Shockley-Read-Hall recombination

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. 

Trap-assisted recombination was first proposed by Shockley et al. and it is also known as Shockley-Read-Hall recombination. This recombination model was first used to study the charge recombination in inorganic semiconductors, and later it was introduced into the field of OSC. This type of recombination involves a trapped charge and a mobile charge with the... 

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. 

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. 

To find the occupation statistics for a trap - the Shockley-Read-Hall statistics [232,233] - we need to consider the four processes shown in Fig. 10. A single trap can capture and emit an electron and capture and emit a hole. If the same trap captures a hole and an electron, one recombination event happens. If a trap captures and emits an electron or a hole, the trap will have slowed down transport only. Table 3 summarizes the four rates that we need to consider. However, the four rates are not independent of each other in quasi-equilibrium. Because in equilibrium, detailed balance between inverse processes must be obeyed, the capture and emission processes must be connected. In addition, in thermal equilibrium the occupation function for all charge carriers (free or trapped, electrons or holes) must be the Fermi-Dirac function in thermal equilibrium, i.e. 

Fig. 10 Definition of the four rates of capture and emission of electrons and holes by a single trap level. These four rate equations are the basis of Shockley-Read-Hall statistics, which defines the occupation probability and the recombination rate via this trap...

Shockley-Read (SR) [55] or Shockley-Read-Hall [56] generation-recombination processes proceed via imperfections ( traps ), i.e., centers of capture in semiconductor crystal lattice. Acceptor levels capture electrons and donor levels holes, or they emit them at rates dependent on the nature and the concentration of traps, as well as on the occupancy of energy levels. At that, within the bandgap there may be one or more impurity levels. SR mechanisms are more marked in technologically lower-quality material (with a larger concentration of defects and impurities), i.e., this mechanism is not fundamental. 

Specific energy, the rate law for this type of recombination has been described by several workers and is referred to as the Shockley-Read-Hall (SRH) model. The expression for this recombination rate, Rsgjj (cm s" ), is... 

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-... 

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]... 

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

Surface recombination is analyzed using Hall-Shockley-Read recombination analysis. With the usual approximation, the recombination flux, Jr, is given by... 

The influence of deep-level states or traps on the statistics of electron-hole recombination was first described by Shockley and Read and Hall. Deep-level states, as their name implies, lie close to the middle of the energy bandgap of the semiconductor. Due to the large energy separation from the valence-band and conduction-band edges, deep-level states are not fully ionized at room temperature. In contrast, shallow-level states are those considered to be fully iordzed at room temperature due to thermal excitation. 

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