Electrical Conductivity and Optical Properties of Nanoscale Titanium Films on Sapphire for Localized Plasmon Resonance-Based Sensors

The developing area of plasmonics has led to the possibility of creating a new type of high-speed, high-sensitivity optical sensor for biological environment analysis. The functional layer of such biosensors are nanoscale films of noble metals. In this work we suggest using a thin film of titanium as a functional layer. This paper presents the results of the research on electrical and optical characteristics of 5 to 80 nm thick titanium films deposited on sapphire substrates by magnetron sputtering. It is shown that surface plasmon resonance is consistently observed in the investigated titanium films and the theoretical grounds of surface plasmon resonance excitement is given. In structures with titanium films less than 15 nm thick, local plasmon resonance is observed along with surface plasmon resonance. Local plasmon resonance is more sensitive to the surface state of a thin film of titanium, which on the one hand increases the sensitivity of a biosensor, and on the other hand imposes restrictions on the parameters of nanoscale films.


Introduction
There has recently been increased scientific and applied interest in surface plasmons: collective vibrations of metal conduction electrons excited by an electromagnetic wave of light radiation at the interface with a dielectric [1][2][3][4][5]. The excitement of surface plasmon resonance is accompanied by the increased luminescence of the medium, absorption of light radiation, Raman scattering, etc. One of the promising applications of systems where surface plasmon resonance is excited is optical sensors for biological medium analysis [2][3][4][5]. The prospects of optical sensors based on surface plasmon resonance are caused by their non-invasiveness, speed, high sensitivity, availability, and simplicity [2,5].
The functional metal layer of surface plasmon resonance-based optical biosensors is almost always made of nanosize films of noble metals [4,5]. The use of less precious inert metals can extend the applicability and availability of surface plasmon resonance-based biological sensors.
Titanium thin films are a promising material for the creation of biomedical sensory devices for plasmonics and radio photonics, including superconductive ones operating at terahertz frequencies [1,6]. Titanium films have unique electrical, optical, and catalytic characteristics, as well as high adhesiveness

