Charge-Transfer Process in Surface-Enhanced Raman Scattering Based on Energy Level Locations of Rare-Earth Nd3+-Doped TiO2 Nanoparticles

Surface-enhanced Raman scattering (SERS) for semiconductor nanomaterial systems is limited due to weak Raman signal intensity and unclear charge-transfer (CT) processes for chemical enhancement. Here, rare-earth element neodymium-doped titanium dioxide (Nd-TiO2) nanoparticles (NPs) were synthesized by the sol–gel method. The characterizations show that the doping of Nd ions causes TiO2 NPs to show an increase in the concentration of defects and change in the energy level structure. The CT process between Nd-TiO2 NPs substrate and probe molecule 4-Mercaptopyridine (4-Mpy) was innovatively analyzed using the relative energy level location relationship of the Dorenbos model. The SERS signal intensity exhibits an exponential enhancement with increasing Nd doping concentration and reaches its optimum at 2%, which is attributed to two factors: (1) The increase in the defect concentration is beneficial to the CT process between the TiO2 and the probe molecule; (2) the introduction of 4f electron orbital energy levels of rare-earth ions created unique CT process between Nd3+ and 4-Mpy. Moreover, the Nd-TiO2 NPs substrate shows excellent SERS performance in Raman signal reproducibility (RSD = 5.31%), the limit of detection (LOD = 10−6 M), and enhancement factor (EF = 3.79 × 104). Our work not only improves the SERS performance of semiconductor substrates but also provides a novel approach to the development of selective detection of probe molecules.


Introduction
Due to the high sensitivity, good selectivity, non-destructiveness, and information about the structure of adsorbed molecules, surface-enhanced Raman scattering (SERS) has attracted widespread interest [1][2][3]. Meanwhile, SERS has a high enhancement factor (up to 10 8 times or higher), realizing trace detection analysis and even single-molecule-level analysis [4,5]. The mechanisms of SERS enhancement are the electromagnetic mechanism (EM) and chemical mechanism (CM) [6,7]. The EM is related to the localized surface plasmon resonance (LSPR) of noble metal nanoparticles (NPs), such as gold, silver, and copper [8,9]. Due to LSPR, the electric field intensity on the surface of the noble metal NPs is significantly increased, so when the probe molecules are close to the surface, strong Raman scattering will be generated [10]. Studies have shown that the EM has nothing to do with the type of probe molecules, it is a long-range effect, and the Raman signal of molecules within about 2 nm from the substrate surface can be enhanced [11]. The CM is based on the new chemical bonds formed by the adsorption of probe molecules onto the substrate [12,13]. The reasons for enhancement are: (1) The charge-transfer (CT) process between the molecules and substrate; (2) the increase in the polarizability of the probe molecules; (3) electron-hole pairs produce an electronic

Preparation of Nd-TiO 2 NPs
The Nd-doped TiO 2 NPs SERS substrates were prepared by the sol-gel method. First, C 16 H 36 O 4 Ti and Nd(NO 3 ) 3 ·6H 2 O were dissolved in 13.4 mL of ethanol with 0.4 mL of acetylacetone with atomic ratios of 0.5%, 1%, 1.5%, 2%, 2.5%, and 3% under stirring for 20 min. Then, a mixed solution of 0.16 mL HCl and 2.02 mL deionized H 2 O was added into the mixed solution under stirring to carry out hydrolysis, and golden yellow transparent sol was obtained by continuously stirring for 100 s. Finally, the as-prepared sol was dried at 80 • C for 24 h in an oven and then calcined for 500 • C with a heating rate of 2 • C·min −1 and was held at that temperature for 1 h. Meanwhile, the pure TiO 2 substrate was also prepared with the same method.

Characterization
X-ray diffraction (XRD, Model Smartlab; Rigaku Ltd., Tokyo, Japan) using graphite monochromatic copper radiation (Cu Kα) (λ = 0.15406 nm) was used to analyze the crystal structure and phase composition within the term of 2θ in the range 10-90 • at a speed rate of 4 • ·min −1 . The morphologies and microstructure of prepared samples were observed using field emission scanning electron microscopy (FE-SEM, Model JSM-7001F, JEOL, Tokyo, Japan) under the condition of 15 kV and transmission electron microscopy (TEM, Model JSM-2000FX, JEOL, Tokyo, Japan) operating at 200 kV.
The surface component and binding energy were determined using an X-ray photoelectron spectrometer (XPS, Model Axis supra, Shimazu-Kratos Analytical, Manchester, UK) with monochromatized Al Kα X-ray radiation. The optical absorption spectra were recorded on a UV-Vis-NIR spectrophotometer (UV-Vis, Model UV-3600 Plus, Shimadzu, Kyoto, Japan) with BaSO 4 as a reference.

