time unit) are shown.
where Δt = t2 −t1 is called the rate window of the measurement (see Fig. 1). It can be seen from Fig. 1 that for the transient with the high emission rate (i.e. en = 1), ΔC is effectively zero. For the transient with the low emission rate (i.e. en = 0.01), ΔC is small as compared with the one with the moderate emission rate (i.e. en = 0.1). It can be shown that maximum DLTS signal ΔC maximum occurs at:
Accordingly, the DLTS spectrum is obtained by fixing the rate window Δt and measuring the ΔC as a function of temperature. A peak appearing in the DLTS spectrum at the temperature of Tpeak associates with the maximum DLTS signal and thus the corresponding emission rate at the temperature of Tpeak is given by:
Figure 2. (a) Examples of the DLTS spectra taken from GaN Schottky diode using different rate windows; (b) The corresponding Arrhenius plot, i.e. enT−2 against 1/T.
Thus applying different rate windows Δt will result in peaks occurring at different temperatures (for example, Fig. 2(a) which is the DLTS spectra of a GaN film). 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),
