Chalcogenide thin films，due to their excellent optical and electrical properties，are widely used in the fields of phase change random-access memory（PRAM），solar cells，nonlinear optical absorption（NOA）devices and so on ^［1-3］. In particular，these types of materials，which have become a hot topic recently owing to their large nonlinear absorption coefficient，are regarded as efficient nonlinear materials with high potential for areas such as mode-locking and optical limiting ^［4］. Among them，the transition metal chalcogenides including MoS₂，MoSe₂ and MoTe₂ have been found to have the saturated absorption effect in recent years ^［5］. Others，such as CdTe，ZnS and ZnSe，exhibit the inverse saturable absorption effect，that is，the two-photon absorption effect of the light attenuation caused by the simultaneous absorption of two photons by the material ^［6］. To better adapt them to the practical application，a few methods have been researched in the past few years to regulate their NOA properties，which include employing a phase-change ^［7］，modifying the film thickness ^［8］，photodarkening ^［9］ and designing a multilayer structure ^［10］ etc. Among them，doping with Ti is an effective method. For example，Ti is found to have significant effects when regulating the structural and optical properties of the chalcogenide thin film，particularly in the fields of phase memory and lasers ^［11-12］.

As a member of the binary chalcogenides，Sb₂Te₃ is a p-type semiconductor that contains a narrow direct band ^［13］. Considerable efforts have been devoted to its resistance-switching behaviors ^［14］，phase change ^［15］，thermoelectric ^［16］ and excellent optical properties ^［17］. In particular，the widespread application of graphene with nonlinear saturable absorption characteristics ^［18］，Bi₂Te₃，Bi₂Se₃ and Sb₂Te₃ with topological insulating properties^［19］ in chalcogenide compounds exhibit their nonlinear saturated absorptions ^［20-22］，which have promise as a kind of potential materials in nonlinear modulator devices for an ultrafast laser. There are also many doping studies on Sb₂Te₃，although most of them focus on the effects on its crystalline，electrical and thermal conductivity ^［23-24］. Importantly，in the study of the thermoelectric properties of Ti-doped Sb₂Te₃ samples，interesting phenomenon relating to a decrease in the carrier concentration was found^［25］. There is no such effects arise in other dopants such as Cr ^［26］. According to the Moss-Burstein theorem，the optical band gap is directly related to the carrier concentration ^［27］. By regulating of Ti doping concentration，it should also have a large impact on the regulation of nonlinear absorption，due to its effect on the optical band gap of thin film samples.

Based on the factors provided above，titanium as the dopant is chosen. Through analysis of the experimental data，and a theoretical discussion，we concentrate on the regulation effects of the Ti dopant in relation to optical properties of the Sb₂Te₃ thin films. Furthermore，the mouldability of transmittance，optical band gap and nonlinear absorption coefficient of the film samples by Ti dopants is thoroughly analyzed. It is shown that the Ti-doped Sb₂Te₃ films hold great promise for nonlinear optical applications.

The magnetron sputtering system（EBAS，Infovion，South Korea）is used to prepare film samples in the study. Ti-doped Sb₂Te₃ thin films were deposited on fused quartz substrates and Si（100）by radio-frequency（RF）co-sputtering mode using Sb₂Te₃ and Ti targets with a purity of 99.99%. Each substrate is treated respectively with alcohol，acetone，and deionized water in an ultrasonic cleaning equipment，then blown-dried using nitrogen. The working pressure was controlled at 2 mTorr and the chamber temperature was at room temperature. The sputtering power of the Sb₂Te₃ target magnetron was set to 80W constant，and sputtering time of all samples was fixed at 125 s. In order to prepare Ti-doped Sb₂Te₃ samples at different concentrations，the sputtering powers of Ti target magnetron were set up to 0 W，30 W，40 W and 50 W respectively，shown in Table 1. After depositions，to obtain crystalline Ti-doped Sb₂Te₃ films，a set of samples was annealed at 573 K for 30 min in a flowing nitrogen atmosphere. Based on preliminary experiments and previous experimental experiences，it can be ensured that the film samples have had sufficient time to crystallize at the setup temperature.

For the overall morphology and thickness of the samples，the scanning electron microscopy（SEM）（Sigma 300，Zeiss，Germany）mapping scan are employed and the resolution is 1.0 nm @ 15 kV. Further，energy dispersive X-ray spectroscopy（EDS）（Smartedx，Zeiss，Germany）elemental analysis is performed to establish the element composition of the samples，in with particular attention to the Ti doping content.

