Gallium oxide（Ga₂O₃）has five polymorphs：α，β，γ，δ and ε^［1-3］. When heated to a certain temperature，all other phases are converted to the monoclinic β-phase，which is the most stable structure^［4-5］. As an ultra wide bandgap oxide semiconductor（~ 4.9 eV），β-Ga₂O₃ exhibits better optical properties and high breakdown electrical field（~8×10⁶ V/cm）^［6-8］. Therefore，gallium oxide has great application prospects in gas sensors，solar-blind ultraviolet photodetectors，electroluminescent devices，high power devices and other electronic devices^［9-12］. In addition，β-Ga₂O₃ can be used as a window on some types of optical devices due to the high optical transparency below its optical bandgap^［1］. Gallium oxide films can be prepared by metal-organic chemical vapor deposition^［2，13］，molecular beam epitaxy^［14］，radio frequency sputtering^［15］，atomic layer deposition^［16］，sol-gel^［17］，and pulsed laser deposition（PLD）^［18-19］. Among these methods，PLD has its unique advantages：i）it can keep the composition of deposited films and target consistent；ii）it can control the oxygen vacancies in gallium oxide film by adjusting the oxygen partial pressure；iii）it can be used to grow single crystal films at low temperature and low vacuum；iv）it has strong flexibility and a fast growth speed，which could satisfy the needs of previous research on gallium oxide films.

Deposition of gallium oxide films by PLD has been reported by other research groups. Wang et al. reported the effects of deposition temperatures on the performance of gallium oxide films for optoelectronic devices. They finally realized the β-Ga₂O₃ based solar-blind detectors with a good performance of a low dark current（10.6 pA）at 10 V and a high peak responsibility（18.23 A/W）at 255 nm^［20］. For PLD deposition of β-Ga₂O₃ films，oxygen partial pressure，deposition time，laser power and substrate types are essential for the quality of the as-deposited films besides deposition temperature^［21-23］. Under different oxygen partial pressures，oxygen vacancies at gallium oxide films will change，resulting in the variations on optical constants and bandgap. This change can be extracted from the transmission spectra in the ultraviolet-visible-near infrared（UV-vis-NIR）wavelength range.

In this work，the β-Ga₂O₃ films on c-sapphire have been deposited by PLD under different oxygen partial pressures. It is found that the films exhibit a high transparency above 80% in the UV-vis-NIR wavelength region above 255 nm. The influences of oxygen partial pressure on optical properties such as optical constants and optical bandgap have been discussed in detail. The results are helpful to develop the application of Ga₂O₃-based photodetectors.

Gallium oxide films were deposited on c-sapphire substrates by PLD under various oxygen partial pressures（P_O = 5，10，20，and 40 mTorr）. First，sapphire substrates were cleaned by acetone，ethanol，and deionized water for 5 mins in an ultrasonic cleaning bath before deposition. Gallium oxide target was synthesized by gallium oxide powder with a purity of 99.9%. Then，the c-sapphire substrates were heated to 700 °C. A pulsed KrF laser（248 nm）with the energy density of 2.6 mJ/cm² was used at a repetition rate of 10 Hz and the deposition time was 1 h. The pressure in the vacuum chamber was less than 5×10^-4 mTorr，and high purity oxygen（99.999%）was passed into the cavity as active gas. Note that the holder was rotated to deposit a uniform film. The effect of oxygen partial pressure on gallium oxide films has been systematically studied. The structural characteristics of gallium oxide films were analyzed by X-ray diffraction（XRD，Bruker D8 Advance diffractometer）with a Cu Kα radiation λ = 1.541 8 Å at room temperature. The far-infrared（FIR）reflectance spectra in the wavenumber range of 50-700 cm^-1 were recorded by Bruker VERTEX 80V FTIR spectrometer. X-ray photoelectron spectroscopy（XPS，RBD-upgraded PHI-5000C ESCA system，PerkinElmer）with a Mg Kα radiation（hν = 1 253.6 eV）was used to analyze the stoichiometries and valence states of elements in the as-grown Ga₂O_3-δ films. The UV-vis-NIR transmission spectra were measured with a double-beam ultraviolet-infrared spectrophotometer（PerkinElmer Lambda 950）in the photon wavelength range from 200 nm to 1 000 nm（1.24~6.2 eV）with a step of 2 nm. The transmission spectra were fitted by the Tauc-Lorentz model，and the absorption edge and optical constants of β-Ga₂O₃ films on c-sapphire substrates were obtained，which are consistent with the theoretical prediction.

