Optical Properties of III-Nitride Semiconductors

Authored by: Plamen P. Paskov , Bo Monemar

Handbook of GaN Semiconductor Materials and Devices

Print publication date:  October  2017
Online publication date:  October  2017

Print ISBN: 9781498747134
eBook ISBN: 9781315152011
Adobe ISBN:

10.1201/9781315152011-3

 

Abstract

The optical properties of the group-III-nitride materials are obviously of direct relevance for optoelectronic applications, but experiments measuring optical properties also give information on a range of electronic properties. There is already a wealth of data in the literature on the optical properties of III-nitrides [1–4], and here we will concentrate on some of the most recent additions to the scientific knowledge. The focus, looking at the present situation concerning technical applications of these materials, has been on GaN, InGaN, and AlGaN in recent decades. AlGaN materials are important for ultraviolet (UV) emitters and high electron mobility transistor (HEMT) structures and AlGaN optical properties have accordingly been studied over the entire Al composition range. InGaN materials (with In content <50%) have also been studied extensively, and the light-emitting diode (LED) applications based on InGaN/GaN quantum structures have already been awarded a Nobel Prize in 2014. However, the applications of InN are lagging behind. The development of growth procedures for InN and In-rich InGaN has been difficult, and their optical properties were consequently much less studied in the past.

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Optical Properties of III-Nitride Semiconductors

3.1  Introduction

The optical properties of the group-III-nitride materials are obviously of direct relevance for optoelectronic applications, but experiments measuring optical properties also give information on a range of electronic properties. There is already a wealth of data in the literature on the optical properties of III-nitrides [1–4], and here we will concentrate on some of the most recent additions to the scientific knowledge. The focus, looking at the present situation concerning technical applications of these materials, has been on GaN, InGaN, and AlGaN in recent decades. AlGaN materials are important for ultraviolet (UV) emitters and high electron mobility transistor (HEMT) structures and AlGaN optical properties have accordingly been studied over the entire Al composition range. InGaN materials (with In content <50%) have also been studied extensively, and the light-emitting diode (LED) applications based on InGaN/GaN quantum structures have already been awarded a Nobel Prize in 2014. However, the applications of InN are lagging behind. The development of growth procedures for InN and In-rich InGaN has been difficult, and their optical properties were consequently much less studied in the past.

The optical properties of bulk GaN have been studied by several authors by spectrometric ellipsometry, yielding the entire dielectric function over a wide range from deep UV (above bandgap region) to infrared (lattice vibrations). Comparison with band structure calculations has produced an upgraded picture of the near-bandgap region for both valence and conduction bands, although the uncertainties in the theoretical calculations of the band structure still cause problems in the interpretations. Luminescence data has produced accurate knowledge about the excitonic- and impurity-related transitions near the bandgap energy, of relevance for optical emitting devices. Such studies are also very useful to establish optical fingerprints of impurities in the material, helpful for characterization in connection with the growth of device structures. Different growth techniques often give different defects in the material, with corresponding optical spectra.

With the availability of high-quality bulk AlN material, the knowledge about the optical transitions in the near-bandgap region of AlN has been significantly updated. The area of point-defect identification in AlN and AlGaN via the specific optical spectra contains many ongoing activities that are still under development.

The recent results on the optical properties of InN have led to an improved accuracy in the basic data on this material, and the correlation of doping with optical properties has advanced recently. Doping control of InN is now in sight, and the optical data are very helpful in characterizing these properties. InGaN is the core material for visible LEDs and as such has attracted much attention during the last decades. Most studies are on quantum well structures, but there is also basic work on bulk InGaN properties.

In this chapter, we have excluded the discussion of optical phenomena in quantum structures, since these are treated in separate chapters in connection with devices.

3.2  Optical Properties of GaN

3.2.1  Band-to-Band Optical Transitions and Free Excitons

GaN (as the other group-III nitrides) is a direct-bandgap semiconductor with the conduction band minimum and valence band maximum both occurring at the center of the Brillouin zone (Γ point). The Bloch wave function of the bottom conduction band is essentially determined by s atomic functions and has s-like orbital character, while the Bloch wave function of the top valence band is built from p atomic functions and has p-like orbital character. In wurtzite GaN (C4 6v space group symmetry) the crystal field and the spin-orbit interaction split the top valence band into three bands, commonly labeled A, B, and C in order of increasing energy of the holes. In terms of the group theory, the symmetry of the conduction band is Γ7 and the symmetry of the A, B, and C valence bands is Γ9, Γ7, and Γ7, respectively. This implies that the band-to-band transitions between the conduction band and the A valence band are dipole-allowed only for Ec polarization (E is the electric field vector of absorbed/emitted light and c is the hexagonal axis of the crystal), while the transitions between the conduction band and the B and C valence bands are dipole allowed for both polarizations, Ec and Ec. The electron-hole Coulomb interaction gives rise to three free excitons which correspond to the A, B, and C valence bands. These excitons have almost the same binding energy (25–26 meV) as determined in earlier photoluminescence (PL) and optical reflectance (OR) measurements [5,6]. Generally, three parameters (Δ1, Δ2, and Δ3) are required to describe the energy separation between the valence bands (consequently between the ground states of the three free excitons) and the oscillator strengths for all optical transitions [7–9]. In the quasi-cubic approximation [10] (i.e., for an isotropic spin-orbit interaction) the three band parameters are related to the crystal-field splitting (Δcf) and the spin-orbit splitting (Δso) by Δ1 = Δcf and Δ2 = Δ3 = Δso/3 [8]. The most consistent values for the crystal-field and the spin-orbit splitting in GaN are Δcf = 10 meV and Δso = 17 meV, experimentally determined from detailed analysis of the strain dependence of the free exciton energies [7,11].

The basic optical properties of GaN in the near-bandgap region are known with some precision since more than a decade. Accurate free exciton energies, the exciton fine structure due to the spin-exchange interaction, as well as the exciton-polariton branches arising from the exciton-photon coupling were derived from temperature-dependent and polarization-resolved PL measurements in strain-free GaN samples [12,13]. These samples are cut from boules grown by hydride vapor phase epitaxy (HVPE) and represent the high-purity GaN material so far; the residual impurity concentration is <1016 cm−3 (mainly Si and O due to the contamination from the quartzware in the growth reactor). Figure 3.1 shows the low-temperature PL spectra for Ec and Ec polarizations in the free exciton region [13]. The Ec polarized spectrum is dominated by the emission from the Γ5 state of the A exciton (XA) broadened due to nonthermalized polaritons and the two polariton branches of the Γ5 state of the B exciton. For Ec polarization the Γ1 state of the B exciton (XB) is clearly resolved. The doublet in the region of the XA exciton is related to a mixed-longitudinal-transverse state arising from a slight deviation from kc experimental geometry (k is the light wave vector). At higher energies, the excited states of the XA, as well as the excited states of the neutral donor bound exciton (DoXA) are observed in both polarizations (for more details see Reference [13]). In such pure samples, the free exciton energies can be followed up to room temperature, and consequently, the bandgap can be precisely determined. The bandgap in unstrained GaN is found to vary from 3.503±0.001 eV at 2 K to 3.437±0.005 eV at 290 K [13]. For the B bandgap, the corresponding values are 3.507±0.001 eV at 2 K and 3.442±0.005 eV at 290 K. We note that due to the very small energy separation between the A and B valence bands (≈4 meV) polarization-resolved measurements are required in order to distinguish between the A and B band-related optical transitions, especially at elevated temperatures. As for the C bandgap, only the room temperature value of 3.460±0.005 eV can be suggested from our studies [13]. These data are more adequate than the previous ones acquired for GaN grown on sapphire and frequently cited [14]. The biaxial strain existing in heteroepitaxial layers, results in a shift of all optical transitions to the higher energies in the case of compressive strain and the lower energies in the case of tensile strain. Moreover, the strain modifies the valence-band splitting (consequently the exciton energies) and the optical transition oscillator strengths [15].

Low-temperature PL spectra of a bulk GaN samples in the free-exciton region for

Figure 3.1   Low-temperature PL spectra of a bulk GaN samples in the free-exciton region for E⊥c and E∥c polarizations. The polarization degree of the emission defined as ρ = (I⊥/III)/(I⊥ + III), where I⊥(III) is the PL intensity for E⊥c and E∥c polarizations, is also shown.