For the material itself，the crystal structure of the samples is carried out by X-ray diffraction（XRD）（Bruker D8 ADVANCE，Karlsruhe，Germany）with the Cu-Kα（1.540 56 Å）radiation. The 2θ angle is in the range of 10°∼60° with a step of 0.02°. The valence states of its constituent elements are measured by X-ray photoelectron spectroscopy（XPS）（K-Alpha，Thermo Scientific，USA）.

For linear optical properties，the transmission spectroscopic characteristics are determined by spectrophotometer（UV–VIS–NIR，Shimadzu，Japan）. Moreover，the spectroscopic ellipsometry（SE）^［28］，is used and the linear optical constants（include the refractive index n and extinction coefficient κ）are fitted by software FilmWizard^® in the wavelength range of 350∼850 nm.

For nonlinear absorption properties，the open-aperture（OA）mode Z-scan system had been built which introduced in our previous work ^［3］. A Ti-sapphire laser（Spectra Physics，USA）is used to excite the samples with 800 nm wavelength and 100 fs pulse duration. In the experiment，the sample is moved near the laser focus by a focusing lens（300 mm）and a stepping motor. By measurement，the Rayleigh length（Z0）is 4 mm and the focal beam radius（ω）is 32 μm at the focal point that is much larger than the film thickness. This condition is found to be critical in the Z-scan theory ^［29］.

The thickness and the Ti atomic ratios of the Ti-doped Sb₂Te₃ thin films，which is measured by SEM and EDS，are listed in Table 2. It is feasible to increase the doping concentration of the samples with increasing the sputtering power of Ti target magnetron. The atomic ratios of Ti are 0%，4.00%，5.37% and 6.64% of the S1-S4 samples，respectively.

The XRD patterns of the annealed samples（S1-S4）are shown in Fig. 1. After removing the background intensity，the images show four diffraction peaks，indicating that the samples have been in a distinct crystalline state. On a comparison with the standard diffraction PDF card，these four diffraction peaks including（006），（009），（0015）and（0018）are correspond to the R3m rhombohedral structure，in which the lattice constants are a=b=4.262Å and c=30.45Å（JCPDS No：015-0874）. The same structure has been reported in some earlier research ^［30］ about Sb₂Te₃，it also states that Ti is completely enclosed within the crystalline and acts as a doping element.

Moreover，considering the simultaneous effects of crystal size and lattice strain on the XRD diffraction peak broadening，the lattice parameters have been calculated by using the Williamson-Hall relation（1）^［31］ as follows.

where λ is the wavelength of the X-ray radiation（1.54056Å），B is the FWHM of the diffraction peak，and θ is the angle for the Bragg diffraction. The values of the average grain size D and the lattice strain ε are obtained from the intercept and slope. As shown in Table 3，the average grain size in the film decreases with the increase of Ti doping concentration，but the lattice strain and dislocation density increase，indicating effective inhibition of crystallization. Similar findings are found in studies on the phase change of the Ti-doped Sb₂Te₃ thin films ^［32］. This should be due to Ti element doping making certain elements in the Sb₂Te₃ structure be replaced to form a new bonding structure. This type of phase change material shows a nucleation-dominated behavior. For the same volume，more nucleation centers mean smaller grain sizes ^［33］. While the stress，along with the defects on the grain boundaries，also inhibits the grain growth.

X-ray photoelectron spectroscopy（XPS）is applied to characterize the chemical valence and the bonding modes of Ti doped Sb₂Te₃ samples. The XPS test uses Al Kα x-rays（1486.6 eV）to scan the binding energy（BE）spectrum and the concerned peaks of the film samples. Scanning spectra were recorded at energy steps of 1 eV，and the peak regions were recorded at energy steps of 0.1 eV. In order to correct the binding energy of the elements，the raw data from XPS spectrometer were calibrated according to the standard value of C_1s 284.6 eV recommended by the instrument，and then performed peak fittings. As plotted in Figure 2a，the energies of two high intensity peaks are 529.1 eV and 538.5 eV，corresponding to the 3d_5/2 and 3d_3/2 of Sb，respectively. Similarly，two intense peaks are found at 572.6 eV and 583.0 eV，matching with the 3d_5/2 and 3d_3/2 of Te，respectively，in Figure 2b. And there is a small decrease in the binding energies of Sb and Te after doping with Ti，due to the smaller electronegativity of Ti dopant. An interesting found is that，as shown in Figure 2c，unlike the performances of Ti dopant in other compounds，the Ti doped Sb₂Te₃ samples do appear as two obviously independent peaks at about 459.1 eV and 464.8 eV，corresponding to the Ti 2p_3/2 and Ti 2p_1/2，respectively. By comparing this with other energy spectra involving Ti（2+，3+，4+）dopant，this result implies that the Ti dopant behaves as Ti⁴⁺ valence state，as indicated to form TiTe₂ while Ti is doped into the Sb₂Te₃ thin films at a certain doping concentration. This result support our previous research conclusion that a certain concentration of titanium is doped in Ge₂Sb₂Te₅^［34］，apparently the components of GeTe and Sb₂Te₃ in the pseudo-ternary Ge₂Sb₂Te₅ makes the doping effect more complicated. It proves that the regulatory effect on Sb₂Te₃ with the titanium doping directly is more advantageous. This is the original intention of this study expected to effectively regulate the optical properties of Sb₂Te₃ films through titanium doping.

