Single Level Traps

We treat here the case of shallow Gaussian traps. The equations reduce to those applicable to single level traps by making the standard deviation at = 0. If the Poole-Frenkel effect (PEE) is included the J-V relation for a device containing shallow traps is given... 

This equation is solved numerically by the method described earlier for the single level traps. 

In the case of a single level trapping state, Ei is the difference between the energy of the trap and the transport band edge, and a — where iVc,v, is the density... 

Palladium and platinum are also used as carrier lifetime controllers in Si. Pd creates an electron trap at Ec - 0.22 eV and a hole trap at Ev + 0.32 eV in Si (Chen and Milnes, 1980). Pt induces a single electron trap at Ec + 0.28 eV (Chen and Milnes, 1980). All of these levels are passivated by atomic hydrogen (Pearton and Haller, 1983) suggesting that hydrogen might be profitably used during silicide formation to passivate electrically active levels near the silicon-silicide interface. 

Table 7.5. Energetic positions below the conduction band edge (Ec) and densities of shallow (Hi, Alzn) and deep (I ll -E5) donor-like defect levels (traps) in ZnO identified by temperature-dependent Hall effect and deep level transient spectroscopy, respectively, in undoped PLD films and single crystals grown by seeded chemical vapor deposition (Eagle Picher), taken from H. von Wenckstern [57]...

For single energy level traps the distribution can be written as, h(E) = HaS(E-Et),... 

The electric field at the interface of the oxide and the active layer is large. As discussed earlier, the field assists the ionization of the traps due to the Poole-Frenkel Effect. The trap depth is reduced by an amount /9 /F and the number of trapped carriers is reduced. Following Horowitz and Delannoy [157] we consider the traps at a single level located near the band edge [158] in an n-type polymer. The treatment is quite general and can be extended to p-type polymers quite easily. When PFE is included, Eq. (6.3) changes to,... 

G. Horowitz and P. Delannoy, J. Appl. Phys. 70, 469 (1991). The authors described the charge transport in non-substituted sexithiophene on the basis of the model which assumes the presence of a narrow band and a single shallow trap level located near the band. 

Equation (79) implies that the system of Fig. 11 can be treated with the dynamic equations of a single level, but with kinetic coefficients (lifetime, diffusion coefficient) that depend on the steady state. The essence of the quasistatic approximation is to describe the kinetic factors associated to trapping and detrapping in terms of occupation of free and localized states. The quasistatic approximation is explained in more detail in [51, 52, 150, 151]. It has been widely used to describe experimental results of DSCs. 

Fig. 1.7 Schematic presentation of single-level Shockley-Read transitions, a electron capture by trap b electron emission by trap c hole capture by trap d hole emission by trap...

The effect of traps on the SCLC has been widely studied, both theoretically and experimentally. In the case of a single shallow trap level of density lyii g at an energy E below the conduction band (or above the valence band), the current is simply multiplied by a factor 9 - nf/( f -f- t)> where and t are the density of free and trapped carriers, respectively. In the case where tif < n, and assuming that the carrier distribution follows a simple Boltzmann statistic, 9 is given by... 

In the case where there is one single trap level, E, is the energy difference between this level and the delocalized band edge, and a the ratio between the effective density of slates at the delocalized band edge and the concentration of traps. If traps are energy distributed, effective values of N, and a must be estimated. 

However, although it allowed a correct description of the current-voltage characteristics, this model presents several inconsistencies. The main one concerns the mechanism of trap-free transport. As noted by Wu and Conwell [1191, the MTR model assumes a transport in delocalized levels, which is at variance with the low trap-free mobility found in 6T and DH6T (0.04 cm2 V-1 s l). Next, the estimated concentrations of traps are rather high as compared to the total density of molecules in the materials (see Table 14-4). Finally, recent measurements on single ciystals [15, 80, 81] show that the trap-free mobility of 6T could be at least ten times higher than that given in Table 14-4. 

Condensation occurs constantly in steam pipes, and steam traps are installed to separate the steam from the condensate. In long steam-pipe runs most of the carbon dioxide remains in the steam phase, although if only a single neutralizing amine with a low DR is used, much of the amine will be present in the condensate. The result is that the amine feed quickly becomes depleted, and further down the steam/condensate pipe the pH level becomes progressively lower. 

---