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Spectra, energy levels and crystal field calculation of Er3+ doped in AlN nanoparticles
Author’s Accepted Manuscript Spectra, energy levels and crystal field calculation of Er3+ doped in AlN nanoparticles T. Kallel, T. Koubaa, M. Dammak, S.G. Pandya, M.E . Kordesch, J. Wang, W.M. Jadwisienczak, Y. Wang www.elsevier.com/locate/jlumin
PII: DOI: Reference:
S0022-2313(15)30291-X http://dx.doi.org/10.1016/j.jlumin.2015.11.002 LUMIN13699
To appear in: Journal of Luminescence Received date: 22 July 2015 Revised date: 24 October 2015 Accepted date: 4 November 2015 Cite this article as: T. Kallel, T. Koubaa, M. Dammak, S.G. Pandya, M.E . Kordesch, J. Wang, W.M. Jadwisienczak and Y. Wang, Spectra, energy levels and crystal field calculation of Er3+ doped in AlN nanoparticles, Journal of Luminescence, http://dx.doi.org/10.1016/j.jlumin.2015.11.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Spectra, energy levels and crystal field calculation of Er3+ doped in AlN nanoparticles
T. Kallela*, T.Koubaaa, M. Dammaka, S.G. Pandyab, M. E .Kordeschb, J. Wangc, W. M. Jadwisienczakc, Y. Wangd a
Laboratoire de Physique Appliquée, Groupe des Matériaux Luminescents, Université de Sfax, Faculté des Sciences de Sfax, Département de Physique, Route de Soukra, Km 3.5, B.P. 1171 3000 Sfax, Tunisia
b
Department of Physics and Astronomy, Ohio University, USA
c
School of Electrical Engineering and Computer Science, Ohio University, Athens, OH 45701, USA
d
Center for Electrochemical Engineering Research, Ohio University, Athens, OH 45701, USA
Abstract Optical properties of Er-doped AlN nanoparticles (NPs) synthesized by Inert Gas Condensation (IGC) on silicon (111) substrates were investigated. Transmission electron microscopy (TEM) and high resolution TEM (HR-TEM) were used to study the shapes, morphologies and size of the synthesized AlN: Er3+ NPs which have a spherical shape with a mean diameter between 12 nm and 15 nm. The optical properties of AlN: Er3+ NPs were assessed from low temperature cathodoluminescence spectra (CL). The CL spectra show visible and near infrared sharp and broad emission lines associated with Er3+ ions. The observed Er3+ ion transition lines broadening is due to the surface defect in studied NPs. Comparative investigations of the luminescent properties of AlN: Er3+NPs with those of AlN: Er3+ thin films show the presence of some similarities between the lattice sites occupied by Er3+ ions in these hosts. It was found that in AlN NPs the Er3+ ion occupy a second optical center which is the VN-Er complex beside the ordinary substitutional ErAl center observed in the case of AlN:Er3+ epilayers. Assuming the presence of these two sites occupied by Er3+ ions, the majority of CL emission lines were attributed. The experimental Stark energy levels of Er3+ ion manifolds are established for the Er-doped AlN NPs and the correspondent crystal field parameters are calculated.
Key words: Crystal-field calculation; Optical spectroscopy; Stark splitting; AlN nanoparticles --------------------------------------------------------------------------------------------------------------------------*Corresponding author. Tel.: +216 74 274 088; fax: +216 74 274 437. E-mail address: [email protected] (T. Kallel).
1. Introduction Over the last few years, nanostructured materials research has grown rapidly. Research on semiconductor nanoparticles (NPs) has also witnessed a considerable interest because of their potential applications in electronics and optoelectronics including light emitting devices [1, 2]. In addition, these NPs are becoming an indispensable part of functional materials, essentially bridging the gap between biotechnology and material science, with applications in the field of in vivo imaging, gene therapy, cancer treatment, regenerative medicine, tissue engineering, and biomaterials development [3-7]. The III-V nitride semiconductor family (InN, GaN and AlN and their alloys) are technologically important semiconductors because, among other properties, their direct band gaps span a wide region in the electromagnetic spectrum from deep ultraviolet (UV) to infrared (IR), making them attractive for light emitting diodes (LEDs) and laser diodes (LDs) [8, 9]. Among the IIInitrides, AlN has gained considerable attention because of its properties such as wide band gap (6.2 eV), high volume resistivity, high thermal conductivity at low temperature, low dielectric constant and excellent thermal expansion coefficient, excellent chemical stability and good mechanical strength [10-13]. Furthermore, AlN NPs are of interest due to their prospective applications in optoelectronic and field emission nano-devices [14-16]. These properties make AlN NPs a suitable host material for rare earth (RE) ions doping, which offers emission over the entire visible spectrum with reduced luminescence quenching as compared to semiconductors with narrower band gaps [17]. Recently, RE-doped NPs have been proposed for a variety of applications including solid state lasers, display, low intensity IR imaging, watermarking technology, 3D storage media, solar cells and other biological probes [18-27]. The synthesis of different NPs has been demonstrated using several methods including, among others, precipitation in solution, sol-gel methods, mechanical attrition and spray pyrolysis [28-31]. Another method for the synthesis of III-nitride NPs is the inert gas condensation (IGC) process. In IGC, the precursors are sputtered by inert gas atoms [32-39]. The advantage of the gas-phase method over other chemical and physical processes is the high-purity level and chemical stability of resulting NPs due to vacuum. Control over cooling rates and residence time in the gas-phase synthesis methods can be obtained by optimizing the process parameters to tailor NPs properties [40]. As the use of RE doped NPs is becoming increasingly important in industrial applications, there is much interest in understanding their optical properties. In the recent years, the optical features of REdoped oxide semiconductor nanorods as Ga2O3, GeO2 and ZnO have been investigated [41-45]. However, the optical investigations of RE-doped III-nitride NPs are rather scarce. In our previous work, we have studied the optical behaviors of AlN: Er3+ and GaN: Yb3+ epilayers [46-49]. Furthermore, we have studied the optical properties of GaN:Yb3+ nanorods and we have compared all the obtained results with those obtained for GaN:Yb3+ epilayers [50].
In the current work, we aim to continue our previous studies by the investigation of the optical behaviors of Er-doped AlN NPs, synthesized by IGC technique on silicon substrate. The synthesized NPs were analyzed by transmission electron microscope (TEM) and high resolution transmission electron microscope (HRTEM). The optical investigations were carried out using low temperature high resolution cathodoluminescence (CL) spectra. The optical centers occupied by Er3+ ions in AlN NPs were identified and compared with those reported for AlN: Er3+ epilayers. The effect of the nanosize on the AlN:Er3+ optical behaviors was discussed. In addition, using the crystal field theory, the Stark energy levels of the Er3+ ions occupying different optical centers have been calculated and compared with those obtained for Er3+ in AlN epilayers.
2. Experimental details The AlN: Er3+ NPs discussed in this paper were developed using IGC synthesis protocol described elsewhere [32,51]. In short, radio frequency (RF) sputtering was used as the source of the material condensed in the presence of argon (Ar) gas in the condensation chamber. The condensation chamber was separated from the deposition chamber by a small nozzle with 2 mm in diameter. The pressure difference between adjusted chambers results in the formation of a NPs beam. The NPs are deposited on the 2525 mm2 (111) p-type Silicon substrate placed in the deposition chamber. The Silicon substrate is placed precisely in front of the nozzle at a distance of about 1-2 cm. During the deposition process, a target (99.99% of Al disk at 37 nm O.D. with an insert of 99.99% of Er metal pellet) was sputtered in the presence of argon (Ar) and nitrogen (N) gases in ratio 1:1. The ratio of Al to Er metals was 1:8 in terms of their masses. The base pressure of the system was kept up at 10−7 Torr. Sputtering power, pressure difference between the condensation and the deposition chamber, and sputtering time were varied in order to produce NPs of desirable size(s). The effect of the IGC deposition parameters on the NPs size has been discussed elsewhere [32]. The aggregation length describing the distance between nozzle and the sputtering source was kept constant at 10.5 cm. The selected NPs specimens deposited on silicon wafers were heated in vacuum at 500 °C for 1 hr and in air at 1000 °C for 2 hrs, respectively. Structural characterization of the NPs before and after heating was carried out using JEOL 1010 transmission electron microscope (TEM) operated at 100 kV. The sizes and morphology of the NPs were observed by a JEM-2010 high resolution transmission electron microscope (HRTEM) operated at 200 kV and a scanning near-field optical microscope model WITecR-SNOM-300s. The CL spectra were measured in 10–300 K temperature range and excited by an electron gun (Electroscan EG5 VSW) with electron beam acceleration energy not exceeding 5 keV. The emission spectra were dispersed by a 0.3 m spectrograph and analyzed by a Princeton Instruments backilluminated charge- coupled device (CCD) camera with a UV/AR coating, operating in the spectral region 200–1050 nm, and controlled by a computer.