Results
Using the described technology, a series of samples with thicknesses from 5 to 80 nm was produced for these studies with five pieces of each thickness value. In this study, the values of measured parameters of thin titanium films were averaged for samples of each thickness value, respectively.
The first measured parameter of the researched samples was their electrical resistivity. Figure 1 presents experimental data on how the electrical resistivity of thin films deposited by thermal (1) and magnetron (2) sputtering depends on their thickness. The electrical resistivity of films deposited by magnetron sputtering was significantly higher than that of films deposited by thermal evaporation [9]. This difference is due to the composition, defect, and structure of the films [10]. The films obtained by magnetron sputtering were solid but have a "lumpy" texture [11]. The diameter of the "bumps" in 5 to 15 nm thick films varied from several to hundreds of nm (Figure 2b), while their height did not exceed 15 nm (Figure 2b). Numerous studies show that, at a film thickness of 1 to 10 nm, island embryos are formed, mainly of spherical shape, and they grow with the increasing thickness of a film, transforming into five-hex prisms [11][12][13][14]. It was discovered by X-ray diffraction methods that the titanium films obtained by magnetron sputtering are crystalline, regardless of the substrate material (silicon, quartz, or sapphire), and grow in the direction (0001) perpendicular to the substrate surface [13]. When analyzing optical properties, the concept of relative complex permittivity is used. The change of the imaginary part of the material's relative permittivity (ε2), depending on the frequency (ω), along with the change of its electrical conductivity occurs in accordance with the Drude Equation [15]: where ε1 is the real part of the material's relative permittivity, c is the speed of light, σ is the electrical conductivity of titanium, i is the imaginary unit, and ωp is the plasmon resonance frequency. In this case, the second term of the Equation (1), which gives the main contribution to the imaginary part of the relative complex permittivity (absorption index), by its modulus, can significantly exceed the real part, and the relative permittivity can take negative values. A case is of interest when the plasmon resonance frequency is equal to that of laser radiation, with ε2 = 0 [16]. Plasmon resonance frequency in this case is: Figure 1. The dependency of the electrical resistivity of titanium thin films, deposited by heat vaporizing [9] and by magnetron sputtering, on their thickness.
Coatings 2020, 10, x FOR PEER REVIEW 3 of 7 Figure 1. The dependency of the electrical resistivity of titanium thin films, deposited by heat vaporizing [9] and by magnetron sputtering, on their thickness.
Numerous studies show that, at a film thickness of 1 to 10 nm, island embryos are formed, mainly of spherical shape, and they grow with the increasing thickness of a film, transforming into five-hex prisms [11][12][13][14]. It was discovered by X-ray diffraction methods that the titanium films obtained by magnetron sputtering are crystalline, regardless of the substrate material (silicon, quartz, or sapphire), and grow in the direction (0001) perpendicular to the substrate surface [13]. When analyzing optical properties, the concept of relative complex permittivity is used. The change of the imaginary part of the material's relative permittivity (ε2), depending on the frequency (ω), along with the change of its electrical conductivity occurs in accordance with the Drude Equation [15]: where ε1 is the real part of the material's relative permittivity, c is the speed of light, σ is the electrical conductivity of titanium, i is the imaginary unit, and ωp is the plasmon resonance frequency. In this case, the second term of the Equation (1), which gives the main contribution to the imaginary part of the relative complex permittivity (absorption index), by its modulus, can significantly exceed the real part, and the relative permittivity can take negative values. A case is of interest when the plasmon resonance frequency is equal to that of laser radiation, with ε2 = 0 [16]. Plasmon resonance frequency in this case is: Numerous studies show that, at a film thickness of 1 to 10 nm, island embryos are formed, mainly of spherical shape, and they grow with the increasing thickness of a film, transforming into five-hex prisms [11][12][13][14]. It was discovered by X-ray diffraction methods that the titanium films obtained by magnetron sputtering are crystalline, regardless of the substrate material (silicon, quartz, or sapphire), and grow in the direction (0001) perpendicular to the substrate surface [13].
When analyzing optical properties, the concept of relative complex permittivity is used. The change of the imaginary part of the material's relative permittivity (ε 2 ), depending on the frequency (ω), along with the change of its electrical conductivity occurs in accordance with the Drude Equation [15]: where ε 1 is the real part of the material's relative permittivity, c is the speed of light, σ is the electrical conductivity of titanium, i is the imaginary unit, and ω p is the plasmon resonance frequency. In this case, the second term of the Equation (1), which gives the main contribution to the imaginary part of the relative complex permittivity (absorption index), by its modulus, can significantly exceed the real part, and the relative permittivity can take negative values. A case is of interest when the plasmon resonance frequency is equal to that of laser radiation, with ε 2 = 0 [16]. Plasmon resonance frequency in this case is: where N is the concentration of free electrons, m n * is the effective mass of electrons, and ε 0 is the electric constant.
In this paper, the relative complex permittivity of films was measured in the wavelength range from 350 to 1100 nm by the means of a spectral ellipsometer: by registering the main ellipsometric parameters Ψ and ∆. As we know, these parameters carry integral information about both optical parameters and the geometry of films. The results are shown in Figure 3.
where N is the concentration of free electrons, mn* is the effective mass of electrons, and ε0 is the electric constant. In this paper, the relative complex permittivity of films was measured in the wavelength range from 350 to 1100 nm by the means of a spectral ellipsometer: by registering the main ellipsometric parameters Ψ and Δ. As we know, these parameters carry integral information about both optical parameters and the geometry of films. The results are shown in Figure 3. The obtained dependencies at the wavelength of 632.8 nm practically coincide with the data obtained in [17], which testifies to the reproducibility of the method for film production and similarity of technological equipment for titanium film deposition. To determine the complex refractive index, the inverse problem of ellipsometry was solved: an absorbing film on the surface of a nonabsorbing substrate with known optical characteristics. The following values for the complex refractive index (n • ) were obtained using this approach: n • = 1.9 − 2.5i at a wavelength of 632.8 nm and n • = 1.59 − 2.1i at a wavelength of 400 nm, where i is the imaginary unit.
It is known that the plasmon resonance wavelength in monolithic titanium samples is 160 to 170 nm, which is in the vacuum ultraviolet. In a thin-film material, plasma resonance shifts towards longer wavelengths, in the range of 220-240 nm. To determine the wavelength of plasmon resonance in nanometer films of titanium, reflection spectra of the investigated samples were obtained (Figure 4). The obtained dependencies at the wavelength of 632.8 nm practically coincide with the data obtained in [17], which testifies to the reproducibility of the method for film production and similarity of technological equipment for titanium film deposition. To determine the complex refractive index, the inverse problem of ellipsometry was solved: an absorbing film on the surface of a nonabsorbing substrate with known optical characteristics. The following values for the complex refractive index (n • ) were obtained using this approach: n • = 1.9 − 2.5i at a wavelength of 632.8 nm and n • = 1.59 − 2.1i at a wavelength of 400 nm, where i is the imaginary unit.
It is known that the plasmon resonance wavelength in monolithic titanium samples is 160 to 170 nm, which is in the vacuum ultraviolet. In a thin-film material, plasma resonance shifts towards longer wavelengths, in the range of 220-240 nm. To determine the wavelength of plasmon resonance in nanometer films of titanium, reflection spectra of the investigated samples were obtained (Figure 4). The obtained reflection spectra of thin films of titanium on sapphire structures allowed the observation of surface plasmon resonance in thick films of titanium on the sapphire surface, plasmon resonance was observed at wavelengths of 230 to 240 nm, while in monolithic samples the resonance was observed at wavelengths of 160 to 170 nm, which indicates a lower concentration of conduction electrons. With decreasing thickness, the volume plasmon resonance shifted towards longer wavelengths [18][19][20].