As an example，the plane-view and cross-sectional microstructure of the Ga₂O_3-δ film deposited under the oxygen partial pressure of 20 mTorr are shown in Fig. 1（a） and 1（b），respectively. It suggests that the film surface is smooth and its thickness is about 200 nm. Fig. 1（c）shows the XRD patterns of gallium oxide films deposited on c-sapphire substrates under different oxygen partial pressure of 5，10，20 and 40 mTorr. It reveals that all the spectra have obvious characteristic peaks nearby 18.9，38.4，41.9，and 59.1°. The peak at around 41.9° originates from the c-sapphire substrate，corresponding to the（0006）plan^［24］. The peaks nearby 18.9，38.4，and 59.1° are assigned to（-201），（-402）and（-603）planes of β-Ga₂O₃，respectively. It indicates that the polycrystalline monoclinic β-Ga₂O₃ films with high quality are grown with the（-201）preferred orientation（JCPDF No. 41-1103）^［20］. Fig. 1（d）displays the FIR reflectance spectra in the wavenumber range of 50-700 cm^-1. There are three obvious reflection bands，which are located at around 150，220，and 303 cm^-1，respectively. According to the prediction of group theory about β-Ga₂O₃：Γ_opt = 10A_g（Raman）+ 5B_g（Raman）+ 4A_u（IR）+ 8B_u（IR）^［25-26］，the IR-spectra of the samples are very similar to those of monoclinic system. The reflection band of 150.4 cm^-1 is the A_u（TO₁）vibration mode，which is corresponding to the upward and downward movement of gallium ions. The B_u（TO₁）one nearby 219.8 cm^-1 arises from the scissor’s movement of Ga-O-Ga. The A_u（TO₂）vibration（302.8 cm^-1）is related to a symmetrical Ga-O-Ga stretching^［26-27］. Note that the phonon frequencies are almost the same for the β-Ga₂O_3-δ films deposited under various oxygen pressures，while the related intensities of B_u（TO₁）and A_u（TO₂）have an obvious difference. It means the Ga-O-Ga related lattice dynamics and crystalline structure are affected by the oxygen partial pressure.

The survey XPS spectra of the four gallium oxide films on c-sapphire substrates were measured，which have a similar feature. As an example，Fig. 2（a）shows the survey XPS of the β-Ga₂O_3-δ films deposited under the oxygen partial pressure of 5 mTorr. The experimental results were calibrated with the C 1s peak at 284.5 eV. The strong peaks come from Ga 3d，Ga 3p，Ga 3s，Ga 2p，Ga LMM Auger peak，O 1s，C 1s and O KLL^［28］. The appearance of the carbon peak can be ascribed to the adsorption of amorphous carbon pollutants on the film surface^［29］. However，no aluminum peaks were observed，indicating that the substrate ions do not diffuse into β-Ga₂O_3-δ. The XPS spectra contain peaks of O，Ga，and C without other elements，which indicate that the purity of the deposited gallium oxide films is high. The fine scanning spectra and fitted results from Ga 2p and O 1s peaks are depicted in Fig. 2（b）and Fig. 2（c），respectively. The relative atomic ratio and bonding phase of the surface region were calculated by Shirley iterative method and linear function based on the asymmetric shape analysis of Ga 2p and O 1s spectra. The Gaussian-Lorentzian mixture function is used to simulate the experimental spectra by the program XPSPEAK4.1. Fig. 2（b）shows that Ga 2p exhibits two sub peaks（Ga 2p_1/2 and Ga 2p_3/2）nearby 1145 and 1118 eV，respectively. The fitting results suggest that the peaks have a shift to high binding energy from 1144.52 to 1144.55 eV for Ga 2p_1/2 and 1117.65 to 1117.68 eV for Ga 2p_3/2 with increasing the oxygen pressure. Fig. 2（c）shows the XPS fitting results of the O 1s nuclear level spectra. The O 1s peak can be fitted to be composed of the Ga-O bond of Ga₂O₃ at the binding energy of 530.37~531.45 eV，the O-H bond nearby 531.79~531.87 eV and oxygen vacancies at around 530.91~531.11 eV. It indicates that O 1s peaks come from Ga₂O₃，oxygen vacancy and O-H，and shift to higher binding energy as the oxygen partial pressure increases. Many factors，such as charge transfer effect，electric field，hybridization and environmental charge density，could cause the shift of binding energy. Among these factors，charge transfer effect plays an important role^［30］. Finally，we obtained Ga：O ratio values of the β-Ga₂O_3-δ films deposited under the oxygen partial pressures of 5，10，20 and 40 mTorr，which are 2：2.614，2：2.658，2：2.670，and 2：2.714，respectively.

In Fig. 3（a），the UV-vis-NIR transmission spectra of β-Ga₂O_3-δ films deposited under various oxygen partial pressures can be divided into a transparent area in the visible region and an intensely absorbing area in the ultraviolet region. The transmittance of all the films in the vis-NIR range is above 80%，indicating that the films have good optical transmittance. Moreover，there is a sharp absorption edge nearby 255 nm（4.863 eV）. According to the well-known Tauc relationship^［31］：（αE）² ∝（E－E_g），the direct optical bandgap（E_g）decreases from 4.96 to 4.90 eV as the oxygen partial pressure increases from 5 to 40 mTorr，as shown in Fig. 3（b）. Note that the trend is agreeing with that derived by the Tauc-Lorentz dispersion model（cf. Table 1）.

