Recombination time

B. J. Schwartz, J. C. King, J. Z. Zhang, and C. B. Harris, Direct femtosecond measurements of single collision dominated geminate recombination times of small molecules in liquids. Chem. Phys. Lett. 203(5-6), 503-508 (1993). 

Williams (1964) derived the relation T = kBTrQV3De2, where T is the recombination time for a geminate e-ion pair at an initial separation of rg, is the dielectric constant of the medium, and the other symbols have their usual meanings. This r-cubed rule is based on the use of the Nernst-Einstein relation in a coulom-bic field with the assumption of instantaneous limiting velocity. Mozumder (1968) criticized the rule, as it connects initial distance and recombination time uniquely without allowance for diffusional broadening and without allowing for an escape probability. Nevertheless, the r-cubed rule was used extensively in earlier studies of geminate ion recombination kinetics. 

Fig. 7.18 The radiative recombination time r as a function of the blue shift of the photon energy AE from the bulk silicon band edge zero-phonon transitions (dots) TO phonon-assisted transitions (line). This scatter plot shows the radiative time for each member of an ensemble uniformly distributed around a cubic geometry. The top scale indicates the equivalent cube size. Redrawn from [Hy2],...

The main experimental results of charge carrier generation in PVC was explained in the frame of the Pool-Frenkel model [28-30]. The dependence of the recombination time on electric field was due to the change of the mobility in the electric field. Germinate recombination of the electron-hole pairs was investigated by means of luminescence decay characteristics [31]. 

A simulation has been carried out [105, 106, 119] of the process of accumulation of the immobile Frenkel defects restricted by tunnelling recombination of dissimilar defects, as it is observed in many solid insulators. As follows from Chapter 3, in contrast to the ionic process of instant annihilation of close pairs of the vacancy-atom type, it is characterized by a broad spectrum of recombination times. Thus, the probability for a pair of chosen defects that lie at the relative distance r to survive for r seconds is... 

The most rapid bimolecular reactions must be the ion-molecular ones. Their duration can be limited only by the time of collision, thus being 10 13-10 12 s. The recombination time of radicals that have escaped from the cage depends on their concentration in the track. For close pairs of radicals the recombination may already begin in 10 us. From this moment on we can consider the chemical stage of radiolysis to have begun. 

A further disadvantage of using absorptive effects in semiconductors is the recovery time of the excited electrons which are responsible for the large nonlinearity. Recombination times of typically 100 ps to some nanoseconds limit the repetition rate of the switching severely. 

The tacit assumption here is that the recombination time r between oppositely charged carriers is larger than the transit time Tt of the carriers so that the measured current is equal to the rate at which carriers are being produced (multiplied by e to convert the photon current into electrical current). Any electric field dependence of this current then reflects the electric field dependence of the QE of photogeneration. However, in the presence of substantial carrier recombination (r < Tt) the current with blocking contacts is... 

An analysis of the time dependent transient photo-reflectance gives us a good estimate of the effective pair recombination rate [8], The inset in Fig. 1(b) shows the average reflectance change as a function of the delay between pump and probe pulses at 6 K. In accordance with other BCS superconductors the effective recombination time is found to be a few nanoseconds. One important remark is that, within the experimental time resolution, no evidence of multiple decays is found. In fact, ultra-fast pump-probe measurements on MgB2 [12, 13] did not find any evidence for a double relaxation down to the ps regime. 

Taking typical values of D = 0.1 cm2s 1 and d = 20 nm, the average transit time is about 1 ps, which is much shorter than the recombination time so that most charge carriers can reach the surface before recombination. 

The time scale of different steps of electron transfer along the PS I cascade system is also similar to those ofthe electron jump in bacterial RCs. The primary transfer from the excited chlorophyll dimer, primary donor P, to A0 takes place with a time constant of about 25 ps. The next step from A0 to a secondary acceptor occurs in 200-600 ps. The recombination time constants ofP+ with reduced intermediate acceptors increase as the electron moves along the chain, and range from nanoseconds for transition A0 — P+ to millscconds for transition reduce FX to P+ (Shuvalov and Krasnovsky, 1981 Schloder et al., 1998 Shmidt et al., 2000 Shmidt et al., Guergova-Kuras et. al., 2001 Setif et al., 2001 Vassiliev et all., 2001 Gobets et al., 2001 and references therein). Kinetic and spectral inhomogenity of samples of PS I has been reported (Shmidt et al., 2000 ... 

The classic treatment of carrier recombination can be related to the notion of the recombination time. The recombination time represents a combination of the carrier motion time (im), i.e. the time to get the carriers within capture radius (it is often assumed to be the Coulombic radius rc = e2/An o kT), and the elementary capture time (tc) for the ultimate recombination event (actual annihilation of charge carriers), tree1 = m1 -I Tc 1 (cf. Fig. 3). Following the traditional description of recombination processes in ionized gases, a Langevin-like [22] and Thomson-like [23] recombination can be defined if Tcsolid-states physics, these two cases have been distinguished... 

The bimolecular recombination efficiency (j/vr) is determined by the recombination time, Trec, and transit time xt, of the carriers to the electrodes, as defined in Preface and Sec. 5.4,... 

The width of the recombination zone is directly related to the EL efficiency of LEDs, through its definition as a distance traversed by a carrier during the recombination time, Trec [2]... 

Here, tt = d//xF is the carrier transit time dependent on the carrier mobility, n, and electric field, F, operating in the sample. The bimolecular decay of holes and electrons can be expressed by the recombination time... 

To get a better physical picture of the phenomena underlying PR, it is convenient to replace the rate constants by their inverses Trec = k, and xt = k x which have been defined as the recombination time (292) and carrier transit time (248), respectively. Then,... 

Photoluminescence is the radiation emitted by the recombination process and as such is a direct measure of the radiative transition. Information about non-radiative recombination can often be inferred from the luminescence intensity, which is reduced by the competing processes (Street 1981a). The most useful feature of the luminescence experiment is the ability to measure the emission spectrum to obtain information about the energy levels of the recombination centers. The transition rates are found by measuring the transient response of the luminescence intensity using a pulsed excitation source. Time resolution to about 10 s is relatively easy to obtain and is about the maximum radiative recombination rate. The actual recombination times of a-Si H extend over a wide range, from 10 s up to at least 10- s. 

One of the characteristic features of the luminescence in a-Si H is the broad distribution of recombination times. Fig. 8.14 shows the luminescence decay extending from 10" s to 10 s (Tsang and Street 1979). The data are inverted in the lower part of the figure to give the distribution of lifetimes, which has its peak at 10" -10" s at low temperature and is 2-3 orders of magnitude wide. The shape of the distribution is sensitive to the excitation intensity for reasons discussed shortly and the time constants are even longer at very low intensity. 

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