Temperature and doping concentration dependence of the energy band gap in β-Ga 2 O 3 thin films grown on sapphire

This paper presents the effects of temperature and n-type doping concentration on the energy band gap of β-Ga2O3 thin films grown on c-plane sapphire substrates by low pressure chemical vapor deposition (LPCVD). The β-Ga2O3 thin films were grown using high purity gallium (Ga) and oxygen (O2) as precursors, and Si as the n-type dopant. The transmission electron microscopy (TEM) diffraction pattern showed that the thin films are single crystals that have a monoclinic crystal structure. The dependence of the energy band gap on temperature and n-type doping concentration have been experimentally determined from photoluminescence excitation (PLE) and absorbance spectra. The PLE spectra were measured in the temperature range of 77-298 K. The results indicate that both temperature and carrier concentration play important roles in determining the energy band gap of β-Ga2O3 thin films. The optical gap increased with the electron concentration for ne ≤ 2.52x10 cm, which is due to the dominant Burstein-Moss (BM) shift. The sudden decrease in the energy gap at a doping concentration of 6.23x10 – 3.05x10 cm is consistent with the theoretical prediction of Mott criterion for Ga2O3 semiconductor-metal transition. The energy band gap shrinks with an increasing temperature from 77 to 298 K. © 2017 Optical Society of America OCIS codes: (160.6000) Semiconductor materials; (240.0310) Thin films; (300.1030) Absorption; (250.5230) Photoluminescence; (160.4760) Optical properties. References and links 1. S. Kumar, C. Tessarek, G. Sarau, S. Christiansen, and R. Singh, “Self‐Catalytic Growth of β‐Ga2O3 Nanostructures by Chemical Vapor Deposition,” Adv. Eng. Mater. 17(5), 709–715 (2015). 2. T. Kawaharamura, G. T. Dang, and M. Furuta, “Successful growth of conductive highly crystalline Sn-doped αGa2O3 thin films by fine-channel mist chemical vapor deposition,” Jpn. J. Appl. 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Introduction
Ultrawide bandgap (UWBG) gallium oxide (Ga 2 O 3 ) represents an emerging semiconductor material with excellent chemical and thermal stability up to 1400 °C [1].It exists in five different polymorphs: α, β, γ, δ and ɛ [2].Different phases of Ga 2 O 3 exhibit different band gap.Based on the polymorphs, it has an energy band gap of 4.4-5.3eV [2,3], much higher than that of the GaN (3.4 eV) and 4H-SiC (3.2 eV).It exhibits high transparency in the deep ultraviolet (DUV) and visible wavelength region due to its very large band gap and has a transmittance of over 80% in the UV region.The monoclinic β-phase Ga 2 O 3 represents the thermodynamically stable crystal among the known five phases (α, β, γ, δ, ɛ).The breakdown field of β-Ga 2 O 3 is estimated to be 6-8 MV/cm [4], which is about two-three times larger than that of 4H-SiC and GaN.These unique properties make β-Ga 2 O 3 a promising candidate for high power electronic devices [4][5][6] and solar blind photodetectors applications [7][8][9].More advantageously, single crystal β-Ga 2 O 3 substrates can be synthesized by scalable and low cost melting based growth techniques such as edge-defined film-fed growth (EFG) [10], floating zone (FZ) [11] and Czochralski [12] methods.For β-Ga 2 O 3 thin film growth, both molecular beam epitaxy (MBE) [13] and metal organic vapor phase epitaxy (MOVPE) [14] have been demonstrated to produce high quality and controllable doping films but with relatively slow growth rates (2-10 nm/min).Halide vapor phase epitaxy (HVPE) using chloride precursors was demonstrated to grow β-Ga 2 O 3 films with fast growth rates (>5 μm/hr) [15].Recently, we have developed a low pressure chemical vapor deposition (LPCVD) method to grow high quality β-Ga 2 O 3 thin films on both native β-Ga 2 O 3 and c-sapphire substrates with controllable n-type doping and fast growth rates [16][17][18].Besides the aforementioned growth techniques, β-Ga 2 O 3 thin films growth have also been reported by laser MBE [19], radio frequency magnetron sputtering [20] and metal organic chemical vapor deposition (MOCVD) [21].Nevertheless, the fundamental physical properties of β-Ga 2 O 3 thin films have not been well studied or understood yet due to the limited availability of high quality epi-films.