SERS Analysis
SERS signals were detected by a Raman spectrometer (Raman, Model XploRA Plus, HORIBA Scientific, Kyoto, Japan) with 532, 638, and 785 nm He-Ne lasers as excitation sources, the diffraction grid was set as 1200 gr·mm −1 , the data acquisition was set as double 15 s accumulations for the samples, a laser spot area with a diameter of~0.72 µm was probed using a 100× objective lens, and incident power at the sample was 1.0 mW. 4-Mpy was used to be probe molecules. In order to find the optimal Nd doping concentration of TiO 2 substrates, 20 mg of Nd-TiO 2 NPs (atomic ratio = 0.5%, 1%, 1.5%, 2%, 2.5%, and 3%) mixed with 5 mL 4-Mpy (10 −2 M) ethanol solution under 1 h ultrasonic dispersion was used to ensure absolute adsorption and dried under ambient conditions for 24 h. Meanwhile, the reproducibility, sensitivity, and LOD of the SERS substrates were assessed using the same method. A normal Raman signal of 10 −2 M 4-Mpy ethanol solution without substrate was also acquired to calculate EF.

XRD Analysis
XRD was carried out to investigate the crystal structure and degree of crystallinity of the prepared Nd-TiO 2 NPs with different doping concentrations. The XRD patterns of the samples along with corresponding enlarged spectra in the plane peak at the (101) plane are shown in Figure 1. Figure 1a reveals that all samples have the single anatase phase, which is well indexed as reported in JCPDS file No. 21-1272 [34]. No diffraction peak of neodymium oxides could be detected, indicating that Nd doping concentration was extremely low and out of detection limits of the XRD instrument or part of the Nd ions doped in the TiO 2 lattice [35]. Additionally, as the doping content of Nd ions increased, the relative intensity of the peak decreased significantly, the full width at half-maximum of the (101) peak greatly increased, and the average particle size of Nd-TiO 2 at the (101) plane can be estimated according to Scherrer equation: where D is crystalline size, λ the wavelength of X-ray radiation (0.1541 nm), K is a constant usually taken as 0.89, β is the peak width at half-maximum height, and θ is the diffraction angle. The average particle size of samples was calculated to be from about 16.4 nm to 8.2 nm with the increment in Nd doping, which is because the introduction of Nd hinders the crystal growth of TiO 2 NPs. Furthermore, an enlarged peak of the XRD spectra at (101) is shown in Figure 1b [36]. It can be seen that there is no obvious shift of the main peak at (101) as Nd doping in TiO 2 though the ion radius of Nd 3+ (0.0983 nm) is much larger than that of Ti 4+ (0.0605 nm), which might be due to the coeffect of the ionic radius difference between Nd 3+ and Ti 4+ and the reduced particle size [37,38].

XRD Analysis
XRD was carried out to investigate the crystal structure and degree of crystallinity of the prepared Nd-TiO2 NPs with different doping concentrations. The XRD patterns of the samples along with corresponding enlarged spectra in the plane peak at the (101) plane are shown in Figure 1. Figure 1a reveals that all samples have the single anatase phase, which is well indexed as reported in JCPDS file No. 21-1272 [34]. No diffraction peak of neodymium oxides could be detected, indicating that Nd doping concentration was extremely low and out of detection limits of the XRD instrument or part of the Nd ions doped in the TiO2 lattice [35]. Additionally, as the doping content of Nd ions increased, the relative intensity of the peak decreased significantly, the full width at half-maximum of the (101) peak greatly increased, and the average particle size of Nd-TiO2 at the (101) plane can be estimated according to Scherrer equation:

= cos
where D is crystalline size, the wavelength of X-ray radiation (0.1541 nm), K is a constant usually taken as 0.89, is the peak width at half-maximum height, and is the diffraction angle. The average particle size of samples was calculated to be from about 16.4 nm to 8.2 nm with the increment in Nd doping, which is because the introduction of Nd hinders the crystal growth of TiO2 NPs. Furthermore, an enlarged peak of the XRD spectra at (101) is shown in Figure 1b [36]. It can be seen that there is no obvious shift of the main peak at (101) as Nd doping in TiO2 though the ion radius of Nd 3+ (0.0983 nm) is much larger than that of Ti 4+ (0.0605 nm), which might be due to the coeffect of the ionic radius difference between Nd 3+ and Ti 4+ and the reduced particle size [37,38].