(From Monemar, B. et al.: Recombination of free and bound excitons in GaN. Phys. Status Solidi (b). 2008. 1723. 245. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.)

Absorption data from transmission experiments are less straightforward to measure, due to the strong oscillator strengths of the excitons, requiring a sample thickness <1 µm. Reliable data for the above bandgap absorption coefficient at room temperature in undoped and n-doped GaN are available from spectroscopic ellipsometry (SE) measurements (Figure 3.2) [16]. Some data at much higher temperature have also been presented [17]. The proper modeling of the measured imaginary part of the dielectric function (ε2) shows the relevance of the Coulomb enhancement in band-to-band (BB) transitions and the exciton-phonon complexes (EPC) in near-bandgap absorption. The experimental data in Figure 3.2 also implies a value of the Mott density (defined as the electron concentration at which the exciton peak (X) moves into the continuum) of about 2 × 1018 cm−3 [16].

(a) Measured (circles) and fitted imaginary part of the dielectric function (ε

Figure 3.2   (a) Measured (circles) and fitted imaginary part of the dielectric function (ε2) in undoped GaN. The inset presents the absorption coefficient determined from measured dielectric function. (b) Measured ε2 in sample with different free electron concentrations (the numbers indicate the electron concentration in units of 1018 cm−3). The spectra are vertically shifted for clarity. In the inset, ε2 spectra of samples with electron concentration of 3.7 × 1018 cm−3 (dotted) and 2.3 × 1019 cm−3 are compared to the spectrum in undoped GaN (solid line).

(Reprinted with permission from Shokhovets, S. et al., Phys. Rev. B., 79, 045201, 2009. Copyright 2009 by the American Physical Society.)

While the near-bandgap structures have been explored in detail, the band structure over the entire Brillouin zone is less accurately known. Details of the band structure are important for the modeling of certain electronic processes in devices. As an example, for InGaN-based LEDs in the visible spectral range, there has been a recent debate on the possible importance of intrinsic Auger processes for nonradiative recombination in these LEDs at high injection currents [18]. In the modeling of this process, the energy position of the satellite valleys of the conduction band (the lowest one believed to be at the L point of the Brillouin zone) is crucial in order to evaluate the hot-electron transport. In principle, the high-energy critical points can be studied by vacuum UV (VUV) SE on samples with different crystal orientations, where the ordinary and extraordinary dielectric function can be derived [19,20]. Unfortunately, the SE provides a very rough estimate for the energy separation between Γ and L minima of the conduction band even if the transitions related to the excitation of the Ga 3d core levels are examined [19]. Theoretically, the splitting has been predicted to be about 2.2 eV [21,22], while indirect experimental methods, such as pump-probe transient spectroscopy [23] and photoexcited field emission spectroscopy [24], have given a value of 1.1–1.2 eV. Recently, by near-bandgap photoemission spectroscopy study of p-doped GaN activated to negative electron affinity, a value of 0.9 eV has been obtained [25]. The large discrepancy between the experimental and theoretical values for the Γ–L conduction band energy separation as well as the expected complex kinetic energy distribution of hot electrons have provoked the claim for a direct evidence of Auger process in LEDs [26] to be questioned [22].

3.2.2  Bound Excitons in GaN

The optical signatures of the exciton bound to shallow donors (SDs) and acceptors were reviewed for GaN some years ago [13]. All these data were given for strain-free bulk samples, that is, the energies do not suffer from strain shifts, and are accurate within the spectral resolution (<0.2 meV).

There are two dominant SDs in GaN—substitutional oxygen (O) on the nitrogen site (ON) and substitutional silicon (Si) on the gallium site (SiGa). In low-temperature PL spectra, the recombination of the excitons bound to these two neutral donors gives rise to two sharp lines below the A free exciton line [13]. The energy separation from the A exciton, 7.0 meV for the O-related line and 6.2 meV for the Si-related line, represents the binding energy of the corresponding donor bound exciton (DBE). At energies above the two main DBE lines, a number of weak emission lines related to the excited state of the DBEs were also resolved. In the lower energy region (3.44–3.45 eV) the PL spectra showed a rich structure of the so-called two-electron transitions (TETs) which occur from the DBE recombination with simultaneous excitation of the donor to its excited states [13,27]. The temperature-dependent and polarization-dependent PL measurements [27] spectra, as well as the detailed analysis of the donor and DBE excited states [28] allows an accurate determination of the binding energy of the Si and the O donors, 30.2±0.3 meV and 33.5±0.4 meV, respectively. The phonon coupling of the DBEs and the polarization selection rules for the phonon-assisted optical transitions were explored both theoretically and experimentally [29]. The dynamics of the DBE recombination was also studied in detail [13,30]. The PL transients of DBEs generally consist of at least two different parts, originating from different processes (near-surface and bulk-related, respectively). There are different processes associated with the excited DBE states and the very commonly used two-state model for the exciton transfer between the free-exciton and DBE state is, in general, inadequate [30]. Also, the exciton transfer processes of DBEs among the neutral donors cannot be neglected, as evidenced by the often observed much shorter lifetimes for DBEs in samples with donor concentrations ≥1017 cm−3 [31]. Nonradiative recombination processes in the near-surface region of GaN have recently been analyzed in detail, suggesting that care should be taken to remove the oxide layers as well as subsurface damage and H-related defects, in order to increase the radiative efficiency (by two orders of magnitude) in a PL experiment [32].

Recently, a new donor in GaN, substitutional germanium (Ge) on the gallium site (GeGa), has been studied in some detail. The interest of such investigations is stimulated by the observation that much fewer defect problems seem to occur with the Ge doping as compared with the Si doping for GaN grown on sapphire [33,34]. From earlier works, it was known that the binding energy for the Ge donor in GaN is 31 meV (from theoretical calculations [35]) and 30 meV (from optical studies [36]), similar to that of the Si donor. However, the recent PL studies in Ge-doped GaN have not revealed any DBE emission lines because highly doped samples were examined so far [37,38]. An electron carrier concentration above 1020 cm−3 was achieved by Ge doping in GaN grown on sapphire by metalorganic chemical vapor deposition (MOCVD) [37,38]. The PL spectra of such degenerate material (with the Fermi level in the conduction band) clearly demonstrate a broad band-to-band emission with a high-energy cut-off at the Fermi level and a tapering off at lower energies (Figure 3.3) [38]. The PL line shape can be very well approximated by the model for a recombination of free electrons in the conduction band with localized holes [39]. Attaining a high electron concentration with Ge doping have allowed to properly evaluate the interplay between the effects of the Coulomb interaction screening, the bandgap renormalization (BGR) and the Burstein–Moss shift (BMS) on the bandgap edge optical spectra in n-type GaN. Figure 3.4 shows the free-carrier dependence of the exciton energy (extracted from the fitting of ε2 measured by SE) together with theoretical modeling which accounts for all above effects [38]. (Note that the Mott density in Reference [38] was defined as the electron concentration at which the exciton binding energy is approaching zero and was estimated to be 1.5 × 1019 cm−3).

Low-temperature PL spectra of Ge-doped GaN layers (open symbols) and modeled line shape (continuous lines). The vertical lines show the energy positions of renormalized band gap with and without including the Burstein–Moss shift.

Figure 3.3   Low-temperature PL spectra of Ge-doped GaN layers (open symbols) and modeled line shape (continuous lines). The vertical lines show the energy positions of renormalized band gap with and without including the Burstein–Moss shift.

(Reprinted with permission from Feneberg, M. et al., Phys. Rev. B., 90, 075203, 2014. Copyright 2014 by the American Physical Society.)
(Top) Separately calculated contributions of the Coulomb interaction screening (

Figure 3.4   (Top) Separately calculated contributions of the Coulomb interaction screening (E bX), the bandgap renormalization (BGR) and the Burstein–Moss shift (BMS). (Bottom) The exciton energy as a function of the free electron concentration. The squares are the values extracted from the measured imaginary part of the dielectric function while the line represents the theoretical modeling.

(Reprinted with permission from Feneberg, M. et al., Phys. Rev. B., 90, 075203, 2014. Copyright 2014 by the American Physical Society.)

