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Nanostructure of β-Ga2O3 is wide-band-gap material with white-light-emission function because of its abundance in gap states. In this study, the gap states and near-band-edge transitions in β-Ga2O3 nanostrips have been characterized using temperature-dependent thermoreflectance (TR) measurements in the temperature range between 30 and 320 K. Photoluminescence (PL) measurements were carried to identify the gap-state transitions in the β-Ga2O3 nanostrips. Experimental analysis of the TR spectra revealed that the direct gap (E0) of β-Ga2O3 is 4.656 eV at 300 K. There are a lot of gap-state and near-band-edge (GSNBE) transitions denoted as ED3, EW1, EW2, EW3, ED2, , EDB, ED1, E0, and E0′ can be detected in the TR and PL spectra at 30 K. Transition origins for the GSNBE features in the β-Ga2O3 nanostrips are respectively evaluated. Temperature dependences of transition energies of the GSNBE transitions in the β-Ga2O3 nanostrips are analyzed. The probable band scheme for the GSNBE transitions in the β-Ga2O3 nanostrips is constructed.
©2010 Optical Society of America
1. Introduction
The use of ultraviolet (UV) portion light in optical absorber (such as solar cell) and optical emitter (such as white lighting) is crucial for sustainable energy and solid-state lighting fields. For optical absorption and emission of the UV lights, wide-band-gap material plays an important role for such an achievement. In the solar-energy related field, the I-III-VI wide-band-gap material of CuAlS2 (~3.49 eV) was proposed to act as a window material for cascade thin-film solar cell to improve quantum efficiency in the UV region [1,2]. On the other hand, for the solid-state white lighting, the III-V nitride as GaN [3], II-VI compound as ZnO [4], and III-VI compound as Ga2O3 [5,6] are some of the promising candidates. Among them, β-Ga2O3 possesses the largest gap and hence the widest tunable spectral range as comparing to those of the other wide-band-gap semiconductors.
β-Ga2O3 nanostructures have recently received growing attentions in fabrication of white-light broadband emitter [7–9] and nanophotonic switch [10] due to their better performance in optics. The abundance of gap states naturally existed inside the nanowires [7,8], nanobelts and nanosheets [9] of β-Ga2O3, which may emit a wide spectral range of defect emissions from 1.8 to 3.4 eV. Energy band gap is the most important parameter which dominates main optical absorption and emission in semiconductors. The direct band gap of β-Ga2O3 has only been probed by the optical-absorption related methods of transmittance and excitation to date [11,12]. The deviation of choosing energy range in the absorption edge of β-Ga2O3 may be a factor for determining the band gap. Besides, the wide-band-gap character (~4.656 eV) of the β-Ga2O3 nanostructures may arise certain difficulty in making the direct-band-gap emission by using PL because a very short-wavelength pumping laser is needed for the experiment. Therefore, an effective method that can determine and verify the direct band-edge nature of the β-Ga2O3 nanostructures is more essential to be implemented.
In this paper, the whole gap-state and near-band-edge (GSNBE) transitions of β-Ga2O3 nanostrips are characterized by temperature-dependent thermoreflectance (TR) measurements in the temperature range of 30 to 320 K. Modulation spectroscopy such as TR is a powerful technique for the characterization of direct interband transitions in semiconductors [13]. The derivative-like nature of modulation spectra suppresses uninteresting background effects and emphasizes the transition features localized in direct transitions. According to the low-temperature TR spectra of the β-Ga2O3 nanostrips, two band-edge transitions of E0 and E0′ can be detected by the TR measurements. The energy values are E0 = 4.726 eV and E0′ = 4.978 eV at 30 K. The energy separation of the band-edge transitions E0 and E0′ may come from the valence-band splitting of the β-Ga2O3 nanostrips by crystal field. Temperature-dependent PL measurements were also carried out to identify the below-band-gap defect transitions of the β-Ga2O3 nanostrips from 30 to 320 K. Based on the experimental analyses, the whole band-edge and defect structures of β-Ga2O3 nanostrips were thus constructed.
