Midgap level

Careful experiments have not revealed any significant midgap absorption in the undoped polymer. It has been suggested that in the undoped polymer the energy levels due to solitons are close to the band edges. The simple theory which predicts midgap levels in the undoped polymer does not take into account the electron-electron interactions and is very approximate. 

The 0.5 eV midgap state absorption band is quite prominent but is rather broad. The difference in the midgap energy is 0.7 eV and the absorption peak at 0.5 eV is due to the effect of the electron-electron interaction on the transitions [8], Since the initial state involves two electrons in the midgap level and the final state involves only one, the Coulomb interaction lowers the energy of transition. The 0.5 eV band is quite similar to the midgap absorption in the doped r-PA shown in Fig. 2.2. This demonstrates that this band is associated with the same center in both the photoirradiated and the doped polymers. 

PPVs, in which the energy of the I By is 2.5 eV, have suggested that the energy of the lowest triplet state in PPV is 1.35 eV [19,21]. It is therefore suspected that the lowest triplet level in the P3ATs is also considerably below the 1 B , but above the midgap level. 

Fig. 8. LDF valence band structure of [9,2] chiral nanotube. The Fermi level lies at midgap at -3.3 eV. Dimensionless wavenumber coordinate k ranges from 0 to t.

The activation energy Ea - defined as Ec - Ey for the conduction band (and analogously for the valence band), can be used to assess the presence of impurities. Due to their presence, either intentional (B or P dopant atoms) or unintentional (O or N), the Fermi level shifts several tenths of an electron volt towards the conduction or the valence band. The activation energy is determined from plots of logafT) versus 1/7, with 50 < 7 < 160°C. For undoped material Ea is about 0.8 eV. The Fermi level is at midgap position, as typically Eg is around 1.6 eV. 

For undoped a-Si H the (Tauc) energy gap is around 1.6-1.7 eV, and the density of states at the Fermi level is typically lO eV cm , less than one dangling bond defect per 10 Si atoms. The Fermi level in n-type doped a-Si H moves from midgap to approximately 0.15 eV from the conduction band edge, and in / -type material to approximately 0.3 eV from the valence band edge [32, 86]. 

Dislocations are localized interruptions in a crystal s periodic network. These interruptions result in dangling bonds. Dislocations can be localized at a point, along a line or over an area. In the latter case, with the Fermi level pinned near midgap, an areal dislocation forms two Schottky barriers... 

Unfortunately, no reliable estimate of cr is available for any hydrogen species. Since the hydrogen donor level seems to be somewhere near midgap, it is appropriate to recall the range covered by the cr values measured for various deep impurities in silicon (Milnes, 1973, Chapter 10), namely, cr 10-14 - 10 21 cm2. Such values would give r0 values in (22) of the order of microseconds to seconds at 200°C if eD = em. At room temperature, on the other hand, values as long as hours could occur if eD is well below em or o-+e is very small. The range of possibilities for other conceivable carrier emission processes (H°— H + h, H+— H° + h, etc.) is presumably similar. 

Fig. 33. Comparisons of the pseudo-solubility data of Figs. 31 and 29 with model calculations assuming various values of parameter A DH, the binding energy of a positive donor D + and H into DH, AE2, the binding energy of 2H° into H2, and eA, the position of the hydrogen acceptor level relative to midgap. Plots (a) and (b) correspond respectively to the values 1.8 and 1.4 eV for A E2- In each of these, curves are shown for four combinations of the other parameters full curves, AEDH = 0.435 eV, eA = 0 dashed curves, AEDH = 0.835 eV, ea = 0 dotted curves AEDH = 0.435 eV, eA = 0.4eV dot-dash curves, A DH = 0.835 eV, eA = 0.4 eV. The chemical potential fi is constant on each curve and has been chosen to make the model curve pass through one of the experimental points of donor doping near 1017 cm-3, as shown. The solid circles are experimental points for arsenic obtained from Fig. 29 as described in the text. The other points are extrapolations of the phosphorus curves of Fig. 31 to zero depth, as described for Fig. 32, with open circles for the newer data and crosses for the older.

This is accompanied by a structural distortion and thus, according to the above model, to an electronic state which, due to the symmetry of the electronic distribution lies precisely at midgap. This single state, having half occupied levels in the gap, has been termed native solitons. 

At low temperatures, one deep donor level, V +, a few tenths of an elec-tronvolt above the valence band edge, a single acceptor level, V, near midgap, and a double donor level, V=, very near the condition band edge must be present (Figure 5) (7). The levels depicted in Figure 5 represent a best guess based on experiment (8-10). 

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