Size Dependence of the Band Gap of Core–Shell Tantalum and Tantalum Oxide (V) Nanoclusters

Abstract

Monodisperse films of spherical tantalum oxide (V) nanoclusters and spherical tantalum nanoclusters with a tantalum oxide shell with diameters of 1.4–8 nm were obtained by magnetron sputtering. The size of the deposited nanoclusters was controlled using a quadrupole mass filter. The chemical composition was certified using the XPS method. Using the Reflected Electron Energy Loss Spectroscopy (REELS), the dependence of the band gap width on the nanocluster size was determined. It was found that starting from a certain nanocluster size, the band gap width increases as the nanocluster size decreases. Based on experimental data and a theoretical model, the effective mass of electrons dependence as a function of nanocluster size was obtained.

1. Introduction

Nanoclusters, being an intermediate object between individual atoms and bulk matter, allow us to study changes in the properties of substances with a decrease in the number of atoms. At the same time, these properties can change significantly depending on factors such as the size of the nanoparticles, chemical composition, shape and morphology. One of these effects is the change in the density of electron states of a nanocluster near the Fermi energy depending on their size, which can be detected by scanning tunnel spectroscopy. The change in density of electron states leads to a change in the permittivity of the material, which leads to a change in the optical and electronic properties of the material. At the same time, in a material consisting of metal nanoclusters with small diameters, a band gap can be observed [1]. In addition to copper, nanoparticles of refractory metals, such as tantalum, are also an interesting subject for research. Tantalum is widely used in electronics since tantalum (V) oxide has a high permittivity [2], enabling the creation of capacitors with high specific capacitance on its basis and making it a promising material for selective optical coatings [3]. Furthermore, tantalum is a refractory metal, which allows the use of materials based on it under high temperatures (up to 1200 °C). Due to the oxidation of tantalum nanoclusters in the atmosphere and upon contact with oxygen, forming Ta₂O₅, it is difficult to use wet and dry chemistry methods to obtain them, such as sol–gel, colloidal reactors, and hydrothermal synthesis.

However, it is possible to use methods in high vacuum conditions, such as pulsed laser deposition (PLD) and magnetron sputtering. The PLD method allows nanoparticle films in vacuum conditions to be obtained. For example, it was previously demonstrated that it is possible to obtain nanoclusters with rough fractal surfaces and non-spherical shapes [4,5] as well as spherical nanoclusters [6,7]. For instance, in [7], films of nanoparticles with a diameter of 69 nm and standard deviation of 26 nm were obtained. Unfortunately, it is difficult to obtain multilayer films consisting of monodisperse nanoclusters using the PLD method without using any size-filtering technique.

To solve these problems in the present article, we used the combination of magnetron sputtering and quadrupole mass-filtering methods to obtain monodisperse spherical Ta₂O₅ nanoclusters and core–shell nanoclusters of tantalum and its oxides. The method for obtaining nanoclusters is similar to that described in [8,9,10], with the exception that oxidation occurs directly during the deposition. Previously, for individual spherical tantalum metal nanoclusters of different sizes, a change in the differential current–voltage characteristics as a function of the diameter, measured by scanning tunneling spectroscopy, was discovered. This indicates the dependence of the density of electronic states on the nanocluster size [11]. Also, for thin films of tantalum oxide nanoclusters, such effects as a shift in the binding energy as a function of the size of the nanoclusters [9] and how the optical transmittance of nanocluster films depends on the size of the nanoclusters [12] were discovered.

In addition to metallic tantalum, tantalum oxides are also of great interest to researchers. Since Ta₂O₅ is a wide-band-gap dielectric [13], it is possible to create nanoscale systems on its basis by varying the parameters, which makes it possible to change the band gap within fairly wide limits. For example, this was previously demonstrated using a system consisting of thin layers of Ta₂O₅ and SiO₂ [3]. In addition to one-dimensional [14] and two-dimensional [15] nanosystems, quantum dots, which are spherical nanoclusters, also have special quantum properties due to the quantum confinement phenomenon [16]. It was previously found that the band gap and valence band offset could depend on the core–shell nanocluster diameter [8]. Unfortunately, in [8], nanoclusters were oxidized in the atmosphere, which did not make it possible to guarantee the purity of the samples and the constant thickness of the shell [17]. In addition, individual nanoclusters in porous films could oxidize in the atmosphere differently [18] depending on their position and surroundings.

In this work, new materials based on monodisperse core–shell nanoclusters with a core consisting of tantalum metal and a tantalum oxide shell, as well as Ta₂O₅ nanoclusters, are studied. All clusters were oxidized directly during deposition, which ensured uniform oxidation of nanoclusters throughout the entire nanocluster film, regardless of their depth. The samples were analyzed in situ using X-ray photoelectron spectroscopy (XPS) and reflected electron energy loss spectroscopy (REELS). The band gap dependence on the size of the nanoclusters was found and studied. Adjusting the band gap width allows for the optical properties of the material [10,14] to be tuned, which is important for creating selective optical coatings, nonlinear optical materials [19] and photodetectors [20].

