Trap concentration

Figure 12-18. The temperature dependencies of the mobility simulated for different nap depths. The trap concentrations were 3x1 O 2 and the field 2xl05 V em 1 (Ref. 72J).

Figure 12-19. The parameter (aejJa) vs. Hup depih, parametric in the trap concentration (Ref. 72 ).

It is obvious, and verified by experiment [73], that above a critical trap concentration the mobility increases with concentration. This is due to the onset of intertrap transfer that alleviates thermal detrapping of a carrier as a necessary step for charge transport. The simulation results presented in Figure 12-22 are in accord with this notion. The data for p(c) at ,=0.195 eV, i.e. EJa—T), pass through a minimum at a trap concentration c—10. Location of the minimum on a concentration scale depends, of course, on , since the competition between thermal detrapping and inter-trap transport scales exponentially with ,. The field dependence of the mobility in a trap containing system characterized by an effective width aeff is similar to that of a trap-free system with the same width of the DOS. 

Figure 12-22. The dependence of the mobility on trap concentration. The width of the DOS was 0.065 eV, the...

Table 1. Trap depth and density in LPPP T , temperature at peak current, ,rsc and t J 1A are the trap levels obtained from the TSC and PIA experiments respectively, N, and it, are the number of traps and the trap concentration, respectively...

The variation of o,.jj with trap depth is presented in Figure 12-19. The effect of traps on the mobility, reflected in an increase of acjj, becomes noticeable only above a certain critical trap depth that depends on concentration. Above that critical value, a2,.), increases approximately linearly with ,. Figure 12-20 shows complementary information concerning the effect of the trap concentration on a,. at constant trap depth. The data reproduces as a family of parallel straight lines on a (Pr/jlo)2 versus In c plot. Their intersection with the ov)jla— 1 tine indicates the critical concentration c, of traps of depth , needed to effect the mobility (see Fig. 12-21). 

The effect of traps on charge carrier motion does not become noticeable until the trap concentration reaches a threshold value. One can define a critical concentration Ci/2 at which the mobility has decreased to one half of the value of the trap-free system. Eq. (12.19) predicts that. ... 

Baird and Rehfeld express A ° in terms of the trap concentration and the chemical potentials of the empty trap and of the electron in the quasi-free and trapped states. Further, they indicate a statistical-mechanical procedure to calculate these chemical potentials. Although straightforward in principle, their actual evaluation is hampered by the paucity of experimental data. Nevertheless, Eq. (10.13) is of great importance in determining the relative stability of the quasi-free versus the trapped states of the electron if data on time-of-flight and Hall mobilities are available. 

TABLE 7.1. Trap Concentration and Activation Energy of Each Trap Measured by DLTS... 

Devices Trap Level Energy Level (eV) Trap Concentration (cm 3)... 

FIGURE 14.12 Fully automated nano HPLC-MS with autosampler injection of large sample volume using two parallel online sample trapping, concentrating, desalting, and filtering columns. Pumps 1 and 2 transfer sample from loop of the autosampler into trap column 1 while pumps 3 and 4 elute sample in trap column 2 into the analytical column then to MS. 

OIC Analytical Instrument supply the 4460A purge and trap concentrator. This is a microprocessor-based instrument with capillary column capability. It is supplied with an autosampler capable of handling 76 sample vials. Two automatic rinses of sample lines and vessel purge are carried out between sample analyses to minimize carry-over. 

Tekmar are another supplier of purge and trap analysis equipment. Their LSC 2000 purge and trap concentrator features glass-lined stainless steel tubing, a menu-driven programming with four-method storage and a cyrofocusing accessory. 

Cryofocusing traps are often used to interface purge and trap concentrators to gas chromatographs with capillary columns. The enhanced performance characteristics of the design provide a significant improvement over previous systems. The use of a sophisticated cyrotrap with a thermal gradient ensures that the sample will be trapped and injected with high efficiency. 

