Indirect recombination

For Si, in order for an electron at the bottom of the CB to recombine with a hole from the top of the VB, the momentum of the electron must shift from k h to ky, (Figure 4.5b). However, this is not allowed by the Law of Conservation of Momentum. Instead, an indirect recombination mechanism must take place, wherein the electron is captured by an interstitial defect with energy E, which facilitates its relaxation to the top of the VB. This process is accompanied by the emission of phonons, or lattice vibrations rather than light emission. 

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. 

Fig. 1. Schematic diagram of semiconductor materials showing band gaps where CB and VB represent the conduction band and valence band, respectively and 0 and 0, mobile charge. The height of the curve represents the probabiUty of finding an electron with a given momentum bound to an N-isoelectronic impurity, (a) Direct band gap the conduction band minimum, F, is located where the electrons have 2ero momentum, ie, k = 0. The couples B—B, D—A, B—D, and B—A represent the various routes for radiative recombination. See text, (b) Indirect band gap the conduction band minimum, X, is located...

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. 

Using the same threshold ionization mass spectrometry setup, Perrin et al. [317] have measured the temporal decay of radical densities in a discharge afterglow. From these experiments the coefficient p for the radical SiH. has been determined to be 0.28, which is in agreement with already known results from other (indirect) experimental approaches [136,137,318]. For the Si2H5 radical is determined to be between 0.1 and 0.3. The coefficient p for atomic hydrogen on a-Si H lies between 0.4 and 1, and is thought to represent mainly surface recombination to H. ... 

D3) absorption and emission lines (from n = 3 states) in H2 (D2) plasmas were strongly Doppler-broadened which seems to indicate high, nonthermal energies (about 0.3 eV) of the absorbing or emitting H3 molecules. The energy is close to that expected if the excited (n = 3) H3 molecules were formed by recombination of Hj, but in Amano s work no Hj ions should have been present. Perhaps, the fast H3 molecules are produced from H + H2 collisions, and the spectroscopic observations provide indirect evidence for the existence of H3 molecules. The conjecture needs to be examined by more detailed work. 

Excited states of hydrocarbon molecules often undergo nondissociative transformation, although dissociative transformation is not unknown. In the liquid phase, these excited states are either formed directly or, more often, indirectly by electron-ion or ion-ion recombination. In the latter case, the ultimate fate (e.g., light emission) will be delayed, which offers an experimental window for discrimination. A similar situation exists in liquid argon (and probably other liquefied rare gases), where it has been estimated that -20% of the excitons obtained under high-energy irradiation are formed directly and the rest by recombination (Kubota et al., 1976). 

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