Exponential trap distribution

Steady-state space charge limited currents (SCLC) have been applied to study traps in organic solids since the early 1960 s (Mark and Helfrich, 1962 Thomas et al., 1968 Reucroft and Mullins, 1974). Superquadratic dependences of the currents upon voltage, J azVn where n > 2, have been interpreted assuming the presence of traps exponentially distributed over a wide energy range. This may be expressed by (20), where h(e) is the density of states per... 

Figure 12-11. Thickness dependence of the electron only j(V) characteristics at L=0.22, 0.31, and 0.37 pm. Solid lines have been calculated for an exponential distribution of electron traps of the total density 101 cnTJ and a characteristic temperature T,.= 1500 K (Ref. [41[).

The lifetime T and diffusion coefficient D of photoinjected electrons in DSC measured over five orders of magnitude of illumination intensity using IMVS and IMPS.56) fis proportional to the r m, indicating that the back reaction of electrons with I3 tnay be second order in electron density. On the other hand, D varied with C0 68, attributed to an exponential trap density distribution of the form Nt(E) <=< exp[ P(E - Ec)l(kBT) with 0.6. Since T and D vary with intensity in opposite senses, the calculated electron diffusion length L = (JD-z)m does not change linearly with the irradiance. 

Another potential image sensor is the CCD discussed in Chapter 9 by Matsumura. The major problem in using a-Si H for CCD applications is the high density of traps or localized states in the band gap. A theoretical analysis assuming an exponential distribution of gap states permits us to predict the transfer characteristics (residual electron density as a function of time). With state-of-the-art material it should be possible to make usable image sensors. Early experimental results with novel test structures have yielded transfer inefficiencies of less than 1% at clock frequencies between 1 and 200 kHz. 

Extensive work has been done on the exponentially distributed traps. We have devoted one separate section to discuss this work. 

Fig. 3.20. (a) Calculated current density as a function of inverse temperature for V = 10 V for a conducting polymer sample with exponentially distributed traps. The values of the trap distribution parameter Tc are Tc = 2500 K (long dash line), Tc = 1800 K (dash-dot line), Tc = 1500 K (solid line), Tc = 1200 K (dotted line) and Tc = 1000 K (small dash line). The values of the other parameters are Hb = 3 x 1018 cm-3, Nv = 3 - 1020 cm-3, e=2 and /ip = 5 x 10 cm2 V 1 s 1. The inset shows the calculated effective activation energy, Eeb. as a function of the characteristic trap distribution energy ) = kTc. (b) J-V characteristics of a sample of MEH-PPV with a thickness of 94 nm on a log-linear scale. The symbols represent the data of Campbell et al. [46]. The lines represent calculated values using the mobility model. The figure is taken from [42],... 

The observed J-V curves of Alq3 electron only sample from 295 to 83 K are shown in Fig. 3.24. The band model with exponential distribution of traps fits well the data... 

Unified Model with Exponentially Distributed Traps... 

In the case of exponentially distributed traps, the effect of high fields on the trap depths (Poole-Frenkel effect) can be taken into account by the same procedure. The trapped hole density is modified and Eq. (3.40) changes to [38],... 

Space charge limited current in the presence of exponential distribution of traps is given by,... 

In studies of low-mobility insulators, two types of continuous trap distributions are commonly used the exponential distribution of traps [364] and the Gaussian distribution of traps [365]. 

The problem has been solved analytically for an exponential distribution of traps... 

Due to the functional form of Eq. (185), which, except for the constant coefficient, is identical to the SCL j-U characteristics for a continuous exponential distribution of the form (175) or (176) derived in the case of the infinitely sharp point traps, the experimental data arising from the discrete macrotrap background can, without scrutiny, be mistakenly attributed to the continuous exponential distribution of point traps. The transition from the low-to high-field regions of the current occurs at a voltage (see Fig. 71)... 

Fig 8.18 shows the thermal quenching of a-Sij. C iH alloys for different x (Liedke et al. 1989). The parameter 7 is about 25 K in a-Si H and increases with the carbon concentration. It should not be too surprising that the temperature dependence originates from the exponential distribution of band tail states, or that the derivation of Eq. (8.44) follows the multiple trapping approach. Thermal quenching... 

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