The Radiative Recombination

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. 

In LEDs, electrons are generally injected into a type active layer. The internal quantum efficiency, ie, the photons per injected electrons, is given by the radiative recombination rate divided by the total recombination rate ... 

Thushigh internal quantum efficiency requires short radiative and long nonradiative lifetimes. Nonradiative lifetimes are generally a function of the semiconductor material quaUty and are typically on the order of microseconds to tens of nanoseconds for high quahty material. The radiative recombination rate, n/r, is given by equation 4 ... 

Direct and Indirect Energy Gap. The radiative recombination rate is dramatically affected by the nature of the energy gap, E, of the semiconductor. The energy gap is defined as the difference in energy between the minimum of the conduction band and the maximum of the valence band in momentum, k, space. Eor almost all semiconductors, the maximum of the valence band occurs where holes have zero momentum, k = 0. Direct semiconductors possess a conduction band minimum at the same location, k = O T point, where electrons also have zero momentum as shown in Eigure la. Thus radiative transitions that occur in direct semiconductors satisfy the law of conservation of momentum. 

For a simplified case, one can obtain the rate of CL emission, =ft GI /e, where /is a function containing correction parameters of the CL detection system and that takes into account the fact that not all photons generated in the material are emitted due to optical absorption and internal reflection losses q is the radiative recombination efficiency (or internal quantum efficiency) /(, is the electron-beam current and is the electronic charge. This equation indicates that the rate of CL emission is proportional to q, and from the definition of the latter we conclude that in the observed CL intensity one cannot distii pish between radiative and nonradiative processes in a quantitative manner. One should also note that q depends on various factors, such as temperature, the presence of defects, and the... 

The intensity /k, (2 a) of a spectral emission line, i. e. the radiative recombination of an electron of a species A from a higher energy level k to the lower level i, is characteristic of a sputtered element or molecule A and is calculated by use of the equation ... 

An approximation of the lifetime in PS at RT using an electron-hole pair density equal to one pair per crystallite and the radiative recombination parameter of bulk silicon give values in the order of 10 ms [Ho3]. The estimated radiative lifetime of excitons is strongly size dependent [Sa4, Hi4, Hi8] and increases from fractions of microseconds to milliseconds, corresponding to an increase in diameter from 1 to 3 nm [Hy2, Ta3], as shown in Fig. 7.18. For larger crystallites a recombination via non-radiative channels is expected to dominate. The experimentally observed stretched exponential decay characteristic of the PL is interpreted as a consequence of the randomness of the porous skeleton structure [Sa5]. 

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],...

It is clear both experimentally and theoretically that the radiative recombination of two atoms, without a third body, is an improbable process. Experimentally, such... 

Of all the radiative recombinations of type A+BC -> ABCC, the reaction H+NO is the best from the spectroscopic point of view. Only one electronic transition is known, A 1A. Unlike the cases discussed up to now, the... 

The study of the radiative recombination of excitons makes it possible to investigate the influence of the radiation-stimulated destruction of C60 fullerenes (partially of C70) on changes of the singlet states within the energy gap. It is known that the emission of excitons in this case is the result of the presence of own dimeric traps [11] and X-centers, caused by the chemically bound with fullerenes and intercalated impurities [8], and also of taking into account the corresponding phonon states. 

Fig. 18.7. The integral over the bound-free Gaunt factor which enters the expression for the radiative recombination coefficient. Results are for the k distribution family for capture into the ground n = 1 shell of hydrogen. The curves are generated by numerical quadrature over the distribution function. The limiting Maxwellian curve is the analytic expression elH kT Ei(Ib /ET)/T 2 and corresponds to k —> oo. The x-axis coordinate is Tefr = 2E/Z...

The radiative recombination rate, for a transition between an upper and lower state emitting a photon of energy hto, is given by the Fermi golden rule,... 

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