2. Materials and Methods

To obtain spherical Ta₂O₅ nanoclusters and core–shell nanoclusters of tantalum and its oxides, the magnetron sputtering method is used using a Nanogen-50 cluster source with MesoQ quadrupole mass filter (Mantis Deposition Ltd., Thame, UK). Using a dc magnetron in the aggregation zone in an atmosphere of buffer gas—argon (pressure P = 10⁻⁴ mbar − 10⁻³ mbar), the tantalum target (99.95% purity tantalum) is sputtered, and aggregation of tantalum into nanoclusters occurs. Typical gas flows into the chamber are Ar: 15–50 sccm, He: 0–15 sccm, and O₂: 0.2–5.0 sccm. Then, the gas flows through a narrow nozzle with a diameter of d = 3 mm and enters a quadrupole mass filter, which filters nanoclusters by mass. The mass-filter consists of four parallel rods, with opposing rods having the same electrical potential. A combination of alternating voltage (AC) and a direct current (DC) voltage is applied to these rods: ($U+Vcos\left(\mathsf{\omega }\mathrm{t}\right)$ on the first pair and $-(U+Vcos\left(\mathsf{\omega }\mathrm{t}\right))$ on the second pair of rods. The combined effect of these voltages creates regions of stability and instability for the nanoclusters passing the mass filter, as described by the Mathieu equations. In the coordinates $a\left(q\right)$, the region of solutions of the equations of motion for which nanoclusters pass through the mass filter has the shape close to the triangle, where $a={\displaystyle \frac{8\mathrm{eU}}{m{r}_0^2{\mathsf{\omega }}^2}}$, $q={\displaystyle \frac{4\mathrm{eV}}{m{r}_0^2{\mathsf{\omega }}^2}}$, $r_0$ is the distance between the rods and the center of the quadrupole. By choosing appropriate $a$ and $q$ values, the quadrupole can be tuned to allow ions with specific m/z ratios to pass through, effectively filtering the ions based on their mass. In these experiments, $U/V=a/q=0.04$, which made it possible to obtain a flow of monodisperse clusters with a size deviation of Δd/d < 0.03. As all clusters have a charge equal to the charge of the electron ($e$), adjusting the frequency ($\mathsf{\omega }$) of AC voltage leads to a change in the size of the transmitted nanoclusters. The addition of oxygen allows for Ta and Ta₂O₅ to be obtained, as well as core–shell nanoclusters with a shell of Ta₂O₅ and non-stoichiometric oxides TaO₂ and Ta₂O₃. After a quadrupole mass filter, nanoclusters were deposited on a silicon substrate under a potential of +800 V located in the adjacent chamber. The potential value was chosen to be sufficient to focus the flow of nanoclusters onto the sample and achieve good adhesion but not too large to affect the shape of the nanoclusters upon collision with the substrate. In addition, it prevents positively charged buffer gas ions from reaching the sample, which could etch away the already deposited clusters. The scheme of the experiment is shown in Figure 1.

This method was used to obtain samples of nanocluster films on silicon of two types: core–shell nanoclusters Ta+TaOx (samples with average nanocluster diameters (d) of 1.5, 2.0, 4.5, 3.9, 8.1 nm) and Ta₂O₅ nanoclusters (samples with average nanocluster diameters of 1.5, 1.6, 2, 3.8 nm). During the deposition process, the cluster current ($I$) was monitored and recorded, and the value of $k={\int }_0^{t}I\left(t\right)d^{3}dt$ calculated continuously. The relation between the k and deposited mass was previously calibrated using quartz crystal microbalance (QCM). This made it possible to obtain the same film thickness (25 nm) for different nanocluster samples, stopping deposition when a certain value of $k$ was reached. The X-ray photoelectron spectroscopy (XPS) method was used to certify the chemical composition of the obtained nanocluster film. The XPS spectrometer, as well as the electron gun for the Reflected Electron Energy Loss Spectroscopy (REELS) method, are located in the adjacent chamber of the same vacuum facility, which allows in situ studies of the obtained samples without exposure to the atmosphere, which allows for a high frequency of samples, as well as avoiding complete oxidation of core–shell nanoclusters. A typical wide XPS spectrum of a sample of core–shell tantalum nanoclusters on silicon is shown in Figure 2. There are no silicon peaks in the spectrum, which indicates a sufficiently large thickness of the nanocluster film. The absence of carbon peaks indicates the absence of organic contaminants in the sample.