SEM and TEM Analysis
The characterization analysis of the 2%Nd-TiO2 ( Figure 2) and TiO2 (in the Supporting Information, Figure S1) NPs was carried out by SEM and TEM. As shown in Figure  2a,b, it can be seen that the samples are agglomerated in a sharp but irregular block shape and some nanoparticles are present on the surface after Nd doping. The high-resolution transmission electron microscope (HRTEM) image of 2%Nd-TiO2 NPs shows clear lattice fringes with interplanar crystal spacing of 0.35 nm, corresponding to the (101) crystal plane of the anatase TiO2, which is virtually unchanged from that of TiO2 ( Figure S1c), further confirming that only a small amount of neodymium enters the TiO2 lattice. In the selective area electron diffraction (SAED) pattern, it was further verified that the samples are polycrystalline structures of anatase TiO2 with (101), (004), (200), (105), and (213) concentric diffraction rings, which matches previous XRD analyses. The elemental mapping

SEM and TEM Analysis
The characterization analysis of the 2%Nd-TiO 2 ( Figure 2) and TiO 2 (in the Supporting Information, Figure S1) NPs was carried out by SEM and TEM. As shown in Figure 2a,b, it can be seen that the samples are agglomerated in a sharp but irregular block shape and some nanoparticles are present on the surface after Nd doping. The high-resolution transmission electron microscope (HRTEM) image of 2%Nd-TiO 2 NPs shows clear lattice fringes with interplanar crystal spacing of 0.35 nm, corresponding to the (101) crystal plane of the anatase TiO 2 , which is virtually unchanged from that of TiO 2 ( Figure S1c

XPS Analysis
The chemical components at the surface of samples can be studied by the XPS technique. Figure 3a shows the XPS spectroscopic survey spectrum of 2%Nd-TiO2 and TiO2 NPs. XPS peaks showed that the samples contained C, Ti, O, and Nd elements (only C, Ti, and O for TiO2), corresponding to orbits of C 1s, Ti 2p, O 1s, and Nd 3d, respectively. Figure 3b shows the high-resolution XPS spectrum for Ti 2p of samples. There are two characteristic peaks located at 458.7 and 463.3 eV in Nd-TiO2, which correspond to Ti 2p3/2 and Ti 2p1/2 of TiO2, respectively, and the splitting value varies with the chemical components of samples and is about 5.7 eV. It indicates that the Ti element mainly exists as the chemical state of Ti 4+ . The O 1s region of TiO2 can be fitted by two peaks at 529.9 and 531.3 eV (Figure 3c), which are the Ti-O bond in TiO2 and hydroxyl groups. Additionally, three peaks of Nd-TiO2 are located at 529.8 eV, 530.3 eV, and 531.6 eV, which can be ascribed to Ti-O, Nd-O, and the hydroxyl group, respectively [38]. It can be confirmed that Nd 3+ was doped in the TiO2 lattice. Figure 3d shows that the binding energy of Nd 3d is 994.6 eV. Although the peak intensity for Nd was weak, it can be ascribed to the presence of Nd in TiO2 [39][40][41].

XPS Analysis
The chemical components at the surface of samples can be studied by the XPS technique. Figure 3a shows the XPS spectroscopic survey spectrum of 2%Nd-TiO 2 and TiO 2 NPs. XPS peaks showed that the samples contained C, Ti, O, and Nd elements (only C, Ti, and O for TiO 2 ), corresponding to orbits of C 1s, Ti 2p, O 1s, and Nd 3d, respectively. Figure 3b shows the high-resolution XPS spectrum for Ti 2p of samples. There are two characteristic peaks located at 458.7 and 463.3 eV in Nd-TiO 2 , which correspond to Ti 2p 3/2 and Ti 2p 1/2 of TiO 2 , respectively, and the splitting value varies with the chemical components of samples and is about 5.7 eV. It indicates that the Ti element mainly exists as the chemical state of Ti 4+ . The O 1s region of TiO 2 can be fitted by two peaks at 529.9 and 531.3 eV (Figure 3c), which are the Ti-O bond in TiO 2 and hydroxyl groups. Additionally, three peaks of Nd-TiO 2 are located at 529.8 eV, 530.3 eV, and 531.6 eV, which can be ascribed to Ti-O, Nd-O, and the hydroxyl group, respectively [38]. It can be confirmed that Nd 3+ was doped in the TiO 2 lattice. Figure 3d shows that the binding energy of Nd 3d is 994.6 eV. Although the peak intensity for Nd was weak, it can be ascribed to the presence of Nd in TiO 2 [39][40][41]. Nanomaterials 2021, 11, 2063 6 of 14