3. Theoretical modeling Er3+ ion has 4f11 configuration which gives rise to a 4I15/2 ground state and 4F9/2, 4S3/2, 2H11/2, 4F7/2, 2H9/2, 2
P3/2 excited states in the visible range. All the energy levels of Er3+ ion in AlN host split into Kramers
doublet states with E1/2 or E3/2 symmetry in the C3V double-rotation group (C 3V ) [52]. The wave functions and energy levels of these doublets can be calculated through the diagonalization of the operator Hamiltonian: H=HFI +HCF
(1)
Where HFI contains all free-ion interactions and HCF describes the crystal field interactions. The free ion interaction Hamiltonian used in eq.1 has the form:
HFI = E k ek +4f ASO +αL L+1 +βG G 2 +γG R 7 + Ti t i + M k mk + P k pk k
i
k
(2)
k
where H FI consists of 15 parameters controlling interaction between term multiplets, E k (k = 1, 2, 3) is the Racah parameters corresponding to linear combinations of Slater radial integrals, α , β and γ are the parameters associated with the two-body effective operators of configuration interaction , L the orbital angular momentum and G(G2) and G(R7) being the Casimir operators of the groups G2 and R7. The T i (i = 2–4, 6–8) is the radial parts of the corresponding three-body effective operators. The
M k (k = 0, 2, 4) parameters are the magnetic interactions parameters representing the magnetically correlated corrections such as spin–spin and spin–other-orbit interactions, while the P k (k = 2, 4, 6) parameters arise from electrostatic spin-orbit interactions with higher configurations, with pk and mk being the corresponding operators. The remaining free-ion parameter is the spin–orbit interactions between f electrons. The crystal-field term, HCF , takes into account the effect of the electrostatic interactions due to the surrounding ions on the f electrons. Calculations are usually carried out within the single-particle crystal-field theory. Following the Wybourne formalism [53], the one-electron HCF Hamiltonian is expressed as a sum of products of spherical harmonics and real Bkq and complex S kq crystal field parameters (CFPs). The expression of HCF Hamiltonian is given by Eq.3:
k
HCF =
B
k 2,4,6 q 0
q k
C
q k
q q 1 Ck q iSkq Ckq 1 Ck q
(3)
where Ckq and Ck q are the tensorial operators. The number of non-zero CFPs ( Bkq and S kq ) in Eq.3 depends on the local site symmetry of the RE ion. For the trigonal symmetry (C3V ) occupied by Er3+
ion site in AlN host, the serial development of the crystal-field potential involves only six non-zero CFPs describe as:
HCF B20C20 B40C40 B60C60 B43 (C43 C43 ) B63 (C63 C63 ) B66 (C66 C66 )
(4)
In this current study, the energy levels of Er3+ ion in AlN NPs were calculated by simultaneous treatment of both free ion and crystal-field effects using the entire basis set of wave functions.
4. Results and discussions 4.1. Morphology studies of AlN:Er3+ NPs The morphologies of the AlN: Er3+ NPs were analyzed by TEM to differentiate between the crystalline and amorphous phases of NPs. Moreover, this approach gives reliable information about the synthesized NPs surface. Figure 1 (a) shows the TEM images of synthesized AlN: Er3+ NPs which have a spherical shape with a mean diameter of about 12 nm 15 nm, as can be seen from the histogram (Fig. 1(b)) depicting the statistical size distribution of the NPs. This value has been obtained by fitting the size distribution histogram to a Gaussian function. Furthermore, it can be seen that the particles are uniform in shape and there are no signs of coalescence. The HRTEM images of single NPs having different distinct diameters are shown in Fig. 2. The NPs have a crystalline structure with clearly interplanar distances between adjacent crystallographic planes for the AlN: Er3+ NPs. The lattice spacing of 0.19 nm, seen in Fig. 2(a), corresponds to (102) growth directions of hexagonal AlN. Similarly in Fig. 2(c), the lattice spacing of 0.54 nm corresponds to (001) direction of hexagonal AlN whereas the lattice spacing of 0.28 nm corresponds to (100)/(010) direction of hexagonal AlN. Because of the particle nano-size, it is expected that the observed NPs lattice parameters can be slightly different from the bulk material due to the surface tension difference (usually enlarged by decreasing the NP diameter). Based on the obtained HRTEM results, we show that most of the studied AlN: Er3+ NPs have hexagonal crystal structure. Small NPs are single crystalline in nature, whereas some large NPs show polycrystalline behavior. The typical AlN: Er3+ NPs sample used in this study has a 85:15 ratio for single-crystalline:poly-crystalline phases. The Fourier transform of HRTEM images for small and large NPs are shown in Fig.2 (b, d). It gives the corresponding orientations of the crystallographic planes for as-deposited AlN:Er3+ NPs. HRTEM indicates that the AlN: Er3+ NPs are hexagonal and relatively uniform. 4.2. Cathodoluminescence spectrum of AlN: Er3+ NPs In the aim to theoretically model the spectral feature of AlN: Er3+ NPs, CL spectra were measured at 11 K and recorded in the 9900 cm-1 - 26500 cm-1 spectral range. Figure 3 shows the CL spectrum of AlN: Er3+ NPs grown on silicon substrates recorded at 11 K. It is seen that CL spectrum
reveals several groups of peaks corresponding to Er3+ intra-4f 4
4
4
4
2
n
shell transition originated from
2
different excited states ( I11/2, I9/2, F9/2, S3/2, H9/2, G11/2) to (Z1, Z2, Z3,… Z8) 4I15/2 ground state. As shown in Fig. 3, the CL spectra of AlN:Er3+ NPs is dominated by green and red bands, corresponding respectively, to the 4 S3/ 2 4 I15/ 2 and the 4 F9/ 2 4 I15/ 2 transitions. The summary of CL spectra containing 97 emission lines is collected in Table 1 and in Fig. 4 through Fig.6 showing high resolution CL spectra of separated groups of transition lines. These figures clearly show the presence of sharp and broadened emission lines attributed to intra-shell 4f 11 transitions of the Er3+ ion configuration. In case of AlN: Er3+ NPs, the broadening of the emission lines observed in CL is expected. In fact, and according to crystal field theory, the electronic energy levels of RE ions in NPs may vary because of changes in the strength of the local electrostatic field and site symmetry [54]. In NPs, structure disordering and surface defects are inevitable, and emission lines in nanocrystalline materials show extra inhomogeneous broadening with regards to bulk crystals, especially due to the enormous increase in surface sites compared to bulk sites [55]. The broadening of some of the Er3+ ion emission lines observed in the AlN: Er3+ CL spectra means that the Er3+ ion luminescence is affected by the generated surface defects which contribute on the optical behavior of Er 3+ ion incorporated to AlN NPs. It is also worth mentioning that the erbium related luminescence line width broadening suggests that the Er3+ ions most probably occupy more than one optical center in AlN NPs. The discussion of these different optical centers occupied by Er3+ ion in AlN NPs will be presented in the next section. Specifically, In order to understand the effect of the nano-dimension and the surface defects on the optical properties of Er3+ ion, we have compared CL spectra obtained for the AlN:Er3+ NPs synthesized by the IGC method with CL spectra of the AlN:Er3+ epilayers reported in our previous work [48]. Figure 7 shows the assembly of CL spectra of AlN:Er3+ NPs and epilayers in 16000 - 26200 cm-1 spectral range. Comparison of these CL spectra evinces the presence of the same 4f-4f transitions corresponding to the
4
S3/ 2 , 2 H9/ 2 4 I15/ 2 transitions located at 17888 cm-1 and 24310 cm-1; however, the CL
spectrum for AlN:Er3+ NPs does not show any noticeable emission lines originating from the 2H11/2 and 4F7/2 manifolds as observed in the CL spectra of AlN:Er3+ epilayer [48]. In addition, we note that the CL spectra of AlN:Er3+ epilayer is dominated by the blue emission corresponding to 4
F7 / 2 4 I15/ 2 transition. Whereas, in the case of AlN:Er3+ NPs, we note the dominance of red and
green emission lines corresponding, respectively, to
4
F9/ 2 , 4S3/ 2 4 I15/ 2 transitions. The
enhancement of red and green bands and the quenching of the blue emission from Er3+ ion incorporated in AlN NPs can be explained by the presence of (de)populating channels of 4F9/2 and 4S3/2 levels from the 4F7/2 excited states. Among these possible energy transfer pathways, we believe that the multiphonon relaxation and the non-radiative cross relaxation (CR) processes, which occurs between neighboring Er3+ ions in AlN NPs are the most probable to occur. A simplified energy levels
diagram of Er3+ ion in AlN NPs shown in Fig 9 illustrates the possible mechanisms of observed emission and energy transfer processes. It is well known that in Er-doped AlN epilayers, having a low dopant concentration, Er3+ ions are usually randomly distributed in the host lattice and the neighboring Er3+ ions distances are too far apart resulting in a decrease of the energy transfer probability between the Er3+ ions. Because of that, one can observed blue emission from the 4F7/2 manifold in the AlN epilayers. However, in case of the AlN:Er3+ NPs and due to the nano-size dimension, some of the Er3+ ions have closer nearest neighbors resulting in various CR processes between Er3+ ions. This in fact can depopulate the 4F7/2 level and result in effective quenching of radiative emission from this energy state. The related mechanism can be described as follows, in the case of AlN NPs, the short distances between Er3+ ions in AlN host lattice favor interionic interactions, resulting an efficient near resonant CR processes between Er3+ ions, ( 4 F7 / 2 4 F9 / 2 ) and ( 4 I15/ 2 4 I13/ 2 ) transitions, as shown in Fig. 9. The 4F9/2 states became greatly populated from 4F7/2 states through the CR process resulting in intense red emission observed in the CL spectra of ALN:Er3+ NPs. Furthermore, the 4F7/2 states decay nonradiatively to the 4
4
S3/2 states, resulting in observing green emission lines attributed to
S3/ 2 4 I15/ 2 transition. The disappearance of the 2H11/2 transition in the AlN:Er3+ NPs CL spectra
