Diffusion lifetime

Steady-state flow of molecules into the cell, we estimate helium densities used equivalent to about 100 msec diffusion lifetime. 

Starting with the field-free diffusion lifetime, the trap lifetime can be obtained by solving the diffusion equation with the boundary condition that the molecule density be zero at the walls of the cylindrical cell. The lifetime of the lowest-order field-free diffusion mode is given by... 

The effect of the trapping field can be accounted for by numerically solving the diffusion equation with a drift term from the trap [18]. Figure 13.6 shows the calculated lifetime using this approach (in units of the field-free diffusion lifetime, xo) as... 

FIGURE 13.6 Trapped molecule lifetime vs. trap depth in units of the field-free diffusion lifetime, tq (Equation 13.5). The points are data taken for NH [6]. 

The radial motion of fully thermalized A particles, on the other hand, is diffusive. The diffusion lifetime is given by... 

For Na, in-cell laser absorption spectroscopy is used to determine the number of thermalized Na atoms, WNa. and the cold collision diffusion cross-section, Oc,Na-We find A/Na 10 " /pulse for both the metallic Na and NaCl ablation targets. We measure diffusion lifetimes of x (msec) 4 x 10 x nne (cm ). From this we inferac,Na 3 x 10 cm. Previous workwithPbOhas measured an ablation yield of 10 /pulse [38], and our in-cell LIF measurements indicate a comparable yield. 

One might expect the frequency factor A for desorption to be around 10 sec (note Eq. XVII-2). Much smaller values are sometimes found, as in the case of the desorption of Cs from Ni surfaces [133], for which the adsorption lifetime obeyed the equation r = 1.7x 10 exp(3300// r) sec R in calories per mole per degree Kelvin). A suggested explanation was that surface diffusion must occur to desorption sites for desorption to occur. Conversely, A factors in the range of lO sec have been observed and can be accounted for in terms of strong surface orientational forces [134]. 

The situation is very different in indirect gap materials where phonons must be involved to conserve momentum. Radiative recombination is inefficient, resulting in long lifetimes. The minority carrier lifetimes in Si reach many ms, again in tire absence of defects. It should be noted tliat long minority carrier lifetimes imply long diffusion lengtlis. Minority carrier lifetime can be used as a convenient quality benchmark of a semiconductor. 

The defects generated in ion—soHd interactions influence the kinetic processes that occur both inside and outside the cascade volume. At times long after the cascade lifetime (t > 10 s), the remaining vacancy—interstitial pairs can contribute to atomic diffusion processes. This process, commonly called radiation enhanced diffusion (RED), can be described by rate equations and an analytical approach (27). Within the cascade itself, under conditions of high defect densities, local energy depositions exceed 1 eV/atom and local kinetic processes can be described on the basis of ahquid-like diffusion formalism (28,29). 

Under Httle or no illumination,/ must be minimized for optimum performance. The factor B is 1.0 for pure diffusion current and approaches 2.0 as depletion and surface-mode currents become important. Generally, high crystal quality for long minority carrier lifetime and low surface-state density reduce the dark current density which is the sum of the diffusion, depletion, tunneling, and surface currents. The ZM product is typically measured at zero bias and is expressed as RM. The ideal photodiode noise current can be expressed as follows ... 

Obtaining information on a material s electronic band structure (related to the fundamental band gap) and analysis of luminescence centers Measurements of the dopant concentration and of the minority carrier diffusion length and lifetime... 

Thus, in order to reproduce the effect of an experimentally existing activation barrier for the scission/recombination process, one may introduce into the MC simulation the notion of frequency , lo, with which, every so many MC steps, an attempt for scission and/or recombination is undertaken. Clearly, as uj is reduced to zero, the average lifetime of the chains, which is proportional by detailed balance to Tbreak) will grow to infinity until the limit of conventional dead polymers is reached. In a computer experiment Lo can be easily controlled and various transport properties such as mean-square displacements (MSQ) and diffusion constants, which essentially depend on Tbreak) can be studied. 

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