UV-Vis DRS Analysis
UV-Vis diffuse reflectance spectroscopy (DRS) is used to analyze the optical absorption properties under light irradiation in the wavelength range of 350-850 nm. The absorption spectra of TiO2 and Nd-TiO2 NPs are shown in Figure 4a. It is noteworthy that all samples have high optical absorption in the wavelength range below 400 nm, which can be attributed to the CT process between the O 2− and Ti 4+ , related to the electronic excitation from the valence band (VB) to the conduction band (CB) [42]. In addition, a redshift of the absorption edge toward the visible region was observed for all Nd-TiO2 samples compared with pure TiO2, which can be explained by the CT process between the TiO2 valence band and Nd 3+ ion f electrons [43]. Moreover, pure TiO2 does not absorb in the visible light region (wavelength higher than 400 nm), but Nd-TiO2 samples exhibit outstanding absorption properties and have four characteristic absorption peaks at 527, 586, 762, and 804 nm, which are attributed to the 4f shell electron transition of Nd 3+ from 4I9/2 ground to excited states 2 K13/2 and 4 G7/2, 2 G7/2 and 4 G5/2, 4 S3/2 and 4 F7/2, and 4 F5/2 and 2 H9/2, respectively [41]. The optical band gap (Eg) of samples can be obtained by Tauc's formula [44]: where A is a constant characteristic of the material, is frequency, is absorption coefficient, and h stands for Planck's constant. The bandgap is determined by plotting the relationship between (αhν) 2 and photon energy (hν) and extrapolating the line to the X-axis. As shown in Figure 4b, the band gap values of TiO2 and Nd-TiO2 NPs were recorded as 3.20, 3.16, 3.15, 3.14, 3.14, 3.17, and 3. 16

UV-Vis DRS Analysis
UV-Vis diffuse reflectance spectroscopy (DRS) is used to analyze the optical absorption properties under light irradiation in the wavelength range of 350-850 nm. The absorption spectra of TiO 2 and Nd-TiO 2 NPs are shown in Figure 4a. It is noteworthy that all samples have high optical absorption in the wavelength range below 400 nm, which can be attributed to the CT process between the O 2− and Ti 4+ , related to the electronic excitation from the valence band (VB) to the conduction band (CB) [42]. In addition, a redshift of the absorption edge toward the visible region was observed for all Nd-TiO 2 samples compared with pure TiO 2 , which can be explained by the CT process between the TiO 2 valence band and Nd 3+ ion f electrons [43]. Moreover, pure TiO 2 does not absorb in the visible light region (wavelength higher than 400 nm), but Nd-TiO 2 samples exhibit outstanding absorption properties and have four characteristic absorption peaks at 527, 586, 762, and 804 nm, which are attributed to the 4f shell electron transition of Nd 3+ from 4I 9/2 ground to excited states 2 K 13/2 and 4 G 7/2 , 2 G 7/2 and 4 G 5/2 , 4 S 3/2 and 4 F 7/2 , and 4 F 5/2 and 2 H 9/2 , respectively [41]. The optical band gap (E g ) of samples can be obtained by Tauc's formula [44]: where A is a constant characteristic of the material, ν is frequency, α is absorption coefficient, and h stands for Planck's constant. The bandgap is determined by plotting the relationship between (αhν) 2 and photon energy (hν) and extrapolating the line to the X-axis. As shown in Figure 4b, the band gap values of TiO 2 and Nd-TiO 2 NPs were recorded as 3.20, 3.16, 3.15, 3.14, 3.14, 3.17, and 3.16 eV. The results show that Nd doping can narrow the bandgap of TiO 2 , but the bandgap shows less change with the increase in doping concentration. Nd doping can improve the optical absorption property and SERS performance of TiO 2 NPs substrates, which is attributed to morphology, defects, and incorporation of impurities during synthesis in nanomaterials [29,32,45].
Nanomaterials 2021, 11, 2063 7 of 14 the bandgap of TiO2, but the bandgap shows less change with the increase in doping concentration. Nd doping can improve the optical absorption property and SERS performance of TiO2 NPs substrates, which is attributed to morphology, defects, and incorporation of impurities during synthesis in nanomaterials [29,32,45].
The strong bands at about 991 and 1046 cm −1 are assigned to ring breathing and pyridine ring C-H in-plane bending. Other weak bands at about 1201 and 1614 cm −1 are attributed to the CH deformation and NH stretching modes, and the pyridine ring C=C stretching mode. They are consistent with those previously reported for 4-Mpy on TiO2 NPs [46][47][48]. Figure 3b shows the relationship between the SERS intensities of the 991, 1046, and 1201 cm −1 bands of 4-Mpy and the Nd 3+ concentration. The SERS signals are enhanced after Nd 3+ doping and reach a maximum at 2% doping, which is attributed to the CT mechanism.