can also be explained by the CR process between Er3+ ions, ( 2 H11/ 2 4 F9 / 2 ) and ( 4 I13/ 2 4 I11/ 2 ) transitions (see Fig.9). 5. Optical luminescent centers of AlN:Er3+ NPs In general, density function theory is used to investigate RE impurities in the III-V (AlN,GaN) host.[56-58]. Based on available theoretical models, there is a common consensus that the most stable site for the RE3+ ion in a GaN host is a Ga substitutional site. On the other hand, recent theoretical calculations also suggest that it is energetically favorable for incorporated RE ions to create centers such as the VN-RE complexes involving a nitrogen vacancy defects, which are very common defects in the GaN and AlN hosts [59]. We have reported recently, the presence of two main optical centers in the case of GaN: Yb3+ nanorods (NRs), which are the substitutional YbGa and the complex Yb-VN sites [50]. It was shown that the reduced dimensionality of the GaN host (nano-size) promotes the formation of VN-Yb complexes involving VN defects at the expense of the substitutional (RESI) center formation. In order to investigate the optical centers occupied by the Er3+ ions in the AlN NPs, we have presented in the same Fig. 8 the CL spectra corresponding to the 4S3/2 4I15/2 transitions observed for AlN:Er3+ NPs and epilayer hosts. It is clearly seen that in the case of AlN:Er3+ NPs, the presence of the same emission lines as observed for AlN:Er3+ epilayer, along with additional emission lines not observed in AlN:Er3+ epilayer confirms the postulate about Er3+ ion occupying more than one center in the AlN NPs host. We have demonstrated that in the case of Er3+ doped AlN epilayers the dominant optical center occupied by the Er3+ ion is the substitutional ErAl site (RESI) [48]. However,
the presence of new emission lines observed in the CL of AlN:Er3+ NPs confirms the existence of another optical center, which is the VN-Er complex, such as obtained in the case of GaN:Yb NRs [50]. The analysis of presented experimental results leads us to presume the presence of an additional optical center occupied by the Er3+ ion in studied AlN NPs. Based on the reasoning presented
above, we propose that it is the complex Er-VN. In the following we will confirm this assumption by conducting the detailed theoretical analysis of the CL spectra (see Figs. 4-6) obtained for the AlN:Er3+ NPs at low temperature. We assigned the broad emission lines seen in Fig. 4 to 4 I9 / 2 4 I15 / 2 transition to the additional optical center (VN-Er complex) which can be located e.g. at near of AlN NPs surface. This assignment is confirmed by the fact that in case of RE-doped nanocrystals, the REs ions can be located partially inside of the NPs (RESI center) as well as at AlN NPs surface (complex centers) [60]. In fact, one can expect that the incorporation of Er in the NPs volume is smaller than that in an epilayer volume [17]. This prevents the formation of RESI center and promotes the formation of Er-VN complexes involving nitrogen vacancy (VN). It is well known that the exciton Bohr radius of the AlN host is less than a few angstroms [61]. Therefore, quantum size confinement in AlN NPs having 12 nm diameter should not affect the localized electronic states of the Er3+ ion localized 4f-shell electrons. So, it is expected that the Stark splitting of Er3+ ion manifolds when doped to single crystal AlN epilayers or AlN NPs should be very close. The detailed analysis of the observed emission lines of Er3+ ions in AlN NPs will be presented in the next section. 6. Modeling of the Er3+ ion energy levels in AlN NPs grown on silicon substrates Using the formalism developed by Racah and Norman [62, 63], the experimental Stark energy levels of Er3+ in AlN NPs were numerically simulated. It is known that rigorous simulation needs a clear experimental support. The specimens studied here are composed of NPs having varied diameter (see Fig.1). Thus, one can expect that the probability of surface defects occurrence in AlN:Er3+ NPs increases for smaller diameter NPs. Considering the fact that the CL spectra were collected over a large surface area (>0.5 mm2), considered here as global CL spectra, the observed emission from optically active Er3+ ions occupying different sites in NPs having different diameter cannot be spatially resolved. Therefore, the presence of broad Er3+ ion emission lines ( 4 I9/2 , 4 G11/2 4 I15/2 ) in CL spectra are most probably resulting from the superposition of sharp transition lines generated by individual NP having different surface to volume ratio. In order to analyze these observed Er3+ ion emission lines in detail, we have used the multi-Gaussian fitting as shown in Fig.4 and Fig.6. Base on the global CL spectra of AlN:Er3+ NPs, we have established two sets of experimental Er3+ ion Stark energy levels, corresponding to the purely ErAl substitutional site without defects involve in the RESI center and the VN-Er complex. The calculated and experimental energy levels of Er3+ ion occupying substitutional (R) and complex (C) centers in AlN:Er3+ NPs deposited on silicon substrates are shown
in Table 2. The calculated energy levels of Er3+ ions were obtained by diagonilazing the Hamiltonian described in Section 3. It should be noted that the Er3+ ion Stark energy level calculations are performed for the ordinary substitutional ErAl site with trigonal symmetry (C3v). In case of the VN–Er defect complex, we have assumed in calculations that it has the same symmetry as the ErAl substitutional site (C3v) with some distortion [ 50]. The fitting procedure executed here and described in our previous work [64], assumes the selection of adequate sets of free-ion and crystal-field parameters. Since H FI is expected to be largely independent of the host we have used the parameters which were determined previously for the Er3+ ion in AlN epilayers [48] as starting set of free-ion parameters. However, it should be mentioned that M k and P k parameters were not varied in the present fitting procedure. The free ion parameters obtained by the fitting procedure are shown in Table 3. Indeed, it was found that these values are close to those reported in our earlier study for Er3+ ions in AlN epilayers [48]. For the initial CFPs, we have started the fitting process from the initial CFPs used in the case of AlN: Er3+ epilayers obtained by lattice-sum calculations [46- 50]. The parameter values used as a reference point in order to fit the obtained experimental Stark energy levels of Er3+ ion in AlN NPs are collected along with those obtained from the best fit in Table 3. The fitting process involved 97 experimentally observed Er3+ ion energy levels observed between energies of 9900 cm-1 and 26200 cm-1 in the data fitting process. The resulting root mean square deviation is about 3.6 cm-1 in the case of Er3+ ion occupying the substitutional center (RESI) and 2.1 cm-1 for the VN-Er complex that confirms the fitting procedure consistency. The good agreement between the calculated and the experimental Stark energy levels (see Table 2) confirms the proposal that the Er3+ ions in AlN NPs occupy beside the purely substitutional Al center, a second optical center which is the VN-Er complex. 7. Conclusion In this study, AlN:Er3+ NPs were deposited on silicon substrates by using the IGC method. The majority of AlN:Er3+ NPs have spherical shapes with a mean diameter of about 12 nm. The homogeneity of NPs observed using HRTEM confirmed good crystallinity of NPs regardless of their diameter. The CL spectra of AlN:Er3+ NPs were investigated and compared with those reported for AlN:Er3+epilayers. The comparison of the optical features of Er3+ ion incorporated in AlN NPs and to AlN epilayers shows the presence of the substitutional ErAl and the VN-Er complex centers. This complex center is primarily associated with the NPs surface. The broadening of the VN–Er complex emission lines in the AlN NPs CL spectra indicates that the Er3+ ions predominantly reside close or on the NPs surface. Furthermore, the Stark energy levels of Er3+ ions in AlN NPs were calculated using the crystal field theory assuming the presence of two optical centers with C3v symmetry. The calculated Er3+ ion manifolds splitting are in good agreement with the experimental values which confirms that the Er3+ ions in AlN NPs occupy two sites, the substitutional (ErGa) and the complex (VN-Er) centers, respectively.
Acknowledgements Authors would like to acknowledge the Center for Electrochemical Engineering Research (CEER) through the NSF Major Research Instrumentation Grant # CBET-1126350 for the access to Transmission Electron Microscopy facility at OU. WMJ acknowledges the support from the NSF CAREER program under No DMR-1056493.
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Figure captions Fig. 1. TEM images of AlN:Er3+ NPs. The length scale bar is 100 nm in (a), (b) Size distribution histogram for AlN:Er3+ NPs obtained from TEM image seen in (a). Fig. 2. HRTEM images of AlN: Er3+ NPs having different diameters. (a) Small diameter NP having the lattice spacing 0.19 nm of hexagonal AlN corresponding to (102) direction for hexagonal AlN. (b) Fast Fourier Transform (FFT) of the TEM image in (a) confirming the growth direction of (102). (c) Large NP showing lattice constants 0.28 nm and 0.54 nm corresponding to (010)/(100) and (001) direction of hexagonal AlN. (d) FFT of the NP seen in (c) confirming the growth along (001) and (100)/(010) directions. Fig. 3. CL spectrum of AlN: Er3+ NPs grown on silicon substrates recorded at 11 K. Fig. 4. CL spectrum of AlN: Er3+ NPs synthesized using IGC method and observed between (a) 9900-10400 cm-1, (b) 11560-11750 cm-1, (c) 11760-12390 cm-1 corresponding to 4 I11/2 , 4 I9/2 4 I15/2 transitions at 11 K. (c) Example of the observed broadening transition lines deconvoluted using partial Gaussian functions. Blue line curves indicate deconvoluted individual Gaussian functions with peak positions indicated by short vertical lines and associated numbers from Table 1. Red line curve is the sum of all individual deconvoluted individual Gaussian peaks. Fig.5. CL spectrum of AlN: Er3+ NPs synthesized by IGC method and observed between (a) 13500-15400 cm-1 and (b) 17200-18400 cm-1 corresponding to 4 F9/2 , 4S3/2 4 I15/2 transitions at 11 K. The peak positions indicated by short vertical lines are associated numbers from Table 1. Fig.6. CL spectrum of AlN: Er3+ NPs synthesized by IGC method and observed between (a) 23400-24600 cm-1 and (b) 25640-26200 cm-1 corresponding to 2 H9/2 , 4G11/2 4 I15/2 transitions at 11 K. (b) The observed broadening transition lines were deconvoluted using partial Gaussian functions. Blue line curves indicate deconvoluted individual Gaussian functions with peak positions indicated by short vertical lines and associated numbers from Table 1. Red line curve is the sum of all individual deconvoluted individual Gaussian peaks. Fig. 7. Comparison of the low temperature CL spectra of AlN: Er3+ NPs and AlN: Er3+ epilayer reported in Ref. [48]. Fig. 8. Comparison between low temperature CL spectra of AlN: Er3+ NPs and AlN: Er3+ epilayer showing differences in the 4S3/2 4 I15/2 transition lines energies resulting from the crystal field splitting in AlN NPs and AlN epilayer hosts.