2. Experimental details
The β-Ga2O3 nanostrips were grown by a vapor transport method driven by vapor-liquid-solid (VLS) mechanism [14]. A horizontal tube furnace was used for the growth. Molten gallium (0.5g, 99.9999%) was the source material and put into a boat placed at the center of the quartz tube. A thin layer of gold (5 nm) was pre-deposited on silicon (001) as the catalyst by sputtering. Substrates were placed in another boat and positioned downstream. The quartz tube was evacuated and the furnace was heated to 900°C at a rate of 10°C/min. Highly pure oxygen carried by argon gas was fed into the quartz tube. The growth temperature was 600–700°C with a background pressure of 0.5 Torr. Typical growth time was 2 h. After the growth, samples were then cooled down under the same ambient gas.
TR measurements of the β-Ga2O3 nanostrips were carried out using indirect heating manner with a gold-evaporated quartz plate as the heating element [15,16]. The thin sheet-type sample was closely attached on the heating element by silicone grease. The on-off heating disturbance was necessary to avoid any increase of temperature on sample. An 150 W xenon-arc lamp filtered by a PTI 0.2 m monochromator provided the monochromatic light. The average spot size of the incident light was 0.5 mm2. The reflected and scattered lights of the sample were collected and detected by a Hamamatsu H3177-51 photomultiple tube (PMT) module and the signal was recorded from an EG&G model 7265 dual phase lock-in amplifier. A closed-cycle cryogenic refrigerator with a thermometer controller facilitated the temperature-dependent measurements.
The PL measurements were carried out in a spectral measurement system in which a Triax 320 imaging spectrometer equipped with three gratings of 600, 1200, and 2400 groves/mm acted as the optical dispersion unit. A photomultiple tube attached to the outside slit of the spectrometer utilized for the optical detection. AC phase-sensitive detection (PSD) was implemented using a lock-in amplifier to improve the signal-to-noise (S/N) ratio. A Q-switched diode-pumped solid-state laser of 266 nm acted as the pumping light source. The measurements were done in the temperature range between 30 and 320 K with a temperature stability of about 0.5 K or better. A RMC model 22 closed-cycle cryogenic refrigerator equipped with a model 4075 digital thermometer controller facilitated the temperature dependent measurements.
3. Results and discussion
Figure 1 shows the scanning electron microscope (SEM) images (top view and side view) and X-ray diffraction pattern of the as-grown β-Ga2O3 thin-film nanostrips. The β-Ga2O3 nanostrips have the widths of tens to hundreds nanometers grown on Si substrate. The nanostrips and nanobelt-like β-Ga2O3 are not closely dense and which deposited on the Si substrate with an average thickness of ~210 μm. One single nanostrip with width of ~55 nm was also magnified and displayed in the inset of Fig. 1(a) for indication and comparison. The X-ray diffraction pattern presented in Fig. 1(c) reveals narrow linewidth and clear peak features for the as-grown gallium oxide thin film. This result indicates high crystal quality for the gallium oxide nanostrips. The X-ray peak features in Fig. 1 also respectively indexed to the β phase of monoclinic Ga2O3. The lattice constants of the β-Ga2O3 thin-film nanostrips are determined to be a = 12.23 Å, b = 3.04 Å, c = 5.81 Å, and β = 103.83°, respectively.
Fig. 1 SEM images of (a) top view and (b) side view of the as-grown β-Ga2O3 thin-film nanostrips. (c) X-ray diffraction pattern of β-Ga2O3 nanostrips.