SERS Activity and Mechanism
To research the optimum doping concentration of SERS substrates, the Nd-TiO 2 NPs (0%, 0.5%, 1%, 1.5%, 2%, 2.5%, and 3%) were measured with laser lines of 532 nm, 10 −2 M 4-Mpy ethanol solution was used as probe molecules adsorbed on SERS substrates, as shown in Figure 5a, and the Raman peaks were located at 991, 1046, 1201, and 1614 cm −1 . The strong bands at about 991 and 1046 cm −1 are assigned to ring breathing and pyridine ring C-H in-plane bending. Other weak bands at about 1201 and 1614 cm −1 are attributed to the CH deformation and NH stretching modes, and the pyridine ring C=C stretching mode. They are consistent with those previously reported for 4-Mpy on TiO 2 NPs [46][47][48]. Figure 3b shows the relationship between the SERS intensities of the 991, 1046, and 1201 cm −1 bands of 4-Mpy and the Nd 3+ concentration. The SERS signals are enhanced after Nd 3+ doping and reach a maximum at 2% doping, which is attributed to the CT mechanism. Nanomaterials 2021, 11, 2063 7 of 14 the bandgap of TiO2, but the bandgap shows less change with the increase in doping concentration. Nd doping can improve the optical absorption property and SERS performance of TiO2 NPs substrates, which is attributed to morphology, defects, and incorporation of impurities during synthesis in nanomaterials [29,32,45].
The strong bands at about 991 and 1046 cm −1 are assigned to ring breathing and pyridine ring C-H in-plane bending. Other weak bands at about 1201 and 1614 cm −1 are attributed to the CH deformation and NH stretching modes, and the pyridine ring C=C stretching mode. They are consistent with those previously reported for 4-Mpy on TiO2 NPs [46][47][48]. Figure 3b shows the relationship between the SERS intensities of the 991, 1046, and 1201 cm −1 bands of 4-Mpy and the Nd 3+ concentration. The SERS signals are enhanced after Nd 3+ doping and reach a maximum at 2% doping, which is attributed to the CT mechanism. For the SERS substrates of semiconductor materials, the frequency of LSPR is located in the infrared region, far away from the 532 nm laser source [49]. It can be calculated as follows: where n is the electron transmission density, and m e is the electron mass. Therefore, it can be judged that the chemical enhancement mechanism plays a major role in SERS enhancement for this system. Chemical enhancement is primarily due to the charge-transfer between the probe molecule and semiconductor SERS substrates. The CT mechanism for SERS of TiO 2 and Nd-TiO 2 NPs with 4-Mpy is illustrated in Figure 6. From the previous literature, the lowest unoccupied molecular orbital (LUMO) levels and the highest occupied molecular orbital (HOMO) of 4-Mpy are −9.77 and −6.34 eV, respectively [50]. The minimum conduction band (CB) and maximum valence band (VB) of TiO 2 are −7.72 and −4.52 eV, respectively [33]. Ess is the surface state energy level, which is generated by the binding of the electron at surface defects (such as surface oxygen vacancies) of TiO 2 NPs, and Ess is located at about 0.5 eV below the CB [51].
which is generated by the binding of the electron at surface defects (such as surface oxygen vacancies) of TiO2 NPs, and Ess is located at about 0.5 eV below the CB [51].
As shown in Figure 6a, with a 532 nm (ca. 2.33 eV) laser, the electrons can be excited from VB of TiO2 to the Ess, then transferred to the LUMO of 4-Mpy, and return to the CB of TiO2, to release Raman scattered photons. As the pure anatase TiO2 SERS substrate has only a few oxygen vacancies, the SERS intensity is very low. Ess acts as an intermediary in the CT transition of TiO2 to 4-Mpy. As shown in Figure 6b, through Nd doping, (1) Nd 3+ will diffuse into the TiO2 lattice to replace part of the Ti 4+ , narrow the bandgap, and generate more oxygen vacancies, thereby increasing the concentration of defects of TiO2 (more Ess generated), so that increasing numbers of Ess can promote the CT process of TiO2 to 4-Mpy and enhance the SERS signal; (2) in addition, the characteristic energy level of Nd 3+ can be introduced into the bandgap of TiO2 by doping, and the locations of the electronic ground state ( 4 I9/2) and excited state energy levels ( 4 F5/2+ 2 H9/2, 4 S3/2+ 4 F7/2, and 2 G7/2+ 4 G5/2) of Nd 3+ can be calculated with the Dorenbos model [33,52,53], which are at −8.72, −7.17, −7.09, and −6.55 eV, respectively. With a 532 nm laser, the 4f electrons of Nd 3+ can be excited from the ground state ( 4 I9/2) to the excited states ( 4 F5/2+ 2 H9/2, 4 S3/2+ 4 F7/2, and 2 G7/2+ 4 G5/2), then transferred to the LUMO of 4-Mpy, and return to the ground state of the Nd 3+ , to release Raman scattered photons. The above two CT processes after Nd doping work together to enhance the SERS signal and eliminate the fluorescent background.  