Fig.9. Simplified energy levels of Er3+ ion in AlN NPs showing different energy transfer processes responsible for populating the 4S3/2 and 4F9/2 levels.
Fig. 1. TEM images of AlN:Er3+ NPs. The length scale bar is 100 nm in (a), (b) Size distribution histogram for AlN:Er3+ NPs obtained from TEM image seen in (a).
Fig. 2. HRTEM images of AlN: Er3+ NPs having different diameters. (a) Small diameter NP having the lattice spacing 0.19 nm of hexagonal AlN corresponding to (102) direction for hexagonal AlN. (b) Fast Fourier Transform (FFT) of the TEM image in (a) confirming the growth direction of (102). (c) Large NP showing lattice constants 0.28 nm and 0.54 nm corresponding to (010)/(100) and (001) direction of hexagonal AlN. (d) FFT of the NP seen in (c) confirming the growth along (001) and (100)/(010) directions.
Fig. 3. CL spectrum of AlN: Er3+ NPs grown on silicon substrates recorded at 11 K.
Fig. 4. CL spectrum of AlN: Er3+ NPs synthesized using IGC method and observed between (a) 9900-10400 cm-1, (b) 11560-11750 cm-1, (c) 11760-12390 cm-1 corresponding to 4 I11/2 , 4 I9/2 4 I15/2 transitions at 11 K. (c) Example of the observed broadening transition lines deconvoluted using partial Gaussian functions. Blue line curves indicate deconvoluted individual Gaussian functions with peak positions indicated by short vertical lines and associated numbers from Table 1. Red line curve is the sum of all individual deconvoluted individual Gaussian peaks.
Fig.5. CL spectrum of AlN: Er3+ NPs synthesized by IGC method and observed between (a) 13500-15400 cm-1 and (b) 17200-18400 cm-1 corresponding to 4 F9/2 , 4S3/2 4 I15/2 transitions at 11 K. The peak positions indicated by short vertical lines are associated numbers from Table 1.
Fig.6. CL spectrum of AlN: Er3+ NPs synthesized by IGC method and observed between (a) 23400-24600 cm-1 and (b) 25640-26200 cm-1 corresponding to 2 H9/2 , 4G11/2 4 I15/2 transitions at 11 K. (b) The observed broadening transition lines were deconvoluted using partial Gaussian functions. Blue line curves indicate deconvoluted individual Gaussian functions with peak positions indicated by short vertical lines and associated numbers from Table 1. Red line curve is the sum of all individual deconvoluted individual Gaussian peaks.
µ
M Fig. 7. Comparison of the low temperature CL spectra of AlN: Er3+ NPs and AlN: Er3+ epilayer reported in Ref. [48].
Fig. 8. Comparison between low temperature CL spectra of AlN: Er3+ NPs and AlN: Er3+ epilayer showing differences in the 4S3/2 4 I15/2 transition lines energies resulting from the crystal field splitting in AlN NPs and AlN epilayer hosts.
Fig.9. Simplified energy levels of Er3+ ion in AlN NPs showing different energy transfer processes responsible for populating the 4S3/2 and 4F9/2 levels.
Table 1 CL emission lines of 4 I11/ 2 , 2 I9 / 2 , 4 F9 / 2 , 4S3/ 2 , 2 H9 / 2 , 4G11/ 2 4 I15/ 2 transitions recorded for AlN:Er3+ NPs at 11 K shown in Fig. 5-7. (R: RESI and C: complex) Line 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
Eobs(cm-1) 10033 10079 10102 10127 10148 10165 10188 10219 11193 11209 11368 11380 11555 11603 11625 11676 11699 11729 11808 11840 11885 11903 11955 11977 12000 12069 12086 12106 12125 12134 12164 12170 12218 12248 12256 12265 12286 12324 12335 12358 12362 13886 13997 14064 14100 14146 14474 14628 14677
Attribution (R) K1 Z3 (R) K4 Z4 / (C) K1 Z3 (R) K5 Z4 (R)K0 Z2 / (C) K4 Z3 (R) K2 Z2 (R) K1 Z1 (R) K2 Z2 (R) K3 Z1 / (C) K1 Z2 --(R) E0 Z7 / (C )W0 E3 (R) E0 Z6 (C) E1 Z6 (R)E1 Z5 (R)E2 Z5 (R)E0 Z3 (R)E3 Z6 (R)E2 Z3 (R)E0 Z1 (R) E1 Z1 / (C)W0 E1 (R) E3 Z5 (C) E0 Z3 (R)E1 Z0 / (C)E1 Z4 (R) E2 Z0 (C) W2 E1 (C) E1 Z3 (R)W0 E4 / (C) E0 Z1 (R)W1 E4 / (C) W1 E0 (R) E3 Z1 (R) E4 Z1 / ((C) E Z6) (C)W2 E0 (C)E2 Z2 (R) E4 Z0 / (C) E1 Z1 (C) E0 Z0 / (C) E2 Z1 (C) E3 Z5 (R)W3 E4 (R) W0 E2 / (C)W3 E2 (C) W1 K4 (R)W0 K4,K3 (R)W1 K2 / (C)Y1 E0 (R) W2 K0 (C) Y3 E0 (C) T4 Z6 (C) T3 Z5 (C) T0 Z3
Line 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97
Eobs (cm-1) 14694 14765 14807 14875 14930 14975 15014 15038 15068 15119 15159 15183 17354 17520 17634 17705 17751 17772 17825 17857 17906 17916 18027 18068 18097 18126 18176 18209 18256 18299 23680 23898 24033 24185 24225 24263 24330 25720 25748 25784 25810 25852 25871 26005 26035 26049 26127 26138
Attribution (C) T2 Z4 (R)T0 Z5 / (C) T3 Z4 (R)T2 Z5 (R)T0 Z3 (R)T3 Z4 / (C) T1 Z1 (R)T0 Z2 (R) T1 Z1/ (C)T3 Z2 (R) T4 Z3 (R) T3 Z1 (R) T0 Z0 (R) T2 Z0 (R) T3 Z0 (C) V1 Z6 (C) V0 Z5 (R) V0 Z6 (C) V1 Z4 (C) V0 Z3 (R) V0 Z5 (R) V1 Z5 (C) V0 Z2 (R) V0 Z4 (R) V0 Z2 (R) V0 Z1 (C) V0 Z0 (R) V0 Z0 (R) V1 Z0
(C) W4 Z7 (C) W1 Z4 / (C) W0 Z3 (C) W3 Z5 (R) W2 Z2 / (C)W4 Z5 (C) W0 Z0 (R) W3 Z4 (C) Y1 Z5 / (R) Y5 Z7 (C) Y2 Z5 (R) Y0,Y1 Z4 (R) Y2 Z5 (C) Y4 Z5 (C) Y0 Z3 (C) Y0 Z2 (R) Y5 Z3 (R)Y1 Z0 / (C)Y0 Z1 (R)Y4 Z1 (R)Y5 Z2 / (C)Y2 Z2
Table. 2. The experimental and calculated energy levels of Er3+ ion in AlN NPs corresponding to different optical centers (RESI and complex).
Multiplet
4
I15 /2
4
I11/2
2
I9/2
4
F9/2
4
S3/2
2
4
H9/2
G11/2
a
S levelsa Z0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 R0 R1 R2 R3 R4 R5 E0 E1 E2 E3 E4 T0 T1 T2 T3 T4 V0 V1 W0 W1 W2 W3 W4 Y0 Y1 Y2 Y3 Y4 Y5
RESI (ErAl) Calculated Experimental valuesb valuesc 0 0 119 115 144 146 244 247 265 260 351 352 544 543 559 562 10272 10272 10276 10280 10290 10294 10336 10334 10339 10339 10367 10362 11923 11923 11957 11955 11970 11977 12241 12240 12248 12248 15117 15119 15130 15129 15166 15159 15191 15183 15281 15281 18176 18176 18197 18209 24331 24336 24353 24354 24371 24372 24588 24589 24602 24601 26045 26046 26049 26249 26176 26162 26240 26240 26242 26242 26281 26282
Complex (Er-VN) Calculated Experimental valuesb valuesc 0 0 178 175 224 220 351 354 466 469 607 606 867 874 1151 1151 10396 10395 10430 10433 10468 10467 10470 10471 10480 10481 10610 10609 12268 12262 12423 12424 12435 12436 12886 12893 13009 13008 15058 15031 15104 15105 15171 15163 15231 15234 15367 15344 18125 18126 18240 18224 24266 24263 24364 24367 24413 24426 24784 24791 24831 24834 26222 26225 26330 26327 26346 26354 26399 26408 26462 26458 26518 26516
Stark level splitting of the manifold levels 2S+1LJ. Calculated levels corresponding to RESI and complex centres based on the Hamiltonien parameters listed in Table 3. d Experimental energy levels observed in CL spectrum of AlN:Er3+ NPs on Si synthesized by IGC method. b
Table. 3. The free Er3+ ion parameters and CFPs of AlN:Er3+ NPs and AlN:Er3+ epilayer obtained from the best fit between the experimental and the theoretical energy levels. Parameter
a
AlN :Er3+ epilayer
(cm-1)
AlN :Er3+ NPs RESI (ErAl)
Complex (VN-Er)
E1
6367
6364
6365
E2
28
31
31
E3
634
631
635
α
23
23
23
β
-591
-588
-593
γ
1683
1684
1684
T
2
373
360
436
T
3
190
18
97
T
4
171
148
180
T
6
-513
-523
-568
T
7
-979
-821
-896
T
8
-343
-170
-254
ξ
2368
2367
2368
0b
3.86
5.31
4.07
2c
594
594
594
B02
-181
-183
1011
B04
-471
-460
602
B34
-938
-943
-516
B06
945
932
1722
B36
-465
-473
1616
B66
546
550
61
M P
a
Free ion and crystal field parameters established in Ref. [48] used as initial values for the fitting process present in this study. b M 0 , M 2 and M 4 were constrained by the ratios M 2 0.56M 0 , M 4 0.38M 0 . c
P 2 , P 4 and P 6 were constrained by the ratios P 4 0.75P 2 , P 6 0.6P 2 .
