Space-charge limited current model

TOP, mobility obtained from time-of-flight measurements SCLC, mobility obtained from application of space-charge limited current models to I(V) data E, electric field strength. 

Fig. 8 Temperature dependence of the zero field hole mobility in the low carrier density limit in a polyfluorene copolymer. The data are inferred from space-charge-limited current experiments and analyzed in terms of the extended Gaussian disorder model (see Sect. 4.1). From [90] with permission. Copyright (2008) by the American Institute of Physics...

A textbook example for the successful application of the model of Arkhipov et al. is the work of van Woudenbergh et al. [173]. More recently, Agrawal et al. [106] compared injection limited currents and space-charge-limited currents in a copper-phthalocyanine sandwich cell with TTO and Al electrodes. An analysis of experimental data yields consistent values for the width of the DOS distribution as well as for inter-site separation [174]. These studies support the model of thermally activated injection into a Gaussian DOS distribution of hopping sites and confirm the notion that disorder facilitates injection because it lowers the injection barrier, although the transport velocity decreases with increasing disorder. 

Support for the applicability of this model to an explanation of the Meyer-Neldel rule comes from measurements of space-charge limited currents in anthracene where a correlation (see Fig. 20) has been found between the total density of traps H and the distribution parameter Tc (Owen et al, 1974). It has been shown that this effect is not fortuitous as suggested by some workers... 

An alternative approach has been taken by Blom and co-workers, who have developed a model in which the electron and hole currents are limited not by the injection process but by the transport capability of the bulk polymer.47,48 The maximum single-carrier current that can be supported in a trap-free semiconductor is the space-charge-limited current Jscl, given by... 

One of the simplest sheath models is that of a DC high voltage ( T ) sheath that contains no electrons and in which ion flow is collisionless (space-charge limited current). The resulting sheath equation is called the Child-Langmuir law [165]. 

Numerically, the matrix sheath thickness is large and exceeds the Debye radius by 10-50 times at high voltages. A more accmate approach, the so-called Child law sheath, takes into account a decrease in the ion density due to their acceleration across the sheath. In frameworks of the model, the ion current density Jq = n eu is taken from the Child law of space-charge-limited current in a plane diode ... 

The following assumptions enter the model for the space-charge-limited currents (seee.gMl, 11, 12, 38) ... 

In order to analyse these very notable experimental results on the dark current of injected charge carriers in disordered films, we first describe in the next Sect. 8.6.5.2 the model of space-charge-limited currents for the case that the semiconductor is not an ultrapure single crystal, but rather a disordered molecular film. 

Electrons in Alqs the layer-thickness dependence of the current density (Figs. 8.59 and 8.60) is j a dr at a high and constant field strength. It follows from this that the contact is Ohmic and the current is space-charge limited and not limited by the contact. This is the basic condition for the model of space-charge-limited currents. The j(V) characteristics for a film thickness ofd = 294 nm (Fig. 8.28) and the corresponding characteristics for smaller thicknesses are determined by energy-... 

The carrier mobility in the mixed CuPcC o films has been obtained by modeling the current density-voltage (j-V) characteristics for hole- and electron-only devices using the space-charge-limited current (SCLC) theory (Pope and Swenberg, 1999 Rand et al., 2005), viz. ... 

The theories of the electronic and ionic currents have some features in common. One may formulate models in which the current is limited by the injection into the film from the contacts of positively or negatively charged carriers, or one may consider an equilibrium state to exist across either or both interfaces. One may postulate space-charge limited currents, trapping, and recombination processes. One of the chief differences between the ionic and the electronic currents is that the average velocity of the ions is approximately exponentially dependent on the field for fields which produce experimentally observable ionic currents, whereas the average velocity of electrons is linearly dependent on the field at low fields with different types of nonlinearity at high fields. 

The derivation of the exact expression of the space charge limited current would require the resolution of Eq. (27) in the case of a non zero current. Unfortunately, such a resolution cannot be performed analytically. The standard expression of the space charge limited current (Eq. 30), as derived by Lampert [49], was obtained by neglecting the diffusion current (second term of the right hand side of Eq. (26)). It is in fact very close to that deduced from the phenomenological model developed above. 

---