Since the beginning of the research on GaN, doping with several acceptors (Mg, Zn, Cd) have been tried in order to achieve p-type conductivity. All these acceptors (substitutional on Ga site) have relatively large binding energies (200–500 meV) which cause a problem with obtaining a high hole concentration. So far only the Mg acceptor (with a binding energy of ≈225 meV) is proved to work fine, and nowadays it is used for all GaN-based p-n devices.

The optical signatures of the Mg acceptor (MgGa) were briefly reviewed in Reference [13] and then studied in more details in Mg-doped homoepitaxial samples [40–43] where the spectral linewidth of the acceptor bound excitons (ABE) is much smaller than that in the samples grown on sapphire substrates [44]. We want to point out that some researchers apparently are still not convinced that the main donor-acceptor pair (DAP) peaking at 3.27 eV is related to the Mg acceptor [45]. There are several strong indications for that in the literature, however. Here we relate to the ion implantation studies reported in Reference [46]. In Figure 3.5 are shown the DAP signatures of Mg, Zn, and Cd acceptors, as convincing evidence for the attribution of the 3.27 eV DAP to the Mg acceptor [46]. In the same paper, the ABE peak for the Mg-doped sample was reported at 3.466 eV, as also stated in our more recent work [40]. The assignment of the above ABE and DAP signatures to the Mg fulfills the reasonable requirement that these spectra should be strong (or dominant) in all Mg-doped samples up to the high-doping region (1019 cm−3). It is well known that the Mg doping in heteroepitaxially grown GaN leads to a formation of pyramidal inversion domains, and thus deteriorate the structural quality of the material [47,48]. For Mg-doped GaN layers grown on bulk GaN substrates, no such defects were found for Mg concentrations <1020 cm−3 [49]. The main structural defects in such material are numerous small (5–10 nm) basal plane stacking faults (BSFs) which have a shape of two-dimensional islands and do not have any associated threading partials. These defects do however influence the optical properties. It was earlier discovered that there are two separate optical signatures related to the Mg acceptor [40]. The main acceptor bound exciton line at 3.466 eV (labeled ABE1) is accompanied by a lower energy line at about 3.454 eV (ABE2). The broader ABE2 line was recently interpreted as due to a perturbed Mg acceptor, involving interaction with nearby BSFs [43]. The detailed structure of this second acceptor (including the interaction with the BSFs) needs further studies. The two ABE emissions have different transient properties which are consistent with an efficient transfer process of excitons from ABE1 to ABE2 [43]. The second acceptor state related to the Mg acceptor is also evident in the DAP spectra. It was shown that there is a broad spectrum in the background of the Mg-related 3.27 eV DAP, particularly clear in the time-resolved spectrum (see Figure 3.4 in Reference 43).

Low-temperature PL spectra of Mg-, Zn-, and Cd-implanted GaN grown by HVPE, after annealing.

Figure 3.5   Low-temperature PL spectra of Mg-, Zn-, and Cd-implanted GaN grown by HVPE, after annealing.

(Reprinted from Chen, L. and Skromme, B. J., Mat. Res. Soc. Symp. Proc., 743, L11.35.1, 2003. Copyright 2003, Cambridge University Press.)

Some recent efforts on the theory side on the electronic structure and related properties of acceptors in GaN seem to deviate from the recent experimental results. First-principles calculations on the energy levels of the Mg acceptor in GaN [50] come to the conclusion that the Mg acceptor is somewhat deeper (close to 300 meV) than the one experimentally observed (225 meV) and has a very strong phonon coupling (Huang–Rhys factor >>1) while experimentally a value of about 0.5 is found. The reasons for this discrepancy has so far not been examined, in general, an accurate treatment of acceptors in compounds involving d-electrons is difficult. Other authors misinterpret the shallow 3.466 eV ABE PL line as evidence for a nitrogen vacancy shallow donor level [51].

The Zn-related ABEs have also been observed. The low-temperature PL spectrum of bulk GaN grown by the Na-Ga melt method has shown three closely spaced lines around 3.455 eV [52]. The temperature dependence of the spectrum has revealed that these lines are derived from a split ABE ground state. This fact confirms that the ABE ground state in wurtzite semiconductors is not a single state (as obtained if only the top valence band is considered) and a proper treatment including all three top valence bands is needed [53].

3.2.3  Below-Bandgap Emissions Related to Intrinsic and Extrinsic Point Defects

Below the DAP emission at 3.27 eV and its LO phonon replicas, a number of emission bands related to intrinsic or extrinsic defect levels (so-called deep levels) are observed in the PL spectra of GaN. The spectral position of the emission maximum is commonly used for their labeling, for example, red luminescence (RL) at 1.8 eV, yellow luminescence (YL) at 2.2 eV, green luminescence (GL) at 2.4 eV, and blue luminescence (BL) at 2.8–2.9 eV. Low-temperature PL spectra for an undoped bulk GaN grown by HVPE and carbon-doped homoepitaxial GaN layer grown by MOCVD presented in Figure 3.6 show typical below-bandgap emission in GaN.

Low-temperature PL spectra of an undoped bulk GaN layer grown by HVPE and a C-doped homoepitaxial GaN layer grown by MOCVD. The secondary ion mass spectroscopy (SIMS) on these samples reveals Si and O concentration of 1 × 10

Figure 3.6   Low-temperature PL spectra of an undoped bulk GaN layer grown by HVPE and a C-doped homoepitaxial GaN layer grown by MOCVD. The secondary ion mass spectroscopy (SIMS) on these samples reveals Si and O concentration of 1 × 1016 cm−3 and H concentration is of 1 × 1018 cm−3. The C concentration is 1 × 1016 cm−3 in the HVPE sample and 5 × 1017 cm−3 in the MOCVD layer.

The presence and the quantum efficiency of a particular emission depend on the method used for growth of GaN material, the growth conditions (temperature, V/III ratio), as well as on the concentration of the impurities (intentional or unintentional). Nevertheless, there are some common characteristics for these emission bands: (i) at low temperatures the recombination occurs between electrons at SDs and holes at deep acceptors (DAs) (DAP emission), while at elevated temperatures the donors are ionized and the recombination is between conduction band electrons and DA holes (so-called e-A emission); (ii) with increasing temperature the emissions shift toward higher energies, decrease in intensity and eventually quench with a thermal activation energy approximately equal to the energy of the corresponding acceptor level measured from the top of valence band; (iii) at low-excitation intensity an acceptor concentration less than 1015 cm−3 is enough to give rise to a deep level emission; (iv) with increasing excitation intensity the maximum of the emission bands shift toward higher energies, and the intensity saturate; (v) the emission line shapes are quite broad as a result of the strong electron-phonon coupling and the spectral maximum of the emission band does not correspond to the energy position of the defect in the gap; (vi) the PL transients are nonexponential with an effective PL decay time of 1–100 µs, much longer than the typical one for the exciton transitions. When more than one type of deep-level emissions are present, the behavior of PL intensities and the spectral positions with both the temperature and the excitation intensity becomes more complex due to carrier re-distribution among different recombination channels.

The intrinsic and extrinsic point defects which give rise of various deep level emissions in GaN have been studied theoretically in the past [54]. On the other hand, a comprehensive analysis of the experimental results can be found in Reference [45]. These review papers, however, present the status quo in the scientific knowledge as it was more than 10 years ago. In the following, some new theoretical and experimental findings are discussed.

The RL is typically observed in undoped GaN grown by HVPE [45,55,56] (see also Figure 3.6). Among all deep level emissions, the RL exhibits the longest decay time and then saturates at very low-excitation energies [45]. The zero-phonon line (ZPL) of the RL is found to be at 2.36 eV which implies that the DA involved in the emission is located at 1.13 eV above the valence band [57] matching the earlier calculated energy for the (–/2–) transition level of the gallium-vacancy-oxygen-donor complex (VGa-ON) [54,58]. New hybrid functional calculations, however, placed this level at 2.2 eV above the valence band, and thus shifted the related emission in the infrared [50]. Low-energy transition level of VGa-ON or complexes with hydrogen (H) such as VGa-ON-H, VGa-H and VGa-2H can be tentatively associated with the RL [50]. An emission at 1.7–1.8 eV has also been observed in Mg-doped GaN [45,59]. In this case, however, the suggested interpretation for the emission is a deep donor (DD) to shallow acceptor (SA) transitions, where the DD is a nitrogen-vacancy-magnesium-acceptor complex (VN-MgGa) and the SA is MgGa [59,60].

