Shockley-Read Processes

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. 

An energy level of a trap with an energy , between and Ey (index f means trap ) may capture an electron from the conduction band, emit an electron into the conduction band (thermal emission), capture a hole or capture an electron from the valence band. In the course of this process, electron energy may be converted into a phonon or a light quantum, depending on the nature of the center of capture. In calculation of this process we assume that the time between the transition of a 

Let us denote the Fermi function of probability for a capture center to be occupied by an electron by/ and the probability of the occupancy of a state in the conduction band by. The recombination rate of an electron from the conduction band (in the energy interval dE around the value E) on traps in a unit volume of material is proportional to N(E)dE (concentration of electrons with energies within the interval under consideration) and N, (concentration of vacant traps). Let Csr = be the average probability per unit time for an electron from the interval dE to be captured at an empty center. Here v = [Skt T/nm Y is thermal velocity of electron and cr is experimentally determined effective cross section of the electron capture at the center. The parameters Op and Vp are defined for holes in an equivalent manner. The rate of recombination at traps is 

Here a denotes the coefficient of capture of an electron at a center 

The probability of electron emission from a trap into an energy interval dE within the conduction band is proportional to the concentration of fiUed traps and may be represented by an expression in a form of (1.60) as 

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Shockley-Read recombination rate is shown in Fig. 3.15. Its decrease is very modest, i.e., exclusion cannot be utilized for an efficient decrease of Shockley-Read processes. 

Figure 3.35 shows Shockley-Read generation (dotted line) and recombination (solid line). Carrier extraction relatively weakly influences Shockley-Read processes, and this is especially valid for generation. Naturally, the level of SR rates is strongly sensitive to the methods of photodetector single crystal growth. Thus in high-quality materials the levels of Shockley-Read g-r rates may be much lower than presented in Fig. 3.34. Their spatial distribution, however, qualitatively follows a similar functional dependence.

We consider a v-lype magnetoconcentralion detector. The crossed electric and magnetic field cause the depletion of a part of its volume. In an ideal case this would mean that the Auger g-r processes would be sufficiently suppressed to be negligible in comparison to radiative recombination. We further assume that material is sufficiently pure to allow to neglect Shockley-Read processes in bulk. Thus the generation term in the continuity equation reduces to the radiative term. Besides the bulk radiative lifetime we include in it a term of the form US (5 is surface recombination rate which is of SR nature). Then we assume that both of these terms have the identical dependence on the carrier concentration, so that the... 

Fig. 3.50 Shockley-Read process rates across a magnetoconcentration Hgi xCdxTe photodetector for different values of bias voltage. Solid recombination, dotted generation. Numbers near each curve denote bias voltage in volts, x = 0.186, T = 220 K, S = 2 T, = 5 x 10 m. ...

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... 

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. 

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) ... 

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

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... 

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. 

If we look at the definitions of generation and recombination rates (1.85) and (1.86) we conclude that we may try to minimize Shockley-Read, Auger and radiative component of generation and recombination. It was already mentioned in Sect. 1.4.3 that SR processes are not fundamental and that a convenient fabrication technology could reduce them to a low enough level. On the other hand. Auger processes (and especially recombination) are strongly dependent on carrier... 

For instance, to bring an n-type detector to the limit of Auger process suppression, electron concentration must be either equal to the product of nonequilibrium depletion factor and intrinsic concentration or lower than it (if the Shockley-Read noise component can be neglected). Thus, the product between the nonequilibrium depletion factor and intrinsic concentration represents the highest allowed level of doping of a given semiconductor for a given temperature. 

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]. 

The photon management methods also represent a pathway toward a decrease of generation-recombination processes and the related noise phenomena and pose a viable way to overcome obstacles that until recently appeared insurmountable. The mechanism of photon recycling by cavity enhancement ensures direct suppression of radiative noise, while the possibility to localize fields at a subwavelength level ensures vastly smaller photodetector volumes, thus helping overcome problems with Auger and Shockley-Read phenomena as well. 

Since the stmctures and processes used for detector enhancement are interconnected, it often occurs that an approach introduced because of one effect also brings to an improvement of another one. A typical example can be found with methods for optical trapping that were introduced to improve the optical path through the detector (absorption coeflhcient-thickness product), to turn out that these methods not only improve radiative lifetime through photon recycling but even Auger and Shockley-Read lifetimes due to a decrease of overall dimensions of the detector. 

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