Displayed in Fig. 2 are the TR and PL spectra of the GSNBE transitions in the β-Ga2O3 nanostrips at 30 and 300 K, respectively. The TR measuerements were carried out in a wide energy range of 1.25 to 6 eV. The dashed lines are the experimental data and hollow-circle lines are least-square fits to a Lorentzian line-shape function appropriate for the interband transitions expressed as [11,17]:
where and are the amplitude and phase of the line shape, and and are the energy and broadening parameter of the interband transitions of β-Ga2O3 nanostrips. The fits yield transition energies are indicated by arrows in Fig. 2. There are a lot of GSNBE transitions denoted as ED3, EW, , EDB, E0, and E0′ could be detected in the TR spectrum at 30 K while the feature was not clearly detected in the TR spectrum at 300 K due to the thermal ionization and broadened effect contributed to the excitonic transition. There are two band-edge transitions of E0 and E0′ can be detected in the TR spectra at 30 K and 300 K. The energies obtained from the line-shape fits of Eq. (1) are E0 = 4.726 eV and E0′ = 4.978 eV at 30 K, and E0 = 4.656 eV and E0′ = 4.908 eV at 300 K, respectively. The energy separation of E0 and E0′ is about 0.252 eV, which is in agreement with the crystal-field splitting energy that determined by polarized transmittance spectra of E||b and E⊥c for an undoped β-Ga2O3 single crystal [12]. The E0 and E0′ features may come from the ΓV top → ΓC bottom as well as split ΓV → ΓC bottom at Γ point for β-Ga2O3. The E0 and E0′ transitions also demonstrate an energy-redshift behavior as well as an amplitude-reduced character with respect to the increase of temperatures from 30 to 300 K, such as the general semiconductor behavior. It also verifies that the E0 and E0′ features are the band-to-band transitions. The transition energies of EDB obtained from the line-shape fits of Eq. (1) are 3.410 eV at 30 K and 3.373 eV at 300 K, respectively. The temperature-energy shift of EDB shows less sensitive to those of the E0 and E0′ transitions. The EDB transition feature may come from the ΓV top → a defect donor band (DB) constructed by oxygen vacancy (VO) inside the β-Ga2O3 nanostrips. The energy of the feature at 30 K by TR is 3.362 eV. It also presented in a sharp exciton peak in the PL spectrum of β-Ga2O3 nanostrips at 30 K. The emission can be assigned as the bound excitonic luminescence from the ground-state exciton level below the defect donor band DB to the ΓV top. The transition energies of the lower-energy TR features of ED3 and EW analyzed by Eq. (1) are about 2.390 ± 0.008 eV and 2.616 ± 0.008 eV with the temperatures rising from 30 to 300 K. The insensitive character of the temperature-energy shift of the ED3 and EW features indicate that they are coming from the defect-to-defect transitions. The defect transitions are not sensitive to the lattice thermal expansion of β-Ga2O3 nanostrips when temperature is changed. As shown in Fig. 2, there is also a defect transition denoted as ED2 can be detected in the PL spectra while it is so weak and not clearly observed in the TR spectra at 30 and 300 K. This result is due to the ED2 defect transition may come from a lower-electron-density defect state (such as Ga vacancy VGa) to a higher-electron-density defect state (such as O vacancy VO) to render low ED2 transition amplitude in TR but high ED2 luminescence intensity in PL.Fig. 2 The experimental TR and PL spectra of β-Ga2O3 nanostrips between 1 and 6 eV at 30 and 300 K. The hollow-circle lines are the least-square fits to Eq. (1).