As shown in Figure 6a, with a 532 nm (ca. 2.33 eV) laser, the electrons can be excited from VB of TiO 2 to the Ess, then transferred to the LUMO of 4-Mpy, and return to the CB of TiO 2 , to release Raman scattered photons. As the pure anatase TiO 2 SERS substrate has only a few oxygen vacancies, the SERS intensity is very low. Ess acts as an intermediary in the CT transition of TiO 2 to 4-Mpy. As shown in Figure 6b, through Nd doping, (1) Nd 3+ will diffuse into the TiO 2 lattice to replace part of the Ti 4+ , narrow the bandgap, and generate more oxygen vacancies, thereby increasing the concentration of defects of TiO 2 (more Ess generated), so that increasing numbers of Ess can promote the CT process of TiO 2 to 4-Mpy and enhance the SERS signal; (2) in addition, the characteristic energy level of Nd 3+ can be introduced into the bandgap of TiO 2 by doping, and the locations of the electronic ground state ( 4 I 9/2 ) and excited state energy levels ( 4 F 5/2 + 2 H 9/2 , 4 S 3/2 + 4 F 7/2 , and 2 G 7/2 + 4 G 5/2 ) of Nd 3+ can be calculated with the Dorenbos model [33,52,53], which are at −8.72, −7.17, −7.09, and −6.55 eV, respectively. With a 532 nm laser, the 4f electrons of Nd 3+ can be excited from the ground state ( 4 I 9/2 ) to the excited states ( 4 F 5/2 + 2 H 9/2 , 4 S 3/2 + 4 F 7/2 , and 2 G 7/2 + 4 G 5/2 ), then transferred to the LUMO of 4-Mpy, and return to the ground state of the Nd 3+ , to release Raman scattered photons. The above two CT processes after Nd doping work together to enhance the SERS signal and eliminate the fluorescent background.
The CT process between Nd-TiO 2 and 4-Mpy was further validated by SERS analysis using 638 and 785 nm laser wavelengths. As shown in Figure 7, the SERS signal intensity was dramatically reduced with a certain degree of background fluorescence (the intensity curves show an upward trend) with 638 nm (ca. 1.94 eV) laser irradiation, which is due to the inability of the laser energy to transfer the electrons from the ground state ( 4 I 9/2 ) to the excited state ( 2 G 7/2 + 4 G 5/2 ). However, under the irradiation of the 785 nm laser (ca. 1.58 eV), the SERS signal intensity decreased significantly and was accompanied by a strong background fluorescence signal, and the characteristic peak of 4-Mpy could not be observed on the TiO 2 substrate, which may be because the laser energy at 785 nm can only transfer the electrons from the ground state ( 4 I 9/2 ) to the excited state ( 4 F 5/2 + 2 H 9/2 ). The above two SERS analyses under 633 and 785 nm lasers are sufficient to verify the unique CT process of this work. Meanwhile, 2% Nd is used as the optimum doping concentration for TiO 2 NPs SERS substrates since high levels of defects caused by high doping concentrations lead to the recombination of electron-holes and bind electrons for the CT process of Nd-TiO 2 to 4-Mpy [54].
The CT process between Nd-TiO2 and 4-Mpy was further validated by SERS analysis using 638 and 785 nm laser wavelengths. As shown in Figure 7, the SERS signal intensity was dramatically reduced with a certain degree of background fluorescence (the intensity curves show an upward trend) with 638 nm (ca. 1.94 eV) laser irradiation, which is due to the inability of the laser energy to transfer the electrons from the ground state ( 4 I9/2) to the excited state ( 2 G7/2 + 4 G5/2). However, under the irradiation of the 785 nm laser (ca. 1.58 eV), the SERS signal intensity decreased significantly and was accompanied by a strong background fluorescence signal, and the characteristic peak of 4-Mpy could not be observed on the TiO2 substrate, which may be because the laser energy at 785 nm can only transfer the electrons from the ground state ( 4 I9/2) to the excited state ( 4 F5/2 + 2 H9/2). The above two SERS analyses under 633 and 785 nm lasers are sufficient to verify the unique CT process of this work. Meanwhile, 2% Nd is used as the optimum doping concentration for TiO2 NPs SERS substrates since high levels of defects caused by high doping concentrations lead to the recombination of electron-holes and bind electrons for the CT process of Nd-TiO2 to 4-Mpy [54].