According to the Krebs model ^［34］，the Ti atom that occupies the Sb position provides three electrons that participate in the bonding with the Te atoms，and the extra electrons are released. In the Sb₂Te₃ lattice structure，the composition of Ti atoms can be described as follows.

This experimental result further demonstrates the replacement model，showing that the increased titanium content and bonding to Te element replacing Sb element leads to a reduction in the crystalline size. In p-type semiconductors，the electrons released by this bonding mechanism will combine with the holes，which results in a reduction in the carrier concentration，this is also consistent with previous studies on reflectance and the galvanomagnetic of Ti-doped Sb₂Te₃^{［27，35］}.

The optical transmission spectrum，with an infrared range of 750∼1 600 nm applied to the Ti-doped Sb₂Te₃ thin films，is presented in Fig. 3（a）. The spectral curves of the samples are relatively flat with varying different titanium doping ratios. It indicates that a broad spectral working bandwidth can be obtained for the sample films doped in this way. For example，as a saturated absorber，there is no significant change in the linear transmittance in the wavelength range around 1 550 nm for the Er-doped lasers ^［10］. Specifically，the transmittance of the films increases with the increasing of Ti dopant，it can maintain the excellent optical characteristics in the wide working bandwidth controlled by Ti doping at the low concentration. Furthermore，the elliptic polarization parameters were obtained using the SE experiments at the three incident angles of 65，70，and 75. Based on the Lorentz oscillator model，the fitting error was controlled within 0.01 using FilmWizard® software. The refractive index curves are shown in Fig. 3（b）.

To determine the absorption properties of the samples，various formulas can be used that intuitively reflect the extinction coefficient，κ，and the optical band gap，Eg. The linear absorption coefficient，α，is a critical variable，which can be calculated by the following Eq. 3.

According to Tauc’s theory ^［36］，the optical band gap can be estimated by using the following Eq. 4，

where hν is the photon energy，and A is a constant determined from the effective mass. The exponent n depends on the electronic transition properties of materials. Depending on their types，the n have different values，such as 1/2，2，3/2 and 3，corresponding to direct allowed，indirect allowed，direct forbidden and indirect forbidden band gaps，respectively^［37］. For the Sb₂Te₃ thin films with a direct allowed narrow band gap ^［38］，n value is the constant of 1/2. It can also be seen，from the above equation，that the optical band gap Eg can be obtained from the x-axis intercept value of the linear part of the curve，that is，when a value of αhν is set to 0. As a very useful parameter for determining the degree of disorder，the Tauc parameter A，which contains valence and conduction band states，can be obtained from the slope ^［39］. With the increase of the Ti doping concentration，the relative values of A2 corresponding to the slopes of the S1-S4 samples decreased slightly from 29.18 to 16.07 in Fig. 4. It should be due to the disorder increase caused by the diffusion of Ti doped into Sb₂Te₃ thin films. And the optical band gap decreases from 1.32 eV to 1.25 eV. According to Burstein–Moss theory ^［39］，the decrease in the band gap can be written as ∆Eg，which is explicitly given by the Eq. 5，

where n refers to the carrier concentration. At a low doping concentration，it is expected that the effective mass mVC* is either basically the same or has little influence. This Eq. 4 shows that the carrier concentration is positively correlated to the size of the optical band gap. This should be due to the reduction in the number of carriers，which is caused by the Ti doping as previously mentioned in the Ti bonding analysis. It can be expected that the optical band gaps of the samples will also decrease. This is confirmed by the fitting results based on the experimental data presented in Fig. 4.

A self-built open-aperture Z-scan system is employed to determine the NOA characteristics of the Ti-doped Sb₂Te₃ thin films，which is excited by an 800 nm femtosecond laser. Each sample film drives by using a stepping motor to traverse along the Z-axis at a step of 1 mm around the laser focus point. The transmitted light intensity is measured by one detector，and compared with the measuring data of another detector to obtain the normalized transmittance ^［3］. It is noteworthy that the experiment must be performed at a relatively low power to ensure low nonlinear scattering interference and samples damage. Furthermore，possible background nonlinear effects were excluded using the transmission measurements under the same experimental conditions including the substrates.