Temperature-dependent PL spectra of the β-Ga2O3 nanostrips are depicted in Fig. 3 in the temperature range between 30 and 320 K. There are several defect related transition features of ED3, EW1, EW2, EW3, ED2, and can be detected in the low-temperature PL spectrum of 30 K. The ED3 feature can also be clearly detected in the TR spectra of Fig. 2 from 30 to 300 K. The energies of the ED3 feature at various temperatures are nearly invariant to a value of about 2.390 ± 0.008 eV. It should come from a defect-to-defect emission by the donor-to-acceptor recombination. The ED3 feature can be assigned as a defect transition between the DB bottom by VO and the higher-energy state of acceptor defect band by VGa′. There are also three defect emissions of EW1, EW2 and EW3 observed in the low-temperature PL spectra of the β-Ga2O3 nanostrips. They present temperature insensitive of energy shift. Their energy values are EW1≈2.555 eV, EW2≈2.615 eV, and EW3≈2.715 eV at 30 K and the energy spacings are about 60 meV for EW2-EW1 and 100 meV for EW3-EW2, respectively. The defect transition features of EW1, EW2 and EW3 look quite similar to previous peculiar peak structures in the absorption spectra of the thin single crystals of β-Ga2O3 near the band edge at low temperatures [18]. These specific peak structures come from some of the acceptors assembled into low-dimensional defect clusters, in which quantum size effect occurred near the valence-band edge. The defect-clusters model for donor (larger-size cluster) and acceptor (small-size cluster) has been proposed for β-Ga2O3 [19]. The formation of acceptor cluster requires the association of vacancies VO and VGa to from VO-VGa pairs. In that case with quantum size effect, the quantization of transition energies for the acceptor clusters can be expressed as
where EW0 is the energy difference between the exciton level below DB and the top of the acceptor quantum well (referred to Fig. 7 ), and dmax = 1, 2, or 3 for a one- (1D), two- (2D), or three-dimensional (3D) potential well. The parameters of m* and L are, respectively, the hole effective mass for the acceptor clusters and the well width. The EW1, EW2 and EW3 emission features shown in Fig. 3 are hence assigned as the defect luminescences from the DB exciton level to n = 1, n = 2, and n = 3 quantum-well states for the acceptor clusters by VO-VGa pairs in β-Ga2O3 nanostrips. The acceptor state formed by VO-VGa pair is not like that of VGa which is empty of electron. The VGa can obtain electrons from the VO in forming the VO-VGa pairs. This result can be evident in Fig. 2 that the EW feature (by VO-VGa pairs) can be detected in the TR spectrum at 30 K while the ED2 TR feature (by VGa) is absent. As shown in Fig. 3 at 30 K, the analyses of energy values and energy spacings for EW1, EW2, and EW3 using Eq. (2) render the values of EW0≈2.535 eV and π2⋅/(2m*⋅L2) ≈20 meV are determined. The energies of the EW1, EW2 and EW3 features make the acceptor clusters much agree with the 1D model (dmax = 1, quantum dot) that similar to those observed in the absorption spectra below the band edge [18]. Assume the value of hole effective mass m* of the acceptor clusters is set equal to the electron rest mass (1⋅m0 ≈9.1 × 10−31kg), the value of π2⋅/(2m*⋅L2) ≈20 meV renders a well width of the cluster size of L ≈2.2 nm. The size is in reasonable agreements with the previous electron-microscopy observation of the defect clusters with the domain sizes from ~2.2 nm to ~2.8 nm in the annealed and non-annealed β-Ga2O3 [20]. The temperature variation of the EW1, EW2 and EW3 features in Fig. 3 also indicates that the EW1 feature is gradually ionized and combined with the well top with temperatures rising up to 140 K. The EW3 feature is not observed with T ≥ 260K because the nd = 3 well level is approximately merged with the valence band by thermal effect.Fig. 7 Representative band-structure scheme of the gap-state and near-band-edge transitions in β-Ga2O3 nanostrips.