PII: DOI: Reference:
S0022-2313(15)30291-X http://dx.doi.org/10.1016/j.jlumin.2015.11.002 LUMIN13699
To appear in: Journal of Luminescence Received date: 22 July 2015 Revised date: 24 October 2015 Accepted date: 4 November 2015 Cite this article as: T. Kallel, T. Koubaa, M. Dammak, S.G. Pandya, M.E . Kordesch, J. Wang, W.M. Jadwisienczak and Y. Wang, Spectra, energy levels and crystal field calculation of Er3+ doped in AlN nanoparticles, Journal of Luminescence, http://dx.doi.org/10.1016/j.jlumin.2015.11.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Spectra, energy levels and crystal field calculation of Er3+ doped in AlN nanoparticles
T. Kallela*, T.Koubaaa, M. Dammaka, S.G. Pandyab, M. E .Kordeschb, J. Wangc, W. M. Jadwisienczakc, Y. Wangd a
Laboratoire de Physique Appliquée, Groupe des Matériaux Luminescents, Université de Sfax, Faculté des Sciences de Sfax, Département de Physique, Route de Soukra, Km 3.5, B.P. 1171 3000 Sfax, Tunisia
b
Department of Physics and Astronomy, Ohio University, USA
c
School of Electrical Engineering and Computer Science, Ohio University, Athens, OH 45701, USA
d
Center for Electrochemical Engineering Research, Ohio University, Athens, OH 45701, USA
Abstract Optical properties of Er-doped AlN nanoparticles (NPs) synthesized by Inert Gas Condensation (IGC) on silicon (111) substrates were investigated. Transmission electron microscopy (TEM) and high resolution TEM (HR-TEM) were used to study the shapes, morphologies and size of the synthesized AlN: Er3+ NPs which have a spherical shape with a mean diameter between 12 nm and 15 nm. The optical properties of AlN: Er3+ NPs were assessed from low temperature cathodoluminescence spectra (CL). The CL spectra show visible and near infrared sharp and broad emission lines associated with Er3+ ions. The observed Er3+ ion transition lines broadening is due to the surface defect in studied NPs. Comparative investigations of the luminescent properties of AlN: Er3+NPs with those of AlN: Er3+ thin films show the presence of some similarities between the lattice sites occupied by Er3+ ions in these hosts. It was found that in AlN NPs the Er3+ ion occupy a second optical center which is the VN-Er complex beside the ordinary substitutional ErAl center observed in the case of AlN:Er3+ epilayers. Assuming the presence of these two sites occupied by Er3+ ions, the majority of CL emission lines were attributed. The experimental Stark energy levels of Er3+ ion manifolds are established for the Er-doped AlN NPs and the correspondent crystal field parameters are calculated.
Key words: Crystal-field calculation; Optical spectroscopy; Stark splitting; AlN nanoparticles --------------------------------------------------------------------------------------------------------------------------*Corresponding author. Tel.: +216 74 274 088; fax: +216 74 274 437. E-mail address: [email protected] (T. Kallel).
1. Introduction Over the last few years, nanostructured materials research has grown rapidly. Research on semiconductor nanoparticles (NPs) has also witnessed a considerable interest because of their potential applications in electronics and optoelectronics including light emitting devices [1, 2]. In addition, these NPs are becoming an indispensable part of functional materials, essentially bridging the gap between biotechnology and material science, with applications in the field of in vivo imaging, gene therapy, cancer treatment, regenerative medicine, tissue engineering, and biomaterials development [3-7]. The III-V nitride semiconductor family (InN, GaN and AlN and their alloys) are technologically important semiconductors because, among other properties, their direct band gaps span a wide region in the electromagnetic spectrum from deep ultraviolet (UV) to infrared (IR), making them attractive for light emitting diodes (LEDs) and laser diodes (LDs) [8, 9]. Among the IIInitrides, AlN has gained considerable attention because of its properties such as wide band gap (6.2 eV), high volume resistivity, high thermal conductivity at low temperature, low dielectric constant and excellent thermal expansion coefficient, excellent chemical stability and good mechanical strength [10-13]. Furthermore, AlN NPs are of interest due to their prospective applications in optoelectronic and field emission nano-devices [14-16]. These properties make AlN NPs a suitable host material for rare earth (RE) ions doping, which offers emission over the entire visible spectrum with reduced luminescence quenching as compared to semiconductors with narrower band gaps [17]. Recently, RE-doped NPs have been proposed for a variety of applications including solid state lasers, display, low intensity IR imaging, watermarking technology, 3D storage media, solar cells and other biological probes [18-27]. The synthesis of different NPs has been demonstrated using several methods including, among others, precipitation in solution, sol-gel methods, mechanical attrition and spray pyrolysis [28-31]. Another method for the synthesis of III-nitride NPs is the inert gas condensation (IGC) process. In IGC, the precursors are sputtered by inert gas atoms [32-39]. The advantage of the gas-phase method over other chemical and physical processes is the high-purity level and chemical stability of resulting NPs due to vacuum. Control over cooling rates and residence time in the gas-phase synthesis methods can be obtained by optimizing the process parameters to tailor NPs properties [40]. As the use of RE doped NPs is becoming increasingly important in industrial applications, there is much interest in understanding their optical properties. In the recent years, the optical features of REdoped oxide semiconductor nanorods as Ga2O3, GeO2 and ZnO have been investigated [41-45]. However, the optical investigations of RE-doped III-nitride NPs are rather scarce. In our previous work, we have studied the optical behaviors of AlN: Er3+ and GaN: Yb3+ epilayers [46-49]. Furthermore, we have studied the optical properties of GaN:Yb3+ nanorods and we have compared all the obtained results with those obtained for GaN:Yb3+ epilayers [50].
In the current work, we aim to continue our previous studies by the investigation of the optical behaviors of Er-doped AlN NPs, synthesized by IGC technique on silicon substrate. The synthesized NPs were analyzed by transmission electron microscope (TEM) and high resolution transmission electron microscope (HRTEM). The optical investigations were carried out using low temperature high resolution cathodoluminescence (CL) spectra. The optical centers occupied by Er3+ ions in AlN NPs were identified and compared with those reported for AlN: Er3+ epilayers. The effect of the nanosize on the AlN:Er3+ optical behaviors was discussed. In addition, using the crystal field theory, the Stark energy levels of the Er3+ ions occupying different optical centers have been calculated and compared with those obtained for Er3+ in AlN epilayers.
2. Experimental details The AlN: Er3+ NPs discussed in this paper were developed using IGC synthesis protocol described elsewhere [32,51]. In short, radio frequency (RF) sputtering was used as the source of the material condensed in the presence of argon (Ar) gas in the condensation chamber. The condensation chamber was separated from the deposition chamber by a small nozzle with 2 mm in diameter. The pressure difference between adjusted chambers results in the formation of a NPs beam. The NPs are deposited on the 2525 mm2 (111) p-type Silicon substrate placed in the deposition chamber. The Silicon substrate is placed precisely in front of the nozzle at a distance of about 1-2 cm. During the deposition process, a target (99.99% of Al disk at 37 nm O.D. with an insert of 99.99% of Er metal pellet) was sputtered in the presence of argon (Ar) and nitrogen (N) gases in ratio 1:1. The ratio of Al to Er metals was 1:8 in terms of their masses. The base pressure of the system was kept up at 10−7 Torr. Sputtering power, pressure difference between the condensation and the deposition chamber, and sputtering time were varied in order to produce NPs of desirable size(s). The effect of the IGC deposition parameters on the NPs size has been discussed elsewhere [32]. The aggregation length describing the distance between nozzle and the sputtering source was kept constant at 10.5 cm. The selected NPs specimens deposited on silicon wafers were heated in vacuum at 500 °C for 1 hr and in air at 1000 °C for 2 hrs, respectively. Structural characterization of the NPs before and after heating was carried out using JEOL 1010 transmission electron microscope (TEM) operated at 100 kV. The sizes and morphology of the NPs were observed by a JEM-2010 high resolution transmission electron microscope (HRTEM) operated at 200 kV and a scanning near-field optical microscope model WITecR-SNOM-300s. The CL spectra were measured in 10–300 K temperature range and excited by an electron gun (Electroscan EG5 VSW) with electron beam acceleration energy not exceeding 5 keV. The emission spectra were dispersed by a 0.3 m spectrograph and analyzed by a Princeton Instruments backilluminated charge- coupled device (CCD) camera with a UV/AR coating, operating in the spectral region 200–1050 nm, and controlled by a computer.
