Impedance is defined as the frequency domain ratio of the voltage to the current. In other words, it is the voltage-current ratio for a single complex exponential at a particular frequency (). The concept of electrical impedance was first introduced by O. Heaviside [34] in the 1880s and was soon after developed in terms of vector diagrams and complex representation by A. E.

Kennelly [35]. Impedance is a more general concept than resistance because it takes phase differences into account, and it has become a fundamental and essential concept in electrical engineering.

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*In general, impedance is a complex number as represented as Z, and has the *
same unit as resistance, ohm (). As shown in Figure 2-8, the polar form shows
both magnitude and phase characteristics,
*amplitude, j is the imaginary unit and*

### is the phase difference between voltage

*and current. In Cartesian form, the real part of impedance is the resistance R and*

*the imaginary part is the reactance X.*

Figure 2-8 Graphical representation of the complex impedance plane.

Impedance spectroscopy (IS) is a relatively new and powerful method of characterizing many of the electrical properties of materials and their interfaces with electronically conducting electrodes. It may be used to investigate the dynamics of bound and mobile charge in the bulk or interfacial regions of any kind of solid or liquid material: ionic, semiconducting, mixed electronic-ionic, and even insulators (dielectrics). Any intrinsic property that influences the conductivity of an electrode-materials system, or an external stimulus, can be

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studied by IS. The parameters derived from an IS spectrum fall generally into two categories: (1) those pertinent only to the material itself, such as conductivity, dielectric constant, mobilities of charges, equilibrium concentrations of the charged species, and bulk generation-recombination rates;

and (2) those pertinent to an electrode-material interface, such as adsorption-reaction rate constants, capacitance of the interface region, and diffusion coefficient of neutral species in the electrode itself.

The most common approach of IS is to measure impedance by applying a single-frequency voltage or current to the interface and measuring the phase shift and amplitude, or real and imaginary parts, of the resulting current at that frequency using either analog circuit or fast Fourier transform (FFT) analysis of the response. Commercial instruments are available which measure the impedance as a function of frequency automatically in the frequency ranges of about 1 mHz to 1 MHz. The advantages of this approach are the availability of these instruments and the ease of their use, as well as the fact that the experimentalist can achieve a better signal-to-noise ratio in the frequency range of most interest.

There several other measured or derived quantities related to impedance
which often play important roles in IS, all of them are generically called
*where G is the conductance, B is the susceptance, C is the capacitance, f is the *

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frequency, and

###

= 2f is the angular frequency.Admittance spectroscopy (AS) is also a well-known and powerful technique for determining material properties and geometries of semiconductor devices and heterojunctions [36]. Recently, AS based on small signal space-charge-limited current (SCLC) theory has also been proposed to characterize carrier dynamics [37,38,39] and investigate the charge-carrier transport properties of organic materials with high resistivity [27,40,41,42,43,44].

**2.10 ** **Model for thermal admittance spectroscopy study **

Thermal admittance spectroscopy (TAS) [45,46] is a technique for the
*measurement of deep trap levels within pn junctions. By measuring the *
small-signal ac admittance of the junction under different conditions, e.g., with
small-signal frequency and sample temperatures as parameters, one can extract
the density of states, activation energy, and capture cross sections of the traps.

According to the applied dc voltage, zero- and nonzero- bias AS are distinguished.

*Trap levels in the space charge region of a p-n junction contribute to its *
admittance as follows: They are filled with electrons up to the Fermi level and
correspond to the nearest band edge by thermal capture and emission of carriers.

A small-signal AC voltage applied to the junction modulates the position of the Fermi level with respect to the band edges, so the trap levels in the vicinity of the Fermi level change their state of occupancy accordingly. Thus, their charge state also changes and an additional AC charge component is generated, which increases the total junction capacitance, i.e., the imaginary part of the admittance.

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*As the filling and emptying of the traps takes place with the emission rate e**T*

or time constant = 1/e*T*, the trapped AC charge lags behind the applied voltage
at frequencies above the emission rate. This phase shift first means ohmic losses,
so the traps also contribute to the junction conductance at higher frequency.

Second, the trapped charge decreases, because the trap occupancy can no longer follow the rapid jitter of the Fermi level. Consequently, the trap capacitance decreases with increasing frequency. A nonzero bias voltage shifts the mean Fermi level such that trap levels at a different depth in the band gap are measured.

The terms ‘‘high frequency’’ and ‘‘low frequency’’ depend strongly on
*temperature, since the emission rate e**T*

* of a discrete hole trap is given by *

### )

*effective density of states in the valence band, v*th is the thermal velocity of the

*electrons, T is the temperature, k*

*B*

* is the Boltzmann constant, and E*

a* is the *

activation energy. For an ideally discrete level, the usual first-order small-signal
*approximation [46,47,48] leads to a capacitance contribution C*

*T*as shown For the latter, the calculation yields [45,47],

### 2 2

_{0}

### exp( )

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in which the emission factor

###

0 comprises the temperature-independent parts of the product###

*p*

*v*

th*N*

*V*

* and is proportional to the capture cross section, which is *

assumed to be constant.
Due to its strong dependence on temperature and frequency, the admittance of a discrete trap level can easily be separated from other contributions to the total junction admittance by using an equivalent circuit model.

In our experiments, we investigate the electrical properties, such as
*resistance and activation energy, of p-doped and n-doped organic layers and *
demonstrate their effects on carrier injection barrier by temperature-dependent
AS measurements. Then, we also apply these conductive-doped organic layers
into OLED devices