Midgap

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 single-electron spectrum for the antisoliton solution, A,U)=-Av(x ), is exactly the same as for the soliton, except that now the wave function of the midgap state is given by... 

The two intragap stales g (x) arc the symmetric and antisymmetric superpositions of the midgap stales localized near the soliton and the anlisoliton ... 

FIG. 1. Schematic density of states distribution. Bands of (mobile) extended states exist due to short-range order. Long-range disorder causes tails of localized states, whereas dangling bonds show up around midgap. The dashed curves represent the equivalent states in a crystal. 

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]. 

Consequently the photoresponse tTph/deposition rate as about lO exp(Frf). Activation energies amounted typically to 0.7-1.0 eV. From thermally stimulated conductivity (TSC) measurements [489-492] a midgap density of states (DOS) of 1.5 x lO cm eV is determined. The product/zr at 300 K is 9 X 10 cm V . Both DOS and /rr are independent of frequency. 

In a-C H, the tail states are dominated by n electrons, which results, as pointed out by Robertson [99, 100], in an enhanced localization as compared to a-Si H, giving rise to higher band tail density of states and also to higher defect density in the midgap. 

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. 

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