Shockley-Read

By including terms to describe the rate of emission of electrons and holes from filled and empty surface states respectively, constraining the total number of surface states to Nt by N. + Ng = Nt and assuming that the states do not interact, the electron-hole recombination at. tile.surf ace has been analyzed -1— in analogy with Hall-Shockley-Read recombination. These methods are important in the study of semiconductor-... 

Prompt Luminescence. Before going on to discuss the mechanisms by which the stored energy can be released from the lattice we shall pause here to discuss what happens to the electronic excitation energy if it is not stored in the lattice by any of the mechanisms discussed above. In wide-band-gap insulators such as those discussed here direct band-to-band recombination of electrons with holes is not generally observed and indirect, Shockley-Read recombination via localized states in the band gap is the main cause of electron-hole recombination. The recombination process results in the emission of phonons or photons. Since we are interested in luminescence emission in this paper it is the emission of photons that we shall consider. The emission wavelength can be characteristic of the position (in terms of energy) of the localized state within the band gap, or via the process of energy transfer, it may... 

Fig. 60. Rate-limiting regime for Shockley Read statistics the Roman numerals denote the dominance of one particular term in eqn. (352). In terms of the denominator of eqn. (351), the regimes are defined by I, re > re, p, p, II, ret > re, p, pt II2> p, > re, p, re, and III, p > re, p, re,. The single arrows indicate the rate-limiting step in each case.

Recombination is evidently controlled by trapping into defect states, consistent with the other recombination measurements. The recombination transitions through defects with two gap states are illustrated in Fig. 8.24, with electrons and holes captured into either of the two states. This type of recombination is analyzed by the Shockley-Read-Hall approach which distinguishes between shallow traps, for which the carrier is usually thermally excited back to the band edge, and deep traps, at which the carriers recombine. A demarcation energy, which is usually close to the quasi-Fermi energy, separates the two types of states. The occupancy of the shallow states is determined by the quasi-equilibrium and that of the deep states by the recombination processes. No attempt is made here at a comprehensive analysis of the photoconductivity, which rapidly becomes complicated. Instead some approximate solutions are derived which illustrate the processes. 

Many (17), and Wang and Wallis (18), it is explicitly assumed that in adapting the Shockley-Read model (19) of recombination via traps to the surface the volume and surface portions of die conduction bands are in good thermodynamic equilibrium. Garrett (20) has shown, however, that in the case where the region of space charge is much wider than the mean free path of the carriers, the barrier may become the limiting factor. 

According to this equation, the lifetime of excited carriers decreases with increasing majority carrier density and consequently with doping. A similar result is obtained if the recombination process occurs via impurity centers (Shockley-Read equation [20]), which will not be shown here. The recombination rate also influences the stationary density of electrons and holes produced by light excitation. One obtains from Eqs. (6) and (7) ... 

Surface recombination in most of these treatments invokes the Hall-Shockley-Read model [226, 227]. Defining the Gartner limiting expression (Eq. 24) as <1>g, we obtain [14]... 

Figure 12.4 Schematic representation of electronic transitions, including Shockley-Read-Hall processes for a deep-level state.

Figure 16.9 Electrical circuit analogue developed to account for the influence of two Shockley-Read-Hall electronic transitions through deep-level states. See the discussion of Figure 12.8.

In the absence of bimolecular recombination, experimentally verified via the intensity dependence of the steady state photocurrent, and of defect-catalyzed recombination ("Shockley-Read recombination") ( ), K must con-... 

This is the so-called Shockley-Read equation describing recombination via traps. It also plays an important role in the description of recombination processes via surface states, as discussed in Chapter 2. In the above equation one may also replace n and pt by the relations... 

As mentioned above, the slope of the log y l jn-potential dependence given in Fig. 7.35, has a slope of 92 mV/decade. According to the Shockley-Read recombination model (see Section 1.6) which is valid for a recombination in the bulk of a semiconductor, a slope of 60 mV/decade would be expected. In addition, recombination can occur within the space charge layer of a semiconductor which leads to a slope of 120 mV/ decade [52] (see also Section 2.3). With most p-n junctions which are minority carrier devices, a slope between 60 and 120 mV has been found. Therefore, the slope of 92 mV... 

The competition between charge transfer and recombination via surface states can be treated exactly by Hall-Shockley-Read statistics, taking proper account of... 

Deep levels can be described by the Shockley-Read-Hall recombination statistics [5]. However, for a large number of deep states, the capture cross section for one type of carrier is many times larger than that for the other carrier. The state, therefore, interacts principally with only one of the band edges and can be characterised as either an electron or a hole trap. Capacitance techniques, such as DLTS (Deep Level Transient Spectroscopy), are particularly convenient for the determination of trap type and concentration. If additional experimental information is present to allow charge state determination, then the states can be characterised as deep acceptors or donors. 

G is the pair-generating function already defined in that connection, and U is a genered recombination function. For U we take the Shockley - Read singlerecombination-center formula (Shockley and Read, 1952) in the trap-free case ... 

The Shockley-Read-Hall theory assumes a steady-state condition, so that, Up=Un, since 3f = 0. A recombination theory for the more general case does not yet exist. 

The creation of an excess ehp requires an energy equal to the semiconductor band gap. When excess electron-hole pairs recombine they release this energy by one of several distinct physical mechanisms. When the energy is given to phonons or lattice vibrations, the recombination mechanism is known as multiphonon recombination or Shockley-Read-Hall (SRH) recombination. SRH recombination dominates in the indirect band gap semiconductors Si, Ge and GaP. 

Consider Pbi, Sn,Te first and refer to Appendix C. For the detector of our example the Pbo gSno 2Te alloy is required to satisfy condition 1 see (4.104). We are interested in the detector performance theoretically possible using these alloys. Accordingly for conditions 2 and 3 we assume material of high enough perfection that Shockley-Read recombination is negligible and only direct radiative recombination occurs. The electron lifetime in the p-type region of Fig. 

An untrapped hole can recombine with a conduction band electron by any of three mechanisms direct radiative, interband Auger, and Shockley-Read recombination. 

We want to determine the relative magnitudes of the diffusion current and the space-charge layer generation-recombination (gr) current in a p-n junction for a model in which there are no Shockley-Read recombination centers in the... 

---