The YL is by far the most studied mid-bandgap emission in GaN. The YL presents in the PL spectra of undoped or n-doped material independent of the growth method (HVPE, MOCVD or molecular beam epitaxy [MBE]) [45]. The earliest interpretation of the YL was a transition between the SD and the carbon (C) related DA, based on the experimentally found enhancement of the YL intensity with the C doping [61]. Later on, a correlation between the YL intensity and the concentration of VGa, as measured by positron annihilation spectroscopy (PAS), was demonstrated [62]. Since the isolated VGa was found to be unstable at temperatures above 500°C, while the VGa-ON complex was stable up to 1,200°C (the usual growth temperature for HVPE and MOCVD) [63,64], the DA involved in the YL was identified as the VGa-ON complex [45,62]. This assignment was in line with the first principles calculations which gave the (–/2–) transition level of the VGa-ON acceptor at 1.1 eV above the valence band [54,58]. Then a consensus about the origin of the YL was established around the III-nitride research community [45]. As already mentioned, recent theoretical calculations moved the VGa-ON (–/2–) transition level deeper in the gap and some researchers concluded that the VGa-ON complex is not responsible for the YL [65,66]. This conclusion, however, contradicts the experimental findings that the YL is suppressed in Mg-doped GaN where the VGa concentration is negligible [67]. Subsequently, other VGa complexes such as VGa-ON-2H and VGa-3H were suggested to contribute to the YL [50]. On the other hand, the involvement of C in the YL has recently been reinforced. Hybrid functional calculations have predicted that the substitutional C on nitrogen site (CN) is a deep acceptor with a (0/–) transition level at 0.9 eV above the valence band [68], instead of a SA as previously assumed [54]. Thus, the optical transitions from the SD to the CN acceptor are expected to occur at 2.15 eV, that is, at the energy position of the YL. Later on, applying the same theoretical approach, the CN acceptor-related emission was estimated to be at 1.98 eV, and the YL was attributed to the CN-ON complex with a (+/0) transition level at 0.75 eV [65,66]. The stability of the CN-ON complex, however, was questioned [69]. The latest theoretical calculations have shown that the isolated CN acceptor rather than the CN-ON complex gives rise to the YL [70]. Having in mind the correlation of the YL intensity with both the VGa concentration [62,71] and the C doping [72,73] one can conclude that there are at least two DAs involved in the YL.

The GL is most often observed in undoped GaN grown by HVPE [45]. Usually, it emerges at high-excitation intensities, when the YL saturates. The GL intensity increases as a square of the excitation intensities, which implies that the defect responsible for this emission captures two holes before any radiative recombination occurs [45]. Based on the earlier interpretation of the YL (related to the VGa-ON) and the experimentally evidenced transition from YL to GL in the PL spectra, the GL has been attributed to the (0/–) transition level of the VGa-ON [45]. In view of the new theoretical predictions about the CN acceptor levels, this interpretation was changed, and the (+/0) transition level of the CN was suggested as the DA involved in the GL [66]. Recently, from a detailed analysis of the temperature dependence of the GL an excited state of the CN + (CN occupied with two holes) has been proposed to be involved in the emission [74]. However, since the VGa complexes cannot be excluded as a source of the YL, most probably there are two sources for the GL as well. The GL has also been observed in high-resistivity GaN grown under Ga-rich conditions by MBE [45] and in Mg-doped GaN also grown by MBE [75]. In this case, the emission band is relatively narrow for a deep level emission (~230 meV) and has a very high Huang–Rhys factor (~25) and small characteristic phonon energy (~23 meV) [75], which is typical for a DD defect [76]. Then this GL (also called GL2) is attributed to internal transitions within the VN donor [75].

The BL appears in the PL spectra of high-resistivity GaN (C-doped or Fe-doped), n-type and high-resistivity Zn-doped GaN, and p-type Mg-doped GaN [45]. Although in all cases the emission is the 2.8–3.0 region, the defects involved in the emission are different. In C-doped GaN the (+/0) transition level of the CN acceptor (at 0.35 eV above the valence band) has been assigned as the DA involved in the BL [69]. It was suggested that the CN acceptor leads to the YL or BL depending on the position of the Fermi level and the excitation intensity. In lightly C-doped material (n-type) the CN is the most stable charge state and the YL dominates. In heavily C-doped GaN optical excitation with a high intensity stabilizes CN 0 and then the BL emerges. A correlation between the C doping and the BL intensity has been experimentally evidenced in the past [77,78] (see also Figure 3.6). Note that different theoretical results for the CN transition levels lead to different interpretations of the related emissions: in Reference [69] the two CN charge states are suggested to produce YL and BL, while in Reference [66] the corresponding emissions are YL and GL. Recently, the BL in high-resistivity GaN was related to CN or CN-ON complexes with hydrogen (H) interstitial (CN-Hi or CN-ON-Hi) [79]. Surprisingly, the same interpretation was proposed for the BL in the Fe-doped GaN [79]. In Zn-doped GaN the BL with a maximum at 2.9 eV and ZPL at 3.05 eV was attributed to the optical transitions between the SD and the ZnGa acceptor (at 0.45 eV above the valence band) [80]. In heavily Mg-doped GaN, the BL at 2.8 eV was earlier interpreted as a DD to SA transition, where the DD is the VN-MgGa complex, and the SA is the MgGa [81]. Since the BL in Mg-doped GaN was known to be enhanced after annealing [43], while the concentration of the VN-MgGa complex significantly decreases at T > 500°C [82] such an interpretation is improbable. An alternative explanation of the BL, in this case, would be the optical transitions between an H-related DD and the MgGa acceptor [83] or between the SD and Mg-related DA [43].

3.2.4  Luminescence Related to Extended Structural Defects

The extended structure defects in GaN, such as dislocations, inversion domain boundaries, stacking faults (SFs), usually known as nonradiative defects, can capture electrons or/and holes (or excitons) and then produce characteristic emission lines. Up to eight emission lines in the region of 3.1–3.45 eV was observed in low-temperature PL spectra of GaN layers grown by different epitaxial techniques and was related to structural defects, but their exact identification was not clarified [45].

So far the most studied extended defect-related emissions are those associated with the SFs. The SFs are two-dimensional extended defects which occur when the normal stacking sequences of the crystal are changed. In wurtzite GaN the stacking sequences along (0001) direction can be distorted by introducing one, two or three zinc blende (ZB) bi-layers (molecular monolayers). Then, three types of basal plane SFs (BSFs) are distinguished—intrinsic I1-type, intrinsic I2-type, and extrinsic E-type, with a formation energy increasing in the same order [84]. The SFs are also possible on planes other than the (0001) plane. The faults formed on a prismatic (11-20) plane, called prismatic SFs (PSFs), always connect two I1-type BSFs with a stair-rod dislocation. The first identification of the optical signatures of the SFs in GaN dates about 20 years ago [85], but extensive studies have started years later with the development of the GaN growth along nonpolar directions [86–88]. It was found that in heteroepitaxial nonpolar and semi-polar GaN layers SFs of high density are formed, and the near-bandgap PL spectra are often dominated by the SF-related emissions. Comprehensive reviews of the optical studies of the SFs in GaN can be found in References [89] and [90]. Figure 3.7 depicts a typical low-temperature PL spectrum of SFs emissions where three group of lines are discriminated around 3.41 eV, 3.32 eV, and 3.29 eV and attributed to I1-type, I2-type, and E-type BSFs emission, respectively [91]. In other studies, the lines at 3.30 eV were interpreted as related to the PSFs [92] or to impurity decorated stair-rod partial dislocations terminating the I1-type BSFs [87]. In a simple modeling of the BSFs, a thin ZB quantum well (QW) embedded into the wurtzite matrix is considered and then the emission occurs from the recombination of electrons and holes confined in the well [85,93]. The thickness of the QW depends on the interface position between ZB and wurtzite phases and is (1.0±0.5)c, (1.5±0.5)c, (2.0±0.5)c for I1-type, I2-type, and E-type BSFs, respectively, where c is the lattice constant along the (0001) direction in wurtzite GaN [93]. This model approximately reproduces the 3.41 eV emissions from the I1-type BSFs but fails to explain the multiline structure in the PL spectra as well as the energy separation between the lines from different types of BSFs. The model was further developed by including the discontinuity of the spontaneous polarization at the ZB-wurtzite interfaces and the resulting quantum-confined Stark effect [86,91], considering the possibility of type-I or type-II band alignment in the ZB QW [91], and also the interaction between adjacent BSFs [86,88,94]. It was further suggested that donors [95] or acceptors [96] located in a proximity of the BSFs are involved in the emissions. Both the complex physics of the SFs and their experimentally observed rich spectra leave the door open for further investigations in this field.