Theory predicted that β-Ga 2 O 3 is an indirect band gap semiconductor but the indirect gap is only 30-40 meV smaller than the direct band gap [22,23].There has been no experimental confirmation yet on the indirect band gap transition for β-Ga 2 O 3 thin films.In this work, we presented a study on the direct band gap of β-Ga 2 O 3 thin films as a function of temperature and n-type doping concentration.The shift in the band gap was experimentally determined from photoluminescence excitation (PLE) in the temperature range of 77-298 K and room temperature absorbance spectra.

Experimental section
C-plane (0001) sapphire was used as the growth substrate, which was cleaned following standard solvent cleaning procedure, and rinsed by de-ionized water and dried with nitrogen flow prior to growth.High purity gallium (Ga) and oxygen (O 2 ) gas were used as the sources for gallium and oxygen, respectively.Argon (Ar) was used as the carrier gas.The LPCVD growths of β-Ga 2 O 3 thin films on sapphire substrates were carried out at 900 °C for 1 hour.SiCl 4 was used as the n-type dopant source.
The film growth rate, crystal orientation and optical properties of the heteroepitaxial β-Ga 2 O 3 thin films were characterized by using field emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), PLE and absorbance spectroscopy.FESEM images were taken with Helios 650.High resolution transmission electron microscopy (HRTEM) images and selected-area electron diffraction (SAED) were taken using a FEI Tecnai F30 at 300 kV.The PLE spectra were measured using a continuous Xenon lamp source.The room temperature doping concentrations were measured with HMS 3000 Hall measurement system.The absorbance spectra were taken with Cary 6000i UV-VISspectrophotometer in the spectral range from 188 to 1800 nm at an 8° angle of incidence.

Results and discussions
To accurately determine the growth rate of β-Ga 2 O 3 thin films grown on sapphire substrates, cross-sectional SEM was conducted.Figure 1 shows the cross-sectional FESEM image of the focused ion beam (FIB) prepared β-Ga 2 O 3 TEM sample grown on c-sapphire substrate.The β-Ga 2 O 3 thin film was grown at 900 °C for 1 hour having a Si doping concentration of 2.5x10 18 cm −3 .From this image, the thickness of the thin film was estimated to be 6 μm, which corresponds to a growth rate of 6 μm/hr.Cross-sectional SEM characterization on samples with various doping concentrations (not shown) have been performed, which did not show obvious dependence of film growth rate on doping concentration.It is worthwhile to mention that this growth rate is much higher than the growth rates of the β-Ga 2 O 3 thin films grown by MBE, pulsed laser deposition (PLD), or current MOVPE technologies.Some reported growth rates of β-Ga 2 O 3 thin films synthesized by MBE, MOCVD and PLD are 0.13 μm/hr [13], 0.33 μm/hr [14] and 0.22 μm/hr [24], respectively.The crystal quality and interfacial structure of the β-Ga 2 O 3 heteroepitaxial thin film was investigated with HRTEM as well as the SAED pattern.Figure 2(a) and 2(b) show the HRTEM images of the heteroepitaxial layer.The lattice fringes of both the β-Ga 2 O 3 layer and the substrate are clearly visible in the images.The interface between the β-Ga 2 O 3 thin film and c-plane sapphire substrate is not as sharp which can be due to the lattice and crystal symmetry mismatch.The characterization and understanding of defects present in the β-Ga 2 O 3 layer are subject of future studies.Figure 2(c) shows the SAED pattern of the heteroepitaxial layer, which confirms that the grown thin film is single crystalline monoclinic β-Ga 2 O 3 .This result corroborates our conclusion from X-ray diffraction (XRD) measurement; details of which had been reported in our previous paper [16].From XRD measurement, only (−201) and higher order diffraction peaks of β-Ga 2 O 3 were observed, indicating that the asgrown thin films are phase pure with [-201] as the growth orientation.To identify the zone axis and the Miller indices of the diffraction spots present in the pattern, several diffraction patterns of monoclinic β-Ga 2 O 3 along different zone axes were generated using JEMS (a commercialized software package).Such a diffraction pattern is shown in Fig. 2(d).This pattern taken along [172] zone axis matched with the diffraction pattern of Fig. 2(c).By comparing the two patterns together with X-ray diffraction measurement, we confirmed that the (−201) plane is the growth orientation of the β-Ga 2 O 3 thin film grown on c-plane sapphire.