3. Theoretical modeling Er3+ ion has 4f11 configuration which gives rise to a 4I15/2 ground state and 4F9/2, 4S3/2, 2H11/2, 4F7/2, 2H9/2, 2
P3/2 excited states in the visible range. All the energy levels of Er3+ ion in AlN host split into Kramers
doublet states with E1/2 or E3/2 symmetry in the C3V double-rotation group (C 3V ) [52]. The wave functions and energy levels of these doublets can be calculated through the diagonalization of the operator Hamiltonian: H=HFI +HCF
(1)
Where HFI contains all free-ion interactions and HCF describes the crystal field interactions. The free ion interaction Hamiltonian used in eq.1 has the form:
HFI = E k ek +4f ASO +αL L+1 +βG G 2 +γG R 7 + Ti t i + M k mk + P k pk k
i
k
(2)
k
where H FI consists of 15 parameters controlling interaction between term multiplets, E k (k = 1, 2, 3) is the Racah parameters corresponding to linear combinations of Slater radial integrals, α , β and γ are the parameters associated with the two-body effective operators of configuration interaction , L the orbital angular momentum and G(G2) and G(R7) being the Casimir operators of the groups G2 and R7. The T i (i = 2–4, 6–8) is the radial parts of the corresponding three-body effective operators. The
M k (k = 0, 2, 4) parameters are the magnetic interactions parameters representing the magnetically correlated corrections such as spin–spin and spin–other-orbit interactions, while the P k (k = 2, 4, 6) parameters arise from electrostatic spin-orbit interactions with higher configurations, with pk and mk being the corresponding operators. The remaining free-ion parameter is the spin–orbit interactions between f electrons. The crystal-field term, HCF , takes into account the effect of the electrostatic interactions due to the surrounding ions on the f electrons. Calculations are usually carried out within the single-particle crystal-field theory. Following the Wybourne formalism [53], the one-electron HCF Hamiltonian is expressed as a sum of products of spherical harmonics and real Bkq and complex S kq crystal field parameters (CFPs). The expression of HCF Hamiltonian is given by Eq.3:
k
HCF =
B
k 2,4,6 q 0
q k
C
q k
q q 1 Ck q iSkq Ckq 1 Ck q
(3)
where Ckq and Ck q are the tensorial operators. The number of non-zero CFPs ( Bkq and S kq ) in Eq.3 depends on the local site symmetry of the RE ion. For the trigonal symmetry (C3V ) occupied by Er3+
ion site in AlN host, the serial development of the crystal-field potential involves only six non-zero CFPs describe as:
HCF B20C20 B40C40 B60C60 B43 (C43 C43 ) B63 (C63 C63 ) B66 (C66 C66 )
(4)
In this current study, the energy levels of Er3+ ion in AlN NPs were calculated by simultaneous treatment of both free ion and crystal-field effects using the entire basis set of wave functions.
4. Results and discussions 4.1. Morphology studies of AlN:Er3+ NPs The morphologies of the AlN: Er3+ NPs were analyzed by TEM to differentiate between the crystalline and amorphous phases of NPs. Moreover, this approach gives reliable information about the synthesized NPs surface. Figure 1 (a) shows the TEM images of synthesized AlN: Er3+ NPs which have a spherical shape with a mean diameter of about 12 nm 15 nm, as can be seen from the histogram (Fig. 1(b)) depicting the statistical size distribution of the NPs. This value has been obtained by fitting the size distribution histogram to a Gaussian function. Furthermore, it can be seen that the particles are uniform in shape and there are no signs of coalescence. The HRTEM images of single NPs having different distinct diameters are shown in Fig. 2. The NPs have a crystalline structure with clearly interplanar distances between adjacent crystallographic planes for the AlN: Er3+ NPs. The lattice spacing of 0.19 nm, seen in Fig. 2(a), corresponds to (102) growth directions of hexagonal AlN. Similarly in Fig. 2(c), the lattice spacing of 0.54 nm corresponds to (001) direction of hexagonal AlN whereas the lattice spacing of 0.28 nm corresponds to (100)/(010) direction of hexagonal AlN. Because of the particle nano-size, it is expected that the observed NPs lattice parameters can be slightly different from the bulk material due to the surface tension difference (usually enlarged by decreasing the NP diameter). Based on the obtained HRTEM results, we show that most of the studied AlN: Er3+ NPs have hexagonal crystal structure. Small NPs are single crystalline in nature, whereas some large NPs show polycrystalline behavior. The typical AlN: Er3+ NPs sample used in this study has a 85:15 ratio for single-crystalline:poly-crystalline phases. The Fourier transform of HRTEM images for small and large NPs are shown in Fig.2 (b, d). It gives the corresponding orientations of the crystallographic planes for as-deposited AlN:Er3+ NPs. HRTEM indicates that the AlN: Er3+ NPs are hexagonal and relatively uniform. 4.2. Cathodoluminescence spectrum of AlN: Er3+ NPs In the aim to theoretically model the spectral feature of AlN: Er3+ NPs, CL spectra were measured at 11 K and recorded in the 9900 cm-1 - 26500 cm-1 spectral range. Figure 3 shows the CL spectrum of AlN: Er3+ NPs grown on silicon substrates recorded at 11 K. It is seen that CL spectrum
reveals several groups of peaks corresponding to Er3+ intra-4f 4
4
4
4
2
n
shell transition originated from
2
different excited states ( I11/2, I9/2, F9/2, S3/2, H9/2, G11/2) to (Z1, Z2, Z3,… Z8) 4I15/2 ground state. As shown in Fig. 3, the CL spectra of AlN:Er3+ NPs is dominated by green and red bands, corresponding respectively, to the 4 S3/ 2 4 I15/ 2 and the 4 F9/ 2 4 I15/ 2 transitions. The summary of CL spectra containing 97 emission lines is collected in Table 1 and in Fig. 4 through Fig.6 showing high resolution CL spectra of separated groups of transition lines. These figures clearly show the presence of sharp and broadened emission lines attributed to intra-shell 4f 11 transitions of the Er3+ ion configuration. In case of AlN: Er3+ NPs, the broadening of the emission lines observed in CL is expected. In fact, and according to crystal field theory, the electronic energy levels of RE ions in NPs may vary because of changes in the strength of the local electrostatic field and site symmetry [54]. In NPs, structure disordering and surface defects are inevitable, and emission lines in nanocrystalline materials show extra inhomogeneous broadening with regards to bulk crystals, especially due to the enormous increase in surface sites compared to bulk sites [55]. The broadening of some of the Er3+ ion emission lines observed in the AlN: Er3+ CL spectra means that the Er3+ ion luminescence is affected by the generated surface defects which contribute on the optical behavior of Er 3+ ion incorporated to AlN NPs. It is also worth mentioning that the erbium related luminescence line width broadening suggests that the Er3+ ions most probably occupy more than one optical center in AlN NPs. The discussion of these different optical centers occupied by Er3+ ion in AlN NPs will be presented in the next section. Specifically, In order to understand the effect of the nano-dimension and the surface defects on the optical properties of Er3+ ion, we have compared CL spectra obtained for the AlN:Er3+ NPs synthesized by the IGC method with CL spectra of the AlN:Er3+ epilayers reported in our previous work [48]. Figure 7 shows the assembly of CL spectra of AlN:Er3+ NPs and epilayers in 16000 - 26200 cm-1 spectral range. Comparison of these CL spectra evinces the presence of the same 4f-4f transitions corresponding to the
4
S3/ 2 , 2 H9/ 2 4 I15/ 2 transitions located at 17888 cm-1 and 24310 cm-1; however, the CL
spectrum for AlN:Er3+ NPs does not show any noticeable emission lines originating from the 2H11/2 and 4F7/2 manifolds as observed in the CL spectra of AlN:Er3+ epilayer [48]. In addition, we note that the CL spectra of AlN:Er3+ epilayer is dominated by the blue emission corresponding to 4
F7 / 2 4 I15/ 2 transition. Whereas, in the case of AlN:Er3+ NPs, we note the dominance of red and
green emission lines corresponding, respectively, to
4
F9/ 2 , 4S3/ 2 4 I15/ 2 transitions. The
enhancement of red and green bands and the quenching of the blue emission from Er3+ ion incorporated in AlN NPs can be explained by the presence of (de)populating channels of 4F9/2 and 4S3/2 levels from the 4F7/2 excited states. Among these possible energy transfer pathways, we believe that the multiphonon relaxation and the non-radiative cross relaxation (CR) processes, which occurs between neighboring Er3+ ions in AlN NPs are the most probable to occur. A simplified energy levels
diagram of Er3+ ion in AlN NPs shown in Fig 9 illustrates the possible mechanisms of observed emission and energy transfer processes. It is well known that in Er-doped AlN epilayers, having a low dopant concentration, Er3+ ions are usually randomly distributed in the host lattice and the neighboring Er3+ ions distances are too far apart resulting in a decrease of the energy transfer probability between the Er3+ ions. Because of that, one can observed blue emission from the 4F7/2 manifold in the AlN epilayers. However, in case of the AlN:Er3+ NPs and due to the nano-size dimension, some of the Er3+ ions have closer nearest neighbors resulting in various CR processes between Er3+ ions. This in fact can depopulate the 4F7/2 level and result in effective quenching of radiative emission from this energy state. The related mechanism can be described as follows, in the case of AlN NPs, the short distances between Er3+ ions in AlN host lattice favor interionic interactions, resulting an efficient near resonant CR processes between Er3+ ions, ( 4 F7 / 2 4 F9 / 2 ) and ( 4 I15/ 2 4 I13/ 2 ) transitions, as shown in Fig. 9. The 4F9/2 states became greatly populated from 4F7/2 states through the CR process resulting in intense red emission observed in the CL spectra of ALN:Er3+ NPs. Furthermore, the 4F7/2 states decay nonradiatively to the 4
4
S3/2 states, resulting in observing green emission lines attributed to
S3/ 2 4 I15/ 2 transition. The disappearance of the 2H11/2 transition in the AlN:Er3+ NPs CL spectra