Low-temperature micro-PL spectrum of a GaN microcrystal showing a rich structure of sharp lines related to different types of BSFs. The inset shows a top-view scanning electron micrograph of the studied microcrystal.

Figure 3.7   Low-temperature micro-PL spectrum of a GaN microcrystal showing a rich structure of sharp lines related to different types of BSFs. The inset shows a top-view scanning electron micrograph of the studied microcrystal.

(Reprinted with permission from Lähnemann, J. et al., Phys. Rev. B., 86, 081302(R), 2012. Copyright 2012 by the American Physical Society.)

Dislocations in semiconductors are mostly associated with nonradiative recombination, but it turns out that at low temperatures also radiative processes occur. One such example has been studied with a-type screw dislocations in GaN [97], where a bound exciton line is observed at 3.346 eV and related to the dislocations via luminescence topographs. The authors demonstrate via calculations of the electronic structure of this defect that it can bind both electrons and holes in a local potential. Otherwise, such dislocations are known to be serious nonradiative defects at room temperature and higher, participating in the droop process in InGaN-based LED structures [98].

3.3  Optical Properties of AlN and AlGaN Alloys

3.3.1  Free and Bound Excitons in AlN

Like in GaN the top valence band in AlN is split by the crystal field, and the spin-orbit interaction into three bands also labeled A, B, and C in order of increasing energy of the holes. The main difference is that in AlN the crystal-field splitting is negative. Ab initio calculations predict quite scattered values for Δcf, from –59 to –276 meV (see Table III in Reference [99]), while the recent experimentally derived values in bulk AlN are more consistent, Δcf = –230 meV [100], –225 [101], –220 meV [99]. On the other hand, the calculated and the experimental values for the spin-orbit splitting range between 11 and 22 meV [99]. Comparing all available data we tends to conclude that the most reliable values are Δcf = –220±2 meV and Δso = 15±2 meV [99]. The large negative Δcf has significant consequences on the valence band structure, as well as on near-bandgap optical transitions in AlN (Figure 3.8a). First, the top valence band (A band) is the crystal-field-split-off band (with Γ7 symmetry) which has a pz -like orbital character. Second, the optical transitions between the A valence band and the conduction band (Γ7 symmetry) occur predominantly for Ec polarization. Generally, the Γ7–Γ7 transitions are allowed in both Ec and Ec polarizations, however, due to the large Δcf the oscillator strength for Ec polarization becomes vanishing small. The estimates within the quasi-cubic model show that for strain-free AlN the oscillator strength ratio between Ec and Ec polarizations for the band-to-band transitions involving the A valence band is about 1:1000 [100,102,103]. (Note that in the case of GaN this ratio (now involving the C valence band) is about 1:10 [7]). For the same reason (the large Δcf) the transitions between the C valence band (Γ7 symmetry) and the conduction band are mainly Ec polarized. As for the transitions related to the B valence band (⊥9 symmetry) they are allowed only for Ec polarization.

(a) Valence band structure and the band-to-band optical transitions in AlN. (b) The splitting of the A exciton and the dipole allowed exciton transition for spin-exchange constant

Figure 3.8   (a) Valence band structure and the band-to-band optical transitions in AlN. (b) The splitting of the A exciton and the dipole allowed exciton transition for spin-exchange constant j > 0 and j < 0. (The figure is not drawn to scale.) The Γ2 and Γ5 states are virtually degenerate. Note that the exciton oscillator strength for E⊥c polarization is more than two orders of magnitude smaller than that for E∥c polarizations.

The exciton binding energy is generally extracted from the energy separation between the ground state (1s) and the excited state (2s) emission lines of the A exciton. However, the simple hydrogenic model for the excitons does not work well for AlN because of the anisotropy in both the dielectric constant and the effective masses of electrons and holes (these values are not exactly known) [104,105]. Nevertheless, the theoretically predicted [105] and the experimentally deduced [103,106–109] binding energy for the A exciton are quite consistent giving a value of 52±1 meV. (For the exciton fine-structure splitting due to the spin-exchange interaction see the discussion below). There is no available data for the binding energies of B and C excitons, but one can assume values similar to that for the A exciton (as in the case of GaN).

The unusual valence band structure of AlN (in the sense of the optical polarization selection rules) is very challenging for optical investigations. First, polarization resolved measurements are crucial for an accurate determination of the A exciton energy, and correspondingly the bandgap in AlN. This can be done correctly only for the kc experimental geometry, that is, samples with a large and clean surface parallel to the c-axis are needed (e.g., bulk samples). Second, the large energy separation between the A valence band and the other two valence bands makes the revealing of the B and C excitons practically impossible in PL measurements, because the high-energy bands cannot be populated (even at room temperature). Third, the PL experiments are hampered by the high-background impurity concentration in the present AlN material leading to a number of bound exciton emission lines which have to be distinguished from the A free exciton emission.

The inverse valence band ordering in AlN was experimentally proved by OR and PL measurements more than 10 years ago [100–102]. More accurate data for the A, B, and C exciton energies at low and room temperatures were recently obtained from SE measurements on a bulk AlN sample with (1-100) oriented surface grown by physical vapor transport (PVT) [99]. Figure 3.9 shows the experimental imaginary part of the dielectric function (ε2) for Ec and Ec polarizations at T = 10 K together with a line-shape modeling that includes the contributions of the free excitons, the exciton continuum and the EPC. The extracted energies are 6.032 eV, 6.255 eV, and 6.264 eV for A, B, and C excitons respectively. The corresponding values at room temperature (T = 295 K) are lower by 71±1 meV. Note that the A exciton is seen only for Ec polarization, while the B and C excitons are seen only for Ec polarization. In PL measurements (where the spectral resolution is usually 4–5 times better than that in SE) more complicated spectra were acquired. Despite that similar strain-free bulk samples or homoepitaxial layers were studied by different groups the energy position of the A exciton was found to span between 6.029 eV and 6.043 eV depending on the experimental geometry used and in some cases double or triple emission lines were observed [99, 107,108,110,111]. Such peculiarities can only be explained by the fine structure of the A exciton.

Experimental and modeled imaginary part of the dielectric function (ε

Figure 3.9   Experimental and modeled imaginary part of the dielectric function (ε2) in bulk AlN for E⊥c and E∥c polarizations at T = 10 K. The decomposition of the spectra allows to assign the contributions of the free excitons, the EPC, and the exciton continuum.

(Reprinted with permission from Feneberg, M. et al., Phys. Rev. B., 87, 235209, 2013. Copyright 2013 by the American Physical Society.)

The 1s ground state of the A exciton in AlN is four-fold degenerate and consists of a two-fold degenerate spin-singlet state (Γ5 symmetry), a pure spin-triplet state (Γ2 symmetry) and a mixed singlet-triplet state (Γ1 symmetry). The electron-hole spin-exchange interaction (characterized by the spin-exchange interaction constant, j) splits the spin-singlet states from the spin-triplet states. The exciton states of Γ5 symmetry are dipole allowed for Ec polarization, while the Γ1 exciton state is dipole allowed for Ec polarization (Figure 3.8b). The spin-triplet state Γ2 is optically forbidden. The spin-exchange interaction constant in AlN is expected to be quite large following the trend of j with the exciton binding energy (or the exciton Bohr radius) [112,113]. Moreover, due to the large Δcf the A exciton is almost completely decoupled from the other two valence bands. As a result, the Γ2 and Γ5 states are nearly degenerate independent of the j value and the splitting between Γ5 state and Γ1 state is ≈2j (Figure 3.8b).