Figure 5 shows the NOA behavior of the S1-S4 samples，where the data points are measured from the experimental，and yields the fitted curves. It is found that the normalized transmittance first increases with an approach to the laser focus，and then gradually decreases as the measurement point moves away. Obviously，the normalized transmittance curve of each sample in Fig. 5 is positively symmetric for the measurement focus coordinates，indicating a reversible saturation absorption（SA）behavior of the sample at reasonable experimental laser intensity. This property is generated because the optical band gaps of 1.32∼1.25 eV are smaller than the photon energy of the excitation laser at 800 nm wavelength（equal to 1.55 eV）. Thus，the electrons in the valence band are excited by absorbing the energy of the incident photons and transition directly to the conduction band. In this case，when the light intensity is sufficiently strong，the ground state electrons become exhausted. Due to the Pauli exclusion principle，further photon absorption is prevented and a bleaching effect occurs at the position of the laser focusing on the sample film，which is also consistent with the saturated absorption theory.

In order to more specifically reflect the nonlinear absorption of the Ti-doped Sb₂Te₃ thin films，the nonlinear coefficient β，which is defined from α=α0+βI，can be estimated（based on sheik bohea’s Z-scan theory）from the following Eq. 6^［40］.

where TOA is the normalized transmittance，I0 is the laser intensity at the focal point，z refers to the current sample position（the distance from the focal point），z0 is dependent on the optical Rayleigh length，and Leff is the effective thickness calculated from the Eq. 7 that relates to both the linear absorptivity α0 and the physical thickness L of the films ^［41］.

In applications，great attention is often paid to both the nonlinear absorption coefficient and damage threshold of materials. Not only the nonlinear absorption coefficients were measured，but also the damage threshold in this investigation，as shown in Fig. 6 and Table 4. Interestingly，with the increase of Ti doping，the damage thresholds of Ti-doped Sb₂Te₃ films increase from 188.6 to 265.5 GW/cm2，which is advantageous for Sb₂Te₃ films that act as saturated absorbers in nonlinear devices. Notably，the damage threshold here is only a qualitative experimental result，that is，when the laser power gradually increases，the test film can no longer maintain good and reversible nonlinear absorption characteristics，it can be judged that it reaches the damage threshold.

The saturation absorption spectrum is determined only by the line width and laser intensity of the atomic energy level transition involved. Therefore，it is an effective means to regulate the optical characteristics of Sb₂Te₃ films including the optical band gap and the saturation absorption coefficient by controlling the titanium doping concentration. According to the saturation absorption theory where the electron absorbing photons lead to transition occurrence，a narrower optical band gap implies an easier absorption effect. Experimental results show that the nonlinear absorption coefficient does not keep increasing with the decrease of optical band gap in the Ti-doped Sb₂Te₃ films. Combined with the results above on the effect of titanium doping on the sample crystallinity，it is not difficult to speculate on the real reason why the crystallization is inhibited. The inhibition of crystallization will weaken the nonlinear absorption effect. In order to show that this is indeed a competitive factor，the normalized transmittance curves of the amorphous（AM）and crystalline（CR）Sb₂Te₃ is given in Fig. 7，and the other specific parameters are listed in Table 4. Obviously，the nonlinear absorption of the crystalline Sb₂Te₃ is much stronger. Therefore，the increase in Ti doping concentration reduces the optical band gap width and favors saturation absorption while inhibiting the crystallization，resulting in a competitive relationship.

In summary，this investigation confirms that the Sb₂Te₃ thin film microstructure and its optical properties can be effectively regulated by proper titanium doping，especially with its potential value as saturated absorbers in future nonlinear device applications. The Ti-doped Sb₂Te₃ film samples with different titanium doping concentrations are prepared using a magnetron sputtering tool. For the microstructure，the X-ray diffraction results indicate that the samples are crystalline with a R3m rhombohedral structure and it is determined that an increase of doping with Ti inhibits crystallization，which leads to a grain size decrease. For the optical properties，with the increase of the Ti doping concentration，the optical band gap decreases from 1.32 eV to 1.25 eV caused by the reduction in the number of carriers due to the Burstein-Moss effect. By the open-aperture Z-scan system，all the samples exhibited significant nonlinear optical properties for saturated absorption and a high damage threshold with the increase of Ti doping excited by a femtosecond laser at the wavelength of 800 nm. The study found the increase in Ti doping concentration reduces the optical band gap width and favors saturation absorption while inhibiting the crystallization，resulting in a competitive relationship. In conclusion，Ti doped Sb₂Te₃ thin films have broad potential applications in the field of nonlinear devices such as saturated absorbers.