Dictionary of Terms in Organic Electronics. Specific Terms from Q to Z.

Quantum efficiency

Quantum efficiency of photoluminescence
Quantum efficiency of electroluminescence
Quantum efficiency of photovoltaics

Determinations and symbols for quantum efficiency, quantum yield, and energy conversion efficiency vary in different textbooks and original literature sources. Thus, quantum efficiency most commonly denoted with a Greek symbol eta (h), although a Greek letter phi (F) is also in use. The last symbol is also often used for the designation of a quantum yield, which commonly means quantum efficiency in percent expression. Here, we attempt to unify symbols for photoluminescent (PL), electroluminescent (EL), and photovoltaic (PV) quantum efficiencies according to those generally found in original scientific literature.

It is important to understand also, that quantum efficiency may not be equivalent of energy efficiency of an optoelectronic device, because it does not consider energies of both impacting and forming particles, but only considers quantity ratios of them. Thus, photoluminescent (PL) quantum efficiency of many of organic molecules may be close to 100% in diluted solutions, however energies of emitting photons may be significantly lower than that of absorbed ones due to Stokes shift. Therefore, energy conversion efficiency may be significantly lower than 100% and may be calculated as a ratio of sum of energies of emitted and absorbed photons.

Quantum efficiency of photoluminescence

Quantum efficiency of photoluminescence (h_PL) is a property of a luminescent material and it is a # of emitted photons / # of absorbed photons. It may be determined as a product of the efficiency of photoexcitation (g_PL) and the ratio of rates of radiative (k_R) and non-radiative (k_NR) decays of the generated excitons (equation 1). It also may be defined as a function of a ratio of lifetime of luminescence (t_PL) and so-called natural radiative lifetime (t_R) (luminescence lifetime in the absence of the non-radiative decay).

PL quantum efficiency of a new substance (sample) (h_PL(S)) can be determined by measuring of its emission region, optical absorption, and refractive index followed by comparison of the data with that of a reference compound (h_PL(R)) with known PL quantum efficiency (equation 2).

Where:
h_PL = Quantum efficiency of photoluminescence.
g_PL = # of generated excitons/# of absorbed photons = photoexcitation efficiency.
k_R = Rate constant of radiative decay.
k_NR = Rate constant of non-radiative decay.
t_PL = Lifetime of photoluminescence.
t_R = Natural radiative lifetime.
h_PL(S) and h_PL(R) = PL quantum efficiency of a sample substance and a reference compound correspondingly.
A_S and A_R = Areas as a fraction of the emission wavelength of a sample substance and a reference compound correspondingly.
a_S and a_R = Optical absorption of a sample substance and a reference compound correspondingly.
n_S and n_R = Refraction indices of a sample substance and a reference compound correspondingly.

Quantum efficiency of electroluminescence

Quantum efficiency of electroluminescence (h_EL) is subdivided in internal quantum efficiency (h_ELint) and external quantum efficiency (h_ELext). The former is normally a property of a material, whereas the latter is a property of an electroluminescent device, usually a light emitting diode (LED).

Internal quantum efficiency is a # of photons generated in a substance / # of electrons flowing through it. It may be determined as a product of electroexcitation efficiency (g_EL) (probability of the carrier recombination that results in the formation of excitons), singlet exciton formation efficiency (h_r) (ratio of a number of singlet excitons to a number of all excitons, including triplets), and PL efficiency (equation 1).

External quantum efficiency (EQE) is # a of generated photons escaped from a substance or a device / # of electrons flowing through it. Two types of external quantum efficiency of a device are usually distinguished: overall external quantum efficiency and forward external quantum efficiency.

Overall EQE determines density of light running from a device in all directions and it can be measured by placing of a device in a spherical light-detector. The forward external quantum efficiency determines density of light running forward from the front of a device. Forward EQE may be significantly lower than overall EQE due to optical wave-guiding in emitting surfaces to the edges of a device. EQE of light emitting diodes may be expressed also by equation (2), where a is the light output coupling factor that determines light losses on its pass out of a device. Equation (3) defines monochromatic EQE as a function of operating (or driving) voltage and carrier balance inside of emission zone. It shows approximate relation between energy of emitting photons and operating voltage.