SERS Performance
To evaluate the reproducibility of the Nd-TiO2 SERS substrates, the SERS spectra of 4-Mpy were acquired from ten different spots on the substrate. As shown in Figure 8a, the intensity of the main characteristic peaks at 991 cm −1 showed high consistency. Figure 8b gives information about the relative standard deviation (RSD) of the peak intensity at 991 cm −1 . The RSD is about 5.31%, which indicates excellent reproducibility of the SERS substrates for practical applications.
To analyze the SERS sensitivity and the limit of detection (LOD) of the Nd-TiO2 NPs substrates, the SERS spectra of 4-Mpy with different concentrations (10 −2 to 10 −7 M, ethanol solutions) were recorded and are shown in Figure 9a. It can be seen that the SERS intensity of the main characteristic peaks decreased as the concentration decreases. The correlation between Raman intensity at 991 cm −1 and the concentration of 4-Mpy are listed in Figure  9b. The linear relationship equations are y = 1947.55 + 283.15log(x) in the concentration range 10 −7 to 10 −4 M and y = 7781.62 + 1749.16log(x) in the concentration range from 10 −4 to 10 −2 M. The correlation coefficients (R 2 ) are 0.982 and 0.992, respectively. It can be seen that at a low concentration range, the Raman signal intensity changes drastically as the concentration of the probe molecule changes, while in a relatively high concentration region, its intensity changes slowly (the logarithm values of concentration were set as the X-axis so that the slopes in the equation in the low-concentration region were smaller than those