To check the homogeneity of the chemical composition of the obtained nanocluster film, the angular dependences of the XPS were measured and analyzed using the same technique as in [21]. The processing results did not reveal any difference in the intensity ratio of the peak areas of oxygen (O1s) and tantalum (Ta 4f 7/2) at different angles between the sample and the direction of the energy analyzer (all ratios coincided within the experimental error), which indicates the homogeneity of the chemical composition of the obtained nanocluster film in the direction normal to the plane of the sample. In addition, the homogeneity of pure tantalum nanocluster films deposited in this experimental facility was previously assessed using scanning electron microscopy [9].

To determine the stoichiometry of nanoclusters and the thickness of the core–shell of Ta+TaOx nanoclusters, the peaks of tantalum and oxygen were recorded in high resolution. A typical region of the Ta4f doublet of the XPS spectrum of core–shell nanoclusters and Ta₂O₅ nanoclusters is shown in Figure 3 and Figure 4.

Using these data, the thickness of the oxide layer for core–shell nanoclusters was calculated from the ratios of contributions from the Ta 4f peaks using the well-known technique [22]; the results of the calculation are shown in Figure 5.

Since, within the limits of experimental error, the shell thickness does not depend on the nanocluster diameter (the maximum change in shell thickness is smaller than the Ta lattice parameter), we will further designate samples only on the basis of the nanocluster diameter.

3. Results

The band structure analysis was performed using the REELS method. For each experiment, an electron beam energy of 500 eV was used. The typical REELS spectra of a core–shell nanocluster sample with a nanocluster diameter of d = 4.5 nm are shown in Figure 6.

Based on these data, the band gap width was determined for all samples of nanocluster films. For a more accurate determination of the band gap width, the REELS spectra near the band gap and elastic peak were approximated by a model function. The model consists of the convolution of the step function ($I_{mod}\left(E\right))$ with a model hardware function ($S_d\left(E\right))$, which is a combination of the Lorentz and Gaussian functions: $I_{res}\left(E\right)=I_{mod}\left(E\right)\ast S_d\left(E\right)$ where the hardware function is defined as follows:

$$S_d\left(E\right)=\left\{\begin{array}{c}{\displaystyle \frac{1}{(1+M\frac{{\left(E-E_0\right)}^2}{{\beta }^2})\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{\left(1-M\right)\ln \left(2\right){\left(E-E_0\right)}^2}{{\beta }^2}\right)}},E>E_0\\ {\displaystyle \frac{1}{\left(1+M\frac{{\left(E-E_0\right)}^2}{{\alpha }^2}\right)\exp \left(\frac{\left(1-M\right)\ln \left(2\right){\left(E-E_0\right)}^2}{{\alpha }^2}\right)}},E\le E_0\end{array}\right.,$$

And the direct form of the step function is:

$$I_{mod}\left(E\right)=\left\{\begin{array}{c}{I}_0,E_0-E_{gap}<E<E_0\\ \\ I_1,E<E_0-E_{gap}-E_s\\ \\ I_1-{\displaystyle \frac{(I_1-I_0)({E-(E}_0-E_{gap}-E_s))}{E_s}},E_0-E_{gap}-E_s<E<E_0-E_{gap}\\ I_p,E_0-\delta <E<E_0+\delta \\ \\ 0,E>E_0+\delta \end{array}\right.$$

where $E_{gap}$ is the band gap, $E_s$ is the width of the inclined part of the step, $E_0$ is the position of the elastic peak, M is the contribution of the Lorentz function to the elastic peak, ${\beta }^2$ is the width of the first half of the elastic peak, ${\alpha }^2$ is the width of the second half of the elastic peak, $E_0$ is the position of the elastic peak, $I_p$ is the intensity of the elastic peak, δ is the width of the elastic peak before the instrumental broadening (δ = 0.15 eV), $I_1$ is the step height, and $I_0$ is the signal level in the forbidden band.

Using this technique, the dependence of the band gap on the nanocluster diameter was obtained for both sample groups, which is shown in Figure 7.

For nanocluster diameters greater than 8 nm, the band gap of the nanocluster film becomes close to the value for bulk Ta₂O₅. However, when the nanocluster diameter decreases to less than 6 nm, the band gap increases significantly, reaching 7.55 eV for Ta₂O₅ nanoclusters and 6.55 eV for Ta+TaOx nanoclusters. For both types of nanoclusters, the band gap changes due to the quantum confinement effect at d < 6 nm. This change in band gap is much larger than that observed in [8] for nanoclusters oxidized in the atmosphere, where the band gap changed from 4.72 eV to 4.47 eV. This may be due to the different chemical composition and stoichiometry of the nanoclusters in these experiments, as well as the fact that oxidation occurred in the atmosphere, so it was impossible to guarantee the sample purity, the constant thickness of the shell, and the homogeneity of oxidation of different clusters.

