Gaussian trapping

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... 

If we consider a sample with shallow Gaussian traps and include PEE, the sample behaves as if there are no traps and the mobility is field dependent given by Eq. (3.56) far as the dependence of J on V is concerned. The zero field mobility and its temperature dependence are different in the two equations. If the traps are at a single energy level, <7t = 0 and the temperature variation of the mobility also becomes the same in the two cases. Eq. (3.58) represents both the models, it reduces to the existing shallow trap model (without PEE) when = 0 and to the existing field dependent mobility model when 6 = exp(-EtfkT). 

Fig. 16. Density of states showing five Gaussian trap levels, each with total integrated density 1 X 10 cm , plus shallow donor level corresponding to a net donor concentration ofS X 10 cm . The position ofthe bulk Fermi energy is taken to be 50 meV below and the gap energy is assumed to be 1.8 eV.

Fig. 8.62 Comparison of the simulated current-voltage characteristics for exponential and Gaussian trap distributions, as a log-log plot. The simulations were carried out for temperatures of 100 K, 200 K, and 300 K. The other parameters are ji. = 10 cm /Vs, Sf = A,d= 300 nm, and Nc = 2- 10 cm . The parameters for the trap distributions are given in the figure. From [38].

Heather R and Metiu H 1985 Some remarks concerning the propagation of a Gaussian wave packet trapped in a Morse potential Chem. Phys. Lett. 118 558-63... 

Recently the effect of intrinsic traps on hopping transport in random organic systems was studied both in simulation and experiment [72]. In the computation it has been assumed that the eneigy distribution of the traps features the same Gaussian profile as that of bulk states. 

Figures 12-17 and 12-18 show the temperature dependencies of the mobility in a hopping system with a Gaussian DOS of variance <7=0.065 eV as a function of the relative concentration c of traps of average depth ,=0.25 eV and as a function of the trap depth E, at a fixed concentration < =0.03, respectively. For c=0...

Figure 5.1.7 shows the propagator of the motion measured for a clean and a biofilm impacted capillary [14,15] and the residence time distributions calculated for each from these velocity distributions. The clean capillary gives an experimental propagator equal to the theoretical velocity distribution convolved with a Gaussian diffusion curve [14], as shown in Figure 5.1.2. For the flow around the biofilm structure note the appearance of a high velocity tail indicating higher probability of large displacements relative to the clean capillary. The slow flow peak near zero displacement results from the protons trapped within the EPS gel matrix where the...

The deformation of polymer chains in stretched and swollen networks can be investigated by SANS, A few such studies have been carried out, and some theoretical results based on Gaussian models of networks have been presented. The possible defects in network formation may invalidate an otherwise well planned experiment, and because of this uncertainty, conclusions based on current experiments must be viewed as tentative. It is also true that theoretical calculations have been restricted thus far to only a few simple models of an elastomeric network. An appropriate method of calculation for trapped entanglements has not been constructed, nor has any calculation of the SANS pattern of a network which is constrained according to the reptation models of de Gennes (24) or Doi-Edwards (25,26) appeared. 

With the advent of linear quadrupole analyzers the full width at half maximum (FWHM) definition of resolution became widespread especially among instruments manufacturers. It is also commonly used for time-of-flight and quadrupole ion trap mass analyzers. With Gaussian peak shapes, the ratio of / fwhm to Rio% is 1.8. The practical consequences of resolution for a pair of peaks at different m/z are illustrated below (Fig. 3.17). 

M.I. Angelova and B. Pouligny Trapping and Levitation of a Dielectric Sphere with off-Centered Gaussian Beams I Experimental. Pure Appl. Optics 2,261 (1993). 

E. Torrontegui, X. Chen, M. Modugno, A. Ruschhaupt, D. Guery-OdeUn, and I. G. Muga. Fast transitionless expansion of cold atoms in optical Gaussian-beam traps. Phys. Rev. A, 85(3) 033605-033613(2012). 

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