Two groups have attempted to study the fine structure of the A exciton, both have found a large j, however with an opposite sign [99,107,110,111,114]. In Figure 3.10 low-temperature PL spectra taken in the three common polarization geometries for a bulk AlN sample are shown [111]. The emission lines at 6.032 eV (which coincides with the maximum in the Γ2) and at 6.040 eV were identified as the Γ1 and Γ5 exciton states. Based on both the energy separation and the ordering of the states (the Γ5 state is at higher energy than the Γ1 state) the authors concluded that j = –4 meV. Different PL spectra were acquired in a homoepitaxial AlN layer (Figure 3.11) [107]. The broad emission at 6.043 eV, not seen in Ec polarization, was identified as the Γ1 exciton state, while the sharp emission line at 6.029 eV was assigned the Γ5 exciton state [107,114]. Then, the spin-exchange interaction constant was found to be j = 6.8 meV. Unfortunately, in both cases, there is some uncertainty in the interpretation of the PL spectra which is mainly related to the overlook of the exciton-photon coupling and the oscillator strengths expected for the different exciton states for different polarizations. The free exciton origin of the XA5) line in PL spectra on Figure 3.11 was confirmed by temperature-dependent [114] and time-resolved PL measurements [108] but the concerns about its interpretation still remain because the free exciton emission lines are usually much broader than the DBE lines. The detailed theoretical analysis of the A exciton fine structure in AlN along with the experimental finding favors a positive sign j [115]. Moreover, j > 0 is found in all III-V and II-VI semiconductors. One should note, however, that AlN is the only one semiconductor with a negative crystal-field splitting. The conclusion is that more studies are needed in order to clarify the exciton fine structure in AlN.

Imaginary part of the dielectric function (ε

Figure 3.10   Imaginary part of the dielectric function (ε2) for E∥c polarization and PL spectra for different polarization geometries in bulk AlN measured at 10 K.

(Reprinted with permission from Feneberg, M. et al., Appl. Phys. Lett., 102, 052112, 2013. Copyright 2013, American Institute of Physics.)
Low-temperature polarized PL spectra of a homoepitaxial AlN layer

Figure 3.11   Low-temperature polarized PL spectra of a homoepitaxial AlN layer

(Reprinted from Funato, M. et al., Appl. Phys. Express, 5, 082001, 2012. Copyright 2012, The Japan Society of Applied Physics.)

Due to the uncertainty in the energy of the lowest A free exciton state the bandgap value of AlN is somewhat doubtful. Nevertheless, based on all experimental finding in bulk and homoepitaxial samples, one can claim a bandgap of 6.084±0.003 eV at 2 K and 6.013±0.006 eV at room temperature for pure strain-free AlN.

In high-resolution low-temperature PL spectra of bulk AlN and homoepitaxial AlN layers up to four sharp lines below the free-exciton emission are commonly resolved and assigned as recombination of DBEs related to four different donors [108,110,116] (see Figure 3.12). The localization energies (the binding energies) of these DBEs are 8±1, 13±1, 22±1, and 28±1 meV. The corresponding donors still remain unidentified. Only the DBE with the binding energy of 28±1 meV has been identified as related to the SiAl donor in doping experiments [116] and the SiAl binding energy of 63.5±1.5 meV is estimated from the TETs spectra [117]. Recently, more DBE lines were found in m-plane homoepitaxial AlN layers and a DBE with a binding energy of 26 meV (measured from the Γ1 exciton state) was identified as related to the ON donor [118]. This assignment, however, is quite doubtful because of the lack of a doping-dependent study and the inappropriate estimation of the DBE binding energies. The proper localization energies (the binding energies of a DBE) should be estimated from the ground 1s state of the A exciton (the Γ2 state, which in AlN is degenerated with the Γ5 state). One should also note that the DBE symmetry is reduced from C6v to C3v and the spin-exchange splitting and the polarization selection rules are different for the A free exciton and the DBEs arising from it.

Low-temperature PL spectrum of a nominally undoped AlN homoepitaxial layer showing four DBE exciton lines.

Figure 3.12   Low-temperature PL spectrum of a nominally undoped AlN homoepitaxial layer showing four DBE exciton lines.

(From Neuschl, B. et al.: Optical identification of silicon as a shallow donor in MOVPE grown homoepitaxial AlN. Phys. Status Solidi (b). 249, 511, 2012. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.)

The problem with the identification of the donors related to the DBEs is because all dopants commonly used for n-type conductivity in GaN (O, Si, Ge, Sn) form the so-called “DX centers” in AlN [119]. The DX centers appear when a neutral substitutional donor captures another electron and undergoes a large lattice relaxation, forming a lower-lying negatively charged state (DX ) which acts as a deep acceptor. The DX behavior of the ON in AlxGa1-xN has been experimentally evidenced by the pressure-dependent Raman scattering two decades ago [120]. It was found that ON becomes a DX center for Al composition x > 0.4, while hybrid functional calculations got x > 0.61 [119]. The DX onset for of GeGa and SiGa donors in AlxGa1-xN was predicted to occur at x > 0.52 and x > 0.94, respectively [119]. The fact that the SiGa remains an effective-mass-like donor up to a high-Al composition results in a quite specific situation in AlN, as revealed by temperature-dependent electron paramagnetic resonance (EPR) measurements [121,122]. In these studies, the stable SiGa DX state in AlN is found to be at ~240 meV below the conduction band minimum. In addition, an existence of a metastable DX state at energy ~11 meV below the donor neutral charge state (at ~65 meV) is predicted. (Note that for DX centers in wurtzite crystals the bond rupture can take place either along a bond parallel to the c-axis or along one of the three other equivalent bonds [123].) Then, in nonequilibrium optical measurements (as PL) electrons from the metastable DX state can easily be excited to neutralize the positively charged donor state, and the exciton bound to a neutral donor can be seen in the spectra [116,117]. On the other hand, to get n-type conductivity electrons from the stable DX state have to be promoted to the conduction band. This can explain the donor activation energy of 250–280 meV usually obtained in transport measurements [124,125]. For all other donor dopants (ON, GeGa, SnGa) the DX state is lying deeper in the gap and no effective-mass-like behavior is expected in AlN; thus, no DBE lines should appear in PL spectra. Then, the sharp PL lines observed above the Si DBE [108,110,116,117] can be speculatively attributed to the excited DBE states. Recently, it was theoretically predicted that the substitutional sulfur (S) on nitrogen site (SN) is a very attractive donor dopant for AlN because SN does not form DX center [126]. However, experimental evidence for this prediction is still missing.

Owing to the large bandgap the acceptors in AlN are expected to be quite deep. In analogy to GaN, an obvious acceptor dopant in AlN is Mg. A PL study of the Mg-doped layers grown by MOCVD on sapphire substrate revealed an ABE with a binding energy of ~40 meV and an acceptor binding energy of ~510 meV [127]. Although these values are not confirmed by other studies the Mg acceptor binding energy is fairly close to that obtained from electrical measurements (~630 meV) [124]. The large Mg acceptor binding energy implies a very low free hole concentration, only ~1010 cm−3 has been achieved at room temperature [124]. Recently, a surprising improvement of this status was reported for AlN nanowires (NWs) grown by MBE, where axial p-n junctions were incorporated [128]. Under suitable growth conditions, a rather high-Mg concentration could be achieved in the structure, leading to an estimated hole concentration of the order 1016 cm−3. It was suggested that hopping conduction in the Mg impurity band at high-Mg concentration might be responsible for the very low-activation energy (~23 meV) of the Mg acceptor in this case [129]. These findings, however, are quite ambiguous and need to be confirmed. Other acceptor dopant (Zn, Be) have also been tried in order to achieve p-conductivity in AlN. In a PL study of Zn-doped heteroepitaxial AlN layers an acceptor binding energy of 740 meV was deduced [130] which is larger than that for the Mg acceptor in contrast to the theoretical predictions [131]. For the Be dopant, an acceptor binding energy of 330 meV and an ABE binding energy of 33 meV have been estimated [132].

