Recombination lifetime

Radiative recombination of minority carriers is tlie most likely process in direct gap semiconductors. Since tlie carriers at tlie CB minimum and tlie VB maximum have tlie same momentum, very fast recombination can occur. The radiative recombination lifetimes in direct semiconductors are tlius very short, of tlie order of tlie ns. The presence of deep-level defects opens up a non-radiative recombination patli and furtlier shortens tlie carrier lifetime. 

Figure 7. Rate data for photoinduced charge separation in the dyads 2(n). Charge separation rates, ka, were measured in THF. Dipole moments, n, were measured in benzene as were the charge recombination lifetimes, r,T, with the exception of 2(13), whose Tcr was measured in 1,4-dioxane (that for 2(4) was measured in cyclohexane).

It is important to consider the magnitude of the recombination rate in studies of this type. For methane, is 1.7 x 10 sec at 93 K [81]. Thus if a concentration of ions of 0.1 pM was formed in the pulse, the electrons would disappear with a first half-life of 50 psec. For 2,2,4-trimethylpentane, k,. is 3.6 x 10 sec and for a similar concentration of electrons, the recombination lifetime would be a few nanoseconds. Where the electron mobility is lower, the recombination rate is slower. For methylcyclohexane,... 

Additionally, in order to examine the charge-recombination dynamics we turned to complementary nanosecond transient absorption measurements. Once more, the spectral fingerprints of the radical ion pair state emerged immediately after the laser pulse and their decays yielded charge-recombination lifetimes in the order of 4.0 ps (Fig. 9.38). 

FIGURE 4 Temperature dependence of the recombination lifetimes of the excitonic transitions in Ill-nitride epilayers and MQWs. 

For reasonable functioning of these low cost, low mobility semiconductor solar cells, a considerable amount of the photogenerated chemical potential epc — fv of the electron hole ensemble must be used for carrier transport. An acceptable charge collection may be achieved if the extraction times for electrons and/or holes are smaller than their recombination lifetimes, i.e.,... 

We then translate them into times for extraction across the distances t d to the n-mombraiie for the electrons and (1 — )d to the p-membrane for the holes. With (4.88), the conditions for the recombination lifetime are... 

With identical recombination lifetimes Trec,e = Trec,h = Trec, the optimum ratio of electron and hole travel lengths becomes... 

Improved Carrier Extraction by Intercalating Membranes. With light trapping, the condition for good extraction of electrons and holes requiring Le,h l, is also relaxed, since a smaller thickness of the solar cell is possible. For low mobility organic materials, this condition is still a problem. It ensures that electrons and holes generated in the absorber reach the membrane within their recombination lifetime. They can then pass into the external circuit. The distance of the membranes, however, is not limited by the thickness l of the absorber, as can be seen in Fig. 4.11, and can be made arbitrarily short. 

As a result of light trapping and intercalation, thin film solar cells can be made of a thickness /, which apparently violate the condition Le,h l 1 /a. Even with light trapping, the thickness l must be of the order of the penetration depth /a of the light. The diffusion length, on the other hand, can be arbitrarily small, if caused by a small diffusion coefficient. The recombination lifetime should always be as large as possible and should approach the radiative lifetime. 

Fig. 8.31. Calculated IMPS responses showing the influence of the electron recombination lifetime r. Film thickness 12 xm, D= I0 4cm2s, a = lO cm-1. Illumination from the substrate side. Note that the characteristic frequency tends towards 1/r as r becomes smaller.

Where R is the reflectivity and d is the thickness. Very accurate values of R and T are needed when the absorptance, (id, is small. The technique of photothermal deflection spectroscopy (PDS) overcomes this problem by measuring the heat absorbed in the film, which is proportional to ad when ad 1. A laser beam passing just above the surface is deflected by the thermal change in refractive index of a liquid in which the sample is immersed. Another sensitive measurement of ad is from the speetral dependence of the photoconductivity. The constant photocurrent method (CPM) uses a background illumination to ensure that the recombination lifetime does not depend on the photon energy and intensity of the illumination. Both techniques are capable of measuring ad down to values of about 10 and provide a very sensitive measure of the absorption coefficient of thin films. 

