Percolation paths

Lee JH, Kim GS, Choi YM, Park WI, Rogers JA, Paik UG. Comparison of multiwalled carbon nanotubes and carbon black as percolative paths in aqueous-based natural graphite negative electrodes with high-rate capability for lithium-ion batteries. J Power Sources 2008 184 308-311. 

In order to form a conductive pattern from nanoparticle inks, the potentially conductive particles must be consolidated to create a continuous percolated path for the conduction of electric current. 

Dielectric breakdown in nanosize gate stack of state-of-the-art Si nanoelectronic devices has been one of the key reliability concerns. We present the recent development in using physical analysis techniques to decode the nature of the breakdown path or more commonly called as percolation path in ultrathin SiON and HfOi-based gate materials. 

Dielectric breakdown induced epitaxy (DBIE), an important physical signature of the breakdown and a nanomarker, is used to identify the breakdown location. In this approach, the invisible percolation path can be located unambiguously [14-16],... 

Once the breakdown location is identified using DBIE, electron energy loss spectrometry (EELS) was performed using a FEI-TITAN 300 kV TEM/STEM to analyze the chemical nature of the percolation path [10,11]. Fig. 2 illustrates a close-up view of the sample configuration and beam-sample interaction. STEM/EELS spectra were collected at 80 keV beam voltage using point-to-point vertical and horizontal scans as shown in Fig. 2b across the dielectric layer at the breakdown site identified by a DBIE and at the non-breakdown site that were far away from the DBIE. 

Using the intensity counts integrated from 532 to 552 eV, we estimated the x value of the defective oxide SiO in the percolation path [11]. For the sample shown in Fig. 5, it is SiOu at the BD center (Position 3) and SiOi e-i.g at the outer shell. The x values imply that there are missing of 1 (SiOu) and 2 (SiOu)... 

Equation (8-11) can be simplified and the tunnel feature directly disclosed if 1) only the shortest tunneling percolation path through nearest-neighbour interactions is important and 2) all the intermediate group exchange interactions and energy gaps take the same values, p and As, respectively, i.e. = p and s - Sk oi - k = As. Eqn. (8-11) then reduces to... 

Once the charge carriers have been successfully separated, they need to be transported to the respective electrodes to provide an external direct ciu rent. Here the donor material serves to transport the holes whereas the electrons travel within the acceptor material. Thus, percolation paths for each type of charge carrier are required to ensure that the charge carriers will not experience the fate of recombination due to trapping in dead ends of isolated domains [60-62]. As such the bulk heterojunction has to consist of percolated, interpenetrating networks of the donor and acceptor phases. 

Fig. 53 Dependence of open circuit voltage Vqc on the architecture of PFB F8BT solar cells. When the PFB phase can form percolation paths between both electrodes, the Toe is reduced considerably. (Reproduced with permission from [246], 2004, Wiley-VCH)...

It is remarkable, however, that despite a roughness which is larger than the film thickness in some of our films (see below), all of them show n-channel as well as p-channel transport. Obviously, there still exists a percolation path for conduction in both materials independent of phase separation and order formation. We also note that the bulk morphology does not necessarily provide precise information for organic ficld-cffcct transistors since in these devices the active channel is restricted to the first few molecular layers at the interface to the gate dielectric [48-50]. 

Fig. 3-21. Percolation into random uncorrelated media with varying site occupation probabilities (areal porosities). Solids are black. Continuity of major percolation paths from upper boundary indicated by shading.

Fig. 3-22. Percolation into randomized Sierpinski carpels with (A) porosity = 0.64, and (It) porosity = 0.6864. Solids are black. Continuity ol major percolation paths Irom upper boundary indicated by shading.

It should be noted that this ratio is significantly lower than that usually applied in polymcr/C tll bulk heterojunction devices, where the Copolymer ratio is typically 4 1 to allow the formation of C50 percolation paths for electron collection [59]. 

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