To study the temperature dependence of the optical band gap of β-Ga 2 O 3 thin films, PLE spectra were collected at different temperatures ranging from 77 K up to 298 K. PLE is a method of obtaining information about the structure of the absorption edge [25].In PLE, the emission wavelength remains fixed and the excitation energy is varied to see all the energy states contribution to the luminescence of the selected emission wavelength.In this method, crystals of arbitrary thickness and geometry can be used, unlike the transmission absorption measurements.Accurate results for absorption edge structures and fundamental transitions have previously been obtained for III-V and III-nitride compounds [26,27].PLE has also been used to identify the absorption edge of β-Ga 2 O 3 thin films grown by metal organic deposition [28] and pulsed laser deposition [29].It is still difficult to observe near band edge emission peak in the standard PL measurements, and the reason for which is still unclear.Figure 3(a) plots the PLE spectra of a Si-doped β-Ga 2 O 3 thin film with a doping concentration of 2.5x10 18 cm −3 .Note that the temperature dependent PLE measurements were performed on unintentionally doped β-Ga 2 O 3 thin films grown by the same method, which shows a very similar trend.The PLE spectra were collected at an emission wavelength of λ emission = 415 nm.Note that relatively broad band edge absorptions were observed at different temperatures, which could be due to the impurities and defects that exist in the heteroepitaxially grown films.With the comparison of the band gap values extracted from the absorbance measurements, the PLE peak values are identified as the optical band gap in the band gap temperature dependence analysis.The PLE peaks redshifted with increasing temperature from 257 nm (T = 77K) to 266.4 nm (T = 298K).This corresponds to a band gap narrowing from 4.82 eV to 4.65 eV as the temperature increases from 77K to 298K.Such dependence of band gap on temperature has been reported for other semiconductor materials [30,31].Note that the PLE peak intensity reduced and the peak was broadened with the increase of temperature.At higher temperatures, the carriers have sufficient energy to be excited to the non-radiative recombination centers.As a result, the intensity of the PLE peak reduces.In addition, the electron-phonon interaction increases with increasing temperature.This leads to a broadening of the PLE peaks and the overlapping of bands with close energies.We measured the temperature dependence PLE properties of the intrinsic thin films as well as thin films with intentional doping concentrations (not shown).We did not observe obvious PLE peak intensity reduction or peak broadening dependence on the doping concentration that are discussed here.In this paper, temperature dependence of direct absorption edge had been measured.In monoclinic crystal structure, valence band splitting occurs under the influence of crystal field [32,33].Polarized lights can be used to selectively excite various transitions from valence bands to conduction band minimum (CBM) [32,34].For our PLE measurements, unpolarized light was used as the excitation source.Therefore, the measured band gap values correspond to the narrowest direct band gap of β-Ga 2 O 3 .This conclusion is also supported from the absorption spectra measurements shown in Fig. 4. The estimated band gaps reported in this paper also match with the previous reported values [22,23].
Figure 3(b) summarizes the dependence of the PLE peak positions as a function of temperature for Si-doped β-Ga 2 O 3 thin films with doping concentration n = 2.5x10 18 cm −3 .From Fig. 3(b), the energy band gap shrinks as the increase of temperature.The shrinkage of energy band gap with increasing temperature occurs mainly due to two contributing factors: (i) Thermal dilation of crystal lattice which reduces the overlap between the electron wave functions of neighboring atoms; and (ii) Electron-phonon interaction at finite temperature which changes the bond energy of the electron.At moderate temperature, lattice phonons are excited in large numbers.They influence the electron bonding energy through various orders of electron-phonon interactions.The change of bonding energy in turn alters the optical band gap [35][36][37].It has been reported previously that the major contribution for the temperature dependence of the bandgap comes from the electron-phonon interaction [35].However, for quantitative analysis of the thermal expansion of β-Ga 2 O 3 in the studied temperature range, temperature dependent X-ray diffraction measurement needs to be conducted which is part of our future studies on this material.To determine the Varshni parameters for the temperature dependence of β-Ga 2 O 3 band gap, the band gap vs temperature curve was fitted using the Varshni equation [35]: where E g (0) is the bandgap value at 0 K, α and β are Varshni parameters.From the fitting curve, the Varshni parameters governing the temperature variations of the energy band gap of β-Ga 2 O 3 are extracted to be α = 4.45x10 −3 eV/K and β = 2000 K. Temperature dependence of the band gap of β-Ga 2 O 3 has been reported previously for Mg doped (010) and unintentionally doped (001) single crystal commercial substrates [38].The Varshni parameters reported in this work are expected to be different since the growth methods of these materials are different and therefore affecting the material quality as well as the optical properties.
