Space charge limited conditions

The total concentration of holes nh is a sum of the concentration of trapped (nht) and free (nhf) carriers. However, often rihf/nht —> 0, nh nht due to a large concentration of traps. Then, the excitons are quenched by trapped carriers and the annihilation rate constant yTq is equivalent to the mobile exciton-immo-bile (trapped) charge carrier interaction rate constant yxq. Under space-charge-limited conditions, the concentration of charge is simply proportional to the applied voltage (U), nht = (3/2) o U/ed2, where d is the sample thickness, e is the electronic charge, s is the dielectric constant of the sample material, and s0 is the permittivity of free space. Thus, it may be seen that the fractional change in the triplet exciton decay rate... 

The experimental results are usually analyzed from plots of the logarithm of the rate of potential discharge versus the logarithm of time under space-charge-limited conditions (pQ = 1). For these conditions, Eqs. (47) and (49) can be simplified to the following. For / < tt... 

Figure 8 The rate of potential discharge for flash exposures under space-charge-limited conditions for different values of the initial potential VQ.

SCLCs require that the contacts on the polymer be able to act as an infinite carrier reservoir with respect to bulk demands this requirement is just an alternative operational description of an ohmic contact. To reiterate, unambiguous determination of mobility directly from steady-state electrical measurements requires ohmic contacts and space-charge-limited conditions. The observation of linear curves ofj versus E is usually of no significance. 

Figure 2. Representation of space charge limited conditions in one dimension showing the profile of concentrations of positive (P) and negative (N) species and electric field variations at time of the field application (t — 0) and at some later time...

It appears that many of the results from similar LC systems reported in the literature (31,32,33) were unknowingly obtained under space charge limited conditions. 

Considering the same space-charge-limited conditions for the reaction of a single primary ion to give several products discussed previously, the ratio of secondary ion rate constants for secondary ions i and j can be shown... 

If the discharge cell has windows of optical quality, it can be placed inside the laser resonator to take advantage of the -fold laser intensity (Sect. 6.2.2). With such an intracavity arrangement. Doppler-free saturation spectroscopy can also be performed with the optogalvanic technique (Sect. 7.2 and [6.101]). An increased sensitivity can be achieved by optogalvanic spectroscopy in thermionic diodes under space-charge-limited conditions (Sect. 6.4.5). Here... 

In order to obtain an equation describing the space charge-limited condition, we follow Halpern and Corner, who simplified the problem of calculation by assuming that the tip/plane electrode assembly can be approximated as two concentric spheres with an inner radius, r, and an outer radius, R. The emission is to occur into a solid angle cotc, with co 0.6 (see Figure 23). The Poisson equation gives... 

The analysis of the experimental results is based on the assumption that mobility can be described by a power law field dependence. Por the space charge limited conditions the surface potential V decay rates can be written as... 

Important electrical informations about OLEDs, such as charge transport, charge injection, carrier mobility, etc., can be obtained from bias-dependent impedance spectroscopy, which in turn provides insight into the operating mechanisms of the OLED [14,15,73,75 78]. Campbell et al. reported electrical measurements of a PLED with a 50-nm-thick emissive layer [75], Marai et al. studied electrical measurement of capacitance-voltage and impedance frequency of ITO/l,4-Mv-(9-anthrylvinyl)-benzene/Al OLED under different bias voltage conditions [76], They found that the current is space-charge limited with traps and the conductivity exhibits power-law frequency dependence. 

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...

The C.P.D. is obtained directly by the magnetron and the capacitor (or Kelvin) methods. Other methods which have proved successful rely on the variation of anode potential in a diode with constant cathode conditions. In this case, since adsorption changes the effective anode potential, the applied potential necessary to restore the anode current to its original value is equal to the C.P.D. between the two surfaces. As considered in Sec. II, a true average work function is measured in the C.P.D. method when the two conductors are separated by a distance which is much greater than the size of the patches on the surface. These conditions are invariably fulfilled in the capacitor and the space-charge-limited diode methods. 

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... 

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]. 

FIG. 3.35. Experimental J—V characteristics of an ITO/PEDOT PSS/PCBM/Au injection limited electron current (triangles) and calculated space charge limited hole current in OC4C10-PPV (circles) for a thickness of L = 170 nm and temperature T = 290 K. The inserted figure represents die device band diagram under the flat band condition of a bulk heterojunction solar cell using Au as a top electrode [65]. 

Figure 107 Mobility-dependent hole injection currents for six TPD PC samples at 0.4MV/cm, under space-charge-limited O scl) and injection-controlled O inj) conditions. Inset mobility dependence of the injection efficiency defined by the ratio 0ilc/7scl)-After Ref. 394. Copyright 2001 American Physical Society.

Fig. 4.20. The density of states distribution obtained from space charge limited current measurements on undoped a-Si H. The various symbols represent different samples and deposition conditions. Field efiect (FE) and DLTS data are shown for comparison. is the substrate temperature during growth (Mackenzie, LeComber and Spear 1982).

Figure 6 The photoinduced discharge under emission-limited (dashed line) and space-charge-perturbed conditions (solid lines).

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