can also be explained by the CR process between Er3+ ions, ( 2 H11/ 2 4 F9 / 2 ) and ( 4 I13/ 2 4 I11/ 2 ) transitions (see Fig.9). 5. Optical luminescent centers of AlN:Er3+ NPs In general, density function theory is used to investigate RE impurities in the III-V (AlN,GaN) host.[56-58]. Based on available theoretical models, there is a common consensus that the most stable site for the RE3+ ion in a GaN host is a Ga substitutional site. On the other hand, recent theoretical calculations also suggest that it is energetically favorable for incorporated RE ions to create centers such as the VN-RE complexes involving a nitrogen vacancy defects, which are very common defects in the GaN and AlN hosts [59]. We have reported recently, the presence of two main optical centers in the case of GaN: Yb3+ nanorods (NRs), which are the substitutional YbGa and the complex Yb-VN sites [50]. It was shown that the reduced dimensionality of the GaN host (nano-size) promotes the formation of VN-Yb complexes involving VN defects at the expense of the substitutional (RESI) center formation. In order to investigate the optical centers occupied by the Er3+ ions in the AlN NPs, we have presented in the same Fig. 8 the CL spectra corresponding to the 4S3/2 4I15/2 transitions observed for AlN:Er3+ NPs and epilayer hosts. It is clearly seen that in the case of AlN:Er3+ NPs, the presence of the same emission lines as observed for AlN:Er3+ epilayer, along with additional emission lines not observed in AlN:Er3+ epilayer confirms the postulate about Er3+ ion occupying more than one center in the AlN NPs host. We have demonstrated that in the case of Er3+ doped AlN epilayers the dominant optical center occupied by the Er3+ ion is the substitutional ErAl site (RESI) [48]. However,
the presence of new emission lines observed in the CL of AlN:Er3+ NPs confirms the existence of another optical center, which is the VN-Er complex, such as obtained in the case of GaN:Yb NRs [50]. The analysis of presented experimental results leads us to presume the presence of an additional optical center occupied by the Er3+ ion in studied AlN NPs. Based on the reasoning presented
above, we propose that it is the complex Er-VN. In the following we will confirm this assumption by conducting the detailed theoretical analysis of the CL spectra (see Figs. 4-6) obtained for the AlN:Er3+ NPs at low temperature. We assigned the broad emission lines seen in Fig. 4 to 4 I9 / 2 4 I15 / 2 transition to the additional optical center (VN-Er complex) which can be located e.g. at near of AlN NPs surface. This assignment is confirmed by the fact that in case of RE-doped nanocrystals, the REs ions can be located partially inside of the NPs (RESI center) as well as at AlN NPs surface (complex centers) [60]. In fact, one can expect that the incorporation of Er in the NPs volume is smaller than that in an epilayer volume [17]. This prevents the formation of RESI center and promotes the formation of Er-VN complexes involving nitrogen vacancy (VN). It is well known that the exciton Bohr radius of the AlN host is less than a few angstroms [61]. Therefore, quantum size confinement in AlN NPs having 12 nm diameter should not affect the localized electronic states of the Er3+ ion localized 4f-shell electrons. So, it is expected that the Stark splitting of Er3+ ion manifolds when doped to single crystal AlN epilayers or AlN NPs should be very close. The detailed analysis of the observed emission lines of Er3+ ions in AlN NPs will be presented in the next section. 6. Modeling of the Er3+ ion energy levels in AlN NPs grown on silicon substrates Using the formalism developed by Racah and Norman [62, 63], the experimental Stark energy levels of Er3+ in AlN NPs were numerically simulated. It is known that rigorous simulation needs a clear experimental support. The specimens studied here are composed of NPs having varied diameter (see Fig.1). Thus, one can expect that the probability of surface defects occurrence in AlN:Er3+ NPs increases for smaller diameter NPs. Considering the fact that the CL spectra were collected over a large surface area (>0.5 mm2), considered here as global CL spectra, the observed emission from optically active Er3+ ions occupying different sites in NPs having different diameter cannot be spatially resolved. Therefore, the presence of broad Er3+ ion emission lines ( 4 I9/2 , 4 G11/2 4 I15/2 ) in CL spectra are most probably resulting from the superposition of sharp transition lines generated by individual NP having different surface to volume ratio. In order to analyze these observed Er3+ ion emission lines in detail, we have used the multi-Gaussian fitting as shown in Fig.4 and Fig.6. Base on the global CL spectra of AlN:Er3+ NPs, we have established two sets of experimental Er3+ ion Stark energy levels, corresponding to the purely ErAl substitutional site without defects involve in the RESI center and the VN-Er complex. The calculated and experimental energy levels of Er3+ ion occupying substitutional (R) and complex (C) centers in AlN:Er3+ NPs deposited on silicon substrates are shown
in Table 2. The calculated energy levels of Er3+ ions were obtained by diagonilazing the Hamiltonian described in Section 3. It should be noted that the Er3+ ion Stark energy level calculations are performed for the ordinary substitutional ErAl site with trigonal symmetry (C3v). In case of the VN–Er defect complex, we have assumed in calculations that it has the same symmetry as the ErAl substitutional site (C3v) with some distortion [ 50]. The fitting procedure executed here and described in our previous work [64], assumes the selection of adequate sets of free-ion and crystal-field parameters. Since H FI is expected to be largely independent of the host we have used the parameters which were determined previously for the Er3+ ion in AlN epilayers [48] as starting set of free-ion parameters. However, it should be mentioned that M k and P k parameters were not varied in the present fitting procedure. The free ion parameters obtained by the fitting procedure are shown in Table 3. Indeed, it was found that these values are close to those reported in our earlier study for Er3+ ions in AlN epilayers [48]. For the initial CFPs, we have started the fitting process from the initial CFPs used in the case of AlN: Er3+ epilayers obtained by lattice-sum calculations [46- 50]. The parameter values used as a reference point in order to fit the obtained experimental Stark energy levels of Er3+ ion in AlN NPs are collected along with those obtained from the best fit in Table 3. The fitting process involved 97 experimentally observed Er3+ ion energy levels observed between energies of 9900 cm-1 and 26200 cm-1 in the data fitting process. The resulting root mean square deviation is about 3.6 cm-1 in the case of Er3+ ion occupying the substitutional center (RESI) and 2.1 cm-1 for the VN-Er complex that confirms the fitting procedure consistency. The good agreement between the calculated and the experimental Stark energy levels (see Table 2) confirms the proposal that the Er3+ ions in AlN NPs occupy beside the purely substitutional Al center, a second optical center which is the VN-Er complex. 7. Conclusion In this study, AlN:Er3+ NPs were deposited on silicon substrates by using the IGC method. The majority of AlN:Er3+ NPs have spherical shapes with a mean diameter of about 12 nm. The homogeneity of NPs observed using HRTEM confirmed good crystallinity of NPs regardless of their diameter. The CL spectra of AlN:Er3+ NPs were investigated and compared with those reported for AlN:Er3+epilayers. The comparison of the optical features of Er3+ ion incorporated in AlN NPs and to AlN epilayers shows the presence of the substitutional ErAl and the VN-Er complex centers. This complex center is primarily associated with the NPs surface. The broadening of the VN–Er complex emission lines in the AlN NPs CL spectra indicates that the Er3+ ions predominantly reside close or on the NPs surface. Furthermore, the Stark energy levels of Er3+ ions in AlN NPs were calculated using the crystal field theory assuming the presence of two optical centers with C3v symmetry. The calculated Er3+ ion manifolds splitting are in good agreement with the experimental values which confirms that the Er3+ ions in AlN NPs occupy two sites, the substitutional (ErGa) and the complex (VN-Er) centers, respectively.
Acknowledgements Authors would like to acknowledge the Center for Electrochemical Engineering Research (CEER) through the NSF Major Research Instrumentation Grant # CBET-1126350 for the access to Transmission Electron Microscopy facility at OU. WMJ acknowledges the support from the NSF CAREER program under No DMR-1056493.
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Figure captions Fig. 1. TEM images of AlN:Er3+ NPs. The length scale bar is 100 nm in (a), (b) Size distribution histogram for AlN:Er3+ NPs obtained from TEM image seen in (a). Fig. 2. HRTEM images of AlN: Er3+ NPs having different diameters. (a) Small diameter NP having the lattice spacing 0.19 nm of hexagonal AlN corresponding to (102) direction for hexagonal AlN. (b) Fast Fourier Transform (FFT) of the TEM image in (a) confirming the growth direction of (102). (c) Large NP showing lattice constants 0.28 nm and 0.54 nm corresponding to (010)/(100) and (001) direction of hexagonal AlN. (d) FFT of the NP seen in (c) confirming the growth along (001) and (100)/(010) directions. Fig. 3. CL spectrum of AlN: Er3+ NPs grown on silicon substrates recorded at 11 K. Fig. 4. CL spectrum of AlN: Er3+ NPs synthesized using IGC method and observed between (a) 9900-10400 cm-1, (b) 11560-11750 cm-1, (c) 11760-12390 cm-1 corresponding to 4 I11/2 , 4 I9/2 4 I15/2 transitions at 11 K. (c) Example of the observed broadening transition lines deconvoluted using partial Gaussian functions. Blue line curves indicate deconvoluted individual Gaussian functions with peak positions indicated by short vertical lines and associated numbers from Table 1. Red line curve is the sum of all individual deconvoluted individual Gaussian peaks. Fig.5. CL spectrum of AlN: Er3+ NPs synthesized by IGC method and observed between (a) 13500-15400 cm-1 and (b) 17200-18400 cm-1 corresponding to 4 F9/2 , 4S3/2 4 I15/2 transitions at 11 K. The peak positions indicated by short vertical lines are associated numbers from Table 1. Fig.6. CL spectrum of AlN: Er3+ NPs synthesized by IGC method and observed between (a) 23400-24600 cm-1 and (b) 25640-26200 cm-1 corresponding to 2 H9/2 , 4G11/2 4 I15/2 transitions at 11 K. (b) The observed broadening transition lines were deconvoluted using partial Gaussian functions. Blue line curves indicate deconvoluted individual Gaussian functions with peak positions indicated by short vertical lines and associated numbers from Table 1. Red line curve is the sum of all individual deconvoluted individual Gaussian peaks. Fig. 7. Comparison of the low temperature CL spectra of AlN: Er3+ NPs and AlN: Er3+ epilayer reported in Ref. [48]. Fig. 8. Comparison between low temperature CL spectra of AlN: Er3+ NPs and AlN: Er3+ epilayer showing differences in the 4S3/2 4 I15/2 transition lines energies resulting from the crystal field splitting in AlN NPs and AlN epilayer hosts.
Fig.9. Simplified energy levels of Er3+ ion in AlN NPs showing different energy transfer processes responsible for populating the 4S3/2 and 4F9/2 levels.