Also shown in Fig. 3, one prominent defect exciton peak of of ~3.362 eV was observed in the PL spectrum of the β-Ga2O3 nanostrips at 30 K. The feature shows a slight energy red-shift behavior and a line-shape broadened character with respect to the increase of temperatures. The energy red-shift behavior as compared to that of ED2, EW1-EW3, and ED3 (i.e. defect to defect transition) is due to the emission is originated from the recombination of a DB exciton level to the valence band. With the energy lower than the emission, it also shows several small emission peaks periodically repeated and extended below the main peak. The character of equal-energy spacing for the small peaks indicates that they are coming from the optical-phonon replicas such as those observed in the PL emission of III-V nitride compounds at low temperatures [21]. Figure 4(a) shows the magnification of energies near the peak. The character of the small periodical peaks of 1O, 2O, 3O, etc. reveals that they are coming from the optical-phonon replicas that reproduced by the main peak. The energy spacing of the phonon replicas in Fig. 4(a) is about 43 meV. In order to evaluate the origin of the phonon replicas, Raman spectroscopy of the thin-film β-Ga2O3 nanostrips is carried out at room temperature. Figure 4(b) displays the Raman spectrum of the β-Ga2O3 nanostrips sample between 100 and 700 cm−1 at room temperature. There are essentially three groups of vibration modes for the optical phonons of β-Ga2O3 [22–24]. As shown in Fig. 4(b), the group C (> 580 cm−1) contains two high-frequency modes of 650 cm−1 and 627 cm−1 with Ag symmetry that are contributed by the GaO4 tetrahedra related optical phonons [22,23]. The group B possesses three main peak modes of 346 cm−1 (Ag), 415 cm−1 (Ag), and 472 cm−1 (Ag), which are coming from the in-plane Ga2O6 octahedra related optical modes. For the group A (< 230 cm−1), three low-frequency modes of 200 cm−1 (Ag), 170 cm−1 (Ag), and 145 cm−1 (Bg) are found, which are coming from the vibration modes by libration and translation of tetrahedra-octahedra chains in β-Ga2O3 [22,23]. The energy spacing of phonon replicas of in Fig. 4(a) is about 43 meV, matches well with the optical mode of group B near the 346 cm−1 peak (~42.9 meV). This mode is dominant in the in-plane symmetric Ga-O vibration mode [22] in the β-Ga2O3 nanostrips. The phonon-replicas emissions had ever been found in the cathodoluminescence (CL) spectra of N-doped β-Ga2O3 nanowires with an energy separation of 20 meV at 88 K [8]. The phonon energy matches well with the optical modes of group A in Fig. 4(b). The difference in optical-phonon replicas (i.e. 43 meV vs. 20 meV) is maybe due to their arising from different growth directions of nanostructures and hence different symmetric modes of the vibrated phonons are enhanced in the nanostrips or nanowires.
Fig. 4 (a) The low-temperature PL spectrum and phonon replicas of β-Ga2O3 nanostrips near the defect emission. (b) The Raman spectrum of β-Ga2O3 thin-film nanostrips.
Figure 5 shows the temperature-dependent TR spectra of the β-Ga2O3 thin-film nanostrips between 30 and 320 K. The dashed lines are the experimental data and solid lines are fitted to Eq. (1). The obtained transition energies are shown by arrows and their variation traces indicated by dotted lines. The ED3 and EW2 features reveal nearly temperature-invariant character of energy shift with temperatures rising from 30 to 320 K due to their intrinsic property of defect-to-defect transition. The EDB related transitions show slightly red-shift behavior owing to that EDB is coming from ΓV → DB. The band-edge transitions of E0 and E0′ are nearly identical to the values of 4.726 and 4.978 eV from 30 to 77 K. The unshifted behavior is similar to the absorption edge measurement for a bulk β-Ga2O3 crystal at 4-77 K [11]. For T>77 K, the energies of E0 and E0′ show gradually red shift with the increase of temperature such as the general semiconducting behavior. It is noticed that an additional defect feature of ED1 presents only in the TR spectra of temperature range from 100 to 260 K. The ED1 feature cannot be clearly detected at low temperatures of 30-77 K because it maybe comes from the VGa defect acceptor level, which is initially empty of electron. For T = 100-260 K, the ED1 feature is detectable and its energy is nearly invariant to a value of ~4.232 eV. This result indicated that it is a defect-to-defect transition. The ED1 can be assigned as the transition of VGa to the highest defect state in DB by either a VO′ or a Gai located near the conduction-band edge. For T≥300 K, The VO′ or Gai defect state is nearly ionized and merged with the conduction band that reduces the TR amplitude of the ED1 feature as shown in Fig. 5.