Discussion
When the film thickness is less than 15 nm, a band associated with surface plasmon resonance in individual titanium "nanobumps" appeared in the reflection spectrum (Figure 4). Localized The obtained reflection spectra of thin films of titanium on sapphire structures allowed the observation of surface plasmon resonance in thick films of titanium on the sapphire surface, plasmon resonance was observed at wavelengths of 230 to 240 nm, while in monolithic samples the resonance was observed at wavelengths of 160 to 170 nm, which indicates a lower concentration of conduction electrons. With decreasing thickness, the volume plasmon resonance shifted towards longer wavelengths [18][19][20].

Discussion
When the film thickness is less than 15 nm, a band associated with surface plasmon resonance in individual titanium "nanobumps" appeared in the reflection spectrum ( Figure 4). Localized surface plasmon, in this case, was a collective electronic excitation of metallic nanoparticles smaller than the wavelength of the excitation electromagnetic radiation. It is known that the vibration frequencies of localized surface plasmon and surface plasmon are less than those of bulk plasmon by √ 3 and √ 2 times respectively [1].
The reflection and scattering of optical radiation by nanoparticles in thin films of titanium under the study can be described by means of the Mie theory [21]. The total effective section of the extinction (C ext ) is determined with a formula: where ε m is the real part of the dielectric constant of the substrate, ε 1 and ε 2 are the real and the imaginary part of the dielectric constant of the nanoparticle's material, R is the radius of the nanoparticle, and λ is the wavelength of the falling light. Based on the ratio (1), local plasmon resonance in a particle occurs when ε 1 = −2ε m . When the frequency of the external field coincided with that of the localized surface plasmon, a resonance occurred, resulting in a sharp strengthening of the field on the particle's surface and an increase in the extinction Section (3) [22]. Since the spread of the "bumps" of the examined titanium films was quite large in size (Figure 2), the measured spectrum of local plasmon resonance ( Figure 4) had a large width and covered the range of wavelengths from 290 to 700 µm. Therefore, to excite plasmon resonance in a narrow wavelength range to create highly sensitive optical biological sensors, along with the choice of the type of plasmon material and its thickness, it is necessary to further develop the technology of its deposition on the substrates to ensure optimal texture surface.

Conclusions
Surface plasmon resonance is consistently observed in the nanosize films of titanium. As the thickness of the film decreases, the band of test plasmon resonance shifts towards longer wavelengths. This is due to a decrease in the concentration of conduction electrons. Research of structures with thin films of titanium on sapphire substrate has shown that local plasmon resonance, along with surface plasmon resonance, is also observed in structures with titanium films of thickness less than 15 nm. Reflection spectra of structures with thin titanium film on sapphire (Figure 4) showed that local plasmon resonance is more sensitive to the surface state of a thin titanium film. However, at thicknesses at the single nanometer level, the local plasmon resonance spectrum is wider and less informative. Thus, titanium films with a thickness of 10 nm are the most promising for the creation of optical biomedical sensor devices in plasmonics.

Funding:
The work was carried out with financial support from the Ministry of Science and Higher Education of the Russian Federation (Project name: Theoretical and experimental studies of ultra-wideband optoelectronic devices of fiber-optic information systems and microwave photonics based on photonic integrated circuits own development; Agreement No. 075-03-2020-237/1 from 5 March 2020; project number FEWM-2020-0040). The experimental results were obtained by the team from the Integrated Optics and Microwave Photonics Laboratory of the Tomsk State University of Control Systems and Radioelectronics using equipment of the "Impulse" center of collective usage (registration number 200568).

Conflicts of Interest:
The authors declare no conflict of interest.