Fig. 1. TEM images of AlN:Er3+ NPs. The length scale bar is 100 nm in (a), (b) Size distribution histogram for AlN:Er3+ NPs obtained from TEM image seen in (a).
Fig. 2. HRTEM images of AlN: Er3+ NPs having different diameters. (a) Small diameter NP having the lattice spacing 0.19 nm of hexagonal AlN corresponding to (102) direction for hexagonal AlN. (b) Fast Fourier Transform (FFT) of the TEM image in (a) confirming the growth direction of (102). (c) Large NP showing lattice constants 0.28 nm and 0.54 nm corresponding to (010)/(100) and (001) direction of hexagonal AlN. (d) FFT of the NP seen in (c) confirming the growth along (001) and (100)/(010) directions.
Fig. 3. CL spectrum of AlN: Er3+ NPs grown on silicon substrates recorded at 11 K.
Fig. 4. CL spectrum of AlN: Er3+ NPs synthesized using IGC method and observed between (a) 9900-10400 cm-1, (b) 11560-11750 cm-1, (c) 11760-12390 cm-1 corresponding to 4 I11/2 , 4 I9/2 4 I15/2 transitions at 11 K. (c) Example of the observed broadening transition lines deconvoluted using partial Gaussian functions. Blue line curves indicate deconvoluted individual Gaussian functions with peak positions indicated by short vertical lines and associated numbers from Table 1. Red line curve is the sum of all individual deconvoluted individual Gaussian peaks.
Fig.5. CL spectrum of AlN: Er3+ NPs synthesized by IGC method and observed between (a) 13500-15400 cm-1 and (b) 17200-18400 cm-1 corresponding to 4 F9/2 , 4S3/2 4 I15/2 transitions at 11 K. The peak positions indicated by short vertical lines are associated numbers from Table 1.
Fig.6. CL spectrum of AlN: Er3+ NPs synthesized by IGC method and observed between (a) 23400-24600 cm-1 and (b) 25640-26200 cm-1 corresponding to 2 H9/2 , 4G11/2 4 I15/2 transitions at 11 K. (b) The observed broadening transition lines were deconvoluted using partial Gaussian functions. Blue line curves indicate deconvoluted individual Gaussian functions with peak positions indicated by short vertical lines and associated numbers from Table 1. Red line curve is the sum of all individual deconvoluted individual Gaussian peaks.
µ
M Fig. 7. Comparison of the low temperature CL spectra of AlN: Er3+ NPs and AlN: Er3+ epilayer reported in Ref. [48].
Fig. 8. Comparison between low temperature CL spectra of AlN: Er3+ NPs and AlN: Er3+ epilayer showing differences in the 4S3/2 4 I15/2 transition lines energies resulting from the crystal field splitting in AlN NPs and AlN epilayer hosts.
Fig.9. Simplified energy levels of Er3+ ion in AlN NPs showing different energy transfer processes responsible for populating the 4S3/2 and 4F9/2 levels.
Table 1 CL emission lines of 4 I11/ 2 , 2 I9 / 2 , 4 F9 / 2 , 4S3/ 2 , 2 H9 / 2 , 4G11/ 2 4 I15/ 2 transitions recorded for AlN:Er3+ NPs at 11 K shown in Fig. 5-7. (R: RESI and C: complex) Line 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
Eobs(cm-1) 10033 10079 10102 10127 10148 10165 10188 10219 11193 11209 11368 11380 11555 11603 11625 11676 11699 11729 11808 11840 11885 11903 11955 11977 12000 12069 12086 12106 12125 12134 12164 12170 12218 12248 12256 12265 12286 12324 12335 12358 12362 13886 13997 14064 14100 14146 14474 14628 14677
Attribution (R) K1 Z3 (R) K4 Z4 / (C) K1 Z3 (R) K5 Z4 (R)K0 Z2 / (C) K4 Z3 (R) K2 Z2 (R) K1 Z1 (R) K2 Z2 (R) K3 Z1 / (C) K1 Z2 --(R) E0 Z7 / (C )W0 E3 (R) E0 Z6 (C) E1 Z6 (R)E1 Z5 (R)E2 Z5 (R)E0 Z3 (R)E3 Z6 (R)E2 Z3 (R)E0 Z1 (R) E1 Z1 / (C)W0 E1 (R) E3 Z5 (C) E0 Z3 (R)E1 Z0 / (C)E1 Z4 (R) E2 Z0 (C) W2 E1 (C) E1 Z3 (R)W0 E4 / (C) E0 Z1 (R)W1 E4 / (C) W1 E0 (R) E3 Z1 (R) E4 Z1 / ((C) E Z6) (C)W2 E0 (C)E2 Z2 (R) E4 Z0 / (C) E1 Z1 (C) E0 Z0 / (C) E2 Z1 (C) E3 Z5 (R)W3 E4 (R) W0 E2 / (C)W3 E2 (C) W1 K4 (R)W0 K4,K3 (R)W1 K2 / (C)Y1 E0 (R) W2 K0 (C) Y3 E0 (C) T4 Z6 (C) T3 Z5 (C) T0 Z3
Line 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97
Eobs (cm-1) 14694 14765 14807 14875 14930 14975 15014 15038 15068 15119 15159 15183 17354 17520 17634 17705 17751 17772 17825 17857 17906 17916 18027 18068 18097 18126 18176 18209 18256 18299 23680 23898 24033 24185 24225 24263 24330 25720 25748 25784 25810 25852 25871 26005 26035 26049 26127 26138
Attribution (C) T2 Z4 (R)T0 Z5 / (C) T3 Z4 (R)T2 Z5 (R)T0 Z3 (R)T3 Z4 / (C) T1 Z1 (R)T0 Z2 (R) T1 Z1/ (C)T3 Z2 (R) T4 Z3 (R) T3 Z1 (R) T0 Z0 (R) T2 Z0 (R) T3 Z0 (C) V1 Z6 (C) V0 Z5 (R) V0 Z6 (C) V1 Z4 (C) V0 Z3 (R) V0 Z5 (R) V1 Z5 (C) V0 Z2 (R) V0 Z4 (R) V0 Z2 (R) V0 Z1 (C) V0 Z0 (R) V0 Z0 (R) V1 Z0
(C) W4 Z7 (C) W1 Z4 / (C) W0 Z3 (C) W3 Z5 (R) W2 Z2 / (C)W4 Z5 (C) W0 Z0 (R) W3 Z4 (C) Y1 Z5 / (R) Y5 Z7 (C) Y2 Z5 (R) Y0,Y1 Z4 (R) Y2 Z5 (C) Y4 Z5 (C) Y0 Z3 (C) Y0 Z2 (R) Y5 Z3 (R)Y1 Z0 / (C)Y0 Z1 (R)Y4 Z1 (R)Y5 Z2 / (C)Y2 Z2
Table. 2. The experimental and calculated energy levels of Er3+ ion in AlN NPs corresponding to different optical centers (RESI and complex).
Multiplet
4
I15 /2
4
I11/2
2
I9/2
4
F9/2
4
S3/2
2
4
H9/2
G11/2
a
S levelsa Z0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 R0 R1 R2 R3 R4 R5 E0 E1 E2 E3 E4 T0 T1 T2 T3 T4 V0 V1 W0 W1 W2 W3 W4 Y0 Y1 Y2 Y3 Y4 Y5
RESI (ErAl) Calculated Experimental valuesb valuesc 0 0 119 115 144 146 244 247 265 260 351 352 544 543 559 562 10272 10272 10276 10280 10290 10294 10336 10334 10339 10339 10367 10362 11923 11923 11957 11955 11970 11977 12241 12240 12248 12248 15117 15119 15130 15129 15166 15159 15191 15183 15281 15281 18176 18176 18197 18209 24331 24336 24353 24354 24371 24372 24588 24589 24602 24601 26045 26046 26049 26249 26176 26162 26240 26240 26242 26242 26281 26282
Complex (Er-VN) Calculated Experimental valuesb valuesc 0 0 178 175 224 220 351 354 466 469 607 606 867 874 1151 1151 10396 10395 10430 10433 10468 10467 10470 10471 10480 10481 10610 10609 12268 12262 12423 12424 12435 12436 12886 12893 13009 13008 15058 15031 15104 15105 15171 15163 15231 15234 15367 15344 18125 18126 18240 18224 24266 24263 24364 24367 24413 24426 24784 24791 24831 24834 26222 26225 26330 26327 26346 26354 26399 26408 26462 26458 26518 26516
Stark level splitting of the manifold levels 2S+1LJ. Calculated levels corresponding to RESI and complex centres based on the Hamiltonien parameters listed in Table 3. d Experimental energy levels observed in CL spectrum of AlN:Er3+ NPs on Si synthesized by IGC method. b
Table. 3. The free Er3+ ion parameters and CFPs of AlN:Er3+ NPs and AlN:Er3+ epilayer obtained from the best fit between the experimental and the theoretical energy levels. Parameter
a
AlN :Er3+ epilayer
(cm-1)
AlN :Er3+ NPs RESI (ErAl)
Complex (VN-Er)
E1
6367
6364
6365
E2
28
31
31
E3
634
631
635
α
23
23
23
β
-591
-588
-593
γ
1683
1684
1684
T
2
373
360
436
T
3
190
18
97
T
4
171
148
180
T
6
-513
-523
-568
T
7
-979
-821
-896
T
8
-343
-170
-254
ξ
2368
2367
2368
0b
3.86
5.31
4.07
2c
594
594
594
B02
-181
-183
1011
B04
-471
-460
602
B34
-938
-943
-516
B06
945
932
1722
B36
-465
-473
1616
B66
546
550
61
M P
a
Free ion and crystal field parameters established in Ref. [48] used as initial values for the fitting process present in this study. b M 0 , M 2 and M 4 were constrained by the ratios M 2 0.56M 0 , M 4 0.38M 0 . c
P 2 , P 4 and P 6 were constrained by the ratios P 4 0.75P 2 , P 6 0.6P 2 .