ET can be found by plotting Arrhenius plot of enT−2 against 1/T (Fig. 2(b)), with the corresponding emission rate en given in Eq. (10))
Additionally, there are other variants of the junction spectroscopic methods like Laplace deep level transient spectroscopy (LDTLS) which is the high resolution version of DLTS, admittance spectroscopy, optical DLTS, minority carrier transient spectroscopy (MCTS) and etc. More details of the junction spectroscopies can be found in Peaker et al. [19] and references therein.
3. Optical Characterization
There are many techniques used to characterize the materials optical properties, as reviewed for example by Davies [20], Dragoman and Dragoman [21], Schroder [6], and Grundmann [8]. These methods include studying the luminescence, optical absorption, and inelastic Raman scattering, etc. Configuration coordinate diagram of defect can be used to understand the processes of luminescence, light absorption and nonradiative capture, as reviewed by Alkauskas et al. [22].
Figure 3. (a) The electron hole pair generation; and (b–e) transitions that could lead to photon emissions.
In particular, the luminescence spectroscopy in forms of either photoluminescence (PL) or cathodoluminescence (CL), is widely employed method to identify optical active defects. A laser with photon energy larger than the material band gap is usually employed to excite electrons from valance band to conduction band for PL, while the excitation in CL is achieved via the accelerated electrons (Fig. 3(a)). The depth resolved CL can also be carried out to obtain the defect depth profiles by varying the electron incident energy while keeping the excitation power constant [23, 24], while the depth information of electron energy loss can be obtained from the Monte Carlo simulations [25].
Characteristic “defect emission” occurs as a result of the electron transitions from the conduction band to the defect level, or from the defect level to the valance band (Figs. 3(c) and (d)), so that the photon energy emitted can be assigned to a specific defect [26]. Otherwise, the donor-acceptor pair (DAP) emission is originated from the recombination between an electron of a neutral donor and a hole of a neutral acceptor (Fig. 3(e)) and the emitted photon energy is:
where Eg is the band gap, while R is the distance between the donor and acceptor, ED and EA are the donor and acceptor energy levels, respectively. Free recombination between free electrons and holes yields photons with energy equal to the band gap. However, due to the Columbic attraction, an electron at the conduction band and a hole at the valance band can also form a hydrogen like state called free exciton. The photon energy emitted from the free exciton recombination is:
where EX is the exciton binding energy. For materials with low exciton binding energy (like GaAs, EX ∼ 4.2 meV), free exciton emission is only observed at low temperatures. For materials having large exciton binding energy (like ZnO, EX ∼ 60 meV), free exciton emission is observed at the room temperature. Excitons can be bound to donors, acceptors or other potential fluctuations. For example, the transition energy for the donor bound exciton (D0X) is given by:
where Q is the binding energy of the exciton to the donor.
4. Structural Characterization
There are many spectroscopic techniques to reveal the structural properties of defects in materials. High resolution transmission microscopy (HRTEM) and scanning probe microscopy (SPM) are capable of visualizing the defect structure in atomic scale (Schwander et al. [27]; Jäger and Weber [28] and references therein) and their applications in studying defects in 2D nanomaterials are discussed in Chapter 2 of the present book. Nuclear and ion-beam analysis methods can be used for obtaining depth impurity profiles as well as lattice defect distributions [29, 30]. For example, Rutherford backscattering spectroscopy (RBS), RBS with channeling, (RBS/C), nuclear reaction analysis (NRA), secondary ion mass spectrometry (SIMS) are widely employed techniques for studying defects in functional materials.
Positron annihilation spectroscopy (PAS) is a non-destructive probe for neutral or negatively charged vacancy type defects in semiconductors, reviewed by Schultz and Lynn [31], Krause-Rehberg and Leipner [32], Coleman [33], and Tuomisto and Makkonen [34]. Positron is the anti-particle of electron having the same mass but opposite charge. Positron-electron annihilation produces two gamma photons (511 keV because of mass-energy conservation), if the positronium process is not involved. Positronium (the hydrogen-like state of a positron and an electron) does not form in metals or semiconductors because the bound positron-electron pair in the degenerate electron gas would polarize the medium and then screen the positron-electron interaction. However, positronium could form in solid surfaces, amorphous materials, some molecules and ionic solids.
In more details, positrons injected into the sample from a monoenergetic positron beam or a β+ radioactive source like 22Na rapidly thermalized (∼10 ps) and then undergo diffusion. The positron could annihilation in the delocalized state (or bulk state) during the diffusion. Alternatively, neutral or negatively charged vacancy type defect acts as trap for the positively charged positron. If the positron binding energy of the positron trap is large enough to prohibit thermal de-trapping, the positron will finally annihilate in the trapped state. This implies that the annihilation from the different positron states are in competition. The principal of PAS is that the outgoing gamma photons originated from the annihilation between the positron trapped in the defect and its surrounding electron, carry the information of electronic environment of the defect site, which is a fingerprint of the defect. Using the monoenergetic positron beam as the positron source, the positron energy can be varied up to ∼30 keV, i.e. corresponding to the implantation depth of up to several hundred nm e.g. in Si. Thus, the defect depth profile can