At high-excitation intensities (~MW/cm2) all DBE-related emissions are saturated, and emission bands related to the bi-excitons (M band), the exciton-exciton scattering (P band) and the electron-hole plasma (EHP band) are observed [110,133,134]. The bi-exciton energy in AlN was estimate as 19 meV [133], 27 meV [134], and 28.5 meV [110]. The P band was found to shift to lower energies with increasing excitation intensity while the energy position of the EHP band (5.83 eV at low temperature) remained constant. At room temperature, the P band merges with the band-to-band recombination and the EHP band becomes the dominant recombination process [110].

As in GaN the biaxial in-plane strain in heteroepitaxial AlN layers causes a shift of all optical transitions from their strain-free energy positions. In the case of a compressive strain (AlN grown on sapphire substrate) the shift is toward higher energies, while for a tensile strain (AlN grown on SiC or Si substrate) the shift is toward lower energies. According to the Bir and Pikus theory [135], the amount of the shift is proportional to the strain via a set of six deformation potentials. In AlN the values of the deformation potentials have been determined from the analysis of the experimental strain dependence of the exciton energies [103,104,136] and by OR measurements under uniaxial stress [114]. Under a higher compressive biaxial strain the valence band ordering is expected to be changed from (Γ7, Γ9, Γ7) to (Γ9, Γ7, Γ7). The critical strain value for this switching was estimated to be 0.7% out-of-plane tensile strain (corresponding to –1.2% in-plane compressive strain) [103]. Note that in Reference [103] the crystal-field splitting of –152.4 meV is assumed, for the more correct value Δcf = –220 meV [99] the critical out-of-plane (in-plane) strain is –1% (1.7%).

3.3.2  Near-Bandgap Optical Transitions in AlGaN

As in all semiconductor ternary alloys, the bandgap in AlxGa1-xN is expected to follow the Vegard law, that is, Eg(AlxGa1-xN) = xEg(AlN) + (1–x)Eg(GaN) – bx(1–x), where b is the so-called bandgap bowing parameter. Values for b reported in literature vary from 0.7 to 1.3 eV [14]. Two issues should be considered when extracting the bandgap from optical measurements in alloys: (i) in all heteroepitaxial layers the strain should be taken into account for a proper analysis of data; (ii) due to random alloy fluctuations the excitons are localized and the PL peaks do not represent the exact energy of the free excitons particularly at low temperatures (so-called Stokes shift). Thus, the OR and SE measurements provide more accurate data. In the case of AlxGa1-xN there is another problem, namely the change of the valence band ordering. As already discussed the top valence band in GaN has Γ9 symmetry, and the lowest free exciton emission is Ec polarized, while the top valence band in AlN has Γ7 symmetry and the lowest free exciton emission it is Ec polarized. Experimentally, the polarization switching was found to occur at Al content of x = 0.1–0.25 [137–139]. The scattering of data can be attributed to the accuracy of the polarized PL measurements and different strain present in the layers. On the other hand the theoretical examination for bulk strain-free AlxGa1-xN have predicted x = 0.145 [103] and x = 0.05 [139] for the Γ9–Γ7 valence bands crossing. (Note again the lower value for the crystal-field splitting, Δcf = –152.4 meV, used in Reference [103]) In a refined analysis where the nonlinear composition variation of Δcf was also included, x = 0.09 was deduced, probably the most accurate value so far [139]. Returning to the bandgap in AlxGa1-xN, the proper way to describe the variation in the Al content is to use two Vegard-like equations (with the same bowing), one for the Γ9 valence band and another one for the Γ7 valence band. The bowing parameter for the Γ9 band was recently determined as b Γ9 = 0.85–0.9 eV [139,140].

As already mentioned at low temperatures the random alloy fluctuations cause a Stokes shift of the exciton emission peak. The difference between the PL peak energy and the energy of the free exciton is called the localization energy (E loc). With increasing temperature, the excitons start to delocalize and the PL peak moves to the higher energies. At some elevated temperatures, all excitons are delocalized and the PL peak corresponds to the free exciton energy. This behavior is illustrated in Figure 3.13 [139], where the PL spectra for an AlxGa1-xN (x = 0.142) sample at different temperatures are presented. The characteristic S-type shape of the temperature dependence of the emission peak energy is clearly evident. At temperatures above 100 K, the emission energy follows the temperature dependence of the bandgap approximated by the Pässler model [141]. It is also seen that the linewidth (or full width at half maximum (FWHM)) of the emission is quite large even in the low-temperature PL spectra. The broadening is also due to the alloy fluctuations. Both the FWHM and the E loc principally depend on the slope of the bandgap composition dependence (i.e., dE g(x)/dx) and the exciton volume, and in AlxGa1-xN both have maximum values at x ≈0.75 [142,143].

(Left) PL spectra for an Al

Figure 3.13   (Left) PL spectra for an AlxGa1-x N (x = 0.142) layer at different temperatures. (The temperature increases from top to bottom.) (Right) Energy position of the PL band as a function of the temperature. The solid line is the fit using the model in Reference [141].

(Reprinted with permission from Neuschl, B., J. Appl. Phys., 116, 113506, 2014. Copyright 2014, American Institute of Physics.)

Owing to the alloy broadening the DBEs and ABEs cannot be resolved separately from the localized excitons even in the low-temperature spectra in undoped AlxGa1-xN materials. The Si and Mg doping further increases the linewidth and quite broad emission bands are usually observed [144,145].

3.3.3  Below-Bandgap Absorption and Emission AlN and AlGaN

The most prominent below bandgap emissions in AlN are observed at 2.8 eV [146,147], 3.1 eV [148,149], 3.7 eV [150–152], and 4.5 eV [148,150,153]. The emissions are quite broad and in different studied samples their energy position varies depending on the growth technique used, as well as on the concentration of the impurities (i.e., on the position of the Fermi level). For bulk AlN, regarded as the best substrate for deep UV LEDs, a number of optical absorption studies have also been reported. Absorption bands at 2.8 eV [153], 3.4 eV [154], 4.0 eV [153], and 4.7 eV [155] were observed. As main defects responsible for these emission and absorption bands, the vacancies of the Al (VAl) and nitrogen (VN) and their complexes with impurities have been considered. The VAl and VN have been predicted by the theory to have low formation energy in n-type and p-type AlN, respectively [156–158]. The VN has been identified by EPR in electron-irradiated PVT grown AlN [159]. In the same type of material VAl of a concentration in the range of 1018 cm−3 have been measured by PAS and almost all of them are found to be complexed with ON in as-grown samples [154]. Note that the O is the most abundant impurity in AlN and is present in concentrations above 5 × 1017 cm−3 independent of the growth method [147,148,155,160].

Recent hybrid functional calculations for the transition states of the vacancies and vacancy-oxygen defects in AlN and the related optical transitions have provided a satisfactory explanation of the most of emission and absorption bands [158]. The VAl, double and single VAl-ON complexes have been suggested as DAs involved in the 2.8 eV, 3.1 eV, and 3.7 eV emissions, respectively. The calculations for the VAl and double VAl-ON acceptor have also predicted absorption peaks at 3.43 eV and 3.97 eV in agreement with the experimental finding [153,154]. Being a deep acceptor CN was also considered as a source of below-bandgap emission and absorption. In fact, both 2.8 eV and 3.7 eV emissions, as well as the absorption at 4.7 eV have been found to increase with C doping concentration [155,160,161]. From a theoretical point of view, the optical properties related to the CN in AlN are similar to those in GaN [69]. The excitation from the (0/–) transition level (at 1.9 eV above the valence band) into the conduction band gives rise to an absorption peaking at 4.7–4.8 eV [69,155]. The corresponding emission (CN 0→CN ) occurs at 3.6–3.7 eV. At high-C concentration the ground state of the CN is its neutral charge state and the absorption and the emission associated with the (+/0) transition level are predicted to be at 5.66 eV and 4.5 eV, respectively [69]. The accounting for the (+/0) transition level can explain the shift of the 3.7 eV emission toward high energies with increasing C doping [155,160]. The 2.8 eV emission has been interpreted as a DAP recombination between the VN and CN (VN donors are expected to form as compensating defects at high-C doping) [161,162]. It was also suggested that the C and Si co-doping suppress the 2.8 eV emission and 4.7 eV absorption due to the formation of CN-SiAl complexes [162].