According to [23], the effective mass of charge carriers in nanoclusters can be calculated from the band structure $E_c\left(\mathit{k}\right)$ as follows: ${\left({\displaystyle \frac{1}{m^{\mathrm{*}}}}\right)}_{ij}={\displaystyle \frac{1}{{\mathrm{\hslash }}^2}}{\left({\displaystyle \frac{{\partial }^2{E}_c}{\partial k_i\partial k_j}}\right)}_{k=k_0}={\displaystyle \frac{1}{m}}{\delta }_{ij}+{\displaystyle \frac{2}{m^2}}\sum _{n=c}{\displaystyle \frac{\left.⟨u_{c{k}_0}\right|p_i\left|u_{n{k}_0}\right.⟩\left.⟨u_{c{k}_0}\right|p_j\left|u_{c{k}_0}\right.⟩}{E_c\left({\mathit{k}}_0\right)-E_n\left({\mathit{k}}_0\right)}}$.

In this case, the energy levels in a nanocluster can be found as a solution to the Schrödinger equation for a particle in a spherically symmetric potential well [24,25] as follows: $E_{nl}={\displaystyle \frac{{\mathrm{\hslash }}^2}{2m}}{\displaystyle \frac{{\chi }_{nl}^2}{R^2}}$ and wave vector $k={\displaystyle \frac{1}{R}}{\chi }_{nl},$ where ${\chi }_{nl}$ are the roots of the equation $j_l\left(kR\right)=0$, where $j_l\left(kr\right)=\sqrt{{\displaystyle \frac{\pi }{2kr}}}{J}_{l+{\displaystyle \frac{1}{2}}}\left(kr\right)$, R is the nanocluster radius, a is the interatomic distance, k is the wave vector, m is the electron mass, $\mathrm{\hslash }$ is the reduced Planck constant, m* is the effective electron mass, ${\delta }_{ij}$ is the Kronecker symbol, and $J_{l+{\displaystyle \frac{1}{2}}}$ is the Bessel function.

Using the similar approximation as in [26], if we assume that the matrix element values are close to each other: $\left.⟨u_{c{k}_0}\right|p\left|u_{n{k}_0}\right.⟩\approx \mathrm{B}\mathrm{\hslash }/a$, and the band gap of nanoclusters depends on their radius (R) as $E_g=\mathsf{\Delta }{E}_g^0+{\displaystyle \frac{{\mathrm{\hslash }}^2{\chi }^2}{2m{R}^2}}$, then ${\displaystyle \frac{m}{m^{\mathrm{*}}}}\approx 1+2{\displaystyle \frac{B\frac{{\mathrm{\hslash }}^2}{m{a}^2}}{E_g}}$. Where B is the model parameter (shows how many times the average momentum is larger than $\mathrm{\hslash }/a$), $a$ is the interatomic distance, m is the effective mass of an electron in the bulk material, m* is the effective mass of an electron in a nanocluster. Based on the experimental values of the band gap of nanoclusters, the dependence of the effective mass of electrons in core–shell tantalum nanoclusters and Ta₂O₅ nanoclusters on the nanocluster diameter was obtained using this formula. These dependences were compared with the numerical calculation, and the optimal values of the parameter B for both types of nanoclusters were found. For core–shell nanoclusters $B=2.20\pm 0.21$, for Ta₂O₅ nanoclusters $B=2.00\pm 0.11$. The values of electron effective masses for both types of nanoclusters calculated using the found parameter values and the theoretical curve found by the numerical method are shown in Figure 8.

With small sizes of nanoclusters, the effective mass of electrons increases significantly, decreasing with the increase of the diameter, and reaches a constant at diameters d > 6 nm.

4. Conclusions

In summary, two types of monodisperse nanocluster film samples with spherical cluster diameters in the range of 1.5–8 nm were obtained: tantalum oxide (V) nanoclusters and core–shell nanoclusters. A band gap dependence on the diameter of the nanocluster was found, which indicates the manifestation of quantum-size effects with decreasing cluster size. In the case of tantalum oxide nanoclusters, with a decrease in the nanocluster radius from 6 nm to 1.5 nm, a sharp change in the band gap is observed. The energy gap changes from values, therefore typical for bulk tantalum oxide, to values ~1.9 times greater. Core–shell nanoclusters exhibit similar behavior of this dependence, but the band gap width increases 1.57 times. In addition, the nature of the dependence becomes non-monotonic, which may be due to the discreteness of the electron levels in the metal core of the nanocluster at its size d < 2 nm and the metal–non-metal transition. The ability to modify the band gap width of the nanocluster film in a wide range might allow the electronic and optical properties of the material to be regulated, which is important for the development of selective optical coatings, nonlinear optical materials and photodetectors.