Where:
h_ELint = Internal quantum efficiency of electroluminescence.
h_ELext = External quantum efficiency of electroluminescence.
g_EL = Electroexcitation efficiency = #exciton formation events/#electrons flowing in the external circuit = probability of carrier recombination with formation of excitons.
h_r = Efficiency (probability) of the formation of singlet excitons = #singlet excitons/#all excitons (singlet + triplet). Also known as singlet to triplet branching ratio.
h_PL = PL quantum efficiency of a material.
a = Light output coupling factor = 1/(2n²), where n = refractive index. b_I = carrier balance in the emission layer = #minor carriers/#major carriers.

Quantum efficiency of photovoltaics

The definitions of internal (h_PVint) and external (h_PVext) quantum efficiency of photovoltaics are used for the determination of overall quantum efficiency of a photovoltaic material and a photovoltaic device correspondingly. For the case of monochromatic quantum efficiency of PVs, the definitions of incident photon to current efficiency (IPCE), absorbed photon to current efficiency (APCE), and light harvesting efficiency (LHE) are most commonly used. The latter definitions are generally applied for the description of efficiency of dye-sensitized solar cells.

Internal quantum efficiency (h_PVint) is a # of electrons penetrating in an external circuit / # of absorbed photons. It may be determined as a product of exciton diffusion efficiency (h_ED), charge transfer efficiency (h_CT), and charge collection efficiency (h_CC) (equation 1). Exciton diffusion efficiency (h_ED) is a fraction of photogenerated excitons that reaches p-n-junction. Charge transfer efficiency (h_CT) (also known as dissociation efficiency or charge injection efficiency) is a function of a rate constant for electron injection (k_inj) and excited state lifetime in the absence of injection (t) (equation 2). Charge collection efficiency (h_CC) is a function of a charge collection length (L_c) and thickness of the active layer of a device (d) (equation 3). The charge collection length (L_c), in turn, is determined by a sum of the hole and electron drift lengths, that are functions of charge carrier mobility.

External quantum efficiency (h_PVext, or EQE) is a # of electrons penetrating in an external circuit / # of incident photons of all energies, e.g. photons that hit the surface of a photovoltaic cell. It may be determined as a product of absorbance efficiency in the photoactive region (h_A) and internal quantum efficiency of a material (h_PVint) (equation 4).

Where:
h_PVint = Internal quantum efficiency of a photovoltaic material.
h_PVext = External quantum efficiency (EQE) of a photovoltaic device.
h_ED = Exciton diffusion efficiency.
h_CT = Charge transfer (or charge injection) efficiency.
h_CC = Charge collection efficiency.
k_inj = Rate constant for electron injection.
t = Exciton lifetime in the absence of the injection.
L_c = Charge collection length.
d = Thickness of the photoactive layer.
h_A = Efficiency of absorption of incident photons in the active layer.

Incident photon to current efficiency (IPCE) is a "monochromatic version" of EQE, and it determines the ratio of photons that generate electrons in the external circuit to incident photons of monochromatic light. In contrast to EQE, IPCE may be determined from measuring of monochromatic light power density, and calculated as a function of short circuit current density (J_sc), incident light power density (P_in), and wavelength l (equation 5).

Absorbed photon to current efficiency (APCE) is a "monochromatic version" of internal quantum efficiency, and it determines the portion of absorbed photons that generate electrons in the external circuit. Relation between IPCE and APCE is shown in equation (6), where LHE corresponds to the light harvesting efficiency. LHE quantifies absorbance of monochromatic light by a device as a function of absorption (or extinction) coefficient (equation 7). IPCE may also be expressed as a product of LHE, charge injection efficiency (h_CT), and charge collection efficiency (h_CC) (equation 8).

Where:
IPCE = Incident photon to current efficiency = # electrons/# incident photons.
APCE = Absorbed photon to current efficiency = # electrons/# absorbed photons.
LHE = Light harvesting efficiency.
J_sc = Short circuit current density mA/cm².
P_in = Incident light power density mW/cm².
l = Wavelenght (nm).
abs(l) = Monochromatic absorbance as a function of concentration of a light-harvesting component (e.g. sensitizing dye) and extinction coefficient.
h_CT = Charge transfer (or charge injection) efficiency.
h_CC = Charge collection efficiency.

Transistors

Transistors are simple logic semiconductor electronic devices that generate electric output depending on two different inputs information. Used mainly for current amplification in analog circuits and for current switching in digital circuits.

Main types of transistors:
1. Bipolar Junction (BJT) or Heterojunction Bipolar (HBT) transistors:
Composed of emitter, collector, and base (see scheme below). Operation based on input current to the base. Used predominantly for the current amplification in analog circuits.