Optical absorbance spectroscopy was used to study the effects of doping concentration on the optical band gap of β-Ga 2 O 3 thin films grown on double-side polished c-sapphire substrates.Absorbance measurement is an accurate method to estimate the optical band gap of the semiconductor materials [39,40].For our absorbance measurements, the samples were loaded at the center of an integrating sphere.The integrating sphere collected the signals and then calibrated them with the reference signal.All the thin films used for the measurements have similar thicknesses and same crystal orientations.The doping concentration, mobility and resistivity of the thin films were measured by Hall measurements using van der Pauw method.The Hall mobility varied in the range between ~12-42 cm 2 /V•s depending on the carrier concentration [16].The sample with the highest mobility has a Hall resistivity of 1.11x10 −1 Ω-cm.Note that the electron Hall mobility strongly depends on the sample growth condition.Further optimization of the growth condition will improve the material quality as well as the electron Hall mobility.The background doping concentration for an unintentionally doped β-Ga 2 O 3 film grown on c-sapphire substrate was measured at 3x10 16 cm −3 .Figure 4(a) plots the optical absorbance spectra of Si-doped β-Ga 2 O 3 thin films with various carrier concentrations ranging from high-10 16 to high-10 19 cm −3 .The optical band gaps of the thin films were estimated from Tauc plots shown in the inset of Fig. 4(a).For carrier concentration up to 2.52x10 18 cm −3 , the band gap increased from ~4.69 eV to ~4.716 eV.The widening in band gap with increasing doping concentration is due to the dominant Burstein-Moss (BM) band-filling effect for a doped semiconductor [39,41,42].In the case of a doped n-type semiconductor, states near the conduction band edge have a nonzero occupancy.As a result, the photon energy required for excitation across a direct band gap becomes higher which results in an increase in the optical band gap.In general, both BM Fermi-band filling effect (bandgap widening) and many-body bandgap renormalization effect (band gap narrowing) competitively affect the optical bandgap of semiconductor materials with relatively heavy doping.The bandgap narrowing effect was considered due to the mutual exchange and Coulomb interactions between the added free electrons in the conduction band and electron-impurity scattering [43].Therefore, the measured optical band gap is a result of the competing BM effect and band gap renormalization effect.
For the thin films with doping concentrations ranging in 6.23x10 18 -3.05x10 19cm −3 , the band gaps suddenly reduced to ~4.7-4.68 eV.The sudden decrease of the band gap can be due to the Mott semiconductor-metal transition.We did not observe obvious peaks in the absorbance spectra that corresponds to bound exciton states.This could be due to the existence of defects in the heteroepitaxially grown β-Ga 2 O 3 thin films which results in the broadening of the absorbance spectra.Recently, the Mott semiconductor-metal transition is calculated to occur at carrier concentration of n c ~4x10 18 cm −3 for Ga 2 O 3 [44].According to the theoretical prediction, the onset of the Mott semiconductor-metal transition can occur in the range between n c to 10 n c [42].The experimental observation of the sudden decrease of band gap in our LPCVD grown β-Ga 2 O 3 thin film (6.23x10 18 -3.05x10 19cm −3 ) is in agreement with the theoretical prediction.Above this critical concentration range, the overall band gap increased again for a thin film with a doping concentration of n>7.23x10 19 cm −3 , which is due to the competing BM effect and band gap renormalization effect.Band gap narrowing can also occur due to the random impurity distribution in a heavily doped material [45].This random distribution causes fluctuation of the electrostatic potential which in turn results in a tailing of both the conduction and valence band.Such narrowing of band gap can be determined by electrical measurements [46].

Conclusion
In summary, the temperature and doping concentration dependence of the direct optical band gap were studied for Si-doped β-Ga 2 O 3 thin films grown via LPCVD.The crystal orientation and epitaxial relationship of β-Ga 2 O 3 thin films on c-plane sapphire substrate were established by TEM measurement.The band gap of β-Ga 2 O 3 shrinks as temperature increases.The band gap extracted from the absorbance measurement increases with doping concentration for n e ≤ 2.52x10 18 cm −3 due to the dominant Burstein-Moss shift.The sudden decrease in energy gap occurs at 6.23x10 18 -3.05x10 19cm −3 is consistent with the predicted onset of semiconductormetal transition for Ga 2 O 3 .The understanding of such fundamental physical properties of β-Ga 2 O 3 thin films are critical for future device applications.