Studies that address the below-bandgap emissions in AlxGa1-xN alloys are rare so far. As expected the energy positions of the emissions related to the cation vacancies (VGa, VAl) and their complexes were found to follow the trend of the bandgap with Al composition [163]. The same was observed in Mg-doped AlxGa1-xN, where the Mg-related emission at 2.8 eV in GaN was transformed to a 4.7 eV emission in AlN [164].

3.4  Optical Properties of InN and InGaN Alloys

3.4.1  Optical Properties of InN in the Near-Bandgap Region

The properties of InN have by tradition been studied on thin film samples grown on foreign substrates, in particular, sapphire (GaN/sapphire templates). These samples typically have a large defect density, with threading dislocation densities as large as 1010 cm−2. The reason for this situation is the lack of bulk InN substrates, meaning that studies of low-defect density bulk InN properties could not be performed experimentally. This situation is behind many properties ascribed to the InN material, such as degenerate n-type conductivity and Fermi level pinning to the conduction band [165], and problems to produce p-type material [166].

The bandgap of InN was for a long time assumed to be about 1.9 eV [167]. However, about 15 years ago the absorption and PL measurements on MBE grown single-crystalline InN epitaxial layers have evidenced a bandgap of ~0.7 eV [168]. The experimentally obtained smaller bandgap has later been confirmed by theoretical calculations of the InN band structure [21,169,170]. The splitting of the top valence band due to the crystal field and the spin-orbit interaction is quite small, just a few meV (as in the case of GaN) [21], and could so far not be resolved experimentally in optical data.

Since the dopant/defect density in the heteroepitaxial InN samples studied are well above 1017 cm−3, the free or bound excitons could not be resolved (the free electron concentration at such a doping density is above the Mott density in InN, ∽2 × 1017 cm−3 [171]). The near-bandgap emission spectra in degenerate n-type InN was explained as a recombination of the free electrons with localized holes [172] or as governed by Mahan excitons [173]. Nominally undoped InN material such as NWs grown by MBE under suitable conditions shows a Fermi level position near to the middle of the bandgap, (i.e., no electron accumulation in the conduction band occurs), and thus has the closest to intrinsic properties reported so far [174]. Exciton PL was claimed to be observed for the first time in such nominally undoped InN NWs, with a linewidth down to 9 meV [175] (see Figure 3.14). Future studies need to confirm whether these data at low temperature relate to free excitons (as claimed in Reference [175]) or to bound excitons related to impurities. The PL data are consistent with a binding energy of just a few meV for the excitons (a thermal activation energy about 3 meV was measured). The NW data confirm that the commonly observed degenerate n-type property, typical for planar samples grown on sapphire, is related to the high-defect density (the defects are believed to create donor-like states in the conduction band), or to the surface segregation of donor species [175].

Low-temperature spectrum of intrinsic InN nanowires taken at an excitation power of 0.5 μW.

Figure 3.14   Low-temperature spectrum of intrinsic InN nanowires taken at an excitation power of 0.5 μW.

(Reprinted with permission from Zhao, S., Nano Lett., 12, 2877, 2012. Copyright 2012, American Chemical Society.)

For InN layers grown on sapphire a p-type material can be obtained by Mg doping in the 1018–1019 cm−3 doping window [176,177], but for a Mg concentration of above 1020 cm−3 the material converts to n-type due to a simultaneous creation of a high concentration of structural defects like SFs [178]. The situation appears to be different for the case of InN NWs, which can be grown virtually defect (dislocation) free even on foreign substrates [174,175]. Such material can be doped with Mg in a controlled manner without severe compensation [179]. In Figure 3.15 are shown the PL spectra in Mg-doped NWs at different excitation powers [180]. The lower energy PL peak is Mg-related and is situated about 60 meV below the near-bandgap emission, in agreement with earlier studies on thin films [181].

Low-temperature PL spectra of low Mg-doped InN nanowires measured at different excitation powers. At the lowest excitation power (0.1 mW) the FWHM is 17 meV.

Figure 3.15   Low-temperature PL spectra of low Mg-doped InN nanowires measured at different excitation powers. At the lowest excitation power (0.1 mW) the FWHM is 17 meV.

(Reprinted with permission from Zhao, S., Appl. Phys. Lett., 103, 203113, 2013. Copyright 2013, American Institute of Physics.)

At this stage, detailed studies of the optical properties of InN are quite difficult because defect free macroscopic crystals are still lacking. A development of growth techniques for bulk InN crystals is highly desired.

3.4.2  Absorption and Emission in InGaN Alloys

InxGa1-xN alloys are the basic materials for visible light emission in nitride-based LEDs. InxGa1-xN has not been studied much as bulk material, due to difficulties to grow thick layers by MOCVD or MBE. Recently some success has been demonstrated by HVPE growth on GaN substrates, where InxGa1-xN layers of a thickness of >10 µm have been demonstrated [182]. Near-bandgap emissions of MOCVD grown InxGa1-xN layers on sapphire have been studied since decades, mainly with the ambition to determine important parameters for the InxGa1-xN alloy system, such as the bandgap variation according to the Vegard law Eg(InxGa1-xN) = xEg(InN) + (1–x)Eg(GaN) – bx(1–x). The studies usually combine optical emission data with a determination of the absorption edge (preferably via SE). Such a study including both N-face and metal-face samples was performed in In-rich alloys and the bandgap values corrected for free carrier density were obtained [183]. Later the data was additionally corrected for the strain and the study was extended to Ga-rich alloys [184]. The In dependence of the transition energies for the high-energy critical points was also examined. The experimental data is shown in Figure 3.16. The best fit for the bandgap energy with the end-point values Eg(GaN) = 3.435 eV and Eg(InN) = 0.675 eV results in a bowing parameter b = 1.65 ± 0.07 eV in strain-free InxGa1-xN at room temperature. The bowing parameter for the high-energy critical points was found to smaller (~1 eV) [184]. The bandgap bowing parameter varies between large limits in early works mainly due to the small range of In composition considered or/and to using Eg(InN) = 1.9 eV [14]. It has been predicted by the theory that the bowing parameter in InxGa1-xN depends on In content, and thus, the Vegard law cannot satisfactorily describe the bandgap variation in the entire composition range [185].

Bandgap and high-energy inter-band transition energies in In

Figure 3.16   Bandgap and high-energy inter-band transition energies in InxGa1-xN as a function of In content. The full symbols present the energies determined from the imaginary part of dielectric function measured by SE [183,184], while the open symbols are literature data obtained from optical absorption measurements. The solid lines represent the best fits for determining the bowing parameters.

Regarding the near-bandgap emission in InxGa1-xN alloys, all comments about the exciton localization we put above for AlxGa1-xN are valid for InxGa1-xN as well. However, for the same In and Al content, the E loc and the emission broadening are larger in InxGa1-xN alloys. The strong exciton localization in InxGa1-xN is believed to be a result of the capture of the holes by localized valence states associated with atomic condensates of In-N [186]. In fact, the exciton/carrier localization has been considered as the main reason for the high-internal quantum efficiency InGaN/GaN LEDs emitting in blue and UV spectral region.

3.5  Conclusions

The optical properties of the III-nitrides have been studied over about half a century, along with the development of growth techniques. GaN properties are now quite well covered in the literature, and for AlN, the situation is rapidly improving, since doping is getting under control. Recent results on InN promises more detailed knowledge, but a bulk material of more than nanometer size is indeed needed in the future. The alloys InGaN, AlGaN, and AlInN are very important for devices, and here, the influence of several effects like composition fluctuations and strain from substrates or other layers still restricts the accuracy of data in many cases. The increasing relevance of quantum size structures for optical III-nitride devices has created a new subfield that is not discussed in any detail in this chapter.

Acknowledgments

We would like to thank Prof. R. Goldhahn, Prof. Z. Mi, Prof. B. Skromme, Dr. M. Feneberg, Dr. M. Funato, Dr. J. Lähnemann, Dr. B. Neuschl, and Dr. S. Shokhovets for providing electronic data for the figures. P. P. Paskov acknowledges the partial support from the Swedish Energy Agency.

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