2. Field Effect Transistors (FETs):
Composed of channel and gate for junction FETs (JFETs) plus gate insulator for insulated gate FETs (IGFETs) (see scheme below). Connected to three terminals: Source, Drain, and Gate. Operation based on input voltage to the gate. Used predominantly for the current switching in digital circuits.

Organic Field Effect Transistors (OFETs) and Organic Thin Film Transistors (OTFTs):
Organic field effect transistors (OFETs) contain at least one organic functional component that can be either a channel semiconductor (most commonly), or a gate dielectric, or a gate substrate.

Organic FETs are classified by:

1). Transistor geometry
Top-contact bottom-gate (TC/BG) (see scheme below) is a 'classic' type of FETs possessing usually minimal contact resistance, higher mobility and drive currents due to efficient semiconductor and contact deposition procedures. Drawbacks: minimal device dimensions are limited to 5 mm due to 'shadowing effects'.
Bottom-contact bottom-gate (BC/BG). Advantages: direct charge injection into near-gate channel region can be useful for a variety of applications and allows smaller device dimensions; potential for lower-cost manufacturing involving lithographical methods. Drawbacks: inferior charge transporting properties compared to top-contact devices due to poorer ordering of layers of an organic semiconductor.
Bottom-contact top-gate (BC/TG). It was shown, that this type of transistors is best suitable for ambipolar regimes (see below).

2). Transistor operating regime
Unipolar FETs operate only in either p-channel or n-channel regime.
Ambipolar (bipolar) FETs may operate in both p-channel and n-channel regimes. Organic ambipolar transistors are a new technology with development span since 2001. Challenges: 1. Ambipolar properties require an organic channel semiconductor/blend to possess both p-type and n-type conductivity; 2. Selection of a proper source and drain electrode material is challenging because it must inject both holes and electrons into an organic semiconductor with similar efficiency.
Types of ambipolar OFETs: bilayer, organic blend, and single-component FETs (see scheme below).

3). Material for channel semiconductor
Small molecule channels consist of small molecules or oligomers that are usually vacuum-deposited. Channels may be either polycrystalline (composed of many microscopic crystals) or monocrystalline (composed of just a single crystal). Small molecule channels, especially monocrystalline ones exhibit high carrier mobility and reproducibility of properties. Oligoacenes and oligothiophenes are primary compounds for use in small molecule OFETs.

Polymer-based channels consist of amorphous or polycrystalline polymers that may be fabricated from a solution. They exhibit inferior mobility and reproducibility of properties compared to small molecule semiconductors, however simple, solution-based fabrication of devices is a major advantage of the polymer-based OFETs. Polythiophenes (PTs), poly-para-phenylenes (PPPs), and poly-para-phenylene-vinylenes (PPVs) are the most commonly used polymers in polymer-based OFETs.

Thin film transistors (TFTs) are modifications of FETs that consist of thin films of a channel, a gate insulator, and a gate. TFTs (based on amorphous silicon) are widely used in electronics, especially in the backplanes of modern LCD displays. Organic TFTs (OTFTs) contain at least one organic functional component correspondingly. Advantages of organic TFTs are in potential flexibility, transparency, and low cost due-to simple, solution-based fabrication (casting, printing etc).

Light-emitting transistors, please see a special article in our dictionary.

The most important characteristics of FETs:
1. Field-effect mobility
2. On/Off ratio
3. Threshold voltage
4. Saturation voltage
4. Operating voltage
5. Thermal conductivity
6. Thermal and Enviromental stability

Organic materials for OFETs, general overview:

Summary of conducting oligomers for small molecule OFETs
Summary of conducting polymers for polymeric OFETs

Latest developments in organic materials for OTFTs:
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Improving mobility of regioregular P3HT for OTFT applications
Dry microcontact printing for patterning of P3HT-based transistors
Novel solution-processible thiophene oligomer for OTFT applications
Novel thiophene polymers with improved esnvironmantal stability, on/off ratio, and mobility
Gate dielectric insulator based on a cross-linked polymer
Gate dielectric insulator based on a hybrid organic-inorganic "core-shell" material
New thiophene derivatives for small molecule channel semiconductors
New self-assembled oligoacene structures for small molecule channel semiconductors
New tetrathiafulvalenes for small molecule channel semiconductors
Preparation of acene monocrystals for small molecule channel semiconductors

Detailed and comprehensive scientific information on organic FETs and OTFTs may be found in a series of books and latest scientific reviews.