Space-Charge Limited Currents

Space-charge limited current (SCLC) occurs in materials with very low concentrations of free carriers (ideally, perfect insulators). When such materials are put into 

When charges diffuse into an insulating material, they give rise to an electrostatic field that acts against the penetration of additional charges into the material. The resulting carrier profile can be calculated from Maxwell s equations, the more pertinent of which is Poisson s equation  

e is the dielectric constant of the insulator, and o the permittivity of free space. The electric field created by the injected charges generates a current density J, which is the sum of a drift and a diffusion current 

This second order differential equation cannot be analytically solved in the general case. In 1940, Mott and Gurney derived an exact solution in the particular case where 7 = 0, for a semi infinite material, and assuming that the electric field is zero at X = 00 [48]. The charge density and potential are then given by 

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Two main methods have been used to measure the charge carrier mobility in electroluminescent polymers time of flight (TOF) carrier transit time measurements and analysis of the current-voltage (1-V) characteristics of single carrier devices in the space charge-limited current (SCLC) regime. A summary of the results for the hole mobility of PPV and PPV-related polymers is given in Table 11-1 [24, 27-32]. For... 

One result of the field-dependent mobility is that the space charge-limited current (SCLC, the maximum current that can How in the bulk of the sample) does no longer follow a simple V2H scaling [132] on the voltage Land sample thickness L. Muigatroyd [133] was able to show that, for a mobility as in Eq. (13.4), the monopolar SCLC current could be well approximated by ... 

A.J. Campbell, D.D.C. Bradley, H. Antoniadis, M. Inbasekaran, W.W. Wu, and A.P. Woo, Transient and steady-state space-charge-limited currents in polyfluorene copolymer diode structures with ohmic hole injection contacts, Appl. Phys. Lett., 76 1734-1736, 2000. 

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...

In fact, in their recent work, Mensfoort et al. [90] conclude that in polyfluorene copolymers hole transport is entirely dominated by disorder. This is supported by a strictly linear In p cx dependence covering a dynamic range of 15 decades with a temperature range from 150 to 315 K (Fig. 8). Based upon stationary space-charge-limited current measurement, where the charge carriers are in quasi equilibrium so that dispersion effects are absent, the authors determine a width a of the DOS for holes as large as 130 meV with negligible polaron contribution. 

Fig. 13 Experimental (symbols) and theoretical (lines) data for the current-density as a function of applied voltage for a polymer film of a derivative of PPV under the condition of space-charge-limited current flow. Full curves are the solution of a transport equation that includes DOS filling (see text), dashed lines show the prediction of Child s law for space-charge-limited current flow assuming a constant charge carrier mobility. From [96] with permission. Copyright (2005) 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. 

An example of the difficulties encountered when trying to fabricate an ohmic electrode, able to sustain a space-charge-limited current, is the recent work of the Neher group [179]. The authors deposited barium as an electron injection cathode on top of an electron transporting polymer based on a naphthalene diimide core whose LUMO is as low as 4 eV below vacuum level. Although the Fermi level of barium should be above the LUMO of the polymer, the electron current is. 

Young RH (1994) Trap-free space-charge-limited current - analytical solution for an arbitrary mobility law. Phil Mag Lett 70 331... 

Agrawal R, Kumar P, Ghosh S, Mahapatro AK (2008) Thickness dependence of space charge limited current and injection limited current in organic molecular semiconductors. Appl Phys Lett 93 073311... 

Koo Y-M, Choi S-J, Chu T-Y, Song O-K, Shin W-J, Lee J-Y, Kim JC, Yoon T-H (2008) Ohmic contact probed by dark injection space-charge-limited current measurements. J Appl Phys 104 123707... 

As soon as the concentration of free carriers (n ) injected from Ohmic contacts exceeds the concentration of carriers (no) produced by intrinsic or extrinsic excitation, space-charge-limited currents (SCLC) appear. In this case the Ohmic current... 

Mark, P., and W. Helfrich Space charge limited currents in organic crystals. J. AppL Phys. 33, 205 (1962). 

Ohmic contacts. An ohmic contact is defined as one which supplies a particular crystal with an infinite supply of either electrons or positive holes. Under an applied field these charge carriers are drawn into the material setting up a space charge. The subsequent currents are thus termed space-charge limited currents. In general the activation energy required to inject a positive hole from an electrode of work function W into a crystal is Ic — W and that to inject an electron W — Ac. Thus for ohmic contacts the conditions to be satisfied for holes and electrons are respectively (12a) and (12b). Although... 

Steady-state space charge limited currents (SCLC) have been applied to study traps in organic solids since the early 1960 s (Mark and Helfrich, 1962 Thomas et al., 1968 Reucroft and Mullins, 1974). Superquadratic dependences of the currents upon voltage, J azVn where n > 2, have been interpreted assuming the presence of traps exponentially distributed over a wide energy range. This may be expressed by (20), where h(e) is the density of states per... 

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... 

Space Charge Effect. Space charge effect of electrical properties of liquids have been studied in at least two aspects. One is the "concentration effect" in electrochemistry and the other, the "SCLC effect," or, the space-charge-limited-current effect in liquid crystals. We would like to discuss these two effects separately in the following. 

Estimated from the trap-free space charge limited current (SCLC) method... 

The equation which describes the conduction for space charge-limited current in the case of a trap-free solid [32,120] is the Mott-Gurney equation [121]... 

The conditions of the experiment discussed here are different than the restrictions imposed to obtain the Mott-Gurney equation. However, at least qualitatively, Equation 8.38 can describe the space charge-limited current effect. To test this hypothesis, Equation 8.38 was experimentally tested, and it was shown that it is approximately satisfied (see Figures 8.13 and 8.14) [112]. 

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