In order to extract the fundamental optical parameters of gallium oxide films，the transmission spectra are analyzed by using a multilayer model（void/film/sapphire）. The structure model was constructed under the hypothesis that the films grown on the substrates were treated as isotropic materials. Furthermore，the electron transitions between energy bands can be expressed by dispersion functions. The dielectric functions can be derived by the Tauc-Lorentz（TL）dispersion model，which originates from the standard Lorentz form for the imaginary part ε₂ of a collection of noninteracting atoms and the Tauc joint density of states. The TL model is extensively used to many amorphous and crystalline materials from transparent to strong absorption regions^［32-33］. The imaginary part of the TL dispersion function is

The real part（ε₁）is derived from the Kramers-Kronig relation：

where A is the transition matrix element，E₀ is the peak position energy，C is the broadening term，E_n is the electronic transition energy，and ε_∞ is the high frequency dielectric constant. The appropriate value of ε_∞ depends on the dispersion model at lower energies. So，ε_∞ is fixed to a certain value（ε_{∞= 1）for all films in order to reduce the number of parameters and enhance the comparison between different films. For example，the experiment（dotted lines）and best-fitted（solid lines）spectra for the sample（Po = 40mTorr）are shown in Fig. 3（c）. The optimized parameter（electronic transitions，film thickness，etc.）values of the TL model are summarized in Table 1. The derived optical constants（n~=n+ik=ε~=ε1+iε2）as a function of photon energy are shown in Fig. 3（d） and 3（e），respectively. In the visible-near ultraviolet region，the refractive index n increases with increasing photon energy and the extinction coefficient k is nearby zero due to the lower absorption. In the higher photon energy region above 4.5 eV，the refractive index n reaches a maximum at around 5.2 eV and the extinction coefficient k increases rapidly with increasing photon energy，indicating that the occurrence of interband transitions. These phenomena suggest that it can be used in the field of ultraviolet photodetect^［34-36］. In addition，the extracted thickness values of β-Ga2O3-δ films are various between 124 and 202 nm，which is in accordance with the results of SEM（Fig. 1b）. The absorption edge is various from 4.65 to 4.25 eV，as depicted in Fig. 3（f）. It reveals that the oxygen partial pressure can affect film deposition speed and absorption edge/bandgap.}

To further understand the mechanism of optical properties of the as-deposited β-Ga₂O_3-δ films，the first-principles calculations were performed based on the density functional theory（DFT），using the projector augmented-wave method as implemented in the Vienna Ab initio Simulation Package（VASP）code^［37-38］. A plane-wave basis set with a cutoff of 350 eV and a k-mesh of 5×5×5 were adopted to sample the first Brillouin zone. The conjugate gradient scheme is used for the geometric optimization until the force on each atom is less than 0.01 eV/Å，and the total energy change is less than 10^-6eV to acquire good convergence. The electronic properties of β-Ga₂O₃ are calculated using the HSE06 methods with a mixing exchange parameter of 0.25 and a screening parameter of 0.2 Å^-1. The calculated band structure and density of states（DOS）of the intrinsic β-Ga₂O₃ are plotted in Figs. 4（a） and 4（b），respectively. The bandgap of β-Ga₂O₃ in our calculation result is above 3.67 eV，and both the valence band maximum（VBM）and conduction band minimum（CBM）are situated at the Γ point. It means the intrinsic β-Ga₂O₃ is direct bandgap semiconductor，which is suitable for the application of optoelectronic devices^［39］. The band structure of β-Ga₂O₃ exhibits a very flat valence band，indicating a large hole effective mass and leading to a low hole mobility. From the partial DOS results，the CBM of the intrinsic β-Ga₂O₃ is formed mainly by Ga-3d states，in which the VBM is mainly composed by the O-2p，Ga-4p and Ga-4d states. Therefore，the variation in optical bandgap of the as-deposited β-Ga₂O_3-δ films originates from the VBM tuned by the oxygen partial pressure.

In conclusion，a series of monoclinic β-Ga₂O_3-δ films on c-sapphire substrates were deposited by PLD under the oxygen partial pressure range of 5 mTorr to 40 mTorr. XPS results indicate that the Ga：O ratio approaches to the ideal value（2：3）as the oxygen partial pressure increases. The influence of oxygen partial pressure on optical constants（refractive index n and extinction coefficient k），electronic transitions，and thickness of the as-deposited films were extracted by fitting transmittance spectra using the TL dispersion model. In particular，the optical bandgap is various with different partial oxygen pressures due to the change of the valence band maximum，which is mainly composed by O-2p，Ga-4p and Ga-4d states. It has been found that the optimum value of oxygen partial pressure is around 20 mTorr. This work provides comprehensive support to the β-Ga₂O₃ based opto-electronic applications.