η_{L} = \frac{L}{J}$ $η_{L} = \frac{L}{J}$

(2.27)

The power luminous efficiency [η_P (lm W⁻¹)] can be calculated from η_L, assuming the emission of an electroluminescent device, such as a Lambertian emitter, according to

$η_{P} = \frac{π}{V} η_{L}$ $η_{P} = \frac{π}{V} η_{L}$

(2.28)

Another figure of merit that can be calculated is the external quantum efficiency (EQE), which is the ratio between the number of photons obtained and the amount of charge carriers injected into the system. Considering the integrated angle spectrum of electroluminescence (optical power) [P_OLED(λ)], whose emission is a function of a given wavelength (λ), the number of photons generated in unit time (N_F) is given by [152]

$N_{F} = \int_{0}^{\infty} \frac{P_{OLED} (λ)}{h c} λ d λ$ $N_{F} = \int_{0}^{\infty} \frac{P_{OLED} (λ)}{h c} λ d λ$

(2.29)

where c is the speed of light and h is Planck’s constant. In turn, the number of charge carriers passing through the device subject to current I in unit time is given by N_PC = I/q, where q is the electron charge. Therefore, EQE, which is dimensionless, can be obtained by [152]

$\frac{N_{F}}{N_{PC}} = \frac{e}{h c I} \int_{0}^{\infty} \frac{P_{OLED} (λ)}{h c} λ d λ$ $\frac{N_{F}}{N_{PC}} = \frac{e}{h c I} \int_{0}^{\infty} \frac{P_{OLED} (λ)}{h c} λ d λ$

(2.30)

In the calculation of EQE, the photopic response function V(λ) and η_L can be taken into account according to [152]

$η_{EQE} = \frac{π e λ_{D}}{K (λ_{D}) h c} η_{L}$ $η_{EQE} = \frac{π e λ_{D}}{K (λ_{D}) h c} η_{L}$

(2.31)

which can be approximated using the numerical constant values given by

$η_{EQE} = \frac{3.7 \times 10^{3} λ_{D}}{V (λ_{D})} η_{L}$ $η_{EQE} = \frac{3.7 \times 10^{3} λ_{D}}{V (λ_{D})} η_{L}$

(2.32)

in which the dependence of h_EQE is observed relative to the dominant wavelength (λ_D), the photopic response function V(λ) and η_L. The value of λ_D is obtained directly from the chromaticity diagram of CIE, using, for example, the pattern 1931, as defined by the colorimetry theory, which is not covered in this chapter [152].

Fig. 2.19 shows the photographic register of a high-performance OLED, whose thin film is composed of a polymeric matrix and a rare earth complex, produced in the laboratory and polarized with voltages of 10, 15, 20, and 30 V. The same figure presents the CIE 1931 chromaticity diagram with coordinates related to the polarization imposed on the OLED.

Figure 2.19 Photographic record of an organic light-emitting diode (OLED) produced in the laboratory and chromaticity diagram with coordinates related to the polarization of the OLED.

List of Symbols

ɛ_r Relative dielectric constant

ɛ₀ Vacuum permittivity (F m⁻¹)

η Ideality factor in the Schottky thermionic emission model

η_EQE External quantum efficiency

η_L Luminous efficiency (cd A⁻¹)

η_P Power efficiency of current (lm W⁻¹)

η_WW Power or wall plug efficiency

θ Polar angle (rad)

λ_D Dominant wavelength (m)

μ Effective mobility of charge carriers (cm² V⁻¹ s⁻¹)

φ Azimuthal angle (rad)

ϕ_B Height of the potential barrier (eV)

Φ_tot Total luminous flux (lm)

Ω Emission angle (rad)

A Geometric area of the electrical contact device

A^** Richardson’s constant (A m⁻² K⁻²)

C_i Capacitance per area (F m⁻²)

c Speed of light (m s⁻¹)

d Thickness of the thin film (m)

F Electric field

h Planck’s constant (Js)

I Electric current (A)

I_D Current between the source and drain in the transistor (A)

I_leakage Leakage current of the transistor dielectric (A)

I_off Cut-off current of the transistor (A)

I_on Operating current of the transistor (A)

I_on/off Current modulation of the transistor

i Luminous intensity or stereo-radian photon flow

k_B Boltzmann’s constant (J K⁻¹)

L Channel length of the transistor (m)

L_OLED Luminance (cd m⁻²)

m^* Effective electron mass (kg)

N_c Effective density of states in the conduction band (1 cm⁻³)

N_F Number of photons generated per unit time (1 s⁻¹)

N_PC Number of charge carriers crossing the device

N_v Effective density of states in the valence band (1 cm⁻³)

n Density of free carriers (1 cm⁻³)

n_Q Charge density in the transistor channel (1 cm⁻²)

n_t Density of trapped carriers (1 cm⁻³)

n₀ Free thermally generated carriers (1 cm⁻³)

P_ele Electric power (W)

P_OLED Optical power in a wavelength (W)

P_opt Optical power (W)

q Charge of the electron or element (C)

r Radius (m)

R_channel Channel resistance in the triode transistor regime (Ω)

R_on Resistance in the triode transistor regime (Ω)

R_s Series resistance (Ω)

T Temperature (K)

T_g Glass transition temperature of polymers (K)

V Electric potential (V)

V_DS Voltage between the source and drain of the transistor (V)

V_GS Voltage between the gate and drain of the transistor (V)

V_T Threshold voltage of the transistor (V)

x_i Thickness of the dielectric film in the transistor (m)

W Width of the transistor channel (m)

μCP Microcontact printing

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Table of Contents for 2: Nanoelectronics

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