SERS Performance
To evaluate the reproducibility of the Nd-TiO 2 SERS substrates, the SERS spectra of 4-Mpy were acquired from ten different spots on the substrate. As shown in Figure 8a, the intensity of the main characteristic peaks at 991 cm −1 showed high consistency. Figure 8b gives information about the relative standard deviation (RSD) of the peak intensity at 991 cm −1 . The RSD is about 5.31%, which indicates excellent reproducibility of the SERS substrates for practical applications. in the high-concentration region). This linear phenomenon has also been reported in Qin and Cheng's previous works [55,56], and is due to the multi-layer adsorption of probe molecules at high concentrations, which weaken the enhancement effect. However, at low concentrations, the probe molecules will directly act on the surface of the SERS substrate, resulting in a significant enhancement with a high correlation coefficient. The LOD was calculated as 10 −6 M, which is much lower than other semiconductor SERS substrates. These results show excellent SERS sensitivity and ultra-low LOD on the Nd-TiO2 substrates.  To analyze the SERS sensitivity and the limit of detection (LOD) of the Nd-TiO 2 NPs substrates, the SERS spectra of 4-Mpy with different concentrations (10 −2 to 10 −7 M, ethanol solutions) were recorded and are shown in Figure 9a. It can be seen that the SERS intensity of the main characteristic peaks decreased as the concentration decreases. The correlation between Raman intensity at 991 cm −1 and the concentration of 4-Mpy are listed in Figure 9b. The linear relationship equations are y = 1947.55 + 283.15log(x) in the concentration range 10 −7 to 10 −4 M and y = 7781.62 + 1749.16log(x) in the concentration range from 10 −4 to 10 −2 M. The correlation coefficients (R 2 ) are 0.982 and 0.992, respectively. It can be seen that at a low concentration range, the Raman signal intensity changes drastically as the concentration of the probe molecule changes, while in a relatively high concentration region, its intensity changes slowly (the logarithm values of concentration were set as the X-axis so that the slopes in the equation in the low-concentration region were smaller than those in the high-concentration region). This linear phenomenon has also been reported in Qin and Cheng's previous works [55,56], and is due to the multi-layer adsorption of probe molecules at high concentrations, which weaken the enhancement effect. However, at low concentrations, the probe molecules will directly act on the surface of the SERS substrate, resulting in a significant enhancement with a high correlation coefficient. The LOD was calculated as 10 −6 M, which is much lower than other semiconductor SERS substrates. These results show excellent SERS sensitivity and ultra-low LOD on the Nd-TiO 2 substrates.
in the high-concentration region). This linear phenomenon has also been reported in Qin and Cheng's previous works [55,56], and is due to the multi-layer adsorption of probe molecules at high concentrations, which weaken the enhancement effect. However, at low concentrations, the probe molecules will directly act on the surface of the SERS substrate, resulting in a significant enhancement with a high correlation coefficient. The LOD was calculated as 10 −6 M, which is much lower than other semiconductor SERS substrates. These results show excellent SERS sensitivity and ultra-low LOD on the Nd-TiO2 substrates.  To quantitatively investigate the enhancement ability, the enhancement factor (EF) for as-prepared SERS substrate can be calculated by the following equation: where ISERS and IBulk are the Raman intensities of 4-Mpy in the SERS spectra and standard Raman spectra and NSERS and NRaman present the numbers of 4-Mpy molecules adsorbed on the SERS substrate and in the bulk condition, respectively. The ratio of intensities (ISERS/IBulk) can be obtained by 4-Mpy in the SERS spectra and standard Raman spectra ( Figure S2), and is 37.57. The NBulk and NSERS are 7.83 × 10 10 and 7.79 × 10 7 , respectively (the detailed calculation process is shown in the Supporting Infor- To quantitatively investigate the enhancement ability, the enhancement factor (EF) for as-prepared SERS substrate can be calculated by the following equation: where I SERS and I Bulk are the Raman intensities of 4-Mpy in the SERS spectra and standard Raman spectra and N SERS and N Raman present the numbers of 4-Mpy molecules adsorbed on the SERS substrate and in the bulk condition, respectively. The ratio of intensities (I SERS /I Bulk ) can be obtained by 4-Mpy in the SERS spectra and standard Raman spectra ( Figure S2), and is 37.57. The N Bulk and N SERS are 7.83 × 10 10 and 7.79 × 10 7 , respectively (the detailed calculation process is shown in the Supporting Information). Therefore, the EF of Nd-TiO 2 NPs SERS substrate at the main characteristic Raman band of 991 cm −1 can reach about 3.79 × 10 4 , which is higher than the other reported semiconductor SERS substrates [32,57].

Conclusions
In conclusion, Nd-TiO 2 NPs were synthesized with different atomic ratios of Nd by the sol-gel method and 4-Mpy was used as a probe molecule to investigate its SERS properties and the CT process in chemical enhancement mechanisms. The results indicated that the enhanced intensities of SERS signals by Nd 3+ doping could be summarized as, on the one hand, increased defect concentrations promoting the CT process between TiO 2 and 4-Mpy while, on the other hand, the introduction the 4f orbital energy level of Nd 3+ created a unique CT process between Nd 3+ and 4-Mpy. Moreover, it is innovative to use a rare-earth element (Nd) and the Dorenbos model to study the CT mechanism of SERS. The SERS analysis was validated under different excitation wavelengths. Meanwhile, the SERS substrate has high reproducibility of SERS signals, and the LOD can be expanded to 10 −6 M with the EF to 3.79 × 10 4 , which is superior to other semiconductor SERS substrates. This work provides new ideas for the selective detection of different probe molecules, which will attract more attention in the field of application.