Illumination creates excess electrons and holes which populate the extended and localized states at the band edges and give rise to photoconductivity. The ability to sustain a large excess mobile carrier concentration is crucial for efficient solar cells and light sensors and depends on the carriers having a long recombination lifetime. The carrier lifetime is a sensitive function of the density and distribution of localized gap states, so that the study of recombination in a-Si H gives much information about the nature of the gap states as well as about the recombination mechanisms. 

The recombination process comprises two sequential steps, as illustrated in Fig. 8.1. An excited electron or hole first loses energy by many transitions within the band, in which the energy decrements are small but frequent. This process is referred to as thermalization. The thermalization rate decreases as an electron moves into the localized band tail states and the density of available states is lower. Eventually the electron completes the recombination by making a transition to a hole with the release of a large energy. Recombination lifetimes are generally much longer than the thermalization times, so that the two processes usually occur on distinctly different time scales. 

In the first case, pairs are isolated from each other and the recombination is monomolecular, with a rate which is independent of illumination intensity. The non-geminate electrons and holes act as independent particles and the recombination rate is proportional to the product of the two densities (here assumed equal). The observable difference is a recombination lifetime which is independent of the excitation intensity for geminate recombination, but which decreases with increasing illumination intensity for non-geminate recombination. The simple rate equations also predict a different form of the time dependence, but a more realistic model must also include a distribution of recombination rates due to the tunneling recombination. 

Fig. 8.16. Distribution of the electron-hole pair distances showing the large range of recombination lifetimes (Biegelsen et al. 1983).

The reconciliation of these two apparently conflicting results is quite interesting and is connected to the broad distribution of recombination lifetimes. Those electron-hole pairs which are created with small separations are more likely to result in geminate recombination than the more distant pairs. The close pairs are also more likely to contribute to the luminescence and the distant pairs to LESR. Thus the two experiments are selectively measuring different parts of the distribution. The density of geminate pairs of separation, R, is given by. 

The second expression uses the experimental information about the conductivity prefactor derived in Eq. (7.19). The descriptions of the photoconductivity in terms of the recombination lifetimes or the quasi-Fermi energies are equivalent. 

The photoconductivity response of a-Si H nipi structures has an extremely long recombination lifetime. A brief exposure to illumination causes an increase in the conductivity which persists almost indefinitely at room temperature (Kakalios and Fritzsche 1984). An example of this persistent photoconductivity is shown in Fig. 9.32. The decay time exceeds 10 s at room temperature and decreases as the temperature is raised, with an activation energy of about 0.5 eV. 

Ion-recombination lifetimes /r = ( ) range between about 10 — 10 s (Fig. 2). When compared with ion lifetimes /a against collision with aerosols [36] (also shown in Fig. 2), /r is much smaller throughout the stratosphere. 

Fig. 2. Typical ion-recombination lifetimes (

The extremely large sensitivity of PACIMS is due to both the relatively large ion-recombination lifetime, /r, and the large rate coefficients, k, for ion-molecule reactions. Assuming that an ion, C, is formed by... 

Figure 21. Dependence of the lifetime of the CS state of 23( ) on the number of intervening a bonds for benzene and dioxane solvents. The straight lines drawn through the data (extended as a dashed line for benzene) correspond to an exponential dependence of the charge recombination lifetime, on n [74], Note that the experimentally determined charge recombination lifetime. t , is not necessarily equal to l/it , because it also includes a contribution from the lifetime of the BET process...

The effect of a limited mobility of holes in the material may be accounted for in Eq. (1) by using a parameter called the mobility field, E, which is the electric field necessary for a hole to drift 1 radian across a sinusoidal intensity pattern in one hole recombination lifetime. The assumptions of long lifetime and high mobility make the mobility field small in comparison with the projection of the poling field along... 

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