Shockley-Read-Hall Processes

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. 

The interaction between a deep-level state and electrons and holes can be described by processes 1 to 4 represented in Figvire 12.4. Process 1 involves the emission of a valence-band electron to the deep-level state after receiving energy (Et — Ep). This can also be thought of as hole emission from the deep-level state to the valence band since an electron vacant deep-level state has been filled by a valence-band electron, thus leaving a hole in the valence band. 

Process 3 involves a trapped electron being emitted to the conduction band after receiving an amoimt of energy equal to (Ec — E() from optical or thermal excitation. Process 4 involves a conduction-band electron that comes in the vicinity of a deep-level state and is trapped by it. In order for this electron to be trapped, it must lose an amount of energy equal to (Ec — Ef) by radiative (photon) or non-radiative (phonon) processes. 

Process 5 represents excitation of a valence-band electron to the conduction band, thus producing an electron and a hole. The reverse process 6 can be considered to be recombination of an electron and hole. Processes 5 and 6 do not require presence of deep-level states. 

The spatial dependence of the energy bands can be described in terms of a single potential variable. In terms of a potential referenced to the potential in the electrically neutral region of the semiconductor, the vcilence-band energy can be expressed as 

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

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. 

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. 

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. 

Nowadays an important position belongs to the infrared detectors incorporating the mentioned wide-bandgap semiconductor barrier [368-370] (the BIRD detector —Barrier Infrared Detector). Maimon and Wicks proposed to use unipolar BIRDs —i.e., the built-in barrier layer blocks one carrier type, but allows free flow of the other type [371]. Such structures are for instance nBn. Ting et al. proposed the use of complementary barriers, one for electrons, another for holes, positioned at different depths [372]. Itsuno et al. analyzed NBvN and nBn detectors (where B stands for Barrier) [373, 374]. In their 2013 paper Martinyuk et al. quoted that besides Auger suppression the BIRD devices also suppress Shockley-Read-Hall g-r processes [375]. 

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