Temperature dependences of transition energies of the EDB, E0 and E0′ features obtained by the temperature-dependent TR spectra of Fig. 5 are depicted in Fig. 6 . The solid lines are fitted to a Bose-Einstein expression Ei(T) = EiB-aiB⋅{1 + 2/[exp(θiB/T)-1]}, where i is the respective transition feature, aiB represents the strength of the electron-phonon interaction and ΘiB corresponds to the average phonon temperature. The fitted values of EiB, aiB and ΘiB for the β-Ga2O3 nanostrips are 5.209 ± 0.102 eV, 230 ± 103 meV, and 560 ± 100 K for E0′ transition, 4.950 ± 0.100 eV, 224 ± 100 meV, and 560 ± 100 K for E0 transition, and 3.528 ± 0.101 eV, 115 ± 55 meV, and 560 ± 100 K for the EDB transition, respectively. The values of aiB for the E0 and E0′ (band-to-band transition) are about doubled to that of EDB with valence band to DB transition. It indicates that the variation speed of temperature-energy shift for E0 and E0′ is faster than that of EDB as those in Fig. 6. The average phonon temperature ΘiB for the EDB, E0 and E0′ transitions is 560 ± 100 K. The phonon energy value (by kT) agrees well with the phonon replicas of ~43 meV that induced by the group B Raman mode in the β-Ga2O3 nanostrips as shown in Fig. 4(b).
Fig. 6 Temperature dependences of transition energies of E0′, E0, and EDB transitions in β-Ga2O3 nanostrips.
Based on the experimental analyses of TR and PL measurements, the near-band-edge structure of β-Ga2O3 nanostrips is thus constructed and depicted in Fig. 7. The transition energies of defect and band-edge transitions of β-Ga2O3 at 30 K are also listed for comparison. The top of valence band (ΓV) is consisted of oxygen 2p orbital and the lowest of conduction band (ΓC) constructed by Ga 4s electrons [11,25] to render a direct gap E0 of 4.726 eV at 30 K. The valence-band top separates into higher ΓV and lower ΓV by crystal-field splitting with the energy of ~0.252 eV. The E0′ transition comes from the lower split ΓV → ΓC. The defect donor band (DB) is mainly consisted by oxygen-vacancy series levels VO as well as the highest defect donor of VO′ or Gai. The acceptors of β-Ga2O3 nanostrips may have Ga vacancies VGa and VGa′ to form an acceptor band and VGa-VO vacancy-pair clusters to form near 1D quantum-well structure with size of L~2.2 nm. Experimental TR and PL results indicated that there is an excitonic level with a binding energy of ~40-50 meV located below the DB band. All the transition assignments and transition energies of the ED3, EW1, EW2, EW3, ED2, , EDB, ED1, E0, and E0′ transitions are indicated distinctly in Fig. 7. An overall gap-state and near-band-edge picture for the β-Ga2O3 nanostrips is hence being realized by the experimental study.
4. Conclusions
Optical characterization of gap-state and near-band-edge transitions in β-Ga2O3 nanostrips by using temperature-dependent TR measurements was firstly reported in the temperature range between 30 and 320 K. PL experiment was carried out to verify and identify the property of the gap-state and near-band-edge transitions in the β-Ga2O3. Transition origin, transition energy, optical-phonon behavior, and temperature dependence of gap-state and near-band-edge transitions in β-Ga2O3 nanostrips are characterized via the experimental analyses of TR, PL, and Raman spectroscopy. The whole band-edge structure below and above the band gap of β-Ga2O3 nanostrips was thus constructed.
Acknowledgments
The authors would like to acknowledge the financial support from the National Science Council of the Republic of China under the grant Nos. NSC 98-2221-E-011-151-MY3 and NSC97-2112-M-259-008-MY2.
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