The method of spin traps is used to perform not only qualitative but also quantitative measurements. For quantitative determinations, the spin-trap method is applied if the rate constant of radical initiation is 10 -10 L mol s and trap concentration is not below 10 M (Freidlina et al. 1979). 

The techniques for trapping, concentrating, isolating, and identifying volatiles have been developed by flavor chemists and insect pheromone researchers and are not detailed here. Some of the techniques useful for mammals are summarized in Albone (1984) and Millar and Haynes (1988). 

For the simplest case of a single set of localized states sitnated at a particular energy Ei, the trap-limited drift mobility of carriers moving in extended states at is readily compnted from equation (3.3). If the effective density of extended states at Ep is Np and the trap concentration is N, then we may write... 

As can be seen from Eqs. (18) and (21), the initial amplitude of the current or capacitance transient is proportional to nT(0). Therefore, if the bias has been kept at zero for a time sufficiently long to fill all traps with electrons, then nT(0) = NT and the trap concentration can be determined from the initial amplitude of the transient. The thermal capture rate is measured by restoring the reverse bias before the traps are completely filled by electrons. Adjusting conditions (low temperature) such that inequality (15) holds, then for a width tf of the filling pulse, the initial amplitude of the trap-emptying transient is given by... 

The sample, a reverse-biased p-n or metal-semiconductor junction, is placed in a capacitance bridge and the quiescent capacitance signal nulled out. The diode is then repetitively pulsed, either to lower reverse bias or into forward bias, and the transient due to the emission of trapped carriers is analyzed. As discussed in the preceding section, for a single deep state with JVT Nd the transient is exponential with an initial amplitude that gives the trap concentration, and a time constant, its emission rate. The capacitance signal is processed by a rate window whose output peaks when the time constant of the input transient matches a preset value. The temperature of the sample is then scanned (usually from 77 to 450°K) and the output of the rate window plotted as a function of the temperature. This produces a trap spectrum that peaks when the emission rate of carriers equals the value determined by the window and is zero otherwise. If there are several traps present, the transient will be a sum of exponentials, each having a time... 

Fig. 9. The behavior of the occupied trap concentration n, [Eq. (63)] and the free electron concentration n [Eq. (65)] during and after a light pulse of duration tp. For part (a) the parameters are eni = 0.6ms-1, / = 1.2 ms-1, and x"1 = 11.8 ms"1. For part (b) the parameters are e.i = 0.06, 0.6, and 6 ms"1, respectively, for curves (i), (ii), and (iii). The choice of parameters is for illustrative purposes only and may not reflect a realistic situation. The shape of n, is only approximately correct in the dotted portions. Part (c) shows the gating functions for boxcar and lock-in amplifiers, respectively.

D = Da + Db, t-o is a trapping radius and nB is trap concentration) is valid only if one neglects fluctuations of the volume of the Wiener sausage. In the opposite case at long times the kinetics for mobile donors A becomes fluctuation-controlled and as t -a oo obeys finally equation (2.1.106). Of our special interest here are arguments and results for the case of mobile traps B and d 3 based on simple estimates similar to those which resulted in equation (2.1.106). 

These results are complemented by theoretical calculations and computer simulations [110, 111] ford = l,2and3 ofbimoleculartrapping/annihilation reaction A + A—>0, A + T — Ax and A + Ax —> T (T is an immobile trap making A particle to become immobile too) and unimolecular trapping/annihilation, A + A —> 0, A — Ay, A + Ax —> 0. It was found that the kinetics of trapped particles can be described by the mean-field theory for bimolecular but not for unimolecular reactions. The kinetics of free A s is described by mean-field theory at short times, but at long times and low trap concentrations the concentration of free A s decays as (2.1.106). 

Tekmar LSC-2000 purge-and-trap concentrator packed with Tenax, or equivalent, with appropriate sampling tube... 

Attach the sampling tube to a purge-and-trap concentrator (dynamic headspace). 

Breath, bl ood uri ne Breath collected on Tenax, blood and urine subjected to purge-and-trap, concentrated on cryogenic capillary trap, thermally removed to GC. GC/MS No data No data Barkley et al. 1980... 

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